I 
 
 "I '' 
 
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IN MEMORIAM 
 FLOR1AN CAJORI 
 

PRACTICAL BUSINESS 
 ARITHMETIC 
 
 BY 
 
 JOHN H. MOORE 
 
 COMMERCIAL DEPARTMENT, CHARLESTOWN HIGH SCHOOL, BOSTON 
 AND 
 
 GEORGE W. MINER 
 
 COMMERCIAL DEPARTMENT, WESTFIELP (MASS.) HIGH SCHOOL 
 
 GINN & COMPANY 
 
 BOSTON - NEW YORK CHICAGO LONDON 
 
COPYRIGHT, 1906, BY 
 JOHN H. MOORE AND GEORGE W. MIXER 
 
 ALL RIGHTS RESERVED 
 
 (Cftc gtftenaum 
 
 GINN & COMPANY PRO- 
 PRIETORS BOSTON U.S.A. 
 

 
 PREFACE 
 
 THIS work has been prepared with the belief that it will be 
 of genuine service to all interested in business education. It 
 is particularly planned for students pursuing a commercial 
 course in business schools, high schools, and normal schools. 
 
 The constant aim of the authors has been to develop the 
 subject in such a way as to make it possible for the student to 
 realize both the utilitarian and the cultural value of arithmetic. 
 The topics have been selected with great care, and a logical 
 unfolding of the whole subject has been kept in view. An 
 attempt has been made to give problems which appeal to the 
 needs and interests of the business student, and so to grade and 
 group these problems as to make the mind-furnishing and mind- 
 developing qualities of the subject go hand in hand. Inherited 
 puzzles and manufactured conditions which give a false notion 
 of business have been studiously avoided. The subject as a 
 whole has been modernized, and the exercises made simple, 
 natural, and straightforward. 
 
 The most important part of the arithmetic, considered from 
 a business standpoint, is that part devoted to the four funda- 
 mental'processes and fractions. Particular attention has there- 
 fore been devoted to the chapters in this part of the book. The 
 need for speed and accuracy is emphasized in many different 
 ways. There are many speed exercises, and the student is 
 taught to check his work at every step. To make the work 
 more real, many self-checking problems, taken from actual 
 business transactions, are given. 
 
 Many classes in high schools study business arithmetic before 
 they have taken up the subject of bookkeeping. To bring all 
 
 Hi 
 
iv PREFACE 
 
 the work of the text within the understanding of such classes, 
 the principles of debit and credit and of simple account-keeping 
 are developed in the chapter on subtraction. 
 
 The method of introducing all new topics is inductive rather 
 than deductive. The student is led to discover as much as 
 possible for himself. Useless lists of so-called "principles" 
 and all worthless definitions have been omitted ; but principles 
 which portray business customs and definitions which are 
 understandable and valuable have been carefully stated. No 
 arbitrary rules are given. When a rule is thought necessary 
 to promote facility and rapidity in numerical calculation, the 
 student is induced to make it for himself. 
 
 Many new topics have been added, and many of the obsolete 
 topics which have so long encumbered the arithmetics of the 
 schools have been eliminated. The simple exercises on graphic 
 methods of representing statistics, the exercises on plotting and 
 on reading scales, and the exercises on calculation tables, tariffs, 
 freight and express schedules, price lists, stock and bond quo- 
 tations, etc., will, it is believed, be welcomed by progressive 
 teachers. On the other hand, the elimination of cube root and 
 its applications, compound proportion and compound partner- 
 ship, unreal fractions of all kinds, all of the useless matter com- 
 monly given under denominate numbers, present worth and 
 true discount, and various other obsolete topics, will add to the 
 effectiveness of the course. 
 
 Many students who can solve the difficult problems of a text- 
 book often fail in the solution of the ordinary problems of 
 business. One reason for this is that the problems of business 
 are never labeled according to the case or the principles in- 
 volved in their solution. Recognizing this, the authors have 
 avoided the usual division of the topics into cases. General 
 principles are developed and applied through groups of related 
 problems. These problems enable the student to view a ques- 
 tion from all sides and to acquire a knowledge of current busi- 
 ness methods as well as skill in numerical calculation. 
 
 To make the problems vivid and lifelike numerous photo- 
 
PREFACE V 
 
 graphs of actual business papers have been reproduced. These 
 facsimiles serve two good and useful purposes, one, to place 
 the problems before the student just as they will come to him 
 in real business ; the other, to give him that familiarity with 
 common business forms which of itself is an invaluable part of 
 any training in business arithmetic. Pictures and diagrams 
 have been freely used whenever they seemed likely to throw 
 light on either principles or problems. 
 
 The abundance of oral work given in connection with every 
 chapter will, it is thought, add to the value of the book. 
 These exercises are used to illustrate new principles, to prepare 
 the student for written work, to introduce and develop short 
 processes, to cultivate rapidity and accuracy in calculation, and 
 to teach close and accurate thinking. Such oral work as is 
 given is an absolute business requirement and a tool for proper 
 training in analysis and expression. 
 
 The authors wish to acknowledge their indebtedness to 
 Dr. David Eugene Smith, Professor of Mathematics, Teachers 
 College, Columbia University, New York, who read the com- 
 plete manuscript and much of the proof, and kindly made 
 numerous suggestions for the betterment of the book ; to Mr. 
 George M. Clough for the larger part of the material in the 
 chapter on life insurance ; to Mr. George Abbot of Brown 
 Bros. & Co., Boston, and to Mr. H. T. Smith, Assistant Cashier 
 of the Shawmut National Bank, Boston, for valuable assistance 
 on the chapters on interest and banking. 
 
CONTENTS 
 
 FUNDAMENTAL PROCESSES 
 
 CHAPTER PAGE 
 
 I. INTRODUCTION 1 
 
 II. NOTATION AND NUMERATION 2 
 
 III. UNITED STATES MONEY 8 
 
 IV. ADDITION . . . . . . . . . . .10 
 
 V. SUBTRACTION 31 
 
 VI. MULTIPLICATION ......... 50 
 
 VII. DIVISION 64 
 
 VIII. AVERAGE . 79 
 
 IX. CHECKING RESULTS 81 
 
 FRACTIONS 
 
 X. DECIMAL FRACTIONS 85 
 
 XI. FACTORS, DIVISORS, AND MULTIPLES 107 
 
 XII. COMMON FRACTIONS 113 
 
 XIII. ALIQUOT PARTS 150 
 
 XIV. BILLS AND ACCOUNTS 160 
 
 DENOMINATE NUMBERS 
 
 XV. DENOMINATE QUANTITIES 181 
 
 XVI. PRACTICAL MEASUREMENTS 193 
 
 PERCENTAGE AND ITS APPLICATIONS 
 
 XVII. PERCENTAGE 227 
 
 XVIII. COMMERCIAL DISCOUNTS 242 
 
 XIX. GAIN AND Loss 252 
 
 XX. MARKING GOODS . . 260 
 
 XXI. COMMISSION AND BROKERAGE 266 
 
 vii 
 
Vlll 
 
 CONTENTS 
 
 CHAPTER 
 
 XXII. PROPERTY INSURANCE 
 
 XXIII. STATE AND LOCAL TAXES 
 
 XXIV. CUSTOMS DUTIES 
 
 PAGE 
 
 273 
 
 280 
 285 
 
 INTEREST AND BANKING 
 
 XXV. INTEREST 
 
 XXVI. BANK DISCOUNT 
 
 XXVII. PARTIAL PAYMENTS 
 
 XXVIII. BANKERS' DAILY BALANCES . 
 
 XXIX. SAVINGS-BANK ACCOUNTS 
 
 XXX. EXCHANGE 
 
 EQUATIONS AND CASH BALANCE 
 
 XXXI. EQUATION OF ACCOUNTS .... 
 XXXII. CASH BALANCE 
 
 DIVIDENDS AND INVESTMENTS 
 
 XXXIII. STOCKS AND BONDS 
 
 XXXIV. LIFE INSURANCE 
 
 294 
 320 
 332 
 340 
 343 
 346 
 
 376 
 385 
 
 388 
 410 
 
 PARTITIVE PROPORTION, PARTNERSHIP, AND STORAGE 
 
 XXXV. PARTITIVE PROPORTION AND PARTNERSHIP . . . 416 
 XXXVI. STORAGE 433 
 
 APPENDIX 439 
 
 TABLES OF MEASURES 439 
 
 ABBREVIATIONS AND SYMBOLS . 442 
 
 INDEX .... 443 
 
PRACTICAL BUSINESS ARITHMETIC 
 
 FUNDAMENTAL PROCESSES 
 CHAPTER I 
 
 INTRODUCTION 
 
 1. It is assumed at the outset that the student is familiar 
 with the ordinary symbols of operation ; that he can read and 
 write numbers ; that he can add, subtract, multiply, and divide 
 integers ; that he can do simple work in United States money 
 and in common and decimal fractions ; and that he knows 
 many of the most common uses of arithmetic. 
 
 2. In this course in business arithmetic he may learn more 
 about methods of working with numbers ; the uses of arithmetic 
 in the most important lines of business and in the ordinary 
 affairs of everyday life ; how to acquire skill in handling 
 numbers ; how to check results ; and how to make problems 
 and solve them. Besides all this, he may learn a great deal 
 about system and economy in the home and in the office ; 
 current business practices and usages ; business phraseology 
 and literature ; the quantitative side of commerce and indus- 
 try ; and many other useful arid interesting items of informa- 
 tion pertaining to his active participation in life. 
 
 3. The fundamental processes are the foundation of all arith- 
 metic. The student should therefore be able to perform these 
 essential processes with speed, absolute accuracy, and intelligence 
 before he attempts to take up the more advanced work. 
 
 Where work in the fundamental processes is not thought to be advisable 
 it may of course be omitted. 
 
 1 
 
CHAPTER II 
 
 NOTATION AND NUMERATION 
 ORAL EXERCISE 
 
 1. How many different figures are used to express numbers ? 
 
 2. What is the meaning of the syllable teen in the numbers 
 from 13 to 19 inclusive ? 
 
 3. What is the meaning of the syllable ty in such numbers 
 as 20, 30, 40, 45, 75, 87, 96 ? 
 
 4. What name is given to 10 tens? to 10 hundreds? to 1000 
 thousands? to 1000 millions? 
 
 5. In 7, 70, 700, 7,000, and 70,000 how does the 7 change in 
 value ? In 7007 how do the values of the 7's compare? 
 
 6. What is the value of the cipher in any number ? Why is 
 it used ? Explain the use of the ciphers in 900,905. 
 
 7. Upon what two things does the value of a figure depend ? 
 Illustrate your answer, using the number 121,000,121. 
 
 8. Mention five things that are counted in thousands ; three 
 things that are counted in millions ; two things that are counted 
 in billions. Can you think of any use for trillions ? 
 
 9. Read aloud the following : 
 
 a. The coinage of the mints at Philadelphia, New Orleans, 
 and San Francisco during a recent year amounted to 176,999,132 
 pieces, of a value of $136,340,781. Of this 199,065,715 was in 
 gold coin, 124,298,850 in silver dollars, and $12,976,216 in 
 fractional silver and minor coins. 
 
 b. In the United States Bureau of Engraving and Printing 
 there are printed yearly about 20,000,000 sheets of United 
 States notes, certificates of deposit, bonds, and national currency 
 to the amount of about 1500,000,000. In addition to this there 
 are printed about 1,000,000,000 internal revenue stamps, and 
 more than 3,000,000,000 postage stamps. 
 
 2 
 
NOTATION AND NUMERATION 
 
 THE ARABIC SYSTEM 
 
 4. This is the common system of notation. It is generally 
 called the Arabic system because the numerals which it employs 
 were introduced into Europe by the Arabs. 
 
 The Arabic numerals 1,2, 3, and so on to 9 originated in India about 2000 
 years ago. When only these numerals were used, the system proved to be cum- 
 bersome, and all mathematical operations involved great difficulty. About 
 1200 years ago the cipher was added, thus making a system sufficiently 
 ample and simple for ordinary purposes of analysis and investigation. The 
 Arabs introduced the system into Europe in the twelfth century, but it was 
 not until about 300 years later that it displaced the clumsy Roman system. 
 
 5. The distinctive feature of the Arabic system is the 
 place value of the numerals employed. The value of an Arabic 
 numeral depends as much upon its place in the number as 
 upon its simple or digit value. 
 
 Thus, in the Roman system, VII = 5 + 1 + 1. In the Arabic system, 
 511 = 5 hundreds + 1 ten + 1. 5 has not only the unit value Jive, but also 
 the place value hundreds; and the 1 following has not only the unit value 
 one, but also the place value ten. 
 
 6. The successive places a figure may occupy in a number 
 are called orders of units. 
 
 7. Orders of units increase from right to left and decrease 
 from left to right in a tenfold ratio. Therefore, 
 
 8. The Arabic system of notation is properly called a 
 decimal system, from the Latin decem, meaning ten. 
 
 9. A comma (separatrix) or a greater space than that between 
 other figures may be used to separate a number into periods. 
 
 Thus, twenty-five thousand four hundred twenty-one may be written 
 25,421 or 25 421. 
 
 ORAL EXERCISE 
 
 .Head aloud the following numbers: 
 
 1. 1,482. 3. 375,214. 5. 8217000214. 
 
 2. 7,009. 4. 278,900. 6. 7000421817. 
 
4 PRACTICAL BUSINESS ARITHMETIC 
 
 10. For convenience in reading, the successive orders of units 
 are divided into groups of three figures each, called periods. 
 The first four periods are shown in the following numeration 
 table. The number used for illustration is sixty-seven billion, 
 four hundred twenty-one million, five thousand, two hundred 
 sixteen, and seven hundred fifty-one thousandths. 
 
 NUMERATION TABLE 
 
 PERIODS : Billions Millions Thousands Units Thousandths 
 
 RDERS: 
 
 33 2 a = '3 a 3 
 
 o H o s 
 
 W H > H H P M H > K H t> Q H M H 
 
 67, 421, 005, 216 . 751 
 
 11. In reading integers do not use the word and. In deci- 
 mal fractions and has an office to perform, and if it is used in 
 reading integers, misunderstandings may occur. 
 
 Thus, 400.011 is read four hundred and eleven thousandths ; but 
 
 .411 is read /bur hundred eleven thousandths ; and 
 411. is read/our hundred eleven. 
 
 WRITTEN EXERCISE 
 
 Write in figures the following : 
 
 1. Six million, six thousand, five. 
 
 2. Seven hundred fifty-three billion. 
 
 3. Four million, one hundred twenty-five. 
 
 4. Three hundred twenty-one million, six. 
 
 5. Three million four dollars and five cents. 
 
 6. Ten billion, one thousand, one hundred three. 
 
 7. Twenty-seven and one hundred twenty-five thousandths. 
 
 8. Sixty-two thousand and four hundred twenty-five thou- 
 sandths. 
 
 9. Three million four hundred twenty thousand one dollars 
 and fifteen cents. 
 
NOTATION AND NUMERATION 5 
 
 12. Integers should be read in the shortest way possible. 
 
 Thus, 1946 should be read nineteen hundred forty-six, not one thousand 
 nine hundred forty-six. The space for writing the amount on a check, 
 
 ffirst National 3$ank 
 
 19 __ Y 
 
 Way to the 
 
 
 " 
 
 note, or other business paper is generally limited to one line, and it is im- 
 portant that the amount be expressed in the fewest words possible. 
 
 ORAL EXERCISE 
 
 Head aloud the, following : 
 
 1. In a recent year the railroad trackage of the world was 
 about 550,400 mi., distributed as follows:. North America, 
 237,600 mi.; Europe, 179,500 mi.; Asia, 75,400 mi.; South 
 America and West Indies, 29,100 mi. ; Australasia, 16,900 
 mi. ; Africa, 11,900 mi. 
 
 2. The trackage in North America in the same year was 
 distributed approximately as follows : United States, 208,000 
 mi. ; British North America, 18,900 mi. ; Mexico, 9,200 mi. ; 
 Central America, 900 mi. ; Newfoundland, 600 mi. 
 
 3. In the same year the railways of the United States aggre- 
 gated about one half the total mileage of the world, and 
 over this enormous trackage about 44,500 locomotives and 
 1,562,900 coaches and cars carried about 696,950,900 passen- 
 gers and 1,306,628,800 tons of freight. 
 
 4. In the same year the aggregate capital stock of these 
 railways was about 16,500,000,000, the gross earnings about 
 81,908,800,000, and the net earnings 8592,509,000. 
 
6 PRACTICAL BUSINESS ARITHMETIC 
 
 THE ROMAN SYSTEM 
 
 ORAL EXERCISE 
 
 1. Make a list of the Roman numerals used in the headings 
 marking the divisions of this book, and read the list so prepared. 
 
 2. What symbol ordinarily appears on a watch face for four? 
 
 13. This system of writing numbers is called Roman notation 
 because it was first used by the Romans. It is now rarely 
 used except for numbering books and their parts, for writing 
 inscriptions on buildings, and for marking the hours on the 
 dials of clocks and watches. It employs seven capital letters : 
 
 I V X L C D M 
 
 1 5 10 50 100 500 1000 
 
 14. Other numbers are expressed by a combination of these 
 letters on the general principle that 
 
 A combination of letters arranged from left to right in the order 
 of value is equal to the sum of the constituent letters. 
 
 15. But the use of the same letter four or more times is 
 avoided by employing the sub-principle that 
 
 When one letter precedes another of greater value the value of 
 the two is that of their difference. 
 
 Thus, II = 2 ; VIII = 8 ; and CCC = 300. But IV or IIII = 4 ; XL = 
 40; XC =90; and CD = 400. 
 
 ORAL EXERCISE 
 
 1. Multiply twenty-seven by itself in Roman numerals. 
 
 2. Why is the Arabic system better than the Roman system ? 
 
 3. Read the following inscription: MDCCCXLVIII- 
 Charlestown High School MCMVI. 
 
 Nineteen hundred was formerly written MDCCCC, but it is now often 
 written MCM. 
 
 4. Read the following numbers of chapters in a book : XXIX, 
 XXXVIII, LXIX, LII, LXVII, LXXVI, LXXIX, CLIII. 
 
 5. Read the following numbers of years : MDCCXCV, 
 MCMVII, MDCCLXXVI, MCMIX, MDCCCXCVIII. 
 
NOTATION AND NUMERATION 7 
 
 WRITTEN EXERCISE 
 
 1. Write in the Roman system : 19, 88, 99, 124, 1907, 1910, 
 
 2. Write the largest possible number using the six follow- 
 ing numerals : 1, 0, 8, 0, 9, 5. 
 
 3. Write in Arabic numerals the following number : five 
 billion, two hundred seventeen million, two hundred ten thou- 
 sand, and fifteen thousandths. 
 
 4. Write in the Roman system the following historical years : 
 the discovery of America ; the landing of the Pilgrim Fathers 
 at Plymouth ; the declaration of independence. 
 
 5. Write in Arabic numerals the number in problem 3 
 increased by two hundred seventy-one and four hundred fifteen 
 thousandths ; diminished by two thousand, four hundred sixty, 
 and eleven thousandths. 
 
 16. A unit is a standard quantity by which other quantities 
 of the same kind are measured. 
 
 The simplest form of a unit is a single entire thing by which other simi- 
 lar things can be measured by integral enumeration. Thus, the unit of dis- 
 tance is an inch; a group of 12 in. taken in succession is a foot; 3 ft. is a 
 yard ; and so on. 
 
 17. Numbers that have units of the same kind are called 
 like numbers. 
 
 Thus, $12 and $15, and 8 hr. and 3 lir., are like numbers. 
 
 ORAL EXERCISE 
 Name the unit in each of the following : 
 
 1. A barrel of sugar sold by the pound. 
 
 2. A car load of apples bought by the barrel. 
 
 3. A car load of lumber sold by the thousand feet. 
 
 4. Sixty-four thousand bricks sold by the thousand. 
 
 5. Forty and one-half yards of carpet sold by the yard. 
 
 6. Twenty-five hundred pounds of beef bought by the 
 hundredweight. t 
 
 7. When the value in a five-dollar gold piece is thought of, 
 what is the unit ? 
 
CHAPTER III 
 
 * 
 
 UNITED STATES MONEY 
 ORAL EXERCISE 
 
 Read the following expressions, supplying the missing word or 
 words : 
 
 1. The denominations of United States money used in busi- 
 ness are dollars, , and . 
 
 2. mills or cents equal one dollar. 
 
 3. The is not a coin, but it is sometimes used in mak- 
 ing calculations. 
 
 4. The first two figures at the right of dollars denote , 
 
 and the third figure denotes . 
 
 5. The two figures denoting cents express of a dollar ; 
 
 the figure denoting mills expresses of a dollar. 
 
 6. One thousandth of a dollar is mill ; seven mills are 
 
 of a dollar. 
 
 7. Fifteen hundredths of a dollar are ; nine tenths 
 
 of a dollar are nine or cents. 
 
 8. $25 = t\ 3700^ = i ; $17.85 = *; 4925^ 
 
 9. State a short method of reducing dollars to cents ; dol- 
 lars and cents to cents ; cents to dollars. 
 
 18. The following kinds of currency are in daily use in the 
 United States at the present time : gold coins ; silver dollars ; 
 subsidiary coins (small change) ; gold certificates ; silver cer- 
 tificates; United States notes and treasury notes of 1890; 
 national bank notes. 
 
 The coins now authorized by the United States government are as follows-? 
 
 1. The gold double eagle, eagle, half eagle, and quarter eagle. 
 
 2. The silver dollar, half dollar, quarter dollar, and dime. 
 
 3. The nickel five-cent piece and the bronze one-cent piece. 
 
UNITED STATES MONEY 9 
 
 19. Gold or silver in bars or ingots is called bullion. 
 The paper money of the United States is at present as follows : 
 
 1. Gold certificates, issued for gold deposited in the U. S. Treasury. 
 
 2. Silver certificates, issued for silver deposited in the U. S. Treasury. 
 
 3. United States notes (greenbacks), promises of the government to pay to 
 the holder on demand a definite number of gold or silver dollars. 
 
 4. National bank notes, issued by national banks under the supervision 
 of the National Government. These notes are secured by U. S. bonds and 
 are redeemable on demand in lawful money. 
 
 5. Treasury notes, which were issued for silver bullion deposited in the 
 U. S. Treasury. These notes are not now issued. 
 
 ORAL EXERCISE 
 
 1. What is meant by money, currency, legal tender? 
 
 In such exercises as the above the student should not try to repeat defini- 
 tions, but should explain the terms in his own way. 
 
 2. Name the gold "coins of the United States; the silver 
 coins ; the paper money ; give the value of each of the gold coins. 
 
 3. Read in three ways : 14.8665; I25.87J; 1178.475. 
 
 4. Name the largest gold and silver coins that will exactly 
 express each of the following amounts: 127.95; 28.24; $75.82. 
 
 20. When it is desirable to express United States money in 
 written words, the cents should be written in fractional form, 
 as in the following note : 
 
CHAPTER IV 
 
 ADDITION 
 ORAL EXERCISE 
 
 1. Find the sum of 1, 2, 3, 4, 5, 6, 7, 8, and 9. 
 
 2. Read each of the numbers in problem 1 increased by 2 ; 
 by 5; by 3; by 7 ; by 8; by 9 ; by 17; by 23. 
 
 ^3. Find the sum of 8, 7, 9, 5, 6, 11, and 12. 
 
 4. Read each of the numbers in problem 3 increased by 12; 
 by 15; by 18; by 24 ; by 42; by 19; by 16. 
 
 5. Illustrate what is meant by like numbers. 
 
 21. Only like numbers can be added. 
 
 22. To secure speed and accuracy in addition name results 
 only and express these in the fewest words possible. 
 
 Thus, in adding 2, 4, 7, 8, 3, 2, and 8 say 6, 13, 21, 4, 6, 34 ; do not say 
 2 and 4 are 6 and 7 are 13 and 8 are 21 and 3 are 24 and 2 are 26 and 8 are 34. 
 
 ORAL EXERCISE 
 
 Name the sum in each of the following problems : 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 3 
 
 2 
 
 2 
 
 8 
 
 1 
 
 5 
 
 8 
 
 1 
 
 3 
 
 5 
 
 5 
 
 1 
 
 3 
 
 4 
 
 2 
 
 2 
 
 1 
 
 4 
 
 2 
 
 3 
 
 2 
 
 2 
 
 3 
 
 3 
 
 1 
 
 4 
 
 7 
 
 2 
 
 5 
 
 7 
 
 1 
 
 6 
 
 3 
 
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 6 
 
 1 
 
 3 
 
 6 
 
 4 
 
 6 
 
 4 
 
 2 
 
 J 
 
 2 
 
 3 
 
 2 
 
 8 
 
 2 
 
 2 
 
 4 
 
 3 
 
 7 
 
 4 
 
 2 
 
 2 
 
 3 
 
 7 
 
 5 
 
 8 
 
 5 
 
 8 
 
 4 
 
 1 
 
 3 
 
 4 
 
 4 
 
 4 
 
 9 
 
 8 
 
 7 
 
 2 
 
 3 
 
 2 
 
 6 
 
 4 
 
 4 
 
 8 
 
 4 
 
 4 
 
 3 
 
 7 
 
 7 
 
 5 
 
 3 
 
 3 
 
 1 
 
 4 
 
 8 
 
 4 
 
 2 
 
 5 
 
 6 
 
 3 
 
 5 
 
 2 
 
 2 
 
 3 
 
 8 
 
 6 
 
 2 
 
 
 
 5 
 
 2 
 
 5 
 
 1 
 
 6 
 
 
 
 6 
 
 2 
 
 3 
 
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 4 
 
 2 
 
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 5 
 
 7 
 
 2 
 
 6 
 
 3 
 
 4 
 
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 8 
 
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 7 
 
 7 
 
 6 
 
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 1 
 
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 7 
 
 7 
 
 1 
 
 2 
 
 3 
 
 3 
 
 6 
 
 2 
 
 2 
 
 4 
 
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 4 
 
 3 
 
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 8 
 
 3 
 
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 5 
 
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 2 
 
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 4 
 
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 9 
 
 8 
 
 7 
 
 id 
 
ADDITION 11 
 
 23. Addition is the basis of all mathematical processes. It 
 constitutes a large part of all the computations of business 
 life and concerns, to some extent, every citizen of to-day. 
 Ability to add rapidly and accurately is therefore a valuable 
 accomplishment. 
 
 24. Rapid addition depends mainly upon the ability to group ; 
 that is, to instantly combine two or more figures into a single 
 number. In reading it is never necessary to stop to name the 
 individual letters in the words. All the letters of a word are 
 taken in at a glance ; hence the whole word is known at sight. 
 Words are then grouped in rapid succession and a whole line 
 is practically read at a glance. This is just the principle upon 
 which rapid addition depends. From two to four figures 
 should be read at sight as a single number, and the group so 
 formed should be rapidly combined with other groups until the 
 result of any given column is determined. This can be done 
 only by intelligent, persistent practice. 
 
 25. The following list contains all possible groups of two 
 figures each. 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of the following groups: 
 a b cd e f g h i j klmno 
 
 1. 11224133'4314247 
 13121523^673567 
 
 2. 898564557156689 
 ^ 8 i i i i ^ 5 ? 5 ^ i 
 
 3. 877497675324576 
 
 235838799899842 
 
 The above exercise may be copied on the board and each student in turn 
 required to name the results from left to right, from right to left, from top 
 to bottom, and from bottom to top. The drill should be continued until 
 the sums can be named at the rate of 150 per minute. This is the first 
 and most important step in grouping. 
 
PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 Name the sum in each of the following problems : 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 6 
 
 7 
 
 3 
 
 5 
 
 6 
 
 7 
 
 9 
 
 9 
 
 9 
 
 1 
 
 2 
 
 5 
 
 8 
 
 2 
 
 8 
 
 3 
 
 1 
 
 4 
 
 2 
 
 4 
 
 7 
 
 9 
 
 8 
 
 8 
 
 4 
 
 7 
 
 2 
 
 3 
 
 7 
 
 2 
 
 8 
 
 7 
 
 7 
 
 5 
 
 8 
 
 2 
 
 5 
 
 9 
 
 4 
 
 5 
 
 8 
 
 3 
 
 5 
 
 4 
 
 1 
 
 7 
 
 '9 
 
 6 
 
 9 
 
 3 
 
 9 
 
 8 
 
 4 
 
 7 
 
 1 
 
 1 
 
 7 
 
 9 
 
 5 
 
 9 
 
 3 
 
 8 
 
 5 
 
 3 
 
 8 
 
 1 
 
 6 
 
 4 
 
 9 
 
 2 
 
 6 
 
 5 
 
 7 
 
 3 
 
 4 
 
 9 
 
 4 
 
 7 
 
 7 
 
 2 
 
 9 
 
 8 
 
 5 
 
 1 
 
 3 
 
 5 
 
 7 
 
 6 
 
 5 
 
 5 
 
 5 
 
 6 
 
 6 
 
 8 
 
 2 
 
 4 
 
 4 
 
 3 
 
 6 
 
 3 
 
 6 
 
 8 
 
 7 
 
 4 
 
 6 
 
 5 
 
 6 
 
 5 
 
 5 
 
 7 
 
 5 
 
 4 
 
 2 
 
 1 
 
 3 
 
 6 
 
 4 
 
 9 
 
 4 
 
 8 
 
 2 
 
 3 
 
 2 
 
 1 
 
 1 
 
 2 
 
 3 
 
 1 
 
 1 
 
 2 
 
 5 
 
 3 
 
 8 
 
 1 
 
 9 
 
 4 
 
 3 
 
 3 
 
 1 
 
 4 
 
 2 
 
 1 
 
 5 
 
 6 
 
 4 
 
 5 
 
 9 
 
 7 
 
 6 
 
 6 
 
 Name the results only and make groups of two figures each. Thus, in 
 problem 1, beginning at the bottom and adding up, say 6, 16, 28, 43, 52. 
 
 16-45. Add the numbers in the exercise on page 10 by 
 groups of two figures each. 
 
 26. It is practically as easy to add 54 and 9, 59 and 6, etc., 
 as it is 4 and 9, 9 and 6, etc. 4 and 9 are always equal to 1 
 ten and 3 units, and 9 and 6 to 1 ten and 5 units. Hence in 
 adding 54 and 9 think of the tens as increased by 1, call the 
 units 3, and the result is 63 ; in adding 59 and 6 think of the 
 tens as 6, the units as 5, and the result as 65. 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of each of the following groups : 
 i. 27 48 59 77 58 52 59 75 95 84 39 59 84 76 91 
 
 2. 75 59 77 88 74 23 24 44 89 78 67 37 56 58 68 
 J^J^_^J>J>_^J?1J?-1_?-1-1 - 
 
 3. 37 49 38 37 45 95 98 87 54. 72 63 42 73 97 88 
 
 587698779989859 
 
ADDITION 13 
 
 27. In combining numbers between 10 and 20 think of them 
 as one ten and a certain number of units and not as a certain 
 number of units and 1 ten. 
 
 Thus, in combining 17 and 18 think of 28 and 7, or 35; in combining 19 
 and 15 think of 29 and 5, or 34 ; and so on. 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of each of the following groups : 
 abcde fghi jklmno 
 
 1. 12 17 12 16 11 12 18 16 17 11 19 13 18 12 17 
 1517121314111812181915 13 121419 
 
 2. 13 11 15 19 14 19 17 15 13 19 16 14 18 18 12 
 
 3. 11 17 12 17 15 15 12 18 16 14 19 14 19 17 11 
 111413131715171616131918131115 
 
 The above exercise contains all combinations possible with the numbers 
 from 11 to 19 inclusive. Drill on the exercise should be continued until re- 
 sults can be named at the rate of 120 per minute. 
 
 23. Numbers between 10 and 20 may be combined with num- 
 bers above 20 in practically the same manner as in 27 
 
 Thus, in adding 62 and 12 think of 72 and 2, or 74; in adding 79 and 17 
 think of 89 and 7, or 96. 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of the following numbers.: 
 
 1. 25 48 59 87 91 75 86 75 48 78 57 89 37 56 75 
 nni6U181819121^131614171814 
 
 2. 29 47 83 92 36 54 59 78 67 92 77 86 53 78 85 
 1314191419^1318151313^191917 1414 
 
 3. 31 32 45 69 74 95 98 92 96 87 86 34 43 64 38 
 19 17 19 15 8 18 14 19 15 17 19 18 18 19 17 
 
14 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. Count by 7's from 1 to 85. 
 
 SOLUTION. 8, 15, 22, 9, 36, 43, 50, 7, 64, 71, 8, 85. 
 
 Count by : 
 
 2. 2's from 39 to 55. 14. 8's from 10 to 138. 
 
 3. 5's from 11 to 86. 15. 7's from 19 to 152. 
 
 4. 6's from 15 to 63. 16. 6's from 20 to 128. 
 
 5. 5's from 2 to 107. 17. 6's from 15 to 111. 
 
 6. 7's from 11 to 60. 18. 9's from 12 to 102. 
 
 7. 8's from 25 to 89. 19. 8's from 17 to 113. 
 
 8. 9's from 31 to 112. 20. 7's from 24 to 108. 
 
 9. 8's from 32 to 192. 21. 6's from 27 to 117. 
 
 10. 7's from 18 to 102. 22. 4's from 19 to 183. 
 
 11. 6's from 72 to 126. 23. ll's from 14 to 102. 
 
 12. 9's from 10 to 136. 24. 12's from 17 to 161. 
 
 13. 9's from 17 to 152. 25. 13's from 17 to 121. 
 26. Beginning at 1 count by 4's to 17 ; going on from 17 
 
 count by 7's to 52 ; from 52 count by 9's to 133 ; from 133 
 count by 5's to 158 ; from 158 count by 12's to 206 ; from 
 206 count by 13's to 271. 
 
 This exercise furnishes one of the best possible drills in addition, and it 
 should be continued until the successive results can be named at the rate of 
 150 per minute. 
 
 29. If the student is accurate and rapid in making groups 
 of two figures each, he is ready for practice in groups of three 
 figures each. In the following exercise are all the possible 
 groups of three figures each. 
 
 ORAL EXERCISE 
 
 Name at sight the sum of each of the following groups: 
 
 4, 2, and 3 should be thought of as 9 just as p-e-n is thought of as pen. 
 
 l. 419811318145178 
 131223173314414 
 332175631941641 
 
ADDITION 15 
 
 2. 
 
 1 
 
 6 
 
 1 
 
 4 
 
 1 
 
 2 
 
 1 
 
 1 
 
 1 
 
 1 
 
 7 
 
 6 
 
 9 
 
 8 
 
 1 
 
 
 4 
 
 1 
 
 2 
 
 1 
 
 2 
 
 2 
 
 9 
 
 1 
 
 1 
 
 6 
 
 6 
 
 6 
 
 5 
 
 5 
 
 5 
 
 
 9 
 
 2 
 
 5 
 
 2 
 
 3 
 
 1 
 
 1 
 
 8 
 
 7 
 
 8 
 
 1 
 
 1 
 
 1 
 
 1 
 
 7 
 
 3. 
 
 6 
 
 5 
 
 2 
 
 5 
 
 2 
 
 3 
 
 9 
 
 2 
 
 2 
 
 2 
 
 2 
 
 6 
 
 1 
 
 1 
 
 2 
 
 
 1 
 
 1 
 
 3 
 
 3 
 
 3 
 
 2 
 
 2 
 
 8 
 
 7 
 
 6 
 
 5 
 
 1 
 
 1 
 
 1 
 
 2 
 
 
 5 
 
 5 
 
 6 
 
 2 
 
 4 
 
 3 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 1 
 
 5 
 
 4 
 
 4 
 
 4. 
 
 3 
 
 2 
 
 1 
 
 2 
 
 2 
 
 6 
 
 2 
 
 6 
 
 5 
 
 5 
 
 7 
 
 1 
 
 1' 
 
 1 
 
 1 
 
 
 2 
 
 2 
 
 1 
 
 7 
 
 6 
 
 8 
 
 6 
 
 2 
 
 2 
 
 2 
 
 2 
 
 1 
 
 1 
 
 6 
 
 9 
 
 
 2 
 
 2 
 
 3 
 
 7 
 
 9 
 
 2 
 
 7 
 
 6 
 
 9 
 
 8 
 
 5 
 
 2 
 
 1 
 
 9 
 
 9 
 
 5. 
 
 9 
 
 8 
 
 9 
 
 8 
 
 7 
 
 3 
 
 4 
 
 5 
 
 6 
 
 6 
 
 5 
 
 4 
 
 3 
 
 3 
 
 4 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 5 
 
 8 
 
 7 
 
 7 
 
 7 
 
 5 
 
 4 
 
 4 
 
 4 
 
 4 
 
 
 8 
 
 8 
 
 7 
 
 7 
 
 7 
 
 5 
 
 4 
 
 5 
 
 9 
 
 8 
 
 6 
 
 7 
 
 9 
 
 8 
 
 6 
 
 6. 
 
 5 
 
 6 
 
 6 
 
 9 
 
 5 
 
 7 
 
 3 
 
 4 
 
 9 
 
 6 
 
 6 
 
 8 
 
 3 
 
 3 
 
 3 
 
 
 5 
 
 7 
 
 6 
 
 4 
 
 4 
 
 3 
 
 4 
 
 4 
 
 4 
 
 8 
 
 7 
 
 4 
 
 9 
 
 4 
 
 4 
 
 
 5 
 
 7 
 
 9 
 
 9 
 
 4 
 
 4 
 
 6 
 
 4 
 
 8 
 
 6 
 
 6 
 
 8 
 
 9 
 
 5 
 
 4 
 
 7. 
 
 3 
 
 4 
 
 6 
 
 9 
 
 8 
 
 5 
 
 4 
 
 3 
 
 3 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 8 
 
 
 8 
 
 7 
 
 6 
 
 9 
 
 9 
 
 9 
 
 7 
 
 8 
 
 3 
 
 5 
 
 3 
 
 7 
 
 7 
 
 8 
 
 8 
 
 
 9 
 
 9 
 
 6 
 
 9 
 
 9 
 
 9 
 
 8 
 
 8 
 
 9 
 
 6 
 
 8 
 
 9 
 
 7 
 
 9 
 
 8 
 
 8. 
 
 8 
 
 5 
 
 4 
 
 3 
 
 3 
 
 5 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 7 
 
 7 
 
 5 
 
 4 
 
 
 8 
 
 8 
 
 9 
 
 8 
 
 7 
 
 2 
 
 4 
 
 3 
 
 7 
 
 6 
 
 7 
 
 9 
 
 8 
 
 7 
 
 6 
 
 
 9 
 
 5 
 
 6 
 
 7 
 
 3 
 
 5 
 
 9 
 
 6 
 
 7 
 
 8 
 
 9 
 
 9 
 
 9 
 
 8 
 
 7 
 
 9. 
 
 3 
 
 3 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 7 
 
 9 
 
 9 
 
 9 
 
 7 
 
 3 
 
 6 
 
 
 6 
 
 3 
 
 4 
 
 4 
 
 3 
 
 6 
 
 6 
 
 7 
 
 8 
 
 7 
 
 6 
 
 5 
 
 6 
 
 3 
 
 4 
 
 
 9 
 
 5 
 
 8 
 
 7 
 
 4 
 
 8 
 
 6 
 
 7 
 
 8 
 
 7 
 
 5 
 
 4 
 
 3 
 
 3 
 
 2 
 
 10. 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7 
 
 9 
 
 6 
 
 6 
 
 
 4 
 
 9 
 
 6 
 
 5 
 
 6 
 
 7 
 
 4 
 
 8 
 
 5 
 
 5 
 
 6 
 
 7 
 
 9 
 
 6 
 
 5 
 
 
 5 
 
 9 
 
 6 
 
 8 
 
 8 
 
 8 
 
 4 
 
 9 
 
 9 
 
 7 
 
 7 
 
 7 
 
 6 
 
 5 
 
 4 
 
 11. 
 
 8 
 
 8 
 
 9 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 8 
 
 8 
 
 9 
 
 6 
 
 8 
 
 7 
 
 
 6 
 
 8 
 
 3 
 
 3 
 
 7 
 
 5 
 
 5 
 
 5 
 
 8 
 
 8 
 
 5 
 
 4 
 
 5 
 
 7 
 
 3 
 
 
 3 
 
 2 
 
 2 
 
 8 
 
 9 
 
 7 
 
 5 
 
 9 
 
 9 
 
 6 
 
 6 
 
 4 
 
 3 
 
 2 
 
 2 
 
 This exercise should be drilled upon until the sums of the groups, in any 
 order, can be named at the rate of 120 per minute. 
 
16 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1-15. Turn to the exercise on page 10 and find the sum of 
 the numbers given. 
 
 Name results only, and make groups of three figures each. Thus, in 
 problem 1, say 9, 23, 37, 43. 
 
 Add from the bottom up and check the work by adding from the top down. 
 Find the sum of the following problems : 
 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 131422244512954 
 
 1 
 
 1 
 
 3 
 
 3 
 
 3 
 
 1 
 
 6 
 
 3 
 
 9 
 
 5 
 
 7 
 
 4 
 
 
 
 7 
 
 3 
 
 1 
 
 1 
 
 4 
 
 1 
 
 5 
 
 2 
 
 2 
 
 4 
 
 5 
 
 
 
 2 
 
 4 
 
 1 
 
 2 
 
 1 
 
 2 
 
 1 
 
 3 
 
 1 
 
 3 
 
 1 
 
 4 
 
 1 
 
 8 
 
 8 
 
 9 
 
 2 
 
 8 
 
 
 
 1 
 
 2 
 
 4 
 
 1 
 
 4 
 
 6 
 
 4 
 
 5 
 
 8 
 
 3 
 
 2 
 
 
 
 3 
 
 
 
 
 
 6 
 
 2 
 
 2 
 
 3 
 
 8 
 
 1 
 
 1 
 
 2 
 
 1 
 
 7 
 
 1 
 
 1 
 
 5 
 
 2 
 
 5 
 
 8 
 
 2 
 
 4 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 8 
 
 3 
 
 5 
 
 7 
 
 2 
 
 6 
 
 1 
 
 5 
 
 2 
 
 1 
 
 4 
 
 5 
 
 3 
 
 7 
 
 6 
 
 2 
 
 7 
 
 3 
 
 7 
 
 2 
 
 6 
 
 6 
 
 1 
 
 2 
 
 9 
 
 4 
 
 3 
 
 2 
 
 3 
 
 1 
 
 8 
 
 2 
 
 2 
 
 1 
 
 6 
 
 
 
 7 
 
 5 
 
 1 
 
 8 
 
 3 
 
 4 
 
 2 
 
 1 
 
 2 
 
 9 
 
 9 
 
 6 
 
 7 
 
 2 
 
 3 
 
 3 
 
 3 
 
 5 
 
 2 
 
 3 
 
 3 
 
 6 
 
 9 
 
 3 
 
 3 
 
 1 
 
 2 
 
 8 
 
 2 
 
 6 
 
 3 
 
 1 
 
 3 
 
 1 
 
 3 
 
 3 
 
 1 
 
 
 
 5 
 
 6 
 
 3 
 
 7 
 
 
 
 4 
 
 1 
 
 1 
 
 3 
 
 2 
 
 7 
 
 2 
 
 4 
 
 3 
 
 
 
 2 
 
 8 
 
 8 
 
 4 
 
 7 
 
 2 
 
 5 
 
 9 
 
 5 
 
 4 
 
 2 
 
 5 
 
 2 
 
 4 
 
 8 
 
 5 
 
 1 
 
 2 
 
 3 
 
 3 
 
 2 
 
 3 
 
 2 
 
 2 
 
 4 
 
 1 
 
 4 
 
 4 
 
 3 
 
 2 
 
 2 
 
 
 
 4 
 
 3 
 
 
 
 5 
 
 2 
 
 1 
 
 1 
 
 2 
 
 1 
 
 2 
 
 6 
 
 6 
 
 4 
 
 4 
 
 6 
 
 6 
 
 3 
 
 6 
 
 2 
 
 5 
 
 8 
 
 8 
 
 6 
 
 2 
 
 3 
 
 3 
 
 8 
 
 5 
 
 2 
 
 4 
 
 4 
 
 3 
 
 3 
 
 2 
 
 8 
 
 2 
 
 1 
 
 2 
 
 6 
 
 5 
 
 1 
 
 1 
 
 1 
 
 3 
 
 
 
 5 
 
 6 
 
 1 
 
 6 
 
 2 
 
 1 
 
 4 
 
 4 
 
 1 
 
 3 
 
 7 
 
 2 
 
 9 
 
 3 
 
 7 
 
 9 
 
 1 
 
 5 
 
 7 
 
 5 
 
 7 
 
 3 
 
 5 
 
 2 
 
 2 
 
 2 
 
 6 
 
 2 
 
 2 
 
 3 
 
 1 
 
 7 
 
 3 
 
 3 
 
 7 
 
 2 
 
 4 
 
 2 
 
 5 
 
 6 
 
 1 
 
 3 
 
 1 
 
 3 
 
 
 
 3 
 
 2 
 
 2 
 
 1 
 
 3 
 
 1 
 
 4 
 
 2 
 
 1 
 
 2 
 
 1 
 
 2 
 
 2 
 
 7 
 
 7 
 
 7 
 
 1 
 
 1 
 
 9 
 
 2 
 
 2 
 
 9 
 
 7 
 
 2 
 
 2 
 
 3 
 
 8 
 
 3 
 
 1 
 
 & 
 
 3 
 
 9 
 
 1 
 
 2 
 
 5 
 
 2 
 
 1 
 
 3 
 
 4 
 
 4 
 
 4 
 
 1 
 
 7 
 
 7 
 
 1 
 
 
 
 
 
 8 
 
 4 
 
 8 
 
 4 
 
 2 
 
 1 
 
 3 
 
 7 
 
 3 
 
 2 
 
 5 
 
 7 
 
 6 
 
 5 
 
 5 
 
 2 
 
 4 
 
 4 
 
 3 
 
 1 
 
 6 
 
 2 
 
 1 
 
 5 
 
 5 
 
 3 
 
 2 
 
 3 
 
 2 
 
 8 
 
 1 
 
 3 
 
 6 
 
 3 
 
 2 
 
 3 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 2 
 
 1 
 
 2 
 
 1 
 
 5 
 
 7 
 
 1 
 
 1 
 
ADDITION 
 
 17 
 
 30. It is always an advantage to find groups of figures aggre- 
 gating 10 and 20 in the body of a column. 
 
 These groups should be added immediately to the sum already obtained 
 by simply combining the tens of the two numbers. It is not a good plan, 
 however, to take the digits in irregular order in order to form groups of 
 10 and 20. 
 
 ORAL EXERCISE 
 
 Find the sum of the following problems, taking advantage of 
 groups of 10 and %0 wherever possible : 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 11 21 
 
 9J 8j 
 
 I) 
 
 6525343 7 8 259 
 455432554 789 
 
 71 41 
 3J 6J 
 
 !) 
 
 185678556 321 
 9279874 2 581 
 
 2 7 
 
 7 
 
 2431236 9 7525 
 
 16. 17. 
 
 18. 
 
 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 4] 11 
 
 9 1 
 
 146571244161 
 
 8 1 
 
 > 2 
 
 612224223931 
 
 3J 8J 
 
 9J 
 
 352315643218 
 
 7] i 
 
 4 
 
 654475187870 
 
 2 6 
 
 > 1 
 
 224335762349 
 
 lJ 3, 
 
 5, 
 
 232344245750 
 
 6 5 
 
 9 
 
 244866531811 
 
 31. 32. 
 
 33. 
 
 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 
 
 2 3^ 
 
 9 1 
 
 866665866276 
 
 2] 8 
 
 4 
 
 567757439897 
 
 9 9. 
 
 7. 
 
 687868985994 
 
 9J 7 
 
 9 
 
 979787796929 
 
 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 
 
 38 42 25 35 46 14 21 12 18 29 57 17 13 14 15 
 
 32554627 
 34768672 
 84898858 
 67455236 
 
18 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 31. When three figures are in consecutive order the sum may 
 be found by multiplying the middle figure by 3 ; when five 
 figures are in consecutive order the sum may be found by mul- 
 tiplying the middle figure by 5 ; etc. ; or the sum of any num- 
 ber of consecutive numbers may be found by taking one half the 
 sum of the first and last numbers and multiplying it by the 
 number of terms. 
 
 ORAL EXERCISE 
 
 By inspection find the sum of: 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 
 
 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 
 
 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 35 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 70 
 
 75 
 
 80 
 
 11 
 
 16 
 
 21 
 
 26 
 
 31 
 
 36 
 
 41 
 
 46 
 
 51 
 
 56 
 
 61 
 
 66 
 
 71 
 
 76 
 
 81 
 
 12 
 
 17 
 
 22 
 
 27 
 
 32 
 
 37 
 
 42 
 
 47 
 
 52 
 
 57 
 
 62 
 
 67 
 
 72 
 
 77 
 
 82 
 
 13 
 
 18 
 
 23 
 
 28 
 
 33 
 
 38 
 
 43 
 
 48 
 
 53 
 
 58 
 
 63 
 
 68 
 
 73 
 
 78 
 
 83 
 
 14 
 
 19 
 
 24 
 
 29 
 
 34 
 
 39 
 
 44 
 
 49 
 
 54 
 
 59 
 
 64 
 
 69 
 
 74 
 
 79 
 
 84 
 
 31. 
 
 32. 
 
 33. 
 
 34. 
 
 35. 
 
 36. 
 
 37. 
 
 38. 
 
 39. 
 
 40. 
 
 41. 
 
 42. 
 
 43. 
 
 44. 
 
 45. 
 
 7 
 
 10 
 
 13 
 
 16 
 
 19 
 
 22 
 
 25 
 
 28 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 8 
 
 11 
 
 14 
 
 17 
 
 20 
 
 23 
 
 26 
 
 29 
 
 32 
 
 35 
 
 38 
 
 41 
 
 44 
 
 47 
 
 50 
 
 9 
 
 12 
 
 15 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 33 
 
 36 
 
 39 
 
 42 
 
 45 
 
 48 
 
 51 
 
 10 
 
 13 
 
 16 
 
 19 
 
 22 
 
 25 
 
 28 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 52 
 
 11 
 
 14 
 
 17 
 
 20 
 
 23 
 
 26 
 
 29 
 
 32 
 
 35 
 
 38 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 12 
 
 15 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 33 
 
 36 
 
 39 
 
 42 
 
 45 
 
 48 
 
 51 
 
 54 
 
 13 
 
 16 
 
 19 
 
 22 
 
 25 
 
 28 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 52 
 
 55 
 
 14 
 
 17 
 
 20 
 
 23 
 
 26 
 
 29 
 
 32 
 
 35 
 
 38 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 56 
 
 15 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 33 
 
 36 
 
 39 
 
 42 
 
 45 
 
 48 
 
 51 
 
 54 
 
 57 
 
 16 
 
 19 
 
 22 
 
 25 
 
 28 
 
 31 
 
 34 
 
 37 
 
 40 
 
 43 
 
 46 
 
 49 
 
 52 
 
 55 
 
 58 
 
 17 
 
 20 
 
 23 
 
 26 
 
 29 
 
 32 
 
 35 
 
 38 
 
 41 
 
 44 
 
 47 
 
 50 
 
 53 
 
 56 
 
 59 
 
 32. When a figure is repeated several times the sum may be 
 found by multiplication. 
 
ADDITION 19 
 
 ORAL EXERCISE 
 
 By inspection find the sum of the following groups : 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 4 3 
 
 4 
 
 5 
 
 3 
 
 7 
 
 8 
 
 8 
 
 15 
 
 6 
 
 7 
 
 8 15 13 
 
 9 
 
 9 7 
 
 4 
 
 5 
 
 3 
 
 7 
 
 5 
 
 7 
 
 15 
 
 6 
 
 8 
 
 7 14 13 
 
 8 
 
 9 8 
 
 4 
 
 5 
 
 9 
 
 7 
 
 5 
 
 9 
 
 15 
 
 12 
 
 7 
 
 8 15 13 
 
 8 
 
 9 8 
 
 9 
 
 5 
 
 9 
 
 8 
 
 6 
 
 9 
 
 8 
 
 12 
 
 7 
 
 7 14 7 
 
 9 
 
 9 8 
 
 9 
 
 9 
 
 8 
 
 8 
 
 6 
 
 9 
 
 8 
 
 12 
 
 7 
 
 8 15 7 
 
 8 
 
 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 374275 12 2468985 16 
 
 3 7 
 
 4 
 
 2 7 
 
 5 
 
 5 
 
 2 
 
 4 
 
 6 
 
 8 
 
 9 
 
 8 
 
 5 16 
 
 3 7 
 
 4 
 
 2 4 
 
 5 
 
 5 
 
 2 
 
 4 
 
 6 
 
 8 
 
 9 
 
 8 
 
 5 16 
 
 2 2 
 
 7 
 
 8 4 
 
 4 
 
 5 
 
 3 
 
 5 
 
 4 
 
 3 
 
 5 
 
 8 
 
 5 16 
 
 2 2 
 
 7 
 
 8 2 
 
 4 
 
 5 
 
 3 
 
 5 
 
 4 
 
 3 
 
 5 
 
 8 
 
 5 20 
 
 2 2 
 
 7 
 
 8 2 
 
 4 
 
 5 
 
 3 
 
 5 
 
 4 
 
 3 
 
 5 
 
 9 
 
 8 1 
 
 33. In all written work make plain, legible figures of a 
 uniform size, write them equal distances from each other, 
 and be sure that the units of the same order stand in the 
 same vertical column. 
 
 7 
 
 34. Many of the errors that occur in business are in simple 
 addition. Errors in addition result from two main causes : 
 irregularity in the placing of figures ; poor figures. 
 
 35. In business it is important that figures be made rapidly ; 
 but rapidity should never be secured at the expense of legibility. 
 
 WRITTEN EXERCISE 
 
 Copy and find the sum of: 
 
 1. 2. 3. 4. 5. 6. 
 
 1745 1842 1249 4271 6229 1481 
 
 1862 1695 1810 8614 4813 1862 
 
 7529 4716 6241 9217 7142 4129 
 
 8721 8412 1728 8214 6212 2412 
 
20 
 
 PRACTICAL BUSINESS AKITHMETIG 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 11. 
 
 12. 
 
 4216 
 
 2110 
 
 4142 
 
 1061 
 
 4113 
 
 4112 
 
 8912 
 
 8420 
 
 4347 
 
 1875 
 
 8217 
 
 1012 
 
 4729 
 
 1641 
 
 1012 
 
 6214 
 
 8614 
 
 1862 
 
 8624 
 
 1722 
 
 1816 
 
 1931 
 
 1692 
 
 1721 
 
 4829 
 
 1837 
 
 4112 
 
 1648 
 
 1591 
 
 1692 
 
 6212 
 
 4216 
 
 4210 
 
 1721 
 
 1686 
 
 1486 
 
 4110 
 
 4117 
 
 1618 
 
 1728 
 
 2172 
 
 4112 
 
 4210 
 
 1832 
 
 4060 
 
 1421 
 
 1754 
 
 1010 
 
 36. The simplest way to check addition is to add the columns 
 in reverse order. If the results obtained by both processes 
 agree,, the work may be assumed to be correct. 
 
 37. In adding long columns of figures it is generally advis- 
 able to record the entire sum of each column separately ; then 
 if interruptions occur, it will not be necessary to re-add any por- 
 tions already completed. After the total of each column has 
 been found the entire total may be determined by combining 
 the separate totals of the columns. 
 
 38. The best way to test the accuracy of columns added in this 
 manner is to begin at the left and repeat the addition in reverse 
 order. The entire total of each column should again be written 
 and the complete total of the problem found by adding the sepa- 
 rate totals of the several columns. If the results obtained by 
 the tw^Q processes agree, the work may be assumed to be correct. 
 
 39. Example. Find the sum of 54669, 15218, 36425, 45325, 
 and 68619. Check the result. 
 
 SOLUTION. Beginning at the bottom of the 
 right-hand column, add each column in regu- 
 lar order and write the entire totals as shown 
 in (a). Beginning at the top of the left- 
 hand column again add each column and 
 write the entire totals as shown in (6). Next 
 add the totals obtained by the first and 
 second additions and compare the results. 
 Since the total shown by (a) is equal to the 
 total shown by (&), the result, 220,256, is assumed to be correct, 
 addition should be carefully checked. 
 
 (*) 
 
 19 
 28 
 21 
 12 
 36 
 
 54669 
 15218 
 36425 
 45325 
 
 68619 
 
 (a) 
 36 
 12 
 21 
 28 
 19 
 
 220256 
 
 220256 
 
 med to be 
 
 220256 
 
 correct. All work in 
 
ADDITION 21 
 
 WRITTEN EXERCISE 
 
 See how many times the following numbers can be written in 
 one minute. Write each number in form for vertical addition. 
 
 1. 426579. 3. 17983.21. 5. 170812.34. 
 
 2. 123987. 4. 14080.91. 6. $41182.50. 
 
 Thus, in repeating the number in problem 1 write it as follows: 
 
 *t 2. 6 J~ 7 # 
 
 ^ z 6 J~ 7 7 
 
 * 2- 6 J~ 7 <? 
 
 ^ Z J~ 7 7 
 
 Be sure that the spacing between the lines and between the columns is 
 uniform. Increase the speed gradually until from 150 to 200 figures can 
 be written per minute. 
 
 40. Skill in writing figures from dictation should be culti- 
 vated. The dictation should be slow at first, but it should be 
 gradually increased until the requisite speed is acquired. 
 
 41. In calling off numbers to another great care should be 
 taken in order that no errors may be made. In reading 
 United States money the word dollars should be called with 
 each amount. The word cents may be omitted in all cases 
 except where there are no dollars. 
 
 Thus, in calling $400.37 say four hundred dollars, thirty-seven; in calling 
 $25.11 say twenty-five dollars, eleven; in calling $1573.86 say fifteen hundred 
 seventy-three dollars, eighty-six; in calling $5.31 say^ye dollars, thirty-one. 
 
 WRITTEN EXERCISE 
 Write from dictation and find the sum of: 
 
 1. $75.18, $123.95, $147.25, $9.50, $181.45, $172.16, 184.98, 
 $314.95, $49.10, $69.90, $312.60, $415.90. 
 
 2. $3140.19, $310.92, $3164.96, $3162.19, $18.62, $410.95, 
 $690.18, $10.75, $3100.40, $300.40, $200.50, $100.90, $410.80, 
 $100.85, $310.60, $80.90, $399.80, $412.60. 
 
22 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Copy, find the sum, and check : 
 1. 2. 
 
 / J / 
 
 3. 
 
 62 /. 
 
 / 2 & 2 
 2 / J 
 
 2 
 
 / J ^j- 7/*.j-0 / 2J<^2-/ 
 
 37^0 z 6 ^. / 7 
 
 / 23^.23 
 
 2 / 2.4J /2J~^2/ 
 
 2 / 2.J-~t / 3 2 / 
 
 ^ & ^. / (, 2/^/^2 
 
 2 / &.J~4^ 3 / J~/ 2 
 
 2/ ^. 4Cf 2 / / ^"^ 
 
 2^6^62-7. / 3/7^2^-7.6^ /262^7<^. 
 
 . 67 
 
 / 2 
 
 7< 
 
 2 / 
 
 2 
 
 4. 
 
 6. 
 
 72/2 
 / 2 
 
 
 
 
 / 2 
 
 2 
 
 2 / 
 / 7 2 
 
 7 2 /. f 
 
ADDITION 23 
 
 8. 9. 
 
 ^ 6 2 /.ttt // 62-0 / 77.2^~ 
 6 f / 2.0 3J~7<f > <?.^4 : / z,/^z6.^/ 
 27 /^./f / 6^ 2^.7^ / 0/^70 27.60 
 
 /> 
 
 / r f / / 
 
 ~30 37^26/^2 72// 
 22 ^ f ^2.7<T / Z 
 2 6 <?\J~^.rf '0 6> 2 / 
 
 22^^/.37 7^z^67.^<r ^/ 
 
 Z ^ / 6.24? / 2 / 
 
 / Z 7. /V 6 & / 2.7 J~ 
 
 372 
 
 / 2 
 7 ^ 6 0.0 72 <^j~. 6 ^ / 6 2 
 
 360 ^7. 4^6 
 
 & <p */ / ^2 / / 2 / 4^ ^ 0.7 J~ 
 72-/20J7// ^^^76.62 
 
 f2f#J./2- 2-/# t 
 
 7^/627.03 / 2 
 62/26^7^f~ 2-/ 7 2 
 
 2 6 / 2 #. 4^J~ / / 2 / b. 
 
 f6<T3~2./7 ^^20/7. 
 
 / 2/20 2. 60 72/26.73 
 
 7- 
 
 22-<s/^.<^2 & f J ^ f. ^3~ / & / Z 
 
 22tT^.20 70/20.^2 7 2 / 
 
 6 ^3~^.f7 z 77 z 
 
 / z 6 7 z. 6.j~4? / f ^ 2 
 /26/2J~.6J~ 32/6/^.70 6fZ^6.7<f 
 / 6 Z 3 & 7'7 &s 2*/ / 2 
 
24 PRACTICAL BUSINESS ARITHMETIC 
 
 42. Some accountants practice adding two columns at once 
 when the columns are short. The method generally employed 
 is similar to the method explained for combining groups in 
 regular addition. 
 
 43. Example. Find the sum of 83, 72, 89. 
 
 SOLUTION. Beginning at the bottom and adding up, think of 89 and ^ 
 
 72 as 159 and 2, or 161 ; of 161 and 83 as 241 and 3, or 244. 
 In adding name results only. Thus say 159, 161, 241, 244. 
 
 244 
 
 ORAL EXERCISE 
 
 By inspection give the sum of each of the following groups : 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 43 64 52 37 65 38 52 85 93 68 58 76 83 57 62 
 
 25 18 29 56 27 43 67 34 72 75 46 39 47 25 39 
 
 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 53 52 61 34 91 68 48 24 78 54 94 57 92 76 43 
 4643 37 761347699676353644373156 
 
 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 
 
 65 44 46 48 67 44 53 25 54 46 33 16 67 83 88 
 86 57 65 25 48 57 45 31 65 39 64 34 43 82 25 
 752134313921676987877725419831 
 
 HORIZONTAL ADDITION 
 
 44. In some kinds of invoicing arid in short-extending the 
 items of an account numbers to be added are written in horizon- 
 tal lines. Much time may be saved by adding these numbers 
 as they stand. After careful practice it will be found possible 
 to add numbers written in horizontal lines with as much 
 facility as numbers written in vertical columns. 
 
 45. In adding numbers written horizontally care should be 
 exercised to combine only units of the same order. It is gener- 
 ally best to add from left to right and to verify the work from 
 right to left. Grouping may be employed to advantage in 
 horizontal addition. 
 
ADDITION 25 
 
 WRITTEN EXERCISE 
 
 Copy and add the following numbers horizontally. Verify the 
 
 work. 
 
 Thus, in problem 1, beginning at the left, say 10, 20, 32, 52. In verifying 
 the work from the right say 20, 32, 42, 52. 
 
 1. 8, 2, 1, 1, 7, 1, 4, 6, 2, 3, 8, 9. 
 
 2. 7, 9, 6, 5, 4, 8, 7, 4, 3, 7, 3, 1, 3. 
 
 3. 6, 2, 4, 8, 3, 1, 7, 6, 4, 2, 8, 9, 4, 2. 
 
 4. 15, 23, 46, 83, 29, 35, 42, 15, 21, 26. 
 
 5. 64, 48, 56, 35, 47, 87, 32, 45, 67, 91. 
 
 6. 52, 64, 86, 28, 76, 41, 15, 32, 12, 87. 
 
 7. 32, 48, 24, 62, 85, 14, 63, 54, 78, 94, 23, 45. 
 
 8. 42, 76, 49, 81, 17, 42, 17, 19, 21, 43, 64, 17. 
 
 9. 45, 48, 34, 46, 48, 53, 25, 42, 35, 56, 70, 10. 
 
 10. 291, 196, 855, 578, 210, 354, 102, 232, 241, 162. 
 
 11. 469, 388, 962, 764, 351, 899, 111, 232, 190, 175. 
 
 12. 15 25 , 50 25 , 16 84 , 31 42 , 8638, 19 w 23 12 , 10* 3 , 64^ 40. 
 
 It is frequently desirable to express dollars and cents without the dollar 
 sign and the decimal point. This may be done- by slightly raising the cents 
 of the amount. Thus, $ 17.17 may be written 17 17 ; $ 2.08 may be written 2 08 . 
 
 13. 15 25 , 8 93 , 4 88 , 21 84 , 16 35 , 18 46 , 29 14 , 44 60 , 62 90 , 84 60 , 40 50 . 
 
 14. 76< 5 , 84 9 s 67 5 , 95' 4 , 68 63 , 52 21 , 13 25 , 42 18 , 60 95 , 80 13 , 90 62 . 
 
 46. It is important that the student acquire the ability to 
 carry a series of numbers in mind. The following exercises 
 are suggestive of what may be done to cultivate ability in this 
 direction. 
 
 The dictation suggested should not be slower than at the rate of one hun- 
 dred twenty words per minute. Nothing should be written by the students 
 until all of the numbers of a problem have been called by the teacher; then 
 one student may be sent to the blackboard and required to write the numbers 
 from memory. If the numbers are correctly written, the teacher may require 
 another student to give the sum of them without using pen or pencil. The 
 numbers may be written on the board in either vertical or horizontal order 
 as the teacher may direct. 
 
26 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 From the teacher's dictation mentally find the sum of each of the 
 following problems : 
 
 1. 6, 9, 8, 4, and 8 are how many ? 
 
 2. 14, 17, 20, and 5 are how many ? 
 
 3. 24, 17, 16, and 9 are how many? 
 
 4. 5, 6, 7, 1, and 3 are how many ? 
 
 5. 6, 2, 8, 1, and 7 are how many ? 
 
 6. 364, 436, and 657 are how many ? 
 
 7. 438, 212, and 750 are how many ? 
 
 8. 859, 441, and 769 are how many? 
 
 9. 2140, 3160, and 4000 are how many? 
 
 10. 200, 415, 600, and 920 are how many? 
 
 11. 857, 643, 237, and 500 are how many? 
 
 12. 14150, 14050, and $5000 are how many? 
 
 13. $5.15, $2.15, and 16.70 are how many ? 
 
 14. $ 167.14, $232.86, and $150 are how many ? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the sum of all the integers from 2165 to 2260 inclu- 
 sive. 
 
 2. Find the sum of all the integers from 1137 to 1200 inclu- 
 sive. 
 
 3. Complete the following sales sheet. Add by columns 
 and by lines and check the work by adding the vertical and 
 horizontal totals. 
 
 SUMMARY OF SALES FOR WEEK ENDING AUG. 25 
 
 
 PINK 
 
 OAK 
 
 MAPLE 
 
 SPRITE 
 
 WALNUT 
 
 CHERRY 
 
 TOT A L 
 
 Monday 
 Tuesday 
 Wednesday 
 Thursday 
 Friday 
 Saturday 
 
 121G 
 5160 
 6152 
 1216 
 4160 
 3165 
 
 18 
 40 
 18 
 18 
 80 
 80 
 
 16161 
 3214 
 2150 
 2160 
 1215 
 2115 
 
 47 
 
 90 
 18 
 50 
 40 
 
 72 
 
 649 
 316 
 163 
 130 
 315 
 218 
 
 58 
 40 
 59 
 98 
 16 
 50 
 
 860 
 160 
 430 
 115 
 218 
 165 
 
 40 
 50 
 17 
 67 
 90 
 37 
 
 315 
 513 
 968 
 413 
 411 
 118 
 
 64 
 80 
 52 
 60 
 50 
 50 
 
 186 
 216 
 756 
 314 
 132 
 17 
 
 50 
 54 
 14 
 75 
 75 
 05 
 
 _ 
 
 _ 
 
 Total 
 
 
 
 
 
 
 
 
 
ADDITION 
 
 27 
 
 4. Add the following by columns and by lines, and check 
 the work by adding the vertical and horizontal totals : 
 
 21162 
 
 49 
 
 962 
 
 18 
 
 1245 
 
 76 
 
 54168 
 
 97 
 
 52 
 
 19 
 
 
 
 176 
 
 19 
 
 1278 
 
 95 
 
 52698 
 
 13 
 
 7529 
 
 87 
 
 95162 
 
 87 
 
 
 
 2164 
 
 89 
 
 7524 
 
 16 
 
 47612 
 
 87 
 
 6842 
 
 23 
 
 5948 
 
 23 
 
 
 
 76 
 
 95 
 
 87 
 
 14 
 
 2150 
 
 49 
 
 17293 
 
 1745 
 
 86 
 
 
 
 51276 
 
 92 
 
 18187 
 
 95 
 
 75 
 
 19 
 
 162 
 
 14 
 
 5290 
 
 18 
 
 
 
 9834 
 
 18 
 
 92923 
 
 15 
 
 25 
 
 91 
 
 162 
 
 18 
 
 14 
 
 95 
 
 
 
 754 
 
 95 
 
 2167 
 
 92 
 
 2584 
 
 16 
 
 9176 
 
 92 
 
 3164 
 
 82 
 
 
 
 1356 
 
 05 
 
 1314 
 
 93 
 
 7125 
 
 95 
 
 2167 
 
 18 
 
 2645 
 
 97 
 
 
 
 756 
 
 92 
 
 142 
 
 18 
 
 167 
 
 42 
 
 926 
 
 44 
 
 3167 
 
 18 
 
 
 
 75162 
 
 19 
 
 82195 
 
 78 
 
 72162 
 
 18 
 
 9165 
 
 97 
 
 168 
 
 44 
 
 
 
 7162 
 
 95 
 
 4167 
 
 18 
 
 7156 
 
 95 
 
 172 
 
 18 
 
 1 
 
 56 
 
 
 
 2 
 
 15 
 
 6843 
 
 82 
 
 3954 
 
 05 
 
 60 
 
 65 
 
 9 
 
 18 
 
 
 
 8 
 
 85 
 
 9162 
 
 19 
 
 5144 
 
 65 
 
 8162 
 
 18 
 
 91684 
 
 57 
 
 
 
 2416 
 
 45 
 
 1829 
 
 32 
 
 4217 
 
 64 
 
 1492 
 
 95 
 
 8647 
 
 64 
 
 
 
 168 
 
 94 
 
 257 
 
 16 
 
 417 
 
 86 
 
 952 
 
 17 
 
 347 
 
 18 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5. Complete the following sales sheet. Add by columns 
 and by lines and then check the work by adding the vertical 
 and horizontal totals. 
 
 SUMMARY OF CLERKS' DAILY SALES 
 
 ^SAMES OF CLERKS 
 
 MONDAY 
 
 TUESDAY 
 
 WEDNESDAY 
 
 THURSDAY 
 
 FRIDAY 
 
 SATURDAY 
 
 TOTAL 
 FOR WEEK 
 
 J. E. Snow 
 
 167 
 
 18 
 
 194 
 
 67 
 
 98 
 
 46 
 
 241 
 
 80 
 
 175 
 
 66 
 
 314 
 
 90 
 
 
 
 W. B. Moore 
 
 78 
 
 20 
 
 65 
 
 14 
 
 50 
 
 42 
 
 60 
 
 93 
 
 51 
 
 19 
 
 64 
 
 86 
 
 
 
 T. B. Welch 
 
 112 
 
 40 
 
 118 
 
 64 
 
 192 
 
 40 
 
 146 
 
 18 
 
 110 
 
 50 
 
 140 
 
 12 
 
 
 
 E. H. Ross 
 
 164 
 
 90 
 
 143 
 
 18 
 
 192 
 
 64 
 
 214 
 
 10 
 
 110 
 
 60 
 
 190 
 
 18 
 
 
 
 Minnie Davis 
 
 165 
 
 19 
 
 214 
 
 78 
 
 120 
 
 42 
 
 167 
 
 18 
 
 164 
 
 27 
 
 140 
 
 51 
 
 
 
 Ada Bentou 
 
 68 
 
 49 
 
 90 
 
 81 
 
 64 
 
 75 
 
 120 
 
 14 
 
 142 
 
 16 
 
 60 
 
 90 
 
 
 
 Elmer S. Frey 
 
 240 
 
 18 
 
 920 
 
 41 
 
 718 
 
 52 
 
 167 
 
 59 
 
 840 
 
 72 
 
 143 
 
 86 
 
 
 
 Joseph White 
 
 22 
 
 49 
 
 72 
 
 86 
 
 51 
 
 47 
 
 62 
 
 14 
 
 91 
 
 26 
 
 72 
 
 15 
 
 
 
 Margaret Dix 
 
 47 
 
 26 
 
 91 
 
 18 
 
 21 
 
 64 
 
 18 
 
 42 
 
 61 
 
 19 
 
 64 
 
 86 
 
 
 
 F. O. Beck 
 
 127 
 
 16 
 
 95 
 
 27 
 
 114 
 
 82 
 
 162 
 
 15 
 
 102 
 
 15 
 
 112 
 
 61 
 
 
 
 L. O. Avery 
 
 214 
 
 91 
 
 218 
 
 46 
 
 920 
 
 41 
 
 172 
 
 14 
 
 152 
 
 86 
 
 142 
 
 71 
 
 
 
 B. W. Snyder 
 
 162 
 
 14 
 
 153 
 
 46 
 
 118 
 
 64 
 
 162 
 
 14 
 
 182 
 
 15 
 
 69 
 
 58 
 
 
 
 Ella Harding 
 
 21 
 
 27 
 
 18 
 
 92 
 
 17 
 
 65 
 
 28 
 
 64 
 
 59 
 
 18 
 
 72 
 
 41 
 
 
 
 Carrie Simpson 
 
 21 
 
 18 
 
 45 
 
 30 
 
 16 
 
 98 
 
 42 
 
 41 
 
 20 
 
 68 
 
 75 
 
 98 
 
 
 
 W. F. Baldwin 
 
 162 
 
 10 
 
 114 
 
 80 
 
 115 
 
 90 
 
 116 
 
 84 
 
 117 
 
 41 
 
 200 
 
 60 
 
 
 
 E. 0. Burrill 
 
 84 
 
 90 
 
 90 
 
 10 
 
 116 
 
 80 
 
 114 
 
 30 
 
 65 
 
 20 
 
 300 
 
 75 
 
 
 
 Total 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6. Without copying, find the total population of the United 
 States at each census from 1860 to 1900 inclusive. Check. 
 
28 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 POPULATION OF THE UNITED STATES AT EACH CENSUS FROM 1800 TO 1900 
 
 STATES AND TERRITORIES 
 
 I860 
 
 1S70 
 
 1880 
 
 1890 
 
 1900 
 
 
 964,201 
 
 996,992 
 
 1,262,595 
 
 1 513 017 
 
 1 828 697 
 
 Alaska . . . 
 
 
 
 33,426 
 
 30,329 
 
 03 592 
 
 Arizona .... 
 
 
 9,658 
 
 40,440 
 
 59,020 
 
 122 931 
 
 Arkansas .... 
 
 435,450 
 
 484,471 
 
 802,525 
 
 1,128,179 
 
 1,311,504 
 
 California 
 Colorado 
 Connecticut 
 Dakota ... . . 
 
 379,994 
 34,277 
 400,147 
 4,837 
 
 560,247 
 39,804 
 537,454 
 14,181 
 
 864,694 
 194,327 
 622,700 
 135,177 
 
 1,208,130 
 419,198 
 740,258 
 
 1,485,053 
 539,700 
 908,420 
 
 Delaware 
 
 112,216 
 
 125,015 
 
 146,608 
 
 168 493 
 
 184,735 
 
 District of Columbia . . 
 Florida . . . 
 
 75,080 
 140,424 
 
 131,700 
 187,748 
 
 177,624 
 
 209,493 
 
 230,392 
 391,422 
 
 278,718 
 528,542 
 
 Georgia 
 
 1,057,280 
 
 1,184,109 
 
 1,542,180 
 
 1,837,353 
 
 2,210,331 
 
 Hawaii 
 
 
 
 
 
 154,001 
 
 Idaho 
 Illinois .... 
 
 1,711,951 
 
 14,999 
 2,539,891 
 
 32,610 
 3,077,871 
 
 84,385 
 3,826,351 
 
 161,772 
 4,821,550 
 
 Indiana 
 
 1,350,428 
 
 1,680,637 
 
 1,978,301 
 
 2,192,404 
 
 2,516,462 
 
 Indian Territory .... 
 Iowa 
 
 674 913 
 
 1,194 020 
 
 1 624 615 
 
 179,321 
 1,911,896 
 
 392,060 
 2 231,853 
 
 Kansas ... 
 
 107 200 
 
 364,31)9 
 
 990 090 
 
 1,427,090 
 
 1,470,495 
 
 Kentucky 
 Louisiana 
 Maine 
 Maryland 
 Massachusetts 
 Michigan 
 Minnesota 
 Mississippi 
 
 1,155,084 
 708,01)2 
 628,279 
 687,049 
 1,231,060 
 749,113 
 172,023 
 791,30") 
 
 1,321,011 
 726,915 
 620,915 
 780,894 
 1,457,351 
 1,184,059 
 439,700 
 827,922 
 
 1,048,690 
 939,940 
 648,936 
 934,943 
 1,783,085 
 1,636,937 
 780,773 
 1,131 597 
 
 1,858,035 
 1,118,587 
 661,086 
 1,042,390 
 2,238,943 
 2,093,889 
 1,301,826 
 1,289 600 
 
 2,147,174 
 
 1,381,025 
 694,400 
 1,188,044 
 2,805,346 
 2,420,982 
 1,751,394 
 1,551 270 
 
 Missouri . . . 
 
 1,182,012 
 
 1,721,295 
 
 2,168,380 
 
 2,679,184 
 
 3,106,605 
 
 Montana 
 
 
 20 595 
 
 39 159 
 
 132 159 
 
 243 329 
 
 Nebraska 
 Nevada 
 
 28,841 
 6 857 
 
 122,993 
 42 491 
 
 452,402 
 62 '>()() 
 
 1,058,910 
 45 761 
 
 1,060,300 
 42 335 
 
 New Hampshire .... 
 New Jersey 
 
 320,073 
 672,035 
 
 318,300 
 900,096 
 
 340,991 
 1,131 110 
 
 370,530 
 1 444 <)33 
 
 411,588 
 1,883 009 
 
 New Mexico 
 New York j 
 North Carolina .... 
 North Dakota 
 
 93,516 
 3,880,735 
 992,622 
 
 91,874 
 4,382,759 
 1,071,361 
 
 119,505 
 5,082,871 
 1,399,750 
 
 153.593 
 5,997,853 
 1,617,947 
 182 719 
 
 195,310 
 
 7,208,894 
 1,893,810 
 319 146 
 
 Ohio 
 
 2,339,511 
 
 2 665,260 
 
 3 198,062 
 
 3,672 316 
 
 4,157,545 
 
 Oklahoma 
 
 
 
 
 61 834 
 
 398 331 
 
 Oregon 
 
 52 465 
 
 90 923 
 
 174 768 
 
 313,767 
 
 413,536 
 
 Pennsylvania ... 
 
 2 906 215 
 
 3 521 951 
 
 4 282,891 
 
 5,258,014 
 
 6,302,115 
 
 Rhode Island 
 South Carolina .... 
 South Dakota 
 Tennessee . 
 
 174,620 
 
 703,708 
 
 1 109 801 
 
 217,353 
 705,606 
 
 1 258 520 
 
 276,531 
 995,577 
 
 1,542,359 
 
 345,500 
 1,151.149 
 
 328,808 
 1,767,518 
 
 428,556 
 1,340,316 
 401,570 
 2,020,616 
 
 Texas 
 
 604 215 
 
 818,579 
 
 1,591,749 
 
 2,235,523 
 
 3,048,710 
 
 Utah 
 Vermont 
 Virginia . 
 
 40,273 
 315,098 
 1,590,318 
 
 86,786 
 330,551 
 1,225,163 
 
 143,963 
 
 332,286 
 1,512,565 
 
 207,905 
 332,422 
 
 1,655,980 
 
 276,749 
 343,641 
 
 1,854,184 
 
 Washington 
 West Virginia 
 Wisconsin . ... 
 
 11,594 
 
 775,881 
 
 23,955 
 442,014 
 1,054,670 
 
 75,116 
 618,457 
 1,315,497 
 
 349,390 
 762,704 
 
 1,686,880 
 
 518,103 
 958,800 
 2,069,042 
 
 Wyoming 
 
 
 9,118 
 
 20,789 
 
 60,705 
 
 92,531 
 
 Total . . 
 
 
 
 
 
 
ADDITION 29 
 
 7. Arrange the following data in tabular form, in six columns. 
 Add by columns and by lines and check the work by finding 
 the sum of the vertical and horizontal totals. 
 
 The attendance at a state fair for a week was as follows : 
 Monday: officials, 384 ; other adults, 4162 ; children, 875 ; single 
 carriages, 489 ; double carriages, 164. Tuesday: officials, 437 ; 
 other adults, 5286 ; children, 374 ; single carriages, 315 ; double 
 carriages, 100. Wednesday: officials, 311; other adults, 11,438; 
 children, 986; single carriages, 721; double carriages, 209. 
 Thursday: officials, 280 ; other adults, 21,865 ; children, 8219; 
 single carriages, 914 ; double carriages, 286. Friday: officials, 
 118; other adults, 8211; children, 452; single carriages, 136; 
 double carriages, 59. Saturday: officials, 118; other adults, 
 9164; children, 762 ; single carriages, 148 ; double carriages, 56. 
 
 8. Arrange in tabular form, in seven columns, with proper 
 headings, the following data. Show () the total departmental 
 sales, (6) the total monthly sales, and (c) the total yearly sales. 
 Check the results. 
 
 The sales of E. H. Robinson & Co. for the year ending June 
 30,1908, were as follows: July, 1907: books, 14162.18; shoes, 
 89162.17; millinery, 15218.19; dry goods, 827,162.50; gloves, 
 82816.49; furniture, 89267.50. August: books, 82160.59; 
 shoes, 84162.87; millinery, 86714.92; dry goods, 828,146.92; 
 gloves, 81624.80; furniture, 87247.95. September: books, 
 86216.45 ; shoes, 84167.95; millinery, 83142.89; dry goods, 
 824,167.46 ; gloves, 82140.17 ; furniture, 88175.96. October : 
 books, 82786.90; shoes, 84562.18; millinery, 83147.98; dry 
 goods, 822,162.49; gloves, 82478.67; furniture, 88692.14. 
 November: books, 84675.82; shoes, 84864.19; millinery, 
 86416.90; dry goods, 824,160.92; gloves, 82841.16; fur- 
 niture, 8 641 8. 46. December: books, 88746.90; shoes, 84621.19; 
 millinery, 85162.19; dry goods, 827,127.46 ; gloves, 84846.19; 
 furniture, 810,614.92. January, 1908 : books, 84641.19; shoes, 
 82462.18; millinery, 84018.60 ; dry goods, 828,562.14 ; gloves, 
 82417.90; furniture, 88642.14. February: books, 82418.64 ; 
 shoes, 84267.32s millinery, 83742.24; dry goods, 822,140.86; 
 
30 PRACTICAL BUSINESS ARITHMETIC 
 
 gloves, 12019.30; furniture, $4867. 32. March: books, $ 4416.95; 
 shoes, 18618.94; millinery, $8437.46; dry goods, $24,162.18; 
 gloves, $2814.92; furniture, $7596.54. April: books, $2486.14 ; 
 shoes, $2876.90; millinery, $3249.84; dry goods, $22,172.14 ; 
 gloves, $1865.92; furniture, $8714.95. May: books, $2834.16; 
 shoes, $3547.24; millinery, $4214.90; dry goods, $28,137.56; 
 gloves, $2272.18; furniture, $8416.59. June: books, $2816.32; 
 shoes, $4756.19; millinery, $3952.84 ; dry goods, $24,167.49; 
 gloves, $2467.14; furniture, $8619.42. 
 
 9. Arrange the following data in tabular form, in nine 
 columns, with proper headings. Find the amount of milk de- 
 livered by each patron, the amount received at the creamery 
 each day, and the amount received during the week. Check. 
 
 There was received at a creamery, during the first week 
 of June, milk as follows: Sunday : from C. D. Allen, 415 Ib. ; 
 L. B. Brown, 695 Ib. ; W. D. Carroll, 425 Ib. ; J. H. Dean, 
 165 Ib.; F. A. Ellis, 726 Ib.; J. L. Frey, 920 Ib.; I. T. Good, 
 214 Ib.; E. H. Lord, 170 Ib. Monday: from C. D. Allen, 
 416 Ib.; L. B. Brown, 702 Ib.; W. D. Carroll, 426 Ib. ; J. H. 
 Dean, 175 Ib.; F. A. Ellis, 729 Ib.; J. L. Frey, 964 Ib.; L T. 
 Good, 216 Ib. ; E. H. Lord, 172 Ib. Tuesday : from C. D. Allen, 
 420 Ib.; L. B. Brown, 711 Ib. ; W. D. Carroll, 419 Ib.; J. H. 
 Dean, 186 Ib. ; F. A. Ellis, 728 Ib. ; J. L. Frey, 963 Ib.; I. T. 
 Good, 218 Ib.; E. H. Lord, 174 Ib. Wednesday : from C. D. 
 Allen, 432 Ib.; L. B. Brown, 709 Ib.; W. D. Carroll, 430 Ib.; 
 J. H. Dean, 176 Ib. ; F. A. Ellis, 724 Ib. ; J. L. Frey, 962 Ib.; 
 I. T. Good, 217 Ib.; E. H. Lord, 178 Ib. Thursday : from C. 
 D. Allen, 428 Ib.; L. B. Brown, 709 Ib. ; W. D. Carroll, 427 Ib. ; 
 J. H. Dean, 178 Ib.; F. A. Ellis, 729 Ib. ; J. L. Frey, 966 Ib. ; 
 I. T. Good, 217 Ib.; E. H. Lord, 173 Ib. Friday: from C. D. 
 Allen, 432 Ib.; L. B. Brown, 700 Ib.; W. D. Carroll, 420 Ib.; 
 J. H. Dean, 170 Ib.; F. A. Ellis, 746 Ib.; J. L. Frey, 980 Ib.; 
 I. T. Good, 246 Ib. ; E. H. Lord, 170 Ib. Saturday: from C. 
 D. Allen, 450 Ib.; L. B. Brown, 721 Ib. ; W. D. Carroll, 417 Ib. ; 
 J. H. Dean, 178 Ib.; F. A. Ellis, 740 Ib. ; J. L. Frey, 920 Ib.; 
 L T. Good, 314 Ib.; E. H. Lord, 180 Ib. 
 
CHAPTER V 
 
 SUBTRACTION 
 ORAL EXERCISE 
 
 State the number that, added to the smaller number, makes the 
 larger one in each of the following: 
 
 1. 344567889999887 
 1213233^23164412 
 
 2. 12 11 12 11 12 11 12 11 10 11 10 11 10 12 10 
 
 9239834847 _64_75_3 
 
 3. 18 17 16 17 16 15 14 15 14 13 13 16 15 14 13 
 
 _9 _8jr_9_8_6j)jrjB_!_I_^_?j>j) 
 
 4. 13 14 14 15 16 17 18 18 19 19 19 19 18 18 17 
 11121113^213131213111614141X12 
 
 5. 22 21 22 21 22 21 22 21 20 21 20 21 20 22 20 
 191213191813141814171614171513 
 
 6. 38 27 26 37 26 35 44 25 34 53 43 36 45 54 73 
 291817291826391728443729384569 
 
 7. 42 51 72 81 92 71 32 41 70 61 90 81 30 62 50 
 39426379886324386457867427557 
 
 47. A parenthesis ( ) signifies that the numbers included 
 within it are to be considered together. A vinculum has 
 
 the same signification as a parenthesis. 
 
 Thus, 15 - (4 + 2), or 15 - 4 + 2 signifies that the sum of 4 and 2 is to 
 be subtracted from 15. 
 
 31 
 
32 PRACTICAL BUSINESS ARITHMETIC 
 
 48. Examples. 1. Find the difference between 849 and 162. 
 
 SOLUTION. 2 from 9 leaves 7. 6 cannot be subtracted from 4, but 6 
 >m 14 leaves 8. Since 1 of the 8 hundreds 
 7 hundreds remaining. 1 from 7 leaves 6. 
 
 from 14 leaves 8. Since 1 of the 8 hundreds has been taken, there are but /Q 
 
 CHECK. 687 + 162 = 849. 687 
 
 The above is a common method of subtraction. For practical computation, 
 however, the "making change" method is best. It is easily understood and 
 is much more rapid when once learned. The "making change" method is 
 illustrated in the following example and solution. 
 
 2. Find the difference between 7246 and 4824. 
 
 SOLUTION. Think "4 + 2=6," and write 2; "2 + 2 = 4," and 7246 
 
 write 2 ; " 8 + 4 = 12," and write 4 ; " 1 and 4x2= 7," and write 2. 4824 
 
 CHECK. 2422 + 4824 = 7246. ~2422 
 
 ORAL EXERCISE 
 
 1. 16 +23+? = 54? 7. 16+18 + 16 = 25 + ? 
 
 2 . 27 + 14 + ?=72? 8. 72 + 17 + 11 = 37 + ? 
 
 3 . 17 + 36 + ? =62? 9. 14 + 18 + 38 = 42 + ? 
 
 4 . 19 + 17 + 12 + ? =57? 10. 12 + 16 + 12 + 14+? = 75? 
 
 5. 25 + 14 + 11 + ? = 75? 11. 16 + 15 + 19 + 15+? = 93? 
 
 6 . 18 + 17 + 16 + ? = 70? 12. 18 + 17 + 15+ 29+? = 98? 
 
 WRITTEN EXERCISE 
 
 l. Without copying the individual problems, find quickly 
 the sum of the twenty differences in the following: 
 
 $2140.50 
 714.23 
 
 84157.50 
 1236.80 
 
 85000.24 
 249.17 
 
 89000.72 
 1246.18 
 
 81379.54 
 923.18 
 
 83145.62 
 2000.79 
 
 81742.18 
 842.16 
 
 84756.83 
 2738.44 
 
 85500.89 
 2799.14 
 
 81624.14 
 
 957.80 
 
 81985.72 
 645.92 
 
 89275.17 
 842.99 
 
 82446.80 
 1321.44 
 
 83169.14 
 
 874.36 
 
 83156.19 
 1400.72 
 
 88721.13 
 
 2049.79 
 
 87514.85 
 721.92 
 
 87291.80 
 1642.95 
 
 81756.92 
 921.74 
 
 81872.14 
 742.12 
 
SUBTRACTION 
 
 33 
 
 2. Copy the following table and show (a) the total exports 
 for each year given; (5) the excess of exports for each year 
 given; (e) the total exports and imports for the eleven years; 
 (cT) the total excess of exports for the eleven years. Check. 
 
 IMPORTS AND EXPORTS IN THE UNITED STATES FOR TEN YEARS 
 
 YEAR ENDING 
 
 EXPORTS 
 
 TOTAL 
 
 
 EXCESS or 
 
 JUNE 30 
 
 Domestic 
 
 Foreign 
 
 EXPORTS 
 
 
 EXPORTS 
 
 1895 
 
 $793,392,599 
 
 $14,145,566 
 
 
 $731,969,965 
 
 
 1896 
 
 903,200,487 
 
 19,406,451 
 
 
 779,724,674 
 
 
 1897 
 
 1,032,007,603 
 
 18,985,953 
 
 
 764,730,412 
 
 
 1898 
 
 1,210,291,913 
 
 21,190,417 
 
 
 616,050,654 
 
 
 1899 
 
 1,203,931,222 
 
 23,092,080 
 
 
 697,148,489 
 
 
 1900 
 
 1,370,763,571 
 
 23,719,511 
 
 
 849,941,184 
 
 
 1901 
 
 1,460,462,806 
 
 27,302,185 
 
 
 823,172,165 
 
 
 1902 
 
 1,355,481,861 
 
 26,237,540 
 
 
 903,320,948 
 
 
 1903 
 
 1,392,231,302 
 
 27,910,377 
 
 
 1,025,719,237 
 
 
 1904 
 
 1,491,744,641 
 
 25,910,377 
 
 
 991,090,978 
 
 
 1905 
 
 1,491,744,641 
 
 26,817,025 
 
 
 1,117,513,071 
 
 
 Total 
 
 
 
 
 
 
 49. The common method of making change is to add to the 
 price of the goods purchased a sum that will equal the amount 
 offered in payment. 
 
 Thus, if a person buys groceries amounting to 74^ and tenders $1 in 
 payment, the mental process of the clerk in making the change is as follows: 
 "74^ + 1^ + 25^ = $!"; the customer should receive as change a 1-cent, 
 piece and a quarter of a dollar. 
 
 Obviously, the change may usually be made in a number of ways. In 
 the above example two dimes and a 5-cent piece might be given instead of 
 the quarter of a dollar. But, as the different bills and coins are usually 
 sorted in the till, the experienced clerk generally makes change in the sim- 
 plest way ; that is, with the largest possible denominations. In the follow- 
 ing exercise name the largest coins and bills that could be used. 
 
 ORAL EXERCISE 
 
 1. Name the coins and the amount of change to be given 
 from $1 for each of the following purchases : 17 ^ ; 24 ^ ; 31 $ \ 
 
 38^; 45^; 52^; 59^; 66^; 73^; 80^; 87^; 180; 
 29^; 46^; 53 ^j 60^; 67^; 74^; 81^; 88 
 
34 PRACTICAL BUSINESS ARITHMETIC 
 
 2. Name the coins and the amount of change to be given 
 from |2 for each of the following purchases: $1.19; $1.26; 
 
 $1.33; $1.40; $1.47; $1.54; $1.61; $1.68; $1.75; $1.82; 
 $1.89; $1.20; $1.27; $1.34; $1.41; $1.48; $1.55; $1.62; 
 $1.69; $1.76; $1.83; $1.90. 
 
 3. Name the bills and coins and the amount of change to be 
 given from $5 for eacli of the following purchases: $1.21; 
 $1.28; $1.35; $1.42; $2.22; $2.29; $2.36; $4.43; $3.49; 
 $4.50; $3.51; $3.56; $4.57; $2.58; $1.63; $2.64; $1.65; 
 $1.70; $2.71; $3.72; $2.77; $3.84; $1.91; $2.85; $2.92. 
 
 4. Name the bills and coins and the amount of change to be 
 given from $10 for each of the following purchases: $4.93; 
 $3.86; $7.70; $2.44; $8.37; $5.30; $3.23; $5.17; $4.24; 
 $3.31; $8.38; $2.45; $6.52; $4.59; $3.66; $5.73; $4.80; 
 $3.87; $2.88; $7.81; $9.74; $5.67; $3.60; $4.53; $2.46; 
 $3.29; $8.32; $7.25; $2.18; $7.49; $9.42; $3.67; $1.93. 
 
 50. It is frequently necessary to find the difference between 
 a minuend and several subtrahends. If the " making change " 
 method of subtraction is employed, the operation is a simple 
 one. 
 
 51. Example. From a farm of 578 A. I sold at one time 162 
 A., at another 98 A., and at another 121 A. How many acres 
 remained unsold ? 
 
 f rr Q * 
 
 SOLUTION. Arrange the numbers as shown in. the margin. ' A * 
 
 Eleven (1 + 8 + 2) and seven are 18 ; write 7. Three (1 carried 162 A. 
 
 + 2), eighteen (3 + 9 + 6) and nine are twenty-seven; write 9. 93 
 
 Four (2 carried +1 + 1) and one are 5 ; write 1. -.9-1 
 
 CHECK. 197 + 121 + 98 + 162 = 578. -^- 
 
 197 A. 
 
 WRITTEN EXERCISE 
 
 Find the amount each person has remaining on deposit: 
 
 1. A. Deposit, $900; checks, $210, $175, $198. 
 
 2. B. Deposit, $875; checks, $157, $218, $157. 
 
 3. C. Deposit, $750; checks, $120, $117, $121, $118. 
 
 4. D. Deposit, $960; checks, $128, $109, $118, $117. 
 
SUBTRACTION 
 
 35 
 
 5. E. Deposit, 8967; checks, 8192, 8102, 8117, 8128,8146. 
 
 6. F. Deposit, 8998 ; checks, 8 119, 8117, 8105, 8123, 8173. 
 
 Do not neglect to check all work. The bank clerk who makes an error 
 a day in work like the above, and who fails to discover and correct this 
 error, will not long retain his position. 
 
 7. Copy the following, supplying the missing terms and 
 checking the results : 
 
 8148.90 + 8149.75 + 8421.77 = $???.?? 
 118.60+ 172.12+ ???.??= ???.?? 
 242.30+ ???.??+ 210.96= ???.?? 
 ???.??+ 168.72 + 130.41 = ???.?? 
 
 8718.95 + 8698.75 + 8978.60 = 8?? ? ?. ? ? 
 
 The following problem shows a portion of a bank discount register. In 
 the first column are recorded the amounts of several notes that have been dis- 
 counted ; in the second, the discount charges; and in the third, the collection 
 and exchange charges. The proceeds of any note is the difference between 
 the amount (face) of the note and the total charges upon it. 
 
 8. Copy and complete the following bank record. Check 
 the work. (/ + i + h should equal #.) 
 
 FACE OF PAPER 
 
 DISCOUNT 
 
 COLL. & EXCH. 
 
 PROCEEDS 
 
 729 
 
 14 
 
 7 
 
 29 
 
 
 73 
 
 a 
 
 
 862 
 
 29 
 
 4 
 
 31 
 
 
 86 
 
 b 
 
 
 725 
 
 74 
 
 7 
 
 26 
 
 
 73 
 
 c 
 
 
 832 
 
 16 
 
 12 
 
 48 
 
 1 
 
 26 
 
 d 
 
 
 426 
 
 19 
 
 6 
 
 39 
 
 
 43 
 
 e 
 
 
 378 
 
 36 
 
 8 
 
 78 
 
 
 38 
 
 f 
 
 
 9 
 
 
 k 
 
 
 I 
 
 
 j 
 
 
 52. The complement of a number is the difference between 
 the number and a unit of the next higher order. 
 
 Thus, 2 is the complement of 8, 23 is the complement of 77, and 152 is 
 the complement of 848. 3 and 7, 24 and 76, 250 and 750, are complementary 
 numbers. Observe that ichen tivo numbers of more than one figure each are 
 complementary, the sum of the units' figure is 10 and the sum of the figures in 
 each corresponding higher order is 9. 
 
36 PEACTICAL BUSINESS ARITHMETIC 
 
 53. Since numbers are read from left to right, in finding the 
 complement of a number, begin at the left to subtract. 
 
 54. In beginning at the left to subtract take 1 from the 
 highest order in the minuend and regard the other orders as 
 9's, except the last, which regard as 10. 
 
 55. Example. A man gave a 100-dollar bill in payment for 
 an account of $77.52. How much change should he receive ? 
 
 SOLUTIONS, (a) Begin at the left. 7 from 9 leaves 2; 7 from 9 $100.00 
 leaves 2 ; 5 from 9 leaves 4; 2 from 10 leaves 8. Or y r 9 
 
 (6) 7 and 2 are 9 ; 7 and 2 are 9 ; 5 and 4 are 9 ; 2 and 8 are 
 10. $22.48. 
 
 This method of finding the amount of change is used by many clerks and 
 cashiers. The work is in all cases proved by counting out to the customer 
 the bills and coins necessary to make the amount of the purchase equal to 
 the amount offered in payment. 
 
 ORAL EXERCISE 
 
 State the difference between the following amounts : 
 
 1. $1.00 11.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 
 
 .22 .29 .36 .85 .78 .64 _.57 .56 
 
 2. $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 
 
 .54 1.36 2.02 2.17 2.23 5.01 5.23 7.21 
 
 3. $10.00 $10.00 $10.00 $10.00 $10.00 $10.00 $10.00 $10.00 
 
 8.75 5.63 4.68 5.35 2.38 2.89 1.51 8.35 
 
 4. $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 
 
 28.14 17.49 11.52 16.84 14.89 12.52 19.64 21.87 
 
 5. If $100 is offered in payment for each of the following 
 bills, what amount of change should be returned? $27.42; 
 $89.17; $64.11; $53.41; $18.75; $23.14; $37.48; $87.37. 
 
 6. If $20 is offered in payment for each of the following 
 bills, what amount of change should be returned? $4.72; 
 $8.17; $19.21; $17.41; $2.46; $17.48; $11.42 ; $7.43; $12.64; 
 $11.42; $4.96; $1.16; $7.25; $15.98; $16.87; $14.17; $13.56. 
 
SUBTRACTION 37 
 
 ORAL EXERCISE 
 
 State the amount of change in each of the following problems : 
 
 COST OF AMOUNT COST OF AMOUNT 
 
 ITEMS PURCHASED PAID ITEMS PURCHASED PAID 
 
 1. 17^,13^,42^ 12 14. $1.25, $0.75,12.18 $20 
 
 2. 27^,23^,14^ $2 is. $1.50, $2.70, $1.18 $20 
 
 3. 45^, 55 13^ $5 16. $4.60, $1.40, $2.13 $20 
 
 4. 64^, 16 87^ $5 17. $1.50, $1.20, $2.30 $10 
 
 5. 23^,14^,27^ $2 is. $3.17, $4.11, $4.98 $50 
 
 6. 63^17^,59? $5 19. $4.25, $0.75, $3.18 $20 
 
 7. 49^, 84^, 37^ $5 20. $1.29, $2.17, $1.50 $20 
 
 8. 78^,42^,67^ $5 21. $1.64, $1.66, $2.50 $20 
 
 9. 52^, 69^, 88^ $5 22. $1.59, $23.41, $118 $200 
 
 10. 75^,86^,54^ $5 23. $24.17, $20.83, $15 $100 
 
 11. 89^, 46^, 72^ $5 24. 111.48, $10.52, $50 $100 
 
 12. 76^,54^,29^ $5 25. $18.91, $12.09, $45 $100 
 
 13. 75^,25^,89^ $10 26. $21.27, $2.73, $50.50 $100 
 
 56. 19 7 = 9 (the minuend minus 10) + 3 (the comple- 
 ment of the subtrahend); 191 17 = 91 (the minuend minus 
 100) -+ 83 (the complement of the subtrahend) ; 1912 - 178 = 
 912 (the minuend minus 1000) + 822 (the complement of the 
 subtrahend), and so on. 
 
 57. This principle makes it a simple matter to find the dif- 
 ference between a subtrahend and several minuends. 
 
 58. Examples. The following examples illustrate the appli- 
 cation of the principle : 
 
 SOLUTIONS. 1. 2 (the complement of 8), i. 2. 3. 
 
 10, 16; 16 10 = 6. 9 (the complement of 1), QI OQQ on 
 
 HUTi 17-10 = 7. 9, 13, 16; 16-10=6. J JJ 
 
 2. 9, 17, 26; 26-10 = 16; that is, 6 and 1 +-<O + 4 ^ + 111 
 to add to the minuends. 9, 18 (9+8 + 1), 27; 118 -111 219 
 27-10 = 17; that is, 7 and 1 to add to the (j'JQ =676 =203 
 minuends. 9, 14, 16; 16-10=6. 
 
 3. 1, 2, 3. 3 10 is impossible, so subtract 1 ten from the minuend (or add 
 1 ten to the subtrahend). 9, 10. 10-10 = 0. 8, 9, 12. 12-10 = 2. 
 
38 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 59. Example. The following problem shows a concrete appli- 
 cation of the foregoing principle : 
 
 DEPOSITORS' LEDGER 
 
 DEPOSITOR 
 
 BALANCE 
 
 CHECKS 
 
 DEPOSITS 
 
 BALANCE 
 
 A 
 
 |74 
 
 125 
 
 $86 
 
 $135 
 
 B 
 
 |86 
 
 $11 
 
 $99 
 
 $174 
 
 C 
 
 $92 
 
 $79 
 
 $ 81 
 
 9 94 
 
 SOLUTION. Here is a 
 
 depositors' ledger. The 
 data in the first three 
 columns being given, it 
 is required to find the 
 new balance. 
 
 The process is as follows: A. 6, 11, 15, 5; 8, 16, 23, 13; balance, ,$135. 
 
 B. 9, 18, 24, 4 and 1 to add to the minuend. 10, 19, 27, 17; balance, $174. 
 
 C. 1, 2, 4 and 1 to take away from the minuend. 7, 10, 19, 9; balance, $94. 
 
 WRITTEN EXERCISE 
 
 Find the neiv balances, the total old balance, the total checks, the 
 total deposits, the total new balances, and check the work: 
 
 1. 2. 
 
 DEPOSITOR 
 
 BAL. 
 
 CllKCKS 
 
 DEPOSITS 
 
 BAL. 
 
 A 
 
 $758 
 
 * 12S 
 
 $ 421 
 
 a 
 
 B 
 
 921 
 
 154 
 
 175 
 
 b 
 
 C 
 
 934 
 
 214 
 
 122 
 
 c 
 
 D 
 
 862 
 
 162 
 
 218 
 
 d 
 
 E 
 
 478 
 
 187 
 
 126 
 
 e 
 
 F 
 
 921 
 
 215 
 
 124 
 
 f 
 
 G 
 
 756 
 
 157 
 
 137 
 
 <j 
 
 H 
 
 864 
 
 128 
 
 142 
 
 h 
 
 I 
 
 926 
 
 214 
 
 121 
 
 i 
 
 J 
 
 752 
 
 221 
 
 124 
 
 J 
 
 K 
 
 878 
 
 162 
 
 218 
 
 k 
 
 
 / 
 
 m 
 
 n 
 
 o 
 
 DEPOSITOU 
 
 I5.U,. 
 
 CHICKS 
 
 DEPOSITS 
 
 BAL. 
 
 A 
 
 $ 428 
 
 $125 
 
 $ 718 
 
 a 
 
 B 
 
 726 
 
 128 
 
 296 
 
 b 
 
 C 
 
 832 
 
 279 
 
 318 
 
 c 
 
 D 
 
 456 
 
 154 
 
 421 
 
 d 
 
 E 
 
 298 
 
 275 
 
 568 
 
 e 
 
 F 
 
 728 
 
 178 
 
 188 
 
 f 
 
 G 
 
 762 
 
 218 
 
 215 
 
 9 
 
 II 
 
 837 
 
 316 
 
 176 
 
 h 
 
 I 
 
 493 
 
 121 
 
 219 
 
 i 
 
 J 
 
 862 
 
 128 
 
 188 
 
 J 
 
 K 
 
 925 
 
 125 
 
 211 
 
 k 
 
 
 I 
 
 m 
 
 n 
 
 
 
 60. 48 29 = 48 + 1 (30, the next higher order of units than 
 29, -29) -30, or 19; 128-59=128 + 1-60, or 69. 
 
 61. This principle may be applied to advantage in billing 
 items in which the gross weights and the tares are recorded. 
 
 The gross weight is the weight of merchandise, together with bag, cask, 
 or other covering; the tare is the weight of the bag, cask, or other covering 
 
SUBTRACTION 
 
 39 
 
 of merchandise ; the net weight is the difference between the gross weight 
 and the tare. 
 
 62. Example. The gross weights and tares, in pounds, of 3 
 bbl. of sugar are: 332 - 19, 337 - 18 335 - 18. Find the total 
 net weight. 
 
 SOLUTION. The numbers 
 
 would be written on the bill y4H # 
 
 horizontally, as shown in the margin. Adding the units of the tare, the result 
 is 25 ; 30 (the next higher order of units than 25) minus 25 equals 5 ; 5 added 
 to the units of the gross weight equals 19 ; 19 30 is impossible, so write 9 
 and subtract 2 tens (the difference between the tens in 30 and 19) from the 
 gross weight or add 2 tens to the tens of the tare. Adding 2 tens to the tens 
 of the tare, the result is 5 ; 10 5 = 5 ; 5 added to the tens of the gross weight 
 equals 14 ; 14 10 = 4. Adding the hundreds in the gross weight, the result 
 is 9. Net weight is 949 Ib. 
 
 WRITTEN EXERCISE 
 
 Copy the following bills. Verify the net weights given and sup- 
 ply all missing terms. 
 
 1. 
 
 Terms 
 
 Bought of PHILIP ARMOUR & CO. 
 
 2.3 
 
 JUL 
 
PKACTICAL BUSINESS ARITHMETIC 
 
 Chicago, 111., July 20, 19 
 
 Messrs. A. M. THOMPSON & CO. 
 
 Rochester, N.Y. 
 
 of Nelson, Morris & Co 
 
 Terms 50 days 
 
 
 6 
 
 tubs Lard 
 
 
 
 
 
 
 
 72-17 70-14 
 
 
 
 
 
 
 
 69-14 71-14 
 
 
 
 
 
 
 
 71-15 70-16 *** $0.11 
 
 36 
 
 63 
 
 
 
 
 6 
 
 casks Shoulders 
 
 
 
 
 
 
 
 421-65 426-70 
 
 
 
 
 
 
 
 424-72 422-64 
 
 
 
 
 
 
 
 427-72 421-60 **** .12 
 
 256 
 
 56 
 
 
 
 
 6 
 
 casks Hams 
 
 
 
 
 
 
 
 409-72 412-70 
 
 
 
 
 
 
 
 414-71 410-73 
 
 
 
 
 
 
 
 412-70 416-71 **** .12 
 
 245 
 
 52 
 
 *** 
 
 ** 
 
 
 
 3. The gross weights and tares of 6 casks of shoulders are 
 as follows: 428-68, 419-70, 423-65, 432-72, 436-69, 
 434 65 Ib. Find the total net weight. 
 
 4. The gross weight and tares of 12 tubs of lard are as fol- 
 lows : 71-14, 70-15, 69-14, 71-15, 72-17, 73-17, 
 69-15, 71-16, 72-15, 73-16, 74-17, 75-17 Ib. Find 
 the total net weight. 
 
 5. The gross weights and tares of 10 bbl. of sugar are as 
 follows: 319-18, 331-19, 329-17, 334-20, 338-21, 
 325 - 18, 326 - 16, 325 - 19, 327 - 19, 321 - 17 Ib. Find the 
 total net weight. 
 
SUBTRACTION 
 
 41 
 
 BUSINESS TEEMS AND RECORDS' 
 
 63. A debit is an expression of value received ; a credit is 
 an expression of value delivered. 
 
 A buys of B 100 bu. wheat for $100 cash; the value received (debit) 
 by A is 100 bu. wheat and the value parted with (credit), $100. A sells C 
 50 bu. wheat for $75, C agreeing to pay for the same in 10 da. ; the value 
 received by A is C's express or implied promise to pay for the wheat in 10 da. 
 and the value parted with is 50 l>u. wheat. 
 
 64. An account is a collection of related debits and credits. 
 
 65. Some of the common accounts kept in business are the cash 
 account ; personal accounts ; the merchandise account ; the 
 expense account ; the proprietary account. 
 
 66. A resource is any property on hand or any amount owed 
 to a person or concern; a liability is any amount owed by a 
 person or concern. The excess of resources over liabilities is 
 the net capital or present worth ; the excess of liabilities over 
 resources, the net insolvency. 
 
 67. A gain is any sum realized in excess of the cost of a 
 business or of business transactions ; a loss is any sum spent 
 or incurred in excess of the returns of a business or of business 
 transactions. The excess of gains over losses is the net gain ; 
 the excess of losses over gains, the net loss. 
 
 68. The cash account is kept for the purpose of showing the 
 receipts and payments of cash and the amount of cash on hand. 
 
 The receipts of cash are entered on the left or debit side, and the pay- 
 ments, on the right or credit side, of the account. The excess of debits at 
 any time is the amount of cash on hand. 
 
42 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 69. Personal accounts are kept for the purpose of showing 
 whether persons owe us or we owe them, and how much in 
 either case. 
 
 On the left (debit) side of these accounts are placed the amounts which 
 the persons owe us or which we pay them ; on the right (credit) side, the 
 amounts which we owe them or which they pay us. When the debits 
 of an account are in excess of the credits, the account owes us for the amount 
 of the excess; when the credits are in excess of the debits, we owe the ac- 
 count for the amount of the excess. 
 
 70. The merchandise account is kept for the purpose of show- 
 ing the cost of goods purchased, the proceeds of goods sold, and 
 the gain or loss resulting from such dealings. 
 
 /f 
 
 / 60 7 e 
 720 
 
 On the left (debit) side is entered the cost of goods purchased and on the 
 right (credit) side the proceeds of goods sold. When the goods are all 
 disposed of the excess of credits is a gain ; the excess of debits, a loss. 
 When it is desired to show the gain or loss on merchandise before the 
 goods are all disposed of, it is necessary to first enter in the credit side of 
 the account the present market value of the unsold goods. 
 
SUBTRACTION 
 
 43 
 
 71. The expense account is kept for the purpose of showing 
 the cost of outlays incurred in carrying on the business. 
 
 2 <?# 
 
 / 2 ^0 
 
 /z 
 
 J-J 30 
 
 Such outlays are entered on the left (debit) side of the account. Ordi- 
 narily there are no credit entries. When the expense items are all used the 
 debit of the account is a loss. When it is desired to show the loss or gain 
 on expense and there are unused expense items on hand, it is first necessary 
 to enter in the credit side of the account the present value of such items. 
 
 72. The proprietary account is kept for the purpose of show- 
 ing whether the proprietor owes the business or whether the 
 business owes him, and how much in either case. 
 
 
 J/ 
 
 On the right (credit) side are entered all sums invested and the net gain, 
 and on the left (debit) side all sums withdrawn and the net loss. The 
 excess of credits is the present worth of the business. 
 
 ORAL EXERCISE 
 
 1. In the cash account on page 41 what are the total receipts? 
 the total payments ? the balance of cash on hand ? 
 
 2. At the top of page 42 is your account with J. E. 
 King & Co. On what dates did you sell the firm merchandise ? 
 When and how were payments made on account ? What was 
 the balance of the account May 10 ? 
 
44 PRACTICAL BUSINESS ARITHMETIC 
 
 3. In the account with merchandise, page 42, what is the 
 cost of the purchases? the proceeds of the sales? How would 
 the value of the unsold goods be determined in business ? 
 Verify the amount of the gain. Is it correct ? 
 
 4. Verify the amount of the loss in the expense account, 
 page 43. Is it correct? 
 
 5. What are the total withdrawals in the account with 
 F. W. Simpson, Proprietor, page 43 ? the total investment ? 
 
 WRITTEN EXERCISE 
 
 1. Copy the cash account on page 41 and continue it with 
 the following items: Jan. 12, receive cash of Jones & Co., 
 $75; Jan. 14, pay cash for groceries, $165.62; Jan. 15, re- 
 ceive cash for groceries, 1189.75 ; Jan. 18, pay cash to office 
 help, $129.74; Jan. 20, pay cash for stationery, $11.75; 
 Jan. 22, receive cash for groceries, $126.94 ; Jan. 24, receive 
 cash of H. W. Conant, $200,67. Balance the account as shown 
 in the model. 
 
 2. Copy the purchases and sales of the merchandise account, 
 page 42. Assuming that the value of the unsold goods is 
 $327.61, find the gain and close the account. 
 
 3. Copy the purchases and sales of the merchandise account, 
 page 42. Assuming that the value of the unsold goods is $50, 
 find the gain or loss and close the account. Assuming that all 
 of the goods are sold, find the gain or loss and close the account. 
 
 4. Arrange the following data in the form of your account 
 with Benj. F. Butler. June 1, buy of Benj. F. Butler on 
 account (without making payment) dry goods amounting to 
 $627.96; June 10, pay him for invoice of June 1 less $6.28 
 discount; June 28, buy of him dry goods amounting to $472. 69 
 and pay cash to apply on the bill, $172.69; July 15, buy of him 
 on account dry goods amounting to $369.71; July 31, pay him 
 cash to apply on bill of July 15, $79.79; Aug. 2, sell him lace 
 amounting to $14.60. Find the balance of the account and 
 tell whether such balance is a resource or a liability. 
 
SUBTRACTION 
 
 45 
 
 5. Using the above data, write Benj. F. Butler's account of 
 his dealings with you. Balance the account. 
 
 6. Copy the account with F. W. Simpson, Prop., page 43. 
 Continue the account through June, using the following items : 
 June 6, make an additional investment of 1000; June 25, 
 withdraw for personal use 1160; June 30, the net gain for the 
 month, which is to remain as an additional investment, is 
 $369.75. Find the present worth and close the account. 
 
 ORAL EXERCISE 
 
 Classify the following as resources, liabilities, losses, or gains: 
 1. A personal account showing a debit balance of $150. 
 2 A personal account in which the credit balance is $270. 
 
 3. A merchandise account in which there are no goods on 
 hand and the purchases aggregate $7160 and the sales, $8249.50. 
 
 4. The total losses of a business are $480, and the net gain, 
 $ 640.90. What are the total gains ? 
 
 5. The total liabilities of a concern are $2400, and the pres- 
 ent worth, $6280.50. What are the total resources ? 
 
 WRITTEN EXERCISE 
 Copy the following statements, supplying the missing terms: 
 
 32.00 
 
 <?.<?# 
 
46 
 
 PRACTICAL BUSINESS ARITHMETIC 
 2. 
 
 3. A merchant purchased a stock of hardware amounting to 
 45,112.18 and sold from this stock goods amounting to 
 $31,136.85. He then took an account of stock and found that 
 the value of the hardware on hand was $ 18,438.50. Find the 
 amount of his gain. 
 
 4. C. E. Cyr's resources and liabilities at the close of a 
 month were as follows: dry goods on hand, $ 1629.40; store 
 and lot, 13000; cash in bank, 11400.60; C. O. Bond owes the 
 business 1400; L. E. Young, 1390.10; and J. O, Snow, 
 $209.90.. The business owes Roe & Co. 1750; and Doe & Co. 
 $90.75. Make a statement of resources and liabilities. 
 
 5. At the close of the same month C. E. Cyr's business 
 accounts show the following results: stock of dry goods on 
 hand at the beginning of the month, $1270.40; purchases of 
 dry goods for the month, $3229.60; sales of dry goods for the 
 month, $3762.90; market value of the dry goods on hand at 
 the close of the month, $1629.40; expense for the month, 
 $413.95; value of expense items on hand, $250. Make a state- 
 ment of losses and gains. 
 
 6. A real estate agent had property on hand Jan. 1 to 
 the amount of $8155.60. During the year he bought property 
 

 SUBTRACTION 47 
 
 costing 14150.60, added buildings at a cost of 16190.40, and 
 paid taxes 250.90. April 15 a house valued at -11690 was 
 destroyed by fire, and for this loss the insurance company paid 
 him $ 1300. During the year he sold property for 19260.50 
 and received for rents 840.80. If the expenses of the sales 
 aggregated 8240.19 and the value of the property on hand 
 Dec. 31 was $11,250.60, what was his net gain or loss for 
 the year? 
 
 73. Banks and other business 
 houses having a large amount of 
 adding to do, frequently use an add- 
 ing machine. Because it cannot be 
 used to advantage for many kinds of 
 addition, this machine has not done 
 away with the necessity for the hand- 
 and-mind method of addition ; on the 
 other hand, by its rapid and accurate work, it has put a 
 premium on the hand-and-mind method. Business men will 
 no longer tolerate a bookkeeper who is slow and inaccurate in 
 his additions ; but the person who can add with speed, accuracy, 
 and intelligence is more than ever in demand. In the margin 
 is a picture of an adding machine such as is commonly used. 
 The operation of subtraction, or of combined addition and sub- 
 traction, may usually be performed on an adding machine. 
 
 ORAL REVIEW EXERCISE 
 
 1. Find the sum of 45, 45, 45, 45, 45, and 60. 
 
 2. Find the sum of 61, 62, 63, 64, 65, 66, and 67. 
 
 3. Find the sum of 102, 103, 104, 105, 106, 10T, and 108. 
 
 4. Find the sum of all the integers from 6 to 12, inclusive. 
 
 5. How many days from Apr. 15 to June 2? from Mar. 
 15 to May 3 ? from July 30 to Sept. 5? 
 
 6. Count backwards rapidly by 5's from 96 ; by 7's from 
 97 ; by 13's from 100 ; by 12's from 135 ; by 14's from 99. 
 
 7. Subtract each of the following amounts from $50: 
 124.19, 121.76, $42.14, $13.98, $47.29, $19.32, $16.38, $11.43. 
 
48 PRACTICAL BUSINESS AEITHMETIC 
 
 8. State the sum of each of the following groups: 
 
 82? 79^ 74^ 52? 92^ 38^ 73^ 69^ 86? 63? 42? 26^ 81? 27^ 
 35? 18? 87^ 31^ 85^ 57^ 99? 34? 75? 28? 95^ 19^ 93^ 41 ^ 
 
 98? 46? 89? 72? 59^ 30? 91? 80? 73? 53^ 66^ 24? 76? 
 15^ 45? 14? 88^ 77^ 97^ 54^ 78^ 47^ 62^ 49^ 32^ 
 
 13^ 90^ 40^ 96^ 21^ 84^ 56^ 58^ 22^ 48^ 37^ 50^ 
 12^ 94^ 17^ 83^ 61^ 65^ 33^ 44? 16^ 70^ 36? 51? 23? 
 
 9. State the difference between each of the above groups. 
 
 In subtracting 91 and 27 think of 71 and 7, or 64; in subtracting 52 and 
 29 think of 32 and 9, or 23 ; and so on. 
 
 10. State the difference between $ 2 and the sura in each of 
 the above groups ; between 85 ; between $10. 
 
 11. What change should I receive from $2 if I spent: 
 a. 26? and 43?? e. 25? and 37^? i. lo lM and 
 ft. 17? and 59^? /. 42^ and 39^? j. ll 43?, and 
 
 c. 28? and 52?? g. 19^ and 37?? k. 19?, 34?, and 47?? 
 
 d. \lf and 58^? L 16^ and 29?? I 28^, 11^, and 47?? 
 
 12. Add each of the following numbers to each of the num- 
 bers below: 2, 8, 7, 6, 5,4, 9, 11, 12, 3, 14, 15, 16, 13, 18, 17, 19. 
 
 First add by lines and then by columns. Thus, to add 7 by lines say 7, 
 8,11,9, 12, 10, 13, 14, 17, 15, 18, 16, 19, 20, and so on; to add 7 by columns 
 say 8, 20, 32, 44, 56, 68, 80, 92, 104, 116, 11, and so on. 
 
 abode fgh ij kl 
 
 1. 1 4 2 5 3 6 7 10 8 11 9 12 
 
 2. 13 16 14 17 15 18 19 22 20 23 21 24 
 
 3. 25 28 26 29 27 30 31 34 32 35 33 36 
 
 4. 37 40 38 41 39 42 43 46 44 47 45 48 
 
 5. 49 52 50 53 51 54 55 58 56 59 57 60 
 
 6. 61 64 62 65 63 66 67 70 68 71 69 72 
 
 7. 73 76 74 77 75 78 79 82 80 83 81 84 
 a 85 88 86 89 87 90 91 94 92 95 93 96 
 9. 97 100 98 101 99 102 103 106 104 107 105 108 
 
 10. 109 112 110 113 111 114 115 118 116 119 117 120 
 
SUBTRACTION 
 
 49 
 
 WRITTEN REVIEW EXERCISE 
 
 In all exercises of this kind a time limit should be set for the work. The 
 work should also be checked before answers are submitted for examination. 
 Accuracy is of paramount importance in business. One error that passes 
 unnoticed by the student in ten problems of this character is a failure. 
 
 l. Without copying, find quickly the missing terms in the 
 following statement of government receipts and expenditures 
 for the fiscal year closing June 30 in a recent year. Check. 
 
 From customs 
 Internal revenue 
 Miscellaneous 
 Total 
 
 Civil and miscellaneous 
 
 War 
 
 Navy 
 
 Indians 
 
 Pensions 
 
 Interest 
 
 Total 
 
 Surplus 
 
 RECEIPTS 
 
 EXPENDITURES 
 
 $262,068,483 
 
 232,435,695 
 
 46,682,565 
 
 $132,229,913 
 115,337,786 
 102,757,073 
 
 10,437,196 
 142,558,335 
 
 24,618,766 
 
 2. Without copying, find the totals and grand totals of the 
 following table. Check the results. 
 
 COINAGE OF THE MINTS OF THE UNITED STATES 
 
 CALEXDAuYEAUt 
 
 GOLD 
 
 SILVER 
 
 MINOR 
 
 TOTALS 
 
 1793 to 1894 
 1895 
 
 $1,732,552,32300 
 59 616 357 50 
 
 0681,909,71910 
 5 698 010 25 
 
 $25,391,53179 
 882 430 56 
 
 
 1896 
 1897 
 1898 
 
 47,053,06000 
 76,028,485 00 
 77,985,757 50 
 
 23,089,899 00 
 18,487,297 30 
 23,034,033 45 
 
 832,71893 
 1,526,10025 
 1,124,835 14 
 
 
 1899 
 
 111,344,22000 
 
 26,061,51990 
 
 1,S37 451 86 
 
 
 1900 
 
 99 272 942 50 
 
 36 295 321 45 
 
 2 031 137 39 
 
 
 1901 . . . 
 
 101 735 187 50 
 
 30 838 460 75 
 
 2 120 122 08 
 
 
 1902 
 
 61,980,572 50 
 
 30,116,36945 
 
 2 4 k >9 736 17 
 
 
 1903 
 
 45,721,77300 
 
 25,996,536 25 
 
 2 484,691 18 
 
 
 1904 . . 
 
 233.402,428 00 
 
 15,695,609 95 
 
 1 683 529 35 
 
 
 
 
 
 
 
 Grand totals 
 
 
 
 
 
CHAPTER VI 
 
 MULTIPLICATION 
 ORAL EXERCISE 
 
 1. Which of the following numbers are concrete ; that is, re- 
 fer to some particular kind of object or measure ? 12 ; 5^- ; 12 
 ft. ; 2.5 da. ; 15 yd. ; 18 men ; 200; $12 ; 172f 
 
 2. Which of the above numbers are abstract ; that is, do not 
 refer to any particular kind of object or measure ? 
 
 3 . 5 + 4 + 2 + 8 + 9 = ? 
 
 4 . 9 + 9 + 9 + 9 + 9=? 5 times 9 = ? 
 
 5. Could the sum of the numbers in problem 3 be found by 
 any shorter process ? 
 
 6. What is the first process in problem 4 called ? the second? 
 
 7. 9 times 27 = ? 9 times 29 bu. = ? 
 
 8. If 1 bu. of rye weighs 56 lb., what will 12 bu. weigh? 
 
 74. Jn problems 7 and 8 it is seen that the multiplier is 
 always an abstract number ; and the multiplicand and product are 
 like numbers. 
 
 75. Three 5's are equal to five 3's ; 1 3 multiplied by 5 is 
 equal to 1 5 multiplied by 3 ; 4 trees multiplied by 125 is equal 
 to 125 trees multiplied by 4. 
 
 76. It is therefore seen that the product is not affected by 
 changing the order of the factors regarded as abstract numbers. 
 
 77. The multiplicand and multiplier together are called 
 factors (makers) of the product ; the product of two abstract 
 integers is sometimes called a multiple of either of the factors. 
 
 78. Sometimes a number is used several times as a factor. 
 Numbers so used are indicated by a small figure, called an expo- 
 nent, written above and at the right of the factor. 
 
 Thus, 4 used twice as a factor is written 4 2 , 5 used four times as a factor 
 is written 5 4 , and 6 used Jive times as a factor is written 6 5 . 
 
 50 
 
MULTIPLICATION 51 
 
 79. The product arising from using a number two or more 
 times as a factor is called a power of that number. 
 
 Thus, 4 is the second power of 2 ; 64 is the third power of 4 and the sixth 
 power of 2. 
 
 Too much attention should not be given to the definitions like the above. 
 They are valuable only as they help to make clear the matter in the exercises. 
 They are rarely heard in business and therefore should not be memorized. 
 
 ORAL EXERCISE 
 
 1. Multiply at sight each number below by 2 ; by 3 ; by 4 ; 
 by 5 ; by 6 ; by 7 ; by 8 ; by 9. 
 
 Name the products by lines from left to right and from right to left; 
 also by columns from left to right and from right to left. Name results 
 only. Thus, to multiply lines by 4 say 20, 36, 8, 24, 40, 12, 28, 44, 16, 48, 
 32, 52, 68, 84, and so on up to 100 ; and backwards, 100, 80, 96, 64, and so on 
 back to 20. To multiply columns by 4 say 20, 68, 36, 84, and so on to 52, 
 100 ; and backwards 100, 52, 80, 32, and so on to 68, 20. Continue the work 
 until results can be named at the rate of 120 or more per minute. 
 
 5 9 2 6 10 3 7 11 4 12 8 13 
 17 21 14 18 22 15 19 23 16 24 20 25 
 
 2. Multiply as instructed in problem 1 and add 8 (carried) 
 to each product. Also multiply as instructed and add 6, 4, 7, 
 2, 5, 3, and 9 to each product. 
 
 Name results only. Thus, to multiply by lines say 20,28; 36, 44; 8, 
 16 ; and so on. 
 
 3. Multiply by 2 : 27, 35, 81, 36, 28, 32, 47, 93, 56, 39, 54, 
 45, 52, 86, 75, 67, 59. Also by 4, 3, 5, 8, 6, 7, 9. 
 
 4. Find the cost of each of the following: 20 Ib. crackers at 
 8^; 9 Ib. coffee at 34^; 7 Ib. tea at 57^; 11 Ib. beef at \lf\ 
 120 Ib. sugar at 4j*; 134 Ib. sugar at 5^. 
 
 5. Find the cost of each of the following: 44 yd. at 9^; 37 
 yd. at 8^; 123 yd. at 6^; 214 yd. at 4^; 52 yd. at 12^; 29 
 yd. at 8^; 8yd. at $1.03; 7yd. at 11. 01; 5 yd. at 11.35. 
 
 6. Beginning at count by 9's to 81 ; by 10's to 150 ; by ll's 
 to 154; by 12's to 108; by 13's to 117; by 14's to 126; by 
 15's to 135 ; by 16's to 144 ; by 17's to 153 ; by 18's to 162 ; by 
 19's to 171 ; by 20's to 180. 
 
52 PRACTICAL BUSINESS ARITHMETIC 
 
 80. Examples. 1. Find the cost of 2150 Ib. at 5^. 
 
 SOLUTION. Since 1 Ib. costs 5ft 2150 Ib. will cost 2150 times $ 21.50 
 5^; but 2150 times 5^ is equal to 5 times 2150ft 5 times 5 
 
 $21.50 (2150^) equals $107.50, the required result. $ 107.50 
 
 2. Multiply 224 by 46. 
 
 SOLUTION. In multiplying one number by another, 224 224 
 
 there is no practical advantage in beginning with the 46 46 
 
 lowest order of units of the multiplier ; in fact, in - ytt 
 
 some multiplications (see page 140) there is a decided gQ 1 Q_L1 
 
 advantage in beginning with the highest order. The 
 arrangement of work for both methods is shown in 
 the margin. 
 
 CHECK. The work may be checked by multiplying first by one method and 
 then by the other, or by interchanging the multiplier and multiplicand and re- 
 multiplying. (See also pages 83 and 84.) 
 
 3. Multiply 2004 by 1275. 
 
 SOLUTION. When one of two numbers to be mul- 1275 1275 
 
 tiplied contains a number of zeros or ones, it is always 2004 2004 
 
 easier to take that number as the multiplier. Since vfOO 
 
 the product of any number multiplied by is 0, the 9/rcn 
 
 product of 1275 multiplied by the tens and hundreds '- - - 
 
 of the multiplier need not be written. 2555100 2555100 
 
 CHECK. The problem may be checked the same as problem 2. 
 
 When two numbers are to be multiplied, it is generally easier to take as 
 the multiplier the number having the least number of places. Thus, to find 
 the cost of 1647 A. of land at $27 per acre, take 27 as the multiplier. 
 
 If one of the two numbers to be multiplied has two or more digits alike, 
 it is easier to take that number as the multiplier. Thus, to multiply to- 
 gether 6729 and 7777, it is easier to take 7777 as the multiplier. 
 
 ORAL EXERCISE 
 
 1. Find the value of 51 T. of hay at $17 per ton. 
 
 2. Find the cost of 175 Ib. of sugar at 5^ per pound. 
 
 3. How much will a boy earn in 87 hr. at 9^ an hour? 
 
 4. What is the cost of a flock of 52 sheep at 1 7 per head? 
 
 5. At the rate of 47 mi. an hour, how far will a person 
 travel in 12 hr. ? 
 
 6. What is the cost of 12 pr. of shoes at $4.50 per pair, and 
 8 pr. of boots at 13.50 per pair ? 
 
MULTIPLICATION 53 
 
 7. What must be paid for handling 12 loads of freight at 
 12.25 per load? 
 
 8. In an orchard there are 13 rows of trees, each containing 
 21 trees. How many trees in the orchard? 
 
 9. If you buy 5 pencils at 9^ each and 9 penholders at 5^ 
 each, and some stationery costing 25^, how much change should 
 you receive from a two-dollar bill? from a ten-dollar bill? 
 
 10. I bought 6 cd. of wood at $5.75 per cord. If a fifty- 
 dollar bill is offered in payment, how much change should be 
 received? 
 
 11. I bought 12 bu. of wheat at $1.05. If I gave in pay- 
 ment two ten-dollar bills, what change should I receive? 
 
 12. My average marketing expenses per day are $2.10. If I 
 offer a twenty-dollar bill in payment for 7 days' expenses, what 
 change should I receive? 
 
 13. I sold 16 chairs at $7 each, and 5 tables at $9 each. If 
 two one-hundred-dollar bills are offered in payment, how much 
 change should I return? If a one-hundred-dollar bill, a fifty- 
 dollar bill, and a twenty-dollar bill are offered in payment, how 
 much change should I return? 
 
 WRITTEN EXERCISE 
 
 In the following problems find the missing numbers by multiply- 
 ing across and adding down. Check the results by comparing the 
 sum of the line products witli the sum of the multiplicands multi- 
 plied by one of the multipliers. 
 
 1. 2. 3. 
 
 15x211=? 9x1475=? 12x116.50=? 
 
 15x346=? 9x2618=? 12x127.75=? 
 
 15x318=? 9x1575=? 12x114.95=? 
 
 15x721=? 9x1792=? 12x829.86=? 
 
 15x936=? 9x4936=? 12x$49.88=? 
 
 15x849=? 9x7289=? 12x139.62=? 
 
 15x21^=_?_ 9x8728=_?^ 12x186.99= ? 
 
 15 x ? = ? 9 x ? = ? 12 x ? = ? 
 
54 PRACTICAL BUSINESS ARITHMETIC 
 
 4. 5. 6. 
 
 12x192=? 98x2178=? 16 x $18.10=? 
 
 12x721=? 98x1692=? 16 x 17.20=? 
 
 12x836=? 98x2536=? 16 x 21.40=? 
 
 12x456 = ^_ 98 x 2892 = ? 16 x 25.85= ? 
 
 12 x ? = ? 98 x ? = ? 16 x ? = ? 
 
 Problems such as the above are very helpful. They afford a variety of 
 work and suggest a simple method by which the student may test the cor- 
 rectness of his results. The teacher should add as many more problems as 
 circumstances require. 
 
 7. A produce dealer bought 2145 bu. of potatoes at 23 ^ a 
 bushel, and sold them at 47^ a bushel. What did he gain? 
 
 8. A drover bought 125 head of cattle at 115.75 per head. 
 He sold 65 head at 123.40, 15 head at $13.75, and 45 head at 
 $17.75. Did he gain or lose, and how much? 
 
 9. A grocer bought 14 bu. of apples at 35^ per bushel and 
 12 bu. of potatoes at 37^ per bushel. He sold the apples at 30 # 
 a peck and the potatoes at 20^ a peck. What did he gain? 
 
 10. A speculator bought 1247 bbl. of apples at $1.35 per 
 barrel. After holding them for three months he sold them at 
 $3.75 per barrel. If he paid $74.82 for storage, and his loss 
 by decay was equal to 37 bbl. of apples, what was his gain? 
 
 11. The gross weight in pounds, and tare in pounds, of 25 
 tubs of lard are as follows : 71 - 14, 70 - 15, 69 - 14, 72 - 16, 
 71-14, 72-15, 70-15, 69-14, 71-15, 70-15, 69-14, 
 71_16, 71-15, 71-14, 70-15, 68-14, 73-16, 73-15, 
 70-14, 70-14, 71-15, 73-16, 74-18, 71-13, 73-16. 
 Find the cost at 11^ per pound. 
 
 12. The gross weight in pounds, and the tare in pounds, of 
 25 casks of hams are as follows : 400 - 78, 420 - 68, 420 - 71, 
 403-71, 409-71, 418-68, 412-72, 407-67, 423-69, 
 419-67,426-68, 403-70, 399-69, 400-69, 425-71, 
 413-72, 399-67, 412-72, 418-68, 409-71, 408-70, 
 412-68, 402-71, 421-71, 403-71. Find the cost at 
 
 per pound. 
 
MULTIPLICATION 
 
 55 
 
 SHORT METHODS IN MULTIPLICATION 
 
 81. There are many short 
 methods in multiplication, but of 
 these only a few are practical, either 
 because they generally apply to 
 problems that in themselves are 
 not practical or because they have 
 been supplanted by the elaborate 
 use of tables and mechanical de- 
 vices. Many practical tables are in 
 use for figuring pay rolls, interest, 
 discount, and the like. (See pages 
 224 and 315.) Multiplying ma- 
 chines are also used in many offices. 
 
 In the margin is a picture of a multiplying machine. 
 
 82. The short methods given herewith have a wide applica- 
 tion. They are not dependent upon formal rules, and are sug- 
 gestive of many other ways in which the student may exercise 
 his own ingenuity to shorten his work in multiplication. 
 
 MULTIPLICATION BY POWERS AND MULTIPLES OF TEN 
 
 ORAL EXERCISE 
 
 1. 40 is how many times 4? 60 is how many times 6? 100 
 is how many times 10? 150 is how many times 15? 
 
 2. Give a short method for multiplying an integer by 10. 
 
 3. 400 is how many times 4? 600 is how many times 6? 
 1000 is how many times 10? 1500 is how many times 15? 
 
 4. Give a short method for multiplying an integer by 100; 
 by 1000 ; by 10000. 
 
 5. How does the product of 40 x 66 compare with the 
 product of 4 x 66 x 10 ? the product of 400 x 59 with the prod- 
 uct of 4 x 59 xlOO? 
 
 6. Give a short method for multiplying an integer by any 
 number of 10's, 100's, or 1000's. 
 
56 PRACTICAL BUSINESS ARITHMETIC 
 
 7. Multiply 270 by 300. 
 
 SOLUTION. In the accompanying illustration ^ 
 
 it will be seen that 270 x 300 = 27 x 3 x 1000 300 = 3 X 100 
 
 or 81,000. 81000 = 81 X 1000 
 
 8. Formulate a rule for finding the product when there are 
 zeros on the right of both factors. 
 
 9. |7 is how many times 10.70? $90 is how many times 
 $0.90? $500 is how many times $0.50? 
 
 10. State a short method for multiplying United States 
 money by 10 ; by 100 ; by 1000. 
 
 11. Read aloud the following, supplying the missing words : 
 (a) Annexing a cipher to an integer multiplies the integer 
 
 by ; annexing two ciphers to an integer the integer 
 
 by . 
 
 (6) Removing the decimal point in United States money 
 one place to the right - - the number by 10; removing the 
 decimal point two places to the right - - the number by . 
 
 12. Multiply $14.70 by 10; by 100; by 1000. 
 
 83. In the above exercise it is clear that 
 
 Annexing a cipher to an integer multiplies the integer by 10; 
 and 
 
 Removing the decimal point one place to the right multiplies . 
 the number by 10. 
 
 ORAL EXERCISE 
 
 1. Read aloud the following numbers multiplied by 10 ; by 
 100; by 1000: 17; 285; 3712; $413.45 ; $1926.75; 4165.95. 
 
 2. Read each of the following numbers multiplied by 20; by 
 400; by 600; by 5000: 16 ; 19 ; 37 ; 49^; 64^; $122; $2.60. 
 
 3. By inspection find the cost of : 
 
 a. 750 Ib. coffee at 30^. g. 650 yd. silk at $1.20. 
 
 b. 500 Ib. cocoa at 40^. h. 140 bu. beans at $3.50. 
 
 c. 650 Ib. chocolate at 30^. i. 500 bu. beans at $2.50. 
 
 d. 300 bbl. lump salt at $3. /. 240 gro. jet buttons at $3. 
 
 e. 200 bbl. oatmeal at $4.50. k. 500 doz. half hose at $5.50. 
 /. 170 bx. wool soap at $3. 1. 800 yd. taffeta silk at $1.20. 
 
MULTIPLICATION 57 
 
 84. When the multiplier is a number a little less than 10, 
 100, or 1000, the multiplication may be shortened as shown 
 in the following examples. 
 
 85. Examples. 1. Multiply 123 by 99. 
 
 1 9300 
 
 SOLUTION. 99 is 100 diminished by 1; hence, multiply 123 
 
 by 100 and then by 1 and subtract the results. The product is 123 
 
 12,177. Check by retracing the steps in the process. 12177 
 
 2. Multiply 145 by 96. 
 
 SOLUTION. 96 is 100 diminished by 4 ; hence, multiply 145 1450C 
 
 by 100 and then by 4 and subtract the results. The product is 580 
 
 13,920. Check by retracing the steps in the process. 13920 
 
 WRITTEN EXERCISE 
 
 1. Find the total cost of : 
 
 5260 bu. rye at 99^. 834 bu. millet at 95^. 
 
 1521 bu. rye at 92^. 246 bu. wheat at 92^. 
 
 1640 bu. wheat at 98^. 998 bu. millet at $51.04. . 
 
 2994 bu. millet at 97^. 998 bbl. apples at $1.05. 
 
 1112 bu. wheat at 97^. 893 bkt. peaches at $ 1.05. 
 
 2160 bu. millet at 90^. 993 bu. clover seed at 3.35. 
 
 MULTIPLICATION BY 11 AND MULTIPLES OF 11 
 
 86. Example. Multiply 237 by 11. 
 
 SOLUTION. To multiply by 11 is to multiply by 10 -f 1. Hence, annex a 
 cipher to 237 and add 237 ; or, better still, add the digits as follows : 7 ; 3 + 7 = 
 10 ; 3 + 2+1 (carried) = 6 ; bring down 2 ; therefore, the result is 2607. 
 
 ORAL EXERCISE 
 
 1. Multiply each of the following by 11: 
 
 14; 26; 45; 19; 16; 34; 36; 49; 64; 125; 112; 115; 
 128; 192; 175; 116; 142; $4.95; 19.62; i>4.41; $6.82; 
 $5.21; $3.65; $4.31; $21.12; $14.21; $18.32; $3.26. 
 
 2. Find the cost of 11 yd. at 27^; at 91^; at 86^; at 
 95^; at $1.49; at $1.23; at $2.17; at $2.31; at $2.40; at 
 $2.50; at $2.75; at $4.35; at $3.15; at $3.10; at $8.13. 
 
58 PRACTICAL BUSINESS ARITHMETIC 
 
 87. Examples. 1. Multiply 46 by 22. 
 
 SOLUTION. 22 is 11 times 2. Multiply 46 by 11 and by 2, as fol- 
 lows : 2 x 6 = 12 ; write 2 and carry 1. 4 + 6 = 10 ;2x 10+1 (car- 
 ried) = 21 ; write 1 and carry 2. 2x4 + 2 (carried) = 10 ; write 10. 
 'The result is 1012. 1012 
 
 2. Find the cost of 122 bu. of potatoes at 66^ per bu. 
 
 SOLUTION. 6x2 = 12; write 2 and carry 1. 2 + 2 = 4;6x4 j22 
 
 + 1 (carried) = 25 ; write 5 and carry 2. 1 + 2=3; 6x3 + 2 
 (carried) = 20 ; write Oand carry 2. 6x1+2 (carried) = 8. Write 
 8. The result is $80. 52. 80.52 
 
 WRITTEN EXERCISE 
 In the following problems make all the extensions mentally. 
 
 1. Find the total cost of : 
 
 11 Ib. coffee at 42^. 115 bu. rye at 99 
 
 14 doz. eggs at 11 215 bu. peas at 
 
 64 Ib. cheese at 11 344 bu. oats at 
 
 33 bu. carrots at 56^. 300 bu. grain at 
 
 11 bu. potatoes at 65^. 115 bu. barley at 88^. 
 
 88 bu. wheat at 11.13. 400 bbl. apples at 11.65. 
 
 2. Find the total cost of : 
 
 77 bu. peaches at 11.85. 820 bu. rye at 88^. 
 
 151 bu. corn at 66^. 327 bu. oats at 
 
 265 bu. onions at 22^. 314 bu. peas at 
 
 135 bu. apples at 33^. 110 bu. pears at 11.66. 
 
 241 bu. turnips at 44^. 880 bu. barley at 11.17. 
 
 112 bu. tomatoes at 55^. 100 bu. quinces at $1.60. 
 
 A careful computer checks his work at every step. The student who 
 forms the habit of doing this in all his computations will soon find himself 
 in no need of printed answers to problems involving only numerical calcula- 
 tion. 
 
 Checks for multiplication have already been mentioned. To guard 
 against large errors, it is also important to form a rough estimate of an 
 answer before beginning the solution. Thus, in finding the cost of 211 yd. 
 of lining at 32^, at once see that the result will be a little more than 163.00 
 (210 times 30^); this will do away with such absurd results as $6752, 
 $075.20, or $6.75. 
 
MULTIPLICATION 
 3. Copy and find the amount of the following bill: 
 
 Boston, Mass., July 21, 19 
 
 Mrs. GEORGE W. MUNSON 
 
 168 Huntington Ave., City 
 
 Bought of S. S. PIERCE COMPANY 
 
 Terms Cash 
 
 59 
 
 
 15 
 25 
 31 
 55 
 212 
 77 
 
 cs. Horse-radish $0.66 
 Ib. Huyler's Cocoa .44 
 gal. N. 0. Molasses .33 
 Ib. Japan Tea .38 
 u Raisins .11 
 pkg. Yeast Cakes .44 
 
 
 
 
 
 MULTIPLICATION OF NUMBERS FROM 11 TO 19 INCLUSIVE 
 88. Example. Multiply 18 by 17. 
 
 IT 
 
 SOLUTION. 7 x 8 = 56 ; write 6 and carry 5. 7 + 8 (that is 7x1 
 + 1 x 8) + 5 (carried) = 20 ; write and carry 2. 1 x 1 -f 2 (carried) 
 = 3 ; write 3. 
 
 The foregoing method may be summarized as follows : 
 Multiply the units of the multiplicand by the units of the multiplier and write 
 the result as the first figure of the product. Add the units in tie multiplicand and 
 multiplier and write the result as the second figure of the product. Finally bring 
 down the tens of the multiplicand. Carry as usual. 
 
 89. In a similar manner multiply together all numbers of 
 two figures each whose tens are alike. 
 
 90. Example. 1. Multiply 92 by 97. 
 
 SOLUTION. 7 x 2 = 14 ; write 4 and carry 1. 2+7=9; 9x9 
 
 92 
 
 + 1 (carried) = 82 ; write 2 and carry 8. 9x9 + 8 (carried) = 89. 97 
 
 The result is 8942. 8924 
 
 91. The above method may be so modified as to cover all 
 numbers of two figures each whose units are alike. 
 
60 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 92. Example. Multiply 92 by 52. 
 
 SOLUTION. 2x2 = 4; write 4. 9 + 5 = 14; 2 x 14 = 28 ; write 8 
 and carry 2. 5 x 9 + 2 (carried) = 47 ; write 47. The result is 4784. 
 
 ORAL EXERCISE 
 
 92 
 
 4784 
 
 State the product of: 
 
 1. 16 x 15. 5. 14 x 16. 9. 19 x 18. 13. 27 x 23. 
 
 2. 17 x 18. 6. 18 x 13. 10. 24 x 25. 14. 31 x 38. 
 
 3. 19 x 13. 7. 18 x 14. 11. 23 x 21. is. 37 x 32. 
 
 4. 15 x 19. 8. 15 x 14. 12. 24 x 26. 16. 34 x 32. 
 
 WRITTEN EXERCISE 
 
 In the following problems make all the extensions mentally. 
 
 1. Find the total cost of : 
 42 Ib. cocoa at 48*. 
 
 45 Ib. cocoa at 43*. 
 54 Ib. coffee at 24*. 
 15 Ib. raisins at 13*. 
 17 Ib. biscuits at 12*. 
 
 2. Find the total cost of : 
 36 yd. wash silk at 26*. 
 
 54 doz. whalebones at 94*. 
 97 yd. Amazon cloth at 97*. 
 
 17 gro. bone buttons at 19^. 
 
 18 yd. gunner's duck at 17*. 
 
 27 bx. salt at 57*. 
 23 Ib. coffee at 24 *. 
 19 Ib. candy at 18*. 
 32 Ib. chocolate at 22*. 
 85 Ib. Oolong tea at 35*. 
 
 87 yd. flannel at 27 *. 
 19 yd. cottonade at 14*. 
 17 yd. York denim at 15*. 
 
 16 yd. cotton cheviot at 19^. 
 
 17 yd. Hamilton stripe at 12*. 
 
 MULTIPLICATION BY NUMBERS OF Two FIGURES ENDING IN 1 
 
 93. Example. Multiply 412 by 31. 
 
 SOLUTION. Write 2 in the product. 3~~x~~2+ 1 (the tens' figure 
 of the multiplicand) = 7 ; write 7 in the product. 3x1 + 4 (the 
 hundreds' figure of the multiplicand) = 7; write 7 in the product. 
 3 x 4 = 12 ; write 12. The result is 12,772. 
 
 94. In a similar manner multiply by all such numbers as 301, 
 101, and 901. 
 
 
MULTIPLICATION 61 
 
 95. Example. Multiply 126 by 201. 
 
 126 
 201 
 
 SOLUTION. Write 26 in the product. 2x6+1 (the hundreds' 
 figure of the multiplicand) = 13. Write 3 and carry 1. 2 x 12 + 
 1 (carried) = 25. The result is 25,326. 25826 
 
 The two processes just explained are the best for making mental exten- 
 sions on a bill and the like. For general work, however, many persons pre- 
 fer the following methods : 
 
 First problem Second problem 
 
 412 once the number 126 = once the number 
 
 1236 = 30 times the number 252 = 200 times the number 
 
 12772 = 31 times the number 25326 = 201 times the number 
 
 WRITTEN EXERCISE 
 Find the product of: 
 
 1. 214x21. 3. 425x61. 5. 465x121. 7. 746x201. 
 
 2. 315 x 31. 4. 386 x 91. 6. 215 x 401. 8. 859 x 301. 
 
 MULTIPLICATION BY NUMBERS FROM 101 TO 109 INCLUSIVE 
 
 96. Examples. 1. Find the cost of 64 bu. of wheat at $ 1.02. 
 
 SOLUTION. 2 x 64 = 128 ; write 28 and carry 1. 1 x 64 +1 = 
 65 ; write 65. The result is 65.28. 1.02 
 
 Some persons may prefer to work this problem as follows : 64 65.28 
 bu. at$l =$64; 64 bu. at 2^ = $1.28; $64 + $ 1.28 = $65.28. 
 
 2. Find the cost of 251 bu. of barley at $1.04. 
 
 SOLUTION. 4 x 51 = 204 ; write 04 in the product and carry 2. 251 
 
 4x2 + 2 (carried) + 1 (the right-hand figure of the multiplicand) - 
 
 = 11 ; write 1 and carry 1. 1 x 25 + 1 (carried) = 26 ; write 26. 
 The result is $261. 04. 
 
 97. Similarly multiply by such numbers as 201, 302, and 405. 
 
 98. Example. Find the cost of 124 bu. of beans at 8 2.05. 
 
 SOLUTION. 5 x 24 = 120. Write 20 and carry 1. 5x1 + 1 124 
 
 (carried) +2x4 (the right-hand figure of the multiplicand) = 14 ; 205 
 
 write 4 and "carry 1. 2 x 12 + 1 (carried) = 25 ; write 25. The - 
 
 result is $ 254.20. 254.20 
 
 Some persons may prefer the following solution : 124 bu. at $2 = $248; 
 124 bu. at 5? = $6.20; $248 + $6.20 = $254.20. The student should try 
 to exercise his own ingenuity in all this work. 
 
62 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the value of : 
 
 1. 215 T. coal at $ 6.05. 8. 302 bu. peas at 74 t. 
 
 2. 224 bu. rye at $1.02. 9. 104 bu. corn at 89^. 
 
 3. 215 bu. wheat at $1.02. 10. 103 bu. beets at 85 
 
 4. 318 bu. barley at $1.05. 11. 205 bu. turnips at 54^. 
 
 5. 124 bbl. apples at $2.05. 12. 215 bu. pears at $1.05. 
 
 6. 116 bbl. onions at $ 1.08. 13. 411 bu. plums at $1.08 
 
 7. 232 bbl. potatoes at $2.05. 14. 206 bu. parsnips at 
 
 MISCELLANEOUS SHORT METHODS 
 
 99. When one part of the multiplier is contained in another 
 part a whole number of times, the multiplication may be short- 
 ened as shown in the following examples. 
 
 100. Examples. 1. Multiply 412 by 357. 
 
 SOLUTION. 35 is 5 times 7. 7 x 412 = 2884, which 
 write as the first partial product. 5 x 2884 = 14,420, 
 which write as the second partial product. 
 
 CHECK. Interchange the multiplier and multipli- 
 cand and remultiply. 4 x 357 = 1428 ; 3 x 1428 =4284. 
 Add. Since the results by both multiplications agree, 
 the work is probably correct. 
 
 412 
 
 357 
 
 2884 
 14420 
 
 357 
 412 
 1428 
 4284 
 
 1470.84 147084 
 
 2. Multiply 214 by 756. 
 
 214 
 
 756 
 
 SOLUTION. 56 is 8 times 7. 7 x 214 = 1498, which write as the 
 first partial product. 8 x 1498 = 11,984, which write as the second 
 partial product. The sum of these partial products, 161,784, is the 
 entire product. 
 
 Check as in problem 1. (See also pages 83 and 84.) 161784 
 
 1498 
 11984 
 
 WRITTEN EXERCISE 
 Find the product of: 
 
 1. 319x248. 3. 728x287. 5. 12816x10217. 
 
 2. 927x279. 4. 848x369. 6. 14416x12525. 
 101. In multiplying together any two numbers of two figures 
 
 each, the work may be shortened as in the following example. 
 
MULTIPLICATION 
 
 63 
 
 102. Example. Multiply 35 by 23. 
 
 SOLUTION. 3x5 = 15; write 5 and carry 1. 3x3 + 1 (carried) + 
 2 x 5 = 20 ; write and carry 2. 2x3 + 2 (carried) = 8 ; write 8. The 
 result is 805. 
 
 WRITTEN EXERCISE 
 
 Find the product of: 
 
 1. 23 x 25. 3. 56 x 35. 5. 67 x 51. 
 
 2. 72 x 21. 4. 34 x 52. 6. 86 x 42. 
 
 WRITTEN REVIEW EXERCISE 
 
 35 
 
 23 
 
 805 
 
 7. 75x24. 
 
 8. 66 x 82. 
 
 1. Multiply .45,216 by 14 412 in two lines of partial products. 
 
 2. Multiply 31,216 by 10,217 in two lines of partial products. 
 
 3. I bought 15 A. of land at 275 per acre and laid it out in 
 100 city lots. After expending $6750 for grading and taxes, 
 1257 for ornamental trees, and 250 for advertising, I sold 15 
 lots at 625 each, 35 lots at 415 each, and exchanged the re- 
 mainder for a farm of 120 A., which I immediately sold at 
 195 per acre. Did I gain or lose, and how much? 
 
 4. Copy and find the amount of the following bill: 
 
 July 26, 19 
 
 JMr. P. C. GORHAM 
 
 120 Spring Street, City 
 
 Bought of C 6. f erguson & Son 
 
 50 days 
 
 
 
 37 bu. Oats $0.40 
 50 a Corn .67 
 76 u Wheat 1.02 
 75 u Rye 1.04 
 95 u Beans 4.00. 
 16 u Clover Seed 5.50 
 26 u Millet .99 
 
 
 
 
 
CHAPTER YII 
 
 DIVISION 
 ORAL EXERCISE 
 
 1. What is the product of 12 times 15? How many times 
 is 15 contained in 180 ? What is ^ of 180 ? 
 
 2. How much is 11 times 17? How many times is $17 
 contained in 187 ? What is T \ of $187 ? 
 
 3. What is the product of 9 times 12 ft.? How many times 
 is 12 ft. contained in 216 ft.? What is ^ of 225 ft.? 
 
 4. When one factor and the product are given, how is the 
 other factor found ? 
 
 103. The process of finding either factor when the product 
 and the other factor are given is called division. 
 
 104. The known product is called the dividend; the known 
 factor, the divisor ; the unknown factor, when found, the 
 quotient. 
 
 105. The part of the dividend remaining when the division 
 is not exact is called the remainder. 
 
 While definitions such as the above should not be memorized, the ideas 
 which they express should be thoroughly understood. 
 
 106. Since 6 times 7 ft. = 42 ft., 42 ft. -=- 7 ft. = 6, and 
 42 ft. -r- 6 = 7 ft. It is therefore clear that 
 
 1. If the dividend and divisor are concrete numbers the quo- 
 tient is an abstract number ; and 
 
 2. If the dividend is concrete and the divisor abstract, the quo- 
 tient is a concrete number like the dividend. 
 
 In 106 it will be seen that there are two kinds of division: 42 ft.-f- 7 ft. = 
 6 is sometimes called measuring, because 42 ft. is measured by 7ft. ; 42 ft. * 
 6 = 7 ft. is sometimes called partition, because 42 ft. is divided into 6 equal 
 parts. 
 
 64 
 
DIVISION 
 
 65 
 
 ORAL EXERCISF 
 
 1. 
 
 Divide 
 
 by 
 
 2: 
 
 18, 
 
 32, 
 
 78, 
 
 450, 
 
 642, 
 
 964, 
 
 893. 
 
 
 2. 
 
 Divide 
 
 by 
 
 3: 
 
 27, 
 
 57, 
 
 72, 
 
 423, 
 
 642, 
 
 963, 
 
 845. 
 
 
 3. 
 
 Divide 
 
 by 
 
 4: 
 
 64, 
 
 88, 
 
 92, 
 
 488, 
 
 192, 
 
 396, 
 
 728. 
 
 
 4. 
 
 Divide 
 
 by 
 
 5: 
 
 65, 
 
 85, 
 
 95, 
 
 135, 
 
 275, 
 
 495, 
 
 725. 
 
 
 5. 
 
 Divide 
 
 by 
 
 6: 
 
 84, 
 
 9G, 
 
 54, 
 
 246, 
 
 546, 
 
 672, 
 
 846, 
 
 636. 
 
 6. 
 
 Divide 
 
 by 
 
 7: 
 
 63, 
 
 84, 
 
 91, 
 
 217, 
 
 497, 
 
 714, 
 
 791, 
 
 921. 
 
 7. 
 
 Divide 
 
 by 
 
 8: 
 
 72, 
 
 56, 
 
 88, 
 
 248, 
 
 640, 
 
 128, 
 
 144, 
 
 152. 
 
 8. 
 
 Divide 
 
 by 
 
 4: 
 
 56, 
 
 96, 
 
 77, 
 
 241, 
 
 168, 
 
 128, 
 
 920, 
 
 848. 
 
 9. 
 
 Divide 
 
 by 
 
 6: 
 
 78, 
 
 96, 
 
 56, 
 
 272, 
 
 848, 
 
 190, 
 
 725, 
 
 966. 
 
 10. 
 
 Divide 
 
 by 
 
 9: 
 
 98, 
 
 72, 
 
 49, 
 
 279, 
 
 819, 
 
 720, 
 
 189, 
 
 918. 
 
 ORAL EXERCISE 
 
 1. 16 ft. -*- 2 = ? 24 ft. 
 
 2. 825-^5 = ? 829.75 
 
 8 ft. = ? 
 
 5 = ? 8129.78-^-9 = ? 13.40 
 
 4 = 
 
 3. 126 yd. -3 yd. = ? 8125 -v- 25 = ? 86.25 -*- 81. 25 = ? 
 
 4. If 9 T. of coal cost 849.50, what is the cost per ton? 
 
 SOLUTION. $49.50 H- - $5 ; subtracting 9 times $5, the re- 85.50 
 
 suit is $4.50 undivided; $4.50 -=- 9 = $0.50. Therefore the O N~ I0 - A 
 quotient is $5.50. i9 ' D 
 
 5. At -$1.75 a yard, how many yards can be bought for 835? 
 SOLUTION. The divisor contains cents and it is therefore 20 
 
 better to first change both dividend and divisor to cents. It is l7V\Q~77o 
 
 found that $35 would buy 20 times as many yards as $1.75 , or 
 
 20yd. 
 
 6. If 5 T. of coal cost 831.25, what is the cost per ton? 
 
 7. At 8 2.50 per yard how many yards can be bought for 8 550 ? 
 
 ORAL EXERCISE 
 
 1. How many weeks in 98 da. ? 
 
 2. What is fa of 2250 bbl. of apples? T y 1? ^? 
 
 3. The quotient is 8 and the dividend 128. What is the 
 divisor? 
 
 4. How many times can 18 be subtracted from 75, and what 
 will remain? 
 
6G PRACTICAL BUSINESS ARITHMETIC 
 
 5. At 15^ per pound, how many pounds of beef can be 
 bought for $6.30? 
 
 6. The quotient is 5, the divisor 23, and the remainder 2. 
 What is the dividend ? 
 
 7. If 5 men earn $17.50 a day, how much can 8 men earn 
 in 2 da. at the same rate? 
 
 8. What is the nearest number to 150 that can be divided 
 by 9 without a remainder? 
 
 9. If there are 960 sheets in 40 qr. of paper, how many 
 sheets in 5 qr. ? in 11 qr. ? 
 
 10. If 6 bbl. of apples are worth $9, what are 24 bbl. 
 worth at the same rate? 36 bbl.? 
 
 11. If 17 bbl. of flour cost $85, what will 25 bbl. cost at the 
 same rate? 32 bbl. ? 48 bbl. ? 34 bbl. ? 
 
 12. If 8 be added to a certain number, the sum will be 24 
 times the number. What is the number? 
 
 13. If 20 yd. of cloth cost $60, for how much per yard 
 must it be sold to gain $25? to gain $15? 
 
 14. A grocer sold 250 oranges at 5^ each and gained $5. 
 How much did he pay a dozen for the oranges? 
 
 15. A grocer pays $3 for 20 doz. of eggs. At what price per 
 dozen must he sell them in order to gain $1.50? 
 
 16. At $2.50 per yard, how many yards of cloth can be 
 bought for $75? for $150? for $2500? for $750? 
 
 17. How many days' labor at $3.50 per day will pay for 2 T. 
 of coal at $7 a ton and 5 Ib. of tea at 70^ per pound? 
 
 18. A clothier pays $96 for a dozen overcoats. At how 
 much apiece must lie retail them to gain $48 on the lot? 
 
 19. A man exchanged 1140 bu. of wheat at $1 per bushel 
 for flour at $6 per barrel. How many barrels did he receive? 
 
 20. It was found that after 15 had been subtracted 5 times 
 from a certain number the remainder was 4. What was the 
 number? 
 
 21. A man contracts a debt of $175 which he promises to 
 pay in weekly installments of $3.50 each. After paying $35, 
 how many more payments has he to make? 
 
DIVISION 67 
 
 107. Examples. 1. Divide 4285 by 126: 
 
 COMPLETE OPERATION REQUIRED WORK 
 
 126)4285 126)4285 
 
 378 =3 times 126 378 
 
 505 undivided 505 
 
 504 =4 times 126 504 
 
 1 undivided 1 
 
 CHECK. 34 x 126 + 1 = 4285 
 
 The remainder cannot always be written as a part of the quotient. Thus 
 in the problem, " At $7 per head how many sheep can be bought for $37," 
 we cannot say, " 5f sheep," but " 5 sheep and $2 remaining." 
 
 2. A farmer received $283.25 in payment for 275 bu. of wheat. 
 How much was received per bushel for the wheat? 
 
 11.03 
 
 SOLUTION. $283.75-^275 = $! and $8.25 undivided. 275)$ 283.25 
 $8.25 * 275 = $0.03. $1.03 per bushel was therefore re- 975 
 
 ceived for the wheat. 
 
 CHECK. 275 times $1.03 = $283.25. *5 
 
 825 
 
 108. Work in division may be abridged by omitting the 
 partial products and writing only the partial dividends. 
 
 109. Example. Divide $614.80 by 232. 
 
 SOLUTION. 2 times 2 plus = 4; 2 times 3 plus 5 = 
 
 11. 2 times 2 + 1 = 5, and 5 plus 1 = 6. Bring down 8. 232)$ 614.80 
 
 6 times 2 plus 6 = 18; 6 times 3 plus 1 = 19, and 19 + 1 = ' 150 8 
 
 20; 6 times 2 plus 2 = 14, and 14 plus 1 = 15. Bring 11 60 
 
 down and proceed as before. 00 
 
 WRITTEN EXERCISE 
 
 1. Find the value of 8800 Ib. of oats at 45 ^ per bushel 
 of 32 Ib. 
 
 2. How many automobiles, at 1650 each, can be purchased 
 for 14,225,000 ? 
 
 3. By what number must 8656 be multiplied to make the 
 product 8,223,200 ? 
 
68 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 4. If 120 bbl. of flour cost $660, what will 829 bbl. cost at 
 the same rate ? 
 
 5. The product of two numbers is 1,928,205. If one of them 
 is 621, what is the other? 
 
 6. If 380 T. of coal can be bought for 83040, how many 
 tons can be bought for $ 3600? 
 
 7. How many cords of 128 cu. ft. in a pile of wood con- 
 taining 235,820 cu. ft. ? What is it worth at $4.50 per cord ? 
 
 8. A speculator sold a quantity of apples that cost $2500 
 for $4750. If his gain per barrel was $1.12|, how many 
 barrels did he buy ? 
 
 9. A man received a legacy of $11,375 which he invested 
 in railroad stock. He paid a broker $ 125 to buy stock at 
 $112.50 per share. How many shares were bought? 
 
 10. A dealer bought 250 T. of coal by the long ton of 2240 
 Ib. at $4.50 per ton. He retailed the same at $6.75 per short 
 ton of 2000 Ib. What was the total gain ? 
 
 11. In a recent year there were produced in the United 
 States 550,935,925 bu. of wheat on 44,074,874 A. What was 
 the yield per A. ? What was the yield worth at 44.9^ per bu. ? 
 
 12. Copy and complete the following table of corn statistics. 
 Check the work. (The total yield multiplied by the price per 
 bushel should equal the total valuation.) 
 
 PRINCIPAL CORN-GROWING STATES IN A RKCENT YEAR 
 
 STATE 
 
 YIELD IN BUSHELS 
 
 FARM PRICE 
 I-ER BUSHEL 
 
 KAU.M VALUATION 
 
 Illinois 
 
 334 133 680 
 
 44^ 
 
 147018819 
 
 20 
 
 Iowa 
 
 
 44? 
 
 133 337 277 
 
 04 
 
 Nebraska 
 
 
 44 ? 
 
 114814627 
 
 40 
 
 Missouri 
 
 
 44? 
 
 66 669 962 
 
 92 
 
 Indiana 
 
 143 396 852 
 
 44? 
 
 
 
 Texas 
 
 136 702 6!)9 
 
 44? 
 
 
 
 Total 
 
 
 
 
 
 13-15. Make and solve three self -checking problems in division. 
 
DIVISION 69 
 
 SHORT METHODS IX DIVISION 
 
 POWERS AND MULTIPLES OF 10 
 
 ORAL EXERCISE 
 
 1. How many times is 10 contained in 50? 100 in 800? 
 1000 in 9000? 
 
 2. Catting off a cipher in 30 divides it by what number? 
 
 3. Cutting off two ciphers in 800 divides it by what number? 
 
 4. Cutting off three ciphers in 11,000 divides it by what 
 number ? 
 
 5. Read aloud, supplying the missing words : 
 
 a. The number of 10's in any number may be found by 
 cutting off the units' figure ; the number of 100's by cutting 
 off the - and - figures ; the number of - - by cutting 
 off the hundreds' and tens' and units' figures. 
 
 b. In 4561 there are 456 tens and 1 unit, or 456^ tens; 45 
 - and 61 units, or 45-j^g- hundreds; and -- thousands and 
 
 561 units, or 4^^ thousands. 
 
 6. How many times is $0.10 contained in $ 1 ? $0.01 in 
 $1? $0.001 in$l? 
 
 7. What is'^ of $1? T1 L of $1 ? loVo of #1? 
 
 8. Read aloud, supplying the missing words: $0.60 is - 
 of $6 ; $0.06 is - of $6 ; $0.006 is -- of $6. 
 
 9. Formulate a short method for dividing United States 
 money by 10; by 100; by 1000. 
 
 10. By inspection find the quotient of : 
 
 a. 736-s-lO. e. $271 -s- 100. i. 2140 Ib. -f- 100. 
 
 b. 1531-100. /. $519.50-10. j 3145 Ib. -s- 100. 
 
 c. 16351-1000. #.$84.50-100. k. 3416 ft. -r- 1000. 
 
 d. 311219-10000. h. $2150-1000. I. 1279 posts -*- 100. 
 
 11. Read aloud, supplying the missing amounts : 
 
 a. 6400-1600 = - -; 640-10 = -- . 
 
 b. 27000-9000 = - j 2700-900= -- ; 270 -r- 90 = 
 - ; 27-9= -- . 
 
 c. 18801 - 90 = - - 9 ; 214200 - 700 = 2142 - - . 
 
70 PEACTICAL BUSINESS ARITHMETIC 
 
 12. How is the quotient affected by like changes in both 
 the dividend and divisor ? 
 
 13. Divide 1323 by 400. 
 
 SOLUTION. Cut off the two ciphers in the divisor and two 
 digits in the right of the dividend, thus dividing both dividend 4|00")13I23 
 and divisor by 100. 4 is contained in 13 three times with a 
 remainder 1 hundred. Adding to this remainder the 23 units 
 remaining in the dividend after dividing by 100, the true re- 123 
 
 mainder is 123, which write in fractional form. 
 
 14. Read aloud, supplying the missing amounts : 1611 400 
 -; 2847-700 = - -; 1531-300 = - -; 16139-*- 
 
 4000 = . 
 
 15. Formulate a rule for dividing a number by any multiple 
 of ten. 
 
 16. State the quotient of : 
 
 a. 1231-30. /. 96131-400. k. 63571 -r- 3000. 
 
 b. 9647-40. g. 84199-700. I. 16657 -=- 4000. 
 
 c. 6551^50. h. 64137 -v- 800. m. 36119-=- 6000. 
 
 d. 4273-70. i. 45117 -s- 900. n. 18177^9000. 
 
 e. 8197^-90. i. 25121-500. o. 42113^7000. 
 
 ORAL REVIEW EXERCISE 
 
 The diagram on the opposite page is a portion of the New York Central 
 time-table giving the distances between many of the stations from New 
 York City to Suspension Bridge, and the time taken by two different trains 
 to travel this route. 
 
 1. How many miles between New York City and Pough- 
 keepsie? between Poughkeepsie and Utica ? between Utica and 
 Syracuse? between Syracuse and Rochester? between Rochester 
 and Buffido? between Buffalo and Niagara Falls? 
 
 2. What is the distance between New York City and Syra- 
 cuse? between Poughkeepsie and Niagara Falls? between 
 Rochester and Suspension Bridge? 
 
 3. How many miles between Ludlow and each station below 
 it? between Poughkeepsie and each station below it? between 
 Tarry town and each station below it? 
 
DIVISION 
 
 71 
 
 4. How many miles between Montrose and each 
 below it? between Oscawana and 
 
 each station below it? 
 
 5. At 2^ per mile, what is the 
 fare from New York to Niagara 
 Falls? from Poughkeepsie to Syra- 
 cuse ? from Buffalo to Utica ? from 
 Troy to Yonkers? 
 
 6. At 2^ per mile, what is the 
 fare from Rochester to Syracuse? 
 from Rensselaer to Suspension 
 Bridge? from Albany to Niagara 
 Falls? from Syracuse to Buffalo? 
 to Albany? 
 
 7. How long does it take train 
 No. 93 to travel the first 30 mi. 
 toward Poughkeepsie? the first 74 
 mi. toward Albany? 
 
 8. How long is train No. 93 
 in making the run from Fishkill 
 Landing to Camelot? This is ap- 
 proximately how many miles an 
 hour? 
 
 9. How long does it take train 
 No. 73 to make the run from Utica 
 to Syracuse? How long does it take 
 train No. 73 to make the run from 
 Fishkill Landing to Chelsea? This 
 is approximately how many miles 
 an hour? 
 
 10. Add each number in the col- 
 umn marked " Miles " to the one 
 immediately below it. 
 
 station 
 
 Thus, 9, 12, 16, 24, 34, 45, 58, etc. In add- 
 ing 89 and 95 think of 179 and 5, or 184 ; in 
 adding 143 and 149 think first of 243 afid 49 and then of 283 and 9, or 292. 
 
 I 
 
 NORTH 
 AND 
 WEST BOUND 
 
 Midnight 
 Express 
 
 ** 
 
 II 
 
 1 
 
 73 
 
 93 
 
 
 4 
 5 
 7 
 8 
 10 
 11 
 13 
 14 
 15 
 16 
 18 
 20 
 21 
 22 
 23 
 26 
 30 
 31 
 35 
 37 
 38 
 39 
 42 
 47 
 50 
 53 
 56 
 58 
 59 
 63 
 65 
 69 
 74 
 74 
 80 
 84 
 89 
 95 
 99 
 105 
 109 
 111 
 115 
 119 
 [22 
 125 
 131 
 135 
 142 
 143 
 149 
 
 New York 
 Grand Cent. Sta Lv. 
 125th St. Sta " 
 138th St. Sta. " 
 High Bridge " 
 Morris Heights " 
 Kings Bridge " 
 Spuyten Duyvil " 
 Riverdale " 
 Mt. St. Vinceut " 
 Ludlow " 
 Yonkers .*.... . " 
 
 121J10 
 12*23 
 
 ^ 
 
 I 
 I 
 
 12.46 
 
 T09 
 'l.25 
 
 GfOl 
 6*,13 
 6.15 
 6.21 
 6.25 
 6.29 
 6.33 
 
 6.43 
 6.46 
 6.52 
 6.59 
 7.01 
 7.05 
 7.12 
 7.19 
 7.25 
 7.31 
 7.34 
 7.37 
 7.41 
 7.49 
 7.59 
 8.06 
 8.12 
 8.16 
 8.21 
 8.27 
 8.34 
 8.40 
 8.46 
 8*55 
 
 Glenwood " 
 
 Hastings-on-Hudson " 
 Dobbs' Ferry " 
 Ardsley- on -Hudson " 
 Irvington " 
 Tarrytown " 
 
 Scarborough " 
 Ossining " 
 Croton-on-Hudson .. " 
 Oscawana " 
 Crugers " 
 
 Montrose. .. .. " 
 Peekskill " 
 
 1A7 
 
 X 
 
 X 
 
 224 
 2.31 
 
 Highlands " 
 Garrison " 
 Cold Spring " 
 
 Storm King " 
 Dutchess June " 
 Fishkill Landing " 
 Chelsea " 
 New Hamburg " 
 
 Camelot " 
 
 "2.53 
 3.05 
 
 Poughkeepsie Ar. 
 Poughkeepsie Lv. 
 
 Hyde Park " 
 Staatsburgh " 
 Rhinecliff (Rh'b'k).. " 
 Barrytown " 
 Tivoli 
 
 
 
 
 
 Germantown " 
 
 
 
 Linlithgo " 
 Greendale " 
 
 
 
 Hudson : " 
 
 4.47 
 
 
 Stockport " 
 Newton Hook " 
 
 Stuyvesant " 
 Schodack Landing.. " 
 Castleton " 
 
 
 
 Rensselaer " 
 
 "5.50" 
 
 C*,50 
 
 ....... 
 
 Albany Ar. 
 Troy " 
 
 238 
 291 
 371 
 440 
 463 
 464 
 
 Utica Ar. 
 
 8^40 
 9.55 
 11.38 
 1 M P 15 
 
 
 Rochester " 
 
 Buffalo " 
 
 Niagara Falls Ar. 
 Suspension Bridge 
 
 2513 
 
 220 
 
72 PRACTICAL BUSINESS ARITHMETIC 
 
 11. Multiply each number in the column marked "Miles" 
 by 5 ; by 8; by 3; by 7; by 6 ; by 4 ; by 9. 
 
 The numbers in the portion of the time-table illustrated may be used for 
 such other exercises as may seem necessary at this point. Students should 
 be impressed with the importance of being able to add, subtract, multiply, 
 and divide numbers in any relative position. 
 
 12. Five parts of 120 are 15, 18, 32, 10, and 20. Find the 
 sixth part, and multiply it by 15. 
 
 13. From a flock of 170 sheep I sold at different times 12, 
 18, 32, and 9. How many sheep remained? 
 
 14. Multiply each of the following numbers by 11 : 21, 32, 
 43, 54, 65, 76, 87, 98, 61, 28, 37, 14, 21, 62. 
 
 15. At 22^ per yard, what will 18 yd. cost? 21 yd.? 36 
 yd. ? 56 yd. ? 29 yd. ? 73 yd. ? 94 yd. ? 72 yd. ? 
 
 16. Multiply each number in problem 15 by 33 ; by 44. 
 
 17. Multiply each number in problem 15 by 10; by 100; 
 by 30 ; by 300 ; by 500. 
 
 18. What will 102 bu. of wheat cost at 68^ per bushel? 
 at 82^ per bushel? at 91^ per bushel? at 99^ per bushel? 
 
 19. Find the cost of 32 bu. of apples at 45^ per 
 bushel; at 38^ per bushel; at 42^ per bushel; at 28^ per 
 bushel; at 15^ per bushel ; at 21^ per bushel. 
 
 20. I have on hand at the opening of business Monday 
 morning cash amounting to 1800. I pay out $80, $40, arid 
 $30 and have on hand at the close of the day $860. How 
 much cash did I receive during the day? 
 
 Postal information. All mailable matter for transmission by the United 
 States mails within the United States or to Cuba, Mexico, Hawaii, Porto 
 Rico, Canada, and the Philippine Islands is divided into four classes : first- 
 class matter, second-class matter, third-class matter, and fourth-class matter. 
 
 First-class matter includes letters, postal cards, and anything sealed or 
 otherwise closed against inspection. The rate for first-class matter is 2 ^ 
 per ounce or fraction thereof. The cost of an ordinary postal card is 1^; 
 of a reply postal card, 2 ^. 
 
 Second-class matter includes newspapers and periodicals entirely in print. 
 When sent by publishers or news agents, the rate is 1 ^ per pound or fraction 
 thereof ; when sent by others, 1 ^ for each 4 oz. or fraction thereof. 
 
DIVISION 73 
 
 Third-class matter includes books, circulars, pamphlets, proof sheets and 
 manuscript copy accompanying the same, and engravings. The rate is 1 ^ 
 for each 2 oz. or fraction thereof. 
 
 The limit of weight in third-class matter is 4 lb., except single books in 
 separate packages, on which the weight is not limited. 
 
 Fourth-class matter includes all mailable matter not specified in the pre- 
 ceding classes, such as merchandise and samples of every description and 
 kind and specie. The rate is 1 ^ for each ounce or fraction thereof. 
 
 All kinds of postal matter may be registered at the rate of 8^ for each 
 package in addition to the regular rates of postage. 
 
 The rates on special delivery letters are 10 f- per letter in addition to 
 the regular postage. Any matter on which a special delivery stamp is 
 affixed is entitled to special delivery. 
 
 Foreign rates of postage are as follows: letters 5^ per half ounce ; postal 
 cards, 2 ?; newspapers and other printed matter, 1 ? per every 2 ounces. 
 
 21. What is the postage on a letter weighing | oz.? 4|oz.? 
 1J oz.? 3 oz.? 2| oz.? 4J oz.? 
 
 22. Find the total cost of mailing the following to points 
 in Canada: a book, weighing 32 1 oz., which you have regis- 
 tered; a package of jewelry, weighing 19 oz., which you have 
 registered. 
 
 23. What will be the total cost of mailing the following 
 articles at your post office to points within the United States: 
 an ordinary letter, weighing 2 J oz. ; a registered letter, weigh- 
 ing 1 J oz. ; a book, weighing 3 lb. 8 oz. ; and a bundle of 
 papers, weighing 10 oz.? 
 
 24. Find the total cost of mailing the following to points 
 within the United States : a special delivery letter, weighing 
 1J oz. ; a registered letter, weighing 2| oz.; some printers' 
 proofs, weighing 18 oz.; some separate manuscript for printer, 
 weighing 12 oz. ; a pamphlet weighing 6 oz. 
 
 25. Find the mailing price of each of the following articles : 
 
 ARTICLE LIST PRICE WEIGHT WHEN PACKED 
 
 a. A pair of opera glasses $12.50 2 lb. 8 oz. 
 
 b. A pair of ladies' gloves $ 2.50 6 oz. 
 
 c. A copy of Star-Land $1.20 lib. 8 oz. 
 
 d. A copy of Whittier's Poems $ 1.60 1 lb. 12 oz. 
 
 e. A copy of Footprints of Travel 8 1.25 1 lb. 8 oz. 
 
74 PRACTICAL BUSINESS ARITHMETIC 
 
 26. A publishing house advertises books at the following 
 prices. If the wrapping used in preparing the books for mail- 
 ing weighs 4 oz. in each case, what is the weight of the book ? 
 
 BOOK LIST PRICE MAILING PRICE 
 
 a. Wilderness Ways 45^ 
 
 b. Ways of Woodfolk 50^ 
 
 c. Friends and Helpers 60^ 70 ^ 
 
 d. Triumphs of Science 30^ 35 j^ 
 
 e. Industries of To-day 25^ 30^ 
 
 27. A publisher sends 20,000 copies of his magazine by mail. 
 If each magazine and wrapper weighs 14| oz. and the total 
 number is weighed at the post office in bulk, what will the pub- 
 lisher have to pay for postage ? 
 
 28. A subscriber mails two issues of the above magazine to a 
 friend. What will be the cost for postage ? 
 
 29. 25,000 copies of a monthly magazine weighing 14^ oz. 
 were sent by mail. What is the cost to the publisher of 
 mailing ? 
 
 30. Find the total cost for mailing the following : printers' 
 proof weighing 18J oz. ; manuscript and printers' proof in one 
 package, weighing 28J oz. ; a book, weighing 22 oz". ; a special 
 delivery letter, weighing | oz. ; two ladies' pocketbooks, weigh- 
 ing 14 oz. 
 
 WRITTEN REVIEW EXERCISE 
 
 l. Find the total cost of the articles in problem 3 of the oral 
 exercise, page 56. Find the total of the products in the oral 
 exercise, page 60. 
 
 2. A mechanic earns $125 per month and his monthly ex- 
 penses average $72. If he saves the remainder, how long will 
 it take him to pay for a house costing $4352 ? 
 
 3. I spent $24,800 for apples at $2.50 per barrel. The loss 
 from decay was equal to 74 bbl. What was my gain, if the 
 remainder of the apples sold for $3.75 per barrel, and my 
 expenses for storage were $675.80? 
 
 
DIVISION 
 
 4. Without copying find (a) the total number of railway 
 employees in the United States in 1903 and (6) the total num- 
 ber per hundred miles of line in the same year. 
 
 RAILWAY EMPLOYEES iv THE UNITED STATES 
 
 
 1904 
 
 1903 
 
 CLASS 
 
 TOTAL 
 NUMBER 
 
 NUMBER PEK 
 100 MILES 
 
 AVERAGE 
 DAILY WAGES 
 
 TOTAL 
 NUMBER 
 
 NUMBER PER 
 100 MILES 
 
 AVERAGE 
 DAILY WAGES 
 
 General officers 
 
 5,165 
 
 2 
 
 $11.61 
 
 4,842 
 
 2 
 
 $11.27 
 
 Other officers 
 
 5.375 
 
 3 
 
 6.07 
 
 5,201 
 
 3 
 
 5.76 
 
 General office clerks 
 
 46,037 
 
 22 
 
 2.22 
 
 42,218 
 
 21 
 
 2.21 
 
 Station agents 
 
 34,918- 
 
 16 
 
 1.93 
 
 34,892 
 
 17 
 
 1.87 
 
 Other statioumen 
 
 120,002 
 
 57 
 
 1.C9 
 
 120,724 
 
 59 
 
 1.64 
 
 Engineers 
 
 52,451 
 
 25 
 
 4.10 
 
 52,993 
 
 26 
 
 4.01 
 
 Firemen 
 
 55,004 
 
 26 
 
 2.35 
 
 56,041 
 
 27 
 
 2.28 
 
 Conductors 
 
 39,645 
 
 19 
 
 3.50 
 
 39,741 
 
 19 
 
 3.38 
 
 Other trainmen 
 
 106,734 
 
 50 
 
 2.27 
 
 104,885 
 
 51 
 
 2.17 
 
 Machinists 
 
 46,272 
 
 22 
 
 2.61 
 
 44,819 
 
 22 
 
 2.50 
 
 Carpenters 
 
 53,646 
 
 25 
 
 2.26 
 
 56,407 
 
 27 
 
 2.19 
 
 Other shopmen 
 
 159,472 
 
 75 
 
 1.91 
 
 154,635 
 
 75 
 
 1.86 
 
 Section foremen 
 
 37,609 
 
 18 
 
 1.78 
 
 37,101 
 
 18 
 
 1.78 
 
 Other trackmen 
 
 289,044 
 
 136 
 
 1.33 
 
 300,714 
 
 147 
 
 1.31 
 
 All other employees 
 
 244,747 
 
 115 
 
 1.98 
 
 257,324 
 
 125 
 
 1.93 
 
 5. Without copying find (a) the total number of railway 
 employees in the United States in 1904 and (6) the total num- 
 ber per one hundred miles of line in the same year. 
 
 6. Find the total salaries paid to railway employees in 1903 ; 
 in 1904. 
 
 7. Find the average daily wages paid to railway employees 
 in 1903 ; in 1904. 
 
 8. During a certain week a contractor employed help as 
 follows: 34 hands, 8 hr. per day, for 5 da., at 15^ per hour ; 
 16 hands, 9 hr. per day, for 6 da., at 25^ per hour ; 29 hands, 
 10 hr. per day, for 6 da., at 18^ per hour. Find the amount 
 due the employees. 
 
 9. In a recent year there were produced on 27,842,000 A. in 
 the United States 863,102,000 bu. oats, valued on the farm at 
 31.3^ per bushel. What was the average yield per acre? what 
 was the value of the year's crop ? 
 
76 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 10. Complete the following schedule by finding the vertical 
 and horizontal totals. Check the work by comparing the sum 
 of the vertical totals with the sum of the horizontal totals. 
 
 SALARY AND EXPENSE SCHEDULE 
 
 Fish and Game Commission of Massachusetts 
 
 FOR THE MONTH ENDING. 
 
 -, ?/7. 
 
 COMMISSIONERS 
 
 SALARY EXPENSE 
 
 SALARY EXPENSES 
 
 16 
 
 2 
 
DIVISION 
 
 77 
 
 11. Without copying, find quickly the total amount of the 
 following manufacturer's time sheet. Check the work. 
 
 TIME SHEET FOR WEEK ENDING JULY 29 
 
 NAME 
 
 M. 
 
 T. 
 
 w. 
 
 T. 
 
 F. 
 
 s. 
 
 TOTAL 
 TIME 
 
 KATE 
 NEB 
 
 HOUR 
 
 AMOUNT 
 
 Harry Ball .... 
 
 9 
 
 8 
 
 10 
 
 10 
 
 10 
 
 9 
 
 
 0? 
 
 
 
 John Cook . . . 
 
 8 
 
 8 
 
 10 
 
 9 
 
 9 
 
 8 
 
 
 12^ 
 
 
 
 James Easton . . . 
 
 9 
 
 9 
 
 9 
 
 10 
 
 8 
 
 8 
 
 
 Itf 
 
 
 
 Frank King .... 
 
 7 
 
 6 
 
 8 
 
 9 
 
 9 
 
 10 
 
 
 20? 
 
 
 
 Paul Mason .... 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 25? 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 12. From the following data make a statement of losses and 
 gains : Market value of groceries on hand May 1, 84469.40. 
 Bought groceries during the month: for cash, $1279.60; on 
 credit, $2150.40. Sold groceries during the month: for cash, 
 $2160.40; on credit, $2640.10. Gross expenses at the close 
 of the month, $590.50. Account against J. E. Brown & Co. 
 which cannot be collected, $79.80. Market value of groceries 
 on hand at the close of the month, $2842.60. Required, the 
 net gain or net loss. 
 
 13. In the following table find (a) the total number of tickets 
 sold each day, (&) the total number of each class sold during 
 the week, and (c) the aggregate number of tickets sold during 
 the week. Check the work. 
 
 TICKETS OF ADMISSION SOLD AT A STATE FAIR 
 
 CLASS 
 
 PRICE 
 
 MONDAY 
 
 TUESDAY 
 
 WEDNESDAY 
 
 THURSDAY 
 
 FRIDAY 
 
 SATURDAY 
 
 TOTAL 
 
 Children 
 
 $ 0.35 
 
 1240 
 
 1242 
 
 4165 
 
 3169 
 
 3146 
 
 1240 
 
 
 Adults 
 
 .75 
 
 6129 
 
 6129 
 
 12168 
 
 17246 
 
 12174 
 
 9167 
 
 
 Single carriages 
 
 .75 
 
 68 
 
 126 
 
 329 
 
 278 
 
 278 
 
 74 
 
 
 Double carriages 
 
 1.25 
 
 49 
 
 114 
 
 215 
 
 210 
 
 210 
 
 62 
 
 
 Total 
 
 
 
 
 
 
 
 
 
 14. In the above table find (a) the daily receipts from tickets 
 and (5) the aggregate receipts for the week. Check the work. 
 
78 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 Copy the following time sheets and find () the total number 
 of hours worked on each order, () the total number of hours 
 worked each day, (<?) the amount earned on each order, and 
 the total amount earned during the week. Check the work. 
 
 15. 
 BOSTON ELEVATED RAILWAY COMPANY 
 
 Time worked K y 
 
 During the week ending- 
 Rate per hour_s--Ol 
 
 .^^^7 y/T 
 
 Occupation- 
 
 Sun. Moo. Tue 
 
 Wed. Thur. 
 
 16. 
 BOSTON ELEVATED RAILWAY COMPANY 
 
 Time worked by 
 
 During the week ending- 
 Rate per hour 
 
 Occupation. 
 
 >-3 2- 
 
CHAPTER VIII 
 
 AVERAGE 
 ORAL EXERCISE 
 
 1. A earns $3, B earns $4, and C earns $5 per day. What 
 do the three earn in 1 da.? If $12 were paid to these men in 
 equal parts, how much would each receive ? 
 
 2. What sum is intermediate between 6, 7, and 8 ? between 
 6, 8, and 10 ? between 6, 12, and 18 ? 
 
 110. The process of finding a number that is intermediate 
 between two or more other numbers is called average. 
 
 111. Example. What is the average weight of 3 bales of 
 cotton weighing 460, 449, and 475 lb., respectively? 
 
 SOLUTION. The aggregate of the 3 bales of cotton is 1384 lb. 
 1384 lb. divided into three equal parts shows the mean or average 
 weight to be 4611 lb. 
 
 To find the average of consecutive numbers, add the highest 
 number to the lowest, and divide by 2. ^ 
 
 WRITTEN EXERCISE 
 
 - 
 
 1. A tapering board is 14 in. wide on one end and 18 in. 
 on the other. What is the average width of the board? 
 
 2. A manufacturing pay roll shows that 15 hands are em* 
 ployed at $1.25 per day, 12 hands at SI. 75 per day, 16 hands 
 at $2.25 per day, 32 hands at $2.50 per day, and 5 hands at 
 $6.50 per day. Find the average daily wages. 
 
 3. A merchant's sales for a year were as follows : January, 
 $12,156; February, $14,175; March, $16,152; April, $12,175; 
 May, $12,465. 95; June, $12,476.05 ; July, $15,145.40 ; August, 
 $12,431.46; September, $17,245.90; October, $18,256.45; 
 November, $19,250.65; December, $19,654.20. What were 
 his average sales per month? 
 
 79 
 
80 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 4. In a certain school of 300 pupils, 85 are 14 yr. of age ; 
 50, 15 yr. of age ; 25, 16 yr. of age ; 75, 17 yr. of age ; 50, 
 18 yr. of age; 15, 19 yr. of age. What is the average age of 
 the school? 
 
 5. The attendance for a certain school for a week was as fol- 
 lows : Monday, 727 pupils ; Tuesday, 732 pupils ; Wednesday, 
 756 pupils; Thursday, 761 pupils; Friday, 734 pupils. What 
 was the average daily attendance for the week ? 
 
 6. What should a ground feed made from 50 bu. of oats 
 worth 28^ per bushel, 30 bu. of barley worth 78^, and 60 
 bu. of corn worth 59^ sell for in order to make 10^ per 
 bushel on each ingredient used to make the mixture? 
 
 7. Find the aggregate weight and the average weight per 
 box of 100 bx. of cheese weighing 65, 64, 62, 60, 61, 65, 62, 64, 
 
 61, 62, 61, 60, 60, 61, 62, 60, 68, 65, 66, 64, 62, 61, 65, 66, 62, 
 
 64, 67, 58, 62, 59, 59, 60, 62, 64, 66, 67, 58, 60, 65, 58, 62, 69, 
 
 62, 65, 68, 69, 61, 65, 62, 61, 65, 68, 59, 62, 64, 58, 62, 65, 71, 
 70, 58, 67, 58, 62, 64, 58, 62, 64, 65, 69, 65, 65, 62, 64, 60, 60, 
 
 65, 60, 65, 65, 62, 60, 62, 64, 60, 72, 64, 70, 61, 62, 60, 60, 59, 
 65, 60, 70, 58, 62, 61, 64 lb., respectively. 
 
 8. Counting 8 hr. to a day, find the total amount and the 
 average daily wages in the following contractor's time sheet : 
 
 TIME SHEET FOR WEEK ENDING JUNE 30 
 
 NAME 
 
 M. 
 
 T. 
 
 W. 
 
 T. 
 
 F. 
 
 s. 
 
 HOURS 
 
 DAYS 
 
 DAILY 
 WAGES 
 
 AMOUNT 
 
 C. E. Ames 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 SI. 75 
 
 
 
 W. 0. Bye 
 
 9 
 
 10 
 
 9 
 
 10 
 
 10 
 
 8 
 
 
 
 2.00 
 
 
 
 M. E. Carey 
 
 10 
 
 9 
 
 9 
 
 10 
 
 8 
 
 10 
 
 
 
 2.00 
 
 
 
 W. D. Frey 
 
 6 
 
 8 
 
 9 
 
 10 
 
 7 
 
 8 
 
 
 
 2.25 
 
 
 
 G. W. Jones 
 
 10 
 
 10 
 
 10 
 
 8 
 
 10 
 
 8 
 
 
 
 2.25 
 
 
 
 D. 0. Munn 
 
 4 
 
 4 
 
 4 
 
 G 
 
 8 
 
 6 
 
 
 
 2.50 
 
 
 
 E. H. Post 
 
 G 
 
 6 
 
 6 
 
 6 
 
 4 
 
 4 
 
 
 
 3.00 
 
 
 
 L. C. Roe 
 
 10 
 
 10 
 
 10 
 
 10 
 
 4 
 
 4 
 
 
 
 3.25 
 
 
 
 J. H. Small 
 
 6 
 
 8 
 
 8 
 
 10 
 
 12 
 
 12 
 
 
 
 3.25 
 
 
 
 H. M. Young 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 3.50 
 
 
 
 Total 
 
 
 
 
 
 
 
 
 
 
 
 
CHAPTER IX 
 
 CHECKING RESULTS 
 
 112. It has been seen in the preceding exercises on statis- 
 tics, time sheets, etc., that various ruled forms provide for prac- 
 tical and convenient methods of checking results. While it is 
 possible to give a great variety of these problems it is also 
 necessary to give a great many problems that do not furnish 
 such a check. 
 
 113. It is very important that all results be checked. The 
 most common methods of checking addition, subtraction, and 
 division have already been mentioned. Multiplication may 
 be proved by dividing the product by either factor, or as 
 explained on page 52. 
 
 114. The properties of 9 and 11 may also be applied to advan- 
 tage in checking results, especially results in multiplication and 
 division. 
 
 PROPERTIES OF 9 AND 11 
 
 PROPERTIES OF 9 
 
 115. Any number of 10's is equal to the same number of 9's 
 plus the same number of units; any number of 100's is equal 
 to the same number of 99's plus the same number of units ; 
 any number of 1000's is equal to the same number of 999's 
 plus the same number of units ; and so on. 
 
 Thus, 10 = one 9 + 1 ; 40 = four 9's + 4 ; 100 = one 99 + 1 ; 300 = 
 three 99's + 3 ; 500 = five 99's + 5. 
 
 116. Any number may be resolved into one less than as many 
 multiples of 10 as it contains digits. 
 
 Thus, 946 = 900 + 40 + 6 ; 42175 = 40000 + 2000 + 100 + 70-1-5. 
 
 81 
 
82 PRACTICAL BUSINESS ARITHMETIC 
 
 117. The excess of 9's in any multiple of a power of 10 mul- 
 tiplied by a single digit is the same as the significant figure in 
 that number. Hence, 
 
 The excess of 9's in any number is equal to the excess of 9's in 
 the sum of its digits. 
 
 Thus, the excess of 9's in 241 = 2 + 4 + 1, or 7. The excess of 9's in 
 946 9 _|_ 4 _|_ 6, or 19 ; but 19 contains 9, and the excess of 9's in 19 = 1 + 
 9, or 10; but 10 contains 9, and the excess of 9's in 10 = 1 + 0, or 1; the 
 excess of 9's in 946 is therefore shown to be 1. 
 
 118. In finding the excess of 9's in any number, omit all 9's 
 and all combinations of two or three digits which it is seen at 
 a glance will make 9 or some multiple of 9. 
 
 Thus, in finding the excess of 9's in 9458, begin at the left, reject the 
 first digit 9, the sum of the next two digits, 9, and the single 8 will be the 
 excess of 9's in the entire number. 
 
 PROPERTIES OF 11 
 
 119. Any number of 10's is equal to the same number of ll's 
 minus the same number of units; any number of 100's is equal 
 to the same number of 99's plus the same number of units ; any 
 number of 1000's is equal to the same number of 1001's minus 
 the same number of units ; and so on. 
 
 Thus, 40 = four ll's - 4; 500 = five 99's + 5; 7000 = seven 1001's - 7. 
 
 120. It is therefore clear that even powers of 10 are multiples 
 of 11 plus 1 and odd powers of 10 are multiples of 11 minus 1. 
 
 Thus, 10 2 or 100 = nine ll's + 1 ; 10 3 or 1000 = ninety-one ll's - 1 ; 10* 
 or 10,000 = nine hundred nine ll's + 1. 
 
 121. From the foregoing it is evident that : 
 
 The excess of Ifs in any number is equal to the sum of the digits 
 in the odd places (increased by 11 or a multiple of 11 if necessary} 
 minus the sum of the digits in the even places. 
 
 Thus, the excess of ll's in 45 is 1 (5 4) ; the excess of ll's in 125 is 4 
 (5^2 + 1~^0); the excess of ll's in 2473 is 9 [14 (11 + 3) - 7 + 2 (4 - 2) 
 = 9]. 
 
CHECKING RESULTS 83 
 
 CHECKING ADDITION AND SUBTRACTION 
 
 122. Examples, l. By casting out the 9's, show that the 
 sum of 985, 651, 782, and 465 is 2833. 
 
 SOLUTION. The sum of the digits in 935 is 17 ; but since 17 935 = g 
 contains 9, find the sum of the digits in 17 and the result, 8, is the nr^ __ g 
 excess of 9's in the entire number. In like manner find the ex- 
 cess of 9's in 651, 782, and 465. Since 935 is a multiple of 9 + 8, '**' 
 651 a multiple of 9 + 3, 782 a multiple of 9 + 8, 465 a multiple of 465 = 6 
 9 + 6, the sum of these numbers. 2833, should equal a multiple of 2833 = 7 
 9 + (8 + 3 + 8 + 6), or 9 + 25. 25 is a multiple of 9 + 7, and 2833 
 is a multiple of 9 +7 ; hence, the addition is probably correct. 
 
 2. By casting out the ll's, show that the sum of 648, 217, 
 451, and 688 is 2004. 
 
 SOLUTION. 8-4 + 6-0 = 10, the excess of ll's in 648. 648=10 
 1+2 -0=8, the excess of ll's in 217. 12 (11 + 1) -5+ 217= 8 
 
 4 = 11 ; but 11 contains 11, hence, the excess of ll's in 451 
 
 is 0. 8^8 + 6^0=6, the excess of ll's in 688. Since 648 is 
 
 a multiple of 11 + 10, 217 a multiple of 11 + 8, 451 a multiple of 688 = 6 
 
 11, and 688 a multiple of 11 + 6, the sum of these numbers, 2004, 2004 = 2 
 
 should be a multiple of 11 + (10 + 8 + 6), or 11 + 24. 24 is a 
 
 multiple of 11+2 and 2004 is a multiple of 11 + 2; hence, the addition is 
 
 probably correct. 
 
 123. Subtraction may be proved either by casting out the 9's 
 or ll's in practically the same manner as addition. 
 
 The difference between the excess of 9's or ll's in the minuend and sub- 
 trahend should equal the excess of 9's or ll's in the remainder; or the sum 
 of the excess of 9's or ll's in the subtrahend and remainder should equal 
 the excess of 9's or ll's in the minuend. 
 
 These methods are but little used for checking addition and subtraction. 
 Addition is generally checked as explained on page 20, and subtraction as 
 explained on page 32. On the other hand, long multiplications and divi- 
 sions are almost always checked by applying the properties of 9 or 11. 
 
 CHECKING MULTIPLICATION AND DIVISION 
 
 124. Examples. 1. By casting out the 9's show that the 
 product of 64 x 95 is 6080. 
 
 SOLUTION. The excess of 9's in 95 is 5, and in 64, 1. Since 95 95 = 5 
 
 is a multiple of 9 + 5 and 64 a multiple of 9 + 1, the product of ci __ i 
 
 64 x 95 should be a multiple of 9 plus (1x5). 1 x 5 or 5 equals ^ " 
 
 the excess of 9's in 6080 ; hence, the work is probably correct. 6080 = 5 
 
84 PRACTICAL BUSINESS ARITHMETIC 
 
 2. By casting out the ll's show that the product of 46 x 95 
 is 4370. 
 
 SOLUTION. The excess of IPs in 95 is 7, and in 46, 2. Since 95 7 
 
 95 is a multiple of 1 + 17 and 46 a multiple of 11 + 2, the prod- tn> o 
 
 uct of 46 x 95 should be a multiple of 11 plus (2 x 7) or 14; but 
 14 is a multiple of 11 + 3. Since the product 4370 is a multiple of 
 11 + 3, the work is probably correct. 
 
 125. Division may be proved either by casting out the 9's or 
 ll's in practically the same manner as multiplication. The 
 excess of 9's or ll's in the quotient multiplied by the excess 
 of 9's or ll's in the divisor should equal the excess of 9's or 
 ll's in the dividend, minus the excess of 9's or ll's in the re- 
 mainder, if any. 
 
 Casting out the 9's will not show an error caused by a transposition of 
 figures; but casting out the ll's will show such an error. The method of 
 casting out the ll's is therefore considered the better proof. 
 
 WRITTEN EXERCISE 
 
 1. Determine without dividing whether $2.64 is the quo- 
 tient of $1375.44 -v- 521. 
 
 2. Determine without multiplying whether $1807.50 is the 
 product of 482 times $3.75. 
 
 3. Determine without adding whether 4231 is the sum of 
 296, 348, 924, 862, 956, and 845. 
 
 4. Multiply 34,125 by 729 in two lines of partial products 
 and verify the work by casting out the 9's. 
 
 5. Find the cost of 173,000 shingles at $4.27 per thousand, 
 in two lines of partial products, and verify the work by casting 
 out the ll's. 
 
 6. Find the cost of 126,000 ft. of clear pine at $24.60 per 
 thousand, in two lines of partial products, and v verify the work 
 by casting out the 9's. 
 
 7. Find the cost of 2,191,000 ft. of flooring at $32.08 per 
 thousand, in two lines of partial products, and verify the work 
 by casting out the ll's. 
 
FRACTIONS 
 
 CHAPTER X 
 
 DECIMAL FRACTIONS 
 ORAL EXERCISE 
 
 1. In the number $7.62 what figure stands for the dollars ? 
 the tenths of a dollar? the hundredths of a dollar? 
 
 2. What name is given to the point which separates the 
 whole number of dollars from the part of a dollar ? 
 
 3. Read: 3.5 dollars; 3.5ft.; 27.5 lb.; .7 of a dollar; .5 
 of a ton; 16.6; .9; 9.25 dollars; 7.25ft.; 8.75 rd.; .95 of a 
 dollar ; .85 of a pound sterling ; .57. 
 
 4. What is the first place at the right of the -decimal point 
 
 called ? the second place ? 
 
 izD 
 
 5. In the accompanying B 
 
 diagram what part of A is B ? | \ M , ,< \ M | . ( 
 What part of B is C? What 
 part of C is D? 
 
 6. What part of A is C? 
 What part of A is D? 
 
 7. If A is a cubic inch, what is B? C? D? 
 
 8. In a pile of 10,000 bricks one brick is what part of the 
 whole pile? 10 bricks is what part of the whole pile? 100 
 bricks is what part of the whole pile? 1000 bricks is what 
 part of the whole pile ? 
 
 9. How may one tenth be written besides ^? one hun- 
 dredth besides -j-J-^ ? one thousandth besides I-^QQ ? 
 
 126. Units expressed by figures at the right of the decimal 
 point are called decimal units. 
 
 127. A number containing one or more decimal units is 
 called a decimal fraction or a decimal. 
 
 85 
 
86 PRACTICAL BUSINESS ARITHMETIC 
 
 NOTATION AND NUMERATION 
 
 ORAL EXERCISE 
 
 1. Read: 0.7; 0.03 ; 0.25. How many places must be used 
 to express completely any number of hundredth^? 
 
 2. Read: 0.004; 0.025; 0.725. How many places must be 
 used to express completely any number of thousandths ? 
 
 3. Read: .0005; .00007; .000009; .0037; .00045; .000051; 
 .0121; .00376; .000218; .1127; .01525; .004531; .16067. 
 
 4. How many places must be used to express completely any 
 number of ten-thousandths? any number of hundred-thou- 
 sandths? any number of millionths? 
 
 128. In reading decimals pronounce the word and at the 
 decimal point and omit it in all other places. 
 
 Thus, in reading 0.605 or .605 say six hundred five thousandths ; in reading 
 600.005 say six hundred and jive thousandths. 
 
 129. The relation of integers and decimals with their increas- 
 ing and decreasing orders to the left and to the right of the 
 decimal point is shown in the following 
 
 NUMERATION TABLE 
 
 PERIODS : Millions Thousands Units Thousandths Millionths 
 
 ORDERS : | a J 1 j J ! J 
 
 *& - < r & & r-< <"rt ^rt 2 ^ 'M 
 
 I -1 " 2 2l22S 
 
 ^ ! I ill i s 5 1 1 1 1 li = 
 
 O '-^ (U ^ 3<>^ ( ) S^<--5 <D 
 
 KH^ KHH MH^QHMH HfflS 
 987, 654, 321.234 567 
 
 130. Hundredths are frequently referred to as per cent, a 
 phrase originally meaning by the hundred. 
 
 131. The symbol % stands for hundredths and is readier cent. 
 Thus 45% = .45 ; 48% of a number = .48 of it. 
 
DECIMAL FRACTIONS 87 
 
 ORAL EXERCISE 
 
 Read : 
 
 1. 0.073. 5. 532.002. 9. 31.08%. 
 
 2. 0.00073. 6. 60.0625. 10. 126.75%. 
 
 3. 3004.025. 7. 63.3125. 11. 2150.1875. 
 
 4. 300.4025. 8. 126.8125. 12. 3165.00625. 
 
 13. 131.3125 T. 15. A tax of 1.0625 mills. 
 
 14. 240. 0125 A. 16. A tax of 9. 1875 mills. 
 
 17. Read the number in the foregoing numeration table. 
 
 18. Read the following, using the words " per cent ": .17; 
 28; .85; .67; .425; .371. 
 
 19. Read the following as decimals, not using the words 
 "percent": 25%; 75%; 87%; 621%; 27.15%. 
 
 20. Read aloud the following : 
 
 a. The value of a pound sterling in United States money is 
 $4.8665. 
 
 b. A meter (metric system of measures) is equal to 
 39.37079 in.; a kilometer, to 0.62137 mi. 
 
 c. 1 metric ton is equal to 1.1023 ordinary tons ; 1.5 metric 
 tons are equal to 1.65345 ordinary tons. 
 
 d. A flat steel bar 3 in. wide and 0.5 in. thick weighs 
 5.118 Ib. 
 
 e. The circumference of a circle is 3.14159 times the length 
 of its diameter. 
 
 WRITTEN EXERCISE 
 
 Write decimally : 
 
 1. Five tenths ; fifty hundredths ; five hundred thousandths. 
 
 2. Nine hundred and eleven ten-thousandths ; nine hundred 
 eleven ten-thousandths ; five hundred and two thousandths. 
 
 3. One hundred seventy-four millionths ; one hundred 
 seventy-four million and seven millionths ; seven million and 
 one hundred seventy-four millionths. 
 
 4. Seven thousand and seventy-five ten-thousandths; two 
 hundred fifty-seven ten-millionths ; two hundred and forty-six 
 millionths ; two hundred forty-six millionths. 
 
88 PRACTICAL BUSINESS ARITHMETIC 
 
 5. Four million ten thousand ninety-seven ten-millionths ; 
 four million ten thousand and ninety-seven ten-mill ionths; five 
 hundred millionths; five hundred-millionths. 
 
 6. Six hundred six and five thousand one hundred-thou- 
 sandths; six hundred six and fifty-one hundred-thousandths; 
 fifty-six and one hundred twenty-eight ten-billionths. 
 
 7. Seventeen thousand and eighteen hundred seventy-six 
 millionths; seventeen thousand and eighteen hundred seventy- 
 six ten-thousandths ; twenty-one hundred sixteen hundredths. 
 
 132. In the number 2.57 there are 2 integral units, 5 tenths 
 of a unit, and 7 hundredths of a unit. In the number 2.5700 
 there are 2 integral units, 5 tenths of a unit, 7 hundredths of 
 a unit, thousandths of a unit, and ten-thousandths of a unit. 
 2.5700 is therefore equal to 2.57. That is, 
 
 Decimal ciphers may be annexed to or omitted from the right 
 of any number without changing its value. 
 
 ORAL EXERCISE 
 
 Read the following (a) as printed and () in their simplest 
 decimal form : 
 
 1. 0.700. 3. 16.010. 5. 0.50. 7. 0.7000. 
 
 2. 5.2450. 4. 18.210. 6. 0.00950. 8. 12.9010. 
 
 ADDITION 
 
 ORAL EXERCISE 
 
 1. What is the sum of 0.4, 0.05, 0.0065 ? 
 
 2. What is the sum of 0.3, 0.021, 0.008 ? 
 
 3. Find the sum of seven tenths, forty-four hundredths, and 
 two ; of four tenths, twenty-one hundredths, and six thou- 
 sandths. 
 
 133. Example. Find the sum of 12.021, 256.12, and 27.5. 
 
 SOLUTION. Write the numbers so that their decimal points 12.021 
 
 stand in the same vertical column. Units then come under units, o^ft 1 9 
 
 " 
 
 tenths under tenths, and so on. Add as in integral numbers and 
 place the decimal point in the, sum directly under the decimal 
 
 points in the several numbers added. 295.641 
 
DECIMAL FRACTIONS 89 
 
 WRITTEN EXERCISE 
 
 Find the sum of: 
 
 1. 7.5, 165.83, 5.127, 6.0015, and 71.215. 
 
 2. 257.15, 27.132, 5163, 8.000125, and 4100.002. 
 
 3. 0.175, 5.0031, .00127, 70.2116001, and 21.00725. 
 
 4. 51.6275, 19.071, 0.000075, 21.00167, and 40,000.01. 
 
 5. 2.02157, 2.1785, 2500.00025, 157.2165, and 7.0021728. 
 
 6. Copy, find the totals as indicated, and check : 
 
 $1241.50 $9215.45 $1421.12 $1421.32 ? 
 
 1.52 1275.92 1.46 1618.40 ? 
 
 349.21 3725.41 2.18 1920.41 ? 
 
 2975.47 7286.95 7.96 10.20 ? 
 
 27.14 8276.92 14.21 41.64 ? 
 
 9218.49 7271.44 1240.80 126.18 ? 
 
 5.17 8926.95 7216.80 24.17 ? 
 
 12627.85 8972.76 4.75 240.20 ? 
 
 721.92 7214.25 8.16 960.80 ? 
 
 11.41 8142.76 .47 1860.45 ? 
 
 1.21 8136.14 .92 9270.54 ? 
 
 .72 8435.96 9.26 75.86 ? 
 
 14178.21 7926.14 1490.75 45.95 ? 
 
 2172.14 9214.72 1860.54 75.86 ? 
 
 726.95 1241.16 9265.80 72.18 ? 
 
 85.21 4214.71 625.50 9260.14 ? 
 
 75.92 8726.19 240.75 1.20 ? 
 
 72604.25 2140.12 60.50 7.40 ? 
 
 124.61 7146.14 120.41 8.32 ? 
 
 2114.62 7214.86 4101.08 2860.14 
 
 7. Find the sum of twenty-one hundred sixty-five and one 
 hundred sixty-five ten-thousandths, thirty-nine' and twelve 
 hundred sixty-five millionths, twenty-seven hundred thirty- 
 six and one millionth, four and six tenths, six hundred and 
 six thousandths, and six hundred sixty-five thousandths. 
 
90 PRACTICAL BUSINESS ARITHMETIC 
 
 SUBTRACTION 
 
 ORAL EXERCISE 
 
 1. From the sum of 0.7 and 0.4 take 0.5. 
 
 2. From the sum of 0.07 and 0.21 take 0.006. 
 
 3. From seventy-four hundredth 8 take six thousandths. 
 
 4. To the difference between .43 and .03 add the sum of 
 .45 and .007. 
 
 5. Goods on hand at the beginning of a week, $24.50; 
 goods purchased during the week, $35.50; goods sold during 
 the week, $36 ; goods on hand at the close of the week, $36.50. 
 What was the gain or loss for the week ? 
 
 134. Example. From 14.27 take 5.123. 
 
 SOLUTION. Write the numbers so that the decimal points stand 14. 27 
 in the same vertical column. The minuend has not as many places 5 
 
 as the subtrahend ; hence suppose decimal orders to be annexed 
 until the right-hand figure is of the same order, then subtract as 
 in integers and place the decimal point in the remainder directly under the 
 decimal points in the numbers subtracted. 
 
 WRITTEN EXERCISE 
 
 Find the difference betiveen: 
 
 1. 7.2154 and 2.8576. 5. 9 and 5.2675. 
 
 2. 17.2157 and 1.0002. 6. 16 and 5.0000271. 
 
 3. 1.0005 and .889755. 7. .0002 and .000004. 
 
 4. $1265.45 and $87.99. 8. 24.503 and 17.00021. 
 9. The sum of two numbers is 166.214. If one of the 
 
 numbers is 40.21, what is the difference between the numbers? 
 
 10. The minuend is 127.006 and the remainder 15.494. 
 What is the sum of the minuend, subtrahend, and remainder? 
 
 11. From the sum of ninety-nine ten-thousandths, one hun- 
 dred fifty-one and five thousandths, two hundred fifty-two and 
 twenty-five millionths, six tenths, and eighteen and one hun- 
 dred seventy-five thousandths take the sum of twelve hundred 
 fifteen millionths, and one hundred eighty-eight thousandths. 
 
 
DECIMAL FRACTIONS 91 
 
 12. From the sum of two hundred fifty-seven thousandths 
 and eight and one hundred twenty-six millionths take the sum 
 of five hundred ten thousandths and two and one hundred 
 twenty-four ten-thousandths. 
 
 13. A merchant had, at the beginning of a year, goods 
 amounting to $ 8165. 95. During the year his purchases 
 amounted to 15265.90 and his sales to $9157.65. At the close 
 of the year he took an account of stock and found that the 
 goods on hand were worth $7216.56. What was his gain or 
 loss for the year? 
 
 14. A provision dealer had on hand Jan. 1, goods worth 
 $4127.60. His purchases for the year amounted to $4165.95 
 and his sales to $6256.48. Dec. 31 of the same year his in- 
 ventory showed that the goods on hand were worth $3972.50. 
 If the amount paid for freight on the goods bought amounted 
 to $237.50, what was his gain or loss on provisions? 
 
 15. I had on hand Jan. 1, lumber amounting to $4210.60. 
 During the year my purchases amounted to $3126.50, and my 
 sales to $4165.85. I lost by fire lumber valued at $506.75, for 
 which I received from an insurance company $500. Dec. 
 31, my inventory showed the lumber to be worth $5209.08. 
 How much did I gain or lose on lumber during the year? 
 
 16. At the beginning of a year my resources were as follows: 
 cash on hand, $1262.50; goods in stock, $1742.85; account 
 against A. M. Eaton, $146.50. At the same time my liabili- 
 ties were as follows: note outstanding, $156.85; account in 
 favor of Robert Wilson, $521.22. During the year I made an 
 additional investment of $1250.65, and withdrew for private 
 use $275. I sold for cash during the year goods amounting to 
 $1250.75, and bought for cash goods amounting to $530.90 ; I 
 also paid Robert Wilson $320 to apply on account. At the 
 close of the year my inventory showed goods in stock valued at 
 $750.48. What was my gain or loss for the year and my pres- 
 ent worth at the close of the year ? 
 
 Do not fail to check all problems. No phase of arithmetic is more 
 important. 
 
92 PRACTICAL BUSINESS ARITHMETIC 
 
 MULTIPLICATION 
 
 ORAL EXERCISE 
 
 1. How many times .4 is 4? .77 is 7.7? .999 is 9.99? 
 
 2. 44 is how many times .44? 22 is how many times .022? 
 1 is how many times .001 ? .01 is how many times .0001 ? 
 
 3. Read aloud the following, supplying the missing terms : 
 Removing the decimal point one place to the right multi- 
 plies the value of the decimal by - - ; two places, the 
 value by ; three places, - - the value by - . 
 
 4. Multiply 12.1252 by 1000 ; by 100 ; by 100,000. 
 
 5. Multiply $9.375 by 100; by 10,000 ; by 100,000. 
 
 6. Multiply 5. 15 by 10; by 100 ; by 1000 ; by 10,000. 
 
 7. Multiply .000016 by 1000; by 100,000 ; by 1,000,000. 
 
 8. Multiply $67.50 by 10 ; by 100 ; by 1000 ; by 10,000. 
 
 9. Multiply .0037 by 10; by 100; by 1000; by 10,000,000. 
 
 10. What part of 1 is .1 ? of 7 is .7? of 29 is 2.9? 
 
 11. What part of 84 is .84? of 129 is 1.29? of 1275 is 12.75? 
 
 12. What part of .6 is .006? of .64 is .0064? 
 
 Read aloud the following, supplying the missing terms : 
 
 a. Each removal of the decimal point one place to the left 
 the value of the decimal by 10. 
 
 b. To divide a decimal by is to find one tenth (.1) of 
 
 it, or to it by .1. 
 
 13. Give a short method for multiplying a number by .1 ; by 
 .01; by .001; by .0001. 
 
 14. Multiply .009 by .1; by .01; by .001. 
 
 15. Multiply 217.59 by .1; by .01 ; by .001. 
 
 16. Multiply 54.65 by .01; by .00001; by .000001. 
 
 17. Multiply 2.375 by .1; by .01; by .001 ; by .0001. 
 
 18. Multiply 25.215 by .1; by .01; by .001; by .0001. 
 
 19. Multiply 2111 by .01 ; by .001 ; by .0001 ; by .00001. 
 
 20. Compare 2400 x $0.06 with 100x24x80.06 or with 
 24x$6. 
 
 21. Compare 3000 x 612.251 with 1000 x 3 x 612.251, or with 
 3 x 612251. 
 
DECIMAL FRACTIONS 93 
 
 22. Multiply 21.25 by 2400. 
 
 SOLUTION. 2400 is 24 times 100. Multiply by 100 2125 2125 
 
 by removing the decimal point two places to the right. cy\ 04 
 
 The result is 2125. 24 times 2125 equals 51,000, the - - 
 required product. 
 
 In multiplying begin with either the lowest or the 4250 8500 
 
 highest digit in the multiplier as shown in the margin. 51000 51000 
 
 23. Formulate a brief rule for multiplying a decimal by any 
 number of 10's, 100's, 1000's, etc. 
 
 24. Find the cost of : 
 
 a. 500 Ib. at 18 d. 600 Ib. at 29^. g. 900 Ib. at 34^. 
 
 b. 15011). at 14 e. 300 Ib. at 41^. h. 700 Ib. at 51 
 <?. 200 Ib. at 26^. /. 400 Ib. at 12^. i. 1400 Ib. at 5 
 
 135. Examples, i. Multiply 41.127 by 4. 
 
 SOLUTION. 41.127 is equal to 41,127 thousandths. 41,127 thou- 41.127 
 sandths multiplied by 4 equals 161,508 thousandths, or 164.508. That 4 
 
 is, thousandths multiplied by a whole number must equal thousandths. 1(54.508 
 
 2. Multiply 41.127 by .04. 
 
 SOLUTION. The multiplier, .04, is equal to 4 times .01 ; therefore, 41.127 
 
 multiply by 4 and by .01. Multiplying by 4, as in problem 1, the Q^ 
 
 result is 164.508. Multiplying by .01, by simply moving the decimal ' 
 
 point in the product two places to the left, the result is 1.64508. l-^oUc 
 
 It will be seen that the number of decimal places in the product 
 is equal to the decimal places in the multiplicand and multiplier. 
 
 It should not be necessary to memorize the above rule. The student 
 should know at a glance that the product of tenths and tenths is hundredths, 
 of tenths and huudredths is thousandths, and so on. 
 
 ORAL EXERCISE 
 
 1. In multiplying 24.05 by 3.14 can you tell before multiply- 
 ing how many integral places there will be in the product ? 
 how many decimal places ? Explain. 
 
 2. How many integral places will there be in each of the fol- 
 lowing products : 2.5x4.015? 27.51x3.1416? 321.1 x 
 201.51? 1.421x42.267? 126.5 x .01? 1020x5.01? .105x6? 
 2.41 x 10.05 ? How many decimal places will there be in each 
 of the above products ? 
 
94 
 
 PEACTICAL BUSINESS AEITHMETIC 
 
 3. What are 400 bbl. of apples worth at $2.12 per barrel? 
 at fl. 27-|- per barrel? 
 
 4. I bought 60 Ib. of sugar at $0.04J and gave in payment a 
 five-dollar bill. How much change should I receive? 
 
 5. A and B are partners in a manufacturing business, A re- 
 ceiving 52 % and B 48 % of the yearly profits. The profits for 
 a certain year are $5000. Of this sum how much should A and 
 B, respectively, receive ? 
 
 7. 2.531x31000. 
 
 8. .1724x18000. 
 
 9. .15539 x 2002. 
 
 WRITTEN EXERCISES 
 
 Find the product of: 
 
 1. 3.121 x 152. 4. 12.14 x 265. 
 
 2. 3121 x .152. 5. 9.004 x .021. 
 
 3. 31.21 x 15.2. 6. .3121 x .0152. 
 
 10. A man owned 75% of a gold mine and sold 50% of his 
 share. What is the remainder worth if the value of the whole 
 mine is $425,000? 
 
 11. A man bought a farm of 240 A. at $137.50 per acre. 
 He sold 75% of it at $150 per acre, and the remainder at $175 
 per acre. What was his gain ? 
 
 12. Copy and complete the following table of statistics. 
 Check the results. (The total yield multiplied by the price 
 per bushel should equal the total valuation.) 
 
 LARGEST WHEAT-GROWING STATES IN A RECENT YEAR 
 
 STATE 
 
 YIELD IN BUSHELS 
 
 FARM PRICK 
 i'EK BUSHEL 
 
 FARM VALUATION 
 
 Minnesota 
 Kansas 
 North Dakota 
 South Dakota 
 
 68,344,256 
 65,019,471 
 53,892,193 
 31,556,784 
 
 92.4^ 
 92.4^ 
 92.4^ 
 92. 4 J* 
 
 
 Total 
 
 
 
 
 13-15. Make and solve three self-checking problems in multi- 
 plication of decimals. 
 
DECIMAL FRACTIONS 95 
 
 DIVISION 
 
 ORAL EXERCISE 
 
 1. Divide by 8 : 64 ft., .64, .064, 6.4. 
 
 2. Divide by 9 : 63 in., .63, .063, 6.3. 
 
 3. Divide by 16: $640, -16.40, 6.4, .64, .064. 
 
 4. Divide by 15: $15.75, $7.50, $0.75, 30.45, 3.045, .3045. 
 
 5. Divide 337.5 by 45. 
 
 7.5 
 45)337.5 
 
 315 = 45 times 7 
 22.5 undivided 
 22.5 =45 times .5 
 CHECK. 45 times 7.5 = 337.5 ; hence, the work is probably correct. 
 
 136. In the above exercise it is clear that when the divisor is 
 an integer, each quotient figure is of the same order of units as the 
 right-hand figure of the partial dividend used to obtain it. 
 
 ORAL EXERCISE 
 
 1. 500 is how many times 50? $75 is how many times 
 $7.50? 
 
 2. Divide 50 by 5 ; 500 by 50. How do the quotients 
 compare ? 
 
 3. Divide 7.50 by 15 ; $75 by 150. How do the quotients 
 compare ? 
 
 4. 720 is how many times 72 ? 9 is how many times .9? 
 
 5. Divide 720 by 9; 72 by .9; 7.2 by .09; .72 by .009. 
 
 137. It has been seen that multiplying both dividend and 
 divisor by the same number does not change the quotient. 
 
 138. Therefore, to divide decimals when the divisor is not an 
 integer : 
 
 Multiply both dividend and divisor by the power of 10 that 
 shall make the divisor an integer, and divide as in United States 
 money. 
 
96 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 139. Divide 0.3375 by 0.45. 
 
 .3375 -r- .45 = 33.75 -H 45. 33.75 + 45 = .7, with a remainder of . 75 
 
 2.25. 2.25 -T- 45 = .05. The quotient is therefore .75. 45')8d 'J " 
 
 Observe that /ie divisor may always be made an integer if the 01 "r 
 
 decimal point in the dividend is carried to the right as many places 
 
 as there are decimal places in the divisor. 
 
 Should there be a remainder after using all the decimal ^ ^5 
 
 places in the dividend, annex decimal ciphers and continue the division 
 as far as is desired. 
 
 ORAL EXERCISE 
 
 Divide : 
 
 
 1. 
 
 1 by 1. 
 
 2. 
 
 1 by .1. 
 
 3. 
 
 1 by 10. 
 
 4. 
 
 .1 by .1. 
 
 5. 
 
 1 by .01. 
 
 6. 
 
 1 by 100. 
 
 7. 
 
 1 by .001. 
 
 8. 
 
 .10 by .10. 
 
 9. 
 
 .01 b} .01. 
 
 10. 
 
 1 by 1000. 
 
 11. 
 
 1 by .0001. 
 
 12. 
 
 1 by 10,000. 
 
 13. 
 
 1 by .00001. 
 
 14. 
 
 .001 by .001. 
 
 15. 
 
 1 by 100,000. 
 
 16. 
 
 1 by .000001. 
 
 17. 
 
 .0001 by .0001. 
 
 18. 
 
 .00001 by .00001. 
 
 19. 
 20. 
 21. 
 22. 
 23. 
 24. 
 25. 
 26. 
 27. 
 28. 
 29. 
 30. 
 31. 
 32 
 33. 
 34. 
 35. 
 36. 
 
 WRITTEN EXERCISE 
 
 Divide : 
 
 1. 5842 by .046. 6. 2200 by .44. 
 
 2. 2.592 by .108. 7. 231.6 by 579. 
 
 3. 1.750 by 8750. 8. 950 by 19,000. 
 
 33 by .11. 
 33 by 110. 
 .33 by .11. 
 3.3 by 1.1. 
 .0001 by 1. 
 33 by .011. 
 33 by 1100. 
 .0001 by .1. 
 3300 by .11. 
 330 by .011. 
 33 by .0011. 
 33 by 11000. 
 .0001 by .01. 
 .033 by .011. 
 .0001 by .001. 
 .0033 by .0011. 
 .0001 by .0001. 
 .0001 by .00001, 
 
 11. 16 by .0064. 
 
 12. 1.86 by 31,000. 
 
 13. 1600 by 64,000. 
 
 4. .00338 by .013. 9. 81.972 by .00009. 14. .0004 by 20,000. 
 
 5. 1.728 by. 0024. 10. 115.814 by .00079. 15. 100 by .000001. 
 
DECIMAL FRACTIONS 
 
 97 
 
 Find the sum of the quotients : 
 
 16. 
 
 8.1 -h.9. 
 81 -S-.09. 
 8.1 -.09. 
 .81-900. 
 .0081-9. 
 8.1 -=-900. 
 810 -.009. 
 . 0081 -r- 9000. 
 81000 -.009. 
 81 -.000009. 
 8100-90000. 
 .00081-5-90000. 
 
 19. 
 
 8.8-2.2. 
 .88 -i- .22. 
 
 88 -.0022. 
 
 8.8-2200. 
 880 -=-2200. 
 8.8-2.200. 
 880 -.2200. 
 8800 -f- 2200. 
 880 + 22000. 
 880^.00022. 
 88000 -.0022. 
 88000 -.00022. 
 
 17. 
 
 72-8. 
 72+. 8. 
 7.2 + . 8. 
 
 72 -.08. 
 .72 -.08. 
 72 -.008. 
 72 - 8000. 
 72 -.0008. 
 .072 -.008. 
 72 -.00008. 
 .0072 -.0008. 
 .00072 -.00008. 
 
 20. 
 
 17 + 68. 
 1.7 + 6.8. 
 
 .17-?-. 68. 
 1.7 + 680. 
 
 170 - 680. 
 .017 -.068. 
 1.7-68000. 
 1700-6800. 
 1700 - 68000. 
 .0017 -=-.0068. 
 . 00017 H-. 00068. 
 .000017-^.000068. 
 
 18. 
 
 125 - 250. 
 12.5-2.5. 
 1.25 + 2.5. 
 12.5-250. 
 125 + 2500. 
 .125 -.025. 
 12500 -.25. 
 125 - 25000. 
 12500 -.025. 
 125 + 250000. 
 .125 + .00025. 
 12500 -=- .0025. 
 
 21. 
 
 36 -.072. 
 3.6 -.072. 
 .36 + .072. 
 360 -.072. 
 .036 -.072. 
 3.6-72000. 
 36 -=- 720000. 
 360 -.00072. 
 3600 -.0072. 
 .0036 -=-.0072. 
 3.6 -.000072. 
 . 00036 -T-. 00072, 
 
 22. The product of two numbers is 0.00025. If one of the 
 numbers is 0.0025, what is the other? 
 
 23. A retailer bought 450 yd. of cloth for $1237.50 and 
 sold it at $3.25 per yard. How much did he gain per yard? 
 
 24. A drover bought a flock of sheep at the rate of $3.30 
 per head. He sold them at a profit of $0.20 per head and 
 received $700. How many sheep were there in the flock 
 and what was his gain ? 
 
98 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 25. Copy and complete the following table. Check the 
 results. 
 
 LARGEST OAT-GROWING STATES IN A RECENT YEAR 
 
 STATE 
 
 YIELD IN BUSHELS 
 
 FARM PKK.-B 
 PER BUSHEL 
 
 FARM VALUATION 
 
 Illinois 
 Iowa 
 Wisconsin 
 Minnesota 
 
 
 31 t 
 31 f 
 31? 
 
 31? 
 
 36,376,005 
 37,920,192 
 26,887,699 
 26,405,335 
 
 12 
 00 
 
 65 
 93 
 
 Total 
 
 
 
 
 
 26-28. Make and solve three self-checking problems in 
 division of decimals. 
 
 DIVIDING BY POWERS AND MULTIPLES OF TEN 
 
 ORAL EXERCISE 
 
 1. 6.4 is what part of 64? $0.17 is what part of $1.70? 
 
 2. Compare (as in problem 1) $240.60 with $24,060; 17.75 
 ft. with 1775 ft. 
 
 3. Compare (as in problem 1) .1 with 1; .01 with 1; .001 
 with 1 ; .0001 with 1. 
 
 4. Read aloud the following, supplying the missing terms : 
 Removing the decimal - place to the - divides the 
 value of the decimal by 10 ; two places, - the value of the 
 decimal by - ; three places, - the value of the decimal 
 
 by - . ' 
 
 5. Compare the quotient of 28 -4- .7 with the quotient of 
 
 .7 with the quotient of 
 
 .7 x 10 ; the quotient of 28 
 
 28 x 10 
 280-7. 
 
 6. Compare the quotient of 16.4 40 with the quotient of 
 16.4 + 10 -r-40-v-lO; the quotient of 16.4 40 with the quotient 
 of 1.64 -r- 4. What is the quotient of 56.77 divided by 7000? 
 
 SOLUTION. Removing the decimal point three places to the nnctl 
 
 left and dropping the ciphers of the divisor is equivalent to dividing 
 both dividend and divisor by 1000 and does not change the value 0* 05677 
 of the quotient. 
 
DECIMAL FRACTIONS 99 
 
 BUYING AND SELLING BY THE HUNDRED 
 ORAL EXERCISE 
 
 1. Compare 460 -4- 100 x $2 with 4.60 x 12. 
 
 2. Find the cost of 450 Ib. of guano at $ 4 per cwt. 
 
 3. Find the cost of 600 Ib. of wire nails at 34^ per cwt. 
 
 4. Find the cost of 4950 paving stones at 1 8 per C. 
 
 SOLUTION. C stands for 100. 4950 paving stones are 49.5 times 
 100 paving stones. Since 1 hundred paving stones cost $8, 49.5 
 hundred paving stones will cost 49.5 times $8, or $396. . 396.0 
 
 WRITTEN EXERCISE 
 Find the cost : 
 
 
 PRICE PER 
 
 
 PRICE PER 
 
 QUANTITY 
 
 HUNDREDWEIGHT 
 
 QUANTITY 
 
 HUNDREDWEIGHT 
 
 i. 450 Ib. 
 
 55? 
 
 5. 1600 Ib. 
 
 71/f 
 
 2. 510 Ib. 
 
 77^ 
 
 6. 2600 Ib. 
 
 15? 
 
 3. 640 Ib. 
 
 60? 
 
 7. 4900 Ib. 
 
 70? 
 
 4. 330 Ib. 
 
 56^ 
 
 8. 3100 Ib. 
 
 88? 
 
 BUYING AND SELLING BY THE THOUSAND 
 
 ORAL EXERCISE 
 
 1. Compare 3500 -+- 1000 x 19 with 3.500 x 19. 
 
 2. Compare 12200 -*- 1000 x 15 with 12.2 x $5. 
 
 3. Find the cost of 7150 feet of lumber at $11 per M. 
 
 SOLUTION. M stands for thousand. 7150 feet are 7.15 times llu 
 
 1000 feet. Since 1 thousand feet of lumber cost $11, 7.15 thousand 11 
 
 feet will cost 7.15 times 11, or $78.65. 78765 
 
 Find the cost of: 
 
 4. 8500 tiles at $8 per M ; at $9 per M. 
 
 5. 4500 bricks at $6 per M ; at $7 per M. 
 
 6. 7500 shingles at $12 per M ; at $14 per M. 
 
 7. 3200 ft. lumber at $14 per M ; at $12 per M. 
 
 8. 15,OQO ft. lumber at $11 per M ; at $12 per M. 
 
 9. 12,000 ft. lumber at $16 per M ; at $15 per M. 
 
100 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. Find the cost of 17,500 shingles at $4 per M. 
 
 2. What is the cost of 2700 envelopes at $2.25 per M ? 
 
 3. Find the cost of 27,560 feet of oak lumber at $21 per M. 
 
 4. Find the total cost of : 
 
 275 Ib. nails at $3.50 per cwt. 
 750 Ib. wire at $3.75 per cwt. 
 750 Ib. guano at $4.75 per cwt. 
 
 125 bolts at 12.75 per C. 
 750 bolts at $3.50 per C. 
 450 fence posts at $6 per C. 
 
 5. Find the total cost of : 
 7600 shingles at $4 per M. 
 14,400 ft. plank at $9 per M. 
 24,560 bricks at $3.50 per M. 
 
 6. Find the total cost of : 
 760 Ib. bran at $.60 per cwt. 
 5875 Ib. bran at $.70 per cwt. 
 
 9000 tiles at $9.375 per M. 
 2320 ft. lumber at $23 per M. 
 1,270,500 bricks at $6.75 per M. 
 
 4275 Ib. meal at $1.10 per cwt. 
 5600 Ib. feed at $1.10 per cwt. 
 5970 Ib. meal at $1.12 per cwt. 500 Ib. oatmeal at $2.50 per cwt. 
 
 7. Find the total freight on : 
 8000 Ib. oil at 100 per cwt. 
 1500 Ib. fish at 58^ per cwt. 
 
 5100 Ib. salt at 73^ per cwt. 
 
 4950 Ib. ale at 52^ per cwt. 
 9900 Ib. beef at 72^ per cwt. 
 4950 Ib. pork at 57^ per cwt. 
 
 8. Find the amount of the following bill : 
 
 SBangor, 
 
 1Q 
 
 , & id 'rid f e & Qo. 
 
 .Tg/vw.g \5~ / a-f^ 
 
 
 / 2. frt rt 
 
DECIMAL FRACTIONS 
 
 101 
 
 140. The accompanying illustration shows the three dials of 
 a gas meter. Each division on the dial 
 at the right denotes 100 cu. ft. of gas 
 consumed ; each division on the center 
 dial 1000 cu. ft. ; and each division on 
 the dial at the left 10,000 cu. ft. The 
 dials are read from left to right by simply 
 taking the figures which the hands have 
 just passed and adding two ciphers to them. 
 
 Thus, the above dial registers 20,000 cu. ft. + 5000 cu. ft. + 700 cu. ft. 
 = 25,700 cu. ft. ; but it is only necessary to write 257 (2, 5, 7) and add 
 two ciphers to get this result. 
 
 WRITTEN EXERCISE 
 
 1. Read the accompanying meters and find the cost of the gas 
 consumed during the period Jan. 1 to Feb. 1 
 
 at 11.20 per 1000 cu. ft. 
 
 2. The following is the number of cubic 
 feet of gas used in a residence for the six 
 months ending July 1 : January, 2900 ; 
 February, 3200 ; March, 3700 ; April, 2900 ; 
 May, 2700; June, 1200. Find the total gas 
 bill for the six months at $0.90 per 1000 
 cu. ft. 
 
 3. Assuming that gas is worth 80.95 per 1000 cu. ft., find 
 the amount of the following bill, less 
 
 Feb. 1, 1906 
 
 To THE BOSTON GAS AND ELECTRIC LIGHT Co., Dr. 
 
 For Gas supplied by meter 
 
 7-2-/QQ cu. ft. as shown by Meter Dial 
 / /*(* 00 cu. ft. as shown by Meter Dial 
 TOO cu. ft. at $1 .00 per 1 000 cu. ft. 
 
 Discount of 10% allowed if 
 paid on or before 
 
102 PRACTICAL BUSINESS ARITHMETIC 
 
 BUYING AND SELLING BY THE TON OF 2000 POUNDS 
 
 ORAL EXERCISE 
 
 1. Compare 8000 -H 2000 x 8 with 8000 -f- 1000 x 4. 
 
 2. Compare 7000 -=- 2000 x 18 with 7x9. 
 
 3. Find the cost of 4250 Ib. coal at 1 8 per ton. 
 
 SOLUTION. 4250 Ib. is 4.25 times 1000 Ib. If the cost of 2 thou- 4.25 
 sand pounds is $8, the cost of 1 thousand pounds is .$4. Since 1 
 thousand pounds of coal cost $4, 4.25 thousand pounds will cost 4.25 
 times $4, or $17. 17.00 
 
 WRITTEN EXERCISE 
 
 1. At $9 per ton, find the cost of the hay in the following 
 weigh ticket. Also find the cost at 18.75 per ton. 
 
 SCALES OF E. H. ROBINSON & CO. 
 
 No.^L22 Clyde, N.Y.. 
 
 Load of 
 
 From C^-ts^?lL~ To 
 
 Gross weight /^ ^ / V Ib. 
 
 Tare / <T & Ib. 
 
 Net weight .2-&^4~0 * Ib. 
 
 Weigher 
 
 2. At 87.50 per ton find the cost of the coal in the fol- 
 lowing weigh ticket. Also find the cost at $6.95 per ton. 
 
 WELLINGTON -WILD COAL CO. 
 
 726 Main S/rce/. Rochester, N.Y. 
 
 No.: 
 
 l^fs? If, 
 
 TVyiimfar S/fy^e?^?^?^-. KeceiW fy C. '. .7)1 . 1?Y>^. 
 
DECIMAL FRACTIONS 
 
 103 
 
 of 
 
 3. What will 8650 Ib. of hay cost at 112 per ton? 
 
 4. Find the cost of 2150 Ib. of coal at 1 6 per ton. 
 
 5. At $32 per ton, what is the cost of 26,480 Ib. 
 phosphate ? 
 
 6. Find the cost of 54,260 pounds of coal at $5.80 per ton. 
 
 7. Find the cost of 12 loads of coal weighing 4100, 3900, 
 4306, 4100, 4060, 4300, 3286, 3980, 3850, 4130, 3700, 3950 Ib. 
 net, at $5.20 per ton. 
 
 8. Find the total cost of : 5265 Ib. hard coal at $8.40 per ton ; 
 12,200 Ib. soft coal at $3 per ton; 8275 Ib. cannel coal at $11. 75 
 per ton; 34,160 Ib. egg coal at $6.20 per ton; 12,275 Ib. nut 
 coal at $5.75 per ton; 8753 Ib. grate coal at $5.80 per ton; 
 24,160 Ib. stove coal at $6.50 per ton. 
 
 9. During the month of January, in a recent year, there were 
 consumed in a manufacturing plant 72 loads of coal weighing as 
 follows: 6100, 6500, 6700, 6840, 7210, 6680, 7250, 8400, 
 6100, 6100, 6250, 6380, 6480, 6300, 6500, 
 
 6410, 6570, 6480, 6240, 6370, 6430, 6480, 
 
 7620, 7240, 7110, 7220, 7420, 7480, 6390, 
 
 6900, 6270, 6280, 6290, 6270, 6390, 6420, 
 
 6300, 6120, 6430, 6430, 8100, 6100, 6200, 
 
 6170, 6240, 6390, 6140, 6240, 7190, 7240, 7140, 7200, 6340, 
 
 8420, 6310, 7420, 6120 Ib. net. Find the cost at $5.87^ 
 
 per ton. 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Of what number is 25.56 both the divisor and quotient? 
 
 2. The sum of the divisor and quotient is 414.06. If the 
 divisor is .6, what is the dividend? 
 
 3. In what time will 3 boys at $ .75 per day earn as much 
 as 2 men earn in 75 da. at $2.25 per day? 
 
 4. A merchant sold a quantity of flour for $370 and realized 
 a gain of $34. If the selling price was $7.40 per barrel, what 
 was the cost per barrel? 
 
 6410, 6370, 
 7400, 7580, 
 
 6160, 
 
 6300, 
 
 6100, 6250, 6250, 
 
 6120, 6120, 6200, 
 
 6310, 6204, 6160, 
 
104 PRACTICAL BUSINESS ARITHMETIC 
 
 5. What number is that which is 165 times as great as 
 82.5? 
 
 6. If 450 bbl. of beef sold for 85872.50, what was the 
 selling price per hundred barrels? 
 
 7. What will be the cost, at 15^ per yard, of a paper border 
 for a room 8 yd. wide and 12 yd. long? 
 
 8. If .25 be added to a certain number, 15 may be sub- 
 tracted from it 75 times. What is the number? 
 
 9. Wood costing $3.50 per cord is sold for $4.10 per cord. 
 How many cords must be handled to gain $240? 
 
 10. Find the cost of 8 bbl. of pork weighing 280, 281, 286, 
 290, 285, 277, 285, and 290 Ib. net, at $8.50 per hundred 
 pounds. 
 
 11. A flock of 200 sheep was bought for $700. 10 of the 
 sheep died, and the remainder of the flock was sold at $3.95 per 
 head. What was the gain or loss ? 
 
 12. A hardware merchant had .5 of his capital invested in 
 hardware stock, .25 of it invested in government bonds, and the 
 remainder, $4896.25, on deposit in City National Bank. What 
 was his entire capital ? 
 
 13. A, B, and C bought a stock of goods for $7500, A con- 
 tributing $2500, B $3000, and C the remainder. They sold the 
 goods for $8400 and divided the profits equally. How much 
 of the $8400 should A, B, and C, respectively, receive? 
 
 14. A, B, and C unite in forming a manufacturing estab- 
 lishment. A invests .4 of the entire money put into the 
 business; B, .3; C, the remainder, $4500. What was the 
 total amount invested, and what was A's and B's investment, 
 respectively ? 
 
 15. A fails in business. The excess of his liabilities over 
 resources is $ 7500. It is found that he can pay his creditors 
 but $.25 on the dollar. B is given $750 in payment for the 
 amount owed him. What was the full amount of A's indebted- 
 ness, and how much did he owe B? 
 
DECIMAL FRACTIONS 105 
 
 16. What is the total freight on 12,250 Ib. of hardware at 
 $.65 per hundredweight and 15,670 Ib. of hardware at $.60 
 per hundredweight? 
 
 17. A merchant bought 250 yd. of cloth at $3.50 per yard, 
 and 150 yd. at $4.25. At what average price per yard should 
 the whole be sold to realize an average profit of $1 per yard? 
 
 18. What is the cost of 25 bbl. of sugar containing 312, 304, 
 309, 317, 330, 325, 315, 318, 317, 305, 319, 320, 325, 330, 335, 
 330, 325, 315, 315, 320, 320, 330, 330, 315, 315 Ib. net, at 5f ^ 
 per pound ? 
 
 19. A received $1088 from the sale of his barley crop. If he 
 received $0.85 per bushel for the barley and his farm produced 
 an average of 32 bu. to the acre, how many acres did it take 
 to produce the barley? 
 
 20. A shoe manufacturing pay roll shows that 40 hands are 
 employed at $1.45 per day, 50 hands at $1.40 per day, 10 hands 
 at $3 per day, 40 hands at $2.50 per day, and 5 hands at $8 
 per day. Find the average daily wages. 
 
 21. A hardware merchant found that his stock of goods, 
 Jan. 1, amounted to $34,350.65. During the year he bought 
 goods amounting to $211,165.45, and sold goods amounting to 
 $220,540.45. Dec. 31, he took an account of stock and found 
 that the goods on hand at cost prices were worth $81,275.64. 
 What was his gain or loss for the year? 
 
 22. Without copying the following figures, find (a) the sum 
 of each line, and (5) the sum of each column. Prove the work 
 by adding the line totals and comparing the sum with the sum 
 of the column totals. 
 
 17.035 
 
 18.0135 
 
 186.02 
 
 126.42 
 
 6.009 
 
 8.005 
 
 5.07 
 
 142.004 
 
 .0634 
 
 3.14 
 
 32.972 
 
 18.0981 
 
 165 r 42 
 
 1.7538 
 
 9.314 
 
 126.83 
 
 4.931 
 
 .628 
 
 6.75 
 
 .048 
 
 95.16 
 
 6.815 
 
 .8467 
 
 8.41 
 
 .062 
 
 101.215 
 
 21.214 
 
 21.221 
 
 2.61 
 
 18.f)41 
 
106 PRACTICAL BUSINESS ARITHMETIC 
 
 23. Copy and find the amount of the following bill 
 
 
 of IT* Utt* Upton & Co* 
 
 Ccrms 
 
 2-600 7000 
 
 ^_ /? , . . 
 
 ^J-^L^-g^f^L^y 
 
 24. Find the cost, at 112.75 per ton, of the hay in the follow- 
 ing weigh ticket. Also find the cost at $10.75 per ton. 
 
 SCALES OF E. H. ROBINSON & CO. 
 
 C&de, N.Y.,Z 
 
 From. 
 
 Load of. 
 
 Gross weight. 
 
 Tare. 
 
 Net weight. 
 
 Weigher 
 
 25. Find the cost at $14.75 per ton of six loads of hay, the 
 gross weights and tares of which were as follows : 4920 
 1848, 4810-1850, 5220-1960, 5820-2140, 4980-1920, 
 4910 - 1980 lb. 
 

 
 CHAPTER XI 
 
 FACTORS, DIVISORS, AND MULTIPLES 
 FACTOKS 
 
 ORAL EXERCISE 
 
 1. Name two factors of 63 ; of 88 ; of 144 ; of 128. 
 
 2. What are the factors of 49? of 77? of 35? of 21? 
 
 3. Name three factors of 45 ; of 66 ; of 24 ; of 60 ; of 80. 
 
 4. Name a factor that is common to 35 and 77; 36, 63, and 81. 
 
 5. Name three factors that are common to 30, 60, and 210. 
 
 6. Which of the following numbers have no factors except 
 itself and one ? 11, 27, 15, 37, 49, 62, 73, 81, 23. 
 
 141. An even number is an integer of which two is a factor. 
 An odd number is an integer of which two is not a factor. 
 A prime number is a number that has no integral factor except 
 itself and one. A composite number is a number that has one 
 or more integral factors besides itself and one. 
 
 Numbers are mutually prime when they have no common factor greater 
 than one. 
 
 WRITTEN EXERCISE 
 
 1. Make a list of all the odd numbers from 1 to 100 in- 
 clusive ; of all the prime numbers; of all the even numbers; 
 of all the composite numbers. 
 
 ORAL EXERCISE 
 
 1. Is 2 a factor of 28 ? of 125 ? of 42 ? of 49 ? By what 
 means do you readily determine this ? 
 
 2. Is 5 a factor of 125 ? of 170 ? of 224 ? of 1255 ? of 1056 ? 
 By what means do you readily determine this ? 
 
 3. When is a number divisible by 10? by 3 ? by 9 ? 
 
 107 
 
108 PRACTICAL BUSINESS ARITHMETIC 
 
 TESTS OF DIVISIBILITY OF NUMBERS 
 
 142. A number is divisible by: 
 
 1. Two, when it is even, or when it ends with 0, 2, 4, 6, or 8. 
 
 2. Three, when the sum of its digits is divisible by 3. 
 
 3. Four, when the number expressed by its two right-hand figures is 
 divisible by 4. 
 
 4. Five, when it ends with or 5. 
 
 5. Six, when it is even and the sum of its digits is divisible by 3. 
 
 6. Eight, when the number expressed by the last three right-hand 
 figures is divisible by 8. 
 
 7. Nine, when the sum of its digits is divisible by 9. 
 
 8. Ten, when its right-hand figure is a cipher. 
 
 ORAL EXERCISE 
 
 Name one or more factors of each of the following numbers: 
 
 l. 184. 
 2. 2781. 
 3. 1449. 
 4. 638172. 
 
 5. 6984. 
 6. 2750. 
 7. 8975. 
 8. 71168. 
 
 9. 51625. 
 10. 83870. 
 11. 13599. 
 12. 123125. 
 
 13. 14128. 
 14. 66438. 
 15. 31284. 
 16. 17375. 
 
 FACTORING 
 
 143. Factoring is the process of separating a number into its 
 factors. 
 
 144. Example. Find the prime factors of 780. 
 
 780 
 
 SOLUTION. Since the number ends in a cipher, divide it by the prime 
 factor 5 ; since the resulting quotient is an even number, divide it by 2. 
 Since 78 is an even number, divide it by 2 ; since the sum of the digits 
 in the resulting quotient is divisible by 3, divide by 3. The prime 
 factors are then found to be 5, 2, 2, 3, and 13. 
 
 IT)!, 
 
 TS 
 39 
 
 13 
 
 WRITTEN EXERCISE 
 
 Find the prime factors of: 
 
 1. 112. 4. 786. 7. 968. 10. 408. 13. 2718. 16. 6900. 
 
 2. 126. 5. 392, 8. 689. 11. 650. 14. 3240. 17. 2064. 
 
 3. 288. 6. 315. 9. 1098. 12. 762. 15. 3205. 18. 7400. 
 
FACTOKS, DIVISORS, AND MULTIPLES 109 
 
 CANCELLATION 
 ORAL EXERCISE 
 1. (4 x 15) - (4 x 3) = 15 -f- 3. Why ? 
 
 2. Divide 2x5x7 by 5x2; 8x7x5 by .5x2x7. 
 3 3 x7 x8 = ? 5x2x8x3 = ? 2x9x7x5 9 
 
 7x3 2x8x3 5x7x2x3 
 
 4. What effect on the quotient has rejecting equal factors 
 in both dividend and divisor ? 
 
 145. Cancellation is the process of shortening computations 
 by rejecting or canceling equal factors from both dividend and 
 divisor. 
 
 146. Example. Divide the product of 6, 8, 12, 32, and 84 by 
 the product of 3, 4, 6, and 24. 
 
 222 4 28 
 X > *. *? i? =2x2x2. x4x 28= 896. 
 
 SOLUTION. Do not form the products, but indicate the multiplication by 
 the proper signs and write the divisor below the dividend as shown above. 3, 4, 
 and 6 in the divisor are factors of 6, 8, and 12, respectively, in the dividend ; 
 hence, reject 3, 4, and 6 in the divisor and write 2, 2, and 2, respectively, in the 
 dividend ; then cancel the common factor 8 from 24 in the divisor and 32 in the 
 dividend, retaining the factors 3 and 4, respectively ; next cancel the common 
 factor 3 in the divisor from 84 in the dividend and there remains the uncanceled 
 factors 2, 2, 2, 4, and 28 in the dividend. Hence, the quotient is2x2x2x4 
 X 28, or 896. 
 
 WRITTEN EXERCISE 
 
 l. 14 x 21 x 48 + 7 x 21 x 6 = ? 
 
 2. 128 x 48 x 88 -- 64 x 24 x 4 = ? 
 
 3. Divide 128 x 18 x 36 by 64 x 18 x 12. 
 12 x 16x24x8 x 92x28^ ? 
 
 6 x 8 x 23 x 7 
 
110 PRACTICAL BUSINESS ARITHMETIC 
 
 5. If 18 T. of hay cost $270, what will 25 T. cost at the 
 same rate ? 
 
 6. How many days' work at 82.75 will pay for 2 A. of 
 land at $ 110 per acre? 
 
 7. If 75 bbl. of flour may be made from 375 bu. of wheat, 
 how many bushek will be required to make 120 bbl. of flour ? 
 
 8. If 45 men can complete a certain piece of work in 120 
 da., how many men can complete the same piece of work in 
 30 da.? 
 
 9. The freight on 350 Ib. of evaporated apricots is f 1.47. 
 At that rate how much freight should be paid on 7350 Ib. of 
 evaporated apricots? 
 
 10. If 15 rm. of paper are required to print 400 copies of 
 a book of 300 pp., how many reams will be required to print 
 32,000 copies of a book of 300 pp. ? 
 
 DIVISORS AND MULTIPLES 
 COMMON DIVISORS 
 
 ORAL EXERCISE 
 
 1. Name a factor that is common to 35 and 49. 
 
 2. Name two factors that are common to both 48 and 64. 
 
 3. Name the greatest factor that is common to 75 and 100. 
 
 147. A common divisor is a factor that is common to two or 
 more given numbers. The greatest common divisor (g. c. d.) is 
 the greatest factor that is common to two or more given numbers. 
 
 148. Example. Find the g. c. d. of 24, 84, and 252. 
 
 SOLUTIONS, (a) Separate each of the num- 
 bers into its prime factors. The factor 2 occurs (#) 
 twice in all .the numbers and the factor 3 once 24 =2x2x2x3 
 in all the numbers. None of the other factors 84=2x 9 x3x7 
 occur in all the numbers; hence, 2 x 2 x 3, or 
 
 12, is the greatest common divisor of 24, 84, *52 = 2x2x3x3x7 
 and 252. 
 
FACTORS, DIVISORS, AND MULTIPLES 111 
 
 (?>) The common prime factors of two or more given Sl\ 
 
 numbers may be found by dividing the numbers by their 9^04 _ 04 _ oco 
 
 prime factors successively until the quotients contain no ~c t ~~- - 
 
 common factor, as shown in the margin. 2)L'Z 4L 12o 
 
 Ever since decimal fractions came into quite gen- ^ ^ II - 
 
 eral use the subject of greatest common divisor has ^ ~~ ' ~~ "1 
 
 been stripped of most of its practical value. When fractions like f f ^ were 
 quite generally used, it was necessary to reduce them to their lowest terms 
 before they could be conveniently handled in an operation. For this pur- 
 pose, the greatest common divisor (here 97) was found and canceled from 
 each term, thus greatly simplifying the fraction (here if). Now, however, 
 the greatest common divisor of the terms of the fractions used in business 
 is easily found by inspection, and the need for finding the greatest common 
 divisor is slight. 
 
 ORAL EXERCISE 
 
 1. What is the greatest common divisor of 65 and 75? of 12 
 and 32? of 75 and 125? 
 
 2. What is the greatest common divisor of 12, 30, and 96? 
 of 8, 24, and 42? of 36, 90, and 96? 
 
 3. What divisor should be used in reducing -^fe to its 
 lowest terms? iff? 
 
 WRITTEN EXERCISE 
 
 Find the greatest common divisor of: 
 
 i. 48, 240. 2. 42, 28, 144. 3. 88, 144, 220. 
 
 4. A real estate dealer has four plots of land which he wishes 
 to divide into the largest number of building lots of the same 
 size. If the plots contain 168, 280, 182, and 252 square rods, 
 respectively, how many square rods will there be in each build- 
 ing lot? 
 
 COMMON MULTIPLES 
 
 ORAL EXERCISE 
 
 1. Name a multiple of 7 ; of 9; of 16 ; of 64. 
 
 2. Name two other multiples of each of the above numbers. 
 
 3. Name two multiples that are common to 3 and 4 ; to 5 
 and 9; to 8 and 12. Which of the multiples just named is the 
 least common multiple? 
 
PRACTICAL BUSINESS ARITHMETIC 
 
 149. A common multiple is any integral number of times two 
 or more given numbers. The least common multiple (1. c. m.) 
 of two or more numbers is the least number which is an integral 
 number of times e'ach of the given numbers. 
 
 150. Example. Find the 1. c. m. of 28, 42, and 84. 
 
 SOLUTIONS. () Resolve each of the numbers into (<*) 
 
 its prime factors. The factor 2 occurs twice in 28 and 90 9 v 9 ./ 7 
 
 ^O ^J /\ *^ /\ I 
 
 in 84, the factor 3 occurs once in 42 and 84, the factor 7 4 ~ ~ n 
 
 4 x j x 7 
 occurs once in each of the numbers. Therefore, the 
 
 least common multiple is 2 x 2 x 3 x 7, or 84 ; or 84 =2x2xox7 
 
 (6) Arrange the numbers in a horizontal line and divide 
 by any prime factor that will exactly divide any two of C*) 
 
 them. Divide the numbers in the resulting quotient by any 9) 28 42 84 
 prime factor that will divide any two of them, and so con- o \ -11 9! To 
 
 tinue the operation until quotients are found that are prime ^ 
 
 to each other. Find the product of the several divisors and *') * ^*- 
 
 the last quotients and the result is the I.e. in. 2x2x3x7 7) 7 7 7 
 
 = 84, the 1. c. m. ~J J J 
 
 All numbers that are factors of other given numbers may 
 be disregarded in finding the 1. c. m. Thus the common multiples of 4, 8, 
 16, 32, 64, and 80 are the same as the multiples of 04 and 80. 
 
 ORAL EXERCISE 
 
 State the least common multiple of: 
 
 1. 6, 5, and 3. 4. 2, 4, 7, 8, 48, 24. . 
 
 2. 6, 8, 12, and 24. 5. G, 42, 84, 1(38, 336. 
 
 3. 4, 5, 15, and 30. 6. 5, 15, 75, 150, 300. 
 
 WRITTEN EXERCISE 
 
 Find the least common multiple of: 
 
 1. 6, 7, 8, and 5. 5. 4, 20, 12, and 48. 
 
 2. 6, 18, 24, and 84. 6. 62, 78, 30, and 142. 
 
 3. 12, 24, 36, and 96. 7. 35, 105, 125, and 225. 
 
 4. 32, 46, 92, and 128. 8. 114, 240, 72, and 320. 
 9. What number is that of which 2, 3, 5, and 11 are the 
 
 only prime factors? 
 
CHAPTER XII 
 
 COMMON FRACTIONS 
 ORAL EXERCISE 
 
 1. When a quantity is divided into 3 equal parts, what is 
 each part called? into 8 equal parts? into 12 equal parts? 
 
 2. The shaded part of A is what part of the whole hexagon ? 
 the shaded part of B ? the shaded part 
 
 of C? 
 
 3. In the shaded part of A how 
 many sixths ? in the shaded part of B ? 
 
 4. One half of the hexagon is how many sixths of it ? 
 How many sixths in the whole hexagon? 
 
 5. In the unshaded part of B how many thirds? Two thirds 
 are how many sixths? 
 
 6. In the unshaded part of C how many sixths? 
 
 7. Read the following fractions in the order of their size, 
 the largest first : i, f , f , J, J, |, J. 
 
 8. Complete the following statement : Such parts of a unit 
 as .5, .25, ^, |, etc., are called . 
 
 151. Common fractions are expressed by two numbers, one 
 written above and one below a short horizontal line. 
 
 152. The number written above the line is called the 
 numerator of the fraction, and the number written below, 
 the denominator of the fraction. 
 
 153. The numerator tells the number of parts expressed by 
 the fraction ; the denominator names the parts expressed by 
 the fraction. 
 
 Thus,' in the fraction f , 4 tells that a number has been divided into 
 four equal parts and 3 shows that three of these parts have been taken. 
 
 113 
 
114 PRACTICAL BUSINESS ARITHMETIC 
 
 154. It is clear that the greater the number of equal parts 
 into which a unit is divided, the less is the value of each 
 part ; and the less the number of equal parts into which a 
 unit is divided, the greater the value of each part. Hence, 
 
 Of two fractions having the same denominator, the one having 
 the greater numerator expresses the greater value; and 
 
 Of two fractions having the sime numerator, the one having the 
 smaller denominator expresses the greater value. 
 
 155. The terms of a fraction are the numerator and denomi- 
 nator taken together. 
 
 156. A unit fraction is a fraction whose numerator is one. 
 Thus $, |, , and Jg are unit fractions. J in. is read one third of an inch. 
 
 157. An improper fraction is a fraction whose numerator 
 is equal to or greater than its denominator. 
 
 Thus, f, f, and 2 3 5 - are improper fractions. The value of an improper 
 fraction is always equal to or greater than one. 
 
 158. A mixed number is the sum. of a whole number and 
 a fraction. 
 
 Thus, 2} and 4f, read two and one seventh and four and two ffths, are 
 mixed numbers. 
 
 ORAL EXERCISE 
 
 1. What takes the place of the denominator in .5? in .25? 
 
 2. Read aloud the following fractions in the order of their 
 size, the largest first : J, ^ J, J, J, ^, J, |, ^, fa, T J T . 
 
 3. Read aloud the following fractions in the order of their 
 size, the smallest first: f, f, J, f, 1, f, ^ J, f, f, ^, f 
 
 4. Read aloud the following: | mi.; |T. ; 27| yd.; yy^-g- 
 cu. ft.; 275| A.; 250 & lb.; 18& ; X 271 J ; T J sq. ft. 
 
 5. Of the total cotton produced in the United States in a 
 recent year the principal cotton-growing states contributed 
 approximately as follows : North Carolina, ^ ; South Caro- 
 lina, -j 1 ^ ; Georgia, i ; Florida, T ^Q ; Alabama, ^ ; Mississippi, 
 Y ; Louisiana, -^ ; Texas, ^ ; Arkansas, ^ ; Tennessee, -g 1 ^. 
 Name the principal cotton-growing states, in the order .of pro- 
 duction, for this year. 
 
COMMON FRACTIONS 115 
 
 REDUCTION 
 To HIGHER TERMS 
 
 ORAL EXERCISE 
 
 1. How many halves in 1? how many fourths? how many 
 eighths? how many sixteenths? 
 
 2. How many fourths in J? 
 how many eighths? how many 
 sixteenths ? 
 
 3. How many eighths in | ? how many sixteenths ? 
 
 4. How many fourths in -| ? how many eighths in 1 J ? how 
 many halves in T 8 g ? 
 
 5. What effect is produced upon the value of a fraction by 
 multiplying or dividing both terms of a fraction by the same 
 number ? 
 
 6. Change 14 gal. to quarts. Compare the size of the units 
 in 14 gal. with the size of the units in 56 qt. ; the number of 
 units ; the value of the two numbers. 
 
 7. Change i to twelfths ; J; |; J ; f ; |; |. 
 
 8. Name three fractions equal in value to ; to f ; to |. 
 
 159. It has been seen that multiplying or dividing both terms 
 of a fraction by the same number does not change the value of the 
 fraction. 
 
 160. A fraction is reduced to higher terms when the given 
 numerator and denominator are expressed in larger numbers. 
 
 ORAL EXERCISE 
 
 1. Reduce to twelfths : 1, f , f . 
 
 2. Reduce to sixteenths : |, |, | , $-. 
 
 3. Reduce to twentieths: -|, |, y 3 ^, -|, -|. 
 
 4. Reduce to twenty-fourths : |, f , |, ^ j, J- 
 
 5. Reduce to thirty-seconds: J, f, f, f, fV yg-i ^ yV 
 
 6. Reduce to one-hundredths : |, J, -|, y^, ^*> 2lr ?' 2~s* 
 
 7. Reduce | and f to fractions having the denominator 24. 
 
116 PRACTICAL BUSINESS ARITHMETIC 
 
 To LOWEST TERMS 
 
 ORAL EXERCISE 
 
 1. 2 8 f equals how many thirds? J| equals how many halves? 
 
 2. Name the largest possible unit frac- _ 
 tion. Why is this the largest possible 
 unit fraction ? 
 
 3. Change -f% to the largest possible 
 
 unit fraction ; ^ ; T 2 ^ ; ffa ; J^. Express 1 J in its simplest 
 form. Reduce 2 to ^ ts lowest terms. 
 
 161. A fraction is reduced to its lowest terms when the 
 numerator and denominator are changed to numbers that are 
 mutually prime. 
 
 162. Example. Reduce -ffy to its lowest terms. 
 
 SOLUTION. 6 is a common factor of 96 and 108 ; dividing 
 
 both terms by 6, the result is {f. 2 is a common factor of _JL = 1& 1 
 16 and 18 ; dividing both terms by 2, the result is f . 
 
 ORAL EXERCISE 
 
 1. Reduce to fifteenths: 1, f, f, f. 
 
 2. Reduce to eighths : ^ |, f , if, l|, \. 
 
 3. Reduce to fiftieths: J, jj, ^fr, ^, &, 2^0- 
 
 4. Change to twentieths : |> T 7 ^, , f , |, -^, |. 
 
 5. Reduce to lowest terms : ^ g , T 8 ^, T 8 2, f|, ^ f , 
 
 WRITTEN EXERCISE 
 
 1. Reduce to sixteenths : \^ l|, |, |f, f, lf. 
 
 2. Reduce to lowest terms: f T 2 2 \ cu. ft., ^ A., ^Vo T - 
 
 3. Reduce to lowest terms : Jjffl mi., JJ^, |f|| lb., |f mi. 
 
 4. Reduce to three-hundred-twentieths: | mi., | mi., Jg- m i- 
 
 5. Reduce to their simplest common fractional form : |f f $ T., 
 U T, T % A, lfj A., || sq. mi., llf 8 q. mi., ||f mi. 
 
COMMON FRACTIONS 117 
 
 INTEGERS AND MIXED NUMBERS TO IMPROPER FRACTIONS 
 
 ORAL EXERCISE 
 
 1. How many quarts in 1 gal.? in 3 gal.? 
 
 2. How many sixths in 1? in 3? in 5? in 7? 
 
 3. How many fifths in 1? in 1J? in If? in 3J? 
 
 4. Express as fourths : 61, 12|, 13, 87, 6lj, 28J. 
 
 5. Express as eighths: 15, 12, 10 j, 1J, 2f, If, 9|. 
 
 6. Express as halves: 27, 14,301, 1711, 1821, 249. 
 
 WRITTEN EXERCISE 
 
 Reduce to improper fractions : 
 
 1. 831. 4 . 666|. 7. 265^. 10. 3150J. 
 
 2. 166|. 5. ISO^. 8. 319 T 5 g. 11. 1625J. 
 
 3. 3331. 6. 212^. 9. 146l|. 12 . 2: 
 
 IMPROPER FRACTIONS TO INTEGERS OR MIXED NUMBERS 
 
 ORAL EXERCISE 
 
 1. How many quarters of a dollar in $25? iff- = ? 
 
 2. Change to integers : If a, -ija, l^ 2 -, \ 8 /-, i|J^, l||o. 
 
 3. Express 28 J as fourths ; express -^J 3 - as a mixed number. 
 
 4. Change to mixed numbers: ^-, ^p, if 1 , ^f 1 , ^. 
 
 5. What is the value of: - 2 T ^ 8 - lb.? l* lb.? l|A bu.? ^ p k.? 
 
 ft - ? - 4 w- A - ? Hi mi - ? -2- lb - ? ill S( l- ft - ? 
 
 WRITTEN EXERCISE 
 
 Reduce to integers or mixed numbers: 
 
 1. 13 mi. 4. -Vg^A. 7. 4$* lb. 
 
 2. -V&4A. 5. l|i|T. 8. ffflou. ft. 
 
 3. |i||T. 6. IfffT. 9. J^sq.mi. 
 163. Wlien expressing final results reduce all proper frac- 
 
 tions to their lowest terms and all improper fractions to 
 integers or mixed numbers. 
 
118 PRACTICAL BUSINESS ARITHMETIC 
 
 To LEAST COMMON DENOMINATOR 
 
 ORAL EXERCISE 
 
 1. How many pounds in 1 T. 500 Ib. ? 5 T. + 1000 Ib. = ? Ib. 
 5 T. 1000 Ib. = ?*T. 
 
 2. How must numbers be expressed before they can be 
 added or subtracted? 
 
 4. What kind of fractions can be added or subtracted? 
 
 5. Express | as sixteenths. Add | and -f^ ; J and ^ ; f 
 and J. 
 
 o 
 
 6. Express J as eighths. Subtract J and | ; 1 and T 3 g ; | 
 and Jg. 
 
 164. Two or more fractions whose denominators are the same 
 are said to have a common denominator; if this denominator 
 is the smallest possible, the fractions are said to have a least 
 common denominator. Two or more fractions having the same 
 denominator are sometimes called similar fractions. 
 
 ORAL EXERCISE 
 
 Change to similar fractions : 
 
 1. J, f 6. f 1. 11. f, J. 16. J, |, 1. 
 
 2. J,l. 7. f, |. 12. 1, /g. 17. 1, 1, |. 
 
 3. 1 f 8. 1, f . 13. |, ^_ 18- i i> A- 
 
 4. |, 1. 9. |, . 14. j, T V 19. 1, |, |. 
 
 5 ' !' 1 4 0' 10 ' i f 15 ' 8' 1 T 0- 20 - 2' I' T6- 
 
 WRITTEN EXERCISE 
 Change to fractions having the least common denominator : 
 
 T JL _^5 . i8 ^5j^57 ol521 
 
 8' 32' 64" (P 8 1 12' 112' 12' ^' 3^' 48* 
 
 5' 17' 2^5^* ^' "5' 36' 45* 56' 32' It' 6^' 
 
 <a 1 1 1 1 irlT 917 11 153175 
 
 J ' ' 2' ' ^' 7< 1' 16' 32' 64' "' F20' 4' 160' 8* 
 
 4 ^ -7- 3 2. o _9_ _5 _7_ 1 no -LQ- _6_ J -5- 
 
 Change the fractions to form for addition or subtraction: 
 
 13. 81ft, 7ft. 14. 184ft, 112ft. 15. 6126ft, 178ft. 
 
COMMON FRACTIONS 119 
 
 ADDITION 
 
 165. It has been seen that only like numbers and parts of 
 like units can be added. 
 
 ORAL EXERCISE 
 State the sum of: 
 
 1. }, |, f. 7. 21, 8j, 12}, 19}. 
 
 2. |, f, \. 8. 5J, 12}, 7}, 10}. 
 
 3. }, |, f 9 . 7 |, 2 |, 8}, H, 2i. 
 
 I 2 !' A- iV 10 ' 2 3> 6 I' % 12 i 10 f- 
 
 5- }, i f, f f 11. 1}, 10|, 16}, 18}, 121. 
 
 6 - 7 ' I 2 - 
 
 Ity horizontal addition find the sum of: 
 
 13. 2 pieces of gingham containing 41 1 and 43 2 yd. 
 
 In the dry-goods business fourths (quarters) are very common fractions. 
 They are usually written without denominators by placing the numerators 
 a little above the integers. Thus, 5 1 1 equals 51, 54 2 equals 54| (54|), and 
 52 3 equals 52|. 
 
 14. 4 pc. stripe containing 42 1 , 38 1 , 4C 2 , and 49 yd. 
 
 15. 3 pc. fancy plaid containing 42 1 , 40 2 , and 41 yd. 
 
 16. 4 pc. duck containing 48 1 , 47 3 , 46 2 , and 40 2 yd. 
 
 17. 2 pc. monument cotton containing 54 2 and 55 2 yd. 
 
 18. 4 pc. dress silk containing 32 1 , 34 2 , 35 3 , and 32 2 yd. 
 
 166. Examples, l. Find the sum of J- and |. 
 
 SOLUTION. | and f are not similar fractions ; 1. c. m. of 8 and 5 = 40 
 hence, make them similar by reducing them to 7 _ 35.. 2 _ 16 
 
 equivalent fractions having a least common de- 86 1 51 111 
 
 nominator. | = f s and | = i-. f jj + $% = |i 47 + 47 = 4 = ^ 10" 
 
 = 1H- 
 
 2. Find the sum of 56J, 34J, 52|. 
 
 SOLUTION. By inspection determine the least common 56 = 8 
 
 denominator of the given fractions ; then make the frac- ^41. _ ^ 
 
 tions similar and add them, as shown in the margin. __^ . 
 
 The result is lj\, which added to the sum of the inte- ^ 
 gers equals 143 2 \, the required result. 
 
120 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the sum of: 
 
 i. T V f. 7. 12 f, 172-.V 
 
 2. ,jf 8 - 8 iii 
 
 3. 2i,17i. 9. 52|, 59|, 57 
 
 4. 12}, 19^- 10. 60f, 18}, 21, 142 T V 
 
 5. l,4i,19i. 11. 20i, 121, 181, 921, 75f 
 
 6. 21, 4f,'25 T 9 g. 12. 140|, 260J, 145|, 216 J, 3901. 
 
 13. A carpet dealer sold at different times 125| yd., 272^ 
 yd., 1691 yd., 186| yd., 241| yd., 265| yd., 296J yd., and 
 314| yd. of Axrainster carpet, at $>2.65 per yard. If it cost 
 him $2.45 per yard, what was his -gain? 
 
 14. A dry-goods merchant bought 50 pc. of dress silk at 
 81 per yard. If the pieces contained 42 1 , 43 2 , 44 2 , 47 3 , 44 1 , 45 2 , 
 40 3 , 46 2 , 45i, 42, 47i, 48 2 , 40 3 , 40 1 , 40 2 , 40 3 , 50 2 , 40 3 , 47 2 , 48 3 , 40 3 , 
 45 1 , 40 2 , 45 2 , 44 2 , 47 3 , 46 2 , 41 1 , 51 3 , 42 3 , 53 2 , 57 2 , 53 1 , 51 1 , 48 3 , 47 2 , 
 40 1 , 45 2 , 45 2 , 40 3 , 40 1 , 45 3 , 47 2 , 48 1 , 51 1 , 52 2 , 57 2 , 61 3 , 60 2 , 50i yd., 
 respectively, and he sold the entire purchase at $1.25 per yard, 
 what was his gain? 
 
 SHORT METHODS IN ADDITION 
 
 ORAL EXERCISE 
 
 1. i -|- 1 = 1& Observe that the numerator of the sum is 
 
 / y \> o 
 
 equal to the sum of the denominators in the given fractions. 
 
 2. -1 + 1 = ? Give a short method for adding any two sim- 
 ple fractions whose numerators are 1. 
 
 3. | -j- | = ^. Observe that the numerator of the sum is 
 equal to the sum of the denominators multiplied by the numera- 
 tor of either of the given fractions. 
 
 4. | + != ? Give a short method for adding any two frac- 
 tions whose numerators are alike. 
 
 5. Find the sum of J, |, and 1- 
 
 SOLUTION. ^ -f = T 7 Z ; T 7 2 + 3 = |^, the required result. 
 
COMMON FRACTIONS 121 
 
 ORAL EXERCISE 
 
 State the sum of: 
 
 1. -|, J. 7. |, J. 13. \, 1. 19. |, $. 
 
 2. 1,1- 8. i 1, 14. |,f 20. f, T V 
 
 3. A i. 9. if 15. f, f. 21. 1,1,1 
 
 4. A, f 10. f,|. 16. |,f. 22. |,11. 
 
 5. i f 11. |, f . 17. |, |, 23. 1 f f 
 
 6. -l,f 12. |, f. 18. f, |. 24. f, |,|. 
 
 167. The most common business fractions are usually small 
 and of such a nature that they may be added with equally as 
 much ease as integers. The following exercise will be found 
 helpful to the student in learning to add these fractions in 
 practically the same manner that he adds integers. 
 
 168. Example. Find the sum of T 5 g, |, f , and J. 
 
 SOLUTION. By inspection determine that the least common denominator is 
 16. Then mentally reduce each fraction to IGths and add as in whole numbers. 
 Thus, 5, 7, 19, f|, lii. 
 
 ORAL EXERCISE 
 Find the sum of: 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 
 
 iiii i 2. i a i 
 
 3342463^49 
 
 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 
 
 1421171141 
 3 ~5"~3"1F~8~'5~'3"'3~~5"2 
 
 3. 3. 5 3 1 1 3. 1 1 1 
 
 5 5 6 Y 6 3 4 5 2 5 
 
 t . i I. f :- . r . i ,4 .*.. . it . : i 
 
 i i 4 4 t i -i 4 i i 
 
 2 .7^ 3 3 1 314.3.3. 
 
 3 "10 Y 855 
 
 4 A A * I f I I -4 A 
 
 i i% A f i A i 4 4 A 
 -I A A i e 5 41- A 4 i A 
 
122 PRACTICAL BUSINESS ARITHMETIC 
 
 Exercises similar to the foregoing should be continued until the student 
 can name the successive results in the addition without hesitation. 
 
 169. The ordinary mixed numbers that come to an accountant 
 should be arranged for addition practically the same as in- 
 tegers. In adding, the fractions should be combined first and 
 then the integers. 
 
 170. Example. Find the sum of 2J, 5^, and 3|. 
 
 W 2~ 
 SOLUTION. By inspection determine that the least common denomi- c i 
 
 nator of the fractions is 8. Mentally find the sum of the fractions and * 
 the result is If. Add this result to the integers and the entire sum is 11|. 8 
 
 ORAL EXERCISE 
 
 State the sum of : 
 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 
 
 2J 31 3J 81 14i 5f 41 2J 3| 14-1 
 
 H 25J_7J.17fl8JH16|17J. ^i 
 
 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 
 
 9f 5f 11 If 8J 4| 51 41 41 4|- 
 
 41 2| 6J 3| 21 2f 5| 2f . If 
 
 l 7& 5-J 2 T ij 41 41 6| 6 '7f 
 
 4^ 3| 6J 21 8^ 
 
 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 1 2 92 13 53 91 11 11 91 M 
 
 o a 7" I S" 6^ Q ^ ^5~ 
 
 31 11 1J ?| s| 3J- 7f 2J 9f 4 
 
 4 i !J 2 f 2f 51 3J 3| 7| 41 21 
 
 Exercises similar to the above should be continued until the student can 
 add with great facility. If the principles of grouping have not been well 
 mastered, simple addition should be carefully reviewed. 
 
COMMON FRACTIONS 
 
 123 
 
 WRITTEN EXERCISE 
 
 or write from dictation and find the sum of: 
 
 3. 4. 5. 
 
 
 Copy 
 
 or write, fr 
 
 1. 
 
 2. 
 
 1649J 
 
 1672f 
 
 43721 
 
 1485| 
 
 8431| 
 
 16351 
 
 51321 
 
 12641 
 
 16541 
 
 1269f 
 
 1831f 
 
 17481 
 
 1831| 
 
 1936| 
 
 14621 
 
 54131 
 
 18511 
 
 2114ft 
 
 1114ft 
 
 1116ft 
 
 7. 
 
 8. 
 
 91241 
 
 7249J 
 
 2716J 
 
 2724| 
 
 25141 
 
 86921 
 
 29671 
 
 24761 
 
 2964^ 
 
 86951 
 
 68751 
 
 62141 
 
 8875f 
 
 72411 
 
 26581 
 
 86141 
 
 8425| 
 
 4725^ 
 
 8273| 
 
 1649^ 
 
 1782f 
 
 12861 
 
 86951 
 
 62481 
 
 24721 
 
 1286-1 
 
 62731 
 
 8537f 
 
 9685f 
 
 6982^ 
 
 96851J 
 
 3685-1 
 
 1925-/2 
 
 2614f 
 
 4212ft 
 
 87961 
 
 2729 T L 
 
 1592| 
 
 14361 
 
 1390f 
 
 24151 
 
 18671 
 
 16391 
 
 4136| 
 
 16521 
 
 31161 
 
 1439 T V 
 
 2243ft 
 
 9. 
 
 16491 
 27241 
 86951 
 15651 
 27241 
 86191 
 2924f 
 65291 
 85921 
 27251 
 8647| 
 8725f 
 62191 
 84131 
 7226f 
 18251 
 47251 
 2816f 
 25191 
 
 21101 
 16401 
 36801 
 45901 
 2169f 
 8432| 
 40411 
 6542f 
 1862 
 3246 1 
 
 10. 
 
 75291 
 62141 
 
 62141 
 1745J 
 3146f 
 1864-1 
 
 28391 
 
 4036| 
 
 8130ft 
 
 2148ft 
 
 6. 
 
 12141 
 2167^ 
 31591 
 92751 
 7215f 
 52611 
 7215| 
 5144f 
 6257| 
 
 8614f 
 9215f 
 6719f 
 8516^ 
 7528J 
 7216f 
 67291 
 35141 
 1686f 
 1725J 
 2538f 
 1758| 
 2752-1 
 21141 
 22161 
 18721 
 
 11. 
 
 73651 
 26141 
 15831 
 16951 
 17621 
 1875| 
 16291 
 7214| 
 2510-1 
 2625f 
 86141 
 27291 
 28161 
 28141 
 2716| 
 17621 
 18751 
 26141 
 
 12. 
 
 28141 
 2910J 
 
 27141 
 2913J 
 2874f 
 2619f 
 1472^ 
 
 1813^ 
 19621 
 18621 
 17591 
 2864| 
 1624J 
 17291 
 1805| 
 
 1465f 
 
124 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 SUBTRACTION 
 
 ORAL EXERCISE 
 
 1. 172 A. -154 A. = ? f-j = ? Ibu. -3pk. = ? 
 
 2. Find the difference between | and j- ; J and ^; J and ^; 
 f and f . 
 
 171. It is clear that only like numbers and parts of like units 
 can be subtracted. 
 
 172. Examples, l. Find the difference between J and T 5 ^. 
 SOLUTION. The given fractions must be reduced to equivalent fractions having 
 
 a least common denominator. The least common denominator is 24. = f and 
 fa M- li H = ii tne required result. 
 
 2. From 211 take 17J-. 
 
 SOLUTION. Change the given fractions to similar fractions as in example 1. 
 f cannot be subtracted from , hence 1 is taken from 21 and mentally united 
 to f , making f . f from | leaves f , and 17 from 20 leaves 3. The required result 
 is therefore 3|. 
 
 Find the value of: 
 
 2. 
 3- 
 
 * 
 
 -If 
 
 ORAL EXERCISE 
 5. 4|-lf. 
 
 8. I2J-6J. 
 
 9. 5U- 
 
 10. 45-16-f. 
 
 11. 11| 6f. 
 
 12. 70| - 
 
 The following is a recent clipping from a daily paper. It shows the 
 prices of wheat on the Chicago market. The first line of prices is for wheat 
 to be delivered in July, and the second line for wheat to be delivered in 
 September. 
 
 CHICAGO WHEAT QUOTATIONS 
 
 DELIVERY 
 
 PREVIOUS CLOSING 
 
 Ol'KMNG 
 
 HIGHEST 
 
 LOWEST 
 
 CLOSING 
 
 July 
 September 
 
 87^ 
 
 87^ 
 
 13.- What was the difference between the highest and the 
 lowest price of July wheat ? of September wheat ? 
 
 14. What w r as the difference between the opening and the 
 closing price of September wheat ? of July wheat ? 
 
COMMON FRACTIONS 125 
 
 15. What was the difference between the opening price and 
 the previous closing (yesterday's closing) price of July wheat ? 
 of September wheat ? 
 
 16. A bought 1000 bu. July wheat at the lowest price and 
 sold the same at the closing price. What was his gain ? 
 
 SUGGESTION. 1 J ^ = $0.015 ; 1000 times f 0.015 = $ ? 
 
 17. B bought 1000 bu. September wheat at the opening 
 price and sold it at the highest price. What was his gain? 
 Had he bought at the lowest price and sold at the closing price, 
 what would have been his gain ? 
 
 18. C bought 25,000 bu. July wheat at the opening price and 
 sold it at the highest price. What was his gain ? 
 
 WRITTEN EXERCISE 
 Find the value of: 
 
 1. 39-115 5 . 1651 -41^V. 9. l-i-i 
 
 O 3 o 4) o 4 o 
 
 2. 85-21f. 6. 2451-17-!%. 10. J - T 9 6 - - f . 
 
 3. 168 -45f. 7. 177f-17 T V 11. 2J+lf-L&. 
 
 4. 26l T 9 g-131l. 8. 2150-121-if. 12. 251 - 8| - 151. 
 
 173. When the numerators of any two fractions are alike, the 
 subtraction may be performed as in the following examples. 
 
 174. Examples, l. From i take 4. 2. From 4 take f . 
 
 jr i y o o 
 
 SOLUTIONS. 1. 9 7 = 2, the new numerator. x 7 = 63, the new denomi- 
 nator. Therefore, the required result is ^. 2. 8 5x3 = 9, the new numer- 
 ator. 8 x 5 = 40, the new denominator. Therefore, ^ is the required result. 
 
 ORAL EXERCISE 
 
 State the value of: 
 1. 1 - 1. 8. |- - |. 15. i - J. 22. | - f . 
 
 2- i-i- 9- i-i- 16. 1-1- 23. |-f 
 
 3. 1-1. 10. \-\. 17. f-f. 24. f-f. 
 
 4. 1-f 11. i-1. 18. f-f. 25. 12J-6&. 
 
 5. J-l. 12. |-f 19. |-f 26. 131-21. 
 
 6. 1-1. 13. 1-|. 20. |-f. 27. l-H-71. 
 
 7. i-f 14. 1-f 21. f-f. 28. 16f-12|. 
 
126 PRACTICAL BUSINESS ARITHMETIC 
 
 MULTIPLICATION 
 
 ORAL EXERCISE 
 
 1. 12 times 2 A. are how many acres? 12 times 2 fifths (f) 
 are how many fifths ? -^ = ? 
 
 2. 32 mi. divided by 4 equals how many miles? | of 32 mi. 
 equals how many miles? Multiplying by |, J, J, and i, etc., is 
 the same as dividing by what integer ? 
 
 3. If 5 men can dig 125 bu. of potatoes in 1 da., how many 
 bushels can 3 men dig in the same time ? | of 125 bu. equals 
 how many bushels ? 
 
 175. Example. Multiply f by 248. 
 
 00 
 
 SOLUTIONS, (a) 248 times 3 eighths = 744 eighths | X 248 = ^|-= 93 
 = ^=93; but, (J) 
 
 (&) If the multiplication is indicated as in the 
 margin, the work may be shortened by cancellation. 7!$ times 3 __ gg 
 
 P 
 
 176. Therefore, to find the product of an integer and a 
 fraction, find the product of the integer and the numerator, and 
 divide it by the denominator. 
 
 Before actually multiplying, indicate the multiplication and cancel if 
 possible. 
 
 ORAL EXERCISE 
 
 1. If 1 yd. of cloth costs I0.87J (|J), what will 16 yd. 
 cost? 48 yd.? 128 yd.? 72 yd.? 
 
 2. When oats cost $0. 33^ ($l) a bushel, how much must 
 be paid for 29 bu.? for 36 bu.? for 129 bu. ? 
 
 3. A boy earns $0.75 (-If) a day. How much will he earn 
 in 18 da.? in 40 da.? in 84 da.? in 128 da.? in 160 da.? 
 
 4. When property rents for 8720 a year, what is the rent 
 for 1 yr.? for \ yr.? for 1 yr.? for -^ yr. ? for 1 yr.? 
 
 5. A ship is worth 848,000. What is \ of the ship 
 worth ? -Jg of the ship ? f of the ship ? -J of the ship ? ^ of 
 the ship ? 
 
COMMON FRACTIONS 
 
 127 
 
 WRITTEN EXERCISE 
 
 Find the product of: 
 1. 98 x |. 7. | of 95. 
 
 8. fof25. 
 
 9. f of 88. 
 
 2. 80 xf. 
 
 3. 50 X 2 7 . 
 
 4. 97 x T V 
 
 5. 92 X i 5 ^. 
 
 6. 188 x ^ 
 
 13. 784 x f 
 
 14. 459xf 
 is. 400 x Jg 
 
 10. T 9 g of 51. 16. 510 x T 7 o 
 
 11. ^ of99. 
 
 17. 990 x eV 
 
 19. f of 2420. 
 
 20. | of 2500. 
 
 21. | of 3240. 
 
 22. f of 5117. 
 
 23. J of 7254. 
 
 12. ^ of 77. 18. 800 x if. 24. 
 
 177. Example. Multiply 25 by 4|. 
 
 25 
 
 SOLUTION. | of 25 = \ 5 - or 9|. Write f as shown in the margin, 
 and carry 9 to the product of the integers. 4 x 25 + 9 = 109. There- ^"8 
 fore, 25 multiplied by 4f = 109 1. 109| 
 
 178. Therefore, to find the product of a mixed number 
 and a whole number, multiply the integer and the fraction sepa- 
 rately and find the sum of the products. 
 
 ORAL 
 
 Find the cost of: 
 
 1. 15f Ib. of fish at 9 
 
 2. 7| yd. of cloth at 13. 
 
 3. 16 Ib. of beef at 10 * 
 
 4. 16J Ib. of sugar at 5^. 
 
 5. 12 Vd. of cloth at 11 j 
 
 EXERCISE 
 
 6. 6| bu. turnips at 
 
 7. 12-i- bu. of oats at 
 
 8. 10-J yd. of calico at 
 
 9. 16J yd. of ribbon at 
 
 10. 8J gal. of molasses at 25^. 
 
 WRITTEN EXERCISE 
 
 1. Find the total cost of : 
 124 Ib. beef at 9j 
 
 112 1 Ib. beef at 5 
 136 Ib. pork at 5^. 
 
 2. Find the total cost of : 
 27 3 yd. crepe at 1 2. 
 28 2 yd. satin at 1 2. 
 25 3 yd. dress silk at 1 2.50. 
 18 1 yd. velvet ribbon at f 2. 
 
 114f Ib. fish at If. 
 156 Ib. pork at l^t. 
 131 T 7 g Ib. fish at 9 
 
 12 3 yd. fancy stripe at $0.50. 
 43 2 yd. English serge at 11.75. 
 43 2 yd. English camel's hair at f 2. 
 8 pc. fancy black ribbon at f 2. 87J. 
 
128 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 3. A merchant bought 25 pc. of striped denim containing 41 1 , 
 41 1 , 42 2 , 43 2 , 42 1 , 44 2 , 43 1 , 40 2 , 42 1 , 45 3 , 42 1 , 40 2 , 41 2 , 47 3 , 45 1 , 
 41 1 , 43 2 , 47 2 , 443, 423, 432^ 391^ 42 i, 432, an d 47 yd., at 11^ per 
 yard. If he sold the first 11 pc. at 15^ per yard and the 
 remainder at 17^ per yard, what was his gain? 
 
 4. Copy and find the amount of the following bill: 
 
 Terttis 
 
 Bought of 
 
 Eureka Mills 
 
 ^c 
 
 <z^g?^?^ 
 
 ;TZ^/''2^-_. 
 
 / 
 
 -^Z2-4>- 
 
 179. The expressions ^ of | and \ x | have the same meaning ; 
 hence, the sign of multiplication may be read 0/j or multiplied 
 by, when it immediately follows a fraction. 
 
 180. Examples. 1. Multiply f by f . 
 
 SOLUTION. To multiply f by f is to find f of f . 
 
 Let the line AF in the accompanying diagram represent a unit divided into 
 5 equal parts. 
 
 Then AD will represent f. Sub- A 
 divide each of the five equal parts 
 
 into 3 equal parts and the line AF 
 will represent a unit divided into 15 
 equal parts, each of which is ^ of the whole. It is then clear that | of $ 
 equals ^ 5 . Since 1 of is T ^, | of f is T \. But f of f is 2 times | of f ; there- 
 fore, of | equals r %. 
 
 2. Find the product of 2|, |, and T 7 ^. 
 
 SOLUTION. Reduce the mixed number 2 to an im- ^ 
 
 proper fraction and obtain |. Cancel, and there remains in . ^. 
 
 the numerators 2 times 7, and in the denominators 15, from ^ X X = 
 
 which obtain the fraction . JS 15 15 
 
COMMON FRACTIONS 
 
 129 
 
 181. Hence, to multiply a fraction by a fraction : 
 
 Reduce the mixed numbers and integers to improper fractions 
 
 and cancel all factors common to the numerators and denominators. 
 Find the product of the remaining numerators for the required 
 
 numerator, and the product of the remaining denominators for the 
 
 required denominator. 
 
 ORAL EXERCISE 
 
 1. How many yards hi rd. ? feet in f rd. ? 
 
 2. When barley is worth 25|^ per bushel, what is the value 
 of Jbu.? of |bu.? 
 
 3. A book, the retail price of which was $5, was sold at 
 wholesale for of the retail price, with ^ off from that for 
 cash. Find the selling price of 10 books. 
 
 5. 50 x ^ x 7f . 
 
 6. If x 4| x 8f . 
 as much. How much 
 
 WRITTEN EXERCISE 
 
 Reduce to their simplest form : 
 
 1. I of | of f 3. 71 x 25 x f . 
 
 2. I of f of 21 4. 3| x 4-J x 20. 
 
 7. A saves f 9.75 per week and B f 
 
 more will A have than B at the end of the year ? 
 
 8. A merchant bought a piece of cloth containing 43^ yd. 
 at 81.50 per yard. He sold f of it at 11.621 a yard, and the re- 
 mainder at $1.37| a yard. Did he gain or lose, and how much? 
 
 The following is a recent clipping from a daily paper. It shows the 
 prices of corn on the New York market. 
 
 NEW YORK CORN QUOTATIONS 
 
 DELIVERY 
 
 PREVIOUS CLOSING 
 
 HIGHEST 
 
 LOWEST 
 
 CLOSIN 
 
 July 
 September 
 
 56-1 
 
 56 
 
 54!* 
 
 55 
 
 9. D bought 25,000 bu. September corn at the opening 
 price and sold it at the highest price. What was his gain ? 
 Had he bought at the lowest price and sold at the highest 
 price, what would he have gained? 
 
130 PEACTICAL BUSINESS ARITHMETIC 
 
 10. E bought 12,500 bu. July corn at the lowest price and 
 sold it at the closing price. What was his gain ? Had he 
 bought at the lowest price and sold at the highest price, what 
 would he have gained ? 
 
 11. A gold dollar weighs 25.8 Troy grains. For every 90 
 parts of pure gold there are ten parts of alloy. How many 
 grains of each kind in a gold dollar ? in a 5-dollar gold piece ? 
 
 12. A 5-cent piece weighs 77.16 Troy grains. For every 
 part of nickel there are three parts of copper. How many 
 grains of each kind in a 5-cent piece ? 
 
 13. The second general coinage act (1834) of the United 
 States made one silver dollar weigh approximately as much as 
 sixteen gold dollars, and this ratio of sixteen to one has been 
 maintained up to the present time. What is the weight of 
 a silver dollar ? If silver coins are -f$ pure, how much pure 
 silver in 10 silver dollars ? 
 
 SHORT METHODS IN MULTIPLICATION 
 
 182. When mixed numbers are large, they may be multiplied 
 as shown in the following example. 
 
 183. Example. Multiply 255J by 24f. 
 
 2551 
 
 SOLUTION. Multiply the fractions together 9^2 
 
 and obtain -%, which write as shown in the 
 
 margin. Multiply the integer in the multi- 1T> ~ 
 
 plicand by the fraction in the multiplier and 102 = | of 255 
 
 obtain 102. Multiply the fraction in the mul- 8 =24 times 1 
 
 tiplicand by the integer in the multiplier and 1Q20 1 
 
 obtain 8. Multiply the integers together and "" I = 24 times 255 
 
 add the partial products. The result is ^li 
 
 6230 T v 6230 T 2 5 = 24f times 255J 
 
 WRITTEN EXERCISE 
 
 Multiply : 
 
 1. 975 by 18J. 3. 720J by 21f . 5. 512^ by 16-J. 
 
 2. 876| by 21 f 4. 445J by 46|. 6. 450 T ^ by 20|. 
 
COMMON FRACTIONS 131 
 
 SQUARING NUMBERS ENDING IN J OR 5 
 
 184. Examples. 1. Multiply 9| by 9j. 
 
 SOLUTION. \ of \ , which write as shown in the margin. \ 9-i 
 of the integer in the multiplicand plus \ of the integer in the multi- QJ^ 
 plier is equal to either the integer in the multiplicand or multiplier. 
 Therefore, add 1 to the integer in the multiplicand and multiply by the 
 multiplier. 9 x 10 = 90. Then, 9 x 9 = 90|-. 
 
 2. Find the cost of 8.5 T. of coal at 18.50 per ton. 
 
 SOLUTION. The principles embodied in this example are practi- 
 cally the same as those in problem 1. .5 x .6 = .25, 8 x 9 = 72. 
 Therefore, 8.5 tons of coal at $8.50 per ton will cost $72.25. 
 
 3. Find the cost of 75 A. of land at 1 75 per acre. 
 
 SOLUTION. This problem is similar to example 2, the only 75 
 
 difference being in the matter of the decimal point. Since the 7^ 
 
 decimal point has no particular bearing upon the steps in the pro- 
 cess of multiplying, proceed to find the product as in example 2. 
 5 x 5 = 25, which write as shown in the margin. 7 x 8 = 56, which write to com- 
 plete the product. 75 acres of land at $75 an acre will therefore cost $5625. 
 
 ORAL EXERCISE 
 
 Multiply : 
 
 1. 1| by 1|, 6. 6 J by 6J. ll. 13| by 13. 16. 16 J by 16J. 
 
 2. 2|by2|. 7. 7. 5 by 7.5. 12. 14| by 14|. 17. 17| by 17|. 
 
 3. 3lby3|, 8. 8.5 by 8.5. 13. 15J by 15|. 18. 18J by 18J. 
 
 4. 41 by 41. 9. 9.5 by 9.5. 14. 11.5 by 11.5. 19. 195 by 195. 
 5 - 5Jby5f 10. 10.5 by 10.5. 15. 12.5 by 12.5. 20. 205 by 205. 
 
 WRITTEN EXERCISE 
 
 In the following problems make all the extensions mentally. 
 
 1. Find the total cost of: 
 
 85 Ib. of tea at 85 f. 55 Ib. tea at 55 f. 
 
 75 gal. sirup at 75 75 bbl. flour at 17.50. 
 
 45 gal. sirup at 45^. 650 bbl. oatmeal at $6.50. 
 
 2|- bu. beans at |2.50. 25 doz. cans olives at 2.50. 
 
 35 gal. molasses at 35^. 95 cs. salad dressing at 95^. 
 
 65 cs. horseradish at 65 ^. 750 Ib. cream codfish at 7^. 
 
 4J cs. baking powder at 4.50. 3J cs. baking powder at $ 3.50. 
 
in the multiplier is equal to ^ of 6 + 7, or 6^, which added to *> of \ rrj 
 
 equals 6|. Write f as shown in the margin, and carry 6. 6x7+6 
 
 = 48. Therefore, 1\ x 6 = 48. ^\ 
 
 132 PRACTICAL BUSINESS ARITHMETIC 
 
 MULTIPLICATION OF ANY NUMBERS ENDING IN 1 OR .5 
 
 185. Examples. 1. Multiply 7| by 6J. 
 
 SOLUTION. \ of the integer in the multiplicand plus \ of the integer (JX 
 
 the multiplier is equal to i c r ^^ - - 1 - 1 --'- 1 - -**-*- ' - - 
 
 als 6|. Write as shown ii 
 
 8. Therefore, 7| x 6 = 48 
 
 2. Multiply 7-1- by 9J. 
 
 71 
 
 SOLUTION. \ of 7 + 9 = 8, with no remainder. | of | = i, which * 
 
 write as shown in the margin, and carry 8. 7x9 + 8 = 71. There- 2 
 
 fore, ?i x 9| . = 71 J. 71 J 
 
 Observe that : (1) in finding | of any number (dividing a number by 2) 
 there is either nothing remaining or 1 remaining ; (2) in finding | of an 
 even number there can be no remainder, and in finding of an odd number 
 there is always a remainder 1. Hence, to multiply numbers ending in ^ or .5 : 
 
 Mentally determine the sum of the integers in the multiplicand and multiplier. 
 If it is an even number, write \ (.25 or 25} in the product. If it i.s an odd num- 
 ber, write f (.75 or 75) in the product. Multiply the integers and to the product 
 add \ of their sum. 
 
 ORAL EXERCISE 
 
 Multiply : 
 
 1. 3Jby7j. 4. 17| by 2|, 7. 3.5 by 8.5. 
 
 2. 4 by 51. 5. 14| by 6|, 8. 7.5 by 6.5. 
 
 3. 161 by 4J. 6. 211 by 9J. 9. 5.5 by 8.5. 
 
 WRITTEN EXERCISE 
 
 Make the extensions in each of the following problems mentally. 
 
 1. Find the total cost of : 
 
 6.5 T. coal at 18.50. 8.5 T. coal at 19.50. 
 
 2.5 T. hay at 117.50. 16.5 T. hay at 111.50. 
 
 15.5 cd. wood at 13.50. 14.5 cd. wood at $5.50. 
 
 2. Find the total cost of : 
 
 45 bu. beans at $2.50. 350 bu. wheat at 11.05. 
 
 35 bbl. flour at $6.50. 350 bu. beans at $2.50. 
 
 45 bbl. flour at $8.50. 85 bbl. oatmeal at $7.50. 
 
COMMON FRACTIONS 133 
 
 DIVISION 
 
 ORAL EXERCISE 
 
 1. 8 A. -s-4 = ? 8 ninths (|) -s- 4 ? 
 
 2. If 2 Ib. of coffee costs $0.66f (If), what will 1 Ib. cost? 
 Divide f by 2. What is the effect of dividing the numerator 
 of a fraction ? 
 
 3. |-i-2 = ? Jof| = ? 
 
 4. Because -| -t- 2 = -|- of |-, therefore, ^ -r- 5 = ^ of |, or 
 1*1. i x i = ? 
 
 5. What is the quotient of J -r- 5 ? of -s- 8 ? of -J -5- 2 ? 
 Because l -*- 5 = ^ of J, therefore | -;- 5 = 2 times ^ of ^. 
 is-5 = lofor x i=? 
 
 7. How much is f -r- 5 ? -- 3 ? 7J- (-^) ^- 8 ? 3J -i- 6 ? 
 
 8. What is the effect of multiplying the denominator of a 
 fraction ? 
 
 186. In the above exercise it is clear that 
 
 Dividing the numerator of a fraction by an integer divides the 
 whole fraction ; and, 
 
 Multiplying the denominator of a fraction by an integer divides 
 the whole fraction. 
 
 ORAL EXERCISE 
 
 Find the quotient of: 
 
 1. f-f-4. 4. |^-12. 7. ^ +-4. 10. f-r-9. 13. -J-s-19. 
 
 2. ^+-2. 5. f-12. 8. ^ + 9. 11. i^6. 14. ^ + 5. 
 
 3. If. ^5. 6. T ^-3. 9. T ^H-7. 12. 1-5. 15. ^-5. 
 
 187. Examples. 1. Divide 28J by 7. 
 
 SOLUTION. First divide the integers and the result is 4 ; then 44 
 
 divide the fraction by 7 and the result is |. Therefore, 
 
 28|-7 = 4^. 
 
 2. Divide 26| by 8. 
 
 SOLUTION. Divide 26 by 8 and the result is 3 with a remainder 2. 3_5_ 
 
 Join the remainder, 2, with the fraction, |, making 2|. Reduce 2} ~ 
 
 to an improper fraction and the result is f . | -=- 8 = T 5 ^. Therefore, 
 26i - 8 - 3. 
 
134 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 Divide : 
 
 1. 
 
 16* 
 
 by 4. 
 
 5. 
 
 32f 
 
 by 4. 
 
 9. 
 
 21* by 
 
 8. 
 
 13. 
 
 8* 
 
 by 5. 
 
 2. 
 
 18* 
 
 by 9. 
 
 6. 
 
 27J 
 
 by 7. 
 
 10. 
 
 24f by 
 
 6. 
 
 14. 
 
 14f 
 
 by 7. 
 
 3. 
 
 25 
 
 by 2. 
 
 7. 
 
 19* 
 
 by 9. 
 
 11. 
 
 45fby 
 
 5. 
 
 15. 
 
 11* 
 
 by 9. 
 
 4. 
 
 17* 
 
 by 8. 
 
 8. 
 
 20f 
 
 by 10. 
 
 12. 
 
 40fby 
 
 10. 
 
 16. 
 
 26* 
 
 by 10. 
 
 ORAL EXERCISE 
 
 1. How many eighths in one ? 1 + -J = ? 
 
 2. What is the value of: 1 + ^? 3 + *? 17 + J? 
 125-=- T V? 250 + ? 
 
 3. Read aloud the following, supplying the missing word : 
 To divide an integer by a unit fraction, multiply the integer by 
 the of the fraction. 
 
 4. What is the value of 25 + * ? 2.5 + *? 7.5 + *? 25.5 + 
 j_ ? 54^1? 48 + i? 29 + *? 2* + *? 
 
 5. If B, in the accompanying dia- 
 gram, is 1, what is 0? How many 
 blocks like O'mS? 1 + * = ? 
 
 6. If A is 1, what is B ? A is how 
 many times B ? That is, A + B = ? 
 l+f=? A 
 
 7. If 1 + 1 = f (1*), then 2 + f = ? 
 
 8. What is the value of 4 + f ? 5 + f? 12 + -|? 15 + J? 
 
 9. Read aloud the following, supplying the missing words : 
 
 If A is 1, B is , and O is . If B is contained in 
 
 A | (1*) times, it is contained in * of | times or times. 
 
 That is, * + f = * x f = . 
 
 10. What is the value of * + *? f + |? |- + f? + ? 
 
 188. The reciprocal of a fraction is 1 divided by that fraction. 
 Thus, the reciprocal of f is 1 -*- f, or |. That is, the reciprocal of a fraction 
 
 is the fraction inverted. 
 
 189. Reciprocal numbers, as we use the terms in arithmetic, 
 are numbers whose product is 1. 
 
 Thus, 4 and \, \ and f , $ and 6, f and f , are reciprocal numbers, because 
 their product is equal to 1. 
 
COMMON FRACTIONS 
 
 135 
 
 190. It has been seen that the brief method for dividing a 
 fraction or an integer by a fraction is to multiply the dividend 
 by the reciprocal of the divisor. 
 
 The principles of cancellation should be used whenever possible. Inte- 
 gers and mixed numbers should be reduced to improper fractions before 
 applying the rule. 
 
 Divide : 
 
 WRITTEN EXERCISE 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 
 4 by f . 
 ?l by 1. 
 95 by f . 
 88 by f . 
 16 by f . 
 
 by'*- 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 
 4f by f . 
 
 i 9 o by |. 
 6| by I*. 
 160 by 41. 
 250 by 3f . 
 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 
 191. Examples. 1. Divide 2190 by 48|. 
 
 SOLUTION. Multiplying both dividend and divisor by 
 the same number does not affect the quotient ; hence, 
 multiply the dividend and divisor by 3 and obtain for the 
 new dividend and divisor 6570 and 146, respectively. 
 Divide the same as in simple numbers and obtain the 
 result 45. Or, 
 
 Reduce both the dividend and divisor to thirds, obtain- 
 ing 5 3 7 - and i|. Reject the common denominators 
 and divide as in whole numbers. 
 
 2. Divide 
 
 by 12J. 
 
 SOLUTION. Multiply both dividend and divisor by 6, 
 the least common denominator of the fractions, and di- 
 vide as in simple numbers. The result is 5f |. Or, 
 
 Reduce both the dividend and divisor to sixths, obtain- 
 ing as a result - 7 / and $*. Reject the common denomi- 
 nator and divide as in simple numbers. 
 
 Divide: 
 
 1. 2701 by 12|, 
 
 2. 508^ by 30|. 
 
 3. 14311 by 20|. 
 
 WRITTEN EXERCISE 
 
 f by f 
 169 by 4|. 
 640 by 5f . 
 625 by 831 
 920f by 73. 
 
 48f)2190 
 
 _3 3_ 
 
 146) 6570(45 
 584 
 730 
 730 
 
 121)651 
 6 6 
 
 74)393(5ff 
 370 
 23 
 
 4. 
 5. 
 6. 
 
 962 1 by 31|, 
 650f by 26i, 
 16801 by 45i. 
 
 7. 
 
 7552 by 78| . 
 
 8. 470f by 17 J. 
 
 9. 1054| by 1681. 
 
136 PRACTICAL BUSINESS ARITHMETIC 
 
 FRACTIONAL RELATIONS 
 
 ORAL EXERCISE 
 
 1. If / in the accompanying diagram is 
 1, what is e? d? c? b? a? 
 
 2. What part of e is/? of d? of c? of 
 b? of a? What part of 6 is 1? of 5? of 4 ? 
 of 3? of 2? 
 
 __ 3. What part of a is e? d? c? b? What 
 
 part of 6 is 2? 3? 4? 5? 
 
 4. What part of d.isf? What part of b is e? What part 
 of 1 (f) is i ? What part of f is 1 () ? 
 
 5. What part of 7 bu. is 1 bu.? What part of 7 eighths (|) 
 isl eighth (J)? 
 
 6. What part of | is -|? 
 
 SOLUTION, f and f are similar fractions ; hence they may be compared in 
 the same manner as concrete integral numbers. 2 is f of 3 ; therefore, f is f of 
 
 I; or, 
 
 fisf off. = f x$ = f. 
 
 7. f is what part of If (!)? of 2|? of 
 
 8. | is what part of .] ? 
 
 SOLUTION. \ f. \ is \ of f , therefore, \ = % of | 
 
 or 
 
 192. To find what fraction one number is of another, take the 
 number denoting a part for the numerator of the fraction, and the 
 number denoting the whole for the denominator. 
 
 ORAL EXERCISE 
 
 1. If a piece of work can be performed in 12 da., what 
 part of it can be performed in 5 da. ? in 7 da. ? 
 
 2. If A can do a piece of work in 15 da., what part of it 
 can he do in 1 da. ? in 2 da. ? in 5 da. ? in 7 J da. ? 
 
 3. If B can do a piece of work in 7J da., what part of it 
 can he do in 1 da. ? in 2 da. ? in 5 da. ? in 5- da. ? in 6| da. ? 
 
COMMON FRACTIONS 137 
 
 4. I bought a farm for 12000 and sold it for 13000. What 
 part of the cost was realized ? what part of the cost was 
 gained ? 
 
 5. A watch costing 1 75 was sold for $60. What part of 
 the cost was realized? What part of the cost was lost? 
 
 6. A and B hired a pasture together. A pastured 5 cows, 
 7 \vk., and B pastured 7 cows for the same length of time. 
 What part of the price should each pay? 
 
 7. A can do a piece of work in 8 da. which B can do in 9 
 da. How many days will it take them if they join in the 
 completion of the work? 
 
 WRITTEN EXERCISE 
 
 1. What part of 100 is 331? 121? 6 6f? 8|? 25? 75? 
 125? 16 1? 831? 621? 22|? 9 T \? 56 J? 6f? 
 
 2. What part of 81 is 33^? 66|^? 25^? 75*? 16$*? 
 8$*? 6$*? 3J*> 6J*? 62^? 87J*? 37j*> 14f*? 
 
 3. What part of 1000 is 125? 166$? 666f? 625? 333J? 
 
 4. Whatpartof $10 is 13.331? #1.25? $1.66f? $8.331? 
 $2.50? $6.25? $6.66$? 
 
 5. A, B, C, and D hired a pasture for $45. A pastured 4 
 cows for 4| mo.; B, 6 cows for 3J mo.; C, 4 cows for 1| mo.; 
 D, 5 cows for 3 mo. How much should each pay ? 
 
 ORAL EXERCISE 
 
 1. If a in the accompanying diagram is 10 in. high, how 
 high is b? c? dl 10 is | of what number? J of what 
 number? ^ of what number? 
 
 2. If 225 is | of a certain number, what is \ of 
 the number? | of the number? 
 
 3. 192 is -| of what number? ^ of what 
 number? d c b a 
 
 4. After making a payment of $3500 I find that I still owe 
 for | of the cost of my house. What was the cost of my house? 
 How much still remains unpaid? 
 
138 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. The square in the margin represents the 
 total population of the state of New York (state 
 census of 1905), and the shaded area represents 
 the urban (city) population. If the suburban 
 (country) population is 2,420,001, what is the en- 
 tire population of the state ? the urban population ? 
 
 2. In a recent year the population of Massachusetts was 
 3,002,000, and there were three persons living in the cities of 
 the state to every one person living in the country. Represent 
 this graphically as in problem 1, and find the city population 
 and the country population for the state. 
 
 3. Suppose that in the diagram represents the population 
 of the United States in 1870, A the population in 1830, and F 
 the population in 1900. If the population in 1870 was 38,400,000 
 (round numbers), what was the population (round numbers) 
 in 1900? In 1830? 
 
 4. Suppose that F in the diagram represents the population 
 of the United States in 1900, and O the proportion of this popula- 
 tion living in cities in 1900. What proportion of the popula- 
 tion lived in cities in 1900? Suppose that F represents the 
 population in 1860 and A the proportion of this population 
 living in cities. Assuming that the city population in 1860 
 was 5,240,554, find the total population for the same year. 
 
 5. The total population of New Jersey (state census of 
 1905) is 2,144,134, and the urban population, 1,286,480. Rep- 
 resent this graphically and find the country population. 
 
COMMON FRACTIONS 139 
 
 CONVERSION OF FRACTIONS 
 
 ORAL EXERCISE 
 
 1. What is the denominator of the decimal .6? of .75? 
 
 2. What is the numerator of .4? of .04? of .004? of .0004? 
 
 3. Write as a common fraction .7; .23; .079; .0013; .00123. 
 
 193. A decimal may be written as a common fraction. 
 
 194. Examples. 1. Reduce .0625 to a common fraction. 
 
 SOLUTION. .0625 means T $$fo ; but T {fgfo may be 
 
 . . T ; T _Q_25_ _ _5_ = _1_ 
 
 expressed in simpler form. Dividing both terms of 10000 80 16 
 
 the fraction by 625, the result is T V 
 
 WRITTEN EXERCISE 
 
 Reduce to a common fraction or to a mixed number: 
 
 1. 0.375. 5. 0.9375. 9. 0.0335. 13. 260.675. 
 
 2. 0.0625. 6. 1.66|, 10. 0.00561. i4 . 126.1875. 
 
 3. 0.0016. 7. 0.4375. 11. 181.875. 15. 175.0625. 
 
 4. 0.5625. 8. 0.125. 12. 171.245. 16. 172.0075. 
 
 195. A common fraction may be written as a decimal. 
 
 196. Example. Reduce f to a decimal. 
 
 SOLUTION, f equals of 3 units. 3 units equals 3000 thou- _ 
 
 sandths. $ of 3000 thousands equals 375 thousandths (.375). 8)3.000 
 
 ORAL EXERCISE 
 
 1. Reduce to equivalent decimals : , \, f , ^, f, J, f , , | , |, 
 
 i< I' f ' t' lV T2' T 3 6' I' IT' 
 
 2. Reduce to common fractions : .5, .25, .50, .75, .33|-, .66J, 
 .16f, .121, .6, .4, .60, .40, .2, .83J-, .20, .081 .375, .125, .37 J, 
 .87f .875, .0625, .111 .09 T \. 
 
 WRITTEN EXERCISE 
 Reduce to equivalent decimals : 
 
 1. f 3. J ff . 5. yfj. 7. ? \V 9 - 64^0- u - 21 f- 
 
 2. . 4. -/ 5 . 6. fj.. 8. 5 V 10. 5 T L. 12. 165|f 
 
140 PRACTICAL BUSINESS ARITHMETIC 
 
 APPROXIMATIONS 
 
 197. Since results beyond two or three decimal places are 
 seldom required in business, approximations in multiplication 
 are frequently desired. In problems involving dollars and 
 cents, it is sufficient to carry the decimal places in the final 
 results just far enough -to obtain accurate cents. In order to 
 make sure that a product is correct to the nearest cent, it is 
 usually necessary to carry the partial products to three deci- 
 mal places. 
 
 198. Example. If $1 put at compound interest (see 
 page 314) for 10 yr. at 4J% amounts to $1.55297, what will 
 $ 4125.67 amdunt to in the same time at the same rate ? 
 
 SOLUTION. It has been seen FULL PROCESS CONTRACTED PROCESS 
 
 (page 52) that in multiplying there is -j c.> Q7 i r 5297 
 
 no advantage in beginning with the ^-.Qr ^ 7 /nor 7 
 
 lowest order of the multiplier. In this ^ 
 
 example it will be seen that there is a 6211.88 6211.88 
 
 decided advantage in beginning with 155.297 155.297 
 
 the highest order of the multiplier. o-i nrn A o-i 
 
 In beginning the multiplication note n fjA 
 that 4000 times .00007 = .28 and write 
 
 8 in the hundred ths' place. Complete .931 
 
 and point off the first partial product .1087079 .109 
 
 as shown in the process at the left. 
 
 041 
 
 85 7.765 
 
 782 .932 
 
 7399 6407.04 
 
 The other partial products are then 
 formed in natural order 
 
 The work is given in full and in contracted form. Examine both processes. 
 Note that in the full process all of the work on the right of the vertical line is 
 wasted ; also note how much better for practical purposes the contracted form 
 is than the other. In this problem the first two steps are the same by either 
 process. Multiplication by 20 would give a figure in the fourth place. Instead 
 of writing down the product of 20 times .00007, add the nearest ten to the next 
 column. 2x9 + 1 = 19; 2 x 2 -f 1 = 5 ; etc. In multiplying by the next 5 it is 
 not necessary to take the 7 in the multiplicand into account; in multiplying by 
 .6 both 7 and 9 in the multiplicand may be rejected ; in multiplying by .07, the 7, 
 9, and 2 in the multiplicand may be rejected. When any figure in the multipli- 
 cand is dropped, it may be marked off as follows: 1.55 V 2\9 X 7. In finding the 
 sum of the partial products do not set down the result for the third decimal 
 place, but carry the nearest ten (3) to the second decimal place. The required 
 result is finally found to be $6407.04. 
 
COMMON FRACTIONS 141 
 
 199. Approximations in division are also frequently desired. 
 
 200. Example. If 10.134 A. of land cost 1889.26, what is 
 the cost per acre ? 
 
 887.75 
 10134) $ 889260 
 
 8107 = approximately. 8 times 1013 (4) 
 
 785 
 
 709 = approximately 7 times 101 (34) 
 
 76 
 
 71 == approximately 0.7 times 10 (134) 
 
 5 
 5 = approximately 0.05 times 1 (0134) 
 
 SOLUTION. Since the decimal point appears in both dividend and divisor, it 
 is better to first multiply each by such a power of ten as shall make the divisor 
 integral. In such problems as this a result correct to ^0* ~r 
 
 the nearest cent is all that is required. Since 10's - 
 
 (an approximation for the last two figures in the divi- 10134) $ 889260 
 dend) divided by 10000's (an approximation for the 785 
 
 divisor) is less than 0.01, the last two figures of the 76 
 
 dividend will not affect the quotient, and they may r 
 
 therefore be rejected. Hence, also, the divisor may be 
 
 considered 1013 and may be continually contracted ; but in multiplying the 
 divisor by each quotient figure, mentally multiply the figure cut off and carry 
 the nearest ten. When a figure is rejected in the divisor, it may be marked 
 off as explained in 198. The work may be further abridged by omitting the 
 partial products and writing down the remainders only as explained on page 67. 
 
 WRITTEN EXERCISES 
 
 1. Divide 20,000 by 3.1416 correct to .01. 
 
 2. Find the product of 10.48 x 3.14159 correct to two deci- 
 mal places. 
 
 3. If fl placed at simple interest for 1 yr. 7 mo. at 3-| / 
 will amount to $ 1.05541, what will 11869.75 amount to in the 
 same time at the same rate ? 
 
 4. The estimated population of Continental United States 
 for 1906 was 92,500,000 and the area was 3,602,990 sq. mi. 
 What was the average population per square mile for this year, 
 to the nearest unit ? 
 
142 PRACTICAL BUSINESS ARITHMETIC 
 
 THE SOLUTION OF PROBLEMS 
 
 201. The steps in the solution of a problem are : (1) reading 
 the problem to find what is given and what is required; (2) de- 
 termining from what is given how to find what is required;* 
 
 (3) outlining a process of computation and then performing it; 
 
 (4) checking results. 
 
 202. A problem should be thoroughly understood before any 
 attempt is made to solve it ; and when the relation of what is 
 given to what is required has been discovered, the process of 
 computation should be briefly indicated and then performed 
 as briefly and rapidly as possible. 
 
 203. To insure accuracy the work should always be checked 
 in some manner. If the answer to the problem is estimated in 
 advance, it will prove an excellent check against absurd results. 
 
 Thus, 42 doz. boys' hose at $48 a dozen is equal to approximately 
 40 x $50 ; 9|% of 1290 bu. is equal to approximately ^ of 1290 bu. ; etc. 
 
 204. Example. A tailor used 30 yd. of flannel in making 18 
 waistcoats ; at that rate how many yards will he require in 
 making 45 waistcoats ? 
 
 SOLUTION 
 
 1. The quantity needed in making 18 waistcoats is given and the quantity 
 needed in making 45 waistcoats is required. 
 
 2. One waistcoat requires f yd. ; 45 waistcoats will require 45 times ff yd. 
 15 5 
 
 3. = 75 ; that is 75 yd. of flannel are required in making 45 
 
 3 
 
 waistcoats. 
 
 4. f yd. = f yd. ; |4 yd. = f yd. ; therefore the work is probably correct. 
 
 205. If reasons for conclusions, processes, and results are given, 
 they should be brief and accurate. It is also a mistake to try 
 to use the language of the book or teacher. Such artificial 
 work stifles thought and conceals the condition of the learner. 
 
 The subject of analysis should not be unduly emphasized. A correct 
 solution may generally be accepted as evidence that the correct analysis has 
 been made. 
 
COMMON FRACTIONS 143 
 
 ORAL EXERCISE 
 
 In the following problems first find each result as required, and then 
 give a brief, accurate explanation of the steps taken in the solution. Do 
 not use pen or pencil. 
 
 1. If 2 T. cost $8, what will 5 T. cost? 
 
 SUGGESTION. $20; since 2 T. cost $ 8, 5 T., which are 2| times 2 T., will 
 cost 2 1 times $8, or $20. 
 
 2. 24 is f- of what number ? f of what number ? -A- of what 
 
 I O 1 O 
 
 number ? 
 
 3. 220 is ^ less than what number? 450 is | less than 
 what number ? 
 
 4. A, having spent J of his money, finds he has $84 left. 
 How much had he at first ? 
 
 5. $124 is ^ more than what sum of money? $300 is J 
 more than what sum of money? 
 
 6. A man sold -f^ of an acre of land for $35. At that rate 
 what is his entire farm of 100 acres worth ? 
 
 7. A man bought a stock of goods and sold it at ^ 
 above cost. If he received $275, what was the cost of the 
 goods ? 
 
 8. B bought a stock of goods which he sold at ^ below cost. 
 If he received for the sale of the goods $240, what was the cost 
 and what was his loss ? 
 
 9. -j 9 g of the students in a high school are girls and the re- 
 mainder are boys. If the number of boys is 350, how many 
 scholars in the school ? 
 
 10. A bought a quantity of wheat which he sold at J above 
 cost. If he received $300 for the wheat, what did it cost him 
 and what was his gain ? 
 
 11. A bought a quantity of dry goods and sold them so as to 
 realize J more than the cost. If the selling price was $720, 
 what was the cost and what was the gain ? 
 
 12. D bought a stock of carpeting which he was obliged to 
 sell at J below cost. If he received $750 for the sale of the car- 
 peting, what was the cost of same, and what was his loss ? 
 
144 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 In the following problems give both analysis and computation. 
 
 1. If 1- Ib. of tea cost 21 what will 9J Ib. cost ? 
 
 COMPUTATION ANALYSIS 
 
 9 - \ 9 - 9| = V 9 - 5 9| is therefore 19 times |. If $ Ib. cost 
 
 19 x 21 ^ = $3.99 21 ?, 9fc Ib. will cost 19 times 21^, or $3.99. 
 
 2. If | of a pound of tea cost 42 ^, what will 35-J Ib. cost ? 
 
 3. If a drain can be dug in 17 da. by 45 men, how many 
 men will it take to dig ^ of it in 3 da.? 
 
 4. In what time will 3 boys at $0.621 per day earn as much 
 as 4 men at 2.25 each per day will earn in 45 J da. ? 
 
 5. A spends $72 per week or | of his income ; B saves 
 $48 per week or'-| of his income. How long will it take A 
 to save as much as B saves in five weeks ? 
 
 6. If 115 bbl. of wheat are required to make 23 bbl. of 
 flour, how many barrels will be required to make 50 bbl. of 
 flour? 117 bbl. of flour? 259 bbl. of flour? 
 
 ORAL REVIEW EXERCISE 
 
 1. .05x6x0x2-1- = ? 
 
 2. $0'.75 is what part of $3? 
 
 3. What is the sum of |> J, |, and -fa ? 
 
 4. Find the value of .45 + (.25 x 5) - .04. 
 
 5. 60 is f of what number ? f ? f ? J ? f ? 
 
 6. At 25? a yard, what will 2-1 yd. of cloth cost? 
 
 7. is J of what number ? | is ^ of what number ? 
 
 8. If | of an acre of land costs $75, what will 50 A. cost ? 
 
 9. If | of a number is 84, what is 5 times the same number ? 
 
 10. The dividend is 4^ and the quotient is 6f ; what is 
 the divisor ? 
 
 11. If 6 bu. of apples cost $15, what will 80 bu. cost at 
 the same rate ? 
 
 12. At $460 per half mile, what will be the cost of 
 grading 6 mi. of road ? 
 
COMMON FRACTIONS 145 
 
 13. How much will 4 carpenters earn in 10 da. at the 
 rate of 12.25 per day? 
 
 14. At $4.50 per cord, what will be the cost of 4J cd. 
 of wood ? of 6| cd. ? of 12| cd. ? of 7J cd. ? 
 
 15. A bought a horse for $96 and sold it for | of its 
 cost. What part of the cost was the loss sustained ? 
 
 16. A bought 4^ yd. of velvet at $5.20 per yard and 
 gave in payment a $50 bill. How much change should he 
 receive ? 
 
 17. I sold 5 A. of land for $375 and sustained a loss equal 
 to ^ of the original cost of the land. What did the land cost 
 per acre ? 
 
 18. D and E agree to mow a field for $36. If D can do 
 as much in 2 da. as E can do in 3, how should the money 
 be divided ? 
 
 19. N sold a watch to O and received 1 more than it 
 cost him. If O paid $64 for the watch, what did it cost N? 
 What per cent did N gain ? 
 
 20. A earns $125 per month. Of this sum he spends $75 
 and saves the remainder. What part of his monthly earn- 
 ings does he save ? What per cent ? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the cost of 1100 eggs at 23| ^ per dozen. 
 
 2. Counting 2000 Ib. to a ton, find the cost of 5| T. of 
 steel at l T 5 g ^ per pound. 
 
 3. When flour is sold at $6.02 per barrel of 196 Ib., what 
 should be paid for 55J Ib. ? 
 
 4. I bought 300 bbl. of flour at $5.75 per barrel. At what 
 price must I sell it per barrel in order to gain $ 150 ? 
 
 5. The cost of 200 bu. of wheat was $204.50 and the 
 selling price $212.35. What was the gain per bushel? 
 
 6. A can do a piece of work in 5^ da. and B in 7^ da. 
 If they join in the completion of the work, how long will it 
 take them ? 
 
146 PRACTICAL BUSINESS ARITHMETIC 
 
 7. How much will 7 men earn in 6 da., working 10 hr. per 
 day, at 25^ per hour? 
 
 8. At 12.50 per day of 8 hr., how much should a man 
 receive for 11J hours' work ? 
 
 9. A boy works 4^ da. at the rate of $5.75 per week of 6 
 da. How much does he earn ? 
 
 10. W, in 1 of a day, earns $1.25, and Y, in | of a day, earns 
 $0.87-|-. How much will the two together earn in 40| da. ? 
 
 11. A and B together can do a piece of work in 10 da. 
 If A can complete the work alone in 16 da., how long will 
 it take B to do it? 
 
 12. Nov. 1, in a recent year, was on Tuesday. How much did 
 B earn during November if he was employed every working day 
 at the rate of 13.75 per day? 
 
 13. A farm is divided into 6 fields containing, respec- 
 tively, 25f, 26 T 7 g, 32f, 56|, 35 T 9 ^, and 52-^ A. How much is 
 the farm worth at 137.50 per acre? 
 
 14. Find the total cost of : 630 Ib. sugar at 4| ^ ; 375 Ib. 
 tea at 38^; 240 Ib. crackers at 5| ^ ; 65 Ib. rice at 7^ e ^ ; 
 52J Ib. raisins at 7| ^ ; and 250 Ib. coffee at 24| ^. 
 
 15. A retailer bought 5 bbl. of flour at 16.50 per barrel, 
 12 bu. potatoes at 75 ^ per bushel, and gave in payment a 
 fifty-dollar bill. How much change should he receive ? 
 
 16. Five garden lots measuring 2|, 10 1, 12|, 6 T 7 g, and 
 8 T 9 ^ A. respectively, were bought at $ 212. 87 per acre and 
 sold at $250.50 per acre. Find the gain resulting from the 
 transaction. 
 
 17. I bought 4120 2 yd. of silk at $1.02 per yard and sold 
 | of it at $1.50 per yard, and the remainder for $1600. 
 What was the average price received per yard, and how 
 much did I gain ? 
 
 18. A, B, C, and D hire a pasture for $419.50. A put in 
 25 head of cattle for 4 wk.; B, 31 head for 5 wk.; C, 44 
 head for 6 wk.; and D, 40 head for 8 wk. How much 
 should each be required to pay ? 
 
COMMON FRACTIONS 147 
 
 19. A grain dealer bought 6750^ bu. of corn at 60^ per 
 bushel, and 2130J bu. of oats at 32f f per bushel. He sold 
 the corn at 69J ^ per bushel, and the oats at 29f p per bushel. 
 Did he gain or lose, and how much ? 
 
 20. A grocer bought 15 bbl. of molasses, each containing 
 50 gal., at 25| ^ per gallon. He retailed 150| gal. of it at 
 30^ per gallon, 170^ gal. at 28^ per gallon, and the re- 
 mainder at 35^ per gallon. Did he gain or lose, and how 
 much ? 
 
 21. Find the cost of 25 bx. of cheese weighing : 67 4, 
 62-4, 61-3, 72-4, 81-5, 64-4, 66-3, 65-5, 61-4, 
 62-3, 64-4, 66-3, 65-5, 61-4, 62-3, 64-4, 67-3, 
 65-5, 60-3, 62-4, 67-4, 65-4, 60-4, 68-3, 65-4 
 lb., respectively, at 11| ^ per pound. 
 
 22. A dry-goods merchant bought 25 pc. of Scotch 
 cheviot containing 42 1 , 40 2 , 45 3 , 41 1 , 40 1 , 45 2 , 42 1 , 43 3 , 38 1 , 
 35 1 , 36 2 , 41 2 , 44 \ 45 2 , 39 1 , 37 1 , 42 2 , 47, 41, 42 1 , 43 3 , 40 1 , 47 1 , 
 38, 31 yd., respectively, at 39J^ per yard. If he sold the 
 entire purchase at 43f ^ per yard, did he gain or lose, and 
 how much ? 
 
 23. C. W. Bender fails in business. He owes A 1712.25; 
 B, 11421. 25; C, 1625.25; D, 11460.75; his entire resources 
 amount to $ 2109. 75. What fractional part of his indebted- 
 ness can he pay? what per cent? How many cents on $1 ? 
 If his creditors accept payment on this basis, how much will 
 each receive ? 
 
 24. A dry-goods merchant bought 12 pc. of striped 
 denim containing 40 1 , 45 1 , 40 1 , 48 2 , 41 2 , 40 3 , 45 2 , 41 \ 44 2 , 
 39 2 , 51 1 , 38 yd., respectively, at 14| ^ per yard; 15 pieces of 
 cashmere containing 39 \ 41 2 , 42 \ 45 2 , 39, 52, 40, 45, 46, 51, 
 47 2 , 42 \ 41 \ 47 1 , 48 yd., respectively, at 11.12 per yard; 10 
 pc. wash silk containing 35 *, 30, 31 2 , 30, 30, 30, 32 3 , 32, 31 *, 
 32 yd., respectively, at 31^ per yard. He gave in payment, 
 cash, $300, and a 60-da. note for the balance. What was the 
 amount of the note ? 
 
148 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 25. Find the amount of the following bill : 
 
 Boston, Mass., Apr. 15, 19 
 
 MESSRS. CHARLES H. PALMER & Co. 
 
 Springfield, Mass. 
 
 Bought of EDGAR W. TOWNSEND & Co. 
 
 Terms : cash 
 
 
 250 
 
 Ib. Rio Coffee $0.24J 
 
 
 
 
 
 
 450 
 
 " Mocha Coffee .201 
 
 
 
 
 
 
 172 
 
 doz. Eggs .14| 
 
 
 
 
 
 
 990 
 
 Ib. White Sugar .04f 
 
 
 
 
 
 
 900 
 
 ' Brown Sugar .03$ 
 
 
 
 
 
 
 975 
 
 1 Granulated Sugar .06f 
 
 
 
 
 
 
 172 
 
 ' Butter .16$ 
 
 
 
 
 
 
 3021 
 
 ' Ham .131 
 
 
 
 
 
 
 280 
 
 ' Cream Codfish .07| 
 
 
 
 
 
 
 11 
 
 pails Mackerel 1.87$ 
 
 
 
 
 
 
 120 
 
 Ib. Raisins .07f 
 
 
 
 
 
 
 480 
 
 " Starch .03} 
 
 
 
 
 
 
 225 
 
 " Japan Tea .26$ 
 
 
 
 
 
 
 210 
 
 " Young Hyson Tea .24| 
 
 
 
 
 
 
 420 
 
 " Oolong Tea .27| 
 
 
 
 
 
 
 157 
 
 " Pearl Tapioca .03$ 
 
 
 
 
 
 
 17 
 
 pkg. Yeast Cakes .37$ 
 
 
 
 
 
 
 375 
 
 Ib. Java Coffee ,23f 
 
 
 
 
 
 26. C's salary is $17.50 per week of 48 hr. How much 
 should he be paid for 11 da., working 9 hr. per day? 
 
 27. A man earning $2.75 per day of 10 hr. lost 7- hr. 
 during one week of 6 da. How much should he receive for 
 the week's work ? 
 
 28. E begins work at 7:30 A.M. and quits work at 6:30 P.M. 
 If he is paid at the rate of 3.75 per day of 8 hr. and he takes 
 the noon hour off for lunch, how much should he receive for 
 his day's labor? 
 
 29. A factory foreman is paid 3.75 per day of 8 hr. and 
 $0.50 an hour for overtime. How much should he be paid for 
 a week in which he begins work at 7 o'clock A.M., quits work at 
 7:30 o'clock P.M., and takes 1J hr. off each day for lunch ? 
 
COMMON FRACTIONS 
 
 149 
 
 30. Copy the following time sheet and find : (a) the total 
 number of hours worked on each order ; (b) the total number 
 of hours worked each day; (V) the amount earned on each 
 order ; and (<i) the total amount earned during the week. 
 
 BOSTON ELEVATED RAILWAY CO. 
 
 Time worked by E. M. Doe, during the week ending Aug. 15. 
 Rate per hour, 25 cents. Occupation, Lineman. 
 
 Order No. 
 
 Sat. 
 
 Sun. 
 
 Mon. 
 
 Tues. 
 
 Wed. 
 
 Thurs. 
 
 Fri. 
 
 Total 
 Hours 
 
 Amount 
 
 420 
 
 21 
 
 
 4 1 
 
 
 
 
 
 
 
 
 715 
 
 
 
 2* 
 
 
 9^ 
 
 
 
 
 
 
 960 
 
 
 
 
 7- 
 
 
 
 
 
 
 
 318 
 
 4f 
 
 
 H 
 
 
 
 
 
 
 
 
 420 
 
 
 
 
 2 i 
 
 
 4 
 
 H 
 
 
 
 
 715 
 
 
 
 
 
 
 4| 
 
 7* 
 
 
 
 
 Total hr. 
 
 
 
 
 
 
 
 
 
 
 
 31. A foreman in a shoe factory receives $5 per day and 
 10.50 per hour for overtime. His time for two weeks is as fol- 
 lows : Monday, 10 hr. ; Tuesday, 12 hr. ; Wednesday, 8 hr. ; 
 Thursday, 8| hr. ; Friday, 12^ hr. ; Saturday, 10 hr. ; Monday, 
 11 hr. ; Tuesday, 12J hr. ; Wednesday, 10 hr. ; Thursday, 8 hr. ; 
 Friday, 8| hr. ; Saturday, 9J hr. How much should he be paid 
 for the two weeks' work, assuming that a day's work is 8 hr.? 
 
 32. The following is a manufacturer's piece-labor ticket. 
 Copy it and find the totals and amounts as indicated. 
 
 PIECE LA BO R 
 
 Workman's No. 
 Week ending 
 
 /y 
 
 Examined by 
 
 Articles 
 
 M. 
 
 T. 
 
 w. 
 
 T. 
 
 F. 
 
 s. 
 
 Total 
 
 Price 
 
 Extensions 
 
 Amount 
 
 -^^JJ^ 
 
 ,/^ 
 
 ^ 
 
 ^ 
 
 
 yX* 
 
 
 
 ^/-v 
 
 
 
 
 
 
 ^J^ 
 
 //^ 
 
 
 ? /7 
 
 
 ^ x7 
 
 /z 
 
 
 /j^^ 
 
 
 
 
 -ft^^g^ 
 
 
 ^r 
 
 
 
 
 
 
 2-t? fa 9- 
 
 
 
 
 T^^J 
 
 
 
 
 
 
 /^ 
 
 
 /fY*< 
 
 
 
 
CHAPTER XIII 
 
 ALIQUOT PARTS 
 
 206. An aliquot part of a number is a part that will be con- 
 tained in the number an integral number of times. 
 
 Thus, 2, 3|, and 5 are aliquot parts of 10. 
 ORAL EXERCISE 
 
 1. How many cents in || ? in $1? in $? in 
 
 2. What aliquot part of $1 is 25^? 50^? 6| 
 
 3. Read aloud the following, supplying the missing terms: 
 16 x 50^ = 16 x $| = | of 116 ; l 16 x 25^ = 16 x $-*- - \ of $16 ; 
 16 x 12^=16 x$- -of $16; 16x6^=16x$- 
 
 of 116. 
 
 4. Give a short method for finding the cost when the quan- 
 tity is given and the price is 50^; 25^; 12|^; >\<f. 
 
 5. What is the cost of 160 yd. of dress goods at $1? at 
 at 25^? at 12^? at 6|^? 
 
 6. How many cents in |J? in |1? in IjL? in 1^? in 
 
 7. What aliquot part of |1 is 33^? 
 
 8. Read aloud the following, supplying the missing terms : 
 l4f^ = 140 x *i - \ of $140; 90 x 6f0 = 90 x $- 
 
 = - -ofi90; 90x20^ = 90x* - = - of $90. 
 
 9. Read aloud the following, supplying the missing terms : 
 240x33^=240x1 - = J of $240 : 240 x 16f = 240 x 
 $1 = - - of $ 240; 240 x 12^ = 240 x $- - of $ 240. 
 
 10. Give a short method for finding the cost when the quan- 
 tity is given and the price is 33 J^ ; 16|Y; 8J^; 6|^; 14f-^. 
 
 11. Find the cost of 960yd. of cloth at 33^; at 16|^; at 
 
 150 
 
ALIQUOT PAKTS 151 
 
 ORAL EXERCISE 
 
 State the cost of: 
 
 1. 240 Ib. tea at 50^; at 33^; at 25^. 
 
 2. B601b. coffee at 33^; at 26^; at 20 j^; at!2i?. 
 
 3. 720 gal. cider at 6^?; at6f?; at 10?'; at 12^?. 
 
 4. 2400 doz. eggs at 12* ?; at 16f ?; at 20?; at 25?. 
 
 5. 2400 yd. prints at 8^?; at 6f ? ; at 6J?; at 12-|?. 
 
 6. 960 yd. cotton at 6|?; at8J?; at6f?; at 10?; at!2i?. 
 
 7. 2040yd. plaids at 50^; at 33J? ; at 25?; at 20?; at 16f ?. 
 
 8. 480 Ib. lard at 81?; at 6^?; at 121?; at 16f ?; at 10^. 
 
 9. 3600 Ib. raisins at 12^; at!6|^; at 20^; at 25^; at 331^. 
 
 10. 480yd. lining at 8^; at 6^ ; at 10^; atl2-|^; at6|^. 
 
 11. 4200 yd. silesia at 10^; at 20^ ; at 12-J^; at 16|^ ; at 14| \f. 
 
 12. 1500 yd. plaids at$l ; at 50^; at 33^; at 25^; at 20^. 
 
 13. 420yd. stripe at 10^; atl2^; at 14|^; at 16f ^; at 25?. 
 
 14. 120yd. gingham at 8J^; at6J^; at6f^; at loV; atl2-|-^. 
 
 15. 1240 yd. wash silk at 25^; at 50^; at 33^; at 20?. 
 
 16. At the rate of 3 for 50^, what will 27 handkerchiefs 
 cost? 
 
 17. At 33^? per half dozen, what will 12 doz. handkerchiefs 
 cost? 17 doz.? 25 doz.? 7 doz.? 4| doz.? 
 
 18. A merchant bought cloth at 33 J? per yard and sold it 
 at 50^ per yard. What was his gain on 1680 yd.? 
 
 ORAL EXERCISE 
 
 1. What is the cost of 12* yd. of silk at 96 ^ per yard? 
 
 SUGGESTION. The cost of 12| yd. at 96^ = the cost of 96 yd. at 12^. 
 Interchanging the multiplicand and multiplier considered as abstract numbers 
 does not affect the product. 
 
 2. Find the cost of 25 yd. of silk at $1.72 per yard. 
 SUGGESTION. The cost of 25 yd. at 1 1 .72 (172^) = the cost of 172 yd . at 25^. 
 
 3. Find the cost of : 
 
 a. 25 yd. at 16?. c. Q\ Ib. at 32?. e. 25 yd. at 84?. 
 
 b. 12lyd. at 48?. d. 12|lb.at80^. /. 12J yd. at |1.75. 
 
152 PKACTICAL BUSINESS ARITHMETIC 
 
 TABLE OF ALIQUOT PARTS 
 
 Nos. 
 
 1'e 
 2 8 
 
 i's 
 
 * 
 
 iV* 
 
 V* 
 
 r; 
 
 rVs 
 
 iV* 
 
 r 
 
 ftr's 
 
 1 
 
 .50 
 
 .25 
 
 121 
 
 .06 
 
 .331 
 
 .16f 
 
 .081 
 
 .06| 
 
 .20 
 
 .10 
 
 10 
 
 5. 
 
 H 
 
 H 
 
 .62J 
 
 ** 
 
 If 
 
 .831 
 
 .66f 
 
 2. 
 
 1. 
 
 ICO 
 
 50. 
 
 25. 
 
 l*i 
 
 <H 
 
 88J 
 
 l(5f 
 
 B| 
 
 O* 
 
 20. 
 
 10. 
 
 1000 
 
 500. 
 
 250. 
 
 125. 
 
 621 
 
 333$ 
 
 166$ 
 
 831 
 
 66| 
 
 200. 
 
 100. 
 
 WRITTEN EXERCISE 
 
 In the three problems following make all the extensions mentally. 
 
 1. Without -copy ing, find quickly the total cost of : 
 84 Ib. tea at 50^. 6^ Ib. tea at 64^. 
 
 75 Ib. tea at 33J^. 25 Ib. cocoa at 52^. 
 
 72 Ib. coffee at 25^. 12| Ib. cocoa at 48^. 
 
 84 Ib. coffee at 33^. 360 Ib. codfish at 6|^. 
 
 25 Ib. coffee at 28^. 66 Ib. crackers at 
 
 88 Ib. candy at 12^. 25 Ib. chocolate at 
 
 24 Ib. tapioca at 6|^. 25 cs. horseradish at 
 
 2. Without copying, find quickly the total cost of: 
 
 25 yd. silk at 8 
 12| yd. silk at 
 750 pc. lace at 6^ 
 112 yd. ticking at 
 210 yd. plaids at 
 
 128 gro. buttons at 12| ^. 
 68 yd. lansdowne at 
 
 77 yd. duck at 
 6^ gro. buttons at 32^. 
 155 yd. cheviot at 2 
 96 yd. gingham at 
 84 yd. shirting at 12. 
 25 doz. spools thread at 2 
 168 yd. striped denim at 8J ^. 
 3. Without copying, find quickly the total cost of : 
 
 25 bu. corn at $0.84. 
 25 bu. corn at $0.44. 
 25 bu. oats at $0.35. 
 121 bu. r y e at $1.04. 
 6| bu. wheat at $1.20. 
 6| bu. wheat at $1.12. 
 25 bu. timothy seed at $2.40. 
 50 bu. timothy seed at $2.75. 
 
 25 bu. corn at 
 25 bu. corn at -10.72. 
 12-J bu. oats a t 10.36. 
 25 bu. beans at 82.80. 
 12|-bu. wheat at -fl.04. 
 12Jbu. millet at $1.24. 
 25 bu. clover seed at 13.60. 
 50 bu. clover seed at 13.75. 
 
ALIQUOT PARTS 153 
 
 ORAL EXERCISE 
 
 1. Multiply by 10: 4; 15 ; .07 ; 8^; $1.12 ; $ 24.60; 112.125. 
 
 2. Multiply by 100: 3; 17; .09; 12^; $1.64; 121. IT. 
 
 3. Multiply by 1000: 7; 29; .19; 15^; 11.75; 123.72. 
 
 4. What aliquot part of $10 is 12.50? Find the cost of 16 
 articles at $10 each ; at 12.50 each. 
 
 5. Find the cost of 84 bu. of wheat at 11.25. 
 
 SOLUTION. 1.25 is $ of $10. 84 bu. at $10 = $840; of $840 = $105. 
 
 6. Formulate a short method for finding the cost when the 
 quantity is given and the price is $1.25. 
 
 SOLUTION. $1.25 is | of $10; hence, multiply the quantity by 10 and take \ 
 of the product. 
 
 7. Formulate a short method for finding the cost when the 
 quantity is given and the price is $2.50; $3.33; |1.66f. 
 
 8. Find the cost of 168 yd. of cloth at $1.25; at $2.50; 
 at $3.331; a t $1.66|. 
 
 9. What aliquot part of $100 is $25 ? $12.50? $6.25 ? 
 
 10. Find the cost of 72 chairs at $25 each. 
 
 SOLUTION. 72 chairs at $100 = $7200; but the price is $25, which is of 
 $100 ; therefore, \ of $7200, or $1800, is the required cost. 
 
 11. Give a short method for multiplying any number by 25 ; 
 by 12|; by 6-1; by 331; by 8J. 
 
 12. Find the cost of 25 T. coal at $7.20 ; of 6| T. ; of 121 T. 
 
 13. What aliquot part of 1000 is 250? 500? 125? 621? 
 3331? 166f? 200? 100? 83i? 66f? 
 
 14. Formulate a short method for multiplying a number 
 by 250. 
 
 SOLUTION. Since 250 = 10 1 ~, multiply by 1000 and take of the product. 
 
 15. Give a short method for finding the cost when the quan- 
 tity is given and the price is $125; $166|. 
 
 16. Multiply 84 by 50; by 25; by 121; by 16f ; by 331 
 
 17. Multiply 160 by 21; by 11; by 121 ; by 125; by 62-|-. 
 
 18. Multiply 240 by 3| ; by If; by 331; by 16|; by 3331. 
 
154 PEACTICAL BUSINESS ARITHMETIC 
 
 19. Find the cost of 250 sofa beds at 32 each. 
 
 SOLUTION. The cost of 250 beds at $32 the cost of 32 beds at $250. The 
 cost of 32 beds at .$1000 = $32,000 ; but the price is $250, which is \ of $ 1000 ; 
 therefore, \ of $32,000, or $8000, is the required cost. 
 
 20. Find the cost of 720 couches at $12.50 each. 
 
 21. Find the cost of 440 Ib. sugar at 2^. 
 
 SOLUTION. 2^ is i of 10^. The cost of 440 Ib. at 10^ = $44 ; but the price is 
 2^, therefore, \ of $44, or $11 the required cost. 
 
 22. Formulate a short method for finding the cost when the 
 quantity is given and the price is 1-J^. 
 
 SOLUTION. \\<f> = \ of 10^ ; hence, point off one place in the quantity and take 
 \ of the result. 
 
 23. Give a short method for finding the cost when the quan- 
 tity is given and the price is 2|^; 3J^ ; 1|^. 
 
 24. Find the cost of 180 Ik at 2^; at l\f \ at 
 at 1J^. Also of 240 Ib. at each of these prices. 
 
 25. Find the cost of 2400 Ib. at 2| ^; at 1^; at 
 at If ^. Also of 360 Ib. at each of these prices. 
 
 ORAL EXERCISE 
 
 By inspection find the cost of: 
 
 1. 25 Ib. tea at 54^. 16. 1-J yd. silk at 88^. 
 
 2. 25 Ib. tea at 33 j 17. 64 pc. lace at $1.25. 
 
 3. 125 Ib. tea at 64^. 18. 125 yd. silk at 11.12. 
 
 4. 6-| A. land at 1112. 19. 1250 bbl. beef at 124. 
 
 5. 25 T. coal at 18.40. 20. 78 yd. velvet at $2.50. 
 
 6. 25 T. coal at 15.20. 21. 2| bu. -potatoes at 44^. 
 
 7. 18 T. coal at 16.25. 22. 640 bu. apples at 12\f. 
 
 8. 164 A. land at 825. 23. 840 yd. prints at 16| f. 
 
 9. 72 T. coal at $6.25. 24. 12| bu. potatoes at 64^. 
 
 10. 250 yd. silk at 88^. 25. 84lbookcases at 812.50. 
 
 11. 250 yd. silk at 96^. 26. 810 bbl. pork at 812.50. 
 
 12. 25 pc. lace at 86.60. 27. 125 yd. crepon at 3.60. 
 
 13. 250 yd. silk at f 1.12. 28. 12-J- yd. cheviot at 81.04. 
 
 14. 192 A. land at 812.50. 29. 24 "oak sideboards at 8125 
 
 15. 165 gro. buttons at 33^. 30. 12^ yd. gunner's duck at 
 
ALIQUOT PARTS 155 
 
 WRITTEN EXERCISE 
 
 In the following problems make all the extensions mentally. See 
 how many of the problems can be done in 10 minutes. 
 
 1. Without copying, find the total cost of : 
 
 425 Ib. at 10 f. 2500 Ib. at 64 24 Ib. at 11 f. 
 
 310 Ib. at 20 1600 Ib. at 25 f. 48 Ib. at 21 t. 
 
 100 Ib. at 14 f. 1893 Ib. at 31 21 Ib. at 96 
 
 1000 Ib. at 27 2500 Ib. at 14 125 Ib. at 24 
 
 1000 Ib. at 41 f. 1400 Ib. at 25 f. 192 Ib. at 3J 
 
 1250 Ib. at 44 1250 Ib. at 88 f. 88 Ib. at 121 
 
 2. Without copying, find the total cost of : 
 
 88 yd. at 11 f. 174 yd. at 10 f. 24 yd. at 12 t. 
 
 72 yd. at 31 123 yd. at 11 78 yd. at 3 
 
 104 yd. at 2| 127 yd. at 11 f. 165 yd. at 20 
 
 480 yd. at 6| X. 246 yd. at 25^. 114 yd. at 6f 
 
 360 yd. at 8 J A 171 2 yd. at 10 1280 yd. at 61 f. 
 
 121 yd. at 11 1783 yd. at 1.0 X. 192 yd. at 33^. 
 
 3. Copy and find the total cost of : 
 
 450 Ib. at 1 1 f. 249 Ib. at 25 f. 6J Ib. at 88 f. 
 
 820 Ib. at 11 f. 240 Ib. at 3J 92 Ib. at 2| f. 
 
 1200 Ib. at 4J f. 200 Ib. at 3-| f. 121 Ib. at 24 <?. 
 
 1400 Ib. at 6i 450 Ib. at 6f 18 Ib. at 4 J f. 
 
 7961 Ib. at 50 f. 79 J Ib. at 40 f. 125 Ib. at 18 
 
 1293 Ib. at 30 78J Ib. at 50 f. . 648 Ib. at 6J ^. 
 
 1480 Ib. at 40 f. 750 Ib. at 33J 1900 Ib. at 4J 
 
 4. Copy and find the total cost of : 
 
 750 gal. at 8-J 99 gal. at 30 f. 360 gal. at 5 f. 
 
 488 gal. at 6| f. 60 gal. at 6| <f. 625 gal. at 64 f. 
 
 640 gal. at 6-[ f. 50 gal. at 76 ^. 810 gal. at 1^. 
 
 194 gal. at 50 f. 25 gal. at 74 f. 920 gal. at 2J 
 
 176 gal. at 25 f. 12 j gal. at 88 165 gal. at 6| f. 
 
 280 gal. at 12 79 gal. at 331 240 gal. at 621 ^ 
 
 720 gal. at 331 20 gal. at 11.79. 666 gal. at 66| f. 
 
 366 gal. at 16 j^. 61 gal. at $1.96. 1680 gal. at 16f 
 
156 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. How much less than 1 is 75^? what fractional part 
 of |1 less? 
 
 2. Find the cost of 144 pc. of lace at 75 ^ per piece. 
 
 SOLUTION. At $ 1 per piece the cost would be $ 144 ; but the cost is not $ 1 
 but ^ less than $ 1. Deducting of $ 144, the result is $ 108, the required cost. 
 
 3. Find the cost of 124 bookcases at $7.50. 
 
 SOLUTION. $7.50 is \ less than $10. $1240 less \ of itself = $930, the 
 required result. 
 
 4. Formulate a rule for multiplying a number by .75; by 
 7 i ; by 75 ; by 750. 
 
 5. How much more than $1 is |1.12|? What fractional 
 part of $ 1 more ? 
 
 6. Find the cost of 84 yd. of silk at $1.16f per yard. 
 
 SOLUTION. At $ 1 per yard, the cost would be $84 ; but $1.16f is more 
 than $1. Adding \ of $84 to itself, the result is 98, the required cost. 
 
 7. Formulate a short method for finding the cost when 
 the quantity is given and the price is $1.12^; $1.16| ; 
 $1.33j; $11.25; $112.50. 
 
 8. How much less than $1 is 87|^? what fractional 
 part of $1 less? Formulate a short method for multiplying a 
 number by 87|. 
 
 9. Formulate a short method for multiplying a number 
 by .831; by 1.25. 
 
 10. Compare the cost of 87J yd. at 64^ with the cost of 
 64 yd. at 87|^. 
 
 ORAL EXERCISE 
 
 State the cost of: 
 
 1. 24 yd. at 75 1. 7. 87 \ yd. at $ 2.88. 13. 270 yd. at 111 ^ 
 
 2. 75 yd. at 24^. 8. 25yd.at4^. 14. 144yd.atll^. 
 
 3. 192yd. at 871^. 9. 28 yd. at 7-^. 15. lllyd. 
 
 4. 240yd. at 831^. 10. 27yd. at 75^. 16. 1125 yd. a 
 
 5. 871 yd. at $2.48. 11. 75yd.at81^. 17. 1125yd.at32^. 
 
 6. 176 yd. at $1.121. 12. 75yd. at 16^. 18. 1125 yd. at 48^. 
 
ALIQUOT PAKTS 
 
 157 
 
 72yd. at 
 
 87iyd. at 88^. 
 320yd. at 11 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the total of the costs called for in problems 115 in 
 the oral exercise at the top of page 151. 
 
 2. Find the total cost of the items in the oral exercise at the 
 bottom of page 154; of the -items in the oral exercise at the 
 bottom of page 156. 
 
 3. Find the total cost of : 
 
 84 yd. at if. 98 yd. at 9^. 
 
 112| yd. at 5^. 79 yd. at 11^. 
 
 112| yd. at Q^ 17 yd. at 16^. 
 
 4. Find the total cost of : 
 
 71 yd. at 22^. 85 yd. at 30^. 
 
 31yd. at 44^. 17 yd. at 25^. 
 
 82yd. at 88^. 121 yd. at 39^. 
 
 71 yd. at 72^. 250 yd. at 64^. 
 
 5. Find the total cost of : 
 
 192 Ib. at 31^. 167 Ib. at I2>. 
 
 384 Ib. at 6-i f. 184 Ib. at 37^. 
 
 378 Ib. at 6\f. 2164 Ib. at 2-| f. 
 
 149 Ib. at 6J f. 1369 Ib. at 2 1 f. 
 
 6. Copy and find the amount of the following bills, less 3 % 
 
 a. 
 
 Rochester, N.Y., Aug. 2, 19 
 
 30yd. at 
 24 yd. at 
 56yd. at 
 124yd. at il.l2|. 
 
 1151f Ib. at 
 17211 Ib. at 
 29111 Ib. at 
 2706 Ib. at 33 
 
 MR. C. G. GARLIC 
 
 North Rose, N.Y. 
 
 Terms : cash, less 3 %. 
 
 To SMITH, PERKINS & Co., Dr. 
 
 
 
 330 Ib. Granulated Sugar 6 
 32 ' Butter 22^ 
 64 < Cheese 16f? 
 75 ' Young Hyson Tea 24 ^ 
 155 ' Dried Apples 8^ 
 300 ' Brown Sugar 3^ 
 60 ' Oolong Tea 51 ? 
 125 ' Rio Coffee 28^ 
 250 * Mocha Coffee 24^ 
 
 
 
 
 
158 
 
 PEACTICAL BUSINESS ARITHMETIC 
 
 b. 
 
 Buffalo, N.Y., Aug. 5, 19 
 
 MR. GEORGE A. COLLIER 
 
 Savannah, N.Y. 
 
 Bought of GEORGE H. BUELL & Co. 
 
 Terms : cash, less 3 %. 
 
 
 
 72 pr. Boys' Hose 12 tf 
 18 doz. Linen Handkerchiefs 2.50 
 18 " Lace Handkerchiefs 3.33 
 78 yd. Silk Velvet 3.331 
 75 pc. Black Ribbon 28^ 
 347 yd. Pontiac Seersucker 6\f> 
 186 " Washington Cambric 12ty 
 
 
 
 
 
 ORAL EXERCISE 
 
 1. At 33| ^ per pound, how many pounds of coffee can be 
 bought for $12? 
 
 SOLUTION. .33 = $ i ; 3 pounds can be bought for $ 1 ; then, 12 x 3 Ib. 
 = 36 Ib., the required result. 
 
 2. When the cost is given and the price is 25^, how may 
 the quantity be found? 
 
 SOLUTION. When the price is 25 $ , the quantity is 4 times the cost ; hence, 
 multiply the cost by 4. 
 
 3. Give a short method for finding the quantity when the 
 cost is given and the price is 20^; 33^; 12-^; &|^; 6|Y; 
 
 4. Formulate a short method for dividing any number by 
 125. 
 
 SOLUTION. 125 is \ of 1000 ; then the quotient by 125 will be 8 times the 
 quotient by 1000. Therefore, divide by 1000 and multiply the result by 8. Or, 
 T ^ = ToW Therefore, multiply by 8 and move the decimal point three 
 places to the left. 
 
 5. Give a short method for dividing by 6^. 
 
 SOLUTION. 6 = T \ of 100 ; then the quotient by 6| will be 16 times the 
 quotient by 100. Therefore, move the decimal point two places to the left and 
 multiply the result by 16. Or, = ^. Therefore, multiply by 16 and move the 
 decimal point two places to the left. 
 
ALIQUOT PARTS 
 
 159 
 
 6. Give a short method for dividing a number by 12 1 ; by 
 16| ; by 381 . by 6| ; by 66|; by 3331; by 166|. 
 
 7. Formulate a short method for dividing a number by .75. 
 
 SOLUTION. .75 increased by ^ of itself 1. When the divisor is 1 the quo- 
 tient is the same as the dividend. Hence, to divide a number by .75 increase 
 the number by % of itself. 
 
 8. At 75^ per bushel, how many bushels of wheat can be 
 bought for $144? for $192? for $240? for 1780? for 11260? 
 for 8360? for 1 1350? for 1810? 
 
 9. At 17.50 per dozen, how many dozen men's gloves can 
 be bought for 11440? 
 
 SOLUTION. $7.50 -f 1 of itself = 10. To divide by 10 is to point off one 
 place to the left. $ 1440 + * of itself = $ 1920 ; $ 1920 -=- $ 10 = 192, the number 
 of pairs of gloves. 
 
 10. State a short method for dividing a number by 7J ; by 
 75 ; by 750. 
 
 ORAL EXERCISE 
 
 Find the quantity: 
 
 COST 
 
 PRICE PER 
 YARD 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 
 $250 
 $120 
 8215 
 $126 
 $125 
 
 7. 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 
 COST 
 
 $75 
 $12 
 $25 
 $38 
 
 $125 
 $420 
 
 PRICE PER 
 POUND 
 
 If* 
 
 $1.25 
 
 WRITTEN EXERCISE 
 
 Find the quantity : 
 
 PRICE PER 
 COST YARD 
 
 $570.00 75* 
 
 $612.00 
 
 $274.50 
 $281.50 
 $864.50 
 
 75^ 
 
 6. 
 7. 
 8. 
 9. 
 10. 
 
 COST 
 
 $1721.00 
 $1842.50 
 
 $1785.50 
 $2142.00 
 
 $2720.50 
 
 PRICE PER 
 BUSHEL 
 
 871* 
 
CHAPTER XIV 
 
 BILLS AND ACCOUNTS 
 BILLS 
 
 207. A detailed statement of goods sold, or of goods bought 
 to be sold, is called either a bill or an invoice. A detailed state- 
 ment of goods bought to be used or consumed, such as office 
 furniture, stationery, and fuel, or a statement of services ren- 
 dered, or of a work performed, is called a bill. 
 
 Thus, a physician's statement of services rendered, or a transportation 
 company's bill for work performed, and the charges for the same, is called a 
 bill ; but a statement of a quantity of silk bought or sold by a dry-goods 
 merchant in the course of trade is called either a bill or an invoice. 
 
 208. The models following show a variety of current prac- 
 tices in billing. They will therefore be found helpful as studies. 
 
 1. GROCERIES 
 Boston, Mass., Oct. 15, 19 
 
 Messrs. SMITH, PERKINS & CO. 
 
 Rochester, N.Y. 
 
 Bought of E. E. GRAY COMPANY 
 
 Terms 30 days Telephone, Main 167 
 
 
 3 
 
 bbl. Rolled Oats $6.25 
 
 18 
 
 75 
 
 
 
 
 10 
 
 " Gold Medal Flour 6.50 
 
 65 
 
 00 
 
 
 
 
 5 
 
 bx. Wool Soap 3.10 
 
 15 
 
 50 
 
 99 
 
 25 
 
 This is one of the simplest bill forms; it is the form that is common 
 in a great many lines of business. 
 
 160 
 
BILLS AND ACCOUNTS 
 
 161 
 
 2. GROCERIES 
 Boston, Mass., Nov. 12, 19 
 
 Messrs. E. 0. Sherman & Co. 
 
 Charlestown, Mass. 
 
 Bought of S. S. PIERCE COMPANY 
 
 Terms 30 da. ; 3% 10 da. 
 
 10 Red Label Hams 
 20 mats Java Coffee 1500 
 12 6-lb. tins Mustard 72 
 15 6-lb. tins Cocoa 90 
 
 146 Ib. $0.23 $33.58 
 
 .25 375.00 
 
 .36 25.92 
 
 .34 30.60 
 
 $465.10 
 
 Goods bought by the mat, chest, case, etc., are frequently billed by the 
 pound. The above bill shows the form in such cases. 
 
 8. HARDWARE 
 
 The following bill is sometimes used in the hardware business. The first 
 number after the name of the article is the quantity; the number above the 
 horizontal line following, the price ; and the number below the line, the grade. 
 Thus, the first item in the bill shows that 12 doz. porcelain knobs in all were 
 sold, of which 6 doz. were No. 8 at $1,25 and 6 doz. No. 16 at $ 1.331. 
 
 19- 
 
 ^ / 
 
 fbureka J^arctivare Qompany 
 
 / 2- 
 
 
 AL 
 
 > 
 
162 
 
 PRACTICAL BUSINESS ARITHMETIC 
 4. WHOLESALE DRY GOODS 
 
 CHICAGO,- 
 
 M 
 
 19. 
 
 Bought of MARSHALL FIELD & CO. 
 
 Franklin Street and Fifth Avenue 
 
 TERMS 
 
 z^ 
 
 jf-rri^^&S^eXs*? ^4~ 
 
 AZ. 
 
 4-0 37* 40 >/# V -^7 > VJ-* 
 
 & 
 
 rfcrf^W^fr^r^, 
 
 4-2. 
 
 J&. 
 
 *2& 
 
 LZ. 
 
 /2 
 
 42- 40 
 
 /^/ 
 
 2^2,^2. 
 
 
 37%+ 
 
 37 
 
 In the wholesale dry-goods business the price is generally for a yard, and 
 the number of yards to the piece varies in some kinds of cloth. The first 
 item in the above bill is followed by a series of numbers, 41, 42, etc. ; these 
 represent the number of yards in each of the 12 pc. Immediately following 
 these numbers is recorded the total number of yards in the 12 pc. The 
 total number of yards should be found by horizontal addition. 
 
 5. MANUFACTURER'S 
 
 The following is a bill for neckwear. The different styles are distin- 
 guished by the marks at the left of the quantity. This form is common 
 among manufacturers, jobbers, and wholesalers. Bills on which trade 
 discounts (see page 242) are allowed are arranged as shown in this bill. 
 
BILLS AND ACCOUNTS 
 
 163 
 
 Betogorlt, Oct. 10, 
 
 Jttessrs. J. E. Whiting & Co. 
 
 Bos-ton, Mass. 
 
 19 
 
 Cerms Net 30 days 
 
 721 
 
 ji 
 
 doz. Neckwear $4.50 
 
 6 
 
 75 
 
 
 
 1026 
 
 i 
 
 2 
 
 27.00 
 
 13 
 
 50 
 
 
 
 1025 
 
 1 2 
 
 27.50 
 
 41 
 
 25 
 
 
 
 1020 
 
 3 
 
 4 
 
 9.00 
 
 6 
 
 75 
 
 
 
 923 
 
 21 
 
 18.00 
 
 45 
 
 00 
 
 
 
 1015 
 
 1| 
 
 24.00 
 
 42 
 
 00 
 
 
 
 
 
 
 155 
 
 25 
 
 
 
 
 
 Less 2% 
 
 3 
 
 11 
 
 152 
 
 14 
 
 
 
 6. FURNITURE 
 
 In the following bill the goods were sold delivered on the cars (f . o. b.) 
 Boston, but the shippers prepaid the freight to Bangor. The freight is a part of 
 the selling price and is added to the amount of the bill, as shown in the model. 
 
 -'9- 
 
 TERMS 
 
 Bought of E. M. PRAY, SONS & CO. 
 
 Manufacturers of Fine Furniture 
 
 LL. 
 
 'JJ 
 
164 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 7. WHOLESALE COAL 
 F. H. OSBORN & CO. 
 
 SHIPPERS OF 
 
 Anthracite, Bituminous, and Gas Coal 
 
 Sold to 122. 
 
 Terms 
 
 2.0*70 a # 
 
 The above is a form of bill that is generally used for wholesale transactions 
 in coal. It shows that the coal has been paid for, and is called a receipted bill. 
 
 8. RETAIL COAL 
 
 .10. 
 
 uou^t of jT, Jtt (Everett & Co* 
 
 '-0- 2. 
 
BILLS AND ACCOUNTS 
 
 165 
 
 On page 106 is a form of coal bill used by many retailers. The foregoing 
 bill shows another form sometimes used by retailers. The numbers at the 
 left of the hyphen are the gross weights, and the numbers at the right the 
 tares of the different loads. 
 
 9. CHINA AND GLASSWARE 
 
 ^Boston, NOV. 6, /9 
 
 THE WENTWORTH = STRATTON CO. 
 
 Rochester, N.Y. 
 
 of Qsgood, Jrauer <- 
 
 erms 60 da. net; 2% 10 da. 
 
 
 1 
 
 Dinner Set, 130 pieces; viz.: 
 
 
 
 
 
 
 
 
 
 1 doz. Plates, 8 in. 
 
 ] 
 
 88 
 
 
 
 
 
 
 
 1 " 7 " 
 
 i 
 
 63 
 
 
 
 
 
 
 
 1 ' 6 ' ' 
 
 1 
 
 38 
 
 
 
 
 
 
 
 1 ' 7 " (deep) 
 
 1 
 
 63 
 
 
 
 
 
 
 
 1 ' Fruit Saucers, 4 in. 
 
 
 75 
 
 
 
 
 
 
 
 1 * Individual Butters 
 
 
 50 
 
 
 
 
 
 
 
 1/12 doz. Covered Dishes, 8 in. $12.00 
 
 1 
 
 00 
 
 
 
 
 
 
 
 1/12 Casseroles, 8 in. 13.50 
 
 1 
 
 13 
 
 
 
 
 
 
 
 1/4 Dishes, 8 in. 2.50 
 
 
 63 
 
 
 
 
 
 
 
 1/12 10 " 4.50 
 
 
 38 
 
 
 
 
 
 
 
 1/12 12 ' 7.50 
 
 
 63 
 
 
 
 
 
 
 
 1/12 14 ' 10.50 
 
 
 88 
 
 
 
 
 
 
 
 1/6 Bakers, 8 in. 4.50 
 
 
 75 
 
 
 
 
 
 
 
 1/12 Sauce Boats 4.00 
 
 
 33 
 
 
 
 
 
 
 
 1/12 Pickles 3.00 
 
 
 25 
 
 
 
 
 
 
 
 1/12 ' ' Bowls 2.00 
 
 
 17 
 
 
 
 
 
 
 
 1/12 Sugars 6.00 
 
 
 50 
 
 
 
 
 
 
 
 1/12 Creams 2.79 
 
 
 23 
 
 
 
 
 
 
 
 1 Handled Teas 
 
 2 
 
 00 
 
 
 
 
 
 
 
 1/2 " Coffees 2.33 
 
 1 
 
 17 
 
 
 
 
 
 
 
 1/12 Pitchers 6.00 
 
 
 50 
 
 
 
 
 
 
 
 1/12 Covered Butters and 
 
 
 
 
 
 
 
 
 
 Drainers 9.00 
 
 
 75 
 
 19 
 
 07 
 
 
 
 
 25 
 
 more Dinner Sets as above 19.07 
 
 
 
 476 
 
 75 
 
 
 
 
 
 
 
 
 495 
 
 82~ 
 
 
 
 
 
 Crates 
 
 
 
 7 
 
 50 
 
 
 
 
 
 Carting 
 
 
 
 2 
 
 10 
 
 505 
 
 42 
 
 The above form is common in the china and glassware business. In this 
 case a charge is made for the crates used in packing and the prices do not 
 include delivery. The cost of the crate and the cost for carting are there- 
 fore made a part of the bill. 
 
166 PRACTICAL BUSINESS ARITHMETIC 
 
 10. LUMBER 
 3{. ^M. ZBickford 60. 
 
 {Boston, ^Mass., Oct. 8, 
 
 Sold to L. A. Hammond & Co. 
 
 Paterson, N.J. 
 
 Pgt . net cash; bal. in 5 da. less ~L\ 
 
 23, 
 
 289 
 
 ft. 
 
 1 v ol n-i 
 2 A ^2 U-L 
 
 N. 
 
 C. 
 
 Ceiling $ 
 
 (18.50 
 
 $430 
 
 .85 
 
 3, 
 
 520 
 
 * 
 
 " 2 
 
 tt 
 
 tt 
 
 tt 
 
 17.00 
 
 59 
 
 .84 
 
 10, 
 
 307 
 
 tt 
 
 3 v ol -i 
 Q /s c/2 - 1 - 
 
 tt 
 
 tt 
 
 tt 
 
 13.50 
 
 139 
 
 .14 
 
 1, 
 
 690 
 
 tt 
 
 " 2 
 
 it 
 
 It 
 
 tt 
 
 12.50 
 
 21 
 
 .13 
 
 
 
 
 
 
 
 
 
 $650 
 
 .96 
 
 Less 
 
 freight 
 
 (45 
 
 ,200 Ib. at 24^) 
 
 108 
 
 .48 
 
 
 
 
 
 
 
 
 
 $542 
 
 .48 
 
 Lumber is generally sold by the thousand feet. In the above bill the goods 
 were sold free on board cars (f. o. b.) Paterson, N.J., but the shippers have 
 not prepaid the freight. They find that these charges are $108.48 and deduct 
 this amount from the total of the bill. In the wholesale lumber business the 
 prices quoted usually include the cost of delivery, and when the freight charges 
 are not known at the time of making the shipment, they are paid by the 
 consignees and deducted from the amount of the bill on the arrival of the 
 goods. The freight bill is then sent to the shippers for credit. 
 
 WRITTEN EXERCISE 
 
 1. Study the model bill, page 160. Increase the price of 
 each article 25^ and then copy and find the amount of the bill. 
 
 2. Study the first model bill, page 161, and then copy and find 
 the amount of it at the following prices: hams, 27^; coffee, 
 23^; mustard, 31^; cocoa, 39^. 
 
 3. Study the second model bill, page 161, and then copy and 
 find the amount of it at the following prices : porcelain knobs 
 #8, $1.121; #16,81.25; steelyards #64, 811 ; #17,18.331; 
 jack-planes #14, |6; #21,16.25; #48,16.75. 
 
BILLS AND ACCOUNTS 167 
 
 4. Apr. 15, you bought of S. S. Pierce Co., Boston, Mass., 
 for cash: 25 gal. finest New Orleans molasses at 48^; 15 gal. 
 fancy sugar-house sirup at 49/; 75 Ib. raw mixed coffee at 
 29^; 25 Ib. raw Pan-American coffee at 19^; 5 cartons Fowle's 
 entire-wheat flour at 39|^; bbl. Franklin Mills flour at $6.75; 
 l bbl. pastry flour at 15.25. Write the bill. 
 
 5. Mar. 19, Frank M. Richmond & Co., New York City, 
 sold to Charles M. Thompson, Poughkeepsie, N.Y., 12 doz. por- 
 celain knobs: 3 doz. #71 at $6.35, 9 doz. #74 at 16.75; 12 
 doz. shingle hatchets: 6 doz. #16 at 19.75, 6 doz. #34 at 
 $12.50; 7 doz. steel squares: 3 doz. #91 at $35, 4 doz. #73 
 at $33. Terms: 30 da. Write the bill. 
 
 6. Study the model bill on page 162. Increase the prices 
 of the articles marked 124 and 132 five cents each and the re- 
 mainder of the articles one cent each; then copy and find the 
 amount of the bill. 
 
 7. Nov. 15, J. B. Ford & Co., Albany, N.Y., bought of the 
 Clinton Mills, Little Falls, N.Y., 10 pc. percale shirting con- 
 taining 42, 48, 52 1 , 58, 62, 38, 49, 51, 54, and 46 1 yd., at 71 f ; 10 pc. 
 fine wool cheviot containing 58 1 , 42, 49, 51, 44 2 , 46, 48, 41 2 , 39, 
 and 42 yd., at $1.12|; 5 pc. cashmere containing 49 3 , 40 1 , 48 3 , 
 49 1 , and 49 yd. at $1.37-}. Terms: 60 da., or 3% discount 
 for cash within 10 da. Write the bill. 
 
 8. Study the first model bill on page 163. Increase the 
 prices of styles 1026, 1025, 1020, and 923, 25^ each and 
 diminish the prices of the other styles 25^ each; then copy 
 and find the amount of the bill. 
 
 9. Sept, 24, Geo. W. Fairchild, Buffalo, N.Y., bought of 
 E. M. Lawrence & Co., New York City, silk ribbon as follows : 
 12 pc. #1142 at $2.25; 5 pc. #1321 at $1.25; 25 pc. #171 
 at $4.371; 8 pc. # 1927 at $1.75 ; 36 pc. #2114 at $1.66f ; 15 
 pc. #1371 at $1.331; 15 pc. #624 at $4.371 ; 12 pc. #909 at 
 $1.871; 25 pc. #1008 at $3.331; 25 pc. #1246 at $4.75; 18 
 pc. #2119 at $1.121. Terms: 30 da., or 2% discount for cash 
 in 10 da. Write the bill. 
 
168 PRACTICAL BUSINESS ARITHMETIC 
 
 10. Study the second model bill on page 163. Increase the 
 price of the articles marked 65 and 396, 25^ each, and diminish 
 the price of the other articles 12^ each; then copy and find 
 the amount of the bill. Freight added, $ 14.70. 
 
 11. July 20, The Hayden Furniture Co., Rochester, N.Y., 
 bought of John H. Pray & Son, Boston, Mass., 25 #31 card 
 tables at $11 ; 24 #94 china closets at $27.50 ; 15 #16 dining 
 sets at $85; 25 #3060 fancy rockers at $9.25; 15 #35 music 
 cabinets at $2.75 ; 25 #26 mahogany office chairs at $12.50; 
 12 #89 oak sideboards at $125. Terms: 30 da. The prices 
 are free on board Boston, and the shipper prepaid the freight, 
 $34.50. Write the bill. 
 
 12. Study the first model bill on page 164. Increase the 
 price of the stove coal 25^ per ton and the price of each of the 
 other kinds 12|^ per ton; then copy and find the amount of 
 the bill. Receipt the bill for F. H. Osborn & Co. 
 
 13. May 19, C. E. Williams & Co., Cleveland, O., bought of 
 Fairbanks & Co., Scranton, Pa. : 3 car loads of stove coal weigh- 
 ing 20,500, 26,400, and 25,600 lb., respectively, at $4.75 per ton 
 (2000 lb.); 1 car load grate coal weighing 21,900 lb. at $4.25 per 
 ton; 1 car load cannel coal weighing 22,500 lb. at $7.75 per 
 ton. Terms: 30 da., or 3% discount for cash in 10 da. Write 
 the bill. 
 
 14. Study the second model bill, page 164, then copy and 
 find the amount of it at $6.25 per ton for each sale. 
 
 15. Copy the bill in problem 14 in accordance with the model 
 shown on page 106. Make the price of the coal $6.66f. 
 
 16. Study the model bill on page 165. Increase each price 
 given five cents and then copy and find the amount of the bill. 
 Cost of crates used in packing, $6.40 ; carting, $2.80. 
 
 17. July 15, Henry Nelson & Co., Portland, Me., bought of 
 Jones, Stratton & Co., New York City, 5 doz. plates, 8 in., at 
 $1.50; 35 doz. plates, 7 in., at $1.35; 15 doz. plates, 6 in., 
 at $1.10; 10 doz. plates, 5 in., at 90^; 65 do/, handled teas at 
 $1.85 Terms: 30 da. Cost of crate used in packing, $2; 
 cartage, 75^. Write the bill. 
 
BILLS AND ACCOUNTS 169 
 
 18. June 25, F. E. Winter & Co., Batavia, N.Y., bought of 
 E. M. Page & Co., Chicago, 111., provisions as per problems 3, 
 4, and 5, page 40. Terms : note at 60 da. Write the bill, 
 using current prices. 
 
 Find the net weight of each quantity as explained in 60-62. 
 
 19. Jan. 1, John P. Alven, 100 Vine St., bought of E. E. 
 Gray Co., Boston, Mass., 2 Ib. cafS c?es invalides at 38^; 2 gal. 
 maple sirup at $1.35; 1 pkg. magic yeast at 5/; 5 cartons 
 Fowle's entire-wheat flour at 22^ ; 3 cartons Franklin Mills flour 
 at 23 j^; 16 Ib. pastry flour at 3|^; 5 gal. fancy sugar-house 
 sirup at 5(1^; 5 gal. dark molasses at 41^; 6^- Ib. red frosting 
 sugar at 12^; 7 Ib. rock-candy crystals at 9|^; 3 Ib. C. & B. 
 coffee extract at 25^ ; 1 Ib. postum cereal at 22^ ; 2 Ib. Chance's 
 bread soda at 10^; 3 Ib. cream tartar at 40^; 11 Ib. Pyle's sal- 
 eratus at 8^; 50 Ib. granulated sugar at 5|^; 10 Ib. powdered 
 sugar at 5|^; 5 Ib. cut-loaf sugar at 6|^; 5 gal. finest P. R. 
 molasses at 59^; 5 gal. finest N. O. molasses at 61^; 1^ doz. 
 bottles maple sirup at 3.75. Write the bill. 
 
 20. Study the model bill on page 166. Increase each price 
 50^, make the freight charge 2^ per hundred pounds, and 
 then copy and find the net amount of the bill. 
 
 21. Nov. 1, J. B. Bickwell & Co., Worcester, Mass., bought 
 of the Northern Lumber Co., St. Johnsbury, Vt., on 60 days' 
 credit : 3 M extra spruce clapboards at $52.50; 25 M lath at 
 $3.75; 1500 ft. 2" choice cypress lumber at $65 per M ; 1200 
 ft. 2" spruce at $23 per M; 750 ft. rift hard pine at $65 per 
 M; less freight, $42.50. Write the bill. 
 
 22. June 15, Helen M. Stone, Cambridge, Mass., sends 
 Frank M. Spaulding a bill for tuition and supplies to date as 
 follows: tuition, one term, $37.50; music lessons, $9.75; 1 
 Practical Elements of Elocution, $1.65 ; 1 Allen & Greenough's 
 Ccesar, $1.35; 1 Allen & Greenough's Cicero, $1.55; 1 Myer's 
 General History, $1.65. Write the bill and receipt it for 
 Helen M. Stone. 
 
170 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 STATEMENTS 
 
 POLIO 
 
 account u>ith 
 
 / rt 
 
 / V 
 
 209. A statement is an abstract of a customer's account, show- 
 ing under proper dates the details and totals of debits and credits 
 and the balance remaining unpaid. 
 
 FOLIO. 
 
 account utifA 
 
 
 ^^ 
 
 /z 
 
 22. 
 
 Z^ 
 
BILLS AND ACCOUNTS 
 
 171 
 
 The first model on the preceding page is a statement of C. B. McMeni- 
 men's account for January. It shows that the charges aggregate $997.10, 
 the credits $671.40, and that the balance remaining unpaid is $325.70. 
 
 The second model on the preceding page is a statement of C.B. McMeni- 
 men's account for January and February. The items on the January state- 
 ment are summarized in the record "To account rendered, $325.70." The 
 first item on the March statement will be " To account rendered, $412.20." 
 
 WRITTEN EXERCISE 
 
 1. During March, F. E. Smith, Buffalo, N.Y., bought mer- 
 chandise of The Hayden Furniture Co., Rochester, N. Y., as per 
 bills rendered: namely, Mar. 3, 1400.80; Mar. 15, 1360.90; 
 Mar. 20, 1200.70; Mar. 26, 1260.90; Mar. 28, $ 130.50. 
 During the same time he made cash payments on account as fol- 
 lows : Mar. 15, 1400.80; Mar. 23, 1360.90. On Mar. 27 
 he also returned goods for credit amounting to 118.60. Render 
 a statement of F. E. Smith's account. 
 
 2. During April the above account was charged for merchan- 
 dise as follows: Apr. 15, 1720.50; Apr. 27, 1260.90. The 
 account was also credited for cash as follows : Apr. 16, $200.70 ; 
 Apr. 28, 1100.00. Render the April statement. 
 
 3. Copy and find the balance of the following statement: 
 
 Boston, Mass., Feb. 1, 19 
 MRS. C. M. SHERMAN 
 
 931 BEACON ST., City 
 In account with SPENCER, MEAD & Co. 
 
 Jan. 
 
 1 
 
 Account rendered 
 
 13 
 
 64 
 
 
 
 
 3 
 
 2 pr. Gloves 2.50 
 3 yd. Velvet 3.75 
 12 Black Silk 2.10 
 
 
 
 
 
 
 12 
 
 6 pr. Hose 35 ^ 
 2 Hats 9.00 
 
 
 
 
 
 
 
 30iyd. Muslin 12J^ 
 Cr. 
 
 
 
 
 
 
 5 
 15 
 
 2 pr. Gloves 2.50 
 1 Hat 9.00 
 
 
 
 
 
172 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 PAY ROLLS 
 
 PAY ROLL For the week ending_ 
 
 /f f 190 
 
 222 
 
 /r 
 
 /F2.0 
 
 2-7%*- 
 
 %f7f<?F9 
 
 This form is most common among manufacturing establishments, but 
 it is also used by printers, contractors, and builders. 
 
 Checks are sometimes used in paying' off employees, but most large con- 
 cerns find the envelope system the most convenient and satisfactory. To 
 pay off employees by the envelope system it is necessary for the bookkeeper 
 to find first the amount of money required and then the bills and fractional 
 currency that are necessary to pay each employee. The amount required is 
 the total of the pay roll, and the bills and fractional currency desired may be 
 found as shown in the following illustration. This illustration, called a 
 change memorandum, shows the method of finding just the denominations 
 wanted for the pay roll at the top of the page. A change memorandum 
 may be proved correct as shown in the pay-roll memorandum at the top of 
 page 173. 
 
 
 B 1 1. i.s 
 
 Co:xs 
 
 
 $20 
 
 $n 
 
 $5 
 
 $2 
 
 $1 
 
 50 ^ 
 
 2.^ 
 
 i -0 
 
 &l 
 
 11 
 
 1 
 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 
 
 
 
 2 
 
 
 1 
 
 
 1 
 
 
 1 
 
 1 
 
 
 
 
 3 
 
 1 
 
 
 
 
 
 1 
 
 
 1 
 
 1 
 
 
 4 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 
 1 
 
 3 
 
 6 
 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 
 1 
 
 
 6 
 
 1 
 
 
 
 
 
 
 1 
 
 
 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 2 
 
 
 
 8 
 
 
 l 
 
 
 1 
 
 1 
 
 
 
 2 
 
 
 
 9 
 
 
 
 1 
 
 2 
 
 
 1 
 
 1 
 
 
 1 
 
 4 
 
 10 
 
 
 i 
 
 
 
 
 1 
 
 1 
 
 1 
 
 1 
 
 2 
 
 
 2 
 
 1 
 
 4 
 
 1 
 
 5 
 
 6 
 
 6 
 
 
 
 5 
 
 9 
 
BILLS AND ACCOUNTS 
 
 173 
 
 When the amount of the pay roll 
 and the necessary bills and frac- 
 tional currency have been deter- 
 mined, a check payable to the order 
 of Pay Roll is written. A pay-roll 
 memorandum similar to the accom- 
 panying form is then attached to 
 the check and both are sent to the 
 bank. The pay-roll memorandum 
 should foot the same as the pay-roll 
 book, and is therefore a check upon 
 the correctness of the change memo- 
 randum. 
 
 In a large pay roll the adept 
 bookkeeper frequently estimates the 
 kind of change required. This is 
 done by scanning the pay roll first 
 to find the number of pennies re- 
 quired, then the number of nickels, 
 etc. The experienced book-keeper can make a very accurate estimate, 
 
 PAY ROLL For the week ending /faw , 
 
 FIRST 
 
 NATIONAL BANK 
 
 
 Westjield, Mass. 
 
 PAT-ROLL MEMORANDUM 
 
 
 NELSON fcf CO. 
 
 require the following: * 
 
 
 
 
 Nickels 
 
 J- 
 
 2~r 
 
 
 6> 
 
 60 
 
 Quarters . 
 
 ...... j- 
 
 / Z-<r 
 
 Halves 
 
 
 
 J 00 
 
 Dollars . . 
 
 j~ 
 
 J 
 
 
 . 7 
 
 
 c's 
 
 
 2.0 00 
 
 
 7 
 
 70 00 
 
 
 2. 
 
 4-0 00, 
 . s 
 
 
 ^ 
 
 Bills and silver necessary 
 
 Q04^tifa&, 
 
 /fit 
 
 2. /o 7 /6 J~ 7 6 7 
 
 WRITTEN EXERCISE 
 
 1. Study the model pay roll, page 172, and find the amount of 
 
 it at the following wages per hour : #1, 18^; #2, 21f ^ #3, 
 #4, 35^; #5, 331^; #6, 35*; '#7, 37^; #8, 35*; #9, 271*; 
 18|*. Make a change memorandum. 
 
174 
 
 PEACTICAL BUSINESS ARITHMETIC 
 
 2. Study the model pay roll on page 173, and then find the 
 amount of it at the following wages per hour: #1, 50^; $2, 45^; 
 #3, 88J*; #4,35^; #5, 27^; #6, 37-^; #7, 25t; #8, 33J^; #9, 
 44|^; #10,22f/; #11,22}*; #12, 14f*; #18,121*; #14,80*. 
 
 3. j^Jake a pay roll memorandum from problem 2. 
 
 WRITTEN REVIEW EXERCISE 
 
 l. Find the amount of each of the following bills : 
 
 New Tork, May 31, /p 
 AfEssRS. GRAY, SALISBURY & Co. 
 
 Rochester, N.Y. 
 
 Bought of J. E. PAGE, SONS & Co. 
 
 Terms : net, 60 da. ; 2 % 10 da. 
 
 CASE 
 
 Pi EC KS 
 
 DESCRIPTION OF ARTICLES 
 
 YDS. 
 
 PRICE 
 
 ITEMS 
 
 AMOUNT 
 
 #364 
 
 10 
 
 Velveteen 
 
 
 
 
 
 
 
 
 
 42i 40 40 46 38i 
 
 
 
 
 
 
 
 
 
 40 42 42 41 39 
 
 
 25^ 
 
 
 
 
 
 #359 
 
 12 
 
 Corduroy 
 
 
 
 
 
 
 
 
 
 36 38i 392 42 412 392 
 
 
 
 
 
 
 
 
 
 37 37 41 45 41 401 
 
 
 60 1 ^ 
 
 
 
 
 
 #371 
 
 15 
 
 Gray Homespun 
 
 
 
 
 
 
 
 
 
 39 38 35 42 41 
 
 
 
 
 
 
 
 
 
 45 39 41 34 37 
 
 
 
 
 
 
 
 
 
 41 40 41 38 42 3 
 
 
 83* f 
 
 
 
 
 
 #360 
 
 6 
 
 Storm Serge 
 
 
 
 
 
 
 
 
 
 40 42i 43 42 39 42 i 
 
 
 44 ? 
 
 
 
 
 
 #373 
 
 24 
 
 Fine English Serge 
 
 
 
 
 
 
 
 
 
 42 38 42 42 40 2 42 J 
 
 
 
 
 
 
 
 
 
 40 39 40 41 40 1 43 
 
 
 
 
 
 
 
 
 
 42 42 38 2 38 41 42 
 
 
 
 
 
 
 
 
 
 43 44 41 40 37 1 37 
 
 
 1.37^ 
 
 
 
 
 
 #381 
 
 24 
 
 Groveland Flannel 
 
 
 
 
 
 
 
 
 
 32 40 39 42 41 45 
 
 
 
 
 
 
 
 
 
 45 46 35 41 38 41 
 
 
 
 
 
 
 
 
 
 37 42 43 40 37 42 
 
 
 
 
 
 
 
 
 
 37 40 42 41 44 41 
 
 
 334 
 
 
 
 
 
BILLS AND ACCOUNTS 175 
 
 2. Make out a bill for the following order. Bill the English 
 breakfast tea at 41^; Finest oolong tea at 65^; Young Hyson 
 tea at 97|^; Choice Japan tea at 59^; Orinda kaughphy at 
 81.90; raw Java coffee at 30|^; gluten flour at 30^ a carton 
 arid 17.75 per barrel. Assume that half a chest of tea weighs 
 75 lb., and a mat of coffee 70 Ib. 
 
 E. M. BARBER & SON 
 
 RETAIL GROCERS 
 Springfield, Mass., Aug . 13 , 19 
 
 S. S. Pierce Company, 
 
 Boston, Mass. 
 
 Gentlemen: 
 
 Please ship us via B. & A. R.R., the follow- 
 ing goods: 
 
 3 hf. cht. English Breakfast Tea 
 
 3 " " Finest Oolong Tea 
 
 5 " " Young Hyson Tea 
 
 25 lb. Choice Japan Tea 
 
 5 5-lb. cans Orinda Kaughphy 
 
 7 mats Raw Java Coffee 
 
 5 hf. bbl. Gluten Flour 
 
 25 5-lb. ^ cartons Gluten Flour 
 
 Respectfully yours, 
 
 3. Boston, Mass., Apr. 16, E. O. Burrill, Philadelphia, Pa., 
 bought; of Jones, Talcott & Co., on account, 30 da., 25 Turk- 
 ish rugs 41 x 7 at 110.25 ; 750 yd. matting at 55^ ; 225 yd. lin- 
 oleum at 271^; 25 Turkish rugs 8J x 12 at 121.75 ; 25 Persian 
 rugs 6x9 at $12.25; 12 Persian rugs 7 x 11 at 116.25; 10 rolls, 
 each containing 150 yards, Brussels carpeting at 2.25 ; 275 yd. 
 Moquette carpeting at $1.75. Find the amount of the bill. 
 
176 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 4. Fill the following order : English breakfast tea, 47 f ; 
 Formosa oolong tea, 62|^; Japan tea, 62l; Ceylon Pekoe 
 tea, 90f 70 Ib. to each half -chest. 
 
 THE WESTERN TELEGRAPH COMPANY 
 
 INCORPORATED 
 
 21,000 OFFICES IN AMERICA CABLE SERVICE TO ALL THE WORLD 
 
 Receiver's No. 
 
 Time Filed 
 
 Check 
 
 SEND the following message subject to the terms 
 of the Copnpapy, wfcich are herebjr^agreed to 
 
 .-* JL LS; 
 
 To_ 
 
 t 190 
 
 
 5. Yon sold Shepard, Farmer & Co., the following: 5M 
 extra cedar shingles at 1 3. 50 ; 15 M clear cedar shingles at 1 3. 00 ; 
 20 M extra spruce clapboards at $ 45.00 ; 15 M clear spruce clap- 
 boards at 143.00; 1230 ft. random hemlock boards at $13.00; 
 2760 ft. planed spruce boards at $19 00 ; 2090 ft. rough spruce 
 boards at #16.50; 18M spruce lath at $3.25; 6493 ft, 1 x 4" 
 rift flooring at $26.00. Write the bill. 
 
 6. Copy and complete the following time card : 
 
 Time worked by C. E. Small, for the week ending Aug. 13. 
 Rate per hour, 29\tf. Occupation, Painter. 
 
 No. 
 
 HOURS WORKED 
 
 TOTAL 
 HOURS 
 FOR EACH 
 ACCOUNT 
 
 AMOUNT 
 FOR PL-veil 
 ACCOUNT 
 
 Sat. 
 
 Sun. 
 
 Mon. 
 
 Tucs. 
 
 Wed. 
 
 Thtir. 
 
 Fri. 
 
 501 
 
 2f 
 
 
 41 
 
 
 
 
 
 
 
 
 724 
 
 
 
 2| 
 
 
 9^ 
 
 
 
 
 
 
 1029 
 
 44 
 
 
 
 8 1 
 
 
 
 
 
 
 
 476 
 
 H 
 
 
 
 2 ? 
 
 
 
 
 
 
 
 910 
 
 
 
 
 
 
 10| 
 
 9| 
 
 
 
 
 735 
 
 
 
 
 
 
 H 
 
 i 
 
 
 
 
 CHECK 
 
 
 
 
 
 
 
 
 
 
 
BILLS AND ACCOUNTS 
 
 177 
 
 TIME SLIP 
 
 Friday, 4/26, 1906 
 
 TIME SLIP 
 
 4/27, 1906 
 
 1 
 
 2 
 3 
 
 4 
 5 
 6 
 7 
 8 
 9 
 
 IN 
 
 651 
 645 
 644 
 700 
 700 
 640 
 756 
 759 
 756 
 
 OUT 
 
 1159 
 1159 
 1159 
 1159 
 1159 
 1159 
 1159 
 1159 
 1159 
 
 IN 
 
 1256 
 1257 
 1232 
 1257 
 1259 
 1259 
 1259 
 104 
 1255 
 
 OUT 
 
 459 
 459 
 459 
 459 
 459 
 459 
 459 
 506 
 459 
 
 Saturday, 
 
 IN OUT IN OUT 
 
 1 753 1200 1258 459 
 
 2 703 1204 1256 504 
 
 3 753 1150 1256 504 
 
 4 655 1159 1259 459 
 
 5 655 1159 1259 459 
 
 6 701 1159 1255 459 
 
 7 654 1150 1259 459 
 
 8 654 1158 1259 459 
 
 9 654 1159 1254 503 
 
 The above slips show an actual record of time for 9 employees for 2 da. 
 in a large printing establishment. These records are made by a large me- 
 chanical timekeeper and at convenient times are copied in the pay-roll book. 
 Fractions are recorded to the nearest \ of an hour. In the above slips, the 
 time each employee arrived in the morning is recorded in the first column, 
 the time each went away at noon in the second, the time each returned 
 at noon in the third, and the time each went away in the afternoon in the 
 fourth. Thus, #1 arrived at 7:53, Saturday, went away at 12:00, re- 
 turned at 12 : 58 and worked until 4 : 59 ; time, 8 hr. 
 
 7. Copy the following pay roll, enter the time for Friday and 
 Saturday (from the above slips), find the amount of the pay roll 
 as in previous exercises, and make a change memorandum and 
 a pay-roll memorandum. 
 
 PAY KOLL FOR THE WEEK ENDING APRIL 27, 1906 
 
 No. 
 
 NAME 
 
 NUMKER OF HOURS' 
 
 WORK EACH DAY 
 
 TOTAL 
 
 No. OF 
 HOURS 
 
 WAGES 
 
 PER 
 
 HOUR 
 
 TOTAL 
 WAGES 
 
 REMARKS 
 
 M. 
 
 T. 
 
 W. 
 
 T. 
 
 F. 
 
 8. 
 
 1 
 
 A. B. Comer 
 
 9 
 
 8 
 
 9 
 
 9 
 
 
 
 
 55f? 
 
 
 
 
 2 
 
 W. D. Ball 
 
 9 
 
 9 
 
 9 
 
 1 
 
 
 
 
 44f? 
 
 
 
 
 3 
 
 A. M. Snow 
 
 9 
 
 8 
 
 8 
 
 81 
 
 
 
 
 44? 
 
 
 
 
 4 
 
 R. O. Mark 
 
 8 
 
 9 
 
 9 
 
 9 
 
 
 
 
 331? 
 
 
 
 
 5 
 
 Miss Mary Cane 
 
 9 
 
 8* 
 
 9 
 
 9 
 
 
 
 
 331? 
 
 
 
 
 6 
 
 Miss Ellen Kyle 
 
 8 
 
 1 
 
 9 
 
 9 
 
 
 
 
 35? 
 
 
 
 
 7 
 
 D. M. Garson 
 
 9 
 
 81 
 
 8 
 
 91 
 
 
 
 
 35? 
 
 
 
 
 8 
 
 S. D. Lane 
 
 
 
 81 
 
 8^ 
 
 9 
 
 
 
 
 25? 
 
 
 
 
 9 
 
 Miss Cora Knapp 
 
 9 
 
 9 
 
 81 
 
 8 
 
 
 
 
 
 22|? 
 
 
 
 
 
 
 
 
 
 
 
 
 
178 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 EXPEESSAGE AND FREIGHTAGE 
 
 WRITTEN EXERCISE 
 
 1. I wish to express five separate packages from Boston, 
 Mass., to Cincinnati, O. The rate per 100 Ib. is quoted at 
 12.00. If the packages weigh 15 Ib., 73 Ib., 86 Ib., 126 Ib., 
 and 29 Ib., respectively, what will be the express charge? 
 
 Small packages are usually sent by express. The charge varies with the 
 distance and is stated at so much per 100 Ib. The following table shows 
 the rate for smaller weights, when the rate per hundred pounds is $2.00, 
 $2.50, $3.00, $3.50, $4.00, and $4.50 : 
 
 CHARGES FOR PACKAGES WEIGHING LESS THAN 100 POUNDS 
 WHEN THE RATE Is: 
 
 $2.00 
 
 $2.50 
 
 $3.00 
 
 $3.50 
 
 $4.00 
 
 $4.50 
 
 1 Ib. $ .25 
 
 1 Ib. $ .25 
 
 1 Ib. $ .25 
 
 1 Ib. $ .25 
 
 1 Ib. $ .25 
 
 1 Ib. $ .30 
 
 2 .35 
 
 2 .35 
 
 2 .35 
 
 2 .35 
 
 2 .35 
 
 2 .35 
 
 3 .45 
 
 3 .45 
 
 3 .45 
 
 3 .45 
 
 3 .45 
 
 3 .45 
 
 4 .50 
 
 4 .55 
 
 4 .60 
 
 4 .60 
 
 4 .60 
 
 4 .60 
 
 5 .55 
 
 5 .60 
 
 5 .5 
 
 5 .70 
 
 5 .70 
 
 5 .75 
 
 7 .60 
 
 7 70 
 
 7 .75 
 
 7 .80 
 
 7 .85 
 
 7 .90 
 
 10 .70 
 
 10 .75 
 
 10 .80 
 
 10 .90 
 
 10 1.00 
 
 10 1.00 
 
 15 .75 
 
 15 .85 
 
 15 .90 
 
 15 1.00 
 
 15 1.10 
 
 15 1.15 
 
 20 .85 
 
 20 1.00 
 
 20 1.10 
 
 20 1.20 
 
 20 1.25 
 
 20 1.30 
 
 25 1.00 
 
 25 1.10 
 
 25 1.20 
 
 25 1.30 
 
 25 1.50 
 
 25 1.50 
 
 30 1.00 
 
 30 1.15 
 
 30 .30 
 
 30 1.50 
 
 30 1.60 
 
 30 1.70 
 
 35 1.00 
 
 35 1.25 
 
 35 .40 
 
 35 1.60 
 
 35 1.70 
 
 35 1.90 
 
 40 1.00 
 
 40 1.25 
 
 40 .50 
 
 40 1.75 
 
 40 1.85 
 
 40 2.00 
 
 45 1.00 
 
 45 1.25 
 
 45 .50 
 
 45 1.75 
 
 45 2.00 
 
 45 2.25 
 
 50 1.00 
 
 50 1.25 
 
 50 .50 
 
 50 1.75 
 
 50 2.00 
 
 50 2.25 
 
 Pound rates (2^, 2|^, 3^, etc.) are charged for everything over 50 1 b. 
 Weights between those named in the table are charged at the rate for the 
 next higher weight. 
 
 2. The express charge from Boston to Chicago is quoted at 
 $2.50 per hundred pounds. Find the express charges on four 
 separate packages, weighing 47 Ib., 16 Ib., 12 Ib., and 15 Ib., 
 respectively, sent from Boston to Chicago. 
 
BILLS AND ACCOUNTS 
 
 179 
 
 3. A publisher sent a package of books by express, C. O. D., 
 from Boston to Detroit. The rate is quoted at 12.00 per 100 Ib. 
 If the books are worth 1 75 and weigh 56 Ib., how much should 
 the express company collect, expressage included? 
 
 4. The express rate from Lake View, Mich., to Boston is 
 quoted at $ 3.00 per 100 Ib. Find the amount of express 
 to pay this distance on 10 pkg., weighing 12 Ib., 10 Ib., 9 Ib., 21 
 Ib., 27 Ib., 34 Ib., 86 Ib., 121 Ib., 127 Ib., and 54 Ib., respectively. 
 
 5. If the express rate from St. Joseph, Mo., to Boston, 
 Mass., is quoted at 14.50 per 100 Ib., which is the cheaper and 
 how much, to send three separate 2-lb. packages from St. 
 Joseph to Boston by mail or by express? 
 
 6. The express rate from Boston to St. Albans, Mo., is 
 quoted at $3.50 per 100 Ib. Find the express charges on 17 
 separate parcels of merchandise sent from Boston to St. Albans, 
 when the weights are as follows : 15 Ib., 17 Ib., 25 Ib., 14 Ib., 18 
 Ib., 35 Ib., 72 Ib., 37 Ib., 42 Ib., 64 Ib., 92 Ib., 121 Ib., 146 Ib., 5 
 Ib., 15 Ib., 31 Ib., 41 Ib. 
 
 7. Find the amount of the following freight bill : 
 
 Date of W. 3-UuM*9 W. B. No. ^? Albany, N.Y. 
 
 To THE INTERSTATE TRANSPORTATION COMPANT, Dr. 
 
 For Transportation f 
 
 No. 
 
 Bulky goods are generally sent by freight. The articles are divided into 
 different classes, according to quantity and character, and are subject to 
 different rates. All railroads follow some official classification. All official 
 classifications divide freight into six different classes. 
 
180 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 Such freight as organs and pianos in cases, furniture, statuary, etc., is 
 generally designated as first-class matter. Baled hay, iron, etc., in car loads, 
 is generally designated as fifth-class matter. Building blocks, brick, etc., in 
 car-load lots, is generally designated as sixth-class matter. First-class rates 
 are the highest and sixth-class rates are the lowest charged. 
 
 Between most points, shipments weighing less than 100 Ib. are charged 
 as 100 Ib., irrespective of weight. 
 
 BOSTON & ALBANY RAILROAD 
 
 LOCAL FREIGHT TARIFF BETWEEN 
 
 BOSTON, MASS. 
 
 AND 
 
 
 
 KATE PEE 100 LB. 
 
 
 
 RATE PER 100 LB. 
 
 % 
 
 STATIONS 
 
 Classes 
 
 s 
 
 STATIONS 
 
 Classes 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 21 
 
 So. Framingham 
 
 10? 
 
 9? 
 
 7? 
 
 6? 
 
 5? 
 
 4? 
 
 98 
 
 Springfield . . 
 
 21? 
 
 18? 
 
 15? 
 
 13? 
 
 11? 
 
 11? 
 
 3i> 
 
 Westboro . . 
 
 11? 
 
 10? 
 
 9? 
 
 7? 
 
 6? 
 
 5? 
 
 108 
 
 Westfield . . 
 
 22? 
 
 20? 
 
 16? 
 
 14? 
 
 13? 
 
 11? 
 
 44 
 
 Worcester . . 
 
 13? 
 
 12? 
 
 10? 
 
 8? 
 
 8? 
 
 6? 
 
 14(> 
 
 Athol. . . . 
 
 29? 
 
 25? 
 
 21? 
 
 15? 
 
 14? 
 
 13? 
 
 (J2 
 
 Webster . . . 
 
 17? 
 
 15? 
 
 13? 
 
 11? 
 
 10? 
 
 9? 
 
 ir>o 
 
 Pittsfield . . 
 
 29? 
 
 25? 
 
 21? 
 
 15? 
 
 14? 
 
 13? 
 
 8;; 
 
 Palmer . . . 
 
 19? 
 
 16? 
 
 14? 
 
 12? 
 
 11? 
 
 10? 
 
 KYI 
 
 Albany . . . 
 
 30? 
 
 27? 
 
 22? 
 
 15? 
 
 14? 
 
 13? 
 
 8. Using the table, find the amount of freight to charge on 
 27,500 Ib. sixth-class matter, from Boston to Pittsfield. 
 
 9. Using the above table, find the amount of freight to 
 charge on 27,290 Ib. sixth-class matter and 890 Ib. first-class 
 matter from Boston to Albany ; to Westfield. 
 
 10. Using the above table, find the amount of freight to 
 charge on 14,790 Ib. fifth-class matter and 2170 Ib. second-class 
 matter from Boston to Palmer ; to Worcester ; to Pittsfield ; 
 to Springfield. 
 
 11. Using the above table, find the amount of freight to 
 charge on 75 Ib. first-class matter, 125 Ib. second-class matter, 
 1250 Ib. third-class matter, 7290 Ib. fourth-class matter, 21,490 
 Ib. fifth-class matter, and 64,640 Ib. sixth-class matter from 
 Boston to South Framingham ; to Westboro ; to Webster ; to 
 Springfield ; to Athol ; to Albany. 
 
DENOMINATE NUMBERS , 
 CHAPTER XV 
 
 DENOMINATE QUANTITIES 
 REVIEW OF THE COMMON TABLES 1 
 
 ORAL EXERCISE 
 
 1. Which of the following numbers are concrete ? which are 
 abstract? which are denominate? 
 
 a. 16 /. 150 k. 36 min. 
 
 b. 24 yr. g. 21 yd. I. 5 yd. 2 ft. 
 
 c. 64 hr. h. 65 A. m. 3 yr. 4 mo. 
 
 d. 12 men i. 17 books n. 10 T. 75 Ib. 
 
 e. 15 desks j. 34 houses o. 5 A. 61 sq. rd. 
 
 2. Define an abstract number; a concrete number; a de- 
 nominate number; a simple number ; a compound number. 
 
 3. Which of the numbers in question 1 are simple ? which 
 are compound ? 
 
 ORAL EXERCISE 
 
 1. Repeat the table of avoirdupois weight. 
 
 2. Repeat the table of long measure; of surveyors' long 
 measure; of square measure ; of surveyors' square measure. 
 
 3. Repeat the table of cubic measure; of dry measure; of 
 liquid measure; of time ; of angular measure; of United States 
 money ; of English money. 
 
 4. Name a number expressing distance ; two numbers ex- 
 pressing area ; two expressing value ; three expressing capacity. 
 
 5. How many statute miles in a degree of the earth's sur- 
 face at the equator ? how many geographical miles ? How 
 many feet in a statute mile ? how many inches ? 
 
 1 Tables of weights and measures may be found in the Appendix. 
 
 181 
 
182 PRACTICAL BUSINESS ARITHMETIC 
 
 REDUCTION 
 
 ORAL EXERCISE 
 
 1. Change 42 ft. to inches ; to yards. 
 
 2. Express 15 yd. as feet ; as inches. 
 
 3. Reduce 80 qt. to gallons ; to pints. 
 
 4. Change 128 qt. to pecks ; to bushels. 
 
 5. Express 120 pt. as quarts ; as gallons. 
 
 6. What part of a yard is 2 ft.? ft.? \ ft.? 
 
 7. Reduce 5 bu. to pecks ; to quarts ; to pints. 
 
 REDUCTION DESCENDING 
 210. Example. Reduce 4 T. 75 Ib. to ounces. 
 
 SOLUTION. Since 1 T. = 2000 Ib., 4 T. = 4 times 2000 
 2000 Ib. = 8000 Ib.; and with the 75 Ib. added this = 4 
 
 8075 Ib. Since 1 Ib. = 16 oz., 8075 Ib. = 8075 times 16 oz. 
 
 = 129,200 oz., the required result. -, p 
 
 8075 times 16 oz. = 16 times 8075 oz.; therefore 8075 - 
 times 16 oz. is found as shown in the margin. 129200, No. of OZ. 
 
 WRITTEN EXERCISE 
 
 Reduce : 
 
 1. 115' 6" to inches. 5. 3J rd. to feet. 
 
 2. 12 bu. 4 qt. to pecks. 6. 1J T. to ounces. 
 
 3. 16 15s. to shillings. 7. 12 A. to square feet. 
 
 4. 211 rd. 3 ft. to inches. 8. 161 cd. to cubic feet. 
 
 ORAL EXERCISE 
 
 1. How many pecks in | bu.? in | bu.? 
 
 2. Change .25 A. to square rods; .375 A.; 75 A. 
 
 3. Reduce J gal. to pints. Express ^ rd. as inches; as yards. 
 
 WRITTEN EXERCISE 
 Reduce : 
 
 1. | mi. to feet. 4. | yd. to inches. 
 
 2. .75 cd. to cubic feet. 5. .375 mi. to feet. 
 
 3. I* A. to square feet. 6. -^ hr. to seconds. 
 
DENOMINATE QUANTITIES 183 
 
 REDycTioN ASCENDING 
 
 211. Example. Express 176 qt. dry measure in higher de- 
 nominations. 
 
 SOLUTION. Since 8 qt. = 1 pk., divide by 8 and obtain 8)176 qt. 
 as a result 22 pk. Since 4 pk. = 1 bu., divide by 4 and ob- 4)22 pk. 
 tain as a result 5 bu. 2 pk. F~ TL o n ^. 
 
 WRITTEN EXERCISE 
 
 Reduce to higher denominations : 
 
 1. 3840 ft. 5. 816 pk. 9. 15,120" 
 
 2. 1054 pt. 6. 106,590 ft. 10. 51,200 cu. ft. 
 
 3. 14,400 sec. 7. 43,560 sq. in. 11. 145,152 cu. in. 
 
 4. 2000 sq. in. 8. 27,900 Ib. avoir. 12. 27,900 oz. avoir. 
 
 ORAL EXERCISE 
 
 1. Reduce | ft. to the fraction of a yard. 
 
 2. Change .16 cwt. to the decimal of a ton. 
 
 3. What part of a yard is 1 in.? 2 in.? -|- in.? 
 
 4. What decimal part of an acre is 16 rd.? 40 rd.? 
 
 5. What part of 35 bu. is 7 bu.? of 1J bu. is | bu.? 
 
 WRITTEN EXERCISE 
 
 1. Reduce 1J in. to the fraction of a foot; of a yard. 
 
 2. Reduce 10s. 9c?. to the fraction of a pound sterling. 
 
 SOLUTION. The successive divisors for reducing pence to 
 pounds sterling are 12 and 20 respectively. Divide 9d. by 1^) yd. 
 12 and the result is .75s. Put with this the 10s. in the prob- 20)10. 75s. 
 lem and the result is 10.75s. Divide 10.75s. by 20 and the .5375 
 
 result is .5375. Or 
 
 10s. 9eZ. = 129d. 1 = 240d. Therefore 10s. Qd. = = .5375. 
 
 3. Reduce 4 yd. 1| ft. to the decimal of a rod. 
 
 4. Reduce 10s. 6d. 2 far. to the decimal of a pound sterling. 
 
 5. Reduce 5 T. 721 Ib. to tons and decimal of a ton ; 6 T. 
 1750 Ib.; 12 T. 290 Ib.; 29,240 Ib.; 28,390 Ib. 
 
 6. Find the cost of 1750 Ib. of coal at 16.25 per ton; of 
 2170 Ib.; of 690 Ib.; of 1360 Ib.; of 3240 Ib.; of 32590 Ib. 
 
184 PEACTICAL BUSINESS ARITHMETIC 
 
 ADDITION AND SUBTRACTION 
 
 ORAL EXERCISE 
 
 State the sum of: 
 
 1. 2. 3. 4. 
 
 12 ft. 1 in. 5 Ib. 8 oz. 15 rd. 5 ft. 10 mi. 8 rd. 
 
 6 3 6 3 17 2_ 8 40 
 
 5. 6. 7. 8. 
 
 5 rd. 2 ft. 11 ft. 2 in. 5 bu. 1 pk. 5 mi. 20 rd. 
 
 82-i 8 i 80 17 13 
 
 7 2| 3 3 9 1 11 10 
 
 State the difference between : 
 
 1. 2. 3. 4. 
 
 90 mi. 300 rd. 75 rd. 12| ft. 30 yd. 2 ft. 44 bu. 3 pk. 
 75 120 26 4-| 17 1J 29 1_ 
 
 5. 6. 7. 8. 
 
 11 mo. 12 da. 12 mo. 31 da. 11 mo. 15 da. 98 gal. 2 qt. 
 6 6 8 17 _2 9_ 69 1__ 
 
 212. Examples, l. Three jars of butter weighed 48 Ib. 7 oz., 
 45 Ib. 9 oz., and 53 Ib. 11 oz. Find the total weight. 
 
 SOLUTION. Arrange the numbers as in simple addition, 4011 7 
 
 so that units of the same order stand in the same vertical 
 
 -to v 
 
 column. 'Adding the first column at the right, the result is ~ ^ 
 
 27 oz. =1 Ib. 11 oz.; write 11 oz. and carry 1 Ib. Adding ^0 * 
 
 the pounds, the sum is 147. 147 Ib. 11 OZ. 
 
 2. From a barrel containing 379 gal. 1 qt. of molasses, 17 
 gal. 3 qt. were sold. How much remained unsold ? 
 
 SOLUTION. Arrange the numbers as in simple subtraction, gy _, j -j Q ^ 
 so that units of the same order stand in the same vertical ^7 '3 
 
 column. 3 qt. cannot be subtracted from 1 qt.; therefore '- 
 
 mentally take 1 gal. (4 qt.) from 37 gal. and add it to 1 qt., ^ ai ' - c l^ i ' 
 making 5 qt. 5 qt. 3 qt. = 2 qt. Inasmuch as 1 gal. was added to 1 qt., there 
 are but 36 gal. remaining in the minuend ; 36 gal. 17 gal. = 19 gal. 
 
DENOMINATE QUANTITIES 185 
 
 WRITTEN EXERCISE 
 
 Find the sum of : 
 
 1. 
 
 
 2. 
 
 
 
 3. 
 
 
 4. 
 
 140 
 
 6s. 
 
 139 
 
 5s. 
 
 84 
 
 T. 75 Ib. 
 
 279 
 
 T. 840 Ib. 
 
 159 
 
 3 
 
 214 
 
 5 
 
 96 
 
 14 
 
 364 
 
 210 
 
 162 
 
 4 
 
 921 
 
 3 
 
 78 
 
 79 
 
 872 
 
 220 
 
 139 
 
 2 
 
 141 
 
 7 
 
 37 
 
 41 
 
 146 
 
 140 
 
 167 
 
 4 
 
 10 
 
 9 
 
 19 
 
 63 
 
 214 
 
 180 
 
 129 
 
 3 
 
 171 
 
 8 
 
 84 
 
 79 
 
 926 
 
 230 
 
 136 
 
 4 
 
 215 
 
 7 
 
 97 
 
 13 
 
 210 
 
 420 
 
 147 
 
 2 
 
 321 
 
 5 
 
 87 
 
 125 
 
 75 
 
 750 
 
 Find the difference between : 
 
 5. 6. 7. 8. 
 
 11 mo. 17 da. 11 mo. 1 da. 8 mo. 14 da. 9 mo. 17 da. 
 
 8 31 9 31 2 29 2 31 
 
 9. From a pile of wood containing 74| cd., 28 J cd. and 15 J 
 cd. were sold. How much remained unsold? 
 
 10. I owned a farm of 340 A. when I bought an adjoining 
 field of 741 A. I then sold 140 f A. What is the remainder 
 of the farm worth at 75 per acre ? 
 
 11. An English merchant had on hand Jan. 1 goods valued 
 at 5927 10s.; during the following six months he bought 
 goods at a cost of 4920 10s. and sold goods to the amount of 
 7926 4s. If the value of the goods on hand July 1 of the 
 same year was 4120 10s., what has been the gain or loss in 
 English money ? in United States money ? 
 
 FINDING THE DIFFERENCE BETWEEN DATES 
 
 213. In the foregoing problems in addition and subtraction 
 only compound numbers of two denominations were used. 
 These are practically the only compound numbers met with in 
 business, if the case of finding the difference between two dates 
 is excepted. 
 
186 PRACTICAL BUSINESS ARITHMETIC 
 
 214. The difference between two dates may be found by com- 
 pound subtraction, or by counting the actual number of days 
 from the given to the required date. 
 
 In business transactions involving long periods of time, the difference is 
 generally found by compound subtraction ; but in transactions involving 
 short periods of time, the difference is generally found by counting the 
 exact number of days. 
 
 215. Examples. 1. A mortgage dated Oct. 15, 1901, was 
 paid Apr. 6, 1907. How long had it run ? 
 
 SOLUTION. Write the later date as the rninu- 1907 yr. 4 mo. 6 da. 
 end and the earlier date as the subtrahend. April 1901 10 15 
 
 being the 4th and October the 10th month, write r r 01 j 
 
 4 and 10 respectively instead of the names of the 
 months. Consider 30 da. a month and 12 mo. a year and subtract as usual. 
 
 2. Find the difference between Apr. 21 and July 27. 
 
 SOLUTION. Write the number of 9 fa^ j n April 
 days remaining in April, the number gj[ j a i n May 
 in May and June, and finally the on j T une 
 number in July up to and including ^ ^ j n j u jy 
 July 27. The sum of these numbers - ; 
 
 is the required time expressed with 97 da - f rom A P nl 21 to Jul y 27 
 exactness. Observe that the total time excludes the first and includes the last 
 day of the given dates. 
 
 ORAL EXERCISE 
 
 /State the exact number of days between : 
 
 1. Mar. 12 and Apr. 16. 5. July 1 and Oct. 1. 
 
 2. Apr. 27 and May 31. 6. June 30 and Sept. 1. 
 
 3. May 31 and July 18. 7. July 31 and Nov. 7. 
 
 4. June 7 and Aug. 16. 8. Aug. 31 and Dec. 1. 
 
 WRITTEN EXERCISE 
 
 Find the exact number of days between : 
 
 1. Apr. 2 and Nov. 25. 5. Mar. 18 and Nov. 27. 
 
 2. Mar. 1 and Sept. 18. 6. Mar. 17 and July 28. 
 
 3. Mar. 15 and Nov. 2. 7. June 16 and Sept, 18. 
 
 4. Apr. 21 and Dec. 31. 8. June 19 and Nov. 29. 
 9. Find the difference between Jan. 3, 1907, and.each of the 
 
 following dates: May 15, 1904; Sept. 6, 1905; Apr. 8, 1901; 
 Mar. 12, 1889. Find the difference by compound subtraction. 
 
DENOMINATE QUANTITIES 187 
 
 MULTIPLICATION AND DIVISION 
 
 ORAL EXERCISE 
 
 Multiply: Divide: 
 
 1. 3 ft. by 6. 7. 27 yd. by 9. 
 
 2. 1J mi. by 8. 8. 225 ft. by 7J ft. 
 
 3. 9 Ib. 4 oz. by 2. 9. 48 ft. 6 in. by 2. 
 
 4. 18 Ib. 1 oz. by 9. 10. 540 yd. by 18 yd. 
 
 5. IT yd. 2 in. by 9. 11. 164 Ib. 12 oz by 4. 
 
 6. 19 gal. 1 qt. by 3. 12. 640 mi. 160 rd. by 20. 
 216. Examples. 1. How much hay in 8 stacks each contain- 
 ing 5 T. 760 Ib. ? 
 
 SOLUTION. 8 times 760 Ib. = 6080 Ib. = 3 T. 80 Ib. ; 5 ^ -T^Q ITU 
 write 80 in place of pounds and carry 3. 8 times 5 T. = 
 40 T. ; 40 T. -f 3 T. carried = 43 T. The required result 
 
 is therefore 43 T. 80 Ib. 43 T. 80 Ib. 
 
 2. An importer paid 87 10s. for 50 pc. of bric-a-brac. 
 What was the cost per piece ? 
 
 SOLUTION. Since 50 pc. cost 87 10s., 1 pc. costs 1 |5s 
 
 sV of 87 10s. ; of 87 = 1 with an undivided re- r/^ ^ S7 - =po~ 
 mainder of 37 ; write 1 in the quotient and add 
 
 37 to the next lower denomination ; 37 10s. = 750s. ^ of 750s. = 15s. 
 
 3. At 10s. .Qd. per yard, how many yards can be bought for 
 15 15s. ? 
 
 SOLUTION. The dividend and 
 divisor are concrete numbers ; 
 
 therefore reduce them to the 15 15s. = 3780t?. 
 same denomination before divid- 10s Qd = 126t? 
 
 that is 30 yd. can be bought. 
 
 ORAL EXERCISE 
 
 1. At 72 $ per gross what will 2 doz. buttons cost ? 4 doz. ? 
 7 doz. ? 
 
 2. How many 3-oz. packages can be put up from 4 Ib. of 
 pepper ? 
 
 3. Find the cost of 3 T. of bran at 30^ per hundredweight; 
 of 5 T. at 50^ per hundredweight. 
 
188 PRACTICAL BUSINESS ARITHMETIC 
 
 4. How many 1-lb. packages can be put up from 15 T. of 
 breakfast food ? 
 
 5. When coal is $ 6 per ton what will 7000 Ib. cost ? 6400 
 lb.? 3600 Ib. ? 
 
 6. Find the cost of 2400 lb. of flour at $ 2.25 per hundred- 
 weight; of 4400 lb.; of 3200 lb. 
 
 7. At 12 J f per quire what will 480 sheets of paper cost ? 
 240 sheets ? 2880 sheets ? 720 sheets ? 
 
 8. I buy 3 qt. of milk per day. If I pay 5 4 per quart, 
 what is my bill for July and August ? 
 
 9. I bought 3 gro. pens at 60 $ a gross and sold them at the 
 rate of 2 for 1 4 ; what was my gain or loss ? 
 
 10. I bought 3| bu. of apples at $1.00 per bu. and sold 
 them at 50 $ a peck. What was my gain ? 
 
 11. I sold 4 \ cd. of wood for $ 27 and thereby lost $ 9 on 
 the cost. What was the cost per cord ? 
 
 12. A dealer bought 5 rm. of paper at $ 1.25 per ream and 
 retailed it at 20 f a quire. What was his gain ? 
 
 13. At 14.80 per ream what will 3 qr. of paper cost? At 
 13.60 per ream what will 1 qr. cost? 7 qr. ? 
 
 14. If the gross weight of a load of straw is 3380 lb. and the 
 tare 1580 lb., what is the straw worth at $4.00 per ton ? 
 
 15. A dealer bought pens at 60^ a gross and retailed them 
 at the rate of 6 for 5 j. What did he gain on 1 gro.? on 6 
 gro.? on 8 gro.? 
 
 WRITTEN EXERCISE 
 
 1. Find the cost of 10 pwt. 7 gr. of old gold at $'1.25 per 
 pennyweight; of 12 pwt. 4 gr. at $1.10 per pennyweight. 
 
 2. I bought 3J A. of city land at $125 an acre and sold it 
 at 50 f per square foot. Did I gain or lose and how much ? 
 
 3. Give the length of a double-track railroad that can be 
 laid with 352,000 rails 30 ft. long. 
 
 4. I bought a barrel of cranberries containing 2J bu. at $4 
 per bushel and retailed them at 15^ a quart. Did I gain or 
 lose and how much ? 
 
DENOMINATE QUANTITIES 
 
 189 
 
 5. From a farm of 375 A. I sold 25f A. What is the re- 
 mainder worth at $125 per acre ? 
 
 6. Find the cost (a) in English money and (5) in United 
 States money of 360 doz. cotton hose at 5s. 2d. 
 
 SOLUTION, (a) 5s. 2d. = 5Js. 360 times 5$*. = 1860s. = 93, the cost in 
 
 English money. 
 
 (6) 1=$4.8665. 93 times $4.8665 = $452.58, the cost in 
 United States money. 
 
 7. Copy and find the amount of the following invoice : 
 
 Terms. 
 
 Bought of E. M. LLOYD & SON 
 
 5/2, 4/3, and 12/- in the price column = 5s. 2rf., 4s. 3rf., and 12s., 
 respectively. 
 
 8. The distance around a square garden is 48 rd. 12 ft. 
 Find the length of one side of it. 
 
 9. Reduce 12500 to English money. 
 
 SOLUTION. 1 = $4. 8665. #2500 -s- 4.8665 = 51.372. 61.372 x 1 = 51.372. 
 .372 x 20s. = 7.44s. .44 x I2d. = 5.28d. .28 x 4 far.= 1.12 far. Hence $ 2500 = 
 51. 7s. 5d. 1 far. 
 
 10. Find the value in United States money of a post-office 
 money order for <5 18s. 6c?.; for 3 12s. 
 
 11. Change $100 to English money ; 1 135 ; | 250 ; $ 1250. 
 
 12. A coal dealer bought 448 T. of coal by the long ton at 
 14 per ton and sold it by the short ton at $5.25 per ton. Did 
 he gain or lose and how much ? 
 
190 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 13. A druggist bought by avoirdupois weight 5 Ib. of pep- 
 permint oil at $2.501 per pound and retailed it at 50^ an 
 ounce, apothecaries' weight. What was his gain ? 
 
 217. Farm products which are handled in bulk are frequently 
 bought and sold by the bushel. The statutory weights of the 
 bushel for some of the common commodities are shown in the 
 following table : 
 
 STATUTORY WEIGHTS OF THE BUSHEL 
 
 COMMODITIES 
 
 WEIGHT IN 
 AVOIRDUPOIS 
 POUNDS 
 
 EXCEPTIONS 
 
 Barley 
 
 48 
 
 Ala., Ga., Ky., and Penn., 47; Ariz., 45; Cal., 50. 
 
 Beans 
 
 60 
 
 N. H. and Vt., 62. 
 
 Clover Seed 
 
 60 
 
 
 Corn, Shelled 
 
 56 
 
 Ariz., 54; Cal. 52. 
 
 Oats 
 
 32 
 
 Me., N.J., Va.,30; Md.,26. 
 
 Potatoes, Irish 
 
 60 
 
 Md., Penn., and Va., 56. 
 
 Rye 
 
 56 
 
 Cal., 54. 
 
 Wheat 
 
 60 
 
 
 218. Example. What will 4260 Ib. of wheat cost at 80 1 
 per bushel? 
 
 SOLUTION. In examples of this character the 71 
 principles of cancellation may be applied to advan- 
 tage. 
 
 In problems 1-4 in the following exercise the price is per bushel in each case. 
 
 X 80 ff __ & r g OQ 
 
 WRITTEN 
 
 1. Find the total value of : 
 6640 Ib. wheat at 84 
 
 4230 Ib. wheat at 95 
 
 2. Find the total value of : 
 3264 Ib. oats at 25 
 
 2400 Ib. oats at 48^. 
 2560 Ib. oats at 37} 
 
 3. Find the total value of : 
 3660 Ib. clover seed at $4.50. 
 1200 Ib. clover seed at 14.75. 
 2472 Ib. clover seed at $4.20. 
 
 EXERCISE 
 
 1260 Ib. wheat at 90 
 6120 Ib. wheat at 87} 
 
 6951 Ib. oats at 32^. 
 1920 Ib. oats at 33} 
 3840 Ib. oats at 29 j 
 
 5040 Ib. shelled corn at 47} t. 
 2800 Ib. shelled corn at 
 2240 Ib. shelled corn at 
 
DENOMINATE QUANTITIES 191 
 
 4. Find the total value of : 
 
 3793 Ib. rye at 11.12. 6160 Ib. rye at 90^. 
 
 9240 Ib. rye at $1.25. 3080 Ib. rye at 97J 
 
 6720 Ib. rye at $1.121 7924 Ib. rye at $1.12. 
 
 5. The gross weights and the tares of ten loads of wheat 
 were 4260 - 1260, 4310 - 1260, 3890 - 1260, 4160 - 1260, 
 3860-1260, 4180-1260, 4370-1260, 4290-1260, 4370- 
 1260,4480-1260 Ib., respectively. Find the value of the 
 wheat at $1.121 p er bushel. 
 
 ORAL REVIEW EXERCISE 
 
 1. Find the cost of 2500 Ib. of hay at $12 per ton. 
 
 2. What is a ton of wheat worth at 90^ per bushel ? 
 
 3. Change 4860 Ib. to tons ; 3640 Ib.; 4280 Ib.; 6240 Ib. 
 
 4. Change 2.5 T. to pounds; .75 T.; 2.03 T.; 11.004 T. 
 
 5. Change 6 mi. to rods ; 50 rd. to feet ; 330 ft. to rods. 
 
 6. How much more than 1 ton does 70 bu. of oats weigh ? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the total cost of : 
 
 3260 Ib. at $5.25 per ton. 4960 Ib. at $8.00 per ton. 
 
 3840 Ib. at $7.50 per ton. 5800 Ib. at $6.25 per ton. 
 
 4560 Ib. at $6.871 per ton. 5200 Ib. at $5.25 per ton. 
 
 2. Find the total cost of : 
 
 3500 lath at $3 per M. 1500 brick at $8 per M. 
 
 3600 Ib. hay at $9 per ton. 4260 Ib. coal at $4 per ton. 
 
 3150 Ib. pork at $4.50 per cwt. 60 Ib. beef at $4.75 per cwt. 
 
 3. Find the total value of : 
 
 COMMODITY GROSS WEIGHT TARE PRICE 
 
 A load of coal 6460 Ib. 2140 Ib. $6.25 per T. 
 
 A load of straw 3680 Ib. 1680 Ib. $3.25 per T. 
 
 A load of wheat 4160 Ib. 1620 Ib. 851^ per bu. 
 
 A load of oats 4760 Ib. 1560 Ib. 311^ per bu. 
 
 A load of coal 4230 Ib. 1530 Ib. $7.25 per T. 
 
 A load of paper rags 3260 Ib. 1260 Ib. \t per Ib. 
 
 A load of old iron 3480 Ib. 1280 Ib. \t per Ib. 
 
 A load of corn meal 4160 Ib. 1620 Ib. 75^ per cwt. 
 
192 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 4. A church was lighted by kerosene lamps and the amount of 
 oil consumed each evening was 1J qt. If the church was 
 lighted 2 evenings each week for 1 yr., what was the cost of 
 the oil at 14^ per gallon ? 
 
 5. An American lady shopping in Paris bought 10yd. of 
 lace at 20 francs per yard ; 6 pr. of gloves at 10 francs per 
 pair. What was the amount of the bill in United States money? 
 
 6. A local dealer bought 448 T. of coal, by the long ton, 
 at $5.50 per ton and sold it by the short ton at 6. If the 
 waste and loss amounted to 2 short tons, how much did he 
 gain? 
 
 7. Without copying, find the amount of the following in- 
 voice : 
 
 Leith, Scotland,. 
 
 / 
 INVOICE OF HOSIERY 
 
 /Q 
 
 Num- 
 ber 
 
 Quantity 
 
 Article and Description 
 
 Price 
 
 Extension 
 
 CM 
 
 J 
 
 8. Find, by compound subtraction, the difference between 
 Sept. 14, 1908, and each of the following dates: Jan. 8, 1881; 
 Feb. 7, 1883; Mar. 9, 1890; Apr. 27, 1895; May 20, 1897; June 
 17,1899; July 25, 1900; Aug. 15, 1901; Sept. 24,1903; Oct. 
 19, 1904; Nov. 18, 1905; Dec. 15, 1906. 
 
CHAPTER XVI 
 
 PRACTICAL MEASUREMENTS 
 DISTANCES AND SURFACES 
 
 DISTANCES 
 
 219. An angle is the divergence of two lines from a common 
 point. 
 
 Thus the divergence of the lines BA and EC from 
 
 the point B is the angle ABC. 
 
 220. A right angle is the angle formed when one straight line 
 so meets another as to make the two adjacent 
 angles equal. The lines forming the angles are 
 perpendicular to each other. c- 
 
 Thus the two angles ABC and ABD are right angles, and the lines AB 
 and CD are perpendicular to each other. 
 
 221. An acute angle is less than a right angle ; an obtuse 
 A angle is greater than a right angle. 
 
 ^X^ _ Thus the angle ABC is an acute angle, and the angle 
 
 ABD is an obtuse angle. 
 
 222. A surface is that which 
 has length and width, but not 
 measurable thickness. A level 
 surface, as the surface of still 
 water, is called a plane surface 
 or a plane. 
 
 223. A rectangle is a plane figure bounded by four straight 
 
 lines and having four right angles. 
 
 A square is a rectangle whose sides 
 are all equal. 
 
 193 
 
194 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 224. A triangle is a plane figure bounded by three straight 
 lines and having three angles. 
 
 A triangle is called equilateral when all its sides are equal ; 
 isosceles when any two of its sides are equal ; scalene when no 
 two of its sides are equal. 
 
 225. A right angled triangle is a triangle having a right 
 angle. 
 
 A triangle containing an acute angle is sometimes called an 
 acute-angled triangle ; a triangle containing an obtuse angle, an 
 obtuse-angled triangle. 
 
 226. The perimeter of a plane figure is the distance around it. 
 
 227. A circle is a plane figure bounded 
 by a regularly curved line, every point of 
 which is equally distant from a point within 
 called the center. The circumference of a 
 circle is the curved line which bounds it ; 
 the diameter is any straight line passing 
 through the center and terminating in the 
 circumference ; the radius is one half the 
 
 diameter. An arc is any part of the circumference of a circle. 
 
 ORAL EXERCISE 
 
 1. Measure very accurately the diameter and the circum- 
 ference of each of several circular objects, such as an ink-well 
 cover, a coin, a ring, a plate, or a wheel. Record the measure- 
 ments in each case. 
 
 2. Divide each circumference by its diameter, carrying the 
 result to four decimal places. 
 
 3. Find the average of the several quotients. 
 
 4. How many times the diameter of a circle is its circum- 
 ference ? 
 
 5. A piece of circular stove pipe 7 in. in diameter is ap- 
 proximately 22 in. in circumference ; the circumference is 
 approximately how many times its diameter ? If the diameter 
 of a circle is 21 in., what is its circumference ? 
 
PRACTICAL MEASUREMENTS 
 
 195 
 
 228. It is proved in geometry that the circumference of a 
 circle is 3.1416 times the diameter. 
 
 229. Therefore, to find the circumference of a circle when 
 the diameter is given, multiply the diameter by 3.1416. 
 
 230. And, conversely, to find the diameter of a circle when 
 the circumference is given, divide the circumference by 3.1416. 
 
 WRITTEN EXERCISE 
 
 1. Draw neat figures to represent each of the following: 
 rectangle, triangle, square, circle, right-angled triangle, equi- 
 lateral triangle, isosceles triangle, scalene triangle, radius of a 
 circle, arc of a circle. 
 
 2. A parlor is 18 ft. 6 in. long and 12 ft. 3 in. wide. 
 What will be the cost, at 28 j* per foot, of a molding extend- 
 ing around the room ? 
 
 3. The circumference of a circle is 113.0976 ft. What is 
 the length of the longest straight line that can be drawn across 
 the circle? Find the circumference 
 
 of a circle whose radius is 21 ft. 
 
 4. What will be the cost, at 75^ 
 per yard, of carpeting a stairway of 
 18 steps, the tread of each stair being 
 12 in. and the riser 8 in. ? 
 
 5. How many telegraph poles, 
 
 10 rd. apart, will be required for 150 mi. of railroad? 
 
 6. Find the cost, at 75^ per rod, of fencing the fields illus- 
 trated in the accompanying triangles: 
 
 7. A rectangular field 
 is 100 rd. long and 60 rd. 
 wide. How many posts 
 set 1 rd. apart will be re- 
 quired to inclose the field 
 and to divide it into four 
 
 equal fields? ~ 66 ft. 
 
196 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 
 
 
 
 
 
 AREAS 
 ORAL EXERCISE 
 
 1. What is the area of a square 1 rd. on each side ? 
 
 2. How many squares 1 rd. on each side in a 
 rectangle 6 rd. long and 1 rd. wide ? 
 
 3. How many rectangles, 
 each 6 rd. by 1 rd., in a rec- 
 tangle 6 rd. by 3 rd. ? 
 
 4. How many square rods 
 in the area of a rectangle 6 rd. 
 long and 3 rd. wide ? 
 
 5. How many square rods 
 in the area of a rectangle 16 rd. 
 long and 132 ft. wide ? 
 
 SOLUTION. 132 ft. = 8 rd. A rectangle 
 1 rd. on a side contains 1 sq. rd. But the 
 given rectangle is 16 times 1 rd. long and 
 
 6rd. 
 
 132 ft. = 8 rd. 
 8 x 16 sq. rd. = 128 sq. rd. 
 8 times 1 rd. wide. Therefore the required area is 16 x 8 x 1 sq. rd. or 128 sq. rd. 
 
 231. In the foregoing exercise it is clear that the product of 
 the length and width of a rectangle equals the area. 
 
 ORAL EXERCISE 
 
 Find the areas of rectangles having the following dimensions. 
 Make use of the short method explained in 180-182. 
 
 1. 6J- ft. by 6J ft. 
 
 2. 7J rd. by 7J rd. 
 
 3. 6.5 rd. by 6.5 rd. 
 
 232. The dimensions of a 
 triangle are called the base and 
 the altitude. The base is the 
 side on which the triangle ap- 
 pears to stand ; the altitude is 
 the perpendicular distance 
 from the base to the highest 
 point of the triangle. 
 
 4. 9.5 rd. by 9.5 rd. 
 
 5. 12.5 ft. by 4.5 ft. 
 
 6. 14.5 rd. by 6.5 rd. 
 
 Base 
 
PRACTICAL MEASUREMENTS 
 
 197 
 
 ORAL EXERCISE 
 
 1. How does the area of the triangle on the right compare 
 with the area of a rectangle 8 ft. by 4 ft. ? 
 
 2. Compare the area of the triangle on the left with 
 the area of a rectangle 12 rd. by 5| rd. 
 
 3. What is the area of a triangle 
 whose base is 8 ft. and whose alti- 
 
 tude is 9J ft.? 
 
 4. The area of a triangle equals what part of the 
 area of a rectangle having the same base and altitude? 
 
 233. In the above exercise it is clear that one half the prod- 
 uct of the base and altitude of a triangle equals the area. 
 
 ORAL EXERCISE 
 
 State the areas of triangles whose bases and altitudes, re- 
 spectively, are as follows: 
 
 1. 20 ft., 18 ft. 3. 12 ft., 41 ft. 
 
 2. 12 ft., 16 ft. 4. 19J ft., 8 ft. 
 
 234. If a circle be divided as in the figure on the left and the 
 parts rearranged as in the figure on the right, it will be clear 
 
 that the area of the circle equals the area of the twelve tri- 
 angles. The altitude of each triangle is the radius of the circle, 
 and the sum of the bases, the circumference. 
 
 235. It is therefore clear that one half the product of the 
 circumference and radius of a circle equals the area. 
 
 When a circle is divided as in the above figure, the parts are not exact tri- 
 angles ; but it is proved in geometry that the area of a circle is the same as 
 that of a triangle having a base equal to the circumference and an altitude 
 equal to the radius. 
 
198 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. The base of a triangle is 8 in. and the height 11 in. What 
 is the area ? 
 
 2. A field contains 1280 sq. rd. If the width is 32 rd., what 
 is the length ? x 
 
 3. A man sold a lot 10 rd. long and 8 rd. wide at the rate of 
 1260 per acre. How much did he receive ? 
 
 4. A porch is 20 ft. long and 6 ft. wide. How many square 
 feet of oilcloth will be required to cover it ? 
 
 5. A canvas on which a portrait is painted contains 1440 sq. 
 in. If the width is 3 ft., what is the length ? 
 
 WRITTEN EXERCISE 
 
 1. A circular pavilion has a radius of 56|- ft. What is the 
 area of the floor space ? 
 
 2. A city lot contains ^ A. If it is 200 ft. long, what is its 
 width, and what is its value at 50 ^ per square foot ? 
 
 3. The floor of a restaurant 50 ft. long and 40 ft. wide is 
 covered with tiles 8 in. square. How many tiles will be required? 
 
 4. A small park, 50 rd. long and 40 rd. wide, has a walk 
 inclosing it. If the walk is 1 yd. wide, how many square feet 
 does it contain ? 
 
 5. How many square feet of slate will be required to furnish 
 blackboard surface for a schoolroom 30 ft. wide and 42 ft. long, if 
 the slate is 1 yd. wide 
 
 and extends across one 
 end of the room and 
 one third the length 
 on each side ? 
 
 6. The accompany- 
 ing diagram repre- 
 sents a field of wheat. 
 
 It is drawn on a scale of ^ in. to the rod. How much will it 
 cost, at 50 ^ per rod, to build a fence around the field ? 
 
PRACTICAL MEASUREMENTS 
 
 199 
 
 Jin. 
 
 iin. 
 
 lin. 
 
 7. If the field in problem 6 yields an average of 16^ bu. of 
 wheat to the acre, for a certain season, 
 
 what is the crop worth at 10.95 per 
 bushel ? 
 
 8. The accompanying diagram rep- a 
 resents a field of corn. It is drawn on 
 
 a scale of -% in. to the rod. If the field 
 yields an average of 28 bu. to the acre 
 for a certain year, what is the crop worth at 55 f per bushel ? 
 
 PUBLIC LANDS 
 
 236. In the more recently settled parts of the United States, 
 public lands are surveyed by select- 
 ing a north and south line as a prin- 
 cipal meridian and an east and west 
 line intersecting this as a base line. 
 Other lines are then run, at intervals 
 of 6 miles, both east and west of the 
 principal meridian, and north and 
 south of the base line. These lines divide the land into tracts 
 6 mi. square, called townships. The lines of townships running 
 north and south are called ranges. 
 
 Thus A in the above diagram may be described as Tp. 1 N., R. 3 W. ; that is, 
 the first township north of the base line, in the third range west of the principal 
 meridian. 
 
 237. Each township is divided into 36 tracts, each 1 mile 
 square, called sections. The numbering of sections in every 
 township is as shown in the dia- 
 gram at the left. 
 
 Sections are divided into halves 
 and quarters; quarter sections 
 are subdivided into halves and 
 -quarters. 
 
 If diagram 3 is B of diagram 2, and diagram 2 is A of diagram 1, C of dia- 
 gram 3 may be described as the S.E. J of S.E. J, Sec. 19, Tp. 1 N., R. 3 W. 
 
200 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. How many chains in a mile ? how many rods ? how many 
 feet ? How many rods in a chain ? how many feet? 
 
 2. How many acres in a field 50 ch. by 40 ch.? in a field 
 40 ch. square ? in a field 80 ch. by 80 ch. ? 
 
 3. A field has an area of 4 A. If it is 10 ch. long, how wide 
 is it and what will it cost to fence it at 50^ per rod ? at 60^? 
 
 WRITTEN EXERCISE 
 
 1. Make a diagram of a township and locate N. J, Sec. 20. 
 
 2. Draw a diagram illustrating principal meridian, base line, 
 range line, and township lines, and mark Tp. 2 S., R. 2 E. and 
 Tp. 1 N., R. 3 W. 
 
 3. Find the value, at 112.50 per acre, of Tp. 2 N., R. 3 W. 
 
 4. Find the cost at $25 per acre of N.E. of N.W. J, Sec. 
 20, Tp. 1 N., R. 4 W. 
 
 SQUAIIE ROOT AND ITS APPLICATIONS 
 ORAL EXERCISE 
 
 1. What is meant by factor? by exponent? by power of a 
 number ? 
 
 2. State the second power of each of the following numbers : 
 1, 2, 3, 4, 5, 6, 7, 8, 9. How much is 12 2 , 13 2 , 14 2 , 15 2 , 16 2 ? 
 
 3. Name one of the two equal factors of each of the following 
 numbers : 2, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196. 
 
 238. The square of a number is the product arising from 
 the number twice as a factor. The square root of a number 
 wo equal factors of the number, 
 quare root of a number may be indicated by writ- 
 er under the radical sign ^/~ or by placing the 
 )ve and to the right of the number, 
 r 196* indicates the square root of 196. 
 
 oquare root of a number is readily derived from the 
 
 process by which the square is formed. 
 
PRACTICAL MEASUREMENTS 201 
 
 241. Example. What is the square of 42? 
 
 SOLUTION. Since 42 = 40 + 2, the square of 42 may be found as follows : 
 
 40 + 2 
 
 40 + 2 40 2 = 1600 
 
 (40x2)+2 2 2(40x2)= 160 
 
 4Q2 + (4Q x 2) 2 = 4 
 
 40 2 +2(40 x2) + 2 2 = 1764 
 
 242. In the preceding process it is shown that the square of 
 a number is equal to the square of the tens plus twice the product 
 of the tens by the unify plus the square of the units. 
 
 243. I 2 = 1, 10 2 = 100, 100 2 = 10000, and so on ; 9 2 = 81, 99 2 = 
 9801, 999 2 = 998001, and so on. It is therefore evident that the 
 square of an integral number contains twice as many figures or 
 one less than twice as many figures as the number. Hence, if 
 an integral number be separated into groups of two figures 
 each, from right to left, there will be as many figures in the 
 square root as there are groups of figures in the number. 
 
 244. Examples. 1. What is the square root of 529 ? 
 
 SOLUTION. Beginning at the right, separate the number into 5 29(23 
 
 periods of two figures each. The greatest square in 5 is 4 and ^ 
 
 the square root of 4 is 2, the tens' figure of the root. Find the 
 remainder, affix the second period, and the result is 129. This 
 remainder is equal to twice the product of the tens by the units, 1 29 
 
 plus the square of the units ( 242). Twice 2 tens is 4 tens (40) 
 and 4 tens (40) is contained in 129, 3 times ; hence, 3 is the units' figure of the 
 root. Twice the tens multiplied by the units plus the square of the units is the 
 same as twice the tens plus the units multiplied by the units. Therefore, annex 
 3 units to the 4 tens and multiply by 3 ; the result is 129. The square root of 
 529 is thus shown to be 23. 
 
 2. What is the square root of (a) 13.3225 ; (5) of .0961 ? 
 
 13 .32 25(3.65 .09 61(.31 
 
 9 .09 
 
 6.6)4 .32 .61). 00 61 
 
 3 .96 .00 61 
 
 7.25) .36 25 
 .36 25 
 
202 PRACTICAL BUSINESS ARITHMETIC 
 
 245. The process of finding the square root of a number may 
 be summarized as follows : 
 
 Beginning at the units, separate the number into groups of two 
 figures each. 
 
 Find the greatest square in the left-hand group and write its 
 root for the first figure of the required root. 
 
 Subtract the square of the root figure from the left-hand period 
 and annex the second period for a dividend. 
 
 Take twice the root figure already found, considered as tens, 
 and divide the dividend by it. 
 
 Annex the quotient to both the root and the trial divisor and 
 multiply by the units. 
 
 Continue in like manner until all the periods have been used. 
 The result will be the square root. 
 
 If a number contains a decimal, begin at the decimal point and indicate 
 groups to the left for the integral part of the root, and to the right for the 
 decimal part of the root. If the last period on the right of the decimal 
 point has but one figure, annex a decimal cipher, as each decimal period 
 must contain two figures. 
 
 To find the square root of a common fraction, extract the square root of 
 the numerator and denominator separately. If the terms of the fraction 
 are not perfect squares, reduce the fraction to a decimal and then extract 
 the square root. 
 
 WRITTEN EXERCISE 
 
 Find the square root of: 
 
 1. 324. 5. 576. 9. 9025. 13. f|. 
 
 2. 484. 6. 1024. 10. 3364. 14. 
 
 3. 676. 7. 7225. 11. 70.56. is. 
 
 4. 729. 8. 3969. 12. 150.0625. 16. 
 
 246. It has been seen that the area of a square is the product 
 of its two equal sides. It therefore follows that the square root 
 of the area of a square equals. one of its sides. 
 
 247. The hypotenuse is the side opposite the right angle in a 
 right triangle. 
 
PRACTICAL MEASUREMENTS 
 
 203 
 
 248. In the accompanying illustration it will be seen that the 
 square on the hypotenuse is equal to 
 
 the sum of the squares on the other 
 sides. Hence, 
 
 249. To find the hypotenuse take the 
 square root of the sum of the squares of 
 the base and altitude; and 
 
 250. To find the base or the altitude 
 take the square root of the difference be- 
 tween the squares of the hypotenuse and 
 the other side. 
 
 WRITTEN EXERCISE 
 
 1. A square field contains 5.625 A. What is the length of 
 one of its sides ? 
 
 2. Find the side of a square containing the same area as a 
 field 160 rd. long by 90 rd. wide. 
 
 3. What is the hypotenuse of a right-angled triangle the base 
 of which is 30 ft. and the altitude 40 ft. ? 
 
 4. The accompanying diagram represents 
 a piece of land. It is drawn on the scale of 
 -fa in. to the rod. The land is divided into 
 two fields by the line AB. Find the cost, 
 at 50 f per rod, of fencing the two fields. 
 
 5. What will be the cost, at $1.75 per chain, of fencing a 
 square field containing 1.6 A.? 
 
 ROOFING 
 
 251. Roofing is usually measured by the square of 100 sq. ft. 
 
 252. The size of slates used for roofing varies from 6 in. by 
 12 in. to 16 in. by 24 in. 
 
 Contractors and builders generally use prepared tables for estimating the 
 amount of slate to be used. The number of slates per square varies with 
 the size of the slate. Thus, slates 16 in. by 24 in. require 86 per square ; 
 slates 6 in. by 12 in. require 533 per square ; etc. 
 
204 
 
 PKACTICAL BUSINESS ARITHMETIC 
 
 253. All shingles average 4 in. in width and are put up in 
 bundles of 250. The shingles most commonly used are 16 in. 
 or 18 in. long. 16-inch shingles are generally laid 4J in. and 
 18-inch shingles 5J in. to the weather. 
 
 254. A shingle 4 in. wide laid 4J in. to the weather will cover 
 18 sq. in. A square contains 14,400 sq. in. 14,000 sq. in. -*- 
 18 sq. in. = 800. It is therefore clear that 800 16-inch shingles 
 will cover a square of roof. 
 
 255. A shingle 4 in. wide laid 5J in. to the weather will cover 
 22 sq. in. 14,400 sq. in. -T- 22 sq. in. = 655. It is therefore 
 clear that 655 18-inch shingles will cover a square of roof. 
 
 In practice 655 per square is called 700 per square. 
 
 40 ft 
 
 One fourth Pitch 
 
 40ft. 
 
 One half Pitch 
 
 \ 
 
 ORAL EXERCISE 
 
 1. How many bundles in 1000 shingles? in 7500 shingles? 
 in 26,000 shingles ? 
 
 2. What will be the cost, at $4 per 
 square, of tinning a roof 20 ft. by 15 ft. ? 
 
 3. A certain roof requires 7610 shingles. 
 How many bundles of shingles must be 
 bought to cover it ? 
 
 A dealer will not sell a fractional part of a 
 bundle of shingles. 
 
 4. How many slates at 300 to the square 
 will be required for a flat roof 30 ft. by 
 20 ft. ? 
 
 256. The rise in the rafters for each 
 foot in the base of the gable is called the 
 pitch of the roof. 
 
 257. When the rise of the roof is 6 in. 
 per foot, the roof is said to have one-fourth 
 pitch. 
 
 258. When the rise of the rafters is 12 in. per foot, the roof 
 is said to have one-half pitch. 
 
 40ft, 
 
 Gothic Pitch 
 
PRACTICAL MEASUREMENTS 205 
 
 259. When the rise of the rafters is 15 in. per foot, the roof 
 is said to have five-eighths, or Gothic pitch. 
 
 When the rise of the rafters is 6 in. per foot, the perpendicular height of 
 the gable is 1 of the width of the building ; when the rise is 12 in. per foot, 
 the height of the gable is i the width of the building; when the rise is 15 
 in. per foot, the height of the gable is f of the width, or li times | the width 
 of the building. Hence the names one-fourth pitch, one-half pitch, etc. 
 
 ORAL EXERCISE 
 
 Find the height of the gable : 
 WIDTH OF BUILDING PITCH OF ROOF WIDTH OF BUILDING PITCH OF ROOF 
 
 1. 30 ft. 3. 24 ft. Gothic 
 
 2. 50 ft. 12 in. per ft. 4. 36 ft. J 
 
 WRITTEN EXERCISE 
 
 1. The accompanying diagram represents the roof of a shed 
 16 ft. wide. If the ridge- 
 pole is 68 ft., the pitch of 
 
 the roof one half, and the 
 projection of the rafters 
 18 in., how many shingles 
 16 in. long, laid 4J in. to 
 the, weather, will be re- 
 quired to cover the roof ? 
 
 SOLUTION 
 
 1 of 16 ft. = 8 ft. = the base of the triangle ABC. 
 
 The pitch of the roof is ; $ of 16 ft. = 8 ft. = the altitude of the triangle ABC. 
 
 8 2 + 8 2 = 128 ; 128* ='11.31, number of feet in the hypothenuse of ABC. 
 18 in. = 1.5 ft. ; 11.31 ft. + 1.5 ft. = 12.81 ft. = the length of the rafters or 
 the width of each side of the roof. 
 
 2 x 68 x 12.81 ft. = 1742.16 sq. ft. = the entire surface of the roof. 
 1742.16 sq. ft. = 17.4216 squares; 17.4216 x 800 shingles = 13937 shingles. 
 As bundles of shingles are not broken it will be necessary to buy 14000 shingles. 
 
 2. A building is 40 ft. wide. If the length of the ridge- 
 pole is 80 ft. and the projection of the rafters 20 in., how many 
 shingles 18 in. long and laid 5J in. to the weather will be 
 required for the roof, the pitch being J ? 
 
206 PEACTICAL BUSINESS ARITHMETIC 
 
 3. A building is 30 ft. wide. If the length of the ridge- 
 pole is 60 ft. and the projection of the rafters 15 in., how many 
 shingles 16 in. long and laid 4^ in. to the weather will be 
 required for the roof, the pitch being ^? 
 
 PLASTERING 
 
 260. Plastering is usually measured by the square yard. 
 
 261. There is no uniform rule with respect to the allowance 
 to be made for doors, windows, and other openings. 
 
 What allowance, if any, shall be made for openings is usually stated in 
 the contract covering the work. In some sections it is customary to make 
 allowance for one half the area of the openings ; in others, for the full area 
 of the openings ; in still others, for a stated number of square feet. 
 
 In giving the dimensions of a room carpenters, architects, and mechanics 
 write the length first, then the width, and finally the height. They also 
 usually write 5" for 5 in., 5' for 5 ft., and 5' x 5' for 5 ft. by 5 ft. 
 
 ORAL EXERCISE 
 
 1. What is the perimeter of a square room 20' on a side ? 
 
 2. What is the perimeter of a dining room 18' x 12' x 9'? 
 
 3. How many square feet in the four walls of the room in 
 problem 2, not allowing for openings ? in the ceiling ? in the 
 four walls and the ceiling ? 
 
 4. How many square yards in the four walls of a room 24' x 
 16', not allowing for openings ? 
 
 5. At 25^ per square yard, what will it cost to plaster 945 
 sq. ft. ? 1080 sq. ft. ? 1440 sq. ft. ? 
 
 WRITTEN EXERCISE 
 
 1. What will it cost, at 27 ^ per square yard, to plaster the 
 walls and ceiling of a hall 60' x 40' x 24', making an allow- 
 ance of 40 sq. yd. for openings ? 
 
 2. Find the cost, at 26^ per square yard, of plastering the 
 walls and ceiling of a room 18' x 16' 6" x 8' 6", making full 
 allowance for 2 doors each 7' 6" x 4' 3 windows 6' x 4'. 
 
PRACTICAL MEASUREMENTS 
 
 207 
 
 3. What will be the cost of plastering, with hard finish, at 
 34 $ per square yard, the walls of the rooms in the following 
 dwelling ? 
 
 First Floor. Parlor, 14' x 12' ; sitting room, 12' x 12' ; 
 dining room, 12' x 10' ; kitchen, 12' x 10' ; pantry, 8' x 6'. 
 All rooms on this floor are uniformly 8' 6" high. 
 
 Second floor. Front chamber, 14' x 12' ; back chamber, 
 12' x 12' ; middle chamber, 10' x 9' ; hall, 23' x 4'. All rooms 
 on this floor are uniformly 8' high. 
 
 Allowance is made for 40 openings of 17 sq. ft. each. 
 
 PAINTING 
 
 262. Painting is usually measured by the square yard. 
 
 263. It is customary to make no allowance for windows, the 
 painting of window sills and sashes being considered as expen- 
 sive as the painting of the surface area of the entire window. 
 
 WRITTEN EXERCISE 
 
 1. What will it cost, at 25^ per square yard, to paint the 
 walls of a room 20' x 16' x 12', no allowance being made for 
 doors or windows ? 
 
 2. At 6J^ per square yard, what will it cost to kalsomine the 
 walls and ceiling of a room 24' x 18' x 12', allowing for a door 
 9' x 4', 2 windows 7' x 4', and a wainscot 3' high around the 
 regular surface of the room ? 
 
 3. Find the cost, at 24^ per square yard, of painting, with two 
 coats, the outside walls of a 
 
 tobacco barn 68' x 20' x 25' 
 with gables extending 10' 
 above the ends of the walls. 
 
 4. What will be the cost, 
 at 22^ per square yard, of 
 painting the outside walls of 
 
 a barn 100' x 40' x 20' with gables extending 10' above the walls ? 
 with gables extending 12^-' above the walls ? 
 
208 PRACTICAL BUSINESS ARITHMETIC 
 
 FLOORING 
 
 264. Flooring is measured by the square or by the thousand 
 square feet. 
 
 Professional floor layers charge by the square, the price being from 75 ^ to 
 $1.50 per square. Carpenters usually work by the day in laying floors. 
 
 Spruce flooring is 4" or 5j" in width; hardwood flooring is 2' 1 or 2^" in 
 width. In flooring there is considerable waste in forming the tongue and 
 the groove of the boards. When flooring is 3" or more in width, it requires 
 about \\ sq. ft. of material for every square foot of surface to be covered; 
 when flooring is less than 3" in width, it requires 1^ sq. ft. for every square 
 foot of surface to be covered. 
 
 265. Example. How many feet of spruce flooring will be 
 required for a room 32' x 24' ? 
 
 SOLUTION. 32 x 24 = 768, the number of square feet to be covered. 
 
 1^ X 768 sq. ft. = 960 sq. ft., the quantity of flooring required. 
 
 WRITTEN EXERCISE 
 
 1. Find the cost at $45 per thousand square feet of a hard- 
 wood floor for a room 20' x 16'. 
 
 2. A pavilion is 70' x 50'. If the flooring is of spruce, what 
 will be the cost at $ 27 per thousand square feet ? 
 
 3. In a two-story dwelling the floor area measures 35'6" x 26'. 
 The first floor is to be of hardwood and the second floor of spruce. 
 Find the quantity of flooring needed. 
 
 4. What will be the cost of a hardwood floor in a room 
 30' x 28', if the labor and incidentals cost $25.50, the lumber 
 $30.50 per M., and 60 sq. ft. are allowed for waste ? 
 
 5. Find the cost of laying an oak floor 20' x 15', reckoning 
 the labor and incidentals at $9.50, the floor boards at $83^ per 
 thousand, and estimating that there is a waste of 40 sq. ft. 
 
 6. The floors in a three-story dwelling are each 55' 4" x 33' 
 10". The first floor is to be of hardwood worth $50 per 
 thousand square feet and the other floors of spruce worth $27 
 per thousand square feet. If it costs $1.10 per square for 
 labor, what will be the total cost of laying the three floors ? 
 
PRACTICAL MEASUREMENTS 
 
 209 
 
 CARPETING 
 
 266. Carpet is sold by the yard. Such floor covering as 
 oilcloth and linoleum are frequently sold by the square yard. 
 
 267. In determining the number of yards of carpeting re- 
 quired for a room it is necessary to know whether the strips 
 are to run lengthwise or crosswise. 
 
 Carpets are generally laid lengthwise of a room ; but when the matter of 
 expense is an item, it is sometimes more economical to lay the strips cross- 
 wise. 
 
 When the length of the strips required is not an even number of yards, 
 there is usually some waste in matching the pattern. Merchants will sell 
 fractional lengths but not fractional widths of carpeting. It is therefore 
 frequently necessary to cut off or turn under a part of a strip. 
 
 ORAL EXERCISE 
 
 1. How many yards of carpet, 1 yd. wide, must be purchased 
 for a room 5 yd. long by 4 yd. wide ? 
 
 2. The accompanying diagram represents a 
 room drawn on the scale of ^ of an inch to 
 the foot. Find the dimensions of the room. 
 
 3. How many strips of carpet, 1 yd. wide, 
 laid lengthwise of. the room, will be required 
 
 for problem 2 ? How many feet in each strip ? How many yards 
 of carpet will be required for the room ? 
 
 4. The accompanying diagram represents a room drawn on 
 the scale of ^ in. to the foot. 
 
 How many strips of carpet, 
 1 yd. wide, laid lengthwise 
 of the room, will be required 
 to cover it ? What part of 
 a. strip must be cut off or 
 turned under in this case? 
 
 5. How many feet in each 
 strip in problem 4 ? If there is 
 
 . - t UJ.. 
 
 no waste in matching the pat- 
 tern, how many feet of carpet will be required ? how many yards ? 
 
210 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 6. If the strips in problem 4 are run crosswise of the room, 
 how many will be required ? what will be the length of each 
 strip ? If the strips in problem 4 are laid crosswise of the room, 
 it is found that there will be a waste of 6 in. per strip in match- 
 ing. Under these conditions, how many yards will be required? 
 
 7. If the carpet in problem 4 is laid the most economical 
 way, what will it cost at $ 1.50 per yard ? 
 
 268. Example. How many yards of carpet f yd. wide will 
 be required for a parlor floor 20' x 16' 6", if the strips run 
 lengthwise and there is a waste of 6 in. on each strip for 
 matching the pattern ? 
 
 SOLUTION. Since the strips 16' 6" = 3-3'= 3 - 3 yd 
 
 run lengthwise of the room, the 6 
 
 width of the room divided by J d - ^ ! >' d - = 7 i or 8 stn P s 
 the width of the carpet equals 20' + 6" = 20J' 
 
 the number of strips required. g x 20^' = 164' = 54| yd. 
 V yd- * 1 = 7, tne no - of strips ; 
 
 but since an even number of strips must be purchased, 7 strips must be called 8 
 strips. The length of the room is 20' and there is a waste of 6 in. per strip ; 
 hence 20J' of carpet must be purchased for each strip. 8 times 20' = 164' = 
 54f yd., the required result. 
 
 WRITTEN EXERCISE 
 
 1. How many yards of carpet- 
 ing 1 yd. wide will be required to 
 cover the chamber in the accom- 
 panying floor plan, if the strips 
 are to run lengthwise and there is 
 no waste in matching the pattern ? 
 
 2. Find the number of yards of 
 carpet required to cover the room 
 in problem 1 if the strips run 
 across the room and there is a 
 waste of 6 in. per strip in match- 
 ing the pattern. 
 
 3. If the chamber is carpeted in 
 
 the most economical way, what will be the cost at f 1.25 per yard? 
 
PRACTICAL MEASUREMENTS 
 
 211 
 
 4. How many yards of carpet f yd. wide will be required 
 for the parlor in the foregoing floor plan? The strips are 
 to run lengthwise and there is no waste in matching the 
 pattern. 
 
 The cheaper grades of carpet are usually 1 yd. wide. The expensive 
 grades, such as Brussels, Wilton, etc., are | yd. wide. 
 
 5. How many yards of carpet | yd. wide will be required 
 for the dining room in the foregoing floor plan ? The strips 
 are to run lengthwise and there is a waste of 6 in. per strip 
 in matching the pattern. 
 
 6. A rug 18' x 24' is placed cen- 
 trally on a floor 24' x 30' and filling is 
 used to cover the remainder of the 
 room. If the rug cost -$29.50 and the 
 filling 27 1 $ per yard, what is the cost 
 of covering the floor ? 
 
 7. The five chambers in the accom- 
 panying diagram are to be covered 
 with carpet 1 yd. wide, that can be 
 matched without waste. The strips in 
 each room are to run in the direction 
 
 requiring the smaller number of yards. At 85^ per yard, what 
 will it cost to cover the five floors ? 
 
 PAPERING 
 
 269. Wall paper is usually sold in double rolls 18 in. wide 
 and 16 yd. long. 
 
 Single rolls 18 in. wide and 8 yd. long are sometimes used, but it is 
 generally found more economical to use double rolls. These dimensions 
 vary more or less. 
 
 Allowances for openings, such as doors and windows, are made in 
 different ways by different paper hangers. Some make a uniform allow- 
 ance for each opening, while others make allowance for the exact measure- 
 ments of the openings. 
 
 Any whole number of rolls left over after papering may usually be re- 
 turned to the dealer. 
 
212 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. What will the border for a room 15' x 18' cost at 
 per yard? 
 
 2. 18 in. = f ft. 30 ft -r- f ft. = 30 ft. x f ft. = 20. Divide 
 21 ft. by 18 in. 
 
 3. A wall is 15 ft. long and 9 ft. high. If there are no 
 openings, how many strips will be required to cover it ? How 
 many full strips can be cut from each double roll of paper ? 
 What part of a strip will run to waste? How many rolls will 
 be required for the wall ? 
 
 4. Suppose that in problem 2 there is a door 3' x 8'. What 
 is the length of the regular surface of the wall ? Fractional 
 strips must be counted as full strips. Why ? How many 
 strips of paper will be required to cover the regular surface of 
 the wall ? Will dealers sell a fractional part of a roll of 
 paper? How many rolls, then, will be required for the regular 
 surface of the walls? 
 
 5. There is a small surface over the door in problem 5 that 
 has not been considered. What may be used to cover this 
 surface ? 
 
 270. Obviously, to estimate the quantity of paper required 
 for a room: 
 
 From the perimeter of the room subtract the width of the open- 
 ings. Find | of this remainder and the result will be the number 
 of strips required. Divide the number of strips required by the 
 number of full strips that can be cut from each roll of paper and 
 the result is the required number of rolls. 
 
 By this method the ends of the rolls are supposed to be utilized for the 
 surface above the doors and above and below the windows and other irregu- 
 lar places. 
 
 The height of the room, in papering, will be understood to mean the 
 distance from the baseboard to the frieze. 
 
 To estimate the paper required for a ceiling, take f of the width of the 
 room for the number of strips required. Divide the number of strips re- 
 quired by the number of full strips that can be cut from each roll and the 
 result is the number of rolls of paper required. 
 
PRACTICAL MEASUREMENTS 213 
 
 271. Example. How many double rolls of paper will be 
 required for the walls and ceiling of a room 2V x 18' x 8', al- 
 lowing for 2 doors and 3 windows, each 3J ft. wide? 
 
 SOLUTION 
 
 (21' + 18') x 2 = 78', the perimeter of the room. 
 
 5 x 3|' = 17^', the total width of the openings. 
 
 78' - 17i' = 6Qi', the perimeter of the regular surface of the walls. 
 
 f of 60 = 40i, the number of strips of paper necessary for the regular surface. 
 
 48' -=- 8' = 6, the number of strips in each roll. 
 
 40i strips -+ 6 strips = 6 if, or practically 7 rolls of paper required for the walls. 
 
 | of 18 = 12, the number of strips required for the ceiling. 
 
 48' -f- 21' 2|, or practically 2, the number of strips in each roll. 
 
 12 strips -=- 2 strips =6, the number of rolls required for the ceiling. 
 
 6 rolls + 7 rolls = 13 rolls required for the walls and ceiling. 
 
 WRITTEN EXERCISE 
 
 1. The rooms in the floor plan, page 210, are 9 ; high. What 
 will it cost, at 95^ a roll, to paper the walls and ceiling of the 
 parlor, making allowance for 2 double doors, each 6' wide, 1 
 single door 3J' wide, and 2 windows, each 3|' wide? 
 
 2. How many rolls of paper will be required for the walls 
 and ceiling of the dining room in the floor plan, page 210, al- 
 lowing for 1 double door 6' wide, 1 single door 3J' wide, and 2 
 windows each 3^' wide ? 
 
 3. At 43^ per roll how much will it cost to paper the walls 
 and ceiling of the chamber in the floor plan, page 210, allowing 
 for 2 windows, each 3|-' wide, 1 double door 6' wide, and 1 
 single door 3^' wide. 
 
 SOLIDS 
 
 RECTANGULAR SOLIDS 
 
 272. A solid is that which has length, width, 
 and thickness. 
 
 273. A rectangular solid is a solid bounded 
 by six rectangular surfaces. 
 
 274. A cube is a rectangular solid having six square faces. 
 
214 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. If A in the accompanying series of diagrams is 1 cu. ft., 
 how many cubic feet in B ? in C ? in D ? 
 
 2. How many cubic feet in a block of granite 6 ft. long, 1 ft. 
 wide, and 1 ft. high ? in a block 6 ft. long, 3 ft. wide, and 
 1 ft. high ? in a block 6 ft. long, 3 ft. wide, and 3 ft. high ? 
 
 3. Find the volume of a rectangular solid 6 ft. by 4 ft. by 2 
 ft. ; a rectangle 10 ft. by 9 ft. by 9 ft. 
 
 4. A cellar is 40 ft. square and 6 ft. deep. How many cubic 
 yards of earth were removed in excavating it ? 
 
 SOLUTION. A cube 1 ft. on 6 X 40 X 40 X 1 CU. ft. = 9600 CU. ft. 
 the side contains 1 cu. ft. The 96QO ^ f ^ _,_ 97 = 3526 cu> y( J. 
 given cube is 40 x 1 ft. long, 
 
 40 x 1 ft. wide, and 6 x 1 f t. high. Therefore, it contains 6 x 40 x 40 x 1 cu. ft., 
 or 9600 cu. ft. ; and 9600 cu. ft. = 355f cu. yd. , the required result. 
 
 275. Ill the foregoing exercises it is clear that the product of 
 the three dimensions of a solid equals the volume or solid contents. 
 
 WRITTEN EXERCISE 
 
 1. A box car is 50 ft. 6 in. long, 8 ft. 4 in. wide, and 3 yd. 
 high. What is its volume ? 
 
 2. A piece of timber is 60 ft. long and 18 in. square. How 
 many cubic feet does it contain ? 
 
 3. A village constructs a reservoir for a water supply. The 
 length is 100 yd., the width 70 yd., and the depth 15 ft. 
 What will be the cost, at 23^ per cubic yard, of excavating the 
 reservoir ? 
 
PRACTICAL MEASUREMENTS 
 
 215 
 
 WOOD 
 
 276. Wood is measured by the cord. 
 
 277. A cord of wood or stone is a pile 8 ft. long, 4 ft. wide, 
 and 4 ft. high. It con- 
 tains 128 cu. ft. 
 
 The word "cord," as prac- 
 tically used in wood measure, 
 generally means a pile 8 ft. long 
 and 4 ft. high, the price depend- 
 ing on the length of the stick. 
 
 278. Example. How many cords of wood in a pile 32 ft. long, 
 8 ft. wide, and 4 ft. high ? 
 
 SOLUTION. 
 
 4x 
 
 X 
 
 = 8 ; that is, there are 8 cd. in the pile. 
 
 WRITTEN EXERCISE 
 
 1. How many cords in a pile of wood 60 ft. long, 4 ft. wide, 
 and 6 ft. high ? 
 
 2. A pile of wood contains 5 cd. If it is 4 ft. wide and 4 ft. 
 high, how long is it ? 
 
 3. A pile of tan bark contains 150 cd. If it is 4 ft. wide 
 and 8 ft. high, how long is it ? 
 
 4. A pile of wood contains 8 cd. It is 64 ft. long and as 
 high as it is wide. What is the height of the pile ? 
 
 LUMBER 
 
 279. A foot of lumber, sometimes called a board foot, is a 
 
 board 1 ft. long, 12 in. wide, and 1 in. thick, or its equivalent. 
 An exception to this is made in the measurement of boards less 
 than 1 in. in thickness. A square foot of the surface of such 
 boards is regarded as a foot of lumber regardless of the thick- 
 ness. Boards more than one inch in thickness, planks, joists, 
 beams, scantling, and sawed timber are generally measured by 
 the board foot. 
 
216 PEACTICAL BUSINESS ARITHMETIC 
 
 Thus, a board 12 ft. long, 12 in. wide, and 1 in. thick contains 12 sq.ft. 
 of surface, or 12 board feet ; a board 12 ft. long, 12 in. wide, and , |, or | in. 
 thick contains 12 sq.ft. of surface, or 12 board feet ; but a board 12 ft. long, 
 12 in. wide, and 2| in. thick contains 30 board feet. 
 
 Scantling is timber 3| in. wide and from 2 in. to 4 in. thick; joists are 
 narrow and deep sticks of lumber ; planks are thick boards ; lumber heavier 
 than joists or scantling is usually called timber. 
 
 Except when sawed to order and in cherry, black walnut, etc., where the 
 price is 15^ a board foot and upward, the width of a board is reckoned only 
 the next smaller half inch. Thus, a board 10 \ in. wide is reckoned as 10 in., 
 and a board lOf in. wide is reckoned as 10^ in. 
 
 The average width is used in measuring boards that taper uniformly. 
 Thus, a tapering board 12 ft. long, 8 in. wide, at one end and 6 in. wide 
 at the other and 1 in. thick averages 7 in. wide and contains 7 ft. of 
 lumber. 
 
 ORAL EXERCISE 
 
 1. How many square feet in the surface of a board 12 ft. 
 long, 8 in. wide, and 1 in. thick ? How many board feet ? 
 
 2. How many board feet in a board 12 ft. long, 4 in. wide, 
 and -J in. thick ? 
 
 8 
 
 3. How many feet, board measure, in a board 12 ft. long, 
 12 in. wide, and 2 in. thick ? 
 
 4. How many feet of lumber in 65 boards each 12 ft. long, 
 6 in. wide, and 1 in. thick ? 
 
 280. In charging or billing lumber the number of pieces is 
 entered first ; then the thickness and width in inches and the 
 length in feet ; and finally, the article. 
 
 Thus, in billing 12 pc. hemlock, 2 in. thick, 6 in. wide, 12 ft. long, the 
 form would be: 12 pc. 2" x 6", 12', hemlock. 
 
 ORAL EXERCISE 
 
 1. How many board feet in 6 planks, 1|" x 12", 14' ? 
 
 SUGGESTION. By inspection eliminate 12 in the dividend. 
 Then, 1 x 6 x 14 = 126, the required number of board feet. 
 
 2. How many feet, board measure, in 6 planks 2" x 8", 18' ? 
 
 SUGGESTION. By inspection cancel a 12 in the dividend (6x2). 
 Then, 8 x 18 = 144, the required number of feet," board measure. 
 
PRACTICAL MEASUEEMEKTS 217 
 
 3. How many feet of lumber in 6 pc. of scantling 4" x 4", 16' ? 
 SUGGESTION. Mentally picture the problem arranged in form for cancellation 
 Cancel a 12 in the dividend (^ of 6~xl). Then, 2 x 4 x 16, 
 
 12 
 
 or 128, equals the required number of feet of lumber. 
 
 4. How many feet of lumber in 5 sticks, 2" x 6", 16'? 
 SUGGESTION. Mentally picture the problem in form for cancellation 
 
 (- -V Cancel a 12 in the dividend (& of 2~x~6). Then, 5 x 16, or 
 
 80, equals the required number of feet of lumber. 
 
 5. How many feet of lumber in a plank 3"xl2", 16'? in 6 
 planks ? in 10 planks ? How many feet of lumber in a board 
 2" x 6", 12' ? in 5 boards ? in 20 boards ? 
 
 281. Obviously, the number of board feet in lumber 1 in. or 
 less in thickness is -^ of the product of the length in feet by the 
 width in inches ; and the number of board feet in lumber more 
 than 1 in. in thickness is ^ of the product of the length in feet 
 by the width and thickness in inches. But the work may be 
 materially shortened by mentally cancelling 12 from the divi- 
 dend as illustrated in the foregoing exercise. 
 
 ORAL EXERCISE 
 
 State the number of feet, board measure, in the following hemlock: 
 
 1. 5 pc., 3" x 4", 14'. is. 12 pc., 2" x 8", 18'. 
 
 2. 6 pc., 2" x 4", 20'. 14. 6 pc., 8" x 10", 20'. 
 
 3. 6 pc., 2" x 4", 20'. 15. 30 pc., 2" x 6", 20'. 
 
 4. 20 pc., 2" x 6", 14'. 16. 6 pc., 8" x 10", 21'. 
 
 5. 12 pc., 2" x 8", 14'. 17. 25 pc., 3" x 8", 14'. 
 
 6. 25 pc., 3" x 4", 12'. 18. 10 pc., 2" x 6", 13'. 
 
 7. 25 pc., 2" x 6", 20'. 19. 15 pc., 2" x 6", 18'. 
 
 8. 25 pc., 3" x 8", 16'. 20. 15 pc., 2" x 6", 12'. 
 
 9. 10 pc., 3" x4", 14'. 21. 16 pc., 2"x 6", 10'. 
 
 10. 10 pc., 2" x 8", 18'. 22. 10 pc., 8" x 10", 15'. 
 
 11. 14 pc., 2" x 6", 20'. 23. 15 pc., 8" x 10", 12'. 
 
 12. 10 pc., 3" x 6", 20'. 24. 200 pc., 2" x 6", 20'. 
 
218 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 How many feet, board measure, in each of the following ? 
 
 1. 100. joists, 4" x 4", 16'. 4. 70 joists, 2" x 10", 32'. 
 
 2. 65 boards, f " x 6", 12'. 5. 8 beams, 10" x 10", 24'. 
 
 3. 12 timbers, 8" x 8", 40'. 6. 10 beams, 12" x 12", 30'. 
 
 7. At $ 19 per M, find the total cost of : 
 
 6 joists, 2" x 8", 12'. 5 joists, 2" x 8", 18'. 
 
 12 joists, 2" x 8", 13'. 17 joists, 2" x 6", 16'. 
 
 30 joists, 2" x 8", 15'. 30 joists, 2" x 8", 16'. 
 
 8. At $16 per M, find the total cost of : 
 
 7 beams, 9" x 9", 20'. 16 beams, 9" x 9", 18'. 
 
 24 joists, 2" x 10", 18'. 75 planks, 2J" x 8", 12'. 
 
 150 boards, |" x 5", 12'. 576 boards, 1" x 9", 16'. 
 
 27 planks, 1J" x 14", 14'. 40 scantlings, 2" x 4", 12'. 
 
 9. Find the cost, at 1 10 per M, of the lumber required to 
 fence both sides of a railroad 10 mi. long. The boards used 
 are 1" x 6", 16', and the fence is 5 boards high. 
 
 10. Copy and find the amount of the following bill: 
 
 Boston, Mass., Sept. 12, 19 
 
 Mr. JOHN D. MOREY 
 
 Somerville, Mass. 
 
 Bought of E. M. LIVINGSTONE 6- SON 
 
 Terms 30 days net 
 
 20 
 
 pc. 
 
 3" 
 
 x 
 
 4", 
 
 14' Hemlock 280 1 $15 
 
 .00 
 
 10 
 
 tt 
 
 2" 
 
 X 
 
 6", 
 
 16 f 
 
 it 
 
 12 
 
 .00 
 
 25 
 
 H 
 
 3" 
 
 X 
 
 8", 
 
 16 f 
 
 n 
 
 12 
 
 .00 
 
 50 
 
 It 
 
 2" 
 
 X 
 
 4% 
 
 20 f 
 
 n 
 
 15 
 
 .00 
 
 16 
 
 tt 
 
 3" 
 
 X 
 
 8% 
 
 14' 
 
 ti 
 
 15 
 
 .00 
 
 25 
 
 n 
 
 2" 
 
 X 
 
 6", 
 
 20' 
 
 n 
 
 12 
 
 .50 
 
 100 
 
 it 
 
 2" 
 
 X 
 
 6", 
 
 18 f 
 
 n 
 
 13 
 
 .50 
 
PRACTICAL MEASUREMENTS 219 
 
 CYLINDERS 
 
 282. A cylinder is a solid bounded by a uniformly curved 
 surface and two equal parallel circles. 
 
 Two circles are parallel when all the points of 
 one are equally distant from all the points of the 
 other. The curved surface of a cylinder is called 
 its lateral surface : the parallel circles its bases. 
 
 283. If the lateral surface of a cylinder be exactly covered 
 with paper, it will be found that the paper is in the form of a 
 rectangle whose length and width are equal to the circumfer- 
 ence and height, respectively, of the cylinder. Hence, 
 
 The product of the circumference and height of a cylinder equals 
 the area of its lateral surface. 
 
 lare and 
 
 II 
 
 ORAL EXERCISE 
 
 1. If the accompanying diagram is a solid 4 ft. square and 
 12 ft. high, what is the area of its six sides? 
 
 2. Give a brief rule for finding the entire surface 
 (lateral surface and bases) of a rectangular solid ; of 
 a cylinder. 
 
 3. How many cubic feet in a block 2 in. square 
 
 arid 1 in. high? in a block 2 in. square and 10 in. high? 
 
 4. The area of the base of a cylinder is 22 ft. If the cylin- 
 der is 1 ft. high, what is its volume ? if it is 12 ft. high ? 
 
 284. In the foregoing exercise it is clear that the area of the 
 base multiplied by the height of the cylinder equals the volume. 
 
 WRITTEN EXERCISE 
 
 1. What will be the cost, at 40^ per cubic yard, of excavat- 
 ing for a cistern 10 ft. in diameter and 23 ft. deep ? 
 
 2. A man dug a well 6 ft. in diameter and 38 ft. deep. How 
 much should he receive if he was paid $1 for each cubic yard 
 of earth removed ? 
 
 3. What will be the cost, at 12| ^ per square foot, of a sheet- 
 iron smokestack 2J ft. in diameter and 30 ft. high ? 
 
220 PRACTICAL BUSINESS ARITHMETIC 
 
 STONE WORK 
 
 285. Stone work is usually measured by the perch, which is 
 a mass of stone 16^ ft. long, 1| ft. wide, and 1 ft. high, contain- 
 ing 24| cu. ft. 
 
 In some localities the perch contains 16 cu. ft. 
 
 286. Masonry is measured by the cubic yard or the perch. 
 
 In measuring stone work, such as the walls of cellars and buildings, 
 masons take the distance around the outside of the wall (the girt) for the 
 length. In this way the corners are measured twice, but this is considered 
 offset by the extra work required in building the corners. 
 
 The work around openings, such as doors and windows, is also more 
 difficult than the straight work and on this account no allowance is usually 
 made for openings, unless they are very large. 
 
 WRITTEN EXERCISE 
 
 1. How many perches of stone will be required for an 18-in. 
 foundation 72' x 40' x 10'? 
 
 2. How many perches of masonry in the 18-in. walls of a 
 cellar 40' x 30' x 8' ? 
 
 3. How many cubic yards of masonry in the foundation walls 
 of a house 42' x 32' if the walls are 21 ft. wide and 8 ft. high? 
 (Solve (a) by mason's and (6) by actual measure.) 
 
 BRICK WORK 
 
 287. A common brick is 8 in. long, 4 in. wide, and 2 in. thick. 
 
 Bricks vary in size, but the common brick may be taken as a unit for 
 measuring brick work. Contractors and builders do not follow any uniform 
 rule for estimating the number of bricks required for a wall. It is suffi- 
 ciently accurate, however, to reckon 22 common bricks, laid in mortar, for 
 each cubic foot of wall. In estimating material for a brick wall actual 
 measurements are taken and an allowance made for doors and windows and 
 other openings. In estimating labor girt measurements are taken and 
 usually a stated allowance made for openings such as doors and windows. 
 The allowance to be made for openings is generally covered by contract. 
 In some localities a uniform number of cubic feet is deducted for each open- 
 ing ; in others one half the volume of all openings is deducted ; in still others 
 nothing whatever is deducted. 
 
PRACTICAL MEASUREMENTS 221 
 
 WRITTEN EXERCISE 
 
 1. How many common bricks will be required for a wall 84 
 ft, long, 16| ft. high, and 1| ft. thick ? 
 
 2. Find the cost of the bricks required to build a wall 300 ft. 
 long, 12 ft. high, and 18 in. thick, at $6 per thousand. 
 
 3. How many bricks will be required for the four walls of a 
 building 80' x 50' x 25' if the walls are 18 in. thick and 500 
 cu. ft. is allowed for openings ? (Solve (# ) by mason's measure, 
 making allowance for the openings, and (& ) by actual measure.) 
 
 CAPACITY 
 BINS 
 
 288. The stricken bushel is used in measuring grain. The 
 heaped bushel is used in measuring such things as large fruits, 
 vegetables, coal, and corn on the cob. A stricken bushel equals 
 2150.42 cu. in. A heaped bushel equals 2747.71 cu. in. 
 
 ORAL EXERCISE 
 
 1. How many bushels of wheat in 2,150,420 cu. in. ? 
 
 2. State a rule for finding the exact number of stricken 
 bushels in a bin. What part of a stricken bushel is 1 cu. ft.? 
 
 .8 + 
 
 SOLUTION. 2150.42 cu. in. = I bu., stricken measure. 
 
 1728 cu. in. = 1 cu. ft. Therefore, 1 cu. ft. = 172800- 2150.42)1728.000 
 215042, or approximately .8 of a bushel, stricken meas- 1720 336 
 
 ure. 7664 
 
 3. Find the approximate capacity, in stricken bushels, of a 
 cubical bin.the inside of which measures 10 ft. on a side; in 
 cubic inches of 800 bu. of wheat. 
 
 4. State a brief rule for finding the approximate number of 
 stricken bushels in a bin ; the approximate number of cubic 
 feet in any number of stricken bushels. 
 
 5. How many bushels of potatoes in a bin containing 2,747,710 
 cu. in. ? State a rule for finding the exact number of heaped 
 bushels in any number of cubic inches. Reduce a cubic foot 
 to a decimal of a heaped bushel. 
 
222 PRACTICAL BUSINESS ARITHMETIC 
 
 .63- 
 
 SOLUTION. 2747.71 cu. in. = 1 bu., heaped measure. 2747.71)1728.0000 
 Therefore, 1 cu. ft. = 172800 -=- 274771, or approxi- 1648 626 
 
 mately .63 of a bushel, heaped measure. 79 8740 
 
 82 4313 
 
 6. Find the approximate capacity, in heaped bushels, of 
 1000 cu. ft.; in cubic feet, of 630 bu. 
 
 7. State a short method of reducing cubic feet to heaped 
 bushels ; heaped bushels to cubic feet. 
 
 8. Find (a) the approximate capacity and (&) the exact 
 capacity, in stricken bushels, of a bin 10' x 5' x 4'. 
 
 SOLUTIONS 
 
 10'x5'x4'=200cu.ft. 10'x5'x4' = 200cu.ft. 
 
 (a) 200 x 1728 cu. in. = 345600 cu. in. . (6) >g Qf 200 cu ft> = m ^ 
 
 345600 cu. in. -~ 2150.42 - 165.31 + bu. 
 
 9. Find (a) the approximate capacity and (5) the exact 
 capacity, in heaped bushels, of the bin in problem 14. 
 
 SOLUTIONS 
 
 10' x 5' x 4' = 200 cu. ft. 10 , x 5 , x 4 , = 200 cu ft 
 
 (a) 200 x 1728 cu. in. = 345600 cu. in. (&) 63 f cUj f = m fe 
 
 345600 cu. in. -=- 2747.71 = 125.77 bu. 
 
 ORAL EXERCISE 
 
 1. Find the approximate capacity in bushels of a wheat bin 
 10 ft. long, 8 ft. wide, and 5 ft. high. 
 
 2. A square bin 10 ft. high contains, by approximate measure- 
 ments, 800 bu. What is its width? 
 
 3. Approximately, how many bushels of potatoes may be 
 stored in a bin 10 ft. long, 5 ft. wide, and 4 ft. high ? 
 
 WRITTEN EXERCISE 
 
 Find the approximate capacity in stricken bushels of:- 
 
 1. A bin 12 ft. square and 4 ft. deep. 
 
 Inside dimensions are given in all the problems of this and similar exercises. 
 
 2. A box 6 ft. long, 2| ft. wide, and 3| ft. deep. 
 
 3. A wagon box 10 ft. 6 in. long, 4 ft. wide, and 2 ft. deep. 
 
PRACTICAL MEASUREMENTS 223 
 
 4. A farmer wishes to construct a square granary 15 ft. on 
 each side that will hold 800 bu. of grain. How deep must the 
 bin be made? (Approximate rule.) 
 
 5. A man wishes to construct a coal bin that will store 200 
 bu. of stove coal. If the bin is 20 ft. wide and 5 ft. deep, what 
 must be the length? (Approximate rule.) 
 
 6-8. Find the exact capacity, in stricken bushels, of prob- 
 lems 13. 
 
 9-11. Find the approximate capacity, in heaped bushels, of 
 problems 1-3. 
 
 CISTERNS 
 289. A gallon equals 231 cu. in. 
 
 ORAL EXERCISE 
 
 1. How many gallons in 462 cu. in. ? in 1386 cu. in.? 
 
 2. How many gallons of water in a vat 22 in. long, 7 in. 
 high, and 3 in. wide ? 
 
 3. Give a rule for finding the exact number of gallons in a 
 vessel. How many gallons in a cubic foot ? 
 
 SOLUTION. 231 cu. in. = 1 gal. 1728 cu. in. = 1 cu. ft. Therefore, 1 cu. ft. 
 = .yj^s g a } _ 7.48 -f gal., or approximately 1\ gal. 
 
 4. Find the approximate capacity, in gallons, of a vat 5 ft. 
 square and 4 ft. high. 
 
 SOLUTION. 5 f t. x 5 ft. x 4 ft. = 100 cu. ft. 100 times 7| gal. = 750 gal. 
 
 5. State a rule for finding the approximate capacity, in gal- 
 lons, of a vessel. 
 
 WRITTEN EXERCISE 
 
 Find the capacity (approximate and exact), in gallons, of: 
 
 1. A cistern 6 ft. square and 12 ft. deep. 
 
 2. A cistern 6 ft. in diameter and 10 ft. deep. 
 
 3. A tank 5 ft. long, 4 ft. wide, and 6 ft. deep. 
 
 4. A cistern 15 ft. in diameter and 20 ft. deep. 
 
224 PRACTICAL BUSINESS ARITHMETIC 
 
 CALCULATION TABLES 
 
 290. Persons who have a great deal of computing to do 
 frequently use machines (see pages 47 and 55) and calculation 
 tables to aid them in their work. The table on page 225 will 
 give a good idea of the arrangement of calculation tables that 
 are used in making up and proving bills and invoices, comput- 
 ing wages, finding percentages, etc. The following examples 
 will illustrate a few of the many uses of such tables. 
 
 291. Examples. 1. Multiply 58 by 42. 
 
 SOLUTION. Under 58 and opposite 42 find 2436. 
 
 2. How many square yards in a floor 38' x 46' ? 
 SOLUTION. Under 46 and opposite 38 find 1748 ; that is, 1748 sq. yd. 
 
 3. Find the cost of 495 yd. wash silk at 39^. 
 SOLUTION. Under 495 and opposite 39 find 19,305 ; that is, $ 193.05. 
 
 4. Find the cost of 48,000 bricks at 14.95 per M. 
 
 SOLUTION. Under 495 and opposite 48 find 23,760. Since the zeros in 
 48,000 have been rejected, there are but two places to point off. Result $ 2:)7.00. 
 
 5. Find the cost of 46 hr. of labor at 25| ^ per hour. 
 
 SOLUTION. Under 46 and opposite 25 find 1150 ($ 11.50); under 46 and 
 opposite | find 34.50 (35^). $ 11.50 + 35 $ = $ 11.85, the required result. 
 
 ORAL EXERCISE 
 
 By the aid of the table state the product of: 
 
 1. 
 
 27 x 
 
 26. 
 
 5. 
 
 39 x 
 
 27. 
 
 9. 
 
 87 
 
 x 
 
 46^. 
 
 13. 
 
 35 
 
 2. 
 
 27 x 
 
 58. 
 
 6. 
 
 45 x 
 
 58. 
 
 10. 
 
 93 
 
 x 
 
 32^. 
 
 14. 
 
 93 
 
 3. 
 
 45 x 
 
 46. 
 
 7. 
 
 37 x 
 
 46. 
 
 11. 
 
 48 
 
 x 
 
 93^. 
 
 15. 
 
 46 
 
 4. 
 
 47 x 
 
 39. 
 
 8. 
 
 49 x 
 
 58. 
 
 12. 
 
 47 
 
 x 
 
 87^. 
 
 16. 
 
 38 
 
 17. Find the cost of 49,500 Ib. of old rags at \$. 
 
 18. Find the cost of 93,000 bricks at 15.25 per M. 
 
 19. Find the cost of 37 days' labor at 11.35 per day ; at $5.25. 
 
 20. Find the cost of 109 hours' labor at 27^; at 39^; at 46 
 
 21. Find the cost of 49,500 Ib. freight at 31^ per hundred- 
 weight; of 46,000 Ib. at 27^ per hundredweight. 
 
PRACTICAL MEASUREMENTS 
 
 225 
 
 CALCULATION TABLE 
 
 Haiti 
 plier 
 
 27 
 
 39 
 
 46 
 
 58 
 
 Multi- 
 plier 
 
 87 
 
 93 
 
 109 
 
 138 
 
 Multi- 
 plier 
 
 135 
 
 147 
 
 495 
 
 535 
 
 Multi- 
 plier 
 
 1 
 
 27 
 
 39 
 
 46 
 
 58 
 
 1 
 
 87 
 
 93 
 
 109 
 
 128 
 
 1 
 
 135 
 
 147 
 
 495 
 
 525 
 
 1 
 
 3 
 
 54 
 
 78 
 
 92 
 
 116 
 
 3 
 
 174 
 
 196 
 
 218 
 
 256 
 
 3 
 
 270 
 
 294 
 
 990 
 
 1050 
 
 3 
 
 3 
 
 81 
 
 117 
 
 138 
 
 174 
 
 3 
 
 261 
 
 279 
 
 327 
 
 384 
 
 3 
 
 405 
 
 441 
 
 1485 
 
 1575 
 
 3 
 
 4 
 
 108 
 
 156 
 
 184 
 
 232 
 
 4 
 
 348 
 
 372 
 
 436 
 
 512 
 
 4 
 
 540 
 
 588 
 
 1980 
 
 2100 
 
 4 
 
 5 
 
 135 
 
 195 
 
 230 
 
 290 
 
 5 
 
 435 
 
 465 
 
 545 
 
 640 
 
 5 
 
 675 
 
 735 
 
 2475 
 
 2625 
 
 5 
 
 6 
 
 162 
 
 234 
 
 276 
 
 348 
 
 6 
 
 522 
 
 558 
 
 654 
 
 768 
 
 6 
 
 810 
 
 882 
 
 2970 
 
 3150 
 
 6 
 
 7 
 
 189 
 
 273 
 
 322 
 
 406 
 
 7 
 
 609 
 
 651 
 
 763 
 
 896 
 
 7 
 
 945 
 
 1029 
 
 3465 
 
 3675 
 
 7 
 
 8 
 
 216 
 
 312 
 
 368 
 
 464 
 
 8 
 
 696 
 
 744 
 
 872 
 
 1024 
 
 8 
 
 1080 
 
 1176 
 
 3960 
 
 4200 
 
 8 
 
 9 
 
 243 
 
 351 
 
 414 
 
 522 
 
 9 
 
 783 
 
 837 
 
 981 
 
 1152 
 
 9 
 
 1215 
 
 1323 
 
 4455 
 
 4725 
 
 9 
 
 10 
 
 270 
 
 390 
 
 460 
 
 580 
 
 1O 
 
 870 
 
 930 
 
 1090 
 
 1280 
 
 10 
 
 1350 
 
 . 1470 
 
 4950 
 
 5250 
 
 1O 
 
 11 
 
 297 
 
 429 
 
 506 
 
 638 
 
 11 
 
 957 
 
 1023 
 
 1199 
 
 1408 
 
 11 
 
 1485 
 
 1617 
 
 5445 
 
 5775 
 
 11 
 
 13 
 
 324 
 
 468 
 
 552 
 
 696 
 
 13 
 
 1044 
 
 1116 
 
 13-i8 
 
 1536 
 
 13 
 
 1620 
 
 1764 
 
 5940 
 
 6300 
 
 13 
 
 13 
 
 351 
 
 507 
 
 .598 
 
 754 
 
 13 
 
 1131 
 
 1209 
 
 1417 
 
 1664 
 
 13 
 
 1755 
 
 1911 
 
 6435 
 
 6825 
 
 13 
 
 14 
 
 378 
 
 546 
 
 644 
 
 812 
 
 14 
 
 1218 
 
 1302 
 
 1526 
 
 1792 
 
 14 
 
 1890 
 
 2058 
 
 6930 
 
 7350 
 
 14 
 
 15 
 
 405 
 
 585 
 
 690 
 
 870 
 
 15 
 
 1305 
 
 1395 
 
 1635 
 
 1920 
 
 15 
 
 2025 
 
 2205 
 
 7425 
 
 7875 
 
 15 
 
 16 
 
 432 
 
 624 
 
 736 
 
 928 
 
 16 
 
 1392 
 
 1488 
 
 1744 
 
 2048 
 
 16 
 
 2160 
 
 2352 
 
 7920 
 
 84' '0 
 
 16 
 
 17 
 
 459 
 
 663 
 
 782 
 
 986 
 
 17 
 
 1479 
 
 1581 
 
 1853 
 
 2176 
 
 17 
 
 2295 
 
 2499 
 
 8415 
 
 8925 
 
 17 
 
 18 
 
 486 
 
 702 
 
 828 
 
 1044 
 
 18 
 
 1566 
 
 1674 
 
 1962 
 
 2304 
 
 18 
 
 2430 
 
 2646 
 
 8910 
 
 9450 
 
 18 
 
 19 
 
 513 
 
 741 
 
 874 
 
 1102 
 
 19 
 
 1653 
 
 1767 
 
 2071 
 
 2432 
 
 19 
 
 2565 
 
 2793 
 
 9405 
 
 9975 
 
 19 
 
 20 
 
 540 
 
 780 
 
 920 
 
 1160 
 
 3O 
 
 1740 
 
 1860 
 
 2180 
 
 2560 
 
 20 
 
 2700 
 
 2940 
 
 9900 
 
 10500 
 
 3O 
 
 21 
 
 567 
 
 819 
 
 966 
 
 1218 
 
 31 
 
 1827 
 
 1953 
 
 2289 
 
 2688 
 
 31 
 
 2835 
 
 3087 
 
 10395 
 
 11025 
 
 31 
 
 22 
 
 594 
 
 858 
 
 1012 
 
 1276 
 
 33 
 
 1914 
 
 2046 
 
 2398 
 
 2816 
 
 33 
 
 2970 
 
 3234 
 
 10890 
 
 11550 
 
 23 
 
 23 
 
 621 
 
 897 
 
 1058 
 
 1334 
 
 33 
 
 2001 
 
 2139 
 
 2507 
 
 2944 
 
 33 
 
 3105 
 
 3381 
 
 11385 
 
 12075 
 
 23 
 
 24 
 
 648 
 
 936 
 
 1104 
 
 1392 
 
 34 
 
 2088 
 
 2232 
 
 2616 
 
 3072 
 
 34 
 
 3240 
 
 3528 
 
 11880 
 
 12600 
 
 24 
 
 25 
 
 675 
 
 975 
 
 1150 
 
 1450 
 
 35 
 
 2175 
 
 2325 
 
 2725 
 
 3200 
 
 35 
 
 3375 
 
 3675 
 
 12375 
 
 13125 
 
 25 
 
 36 
 
 702 
 
 1014 
 
 1196 
 
 1508 
 
 26 
 
 2262 
 
 2418 
 
 2834 
 
 3328 
 
 36 
 
 3510 
 
 3822 
 
 12870 
 
 13650 
 
 26 
 
 27 
 
 729 
 
 1053 
 
 1242 
 
 1566 
 
 37 
 
 2349 
 
 2511 
 
 2943 
 
 3456 
 
 27 
 
 3645 
 
 3969 
 
 13365 
 
 14175 
 
 27 
 
 28 
 
 756 
 
 1092 
 
 1288 
 
 1624 
 
 38 
 
 2436 
 
 2604 
 
 3052 
 
 3584 
 
 28 
 
 3780 
 
 4116 
 
 13860 
 
 14700 
 
 28 
 
 29 
 
 783 
 
 1131 
 
 1334 
 
 1682 
 
 39 
 
 2523 
 
 2697 
 
 3161 
 
 3712 
 
 29 
 
 3915 
 
 4263 
 
 14355 
 
 15225 
 
 29 
 
 3O 
 
 810 
 
 1170 
 
 1380 
 
 1740 
 
 30 
 
 2610 
 
 2790 
 
 3270 
 
 3840 
 
 30 
 
 4050 
 
 4410 
 
 14850 
 
 15750 
 
 3O 
 
 31 
 
 837 
 
 1209 
 
 1426 
 
 1798 
 
 31 
 
 2697 
 
 2883 
 
 3379 
 
 3968 
 
 31 
 
 4185 
 
 4557 
 
 15345 
 
 16275 
 
 31 
 
 33 
 
 864 
 
 1248 
 
 1472 
 
 1856 
 
 32 
 
 2784 
 
 2976 
 
 3488 
 
 4096 
 
 33 
 
 4320 
 
 4704 
 
 15840 
 
 16800 
 
 32 
 
 33 
 
 891 
 
 1287 
 
 151 
 
 1914 
 
 33 
 
 2871 
 
 3069 
 
 3597 
 
 4224 
 
 33 
 
 4455 
 
 4&51 
 
 16335 
 
 17325 
 
 33 
 
 34 
 
 918 
 
 1326 
 
 1564 
 
 1972 
 
 34 
 
 2958 
 
 3162 
 
 3706 
 
 4352 
 
 34 
 
 4590 
 
 4998 
 
 16830 
 
 17850 
 
 34 
 
 35 
 
 945 
 
 1365 
 
 1610 
 
 2030 
 
 35 
 
 3045 
 
 3255 
 
 3815 
 
 4480 
 
 35 
 
 4725 
 
 5145 
 
 17325 
 
 18375 
 
 35 
 
 36 
 
 972 
 
 1404 
 
 1656 
 
 2088 
 
 36 
 
 3132 
 
 3348 
 
 3924 
 
 4608 
 
 36 
 
 4860 
 
 5292 
 
 17820 
 
 18900 
 
 36 
 
 37 
 
 999 
 
 1443 
 
 1702 
 
 2146 
 
 37 
 
 3219 
 
 3441 
 
 4033 
 
 4736 
 
 37 
 
 4995 
 
 5439 
 
 18315 
 
 19425 
 
 37 
 
 38 
 
 1026 
 
 1482 
 
 1748 
 
 2204 
 
 38 
 
 3306 
 
 3534 
 
 4142 
 
 4864 
 
 38 
 
 5130 
 
 5586 
 
 18810 
 
 19950 
 
 38 
 
 39 
 
 1053 
 
 1521 
 
 1794 
 
 2262 
 
 39 
 
 3393 
 
 3627 
 
 4251 
 
 4992 
 
 39 
 
 5265 
 
 5733 
 
 19305 
 
 20475 
 
 39 
 
 4O 
 
 1080 
 
 1560 
 
 1840 
 
 2320 
 
 40 
 
 3480 
 
 3720 
 
 4360 
 
 5120 
 
 40 
 
 5400 
 
 5880 
 
 19800 
 
 21000 
 
 10 
 
 41 
 
 1107 
 
 1599 
 
 1886 
 
 2378 
 
 41 
 
 3567 
 
 3813 
 
 4469 
 
 5248 
 
 41 
 
 5535 
 
 6027 
 
 20295 
 
 21525 
 
 41 
 
 43 
 
 1134 
 
 1638 
 
 1932 
 
 2436 
 
 42 
 
 3654 
 
 3906 
 
 4578 
 
 5376 
 
 43 
 
 5670 
 
 6174 
 
 20790 
 
 22050 
 
 42 
 
 43 
 
 1161 
 
 1677 
 
 1978 
 
 2494 
 
 43 
 
 3741 
 
 3999 
 
 4687 
 
 5504 
 
 43 
 
 5805 
 
 6321 
 
 21285 
 
 22575 
 
 43 
 
 44 
 
 1188 
 
 1716 
 
 2024 
 
 2552 
 
 44 
 
 3828 
 
 4092 
 
 4796 
 
 5632 
 
 44 
 
 5940 
 
 6468 
 
 21780 
 
 23100 
 
 44 
 
 45 
 
 1215 
 
 1755 
 
 2070 
 
 2610 
 
 45 
 
 3915 
 
 4185 
 
 4905 
 
 5760 
 
 45 
 
 6075 
 
 6615 
 
 22275 
 
 23625 
 
 45 
 
 46 
 
 1242 
 
 1794 
 
 2116 
 
 2668 
 
 46 
 
 4002 
 
 4278 
 
 5014 
 
 5888 
 
 46 
 
 6210 
 
 6762 
 
 22770 
 
 24150 
 
 46 
 
 47 
 
 1269 
 
 1833 
 
 2162 
 
 2726 
 
 47 
 
 4089 
 
 4571 
 
 5123 
 
 6016 
 
 47 
 
 6345 
 
 6909 
 
 23265 
 
 24675 
 
 47 
 
 48 
 
 1296 
 
 1872 
 
 2208 
 
 2784 
 
 48 
 
 4176 
 
 4464 
 
 5232 
 
 6144 
 
 48 
 
 6480 
 
 7056 
 
 23760 
 
 25200 
 
 48 
 
 49 
 
 1323 
 
 1911 
 
 2254 
 
 2842 
 
 49 
 
 4263 
 
 4557 
 
 5341 
 
 6272 
 
 49 
 
 6615 
 
 7203 
 
 24255 
 
 25725 
 
 49 
 
 50 
 
 1350 
 
 1950 
 
 2300 
 
 2900 
 
 5O 
 
 4350 
 
 4650 
 
 5450 
 
 6400 
 
 50 
 
 6750 
 
 7350 
 
 24750 
 
 26250 
 
 5O 
 
 Multi- 
 plier 
 
 37 
 
 39 
 
 46 
 
 58 
 
 Multi- 
 plier 
 
 87 
 
 93 
 
 109 
 
 138 
 
 Multi- 
 plier 
 
 135 
 
 147 
 
 495 
 
 535 
 
 Multi- 
 plier 
 
 % 
 
 338 
 
 488 
 
 575 
 
 725 
 
 % 
 
 1088 
 
 1163 
 
 1363 
 
 1600 
 
 % 
 
 1688 
 
 1838 
 
 6188 
 
 6563 
 
 e 
 
 4 
 
 675 
 
 975 
 
 1150 
 
 1450 
 
 % 
 
 21 75 
 
 2325 
 
 2725 
 
 32 00 
 
 4 
 
 3375 
 
 3675 
 
 123 75 
 
 131 25 
 
 V4 
 
 % 
 
 1013 
 
 1463 
 
 1725 
 
 2175 
 
 % 
 
 :;_> i;;; 
 
 3488 
 
 4088 
 
 4800 
 
 % 
 
 5063 
 
 5513 
 
 18563 
 
 19688 
 
 % 
 
 2 
 
 1350 
 
 1950 
 
 2300 
 
 2900 
 
 X 
 
 4350 
 
 4650 
 
 5450 
 
 6400 
 
 2 
 
 6750 
 
 7350 
 
 24750 
 
 262 5'.' 
 
 2 
 
 % 
 
 1688 
 
 2438 
 
 2875 
 
 3625 
 
 % 
 
 5438 
 
 5813 
 
 6813 
 
 8000 
 
 % 
 
 8438 
 
 9188 
 
 10938 
 
 32813 
 
 % 
 
 % 
 
 2025 
 
 2925 
 
 3450 
 
 4350 
 
 % 
 
 6525 
 
 6975 
 
 8175 
 
 9600 
 
 3 /4 
 
 10125 
 
 11025 
 
 37125 
 
 S93 75 
 
 8 /4 
 
 % 
 
 2363 
 
 3413 
 
 4025 
 
 5075 
 
 % 
 
 7613 
 
 8138 
 
 9538 
 
 11200 
 
 T /8 
 
 11813 
 
 12863 
 
 43313 
 
 45938 
 
 % 
 
226 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 22. Find the cost of 48,000 ft. of lumber at $16 per M ; of 
 93,000 ft. ; of 52,500 ft. ; of 49,500 ft. ; of 58,000 ft. 
 
 23. An agent sold 240 (10 x 21) excursion tickets at $4.95. 
 How much did he receive ? 360 x $5.25 = ? 310 x $1.47 = ? 
 
 24. Find the cost of 45 rm. of paper at $1.35 ; at $ 1.28 ; at 
 $1.09; at 93^; at $4.95. Also find the cost of 38 rm. at each 
 of the above prices ; of 29 rm. ; of 37 rm. ; of 46 rm. 
 
 25. Find the cost of 4600 lb. of coal at $6.40 per ton ($3.20 
 per thousand pounds) ; at $8.40 ; at $4.60 ; at $ 6.80 ; at $7.20 ; 
 at $7.40; at $9.20; at $5.60. Also find the cost of 2700 lb. 
 at each of the above prices ; of 3900 lb. ; of 8700 lb.; of 9300 lb.; 
 of 10,900 lb.; of 12,800 lb.; of 13,500 lb.; of 14,700 lb.; of 
 49,500 lb.; of 52,500 lb. 
 
 WRITTEN EXERCISE 
 
 1. By the aid of the table find the total cost of : 
 
 525 bolts at $1.70 per C. 128 bolts at $1.90 per C. 
 
 495 bolts at $2.40 per C. 525 bolts at $2.70 per C. 
 
 135 bolts at $1.60 per C. 495 bolts at $3.50 per C. 
 
 2. By the aid of the table find the total cost of : 
 
 1280 ft. lumber at $28 per M. 5250 ft. lumber at $27 per M. 
 1350 ft. lumber at $29 per M. 3800 ft. lumber at $27 per M. 
 4950 ft. lumber at $19 per M. 4600 ft. lumber at $18 per M. 
 
 3. By the aid of the table find the total amount of the follow- 
 ing time sheet : 
 
 TIME SHEET FOR WEEK ENDING JULY 14 
 
 NAME 
 
 M. 
 
 T. 
 
 W. 
 
 T. 
 
 F. 
 
 8. 
 
 TOTAL 
 TIME 
 
 KATK 
 
 PER 
 
 Horn 
 
 AMOUNT 
 
 A. M. Ball 
 
 8* 
 
 9 
 
 71 
 
 8 
 
 8 
 
 8 
 
 
 27^ 
 
 
 
 J. B. King 
 
 8* 
 
 7| 
 
 9 
 
 8 
 
 8 
 
 8 
 
 
 390 
 
 
 
 C. E. Frey 
 
 91 
 
 9 
 
 8f 
 
 8 
 
 7 
 
 5 
 
 
 46^ 
 
 
 
 W. D. Hall 
 
 7 
 
 9 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 58 j* 
 
 
 
 M. F. Hill 
 I). M. Muir 
 
 9f 
 8J 
 
 n 
 
 7 
 
 8 
 
 8 
 
 8 
 6f 
 
 
 87^ 
 93^ 
 
 
 
 
 
 
 
 
 
 
 
 
PERCENTAGE AND ITS APPLICATIONS 
 CHAPTER XVII 
 
 PERCENTAGE 
 ORAL EXERCISE 
 
 1. .50 may be read fifty hundredths, one half, or fifty per 
 cent. Read each of the following in three ways : .25, .30, 12|% . 
 
 2. Read each of the following in three ways : ^, J, ^, ^, %, 
 f, f, i, f, f, 2 %, 2|-%, 125%, 6-|-%, 81%, 66J %, 250%, 375%. 
 
 3. 50 % of a number is .50 or |--of the number. What is 
 50% of 1600? 25%? 121%? 10% ? 40%? 20%? 75%? 
 
 292. Per cent is a common name for hundredths. 
 
 293. The symbol % may be read hundredths or per cent. 
 
 294. Percentage is the process of computing by hundredths 
 or per cents. 
 
 ORAL EXERCISE 
 
 Express as per cents : 
 
 1. .28. 3. .001. 5. .331. 7 . .621. 9. .5. 
 
 2. .37. 4. .14f 6. .28f 8. .0075. 10. .2. 
 Express as decimal fractions : 
 
 11. 20%. 13. 72%. 15. 1%. 17. 125%. 19. ^%. 
 
 12. 45%. 14. 18%. 16. \%. is. 250%. 20. 375%. 
 Express as common fractions : 
 
 21. 1%. 23. 21%. 25. 1331%. 27. 871%. 2 9. 1%. 
 
 22. 2%. 24. 31%. 26. 266|%. 28. 1121%. 30 . 175%. 
 Express as per cents : 
 
 31. 1 33. T V 35. If 37. f. 39. |, 
 
 32. 1. 34. T 9 7 . 36. 2f. 38. If 40. -% 4 -. 
 
 227 
 
228 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 IMPORTANT PER CENTS AND THEIR FRACTIONAL EQUIVALENTS 
 
 PER 
 CENT 
 
 FKAOTfONAL 
 
 VAWM 
 
 PER 
 CENT 
 
 FRACTIONAL 
 VALIE 
 
 PER ' 
 
 CKNT 
 
 FRACTIONAL 
 
 \ ALUE 
 
 PER 
 CENT 
 
 FRACTIONAL 
 VALUE 
 
 12* % 
 
 * 
 
 75% 
 
 t 
 
 83 J% 
 
 1 
 
 <U% 
 
 A 
 
 25% 
 
 I 
 
 100% 
 
 1 
 
 20% 
 
 i 
 
 8f% 
 
 A 
 
 37*% 
 
 t 
 
 li% 
 
 1 
 
 40% 
 
 1 
 
 *% 
 
 A 
 
 50% 
 
 i 
 
 33 J% 
 
 i 
 
 60% 
 
 t 
 
 1H% 
 
 i 
 
 62*% 
 
 f 
 
 06f% 
 
 1 
 
 80% 
 
 t 
 
 i^% 
 
 f 
 
 295. The terms us^d in percentage are the base, the rate, 
 and the percentage. The base is the number of which a per 
 cent is taken ; the rate, the number of hundredths of the base 
 to be taken ; tha percentage, the result obtained by taking a 
 certain per cent of the base. 
 
 In the expression "12 % of $50 is $ 6," f 50 is the base, 12 %, the rate, and 
 $6, the percentage. 
 
 296. The base plus the percentage is sometimes called the 
 amount ; the base minus the percentage, the difference. 
 
 FINDING THE PERCENTAGE 
 
 297. Example. What is 15 % of 1 660 ? 
 
 SOLUTION. 15 % of a number equals .15 of it. .15 of $660 = 
 $ 99, the required result. 
 
 899.00 
 
 298. Obviously, the product of the base and rate equals the 
 percentage. 
 
 The bane may be either concrete or abstract. The rate is always abstract. 
 The percentage is always of the same name an the base. 
 
 ORAL EXERCISE 
 
 1. What aliquot part of 1 is .121 ? >2 5? .50? .16| ? .831? 
 .20? .06J? .06f? .081? .111? .14f? 371 %? 621 %? 66f % ? 
 
 2. Formulate a short method for finding 12^ % of a number. 
 SOLUTION. 12| % = .12 = ; hence, to find 12J % of a number, divide by 8. 
 
 3. State a short method for finding 25% of a number; 
 50%; 16|%; 331%; 20%; 6J % ; 6f % ; 81%; 111%. 
 
 .15 
 
PERCENTAGE 229 
 
 To guard against absurd answers in exercises of this character estimate 
 the results in advance as explained on pages 58 and 142. 
 
 4. Find 50% of 960. Also 25%; 37J%; 12}%; 621%; 
 75%; 16f%; 331%; 66|%; 831%; 20%f40%; 60%; 6J%. 
 
 5. By inspection find : 
 
 a. 50% of 1792. e. 25% of 1729. i. 66f % of 2460. 
 
 b. 37-i% of 1320. /. 6f%of$6600. j. 331% of 2793. 
 
 c. 12J% of ^ggo. ^ 6 i^ of 3296. k. 81% of 24,960. 
 
 d. 16f%of$669. h. 831% of 4560. i 20% of 12,535. 
 
 ORAL EXERCISE 
 
 1. Find 10% of 720; of $15.50; of 120 men ; of $127.50. 
 
 2. What aliquot part of 10% is 5% ? 2}%? 1|%? 3|%? If %? 
 
 3. Formulate a short method for finding 1J- % of a number. 
 
 SOLUTION. 11% of a number is |- of 10% of the number ; hence, to find 
 of a number, point off one place to the left and divide by 8. 
 
 4. State a short method for finding 5 % of a number; 
 
 5. By inspection find : 
 
 a. 5% of 720. d. l\% of 1840. g. 3J% of $3900. 
 
 b. 2| % of 840. e. If % of $366. h. 1 j % of 120 mi. 
 
 c. 31% of 1560. /. 2|-% of $720. i. \\% O f 1632 A. 
 
 ORAL EXERCISE 
 
 'I. Compare 24% of $25 with 25% of $24; 21% of $2500 
 with 25 % of $2400. What is 32 % of $25 ? 
 
 SOLUTION. 32 % of 25 = 25 % of $ 32 = \ of $ 32 = $ 8, the required result. 
 
 2. What is 125% of $880? 
 
 SOLUTION. 125% = 1.25 =| of 10; \ of $8800 (10 times $880) -$1100. 
 
 3. Find 125% of 400; of 640; of 3200 ; of 160; of 1280. 
 
 4. Formulate a short method for finding 166f % of a num- 
 ber ; 333-J % of a number ; 250 % of a number. 
 
 5. Compare 88% of 12,500 bu. with 125% of 8800 bu. 
 
 6. Find 32% of $125; of $1250; of $12,500; of $125,000. 
 
 7. Find 250% of $720; of $3200; of $28,800; of $64,800. 
 
230 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 By inspection find : 
 
 1. 48% of 250. 5. 180% of 625. 
 
 2. 32% of 125. 6. 160% of 875. 
 
 3. 128% of 250. 7. 240% of 7500. 
 
 4. 16% of 2500. 8. 125 % of $240.40. 
 
 WRITTEN EXERCISE 
 
 1. A farmer sold 640 bu. wheat, receiving $1.05 per bushel 
 for 87|% of it and 85^ per bushel for the remainder. What 
 was the total amount received ? 
 
 2. A grocer compromised with his creditors, paying 60 % of 
 the amount of his debts. If he owed A $ 756, B 11250, and C 
 $3750, how much did each receive ? 
 
 3. A merchant sold 360 bbl. apples for $1200. If he re- 
 ceived $3.50 per barrel for 66| % of the apples, what was the 
 price received per barrel for the remainder ? 
 
 4. A man bought a house for $12,864.75; he expended for 
 improvements 33^ % of the first cost of the property, and then 
 sold it for $20,000. Did he gain or lose, and how much ? 
 
 5. A commission merchant bought 1200 bbl. apples and 
 after holding them for 3 mo. found that his loss from decay 
 was 10%. If he sold the remainder at $3.75 per barrel, how 
 much did he receive ? 
 
 6. A merchant prepaid the following bills and received the 
 per cents of discount named: 4% on bill of $875.50; 6 % on 
 bill of $378.45; 2% on bill of $940.50; 3-J % on bill of $400. 
 What was the net amount paid ? 
 
 FINDING THE RATE 
 
 ORAL EXERCISE 
 
 1. 8 is what part of 40 ? what per cent of 40 ? 
 
 2. 90 is what per cent of 270 ? of 360 ? of 450 ? 
 
 3. 70 is what per cent of 560 ? of 630 ? of 700 ? 
 
 4. The base is 900 and the percentage 450 ; what is the rate ? 
 
PERCENTAGE 231 
 
 299. Example. $35.50 is what per cent of 1284? 
 
 SOLUTIONS, a. $35.50 is .ff g- or \ of (a) 
 
 $284. $284 is 100% of itself; hence, 55 = 1 = ^1 of 
 $35.50, which is i of $284, must be \ of 
 
 100%, or 121%. Or, (&) 
 
 6. Since the product of the base and .125 = 12^-% 
 
 the rate is the percentage, the quotient 284)35.50 
 obtained by dividing the percentage by the base is the rate. 
 
 300. Obviously, the percentage divided by the base equals the 
 rate. 
 
 ORAL EXERCISE 
 
 What per cent of: 
 
 1. 95 is 19? 7. 1.6 is .008? 
 
 2. 4.8 is 1.2? 8. lyd. is 1 ft.? 
 
 3. |35 is |17l ? 9. 2 da. are 8 hr. ? 
 
 4. 225 A. are 75 A. ? 10. 4 T. are 3000 Ib. ? 
 
 5. 34 bu. are 34 bu. ? 11. 1 yr. are 4 mo. ? 
 
 6. 34 bu. are 68 bu. ? 12. 2 mi. are 80 rd.? 
 
 WRITTEN EXERCISE 
 
 1. A man bought a house for 87500 and sold it for 18700. 
 What per cent did he gain ? 
 
 2. In a certain city, school was in session 190 da. A lost 38 
 da. What per cent of the school year did he attend? 
 
 3. An agent sold a piece of property for $8462.50 and re- 
 ceived $338.50 for his services. What per cent did he 
 receive ? 
 
 4. A commission agent sold 28,600 bu. of grain at 50 f per 
 bushel and received for his services $357.50. What per cent 
 did he receive on the sales made ? 
 
 5. Smith and Brown engaged in business, investing $18,000. 
 Smith invested $10,440, and Brown the remainder. What per 
 cent of the total capital did each invest? 
 
 6. An agent for a wholesale house earned $165.55 during 
 the month of May. If the goods sold amounted to $ 1505, what 
 per cent did he receive on the sales made ? 
 
232 PRACTICAL BUSINESS ARITHMETIC 
 
 FINDING THE BASE 
 
 ORAL EXERCISE 
 
 1. What is 5% of 240 bu. ? 
 
 2. 12 bu. is 5 % of how many bushels ? 
 
 3. 160 is 8 % of what number ? 4 % ? 2 % ? 1 % ? | % ? 
 
 4. The multiplicand is 400 and the multiplier 10; what is 
 the product? The product is 2000 and the multiplicand 100; 
 what is the multiplier? The product is 4000 and the multi- 
 plier 20 ; what is the multiplicand ? 
 
 5. In percentage what name is given to the product ? to 
 the multiplicand? to the multiplier? When the base and rate 
 are given, how is the percentage found ? When the percentage 
 and base are given, how is the rate found ? When the per- 
 centage and rate are given, how is the base found ? 
 
 ORAL EXERCISE 
 
 1. 25 is J of what number ? 25 is 50 % of what number? 
 
 2. 12 is T ^ of what number ? 24 is 6| % of what number ? 
 
 3. 25 is y 1 ^ of what number ? 35 is 8J % of what number ? 
 
 4. 900 is | of what number ? 600 is 75 % of what number ? 
 
 5. 130 is I of what number ? 1300 is 20 % of what number ? 
 
 6. 444 is | of what number ? 44.40 is 80 % of what number ? 
 
 7. 960 is | of what number? 96 is 66f % of what number? 
 
 8. 65 is of what number ? 650 is 83^ % of what number ? 
 
 9. 15 is T L of what number ? 150 is 6 j % of what number ? 
 
 10. 100 is J of what number ? 60 is 11^ % of what number ? 
 
 11. 20 is | of what number ? 200 is 14| % of what number ? 
 
 12. 375 is | of what number ? 2700 is 37* % of what number? 
 
 13. Anything is what per cent of itself ? of J itself ? of twice 
 itself? of | itself? of 2J times itself? 
 
 14. A farmer sold a horse for 66| % of its cost and received 
 $80. How much did the horse cost? 
 
 15. 20 % of the students of a high school are 18 yr. of age. 
 If there are 170 such students, what is the aggregate attend- 
 ance of the school ? 
 
PEKCENTAGE 233 
 
 301. Example. 37.5 is 25% of what number? 
 
 SOLUTION. 25% or ^ of the number = 37.5 
 . . the number = 37.5 -f- = 150. 
 
 302. Obviously, the quotient of the percentage divided by the 
 rate equals the base. 
 
 WRITTEN EXERCISE 
 
 1. N invested 30% of the capital of a firm, H 35%, and W 
 the remainder, $ 1400. What was the capital of the firm? 
 
 2. During the month of May the sales of a clothing mer- 
 chant amounted to $4864.24, which was 8 % of the total sales 
 for the year. What were the total sales for the year? 
 
 3. B sold his city property and took a mortgage for $4375, 
 which was 17 \% of the value of the property. If the balance 
 was paid in cash, what was the amount of cash received ? 
 
 4. In compromising with his creditors, a man finds that his 
 assets are $270,900, and that this sum is 43% of his entire in- 
 debtedness. What will be the aggregate loss to his creditors? 
 
 5. The aggregate attendance in the schools of a certain city 
 for 1 da. was 43,225 students. If this number was 95% of the 
 number of students belonging, how many students were absent? 
 
 6. The owner of city property received in rentals last year 
 $1221.95. He paid for insurance $75, for repairs $353.75, and 
 for taxes $175.20. If his net income was equal to 5% of the 
 money invested, what was the value of the property? 
 
 7. A man bought a suit of clothes for $22.50, a pair of shoes 
 for $5, a hat for 4, and a watch for $18.75, when he found he 
 had expended 12^% of his money. How much money had he 
 at first ? How much had he left after making these purchases ? 
 
 8. In a recent year there were 5,737,372 farms in the United 
 States having a total acreage of 831,591,744 A., of which 
 414,498,487 A. were improved and 424,093,287 A. were unim- 
 proved. What was the average number of acres to a farm? 
 What per cent of farm land was improved ? What per cent 
 was unimproved? (Correct to three decimal places.) 
 
234 PRACTICAL BUSINESS ARITHMETIC 
 
 PER CENTS OF INCREASE 
 
 ORAL EXERCISE 
 
 1. If 2| times a number is 50, what is the number? 
 
 2. If 2.5 times a number is 75, what is the number? 
 
 3. If 250% of a number is $1250, what is the number? 
 
 4. If 250% of a number is 150, what is the number? If 
 250% is 125, what is the number? 
 
 5. If 300% of a number is 15400, what is the number? 
 
 303. Examples, l. A man sold a farm for $3900 and 
 thereby gained 30%. How much did the farm cost? 
 
 SOLUTION. 1.30 of the cost = $3900. 
 
 . . the cost = $3900 -4- 1.30 = $ 3000. 
 
 2. What number increased by 33J% of itself equals 180? 
 
 SOLUTION, f of the number = 180 
 
 . . the number = 180 *- f = 135. 
 
 ORAL EXERCISE 
 
 What number increased by: 
 
 1. 10% of itself is 220? 8. 6|% of itself is 480? 
 
 2. 25% of itself is 125? 9. 125% of itself is 900? 
 
 3. 50% of itself is 300? 10. 37 \% of itself is 440? 
 
 4. 75% of itself is 700? 11. 111% O f itself is 300? 
 
 5. 6J% of itself is 170? 12. 14f % of itself is 328? 
 
 6. 12i% of itself is 180? 13. 200% of itself is 2700? 
 
 7. 66f % of itself is 135? 14. 300% of itself is 2800? 
 
 WRITTEN EXERCISE 
 
 1. I sold 375 bu. of wheat for $427.50, thereby gaining 20%. 
 How much did the wheat cost me per bushel? 
 
 2. A fruit dealer sold a quantity of oranges for 16.75. If 
 his gain was 12^%, what did the oranges cost him? 
 
 3. My savings for March increased 33^% over February. If 
 my savings for March were $84.36, what were my savings for 
 February and March? 
 
PERCENTAGE 235 
 
 4. A merchant sold a quantity of cloth at $1.5Q per yard 
 and thereby gained 20%. What per cent would he have 
 gained had he sold the cloth at $1.87J per yard? 
 
 5. A merchant's total sales for this year were 12^% greater 
 than his sales for last year. What were his sales for this year 
 if the aggregate sales for the two years amounted to 1170,000? 
 
 6. A man paid 142.50 for a second-hand wagon and after 
 spending 120.50 in repairs on it he found that it had cost him 
 5% more than a new wagon. What would have been the cost 
 of a new wagon? 
 
 PER CENTS OF DECREASE 
 
 ORAL EXERCISE 
 
 1. What per cent of a number is left after taking away 
 331% of it ? What fractional part? 
 
 2. If f of a number is 600, what is the number ? If 66| % of 
 a number is 75, what is the number ? 
 
 3. A man spent 40 % of his money and had $60 remaining. 
 How much had he at first ? How much did he spend? 
 
 304. Examples. 1. A man sold a horse for $332, thereby 
 losing 17 %. What was the cost ? 
 
 SOLUTION. 0.83 of the cost =$332. 
 
 . . the cost = $ 332 -=- 0.83 = $ 400. 
 
 2. What number decreased by 25 % of itself equals 375 ? 
 
 SOLUTION, f of the number f 375. 
 
 . . the number = $ 375 -^ f = $ 500. 
 
 ORAL EXERCISE 
 
 What number diminished by: 
 
 1. 61 % of itself equals 75 ? 7.1 of itself equals 750 ? 
 
 2. 8J% of itself equals 440? 8. 1% of itself equals 99.5? 
 
 3. 6f % of itself equals 280? 9. 1% of itself equals 49.5? 
 
 4. 10% of itself equals 270? 10. 25% of itself equals 225? 
 
 5. 331 % of itself equals 66 ? 11. 50 % of itself equals 17| ? 
 
 of itself equals 210 ? 12. 75 % of itself equals 250 ? 
 
236 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. Of what number is 9581.88 77 % ? 
 
 2. A merchant sold 1200 bu. of potatoes for 1640, which 
 was 16J% less than he paid for them. What was the cost per 
 bushel? 
 
 3. In selling a carriage for $75 a merchant lost 25% on the 
 cost. What was the asking price if the carriage was marked 
 to gain 25 % ? 
 
 4. A newsboy sold 92 papers on Tuesday. If this number 
 was 23J% less than the number sold on Monday, how many 
 papers were sold on the two days ? 
 
 5. A dealer sold a quantity of apples at $6 per barrel, and 
 by so doing lost 16|-%. If he paid $309.60 for the apples, 
 how many barrels did he buy ? 
 
 6. After paying 174.35 for mileage, 132.50 for hotel bills, 
 and $13.15 for sundry items, a traveler finds that he has 
 expended 40% of his money. How much had he at first? 
 
 ORAL REVIEW EXERCISE 
 
 1. By inspection find 12| % of the following numbers : 
 
 a. $872. 
 b. 648 bu. 
 c. 1264 A. 
 d. 960 mi. 
 
 e. $2464. 
 /. 2696 A. 
 g. 1624 ft. 
 h. 1832 mi. 
 
 i. $1688. 
 j. 2072 A. 
 k. 11,464 mi. 
 
 1. 37,128 mi. 
 
 m. $24.72. 
 n. $168.48. 
 o. $176.24. 
 
 p. $2184,32. 
 
 2. By inspection find 10 
 25%; 125%; 20%. 
 
 of each of the above numbers ; 
 
 JQ , .LUU yfl , ^v y0. 
 
 \. State the missing term in each of the following : 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 K 
 
 a. 
 
 1600 
 
 7*% 
 
 ? 
 
 / 
 
 966 
 
 16| % 
 
 ? 
 
 b. 
 
 $650 
 
 v 
 
 |39 
 
 9- 
 
 ? 
 
 8i% 
 
 15 bu. 
 
 c. 
 
 ? 
 
 4% 
 
 $18 
 
 h. 
 
 1275 
 
 65 % 
 
 9 
 
 d. 
 
 900 
 
 9 
 
 720 
 
 i. 
 
 9 
 
 <H% 
 
 21 mi. 
 
 e. 
 
 ? 
 
 4% 
 
 20 
 
 J- 
 
 400 
 
 V 
 
 600 
 
PERCENTAGE 237 
 
 4. By inspection find 10 % of each of the following : 
 
 a. 1264. d. $840. g. $232. /. 12448. 
 
 b. $920. e. 1750. h. $144. &. $1432. 
 
 c. $720. /. $364. i. $288. I. $3624. 
 
 5. By inspection find 1^ % of each of the above numbers ; 
 1|% ; 1000% ; 125%; 166f%. 
 
 6. By inspection find the numbers of which 
 
 a. 101 i s 81%. d. 75 is 25%. g. 960 is 320%. 
 
 b. 150isl6|%. e. 125 is 20%. h. 1920 is 32%. 
 
 c. 170 is 331%. /. 750 is 250%. i. 240 is 33J%. 
 
 WRITTEN REVIEW EXERCISE 
 
 1. A collector charged 4% on all amounts collected. If he 
 remitted to his customers in one month $3720.48, how much 
 did he receive for his services? 
 
 2. A father left to his son 60 % of his estate and to his 
 daughter the remainder, $9390.88. What was the value of the 
 estate and how much did the son receive? 
 
 3. A farmer planted 1 bu. 3 pk. of oats on an acre of ground 
 and harvested 56 bu. What per cent of the yield was the 
 planting? What per cent of the planting was the yield? 
 
 4. A merchant paid the following charges on a bill of goods : 
 cartage $12.45, freight $65.32, insurance $41. If the charges 
 represent 5 % of the face of the bill, what was the gross cost of 
 the goods? 
 
 5. A merchant failed in business, his resources amounting 
 to $12,840 and his liabilities to $24,000. What per cent of his 
 indebtedness did he pay, and what was the aggregate loss to 
 his creditors ? 
 
 6. The density of population in Asia is approximately 125 
 per square mile, and in the United States, approximately 25 per 
 square mile. What per cent greater is the density of popula- 
 tion in Asia than that in the United States? What per cent 
 less is the density in population in the United States than that 
 in Asia? 
 
238 PRACTICAL BUSINESS ARITHMETIC 
 
 7. A man had 6 A. of land ; to one party he sold a piece 
 25 rd. by 20 rd., and to another party 140 sq. rd. What per 
 cent of the field remained unsold? 
 
 8. In a recent year 176,774,300 Ib. of fish were landed in 
 Boston, and of this quantity Gloucester furnished 111,367,809 
 Ib. What per cent was furnished by Gloucester ? (Correct to 
 the nearest .01.) 
 
 9. A owned property valued at $12,000 from which he 
 received a yearl} 7 rental of I960. If he paid taxes amounting 
 to 8160, insurance $75.50, and made repairs amounting to 
 $ 184. 50, what per cent net income did he receive? 
 
 10. B owns a field 80 rd. square. During a certain year 
 this field yielded on an average 25 bu. of wheat to an acre. 
 The wheat when sold at $1 a bushel produced an amount equal 
 to 25 % of the value of the field. What was the value of the 
 field? 
 
 11. A landowner rented a field to a tenant and was to 
 receive as rent 16J % of the grain raised. The owner of the 
 field sold his share of the grain for 84^ per bushel, receiving 
 $ 298.20. If the tenant sold his share of the grain for the same 
 price per bushel, how much did he receive ? 
 
 12. Twenty years ago the value of knit goods produced in 
 the United States was 139,271,900, of which New England 
 produced 27 % ; the value of the knit goods manufactured this 
 year was $101,337,000, of which New England produced 18%. 
 What was New England's per cent of increase in 20 yr. ? 
 (Correct to the nearest .01.) 
 
 13. By a recent census report it was shown that the value 
 of all personal property in the state of New York was 
 approximately $ 500,000,000 and the value of all the real estate 
 approximately 13,000,000,000. Draw parallel lines making 
 a comparison of personal property and real estate. The real 
 estate is what per cent greater than the personal property ? 
 The personal property is what per cent less than the real 
 estate ? 
 
PERCENTAGE 239 
 
 14. A young man entered a bank as cashier and at the end 
 of the first year his salary was increased 25% ; at the end of 
 the second year he was given an increase of 20 % ; and at the 
 end of the third year he was given an increase of 25 %, which 
 made his salary $ 4500. What salary did he receive at first ? 
 
 15. A government statistician collected facts regarding wages 
 and income from nearly two thousand private manufacturing 
 concerns, and reported the following : the average wages of all 
 employees, men, women, and children, per year was 1263.06, and 
 the average net profit for each employer was $ 2273. What per 
 cent greater was the income of each employer than of each em- 
 employee ? (Correct to the nearest .01.) 
 
 (Q | . .""FT i . i . i . i . i ~? 16 - T ne population of three 
 
 liiilinlililihlilililililililil cities during a certain year is 
 
 A^M^M"^"^""^"^^""" illustrated by the accompany - 
 
 Bi^""^^"^^"^^"^"^ ing lines, which are drawn on 
 
 iMHMHVHMnEsnraaH a scale of 12,500 inhabitants 
 
 to each -J- of an inch. What is the population of A, B, and C, 
 
 respectively ? The population of each city is what per cent of 
 
 the population of the three cities ? 
 
 17. The annual coal production in the United States, Great 
 Britain, Germany, and France 
 
 for a certain year is illustrated li I i I i I i I i 1 1 I i 1 1 h I i 1 1 1 1 1 1 1 i I 1 1 i 
 
 in the accompanying rectan- united states 
 gles, drawn on the scale of 
 20,000,000 short tons to each 
 -| of an inch. During that 
 year, how many tons did the p,. ance 
 United States, Great Britain, " 
 
 Germany, and France, respectively, produce ? The produc- 
 tion of each country is what per cent of the production of the 
 four countries ? In the same year the rest of the world pro- 
 duced approximately 110,000,000 short tons. Illustrate graph- 
 ically the world's coal production for this year. What was the 
 world's approximate production this year? 
 
240 PRACTICAL BUSINESS ARITHMETIC 
 
 18. The total value of the cotton crop to farmers in a recent 
 year was $453,000,000 and the value of the cotton exported to 
 England in the same year was 1124,000,000. What per cent 
 was exported to England? (Correct to the nearest .01.) 
 
 19. A saleswoman in a city store receives $ 9 per week. She 
 pays $3.50 per week for board and room, 10^ per day for car 
 fare 6 da. in the week, 20^ per day for 6 da. of each week 
 for luncheon, and has incidental expenses amounting to $ 1.70. 
 If she saves the remainder, what per cent of her weekly wages 
 does she save ? What per cent does she spend ? 
 
 20. The production, in bushels, of grain in the United States 
 in two recent years was approximately as follows : 
 
 CEREALS 
 
 1903 
 
 1904 
 
 Corn 
 
 2,240,000,000 
 
 2,470,000,000 
 
 Wheat 
 
 640,000,000 
 
 550,000,000 
 
 Oats 
 
 780,000,000 
 
 900,000,000 
 
 Barley 
 
 131,000,000 
 
 130,000,000 
 
 Rye 
 
 30,000,000 
 
 27,000,000 
 
 Buckwheat 
 
 14,000,000 
 
 15,000,000 
 
 Find the per cent of increase or decrease of each cereal for 
 1904 as compared with the previous year. Then draw a series of 
 parallel rectangles to compare the production of 1904 with the 
 production of 1903. Also draw a series of rectangles to com- 
 pare the production of 1904 with the production of a later year. 
 
 SUGGESTION. This may be represented by one series of rectangles. 
 Each rectangle may be divided into two parts one shaded and the other 
 unshaded. The shaded part may be made to represent the yield for 1904 
 and the unshaded part the yield for 1903. 
 
 21. The silver produced by the leading sources in a recent 
 year was approximately as follows : 
 
 Mexico 60,000,000 oz. Canada 4,500,000 oz. 
 
 United States 55,500,000 oz. Peru 4,000,000 oz. 
 
 Bolivia 13,000,000 oz. Spain 3,500,000 oz. 
 
 Australasia 8,000,000 oz. Chili 3,500,000 oz. 
 
 Germany 6,000,000 oz. Austria-Hungary 2,000,000 oz. 
 
 Draw a set of parallel rectangles to graphically represent the 
 above numbers. 
 
PERCENTAGE 
 
 241 
 
 22. In the following table is shown the population in the 
 United States in a certain year, at least ten years of age, en- 
 gaged in gainful occupations, classified by sexes and kinds of 
 occupations. Supply the missing terms. Check the work. 
 
 KIND or OCCUPATION 
 
 POPULATION ENGAGED IN GAINFUL OCCUPATIONS 
 
 NUMBER 
 
 PER CENT OF TOTAL 
 
 Total 
 
 Male 
 
 Female 
 
 Total 
 
 Male 
 
 Female 
 18.4 
 
 Agricultural pursuits . . . 
 Professional services .... 
 Domestic and personal service 
 Trade and transportation . . 
 Manufacturing and mechanical 
 pursuits 
 
 10,381,765 
 1,258,739 
 5,580,657 
 4,766,964 
 
 7,085,992 
 
 9,404,429 
 828,163 
 3,485,208 
 4,263,617 
 
 5,772,788 
 
 977,336 
 430,576 
 2,095,449 
 503,347 
 
 1,313,204 
 
 35.7 
 
 39.6 
 
 
 All occupations . . . 
 
 
 
 
 
 
 
 100.0 
 
 100.0 
 
 100.0 
 
 Public 
 
 23. Suppose the accompanying diagram illustrates the dis- 
 tribution of school enrollment in the 
 
 public, private, and parochial schools 
 of the United States during a certain 
 year. The private and parochial 
 schools are what per cent of the 
 public schools ? of the entire school 
 enrollment ? The public schools 
 are what per cent of the total en- 
 rollment ? of the private and paro- 
 chial schools combined ? 
 
 24. The gold production, in ounces, in the eight principal 
 gold-producing states in the United States in a recent year was 
 approximately as follows : Colorado, 28,500,000 ; California, 
 17,000,000; Alaska, 8,500,000; Arizona, 4,000,000; Montana, 
 4,500,000; Nevada, 3,000,000 ; South Dakota, 7,000,000 ; Utah, 
 3,500,000. Compare these values by drawing a series of 
 parallel rectangles. 
 
 Parochial 
 
 Private 
 
CHAPTER XVIII 
 
 COMMERCIAL DISCOUNTS 
 ORAL EXERCISE 
 
 1. A set of Scott's works is marked 1 12. If I buy it at this 
 price, less 16f%, what does it cost me? 
 
 2. I buy 190 worth of goods on 30 da. time, or 5% off for 
 cash. What cash payment will settle the bill ? 
 
 3. I owe B 1600, due in 80 da. He offers to allow me 5% 
 discount if I pay cash to-day. I accept his offer and give him 
 a check for the amount. What was the amount of the check ? 
 
 305. A reduction from the catalogue (list) price of an article, 
 from the amount of a bill of merchandise, or from the amount 
 of a debt, is called a commercial or trade discount. 
 
 Business houses usually announce their terms upon their bill heads. The 
 space allowed for recording the terms is usually limited, and bookkeepers 
 find it necessary to use symbols and abbreviations to indicate them. Thus, 
 if a bill is due in 30 da. without discount, the terms may be written 
 N /3o, or Net 30 da. ; if the bill is due in 30 da. without discount, but an 
 allowance of 2% is made for payment within 10 da., the terms may be 
 written 2 /io, Vso, or 2 % 10 da., net 30 da. 
 
 306. Manufacturers, jobbers, and wholesale dealers usually 
 have printed price lists for their goods. To -obviate the neces- 
 sity of issuing a new catalogue every time the market changes, 
 these lists are frequently printed higher than the actual selling 
 price of the goods, and made subject to a trade discount. 
 
 307. The fluctuations of the market and the differences in 
 the quantities purchased by different customers frequently give 
 rise to two or more discounts called a discount series. 
 
 Large purchasers sometimes get better prices and terms than small pur- 
 chasers. Thus, the average customer might be quoted the regular prices 
 less a trade discount of 25%, while an especially large buyer might be quoted 
 the regular prices less trade discounts of 25 % and 10 %. 
 
 242 
 
COMMERCIAL DISCOUNTS 243 
 
 308. When two or more discounts are quoted, one denotes a 
 discount off the list price, another, a discount off the remainder, 
 and so on. 
 
 The order in which the discounts of any series is considered is not 
 material. Thus, a series of 25 %, 20 %, and 10 % is the same as one of 20 %, 
 10 %, and 25 %, or one of 10 %, 25 %, and 20 %. 
 
 309. Catalogue prices are generally estimated on the basis of 
 credit sales, and a cash purchaser is given the usual trade dis- 
 count and a special discount for early payment. This latter 
 discount has the effect of encouraging prompt payments. 
 
 The list price is sometimes called the gross price and the price after the 
 discount has been deducted the net price. 
 
 FINDING THE NET PKICE 
 
 310. Example. The list price of a dozen pairs of shoes is 
 145. If this price is subject to a discount series of 20% and 
 10 %, what is the net selling price ? 
 
 SOLUTION. 20% or ^ of $45 = $9, the first discount. 
 
 $45 _ $9 $36, the price after the first discount. 
 10% or T V of $36 = $3.60, the second discount. 
 $36 - $3.60 = $32.40, the net selling price. 
 
 ORAL EXERCISE 
 Find the net price : 
 
 
 LIST 
 
 TRADE 
 
 
 LIST 
 
 TRADE 
 
 
 LIST 
 
 
 TRADE 
 
 
 
 PRICE 
 
 DISCOUNT 
 
 
 PRICE 
 
 DISCOUNT 
 
 
 PRICE 
 
 DISCOUNTS 
 
 1 
 
 . $4 
 
 25% 
 
 8. $6 
 
 40% 
 
 15. 
 
 $4 
 
 25% 
 
 and 
 
 331% 
 
 2 
 
 . $15 
 
 20% 
 
 9. $4 12| % 
 
 16. 
 
 $30 
 
 331^ 
 
 ?o and 
 
 25% 
 
 3 
 
 . $90 
 
 331% 
 
 10. $24 81% 
 
 17. 
 
 $35 
 
 20% 
 
 and 
 
 25% 
 
 4 
 
 . $20 
 
 10% 
 
 11. $42 
 
 16f% 
 
 18. 
 
 $45 
 
 20% 
 
 and 
 
 16f % 
 
 5 
 
 . $50 
 
 50% 
 
 12. 
 
 $35 
 
 20% 
 
 19. 
 
 $50 
 
 20% 
 
 and 
 
 25% 
 
 6 
 
 . $2.50 
 
 20% 
 
 13. 
 
 $100 
 
 25% 
 
 20. 
 
 $100 
 
 20% 
 
 and 
 
 10% 
 
 7 
 
 . $4.50 
 
 16f % 
 
 14. 
 
 $720 
 
 33J% 
 
 21. 
 
 $600 
 
 16|9 
 
 o and 
 
 20% 
 
 22. A piano listed at $750 is sold less 331 %, 20 %, and 10 %. 
 What is the net cost to the purchaser ? 
 
 23. A dealer offers cloth at $3.50 per yard subject to a dis- 
 count of 20 %. How many yards can be bought for $56 ? 
 
244 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the net price : 
 
 GROSS GROSS 
 
 SELLING PRICE TRADE DISCOUNTS SELLING PRICE TRADE DISCOUNTS 
 
 1. $3360 25% and 10% 4. $2500 20%, 10%, and 5% 
 
 2. $3510 331% and 20% 5. $5400 25%, 20%, and 10% 
 
 3. $4500 20%andl6|% 6. $3960 331%, 20%, and!6f % 
 
 7. The list price of cloth is $4.80 per yard, but this price is 
 subject to discounts of 25% and 20%. How many yards can 
 be bought for $288? 
 
 8. A hardware dealer sold 25 doz. 5-in. files at $2.50 and 
 25 doz. 12-in. files at $7.50, less 50% and 10% ; 150 machine 
 bolts at $21.50 per C, less 20% and 10%. What was the net 
 amount of the bill ? 
 
 9. Study the following model. Copy and find the net 
 amount of the bill, using the discounts named in the bill, and 
 the following prices : 5-in. pipe, $1.45 ; 1-in. pipe, 17^ ; valves, 
 $2.67. 
 
 Bought of GEORGE W. MUNSON & CO. 
 
 Terms rt^^z 
 
 2,0 
 
 Z2L 
 
 22- 
 
COMMERCIAL DISCOUNTS 245 
 
 10. One firm offers a piano for $400, subject to discounts of 
 and 20 % ; another offers the same piano for $ 400 less 
 
 discounts of 25 % and 15%. Which is the better offer? How 
 much better? 
 
 11. A jobber bought a quantity of goods listed at $ 3600, sub- 
 ject to discounts of 25% and 20%. He sold the goods at the 
 same list price, subject to discounts of 20 % and 10 %. Did he 
 gain or lose, and how much? 
 
 12. Make out bills for the following, using the current date 
 and the name and address of some dealer whom you know. 
 Terms in each case, 60 da. net. 
 
 a. You bought 12 doz. hand saws, #27, at 118.50; 7J doz. 
 mortise locks, #271, at $4.25; 25 doz. pocket knives, #27, a 
 $7.50; and If doz. cheese knives at $8. 25. Discount: 25 fo, 10/o. 
 
 b. You bought 41 J' of 2" extra strong iron pipe at 70^; 
 941' of 1|" extra strong iron pipe at 31 J-^; 153J' of \" iron 
 pipe at 6J7; 88|' of f" iron pipe at 7 Discount: 25$fe, lOflb. 
 
 c. You bought 25 kitchen tables at $3.25; 25 dining-roorn 
 tables at $8.75; 15 doz. dining-room chairs at $12.50; 12 
 antique rockers at $12.25; and 15 oak bedroom sets at $32.50. 
 Discount: 16f %, 5%. 
 
 FINDING A SINGLE EATE OE DISCOUNT EQUIVALENT 
 TO A DISCOUNT SERIES 
 
 311. Example. What single rate of discount is equivalent 
 to a discount series of 25 %, 331 % ? all d 10 % ? 
 
 SOLUTION. Represent the list price by 1.00 
 
 100%. Then, 75% equals the price after the 25 (25% of 100 %) 
 
 first discount, 50% the price after the second __ 
 discount, and 45% equals the net selling price. 
 
 100%, the list price, minus 45%, the net selling -25 (33J % of 75 %) 
 
 price, equals 55%, the single rate of discount .50 
 
 equivalent to the given discount series. Q/J /^Q <^ of 50 %^) 
 
 A single discount equivalent to a discount . 
 series may often be determined mentally (see 
 
 312-313). 100 % - 45 % = 55 % 
 
246 PRACTICAL BUSINESS AE1THMETIC 
 
 WRITTEN EXERCISE 
 
 1. Find a single rate of discount equivalent to a discount 
 series of 50%, 25%, 20%, and 10%. 
 
 2. Which is the better and how much, a single discount of 
 65 % or a discount series of 25 %, 20 %, and 20 % ? 
 
 3. The net amount of a bill of goods was $ 450 and the dis- 
 counts allowed were 25%, 33^%, and 10 %. Find the total 
 discount allowed. 
 
 4. I allowed a customer discounts of 50%, 10 %, and 10 % 
 from a list price. What per cent better would a single dis- 
 count of 65 % have been ? 
 
 5. Goods were sold subject to trade discounts of 25 %, 20 %, 
 and 10 %. If the total discount allowed was $460, what was 
 the net selling price of the goods ? 
 
 6. A quantity of goods was sold subject to trade discounts 
 of 20 % and 20 %. The terms were 60 da. net or 5 % off for 
 payment within 10 da. If a cash payment of i 1026 was re- 
 quired 3 da. after the date of the bill, what was the list price 
 of the goods sold ? 
 
 312. Since the first of a series of discounts is computed on 
 100 % of the list price, and the second on 100 % minus the first 
 discount, it follows that the sum of any two separate discounts 
 exceeds the equivalent single discount by the product of the two 
 rates per cent. 
 
 Thus, in a discount series of 20% and 20% the apparent single discount is 
 the sum of the two separate discounts or 40%; but since the second discount 
 is not computed on 100%, but on 80%, 40% exceeds the true single discount 
 by 20 % of 20 %, or 4% ; and the equivalent single discount is 40 % minus 4 %, 
 or 36 %. Hence, 
 
 313. To find the single discount equivalent to a series of 
 two discounts : 
 
 From the sum of the separate discounts subtract their product, 
 and the remainder ivill be the equivalent single discount. 
 
 When two separate discounts cannot be reduced to a single discount 
 mentally, proceed as in 311 ; when they can, proceed as in 313. 
 
COMMERCIAL DISCOUNTS 247 
 
 ORAL EXERCISE 
 
 State a single rate of discount equivalent to a discount series of: 
 
 1. 10% and 10%. 17. 50% and 5%. 33. 25% and 8%. 
 
 2. 20% and 20%. 18. 10% and 5%. 34. 8J% and 24%. 
 
 3. 30% and 30%. 19. 20% and 5%. 35. 8^% and 36%. 
 
 4. 40% and 40%. 20. 40% and 5%. 36. 35% and 10%. 
 
 5. 50% and 50%. 21. 25% and 30%. 37. 20%andl2|%. 
 
 6. 20% and 10%. 22. 25% and 40%. -38. 40% and 121%. 
 
 7. 30% and 10%. 23. 20% and 15%. 39. 60%andl2|%. 
 
 8. 40% and 10%. 24. 40% and 15%. 40. 12% and 121%. 
 
 9. 50% and 10%. 25. 35% and 20%. 41. 24%andl6f%. 
 
 10. 60% and 10%. 26. 45% and 20%. 42. 16|%and20%. 
 
 11. 30% and 20%. 27. 55% and 20%. 43. 14f%and35%. 
 
 12. 40% and 20%. 28. 60% and 25%. 44. 16|%and25%. 
 13.. 50% and 20%. 29. 40% and 25%. 45. 33^% and 15%. 
 
 14. 60% and 20%. 30. 60% and 20%. 46. 66f%andl5%. 
 
 15. 25% and 10%. 31. 25% and 33^%. 47. 11|% and 18%. 
 
 16. 35% and 10%. 32. 45% and 331%. 48, 36% and 111%. 
 
 314. When a discount series consists of three separate rates, 
 the first two may be combined as in 313 and then the result 
 and the third may be combined in the same manner. 
 
 315. Example. Find a single rate of discount equivalent 
 to a discount series of 25%, 20%, and 20%. 
 
 SOLUTION. Combine the first two by thinking 25% + 20%- 5% = 40%, the 
 single discount equivalent to the series 25% and 20%. 20% + 40 % 8% = 52%, 
 or the single rate equivalent to the discount series 25%, 20%, and 20%. 
 
 ORAL EXERCISE 
 
 State a single rate of discount equivalent to a discount series of: 
 
 1. 20%, 25%, and 20%. 7. 20 %, 10%, and 10%. 
 
 2. 20%, 15%, and 10%. 8. 40 %, 10%, and 10%. 
 
 3. 20%, 20%, and 20%. 9. 50%, 10 %, and 10%. 
 
 4. 10%, 10%, and 10%. 10. 30 %, 10%, and 10%. 
 
 5. 20%, 20%, and 10%. 11. 20 %, 25%, and 10%. 
 
 6. 25%, 33J%, and 10%. 12. 20%, 20 %, and 25%. 
 
248 PRACTICAL BUSINESS ARITHMETIC 
 
 316. When it is not desirable to show the separate discounts, 
 the net selling price may be found as shown in the following 
 example. 
 
 317. Example. A mahogany sideboard listed at 1175 is 
 sold subject to trade discounts of 20% and 25%. Find the 
 net cost to the purchaser. 
 
 SOLUTION. By inspection determine that a 100 % 40 % = 60 % 
 discount of 40% is equivalent to a series of 25% ^Q ^ Q JM 75 _ $105 
 and 20%. Represent the gross cost by 100%. 
 
 Then 100% 40% 60%, the net cost to the purchaser; that is, the net cost 
 of the sideboard is 60% of the list price. 60% of $ 175 = $ 105, the net cost to 
 the purchaser. 
 
 ORAL EXERCISE 
 
 By inspection find the net cost of articles listed at: 
 
 1. 1400, less 20% and 25%. 5. $1000, less 50 % and 50%. 
 
 2. 8300, less 20% and 20%. 6. $1000, less 30% and 10%. 
 
 3. $600, less 10% and 10%. 7. $200, less 60% and 25%. 
 
 4. $200, less 30% and 30%. 8. $400, less 20% and 40%. 
 
 WRITTEN EXERCISE 
 
 1. Find the net selling price of a piano listed at $450, less 
 20% and 20%. 
 
 2. Find the net selling price of an oak sideboard listed at 
 $125, less 25%, 33J%, and 10%. 
 
 3. I bought 125 cultivators listed at $8.50, each subject to 
 trade discounts of 20% and 25%. If I paid freight $30.50 
 and drayage $7.90, how much did the cultivators cost me? 
 
 4. The net cost of an article was increased $30 by freight, 
 making the actual cost of it $630. What was the list price of 
 the article, the rates of discount being 25 % and 33^% ? 
 
 5. You desire to buy 24,000 ft. choice cypress : one firm 
 quotes you $60 per thousand feet, less trade discounts of 20 % 
 and 5% ; another firm offers you the same lumber at $75 per 
 thousand feet, less 33J% and 8%. The terms offered by both 
 firms are 1 / 10 , N /3o- You accept the better offer and pay cash. 
 How much does the lumber cost you? 
 
COMMERCIAL DISCOUNTS 
 
 249 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the cost of 125 1-J-" brass ells at 11.25 each, less 
 20 Jfe, and 10 J6. 
 
 2. An agent bought 10 pianos listed at 1450 each, less 
 
 and 10%, and sold them for 1400 each, less 10 % and 5%. Did 
 he gain or lose and how much? 
 
 3. Apr. 15, E. L. Gano bought of W. L. Cunningham & Co. 
 5 phaetons listed at $450 each, less 25% and 20%. Terms: 
 2 /30i Veo- How much ready money would settle the bill? 
 
 4. Study the following bill. Copy and find the net amount 
 of it, using the discounts indicated in the bill, and the follow- 
 ing prices: windmills, 1675; pumps, $610; 1-in. iron pipe, 
 17J^; 4-in. iron pipe, 73^; hose, 97^; elbows, 21^; valves, 
 $1.49. 
 
 Terms 
 
 Bought of E. M. MCGREGOR & co. 
 
 y/*. '/j,. *s< 
 
 ?/? / & a 
 
 ^^ ^1 
 
 2-Q 
 
 /?2- 
 
 IJtf 
 
 /JJ 
 
250 PRACTICAL BUSINESS ARITHMETIC 
 
 5. How much cash would settle the model bill (page 249) 
 Oct. 30? Nov. 8? How much cash would settle the bill called 
 for in problem 4, if it is paid for on the day it is written? If 
 it is paid Nov. 15? Copy the model bill in the form that it 
 would be written if cash accompanied the order ; that is, copy it 
 deducting the 3 % allowed for immediate payment. 
 
 6. Copy and find the net amount of the following bill : 
 
 Leith, Scotland, May 10, 19 
 
 Invoice of Wire Cloth 
 Shipped by the J. M. ROBERTS COMPANY 
 
 In the Steamship Winifredian To Edward M. Davidson & Co. 
 
 Philadelphia, Pa. 
 
 6 pc., each 34' x 5 1 6" 1122 sq. ft. 1/3 70 2 6 
 
 6 " 40' x 6' 6" **** 1/4 ***, * * 
 6 " " 42' x 7- 4" **** 1/5 *** ** * 
 
 3 " " 48' x 7' 2" **** 1/5 ** ** * 
 
 *** ** * 
 
 Less 10% ** ** * *** ** * 
 
 7. E. M. French & Co., Albany, N.Y., bought of Austin 
 Bailey & Co., Boston, Mass., Apr. 12, 3 doz. pr. hinges, 8 in., at 
 $4.20, and 3 doz. pr. hinges, 4 in., at $2.10, less 60%, 10%, 
 and 10% ; 50 Ib. brads, f in., at 90^, and 50 Ib. brads, f in., 
 at 80^, less 50%, 10%, and 5%. Terms: 2 / 10 , N /3o- Find 
 the net amount of the bill Apr. 15. 
 
 8. D. M. DeLong, Portland, Me., sold S. H. Shapleigh 
 & Co., Concord, N.H., on account 30 da., 2% 10 da.: 35 cul- 
 tivators listed at $7.50 each, less 20% and 10% ; 15 doz. table 
 knives listed at $9.75, less 10% ; 15 doz. hair curlers at 90^, 
 less 5% ; 15 doz. locks, No. 534, at $3.75, less 10% and 5% ; 
 | doz. steel squares, No. 8, at $36, less 25% and 10% ; ^ gro. 
 knives and forks, No. 760, at $12, less 20% and 10% ; f doz. 
 cheese knives at $9.75, less 16|%. Find the net amount of 
 the bill 5 da. after date. 
 
COMMERCIAL DISCOUNTS 
 
 251 
 
 9. Aug. 5, you buy of Gray, Salisbury & Son, New York 
 City, 4000 Ib. raisins at 16 less trade discounts of 25%, 20%, 
 and 10%. Terms: 2 / 10 , N /so- You pay cash for freight 13.20. 
 If you pay the bill Aug. 7, what will the raisins cost you? 
 10. Find the net amount of the following bill : 
 
 Jan. 5, 
 
 W. H. Meachum 
 
 Springfield, Mass. 
 
 Ceonarcl, ffi,oss <$ Go., =)/. 
 
 */e/*/ns Net 60 da. 
 
 
 
 1/2 C Machine Bolts 3/8 x 1 1/2" $2.40 
 1/2 C 3" 2.88 
 1/2 C 6 1/2" 4.00 
 1/2 C 1/2x3 1/2" 4.64 
 1/2 C 5" 5.42 
 1/2 C 6" 5.94 
 1/2 C 9" 7.50 
 1/2 C 10" 8.02 
 1/2 C 5/8 x 4" 7.10 
 1/4 C 4 1/2" 7.48 
 1/4 C 3/4 x 5" 10.70 
 1/4 C 10" 15.70 
 1/4 C 16" 21.70 
 
 Discounts: 5056, 1056. 556 
 5 doz. Files 5" $2.50 
 5 6" 3.10 
 2 12" 7.50 
 3 4"3.00 
 2 5" 3.20 
 1 10" 7.40 
 1/2 12" 10.20 
 Discounts: 50%, 10%. 5%, 556 
 
 
 
 
 
 
 
 11. You desire to buy 200 Ib. nutmeg. You find that S. S. 
 Pierce Co., of your city, offer this article at 75^ per Ib., less a 
 discount of 25%, and that Smith, Perkins & Co., New York 
 City, offer it at 70^ per Ib., less discounts of 15% and 10%. 
 The freight from New York to your city on a package of this 
 kind is $1.50. The terms offered by both firms are: y io , N / 30 . 
 You accept the better offer and pay cash. How much does 
 the nutmeg cost you? 
 
CHAPTER XIX 
 
 GAIN AND LOSS 
 ORAL EXERCISE 
 
 1. What is 33^% of $660? How much is gained on goods 
 bought for 8900 and sold at a profit of 331% ? 
 
 2. What per cent greater is 175 than $60? what per cent 
 less is $60 than $75? Goods bought for $100 are sold for 
 $150. What is the gain per cent? 
 
 3. What per cent less is $80 than $100? what per cent 
 more is $100 than $80? Goods bought for $100 are sold for 
 $90. What is the loss per cent ? 
 
 4. If $800 is increased by 25% of itself, what is the result? 
 Goods bought for $1400 are sold at a profit of 25%. What is 
 the selling price ? 
 
 5. If $1500 is decreased by 331% O f itself, what is the 
 result? Goods bought for $2700 are sold at a loss of 331%. 
 What is the selling price ? 
 
 6. State a brief method for finding a gain of 6^%; a gain 
 of 6|%; a gain of 81% ; a gain of 10% ; a gain of \\% ; a gain 
 of lf%; a gain of 2-| %; a gain of 31%. 
 
 7. State a brief method for finding a loss of 11 \%\ a loss 
 of 12|% ; a loss of 14f % ; a loss of 16|% ; a loss of 20% ; a loss 
 of 25% ; a loss of 9 T \ % ; a loss of 37|%. 
 
 8. State a brief method for finding a gain of 33J%; a gain 
 of 22|%; a gain of 50% ; a gain of 66|%; a gain of 75 %. 
 
 318. The gains and losses resulting from business transac- 
 tions are frequently estimated at some rate per cent of the cost, 
 or of the money or capital invested. 
 
 Since no new principles are involved in this subject, illustrative examples 
 are unnecessary. 
 
 252 
 
GAIN AND LOSS 
 
 FINDING THE GAIN OR LOSS 
 
 ORAL EXERCISE 
 
 253 
 
 By inspection find the gain or loss : 
 PER CENT PER CENT 
 
 PER CENT 
 
 
 COST 
 
 OF GAIN 
 
 
 COST 
 
 OF Loss 
 
 
 COST 
 
 OF GAIN 
 
 1. 
 
 $2900 
 
 50% 
 
 9. 
 
 $1500 
 
 10% 
 
 17. 
 
 $7500 
 
 20% 
 
 2. 
 
 $1600 
 
 75% 
 
 10. 
 
 $1600 
 
 1 ~ % 
 
 18. 
 
 $1400 
 
 25% 
 
 3. 
 
 $5600 
 
 284% 
 
 11. 
 
 $3000 
 
 1 ^ tf 
 
 19. 
 
 $2200 
 
 9^1% 
 
 4. 
 
 $2700 
 
 m% 
 
 12. 
 
 $4800 
 
 4% 
 
 20. 
 
 $8100 
 
 1H% 
 
 5. 
 
 $2400 
 
 37 1% 
 
 13. 
 
 $3600 
 
 H% 
 
 21. 
 
 $6400 
 
 12|% 
 
 6. 
 
 $1400 
 
 42f% 
 
 14. 
 
 $3200 
 
 6|% 
 
 22. 
 
 $2800 
 
 14f% 
 
 7. 
 
 $3200 
 
 6*^-^- tfr\ 
 
 15. 
 
 $4500 
 
 6f% 
 
 23. 
 
 $9600 
 
 16^% 
 
 8. 
 
 $2100 
 
 66- tfr\ 
 
 16. 
 
 $8400 
 
 8J% 
 
 24. 
 
 $3600 
 
 22f% 
 
 
 25-48. 
 
 Find the 
 
 selling 
 
 price 
 
 in each 
 
 of the 
 
 above problems. 
 
 WRITTEN EXERCISE 
 
 1. An importation of silks invoiced at <40 10s. was sold at 
 a profit of 25 % - Find the amount (in United States money) 
 of the gain. 
 
 2. An importation of German toys invoiced at 43,750 marks 
 was sold at a gain of 33J %. Find the amount (in United States 
 money) of the gain. 
 
 3. An article that cost $1 was marked 10% above cost. In 
 order to effect a sale, it was afterward sold for 10 % below the 
 marked price. Find the gain or loss on 250 of the articles. 
 
 4. A man bought a city lot for $1150 and built a house on 
 it costing $2650. He then sold the house and lot at a gain of 
 5 %. How much did he gain and what was his selling price ? 
 
 5. A man bought a quantity of silk for $450, a quantity of 
 fancy plaids for $ 120, and a quantity of velvet for $ 90. He 
 sold the silk at a gain of 25%, the plaids at a loss of 5 %, and 
 the velvet at a gain of 33J%. What was his gain, and how 
 much did he realize from the sale of the three kinds of 
 material ? 
 
254 PRACTICAL BUSINESS ARITHMETIC 
 
 FINDING THE PER CENT OF GAIN OR LOSS 
 
 ORAL EXERCISE 
 
 By inspection find the per cent of gain or loss : 
 
 COST GAIN COST Loss COST S pJ S PR"E GAIN 
 
 1. 1100 10 7. $60 #15 13. $80 190 19. 1300 $60 
 
 2. $150 $50 8. $40 $10 14. $90 $80 20. $115 $23 
 
 3. $140 $70 9. $90 $45 15. $60 $75 21. $102 $17 
 
 4. $140 $140 10. $70 $14 16. $75 $60 22. $420 $60 
 
 5. $200 $400 11. $80 $16 17. $10 $50 23. $300 $200 
 
 6. $300 $750 12. $15 $10 is. $50 $10 24. $700 $100 
 
 WRITTEN EXERCISE 
 
 1. A milliner bought hats at $15 a dozen and retailed them 
 at $3 each. What per cent was gained ? 
 
 2. A stationer bought paper at $2 a ream and retailed the 
 same at a cent a sheet. What was his per cent of gain ? 
 
 3. A dry-goods merchant bought gloves at $7.50 a dozen 
 pair and retailed them at $1.25 a pair. What was his per cent 
 of gain ? 
 
 4. A merchant imported 50 gro. of table knives at a cost 
 of $1125. Two months later he found that the sales of table 
 knives aggregated $920 and that the value of the stock unsold 
 was $435. Did he gain or lose, and what per cent ? 
 
 5. An importer bought a quantity of silk goods for 400 5s. 
 After disposing of a part of the goods for $1200 he took an 
 account of the stock remaining unsold and found that at cost 
 prices it was worth $1047.82. Did he gain or lose, and what 
 per cent ? 
 
 6. Jan. 1, F. E. Smith & Co. had merchandise on hand 
 valued at $2500. During the month they purchased goods 
 costing $6000 and sold goods amounting to $7500. If the 
 stock on hand at cost prices Feb. 5 was worth $2500, what 
 was the per cent of gain on the sales ? 
 
GAIN AND LOSS 255 
 
 FINDING THE COST 
 
 ORAL EXERCISE 
 
 By inspection find the cost : 
 
 Loss RATE or Loss GAIN RATE OF GAIN 
 
 1. $150 10% 7. $35 20% 
 
 2. $100 li% 8. $79 25% 
 
 3. $200 1|% 9. 112 111% 
 
 4. $450 2|% 10. $19 16f% 
 
 5. $220 6|% 11. $44 22|% 
 
 6. $115 81% 12. $15 33i% 
 
 SELLING RATE SELLING RATE 
 
 PRICE OF G.VN PRICE OF Loss 
 
 13. $1050 5% 19. $950 5% 
 
 14. $2040 2% 20. $900 50 % 
 is. $3600 20% 21. $150 6| % 
 
 16. $1400 16|% 22. $550 16|% 
 
 17. $1800 12|% 23 |240 33 _i % 
 is. $2400 33|% 24. $500 22| % 
 
 25-36. Find the selling price in problems 1-12. 
 37-48. Find the gain or loss in problems 13-24. 
 
 49. B sold a farm % $2400, thereby losing 25 %. For how 
 much should he have sold it to have gained 10 % ? 
 
 50. By selling a piano at $400 a dealer realizes a gain of 
 33J%. What would be the selling price of the piano if sold 
 at a gain of 25 % ? 
 
 WRITTEN EXERCISE 
 
 1. A sleigh was sold for $64.80, which was 10 % below cost. 
 What was the cost ? 
 
 2. An office safe was sold at $102, which was 20% above 
 cost. What was the cost ? 
 
 3. A merchant marks goods 16| % above cost. What is 
 the cost of an article that he has marked $21.70? 
 
256 PRACTICAL BUSINESS ARITHMETIC 
 
 4. An owner of real estate sold 2 city lots for -112,000 each. 
 On one he gained 25% and on the other he lost 25%. What 
 was his net gain or loss from the two transactions ? 
 
 5. A merchant sold a quantity of goods to a customer at a 
 gain of 25%, but owing to the failure of the customer he re- 
 ceived in settlement but 88^ on the dollar. If the merchant 
 gained 1645.15, what did the goods cost him ? 
 
 6. A manufacturer sold an article to a jobber at a gain of 
 25%, the jobber sold it to a wholesaler at a gain of 20%, and 
 the wholesaler sold it to a retailer at a gain of 33^%. If the 
 retailer paid 1 28 for the article, what was the cost to manufac- 
 ture it ? 
 
 7. A manufacturer sold an article to a wholesaler at a gain 
 of 20%, the wholesaler sold the same article to a retailer at a 
 gain of 33 J%, and the retailer to the consumer at a gain of 
 25%. If the average gain was $40, what was the cost to 
 manufacture the article ? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. A merchant bought goods at 40 % off from the list price 
 and sold the same at 20 % and 10 % off the list price. What 
 was his gain per cent ? 
 
 2. I bought goods at 50% off from the list price and sold 
 them at 25 % and 25 % off from the list price. Did I gain or 
 lose, and what per cent ? 
 
 3. Apr. 15 you bought of Baker, Taylor & Co., Rochester, 
 N. Y., 4000 bbl. Roller Process flour listed at $4.50 a barrel, 
 and 2000 bbl. of Searchlight pastry flour listed at $4.75 a 
 barrel. Each list price was subject to trade discounts of 20 % 
 and 10%. You paid cash $16,000 and gave your note at 30 da. 
 for the balance. What was the amount of the note ? 
 
 4. May 18 you sold to F. H. Clark & Co., New York City, 
 2000 bbl. of the Roller Process flour, bought in problem 3, at 
 33J% above cost. Terms: 2 / 10 , N /3o- F. H. Clark & Co. 
 paid cash. Find the cash payment. 
 
GAIN AND LOSS 257 
 
 5. May 30 you sold Smith, Perkins & Co., Albany, N.Y., 
 the balance of the flour bought in problem 3, at an advance 
 of 33J% on the cost. Terms: 2 /io> N / 30 . The flour was paid 
 for June 8. Find the cash payment. 
 
 6. What is the net gain on the transactions in problems 3, 
 4, and 5 ? the net gain per cent ? 
 
 7. Dec. 15 you bought of E. B. Johnson & Co. 400 bbl. of 
 apples at 2.50 per barrel. Terms : y io , N / 30 . You paid cash. 
 Find the amount of your payment. 
 
 8. May 15 you sold F. E. Redmond the apples bought in 
 problem 7, at $4 a barrel. Terms: Y 10 , N / 30 . At the 
 maturity of the bill Redmond refused payment and you 
 placed the account in the hands of a lawyer who succeeded in 
 collecting 75 % of the amount due. If the lawyer's fee for col- 
 lecting was 4 %, what was your net gain or loss ? 
 
 9. A tailor made 25 doz. overcoats with cloth worth $2 a 
 yard. 4 yd. were required for each coat and the cost of 
 making was $48 per dozen. He sold the overcoats so as to 
 gain 33^%. How much did he receive for each? 
 
 10. Apr. 12 J. D. Farley & Son, Trenton, N. J., bought of 
 Cobb, Bates & Co., Boston, Mass., a quantity of green Java 
 coffee sufficient to yield 2400 Ib. when roasted. If the loss of 
 weight in roasting averages 4%, what will the green coffee cost 
 at 30^ a pound, less a trade discount of 10%? Arrange the 
 problem in bill form. 
 
 11. If the coffee in problem 10 is retailed 33 \% above cost, 
 and there is a loss of 1 % from bad debts, what is the gain on 
 the transactions in coffee ? the gain per cent ? 
 
 12. The Metropolitan Coal Co., of Boston, Mass., decides 
 to bid on a contract for supplying 2240 T. of coal for the pub- 
 lic schools of the city. It can buy the coal at $4.50 per long 
 ton delivered on board track, Boston. It costs on an average 
 75^ per short ton to deliver the coal, and there is a waste of \ % 
 from handling. Name a bid covering a profit of 20%. Terms: 
 cash. 
 
258 PRACTICAL BUSINESS ARITHMETIC 
 
 13. Copy the following, supplying all missing terms 
 
 , 
 
 ^.*~7r7;:3^ 
 
 (3?/H-564^^<^^^?^^ 
 
 \T006 #0 
 
 14. May 1 you began business investing 18000 in cash. 
 mo. later your resources and liabilities were as follows : 
 
 RESOURCES 
 
 Cash on hand, $2500 
 
 Merchandise on hand, 1600 
 
 Real Estate per warranty deed, 5000 
 Office Fixtures on hand 597 
 
 Accounts Receivable unpaid 1950 
 
 LIABILITIES 
 
 Accounts Payable outstanding $1387 
 Notes Payable outstanding 3000 
 
 Make a statement showing your net gain or loss and your 
 present worth Nov. 1. Find the per cent of gain or loss in 
 problem 13 ; in problem 14. 
 
GAIN AND LOSS 259 
 
 15. Copy the following bill, supplying all missing terms : 
 
 to. 
 
 flDanufacturing Co., s>r. 
 
 */. 
 
 y^^^ts^A^frgr^^s/^ sst- 
 
 3/2- a 
 
 /-7V 
 
 16. If the sideboards in problem 15 retailed at $195 and the 
 parlor tables at $21.25 and the delivery charges on sales 
 amounted to $45.47, what was the per cent of gain or loss ? 
 
 17. Copy the following bill, supplying all missing terms: 
 
 - Louis, Mo.,. 
 
 TO F. M. EVERETT & Co., Dr. 
 
 Terms 
 
 18. How much must #16 pocket knives (problem 17) retail 
 for apiece in order to gain 33|% ? #20 pocket knives? 
 
CHAPTER XX 
 
 MARKING GOODS 
 
 319. Merchants frequently use some private mark to denote 
 the cost and the selling price of goods. The word, phrase, or 
 series of arbitrary characters employed for private marks is 
 called a key. 
 
 Many houses use two different keys in marking goods, one to represent 
 the cost and the other the selling price. In this way the cost of an article 
 may not be known to the salesmen, and the selling price may not be known 
 to any except those in some way connected with the business. In large 
 houses, when but one key is used, only the selling price is indicated on the 
 article, it being deemed best to keep the actual cost of the article a secret 
 with the buyers. In small houses, when but one key is used, both the cost 
 and the selling price are frequently written on the article. 
 
 320. If letters are used to mark goods, any word or phrase 
 containing ten different letters may be selected for a key. If 
 arbitrary characters are used, any ten different characters may 
 be selected for a key. 
 
 Some methods of marking are so complicated that it is necessary to 
 always have a key of the system at hand for reference. Goods are so marked 
 in order that important facts, such as the cost of goods, may be kept strictly 
 private. 
 
 321. When a figure is repeated one or more times, one or 
 two extra letters called repeaters are used to make the key 
 word more secure as a private mark. 
 
 The following illustrates the method of marking goods by 
 letters : 
 
 COST KEY SELLING-PRICE KEY 
 
 REPUBLICAN PKRTHAMBOY 
 
 1234507890 1234567890 
 
 Repeaters : S and Z Repeaters : W and D 
 
 260 
 
MARKING GOODS 261 
 
 The cost is generally written above and the selling price below a hori- 
 zontal line on a tag, or on a paster or box. Gloves No. 271, 
 costing $5 a dozen and selling for $6.25 a dozen, might be 
 marked as shown in the margin. Fractions may be desig- 
 nated by additional letters or characters. Thus, W may be 
 made to represent |, K |, etc. in the above key. In marking 
 goods for the retail trade, all fractions of a cent are called another whole cent. 
 
 WRITTEN EXERCISE 
 
 Using the keys given in 821, write the cost and the selling 
 price in each of the following problems : 
 
 FIRST COST FIRST COST 
 
 OF OF 
 
 ARTICLE FREIGHT GAIN Loss ARTICLE FREIGHT GAIN Loss 
 
 1. $2.50 10% 20% 5. 116.00 2J% 37-|% 
 
 2. 11.00 10% 20% 6. 140.00 5% 16|% 
 
 3. .50 831% 7. $ 3.60 2-|% 
 
 4. $4.80 20% 25% 8. 124.00 10% 
 
 Using the following key, write the cost and the selling price in 
 each of the following problems : 
 
 COST KEY SELLING-PRICE KEY 
 
 rL~iJ--ic:Dj--h Tj-unEamwi* 
 
 1234567890 1234567890 
 
 Repeaters: Q JX^ Repeaters: X 
 
 FIRST COST FIRST COST 
 
 OF OF 
 
 ARTICLE CHARGES GAIN Loss ARTICLE CHARGES GAIN Loss 
 
 9. $10.00 5% 20% 12. $15.00 6|% 25% 
 
 10. $20.00 10% 50% is. $18.00 10% 25% 
 
 11. $30.00 6|% 25% 14. $12.00 5% 331% 
 
 322. Wholesalers and jobbers buy and sell a great many 
 articles by the dozen. Retailers buy a great many articles by 
 the dozen, but generally sell them by the piece. In marking 
 goods, therefore, it is highly important that the student be able 
 to divide by 12 with great rapidity. 
 
 To divide by 12 with rapidity, the decimal equivalents of the 12ths, from 
 
 to i inclusive, should be memorized. 
 
262 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 TABLE OF TWELFTHS 
 
 TWELFTHS 
 
 SIMPLEST 
 FORM 
 
 DECIMAL 
 VALUE 
 
 TWELFTHS 
 
 1? I M i> LEST 
 FOKM 
 
 DECIMAL 
 
 VALTK 
 
 A 
 
 
 $.081 
 
 A 
 
 
 $.581 
 
 a 
 
 * 
 
 .16f 
 
 & 
 
 1 
 
 .6(5| 
 
 A 
 
 i 
 
 .25 
 
 A 
 
 f 
 
 .75 
 
 A 
 
 i 
 
 .88J 
 
 H 
 
 1 
 
 .88$ 
 
 A 
 
 
 41| 
 
 H 
 
 
 .01| 
 
 A 
 
 i 
 
 .50 
 
 if 
 
 1 
 
 1.00 
 
 323. Example. What is the cost of one shirt when a dozen 
 shirts cost $19? 
 
 SOLUTION. Divide by 12 the same as by any number of one digit and men- 
 tally reduce the twelfths in the remainder to their decimal equivalent. Thus, 
 say or think 1 T 7 2 , $1.58$, practically $1.58. 
 
 ORAL EXERCISE 
 
 State the cost per article 'when the cost per dozen articles is : 
 
 1. 
 
 $25 
 
 .00. 
 
 7. 
 
 17.00. 
 
 13. 
 
 $23. 
 
 20. 
 
 19. 
 
 $9.00. 
 
 2. 
 
 137 
 
 .00. 
 
 8. 
 
 13.60. 
 
 14. 
 
 $19. 
 
 20. 
 
 20. 
 
 $7.00. 
 
 3. 
 
 $42 
 
 .00. 
 
 9. 
 
 12.40. 
 
 15. 
 
 $66. 
 
 60. 
 
 21. 
 
 $5.00. 
 
 4. 
 
 64 
 
 .00. 
 
 10. 
 
 $5.60. 
 
 16. 
 
 $38. 
 
 00. 
 
 22. 
 
 $7.50. 
 
 5. 
 
 180 
 
 .00. 
 
 11. 
 
 13.40. 
 
 17. 
 
 $17. 
 
 00. 
 
 23. 
 
 $8.40. 
 
 6. 
 
 $13 
 
 .00. 
 
 12. 
 
 $13.20. 
 
 18. 
 
 $11. 
 
 00. 
 
 24. 
 
 $17.50. 
 
 ORAL EXERCISE 
 
 1. Hats costing $48 a dozen must be sold for what price 
 each to gain 25 % ? 
 
 2. Rulers bought at $2 a dozen must be retailed at how 
 much each to gain 50 % f - 
 
 3. Note books costing $1.60 per dozen must be retailed 
 at what price each to gain 12|% ? 
 
 4. Erasers bought at $3.24 per gross must be retailed at 
 how much each to gain 111J% ? 
 
 5. Matches costing $3.60 per gross boxes must be retailed 
 at what price per box to gain 100% ? 
 
MARKING GOODS 263 
 
 6. Envelopes bought at $2 per M must be sold at what 
 price per package of 25 to gain 100%? 
 
 7. Pickles bought at $ 1.80 per dozen bottles must be sold 
 at what price per bottle to gain 33J % ? 
 
 8. Mustard costing 114.40 per gross packages must be re- 
 tailed at what price per package to gain 20%? to gain 50%? 
 
 LISTING GOODS TOR CATALOGUES 
 
 324. In listing goods for catalogues dealers generally mark 
 them so that they may allow a discount on the goods and still 
 realize a profit. 
 
 325. Example. What should be the catalogue price of an 
 article costing $24 in order to insure a gain of 25% and allow 
 the purchaser a discount of 20 % ? 
 
 SOLUTION. \ of $24 = 6, the gain. 
 
 $30 = the selling price, which is 20% below the catalogue price. 
 
 .80 of the catalogue price = $80. 
 
 .-. the catalogue price = $30 -=- .80 = $37-50 
 
 WRITTEN EXERCISE 
 
 1. At what price must you mark an article costing $400 to 
 gain 25 % and provide for a 20 % loss through bad debts ? 
 
 2. What should be the catalogue price of a library table 
 costing $25 in order to insure a gain of 20% and allow the 
 purchaser a discount of 25 % ? 
 
 3. You list tea costing 30 $ a pound in such a way that you 
 gain 331% after allowing the purchaser a trade discount of 
 20 %. What is your list price? 
 
 4. You buy broadcloth at $3.80 per yard. . At what price 
 must you mark it in order that you may allow your cash 
 customers 5 % discount and still realize a gain of 20 % ? 
 
 5. Having bought a quantity of oranges for $3.00 per C 
 you mark them so as to gain 33^% and allow for a 20 % loss 
 through bad debts. What will be your asking price per 
 dozen? 
 
264 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 6. At what price must the articles in the following invoice 
 be listed to gain 20 % and allow discounts of 25 % and 20 % ? 
 
 Boston, Mass., Nov. 24, 19 
 
 Mr. Edgar C. Towns end 
 
 Rochester, N.Y. 
 
 Bought of WELLS, FOWLER & CO. 
 
 Terms Net 30 da. 
 
 #721 
 #924 
 
 50 
 25 
 
 Oak Bookcases $8.00 
 Gentlemen 1 s Chiffoniers 12.00 
 
 Less 10$ 
 
 400 
 300 
 
 
 630 
 
 
 700 
 70 
 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Using the word importance, with repeaters s and w, for 
 the buying key, and the words buy for cash, with repeaters t 
 and m, for the selling key, write the cost and selling price of 
 the articles in the following bill. It is desired to gain 25 % on 
 the pens and pencils, 20% on the cards, and to provide for a 
 loss of 12 % through bad debts. 
 
 Boston, Mass., Oct. 18, 19 
 
 Messrs. WHITE & WYCKOFP 
 
 Holyoke, Mass. 
 
 Bought of C. E. Stevens & Co. 
 
 Terms Net 30 da. 
 
 
 100 
 
 gro. Pens $0.80 
 
 80 
 
 
 
 
 
 25 
 
 " Lead Pencils 3.20 
 
 80 
 
 
 
 
 
 50 
 
 pkg. Record Cards .40 
 
 20 
 
 
 
 
 
 
 
 180 
 
 
 
 
 
 
 Less 12 1/2? 
 
 22 
 
 50 
 
 157 
 
 50 
 
MARKING GOODS 
 
 265 
 
 2. At what price must I mark the following shoes to gain 
 20 % ? 
 
 it, Mich., 
 
 IQ 
 
 Terms 
 
 *s 
 
 Bought of ATWOOD & RANDALL 
 
 Jo 
 
 ^ 
 
 3. You list tea bought for 30^ at an advance of 33^% on 
 the cost. Finding small sale for the article you determine to 
 sell so as to gain but 16|%. What trade discount should you 
 allow ? 
 
 4. What price per pound must be obtained for the follow- 
 ing invoice of coffee to gain 25 % and allow 10 % for loss in 
 roasting and 16| % for loss through bad debts? 
 
 ^o^/o/z, ^/f**., Nov. 25, /9 
 
 . Merchant & Co. 
 
 120 Main St., City 
 
 cBougfit of Go66, cBates &* So. 
 
 50 days 
 
 
 
 2000 Ib. Green Java Coffee 24^ 
 Cartage 
 
 480 
 2 
 
 00 
 50 
 
 482 
 
 50 
 
 
 
CHAPTER XXI 
 
 COMMISSION AND BROKERAGE 
 ORAL EXERCISE 
 
 1. A collected a bill of $350 and received 6% for his 
 services. How much did he make ? 
 
 2. B bought |80 worth of eggs for a dealer who paid him 
 7J-% for his services. How much did B make? 
 
 3. C receives $12 a week, and 5 % of his weekly sales. If 
 he sold $350 worth of goods in a week, what was his income 
 for the week ? 
 
 326. An agent is a parson who undertakes to transact busi- 
 ness for another called the principal. 
 
 327. A great deal of the produce of the country and a large 
 variety of manufactured articles are bought and sold through 
 agents called commission merchants and brokers. 
 
 328. A commission merchant (sometimes called a factor) is 
 an agent who has actual possession and control of the goods of 
 his principal ; a broker is an agent who arranges for purchases 
 or sales of goods without having actual possession of them. 
 
 329. The sum charged by an agent for transacting business 
 for his principal is called commission or brokerage. 
 
 Commission and brokerage are frequently computed at a certain per cent 
 of the amount of property bought or sold, or of the amount of business 
 transacted. Brokerage is also often a fixed rate per bushel, barrel, tierce, 
 or other standard measure. 
 
 330. Agents frequently charge an additional commission, 
 called guaranty, for assuming any risk or guaranteeing the 
 quality of goods bought or sold. 
 
 The person who ships goods is sometimes called the consignor; the person 
 to whom the goods are shipped, the consignee. 
 
 266 
 
COMMISSION AND BROKERAGE 
 
 267 
 
 A quantity of goods sent away to be sold on commission is called a ship- 
 ment; a quantity of goods received to be sold on commission, a consignment. 
 
 331. Aii account sales is an itemized statement rendered by a 
 commission merchant to his principal. It shows in detail the 
 sales of the goods, the charges thereon, and the net proceeds 
 remitted or credited. 
 
 ^Buffalo, JV.y., June 18. /9 
 
 Sate of \*A.enc/ianciise for ^Jccount of 
 
 E. H. Barker & Co., Poughkeepsie, N.Y. 
 
 t iSayto/* dr* 
 
 
 
 | 
 
 
 
 
 
 June 
 
 5 
 
 200 bbl. Roller Process Flour $6.00 
 
 
 
 1200 
 
 00 
 
 
 12 
 
 300 " Old Grist Mill Flour 6.10 
 
 
 
 1830 
 
 00 
 
 
 
 (2/targes 
 
 
 
 
 
 June 
 
 2 
 
 Freight and Drayage 
 
 40 
 
 75 
 
 
 
 
 12 
 
 Commission 5% 
 
 151 
 
 50 
 
 
 
 
 18 
 
 Net proceeds remitted 
 
 2837 
 
 75 
 
 
 
 
 
 
 3030 
 
 00 
 
 3030 
 
 00 
 
 332. An account purchase is a detailed statement rendered 
 lyy a purchasing agent to his principal. It shows in detail the 
 quantity, grade, and price of goods purchased, the expenses 
 incurred, and the gross (total) cost of the transaction. 
 
 Purchase of Merchandise for Account of 
 
 imt f -r^^^rf^^ 
 
 ^ 
 
 By GRAY, DUNKLE & CO. 
 
 t^L 60i 
 
 Charges 
 
 37 
 
 4-7 
 
 
 
268 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. I sold 100 A. of land at $50 per acre on a commission of 
 3%. What was my commission? 
 
 2. A lawyer collected an account of $1000 and received for 
 his services $40. What was his rate of commission ? 
 
 3. A book agent received 25 % on all books sold. In one 
 week, after paying his expenses, $25, lie netted $75. What 
 was the gross amount of the week's sales ? 
 
 4. I bought through a broker 1000 bu. of wheat quoted at 
 89|y per bushel. If the broker charged -J^ per bushel for buy- 
 ing the wheat, what was his brokerage ? How much did the 
 wheat cost me ? 
 
 SELLING ON COMMISSION 
 
 WRITTEN EXERCISE 
 
 1. Copy and complete the following letter : 
 JOHNSON & CO. 
 
 Produce Merchants ^^^ 
 
 Boston, Mass.,_ S//>z?^ts / . TQ 
 
 vSTUDENT'S NAME) 
 
 (STUDENT'S ADDRESS) 
 
 ^t^L^i^^^^^ 
 
 J f&^t^t^J 
 ~^^L^^^L^-^ 
 
 i^^^z^^'t^^^ 
 
COMMISSION AND BROKERAGE 
 
 269 
 
 2. May 15 you sell F. E. Spencer, Brattleboro, from John- 
 son & Co.'s consignment : 200 tubs, 10,000 lb., creamery butter 
 at 23^, and 100 crates, 3000 doz., eggs at 20^, f.o.b. cars Brat- 
 tleboro. You pay freight 1 16 and drayage 82.50. The terms 
 are 2 / 10 , N / 30 . F. E. Spencer pays cash. Make a receipted bill 
 for the transaction. 
 
 3. May 23 you sell Comstock & Co., Montpelier, from John- 
 son & Co.'s consignment : 100 crates, 3000 doz., eggs at 20 ^, and 
 100 boxes, 6000 lb., cheese at 12^, f.o.b. Montpelier. You pay 
 freight $25 and drayage $4.50. Terms: 2 /io' Vso- Comstock 
 & Co. pay cash. Make a receipted bill for the transaction. 
 
 4. Render Johnson & Co. an account sales for the goods 
 shipped May 10. (See form, page 267.) The net proceeds 
 are remitted by New York draft. Commission, 5%. 
 
 5. Find for Johnson & Co., the net gain on the shipment 
 in problem 1. The eggs were bought at 12^, the creamery 
 butter at 15^, and the cheese .at 8^. Johnson & Co. prepaid 
 freight on shipment to you, $38.50. 
 
 6. Pay freight $20.50 on the merchandise enumerated in the 
 following shipping invoice. This sum is 5 % of the cost of the 
 goods. Find the gross cost of the goods. 
 
 New 
 
 Invoice of Merchandise shipped to 
 
 J 
 
 (STUDENTS NAME) 
 
 (STUDENT'S ADDRESS) 
 
 To be sold for account of C. L. BROtTN & CO. 
 
 7. Dec. 15 you sell Morgan & Co., Albany, N.Y., 60 bx. 
 lemons at $4. Terms: 2 /i<r N /so- Morgan & Co. pay cash. 
 What is the amount of the cash payment ? 
 
270 PRACTICAL BUSINESS ARITHMETIC 
 
 8. Dec. 18 you sell Meachum & Co., Troy, N.Y., 50 bx. 
 oranges at $4.50. Terms: 2 /io' N / 30 . Meachum & Co. pay for 
 the goods Jan. 12. What rs the amount of their payment? 
 
 9. Render C. L. Brown & Co. an account sales for the goods 
 received Dec. 8, commission, 5 <jo. Assume that .on Dec. 5 you 
 advanced them $50 on the consignment. Find C. L. Brown 
 & Co's net gain or loss on the shipment in problem 6. 
 
 10. Prepare an account sales, under the current date, for the 
 following, sold by you, for the account of Lewis, Grayson & Co., 
 Rochester, N.Y.": 60 bbl. Pillsbury's flour at $6.25; 75 bbl. 
 XXXX flour at $5.7; 45 bbl. star brand flour at $5 ; 100 bbl. 
 XXX flour at $4.90 ; 50 bbl. peerless flour at $5.15. Charges : 
 freight, $38.95; cartage, $12.60; cooperage, $6.25; commis- 
 sion, 3| % ; guaranty, \%. 
 
 BUYING ON COMMISSION 
 
 WRITTEN EXERCISE 
 
 1. B, a broker, bought for C, a speculator, 3000 bu. wheat 
 at 90 jy, on a commission of \$ per bushel. What was the 
 broker's commission, and what did the wheat cost C? 
 
 2. I bought through a broker 5000 bags coffee, each con- 
 taining 130 lb., at 12|,^. If the broker charged $10 for each 
 250 bags, how much did he earn on .the transaction, and what 
 did the coffee cost me? 
 
 3. I bought through a broker 20,000 bu. of wheat at 
 and three weeks later sold it through the same broker at 
 
 If the broker charged me -^ per bu. for buying and the same 
 for selling, what was rny gain ? 
 
 4. A firm of produce dealers bought through a broker 1500 
 bbl. pork at $12.50, and immediately sold it through another 
 broker at $12.721. If each broker charged a commission of 
 2J^ per barrel, what was gained by the produce dealers? 
 
 5. You buy for your principal 1500 bbl. flour at $4.50, on a 
 commission of 3%, and pa}^ drayage $18.50. What is the cost 
 of the purchase to your principal? 
 
COMMISSION AND BROKERAGE 
 
 271 
 
 6. By your principal's instructions you put the flour (prob- 
 lem 5) in storage and later sold it at 15.25 a barrel, on a com- 
 mission of 8%. The storage charges were 5^ per barrel. 
 What amount should you remit to your principal ? 
 
 7. A broker bought cotton for a manufacturer as follows : 
 Y50 bales, 375,000 Ib. at 10-J* ; 1500 bales, 750,000 Ib. at lOf ^; 
 and 1000 bales, 500,000 Ib. at lOf f. The broker's charges were 
 $5 for each 100 bales. How much did he earn on the trans- 
 action, and what did the cotton cost the manufacturers? 
 
 8. Find the amount to be charged to Roe & Co.: 
 
 NEW YORK, 'N.Y., Mar. 15, 19 
 Purchased by ARAULT & Co. 
 
 For the account and risk of ROE & Co. 
 TELEPHONE, 690 MAIN Poughkeepsie, N.Y. 
 
 
 20 
 20 
 
 hf. ch. Japan Tea 1200 # 30^ 
 hf. ch. Oolong Tea 1000 # 45^ 
 Charges 
 Drayage 
 Commission, 2%, $ ; guaranty, %, $ 
 Amount charged to your account 
 
 4 
 
 50 
 
 
 
 9. Find the rate of commission and the amount due Brown 
 Bros. Co. in the following account purchase. 
 
 ROCHESTER, N.Y., Apr. 20, 19 
 Purchased by BROWN BROS. Co. 
 
 For the account and risk of W. D. SNOW, 
 Telephone, 1291 Main Springfield, Mass. 
 
 
 
 600 bbl. Pillsbury's Best Flour 6.00 
 100 bbl. xxxx Flour 5.50 
 200 bbl. Peerless Flour 5.25 
 Charges 
 Cartage 
 Commission ? % 
 Amount due us 
 
 15 
 104 
 
 00 
 00 
 
 
 
272 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN REVIEW EXERCISE 
 
 1. An agent bought for me a consignment of flour. He 
 charged 3% and received as his commission 38.40. I sold 
 the flour at a gain of 20 %. What was my gain ? 
 
 2. A commission merchant sold 5000 bu. grain and charged 
 \\t per bushel for selling. If the grain was sold at 49^ per 
 bushel, what sum did he remit to his principal ? 
 
 3. I paid a grain merchant 122.26 for selling a quantity of 
 grain. If he charged 2 % commission and sold the grain at 
 $1.06 per bushel, how many bushels did he sell ? 
 
 4. The net proceeds of a consignment were 593.75. The 
 following were the different charges: commission, $26; freight, 
 $8.55; drayage, $3.40; storage, $9.20; advertising, $3; in- 
 surance, $6.10. What was the rate of commission ? 
 
 5. During the months of July and August a college 
 student traveled for the Lester Manufacturing Co., receiving 
 a commission of 10 % on all sales. After paying his expenses, 
 $140.60, he had left as his net earnings $159.40. What was 
 the value of the goods sold ? 
 
 6. A commission merchant charged 3|-% commission and 
 1J% guaranty for buying a stock of provisions. If the com- 
 mission merchant received $22, what sum should the principal 
 remit to cover cost of the provisions, commission, and guaranty? 
 
 7. B was given a difficult account for collection, with the 
 assurance that he should receive 25 % of all he might collect. 
 He collected the account and remitted to the holder $198.42. 
 What was the amount collected ? 
 
 8. A firm of contractors employed an agent to collect their 
 overdue accounts. As a special inducement for closing the 
 accounts, they were to give him 6 % on all collections made the 
 first month, and 3^ % on all collections made the second month. 
 The first month he returned to the firm $4013.80; the second 
 month he returned $2798.50. The returns were made after 
 taking out his commission. What was the agent's commission ? 
 
CHAPTER XXII 
 
 PROPERTY INSURANCE 
 FIRE INSURANCE 
 
 ORAL EXERCISE 
 
 1. One hundred persons have property valued at $ 500,000. 
 They pay into a common fund | % of this sum ; what is the 
 amount of the fund? 
 
 2. These one hundred persons live in widely separated parts 
 of the country. Is it likely that many of them will suffer 
 losses by lire in the same year ? 
 
 3. Suppose the losses to this property by fire for a year 
 amount to $ 2500. What portion of the common fund remains 
 on hand as a surplus? (No interest.) 
 
 4. If this surplus is divided among the 100 persons at the 
 end of the year, how much should A, who paid in $30, receive? 
 
 5. What are the companies organized to receive and control 
 the fund in problem 1 called? 
 
 333. Insurance is a contract whereby for a stipulated con- 
 sideration one person agrees to indemnify another for loss on a 
 specified subject by specified perils. The main heads of prop- 
 erty insurance are fire insurance and marine insurance. 
 
 There are also companies which insure against steam-boiler explosions, 
 failure of crops, death of cattle, burglary, interruption to business by strikes 
 among employees, and numerous other hazards. 
 
 334. Fire insurance is insurance against loss of property or 
 damage to it by fire. 
 
 Fire insurance contracts frequently cover loss caused by lightning, cy- 
 clones, and tornadoes. Fire insurance companies are liable for loss resulting 
 from the use of water applied for the purpose of extinguishing flames; 
 also for the destruction of buildings to prevent fire from spreading. 
 
 273 
 
274 PRACTICAL BUSINESS ARITHMETIC 
 
 335. The insurer, sometimes called the underwriter, is the one 
 who agrees to indemnify. The insured is the one to whom the 
 promise of indemnity is made. The premium is the considera- 
 tion agreed upon. The policy is the written contract. 
 
 336. Insurance companies are usually either stock companies 
 or mutual companies. A stock insurance company is one in 
 which the capital is subscribed, paid for, and owned by persons 
 called stockholders, -who share all the gains and are liable for 
 all the losses. A mutual insurance company is one in which 
 the policy holders share the gains and bear the losses. 
 
 In a mutual insurance company there are no stockholders, and the capital 
 stock consists of the reserve earnings and investments of the company. 
 
 337. Policies of insurance are of various kinds. It is neces- 
 sary to distinguish between the valued and the open policy. A 
 valued policy is one that states the amount to be paid in case of 
 loss. An open policy is one in which the amount to be paid in 
 case of loss, not exceeding a certain sum, is left to be 
 determined by evidence after the loss occurs. 
 
 Valued policies are very generally used in the insurance of ships, but not 
 in the insurance of cargoes. Open policies are generally used in fire 
 insurance. 
 
 338. The standard form of fire insurance policy states the 
 maximum amount for which the company is liable, and this 
 amount is used as a basis for computing premiums. 
 
 If a loss either total or partial occurs under such a policy, the company 
 is bound to pay only so much of the sum stated in the policy as will 
 indemnify the insured; e.g. if a building insured for $3000 is damaged by 
 fire $400, only the actual loss, $400, can be recovered; but if the same 
 building were damaged by fire $3500, the company could not be held for 
 more than the sum stated in the policy, $3000. 
 
 339. Many fire insurance policies contain a co-insurance 
 clause to the effect that the person insured shall keep his 
 property insured for a certain per cent of its value, and that if 
 he fails to do this, the company will pay him only that propor- 
 tion of the loss which the per cent insured bears to the per cent 
 named in the policy. 
 
PROPERTY INSURANCE 275 
 
 Thus, the value of a piece of property is. $ 10,000, and the insured agrees to 
 keep it insured for 80% of its value, or $8000, but fails to do so and carries 
 only $6000 insurance. Should a loss occur, the company will pay only 
 three fourths (f jHHO of the amount of such loss. 
 
 340. The rate of premium is determined by the character 
 of the risk and the length of time for which the policy is issued. 
 It is sometimes stated as a per cent of the amount insured and 
 sometimes as a certain rate on $100. 
 
 In some localities insurance agents sometimes charge a small fee for 
 surveying the premises and making out a policy, but the practice is not 
 common. 
 
 Insurance is usually effected for one or more years. Short rates are 
 charges made for a term less than one year ; they are proportionately higher 
 than yearly rates. 
 
 ORAL EXERCISE 
 
 1. What is the cost of 16500 insurance at | % ? 
 
 2. What is the premium on a 14000 policy at \\ % ? 
 
 3. What is the cost of $6000 worth of insurance at 75^ per 
 $100? 
 
 4. B insures a 16000 barn for f value at \%. What quar- 
 terly premium should he pay ? 
 
 5. A insures a 16000 house for | value, at 50^ per $100. 
 What is the semiannual premium ? 
 
 6. Goods worth $3000 are insured for f value. If the 
 annual premium is $ 30, what is the rate ? 
 
 7. I insure $2400 worth of merchandise for -| of its value at 
 per $100. What premium must I pay ? 
 
 8. I insure a stock of goods worth $ 8000 for $6000 at 2 %. 
 The goods became damaged by fire to the extent of $3000. 
 Under a standard fire insurance policy how much can I recover ? 
 What will be my net loss, premium included? 
 
 9. A brick schoolliouse is insured at 50^ per $100, the 
 annual premium is $50, and the face of the policy f of the 
 value of the building. What is the value of the building ? 
 
 10. A house valued at $20,000 is insured in one company for 
 $8000. and in another for $7000. A fire occurs by which the 
 house is damaged $ 6000. How much should each company pay ? 
 
276 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 State the premium in each 
 
 FACE 
 OF POLICY RATE 
 
 1. $1600 \\% 
 
 2. $1000 \\% 
 State the face of the policy 
 
 PREMIUM RATE 
 
 5. $9 2% 
 
 6. $15 li% 
 State the rate of insurance 
 
 FACE 
 OF POLICY PREMIUM 
 
 9. $1700 $25.50 
 
 10. $1850 $37.00 
 
 of the following problems: 
 
 FACE 
 OF POLICY RATE 
 
 3. $3500 $1.10 per $100 
 
 4. $5000 $1.20 per $100 
 
 in each of the folloiving problems : 
 PREMIUM RATE 
 
 7. $13.50 $1.35 per $100 
 
 8. $24.00 $1.60 per $100 
 in each of the following problems : 
 
 FACE 
 OF POLICY 
 
 11. 
 12. 
 
 $3200 
 $6500 
 
 PREMIUM 
 
 $130.00 
 $40.00 
 
 TABLE OF ILLUSTRATIVE RATES 
 
 RISK 
 
 ANNUAL 
 RATK PEK 
 $100 
 
 RISK 
 
 ANNUAL 
 RATE PER 
 $100 
 
 Frame carriage factory and 
 
 
 Frame store and dwelling, 
 
 
 contents 
 
 $1.75 
 
 and contents 
 
 $0.40 
 
 Frame dwelling and contents 
 
 .25 
 
 Brick store and dwelling, and 
 
 
 Brick business block and con- 
 
 
 contents 
 
 .25 
 
 tents 
 
 .50 
 
 Brick church and contents 
 
 .50 
 
 Frame barn and contents 
 
 1.00 
 
 Brick schoolhouse and con- 
 
 
 Brick dwelling and contents 
 
 .17 
 
 tents 
 
 .50 
 
 WRITTEN EXERCISE 
 
 1. A in the following diagram is a frame carriage factory 
 worth $7000. Its contents are worth $8000. Both are insured 
 at | value. What is the amount of the annual premium ? 
 
 2. B is worth $3400; its contents, $1200. C is worth 
 $1500; its contents, $1100. All of this property is insured 
 for 1 yr. at | valuation. What is the annual premium ? Two 
 annual premiums in advance will pay for three years' insurance. 
 At this rate what will it cost to insure the property for 3 yr. ? 
 
J L 
 
 PROPERTY INSURANCE 
 
 Street 
 
 277 
 J L 
 
 3. D is worth $4800. The contents of the store are worth 
 12400 ; of the dwelling, $800. What will it cost to insure all 
 of this property at full value for 1 yr. ? If three annual 
 premiums in advance will pay for five years' insurance, what 
 will it cost to insure the property for 5 yr. ? 
 
 4. E is worth 120,000 ; its first-floor contents, $ 4500 ; its 
 second- and third-floor contents, $7500. All are insured for 
 1 yr. at 75% valuation. What is the amount of the premium? 
 A fire occurs, and the building and contents are damaged to the 
 extent of $4500. If the contract of insurance (policy) con- 
 tained an 80% co-insurance clause, how much will the com- 
 pany have to pay ? 
 
 5. Suppose that E was insured in Company A for $ 18,000 at 
 the rate in the table, and its contents in Company B for $ 10,000 
 at 75^ per $100; that both policies contained an 80% co-insur- 
 ance clause; and that the building was damaged to the extent 
 of $3000 and the contents to the extent of $ 2500. How much 
 would each company have to pay ? What would be the net 
 loss to the owner of the building ? to the owner of the con- 
 tents? (Premiums included in each case, but no interest.) 
 
 6. F is wortli $10,000 and its contents, $3500. The prop- 
 erty is insured for one year for $ 8100. If the policy contains 
 an 80% co-insurance clause, what is the net loss to the insurance 
 company, premium included, if the property is destroyed by fire ? 
 
278 PRACTICAL BUSINESS ARITHMETIC 
 
 7. A, the owner of G, has paid, annually for 5 yr., insurance 
 on the dwelling and contents. The face of the policy is $ 6000. 
 If the rate for five annual premiums in advance is the same as 
 three separate annual premiums, how much would he have 
 gained had he insured first for 5 yr. ? (No interest.) 
 
 8. H is worth 115,000 and its contents 17500. Find 
 the cost of insuring 80% of its value for 5 yr., three 
 annual premiums in advance paying for five years' insurance. 
 
 9. For insuring I and J and contents at f value, the owner 
 paid an annual premium of $22.50. What is the value of the 
 property, the value of J being % of the value of I? 
 
 10. K, worth f 15,000, is insured in three companies for | 
 value. Company A takes J of the risk at the price in the 
 table ; Company B, | of the risk at 50^ per $ 100 ; Company 
 C, the remainder at f %. What was the total premium? 
 The block becomes damaged by fire to the amount of $ 6000. 
 How much will each company be obliged to pay ? 
 
 11. I insured my block of buildings with the ^Etna In- 
 surance Co. for 175,000, at 75^ per 1100. The ^Etna Insurance 
 Co. later reinsured $15,000 with the Continental Insurance Co. 
 at |% and $20,000 with the German-American Insurance Co. 
 at 1%. The block became damaged by fire $20,000. What 
 was the net loss of the ^Etna Insurance Co.? What was the 
 net loss of the Continental Insurance Co.? of the German- 
 American Insurance Co.? 
 
 MARINE INSURANCE 
 
 341. Marine insurance is insurance against loss to ships 
 and cargoes by perils of navigation. 
 
 342. In marine insurance, the policies usually contain a 
 clause to the effect that if a vessel or cargo, or both, are 
 valued at more than the amount insured, the insurers will 
 pay only such part of the loss, either partial or total, as the 
 amount insured bears to the full valuation. This clause is 
 'called an average clause. 
 
PROPERTY INSURANCE 279 
 
 Thus, should a vessel valued at $20,000, and insured for $15,000, become 
 damaged by fire to the extent of $8000, under an average clause policy the 
 company will pay three fourths ($$$$%) of the loss, or $6000. Should the 
 same vessel and cargo be wholly destroyed, the company will pay the full 
 $15,000, which is three fourths of the entire valuation. In order to be fully 
 protected in a marine risk, the insured must insure his property for full 
 value. Some fire insurance policies contain a clause similar to the average 
 clause of marine insurance policies. ^ 
 
 WRITTEN EXERCISE 
 
 1. A vessel valued at $50,000 is insured (average clause 
 policy) for $18,000 in Company A, and for $17,000 in Company 
 B. A fire occurs by which the vessel is damaged $15,000. 
 What is the amount to be paid by each company ? 
 
 2. I paid $25.40 for insuring a shipment of goods by steamer 
 from Boston to Manila. If the rate was 1| %, less 20%, what 
 was the face of the policy ? If the face of the policy was 
 equal to the value of the goods, what would it cost to make the 
 shipment by sailing vessel at 1J %, less 20%? 
 
 3. You take out a $7500 average clause policy on your stock 
 of merchandise worth $9000. The premium is 75^ per $100, 
 which you pay in advance. A fire occurs by which the stock 
 is damaged $3000. Estimate your total loss and the net loss 
 to the company. (Premium included in each case.) 
 
 4. A of Boston instructed B of Sidney, Australia, to purchase 
 $25,000 worth of hides. B made the investment as instructed 
 and charged 1J% commission. The hides were then shipped 
 by steamer and insured at 1| % for enough to coyer the value of 
 the hides and all charges. What was the amount of the policy 
 and what was the premium ? 
 
 5. A of New York ordered B of Duluth to buy on commission 
 6000 bu. of wheat and 6000 bu. of corn. B bought the wheat 
 at 92^ and the corn at 57^ per bushel, and charged l|^per 
 bushel commission. Before shipping the grain to A by boat, 
 B took out a policy of insurance at 1| % to cover the cost of the 
 goods and all charges. What was the agent's commission ? 
 the insurance premium ? What did the grain cost A ? 
 
CHAPTER XXIII 
 
 STATE AND LOCAL TAXES 
 ORAL EXERCISE 
 
 1. How are the expenses of towns, cities, counties, and 
 states met ? 
 
 2. A has property worth $5000 and B property worth 
 $ 10,000. How should the taxes of these two men compare ? 
 
 3. Mention several purposes for which taxes are raised in 
 your city or town. 
 
 343. A tax is a sum levied for the support of government, 
 or for other public purposes. Taxes are of two kinds : direct 
 taxes, which are taxes levied on a person, his property, or his 
 business ; indirect taxes, which are taxes levied on imported 
 goods, and on tobacco, liquors, etc., produced and consumed in 
 the United States. 
 
 The expenses of town, county, city, and state governments are met by 
 capitation or poll taxes, property taxes, and license fees. The expenses of the 
 National Government are met chiefly by import duties, or customs, and excise 
 duties. 
 
 344. A capitation, or poll tax, is a tax sometimes levied on each 
 male inhabitant who has attained his majority. A property tax is 
 a tax levied on real estate or on personal property. A license fee 
 is a tax paid for permission to engage in certain kinds of business. 
 
 Real estate and personal property belonging to religious or charitable 
 organizations are frequently exempt from taxation. 
 
 345. Property taxes are imposed in nearly all the states by 
 practically the same method, namely : 
 
 1. Officers called assessors are elected in every city and 
 town, whose business it is to set a valuation upon all property 
 subject to taxation. 
 
 280 
 
STATE ANL> LOCAL TAXES 281 
 
 2. In most of the states a County Board of Equalization 
 reviews the original assessments, and the judgment of this 
 body is subsequently passed upon by the State Board of 
 Equalization. 
 
 3. All the taxes for state purposes are then equitably appor- 
 tioned among the different counties, cities, and towns. Each 
 county, city, town, and school district also levies taxes for its 
 own local expenses. 
 
 Real estate is usually assessed at from 25% to 33$% less than its market 
 value. 
 
 346. The tax rate is expressed as so many mills on the dollar 
 or so many dollars on a hundred or a thousand dollars. 
 
 The methods of collecting taxes vary somewhat in the different states. 
 A common method, which, on the whole, seems satisfactory, is for one col- 
 lector in each city or town to collect all the taxes state, county, city or 
 town at one time. If taxes are not paid, the property taxed may be sold. 
 The purchaser of property sold for taxes is given only a tax title to it; but 
 this title becomes complete after a certain period allowed the original 
 owner for redemption. In some states if the poll tax is not paid, the person 
 taxed may be committed to jail. The compensation of a collector is either 
 a fixed salary or a commission on all taxes collected. 
 
 ORAL EXERCISE 
 
 1. If the rate of taxation is 12 mills on a dollar, how much 
 tax must I pay on property assessed at $ 5000 ? 
 
 2. The tax rate is 13 mills on a dollar. B has property 
 valued at $ 8000 and assessed at f value. What is his tax ? 
 
 3. C pays l\% tax on a city lot 100 ft. by 150 ft., valued 
 at $1 per square foot, and assessed at f value. What is the 
 amount of his tax ? 
 
 4. What tax must I pay on #80,000, at 5 mills on $1, the 
 collector's commission being 1 % ? 
 
 SOLUTION. .005 of $ 80,000 = $400, the tax. 
 
 1% of the tax = 4, the collector's commission. 
 
 $404, my property tax. 
 
 5. What tax must I pay on $10,000 at 4| mills on $1, the 
 collector's commission being 1 % ? 
 
282 PRACTICAL BUSINESS ARITHMETIC 
 
 6. If the state tax is 2 mills, the county tax 3 mills, and 
 the district school tax | %, what should you pay on a farm 
 assessed at $ 3000 ? 
 
 7. My total tax this year was $61.25. If I have property 
 valued at $ 10,000, and my poll tax amounts to 11.25, what is 
 the rate of taxation ? 
 
 8. A collector turns over to the county treasurer -$8000. If 
 his commission was 1| % what amount did he collect? If the 
 property taxed was worth $800,000, what was the rate of taxa- 
 tion? Express this rate in three ways. 
 
 9. The assessed valuation of real and personal property in 
 a certain city is $400,000,000. The city has a bonded indebt- 
 edness of $ 2,000,000, on which it pays 4 % interest. Find the 
 tax rate necessary to pay the interest. 
 
 WRITTEN EXERCISE 
 
 Find the total tax : 
 
 1. Valuation, $3600; rate, $0.016; 3 polls at $2. 
 
 2. Valuation, $4550; rate, 9| mills; 1 poll at $1.50. 
 
 3. Valuation, $2875; rate, $0.0175; 1 poll at $1.75. 
 
 4. Valuation, $5600; rate, $1.12J per $100; 1 poll at $2. 
 
 5. Valuation, $6000; rate, $13.40 per $1000; 2 polls at 
 $1.00. 
 
 Find the valuation : 
 
 6. Total tax, $3800; rate, $0,015; 100 polls at $2.00. 
 
 7. Total tax, $11,295; rate $1.40 per $100; 250 polls at 
 $1.50. 
 
 8. Total tax, $8850; rate, $15.00 per $1000; 225 polls at 
 $1.00. 
 
 9. In a town 1040 persons were subject to a poll tax; the 
 assessed valuation of real estate was $3,209,400, and of personal 
 property $265,100. The polls were taxed $1.25 each. The tax 
 levy was $42,994. What was the tax rate ? What was the total 
 tax of Charles B. Lester, who owned real estate valued at $6450, 
 and personal property valued at $1250, and who paid for 2 polls ? 
 
STATE AND LOCAL TAXES 283 
 
 10. In a town taxes were levied as follows : state tax, $4287 ; 
 county tax, 19312.50 ; town tax, 193,156.20. There were 1850 
 polls assessed at 82 each. If the total property valuation was 
 $6,245,800, what was the tax rate per thousand ? 
 
 11. A town made provision by taxation for the following 
 expenses: public schools $18,180; interest on borrowed 
 money $2106; public high ways $4720; officials' salaries $4620; 
 general expenses $11,746; sinking fund $8000. The value of 
 real and personal property was $ 2,450,600, and 2120 polls were 
 assessed $1.50 each; $4531.80 was collected from license fees. 
 What was the tax rate ? 
 
 12. A died leaving property valued at $47,950 to B, his son, 
 and property valued at $17,500 to C, a friend. The statutes of 
 the state in which these three live provide that B, a lineal heir, 
 and C, a collateral heir, shall pay to the state an inheritance tax. 
 The rate for lineal heirs is 1 %, and for collateral heirs 5%. 
 What inheritance tax must B and C, respectively, pay when 
 they come into possession of the property? 
 
 13. A city made the following appropriation for its public 
 schools: teaching and supervision, $36,000; care and cleaning, 
 $3360; fuel, $3000; repairs, $2000; text-books, $1700; supplies, 
 $1700; printing, $300; contingent fund, $775; truant officer, 
 $500; evening schools, $1305; transportation of pupils, $600; 
 kindergarten, $1100; manual training, $700. The assessed 
 value of real estate was $6,709,998 and of personal property 
 $2,130,002. What was the tax rate for school purposes ? 
 
 14. The market value of a certain street railway amounts to 
 $20,881,000. This amount, less the company's real estate, 
 machinery, etc., is subject to a state corporation tax of $17.25 
 per $1000. If the value of the real estate, machinery, etc., is 
 $4,570,700, what is the corporation tax? This corporation tax 
 is distributed according to trackage among the cities and towns 
 in which the railway operates. If 80% of the trackage of the 
 road lies within the city of B, how much of the state corporation 
 tax will that city receive? 
 
284 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 347. In order to facilitate clerical work a table may be used 
 for computing taxes. The following table was made from the 
 published tax lists of a city in Massachusetts: 
 
 TAX TABLE. RATE $18.60 PER $1000 
 
 
 
 
 i 
 
 2 
 
 8 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 .0000 
 
 .0186 
 
 .0372 
 
 .0558 
 
 .0744 
 
 .0930 
 
 .1116 
 
 .1302 
 
 .1488 
 
 .1674 
 
 1 
 
 .1860 
 
 .2046 
 
 .2232 
 
 .2418 
 
 .2604 
 
 .2790 
 
 .2976 
 
 .3162 
 
 .3348 
 
 .3534 
 
 2 
 
 .3720 
 
 .3906 
 
 .4092 
 
 .4278 
 
 .4464 
 
 .4650 
 
 .4836 
 
 .5022 
 
 .5208 
 
 .5394 
 
 3 
 
 .5580 
 
 .5766 
 
 .5952 
 
 .6138 
 
 .6324 
 
 .6510 
 
 .6696 
 
 .6882 
 
 .7068 
 
 .7254 
 
 4 
 
 .7440 
 
 .7626 
 
 .7812 
 
 .7998 
 
 .8184 
 
 .8370 
 
 .8556 
 
 .8742 
 
 .8928 
 
 .9114 
 
 5 
 
 .9300 
 
 .9486 
 
 .9672 
 
 .9858 
 
 1.0044 
 
 1.0230 
 
 1.0416 
 
 1.0602 
 
 1.0788 
 
 1.0974 
 
 
 
 1.1160 
 
 1.1346 
 
 1.1532 
 
 1.1718 
 
 1.1904 
 
 1.2090 
 
 1.2276 
 
 1.2462 
 
 1.2648 
 
 1.2834 
 
 7 
 
 1.3020 
 
 1.3206 
 
 1.331)2 
 
 1.3578 
 
 1.3764 
 
 1.3950 
 
 1.4136 
 
 1.4322 
 
 1.4508 
 
 1.4604 
 
 8 
 
 1.4880 
 
 1.5066 
 
 1.5252 
 
 1.5438 
 
 1.5624 
 
 1.5810 
 
 1.5996 
 
 1.6182 
 
 1.6368 
 
 1.6554 
 
 9 
 
 1.6740 
 
 1.6926 
 
 1.7112 
 
 1.7298 
 
 1.7484 
 
 1.7670 
 
 1.7856 
 
 1.8042 
 
 1.8228 
 
 1.8414 
 
 In the table the rate on each $1000 was made up as follows : state tax 
 $.0807 ; county tax, $.5643 ; state highways, $.003 ; city tax, $17.952. The 
 first figure of the number of dollars assessed is given at the left, ad the 
 second one at the top. 
 
 348. Example. What is the tax on a valuation of $16,400? 
 
 SOLUTION. Tax on $16,000 = $297.60 (1000 times .2976) 
 Tax on 400 7.44 (100 times .0744) 
 
 Tax on $ 16,400 = $ 305.04 
 
 WRITTEN EXERCISE 
 
 Using the table, find the tax on the following valuations: 
 
 1. 12485. 5. $8,478. 9. $34,500. is. $20,000. 
 
 2. $1200. 6. $13,200. 10. $82,500. 14. $27,800. 
 
 3. $1050. 7. $14,700. 11. $98,250. is. $71,690. 
 
 4. $4630. 8. $18,400. 12. $21,850. 16. $89,800. 
 
 Find the tax on the following valuations when the collector's 
 commission is 1 % : 
 
 17. $5500. 21. $9500. 25. $19,000. 29. $21,000. 
 
 18. $7500. 22. $8700. 26. 826,000. so. $89,000. 
 
 19. $2900. 23. $6500. 27. $85,000. si. $10,000. 
 
 20. $4700. 24. $7250. 28. $78,000. 32. $21,000. 
 
CHAPTER XXIV 
 
 CUSTOMS DUTIES 
 ORAL EXERCISE 
 
 1. The expenses of the National Government average about 
 $ 1,500,000 per clay. What is this per year ? 
 
 SUGGESTION. To multiply by 15, multiply by 10 and add \ of the result. 
 
 2. Name five sources of income to the National Government. 
 
 3. Name ten expense items of the National Government. 
 
 349. Duties, or customs, are taxes levied by the National Gov- 
 ernment on imported goods. They are imposed in two forms : 
 ad valorem and specific. An ad valorem duty is a certain per 
 cent levied on the net cost of the importation. A specific duty 
 is a fixed sum levied on each article, or on each pound, ton, 
 yard, or other standard measure, without regard to the cost. 
 
 Ad valorem duties are not computed on fractions of a dollar. If the 
 cents of the net cost are less than fifty, they are rejected; if fifty or more 
 than fifty, one dollar is added before computing the duty. 
 
 Some articles are subjected to both ad valorem and specific duties. Be- 
 fore specific duties are estimated allowance is usually made for tare and 
 breakage. Specific duties are not computed on fractions of a unit. Frac- 
 tions less than of a unit are rejected; fractions \ or more are counted a 
 whole unit. The long ton of 2240 Ib. is used in computing specific duties. 
 
 350. A tariff is a schedule exhibiting the different rates of 
 duties imposed by Congress on imported articles. A free list is 
 a schedule of imported articles exempt from duty. 
 
 351. A customhouse is an office established by the National 
 Government for the collection of duties and the entry and 
 clearance of vessels. A port at which a customhouse is estab- 
 lished is called a port of entry; ports of entry and other ports 
 are called ports of delivery. 
 
 286 
 
286 PRACTICAL BUSINESS ARITHMETIC 
 
 The United States is divided into collection districts, in each of which 
 there is a port of entry and one or more poi ts of delivery. All entries of 
 goods and the payment of duties thereon must be made at the port of entry, 
 after which the goods may be discharged at any port of delivery. 
 
 352. In the most important ports of the United States the 
 customhouse business is distributed among three departments: 
 
 1. The collector's office, which takes charge of the entries and 
 papers, issues the permits, and collects the duties. 
 
 2. The surveyor's office, which takes charge of the vessel 
 and cargo, receives the permits, ascertains the quantities, and 
 delivers the merchandise to the importer. 
 
 3. The appraiser's office, which examines imported merchan- 
 dise and determines the dutiable value and the rate of duty on 
 same. 
 
 One package of every invoice and one package, at least, out of every ten 
 similar packages is. sent to the appraiser's store for examination. Merchan- 
 dise in bulk and all heavy and bulky packages uniform in size and quantity 
 of contents are generally examined on the wharf. 
 
 353. A manifest is a memorandum, signed by the master of the 
 vessel, showing the name of the vessel, its cargo, and the names 
 and addresses of the consignors and consignees. An invoice is a 
 detailed statement showing the particulars of the goods imported. 
 
 All invoices must be made out in the weights and measures of the coun- 
 try in which the goods are purchased ; and if the goods are 'subject to an 
 ad valorem duty they must be invoiced in the currency of the country into 
 which they are imported. Invoices over $100 must be certified before 
 a United States consul, who causes two copies of the invoice to be made. 
 One of these is sent to the collector of the port at which the goods are to be 
 entered and the. other is kept on file in the consul's office. 
 
 When the merchandise is loaded on board the vessel the shippers are 
 given a bill of lading which acknowledges the receipt of the several pack- 
 ages and agrees to deliver the same at destination. The vessel's commander 
 keeps a copy of the bill of lading and from the several that have been issued 
 makes out his manifest of cargo. The shippers mail the invoice and bill of 
 lading to the purchaser, who fills out an entry therefrom and presents it 
 and the invoice at the customhouse where the duties imposed by law on the 
 several classes of merchandise are collected and a permit issued for the land- 
 ing and delivery of the merchandise, subject to examination. 
 
CUSTOMS DUTIES 
 
 287 
 
 354. The values of foreign coins are periodically proclaimed 
 by the Secretary of the Treasury, and these values must be 
 taken in estimating duties unless a depreciation of the value of 
 the foreign currency expressed in an invoice shall be shown by 
 the consular certificate thereto attached. The following esti- 
 mate of the values of foreign coins was recently proclaimed. 
 
 VALUES OF FOREIGN COINS 
 
 COUNTRY 
 
 STANDARD 
 
 MONETARY UNIT 
 
 VALUE IN 
 U. S. GOLD 
 
 Brazil .... . . 
 
 Gold 
 
 Milreis 
 
 $ 546 
 
 Denmark, Norway, Sweden . 
 France, Belgium, Switzerland 
 German Empire .... 
 
 Gold 
 Gold 
 Gold 
 
 Crown 
 Franc 
 Mark 
 
 .268 
 .193 
 
 38 
 
 Great Britain 
 
 Gold 
 
 
 4 866^ 
 
 Japan ... .... 
 
 Gold 
 
 YPH 
 
 .498 
 
 Mexico ... 
 
 Silver 
 
 Dollar 
 
 498 
 
 Netherlands 
 
 Gold 
 
 florin 
 
 402 
 
 Philippine Islands .... 
 Russia 
 
 Gold 
 Gold 
 
 Peso 
 Ruble 
 
 .500 
 .515 
 
 The lira of Italy, and the peseta of Spain, are of the same value as the 
 franc. The dollar, of the same value as our own, is the standard of the 
 British possessions of North America, except Newfoundland. 
 
 355. Depositing goods in a government or bonded ware- 
 house is called warehousing. 
 
 Many importers buy foreign goods in large quantities, withdraw a part of 
 them, and store the remainder in the government warehouse. The goods so 
 deposited may be taken out at any time in quantities not less than an entire 
 package, or in bulk, if not less than one ton, by the payment of duties, stor- 
 age, and labor charges. Foreign goods are sometimes bought three or four 
 months earlier than they can be placed on the market arid are stored in the 
 government warehouse until they are seasonable. In this way importers 
 are able to make better selections and they also get better terms and prices. 
 
 356. A bonded warehouse is a building provided for the 
 storage of goods on which duties have not been paid. 
 
 The importer must give bond for the payment of duties on all goods 
 stored in a bonded warehouse. Goods remaining in bond are charged 10% 
 
288 
 
 PEACTICAL BUSINESS ARITHMETIC 
 
 additional duty after 1 yr. Goods left in the government warehouse beyond 
 3 yr. unclaimed are forfeited to the government and sold under the direction 
 of the Secretary of the Treasury. Goods may be withdrawn from a bonded 
 warehouse for export without the payment of duty. 
 
 357. The two common forms of entry under which duties 
 are collected are known as inward foreign entry and warehouse 
 entry. The former is used for merchandise entered for 
 consumption; the latter for merchandise that is placed in a 
 bonded warehouse under charge of the government storekeeper. 
 
 358. Excise duties are taxes levied on certain goods produced 
 and consumed in the United States. If goods, on which either 
 excise or import duties have been paid, are exported, the 
 amount so paid is refunded. The amount refunded is called a 
 drawback. 
 
 TABLE OF DUTIES ON CERTAIN IMPORTS 
 
 
 DUTY 
 
 
 ARTICLE AND DESCRIPTION 
 
 Specific 
 
 Ad 
 
 Valorem 
 
 Axminster rugs . 
 
 10^ per sq. yd. 
 
 40% 
 
 Barley, 48 Ib. to the bushel 
 
 30^ per bu. 
 
 
 Barley malt, 34 Ib. to the bushel 
 Beans, 60 Ib. to the bushel . . 
 
 45^ per bu. 
 45^ per bu. 
 
 
 Brussels carpets 
 
 44 Der so vd 
 
 40 / 
 
 Books . . . 
 
 
 eu /o 
 
 25% 
 
 Castile soap 
 
 l\0 per Ib. 
 
 
 Cheese 
 
 60 per Ib 
 
 
 China, porcelain, and crockery ware 
 Clocks and watches . 
 
 
 60% 
 
 40% 
 
 Corn 56 Ib to the bushel 
 
 15 per bu 
 
 
 Cotton tablecloths 
 
 
 50 % 
 
 Hay . 
 
 $4 per T. 
 
 
 "V _ 
 
 Ingrain carpets 
 Knit woolens 
 
 22^ per sq. yd. 
 44^ per Ib. 
 
 40% 
 
 50% 
 
 Leather and leather goods 
 Marble 
 
 65^ per cu. ft. 
 
 20% 
 25 "/ 
 
 Plate glass . . .' 
 
 8 fi per sq. ft. 
 
 
 Pocket knives, value not more than 50^ per doz. 
 Potatoes, 60 Ib. to the bushel . ... 
 
 1^ apiece 
 25 ft per bu. 
 
 40% 
 
 Silk dress goods 
 
 11 <j per sq yd 
 
 50 V. 
 
 Sugar 
 
 95 r> er lb. 
 
 
 Toilet soap, all descriptions 
 Wheat 
 
 10IK r 
 
 15^ per Ib. 
 
 25 p per bu. 
 
 
 Window glass 
 
 140 per Ib. 
 
 
 
 
 
CUSTOMS DUTIES 289 
 
 FINDING A SPECIFIC DUTY 
 
 ORAL EXERCISE 
 
 Using the table on page 288, find the duty on: 
 
 1. 67,200 Ib. of hay. 
 
 2. 48,000 Ib. of barley. 
 
 3. 100 pc. plate glass 24" x 30". 
 
 4. 2400 Ib. of window glass 10" x 15". 
 
 5. A quantity of cheese weighing 1000 Ib. 
 
 6. A shipment of wheat weighing 240,000 Ib. 
 
 7. A quantity of castile soap weighing 2100 Ib. ; tare 100 Ib. 
 
 WRITTEN EXERCISE 
 
 1. Using the table on page 288, find the total duty on: 
 2500 bu. potatoes. 95,000 Ib. barley. 44,800 Ib. corn. 
 1275 Ib. toilet soap. 24,000 Ib. beans. 10,000 Ib. cheese. 
 6500 Ib. castile soap. 136,000 Ib. barley malt. 30,000 bu. potatoes. 
 
 2. What is the duty on 175 bx. castile soap, each weighing 
 110 Ib., if 5% is allowed for tare? 
 
 . 3. Calculate the duty on 10 hogsheads of sugar weighing 
 1060-105, 1040-105, 1160-112, 1240-120, 1180-116, 1100-102, 
 1090-101, 1100-100, 1005-100, 1210-118 Ib., respectively. 
 
 4. Richard Roe & Co. imported from Canada 3750 bu. of 
 potatoes invoiced at 20^ per bushel. If the transportation 
 and other charges amounted to 1187.50, how much must be re- 
 ceived per bushel for the potatoes in order to gain 25 % ? 
 
 FINDING AN AD VALOREM DUTY 
 
 ORAL EXERCISE 
 
 Find the total duty : 
 
 1. On 40 clocks invoiced at $4.50 each. 
 
 2. On 12 books invoiced at 11.50 each. 
 
 3. On 25 doz. pocket knives invoiced at 50^ per doz. 
 
 4. On 100 sq. yd. ingrain carpet invoiced at 81 per yard 
 
290 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the duty on : 
 
 1. An Axminster rug, 12' x 18', invoiced at 10. 
 For the values of foreign coins, see page 287. 
 
 2. A 200 lb. box of knit woolen goods invoiced at <100. 
 
 3. An importation of cotton table cloths invoiced at ,100. 
 
 4. An importation of cotton table cloths invoiced at 255. 
 
 5. 300 bx. plate glass, each containing 25 plates 16" x 24". 
 
 6. 20 Axminster rugs, each 12' x 18', invoiced at 8 6s. 
 per rug. 
 
 7. An importation of china and crockery ware invoiced at 
 100 francs. 
 
 8. An invoice of knit woolens weighing 600 lb. and valued 
 at 315 12*. 
 
 9. 200 blocks of marble, each 10' x 4' x 2', invoiced at 
 328,000 lira. 
 
 10. An importation of leather from Sweden invoiced at 
 6750 crowns. 
 
 11. 400 yd. of Brussels carpeting, | yd. wide, invoiced at 
 82 per yard. 
 
 12. 4000 meters of Brussels carpeting, f yd. wide, invoiced 
 at 5 francs per meter. 
 
 A meter equals approximately 1.1 yd. 
 
 13. 4800 meters of silk dress goods, | yd. wide, invoiced at 
 3.75 marks per meter. 
 
 14. A case of silk dress goods containing 200 yd., 1 yd. wide, 
 invoiced at 1000 marks. 
 
 15. An invoice of leather goods from the Netherlands in- 
 voiced at 12,520 florins. 
 
 16. 5 cs. of silk dress goods, each containing 200 yd., | yd. 
 wide, invoiced at 20 marks per yard. 
 
 17. I bought an invoice of Swiss watches, paying 10750 fr. 
 for them in Geneva. What was the total cost of the watches, 
 including the duty? 
 
CUSTOMS DUTIES 
 
 291 
 
 INVOICES AND ENTRIES 
 
 WRITTEN EXERCISE 
 
 1. At what price per pair must the lace curtains in the fol- 
 lowing invoice be sold in order to realize a gain of 33^% ? 
 
 No. 427 Manchester, England, Dec. 15. zp 
 
 Invoice of Lace 
 Shipped by WILLIAM P. FIRTH 6? CO. 
 
 In the Steamer Catalonia 
 
 To R. H. White Company 
 Boston, Mass, 
 
 Marks 
 
 No. 
 
 Quantity 
 
 Articles and Description 
 
 Price 
 
 Extension 
 
 Amount 
 
 <^ 
 
 317 
 
 50 doz . pr . 
 
 Lace Curtains 
 Less 2% 
 
 Insurance and Freight 
 Packing and Carting 
 
 50% ad valorem duty 
 
 3/2/6 
 
 ##*-#*-#* 
 *-**-* 
 
 $***.** 
 
 *#*-**-** 
 4-10-6 
 16-6 
 
 **#-**-** 
 $*** . ** 
 ****** 
 
 2. Find the total cost of the following invoice: 
 
 Antwerp, Belgium, Apr. 2, 19 
 
 Messrs. A. T. Stewart & Co. 
 
 New York City 
 
 Bought of SCHMIDT & WESTERFELDT 
 
 Terms 30 da. 
 
 pc. Black Silk 
 
 39.00, 40.50. 39.00. 
 
 40.00, 41.00, 40.50 
 Insurance and freight 
 Cartage 
 
 5056 ad valorem duty 
 
 11# per yd. specific duty 
 
 240 Rm. 4 
 
 Rm. 
 
 39.00, 40.50, etc., above, equal the number of meters in each piece. 
 
292 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 3. Copy the following invoice, supplying the missing terms 
 
 Bradford, England, Dec. 5. 19 
 Invoice of Woolen Goods 
 Shipped by RADCLIFFE & SON 
 
 In the Steamship Winifredian To R. H. Stearns & Co. 
 Terms 30 da. Boston, Mass. 
 
 R 
 317 
 
 25 
 
 pc. Black Wool Crepon 
 68 69 69 68 69 60 55 60 
 56 54 60 60 60 68 68 60 
 45 65 65 55 60 65 65 60 60 1544 1/9 
 
 Consul's fee 
 
 14 
 
 10 
 
 4. If the foregoing invoice of goods were entered for im- 
 mediate consumption, the following is the entry that would be 
 made out. Complete the computation in the entry. 
 
 Manifest No. 
 
 Invoiced at 
 
 . /x- 
 
 19 
 
 INWARD FOREIGN ENTRY OF MERCHANDISE 
 
 In the S^a rn^r7^^^yi^^^L^^/^fy^r^ 
 
 - ArrivpH 
 " 
 
 Mark 
 
 No. 
 
 Packages and Contents 
 
 Quantity 
 
 Free List 
 
 44c. per Ib. + 
 60% ad valorem 
 
 Duty 
 
 Total 
 
 3/P 
 
 5. How much will R. H. Stearns & Co. have to receive per 
 yard for the foregoing goods in order to realize a gain of 25%? 
 
 6. In a recent year the receipts from customs duties were 
 1280,000,000, and from excise duties, $275,000,000. The cus- 
 toms duties for this year were what per cent greater than the 
 excise duties ? the excise duties were what per cent less than 
 the customs duties ? 
 
CUSTOMS DUTIES 
 
 293 
 
 7. Find the dutiable value and compute the duty on the fol- 
 lowing entries of merchandise : 
 
 a. 
 
 Manifest No- 
 
 Invoiced 
 
 \ Q 
 
 INWARD FOREIGN ENTRY OF MERCHANDISE 
 
 From 
 
 - In the S 
 
 *\^/r-&L4/-4^- 
 
 the Steamer 
 
 Arrived. 
 
 Packages and Contents Quantity ^ valorem '^ C ' PCr ' b ' D " ty T Ul 
 
 7* 
 
 *?.?> 
 
 1 kilogram equals about 2|^ avoirdupois pounds. There is no duty 
 charged on the value of the steel wire, nor on the quantity or value of the 
 sewing needles; but the values of both of these quantities is reduced to 
 United States money by the customhouse officials for statistical purposes. 
 
 Manifest No. 
 
 Invoiced at^a* 
 
 INWARD FOREIGN. ENTRY OF MERCHANDISE 
 
 the Steamer ~tpf^L-S. 
 
 A r ri ved (h&^J>7s_. -3, \ 9 
 
 Mark No. Packages and Contents 
 
 Quantity J 
 
 Free 
 
 60% ad 
 valorem 
 
 65c. per Ib. + 
 25% ad valorem 
 
 Duty Total 
 
 J3 ^- 
 
INTEREST AND BANKING 
 CHAPTER XXV 
 
 INTEREST 
 ORAL EXERCISE 
 
 1. A borrows 1100 of B for 1 yr. At the end of the year 
 what will A probably pay B besides the face of the loan ? 
 
 2. C puts $ 100 in a savings bank and leaves it for 1 yr. 
 What can he draw out at the end of the year besides the 
 money deposited ? 
 
 3. If you wished to borrow money of a bank in your town, 
 what rate of interest would you have to pay ? 
 
 4. If you loaned a man $> 500 for 1 yr., what would you 
 require him to give you as evidence of the loan and security 
 for its payment ? 
 
 359. The compensation paid for the use of money is called 
 interest. Interest is computed at a certain per cent of the sum 
 borrowed. This per cent of interest is called the rate, and the 
 sum upon which it is computed, the principal. 
 
 The rate of interest allowed by law is called the legal rate. Persons rnay 
 agree to pay less than this rate, but not more, unless a higher rate by special 
 agreement is permitted by statute. When an obligation is interest-bearing 
 and no rate is mentioned, the legal rate will be understood. An agreement 
 for interest greater than that allowed by law is called usury. 
 
 360. In the commercial world, 12 mo. of 30 da. each, or 360 
 da., are reckoned as 1 yr. 
 
 This method is not exact, but it is the most common because the most 
 convenient. It has been legalized by statute in some states and is gener- 
 ally used in all the states. 
 
 294 
 
INTEREST 295 
 
 SIMPLE INTEREST 
 THE DAY METHOD 
 
 ORAL EXERCISE 
 
 1. How many days in a commercial year ? 
 
 2. What part of a year is 60 da. ? 6 da. ? What is the interest 
 on $ 1 for 1 yr. at 6 % ? for 60 da. ? for 6 da. ? 
 
 3. How do you find .01 of a number? .001 of a number? 
 What is the interest on $120 for 60 da. at 6 % ? for 6 da. ? 
 
 4. State a short method for finding the interest on any prin- 
 cipal for 60 da. at 6 % ; for 6 da. 
 
 5. 1 da. is what part of 6 da. ? What is J of .001 ? What is 
 the interest on $1200 for 1 da. at 6 % ? on $180 ? on 11500 ? 
 
 6. State a short method for finding the interest on any 
 principal for 1 da. at 6 %. 
 
 361. In the foregoing exercise it is clear that 0.001 of any 
 principal is equal to the interest for 6 da. at 6% ; or 0.001 of any 
 principal is equal to 6 times the interest for 1 da. at 6/ G . 
 
 ORAL EXERCISE 
 
 1. Find the interest on each of the following for 6 da. at 6%. 
 
 a. 1250. e. $560. i. $678. m. $290. q. $890. 
 
 b. $870. /. $435. j. $320. n. $150. r. $750. 
 
 c. $358. g. $430. k. $100. o. $325. s. $580. 
 d: $350. h. $470. 1. $185. p. $990. t. $625. 
 
 2. Find the interest on each of the above amounts for 12 
 da. at 6% ; for 18 da.; for 24 da. 
 
 3. Find the interest on each of the following for 1 da. at 6 % 
 
 a. $360. e. $660. i. $600. m. $480. q. $840. 
 
 b. $450. /. $900. j. $180. n. $780. r. $200. 
 
 c. $300. g. $540. k. $720. o. $400. s. $330. 
 
 d. $420. h. $240. 1. $500. p. $120. t. $960. 
 
 4. Find the interest on each of the above amounts for 
 3 da. at 6%; for 2 da. 
 
296 PRACTICAL BUSINESS ARITHMETIC 
 
 362. Example. Find the interest on 1 450 for 54 da. at 6 %. 
 
 SOLUTION. Pointing off three places to the left 54 x $0.45 = $24. 30 
 gives $0.45, or 6 times the interest for 1 da. &V 30 6 = 84 05 
 Multiplying this result by 54 gives $24.30, or 6 
 
 times the interest for 54 da. Dividing this result by 6 gives $4.05, the required 
 interest. 9 
 
 By arranging the numbers as shown in the 54 x $0.45 
 margin and canceling the work is greatly short- 7 = $4.05 
 
 ened. 
 
 WRITTEN EXERCISE 
 
 At 6% find the interest on each of the following problems. 
 Reduce the time expressed in months and days to days. 
 PRINCIPAL TIME PRINCIPAL TIME PRINCIPAL TIME 
 
 1. $620 54 da. 7. $900.00 29 da. 13. $375.80 2 mo. 15 da. 
 
 2. $175 84 da. 8. $865.45 93da. 14. $300.00 3 mo. 19 da. 
 
 3. $645 42 da. 9. $700.00 96 da. 15. $171.15 1 mo. 14 da. 
 
 4. $300 84 da, 10. $974.30 62 da. 16. $120.00 4 mo. 14 da. 
 
 5. $600 72da. 11. $178.45 40da. 17. $211.16 6 mo. 16 da. 
 
 6. $502 66 da. 12. $438.55 50 da, 18. $665.65 1 mo. 10 da. 
 
 ORAL EXERCISE 
 
 1. What is the interest on $800 for 6 da. at 3 % ? 
 
 SOLUTION. 80 ^ is the interest for 6 da. at 6 %. 3% is \ of 6%; therefore, 
 I of 80^, or 40 0, is the interest for da. at 3%. 
 
 2. If the interest at 6% is $45, what is the interest for the 
 same time at 3 % ? at 12 % ? at 2 % ? at 1 % ? at 1| % ? 
 
 3. Formulate a short method for changing 6% interest to 
 8% interest. 
 
 SOLUTION. 8% is | more than 6%; Hence, the interest at 6% increased by 
 $ of itself equals the interest at 8%. 
 
 4. State a short method for changing 6% interest to 7% 
 interest; to 5% ; to 9% ; to 1\% ; to 4|%. 
 
 5. If the interest at 6% is $120, what is the interest at 7%? 
 a,t 5% ? at 8%? at 4% ? at 7-J%? at 4|-% ? 
 
INTEREST 297 
 
 363. In the foregoing exercise it is clear that 6% interest in- 
 creased by | of itself equals 9 % interest; ~by 1 of itself, 8% interest; 
 by \ of itself, 7\ % interest; by 1 of itself, 7 % interest; also that 
 
 6/o interest decreased by \ of itself equals 4 % interest ; by ^ of 
 itself, 4\ % interest; by 1 of itself , 5% interest', also that 
 
 6 % interest divided by 2 equals 3 % interest ; by 3, 2% inter- 
 est; by 6, 1% interest; by 4, 1 * % interest. 
 
 6 % interest multiplied by 2 equals 12 % interest. 
 
 6 % interest is changed to 10 % interest by dividing by 6 and removing 
 the decimal point one place to the right; to any other rate by dividing 
 by 6 and multiplying by the given rate. 
 
 WRITTEN EXERCISE 
 
 Using the exact number of days, find the interest on : 
 
 1. 12500 from Sept. 18, 1906, to Feb. 6, 1907, at 9%; at 
 3J%; at 4%; at 3%. 
 
 2. $1700 from Nov. 20, 1906, to Jan. 16, 1907, at 8% ; at 
 21 % ; at 5| % ; at 3J % ; at 4 %. 
 
 3. $2750 from Dec. 16, 1906, to Jan. 17, 1907, at 7%; at2%; 
 at 4 % ; at 5 % ; at 1 % ; at 10 % . 
 
 4. $6250 from Dec. 18, 1906, to Feb. 6, 1907, at 7| % ; at 
 10 % ; at 11 % ; at 4* % ; at 9 % ; at 8 % ; at 7 % ; at 3 %. 
 
 THE BANKER'S SIXTY-DAY METHOD 
 ORAL EXERCISE 
 
 1. 60 da. (2 mo.) is what part of a commercial year? 
 
 2. What is the interest on $1 for 2 mo. at 6 % ? for 60 da.? 
 
 3. How can you find 0.01 of a number? What is the interest 
 on $50 for 60 da. at 6%? on $370? on $590? on $214.55? 
 
 4. What fractional part of 60 da, is 30 da.? 20 da. ? 15 da. ? 
 10 da. ? What is the interest on $1680 for 60 da. ? for 30 da. ? 
 for 20 da. ? for 15 da. ? for 10 da. ? 
 
 5. State a simple way to find the interest on any principal 
 for 60 da. at 6 % ; for 30 da. ; for 20 da. ; for 15 da. ; for 
 10 da. 
 
298 PRACTICAL BUSINESS ARITHMETIC 
 
 6. Read aloud the following, supplying the missing words: 
 a. 60 da. minus ^ of itself equals 55 da. ; 60 da. minus 
 
 of itself equals 50 da. ; 60 da. minus of itself equals 40 
 
 da. ; 60 da. minus of itself equals 45 da. 
 
 b. 60 da. plus -^ of itself equals 65 da. ; 60 da. plus 
 
 of itself equals 70 da. ; 60 da. plus of itself equals 75 da. ; 
 
 60 da. plus - - of itself equals 80 da. ; 60 da. plus of 
 
 itself equals 90 da. 
 
 7. What is the interest on $600 for 60 da. at 6%? for 
 55 da. ? for 50 da. ? for 40 da. ? for 45 da. ? 
 
 8. What is the interest on $1200 for 60 da.? for 65 da.? 
 for 70 da. ? for 75 da. ? for 80 da. ? for 90 da. ? 
 
 9. State a short way to find the interest at 6% for 80 da. ; 
 for 90 da. ; for 50 da. ; for 65 da. ; for 55 da. ; for 75 da. ; for 
 70 da. ; for 40 da. ; for 45 da. 
 
 364. In the above exercise it is clear that removing the 
 decimal point two places to the left in the principal gives the 
 interest for 60 da. at 6%. 
 
 365. Examples, l. Find the interest on 11950 for 20 da. 
 at 6%. 
 
 SOLUTION. Removing the decimal point two places to the left $19.50 
 gives the interest for 60 da. 20 da. is \ of 60 da. \ of $ 19.50 = a.,, rn 
 $6.50. 
 
 2. What is the interest on $8400.68 for 75 days ? 
 
 SOLUTION. Removing the decimal point two $$4 0068 
 places to the left gives the interest for 60 da. ^-i AA-I 7 
 
 75 da. is 60 da. increased by of itself ; therefore, 
 
 $84.0068 increased by \ of itself or 105.01 is $105.0085, or $105.01 
 the required interest. In the following exercise determine the separate interest 
 mentally whenever it is possible to do so. 
 
 WRITTEN EXERCISE 
 
 1. Find the total amount of interest at 6% on: 
 $8400 for 60 da. $8400 for 12 da. $7900 for 20 da. 
 
 $8400 for 30 da. $8400 for 10 da. $7900 for 15 da. 
 
 $8400 for 20 da. $7900 for 60 da. $7900 for 12 da. 
 
 $8400 for 15 da. $7900 for 30 da. $7900 for 10 da. 
 
INTEREST 299 
 
 2. Find the total amount of interest at 6% on : 
 
 $ 1600 for 60 da. 1 1600 for 40 da. $ 2800 for 75 da. 
 
 $ 1600 for 55 da. $ 2800 for 60 da. $ 2800 for 80 da. 
 $ 1600 for 50 da. $ 2800 for 65 da. $ 2800 for 90 da. 
 
 $ 1600 for 45 da. 1 2800 for 70 da. $ 7200 for 55 da. 
 
 3. Find the total amount of interest at 6 % on : 
 
 $ 1500.60 for 30 da. $ 832.60 for 90 da. $ 8575.65 for 70 da. 
 $ 1800.72 for 20 da. $ 720.18 for 10 da. I 6282.40 for 15 da. 
 $ 1200.64 for 15 da. $ 440.70 for 40 da. $ 1460.84 for 65 da. 
 $ 8400.60 for 10 da. $ 479.64 for 50 da. $ 1385.62 for 55 da. 
 
 4. Find the total amount of interest at 6% on : 
 
 $ 1800.40 for 90 da. $ 7500.00 for 55 da. $ 216.90 for 20 da. 
 
 $ 9200.50 for 80 da. $ 8200.00 for 75 da. $ 432.65 for 15 da. 
 
 $ 3240.64 for 70 da. $ 6400.00 for 45 da. $ 832.30 for 10 da. 
 
 $4125.18 for 45 da, 11200.45 for 30 da. $926.17 for 20 da. 
 
 ORAL EXERCISE 
 
 1. What is the interest on $ 215 for 6 da. at 6 % ? on I 345 ? 
 on 1415? on 1827.50? on $425.90? on $4520.60? State a 
 simple way to find the interest on any principal for 6 da. 
 at 6%. 
 
 2. What part of 6 da. is 3 da. ? is 2 da. ? is 1 da. ? What is 
 the interest on $720 for 6 da.? for 3 da. ? for 2 da. ? for 1 da. ? 
 State a brief method of finding the interest on any principal 
 for 3 da. at 6%; for 2 da.; for 1 da. 
 
 3. Read aloud the following, supplying the missing words : 
 
 a. 6 da. minus -J- of itself equals 5 da. ; 6 da. minus of 
 
 itself equals 4 da. 
 
 b. 6 da. plus ^ of itself equals 7 da. ; 6 da. plus of itself 
 
 equals 8 da. ; 6 da. plus of itself equals 9 da. 
 
 c. State a short method of finding the interest at 6 % for 4 
 da. ; for 5 da. ; for 7 da. ; for 8 da. ; for 9 da. 
 
 366. In the above exercise it is clear that removing the 
 decimal point in the principal three places to the left gives the 
 interest or 6 da. at 6. 
 
300 PRACTICAL BUSINESS ARITHMETIC 
 
 367. Example. What is the interest on $420 for 8 da. at 
 
 6%? 
 
 SOLUTION. Removing the decimal point three places to the left gives 
 the interest for 6 da., or $0.42. Since 8 da. is da. plus | of itself, I4U 
 $0.42 increased by ^ of itself, Or $0.56 is the required interest. In the $.56 
 following exercises determine the separate interests mentally whenever it is 
 possible to do so. 
 
 WRITTEN EXERCISE 
 
 1. Find the total amount of interest at 6 % on : 
 
 1800 for 6 da. $720 for 6 da. $1500 for 6 da. 
 
 $800 for 3 da. $720 for 7 da. $1500 for 5 da. 
 
 $800 for 2 da. $720 for 8 da. $1500 for 4 da. 
 
 $800 for 1 da. $720 for 9 da. $1500 for 9 da. 
 
 2. Find the total amount of interest at 6% on : 
 
 $1168 for 6 da. $1600 for 6 da. $2400 for 6 da. 
 
 $1168 for 3 da. $1600 for 7 da, $2400 for 5 da. 
 
 $1168 for 2 da. $1600 for 8 da. $2400 for 4 da. 
 
 $1168 for 1 da. $1600 for 9 da. *2400 for 8 da. 
 
 3. Find the total amount of interest at 6 % on : 
 
 $640.50 for 8 da. $800.10 for 7 da. $213.80 for 50 da. 
 
 $920.10 for 20 da. $240.80 for 90 da. $310.40 for 40 da. 
 
 $280.40 for 15 da. $960.70 for 70 da. $135.90 for 10 da. 
 
 $390.60 for 50 da. $845.60 for 90 da. $736.18 for 10 da. 
 
 ORAL EXERCISE 
 
 1. 600 da. is how many times 60 da.? If the interest on $1 
 for 60 da. at 6 % is $0.01, what is the interest for 600 da.? 
 
 2. Give a rapid method for finding 0.1 of a number. What 
 is the interest on $500 for 600 da. at 6 % ? on $350? on $214.60? 
 on $359.80? on $4500? on $9243.80? on $750? on $2150? 
 
 3. What part of 600 da. is 300 da, ? 200 da. ? 150 da. ? 
 75 da. ? 120 da. ? 100 da. ? 50 da. ? 
 
 4. What is the interest on $1400 for 600 da. ? for 300 da. ? 
 for 200 da. ? for 150 da.? for 75 da. ? for 120 da. ? for 100 
 da. ? for 50 da. ? 
 
INTEREST 301 
 
 5. State a brief method of finding the interest for 600 da. 
 at 6 % ; for 300 da. ; for 200 da. ; for 75 da. ; for 50 da. ; for 
 150 da. ; for 200 da. 
 
 6. If the interest on$l for 600 da. is 10.10, what is the inter- 
 est for 6000 da. ? In how many days will any principal double 
 itself at 6 % interest ? 
 
 7. What is the interest on $1 for 6000 da. at 6 % ? on |55 ? 
 on $75.60 ? on 818.90 ? on $350 ? on $725 ? on $9125.70. 
 
 8. What is the interest on each of the amounts in problem 
 7 for 3000 da. ? for 2000 da. ? for 1000 da ? for 1500 da..? 
 
 9. What is the interest on $2500 for 6000 da.? on $2150? 
 on $7500? on $790? on $155.60? 
 
 10. What is the interest on each of the amounts in problem 
 9 for 6 da. ? for 60 da. ? for 600 da ? 
 
 368. In the above exercise it is clear that removing the deci- 
 mal point in the principal one place to the left gives the interest 
 for 6 f JO da. at 6% > a ^ so that any sum of money will double itself 
 in 6000 da. 
 
 WRITTEN EXERCISE 
 
 Find the interest at 6% on : 
 
 1. $240 for 3000 da. 5. $7420.50 for 600 da. 9. $1640 for 150 da. 
 
 2. $318 for 6000 da. 6. $67218.90 for 30 da. 10. $1260. 60 for 1 da. 
 
 3. $912 for 2000 da. 7. $8400.50 for 400 da. 11. $17890 for 10 da. 
 
 4. $316 for 1500 da. 8. $7500.79 for 1500 da. 12. $1696 for 100 da. 
 
 ORAL EXERCISE 
 
 1. How many times is 6 da. contained in 18 da. ? in 24 da. ? 
 in 36 da. ? in 42 da. ? in 54 da. ? in 48 da. ? 
 
 2. What is the interest on $150 for 6 da. ? for 18 da. ? for 
 48 da. ? for 54 da. ? for 36 da. ? for 42 da. ? for 12 da. ? 
 
 3. What is the interest on $350 for 60 da. ? for 180 da. ? 
 for 240 da. ? for 360 da. ? for 420 da. ? for 480 da. ? 
 
 369. Example. Find the interest on $375 for 48 da. at 6%. 
 SOLUTION. 37? equals the interest for 6 da. 48 da. is 8 times 
 
 6 da. Therefore, the interest for 48 da. is 8 times 37$?, or $3. $3.000 
 
302 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. Find the total amount of interest at 6 % on : 
 
 8750 for 6 da. $750 for 36 da. 1750 for 60 da. 
 
 1750 for 12 da. $750 for 42 da. $750 for 180 da. 
 
 $750 for 18 da. $750 for 48 da. $750 for 240 da. 
 
 2. Find the total amount of interest at 6% on: 
 
 $725 for 18 da. $690 for 6 da. $450 for 540 da. 
 
 $824 for 36 da. $129 for 60 da. $727 for 180 da. 
 
 $729 for 42 da. $475 for 600 da. $286 for 240 da. 
 
 $850 for 54 da. $8600 for 54 da. $429 for 420 da. 
 
 3. Find the total amount of interest at 6% on: 
 $317.40 for 240 da. $217.18 for 18 da. $360.40 for 24 da. 
 $218.60 for 180 da. $420.50 for 24 da. $860.50 for 48 da. 
 $419.80 for 420 da. $240.70 for 540 da. $900.60 for 66 da. 
 $425.60 for 120 da. $290.60 for 180 da. $400.80 for 84 da. 
 
 370. In some cases it is advisable to find the interest on the 
 principal for 1 da. and then multiply by the number of days. 
 
 ORAL EXERCISE 
 
 1. What is the interest on $600 for 17 da. at 6 % ? 
 
 SOLUTION. The interest for one day is .000| of the principal, or 10^. The 
 interest for 17 da. is 17 times 10^, or $1.70. 
 
 2. What is the interest on $6000 for 49 da. at 6/0? on $300? 
 on $240? on $3000? on $1800? on $840? on $600? 
 
 3. State the interest at 6jfe on: 
 
 a. $600 for 19 da. e. $6000 for 37 da. i. $ 900 for 17 da. 
 
 b. $300 for 37 da. /. $3000 for 43 da. j. $1500 for 40 da. 
 
 c. $240 for 43 da. g. $2400 for 67 da. k. $ 600 for 139 da. 
 
 d. $180 for 27 da. h. $1800 for 89 da. L $ 300 for 179 da. 
 
 371. Frequently it is well to mentally divide the days into 
 convenient parts of 6 or 60. 
 
 Thus, 97 da. = 60 da. + 30 da. + 6 da. + 1 da. ; 71 da. = 60 da. + 10 da, 
 + 1 da. ; 49 da. = 8 times 6 da. + 1 da. 
 
INTEREST 303 
 
 ORAL EXERCISE 
 
 Separate the days in the following exercise into 6 da. or 60 da., 
 or into convenient parts of 6 da. or 60 da. 
 
 1. 
 
 8 
 
 da. 
 
 7. 
 
 7 
 
 da. 
 
 13. 
 
 86 
 
 da. 
 
 19. 
 
 17 
 
 da. 
 
 2, 
 
 67 
 
 da. 
 
 8. 
 
 22 
 
 da. 
 
 14. 
 
 55 
 
 da. 
 
 20. 
 
 25 
 
 da. 
 
 3. 
 
 27 
 
 da. 
 
 9. 
 
 11 
 
 da. 
 
 15. 
 
 84 
 
 da. 
 
 21. 
 
 85 
 
 da. 
 
 4. 
 
 13 
 
 da. 
 
 10. 
 
 63 
 
 da. 
 
 16. 
 
 14 
 
 da. 
 
 22. 
 
 89 
 
 da. 
 
 5. 
 
 72 
 
 da. 
 
 11. 
 
 37 
 
 da. 
 
 17. 
 
 97 
 
 da. 
 
 23. 
 
 19 
 
 da. 
 
 6. 
 
 43 
 
 da. 
 
 12. 
 
 23 
 
 da. 
 
 18. 
 
 99 
 
 da. 
 
 24. 
 
 29 
 
 da. 
 
 372. Examples. 1. Find the interest on 1840 for 31 da. at 
 6%. 
 
 SOLUTION. 31 da. = 30 da. + 1 da. The interest for 60 da. is 
 
 $ 8.40 and for 30 da. 1 of this sum or $ 4.20. The interest for 6 da. is $4. 20 
 
 $0.84 and for 1 da. 1 of this sum or $0.14. Adding $4.20 and $0.14 .14 
 
 the result is the required interest, or $4.34. $4 34 
 
 2. What is the interest on $2500 for 121 da. at 6 % ? 
 
 125.00 
 
 SOLUTION. 121 da. = 2 x 60 da. + 1 da. The interest for 60 da. 
 is $25 and for 120 da. twice this sum, or $50. The interest for 6 50.00 
 da. is $2.50 and for 1 da. } of this sum, or $0.42. Adding $50 and 42 
 
 $0.42 the result is $50.42, the required interest. 
 
 WRITTEN EXERCISE 
 
 Find the interest : 
 
 PRINCIPAL TIME 
 
 RATE 
 
 PRINCIPAL 
 
 TIME RATE 
 
 1. 
 
 $420 
 
 3 
 
 mo. 
 
 6% 
 
 11. 
 
 $450 
 
 
 4 
 
 mo. 4| % 
 
 2. 
 
 $650 
 
 4 
 
 mo. 
 
 5% 
 
 12. 
 
 $600 
 
 
 2 
 
 mo. 5% 
 
 3. 
 
 $360 
 
 92 
 
 da. 
 
 4% 
 
 13. 
 
 $720 
 
 
 8 
 
 mo. 3% 
 
 4. 
 
 $250 
 
 30 
 
 da. 
 
 3% 
 
 14. 
 
 $840 
 
 
 2 
 
 mo. \\% 
 
 5. 
 
 $380 
 
 24 
 
 da. 
 
 1% 
 
 15. 
 
 $120 
 
 
 7 
 
 mo. 6% 
 
 6. 
 
 $900 
 
 55 
 
 da. 
 
 6% 
 
 16. 
 
 $280 
 
 
 9 
 
 mo. 3J% 
 
 7. 
 
 $550 
 
 47 
 
 da. 
 
 3% 
 
 17. 
 
 $885 
 
 .90 
 
 20 
 
 da. 3% 
 
 8. 
 
 $800 
 
 29 
 
 da. 
 
 5% 
 
 18. 
 
 $240 
 
 .00 
 
 21 
 
 da. 6% 
 
 9. 
 
 $400 
 
 90 
 
 da. 
 
 4% 
 
 19. 
 
 $420 
 
 .18 
 
 25 
 
 da. 2-|% 
 
 10. 
 
 $270 
 
 11 
 
 da. 
 
 1% 
 
 20. 
 
 $560 
 
 .17 
 
 27 
 
 da. 6% 
 
304 PRACTICAL BUSINESS ARITHMETIC 
 
 373. It has been observed that 6 times 1800 = 800 times 86 ; 
 that 0.01 of 1715 = 715 times $0.01 ; etc. Hence, 
 
 374. The principal in dollars and the time in days may be 
 interchanged without affecting the amount of interest. 
 
 375. Example. Find the interest on $600 for 179 da, at 6%. 
 
 SOLUTION. $600 for 179 da. = $179 for 600 da. ; fa of the principal equals, 
 the interest for 600 da. ; fa of $ 179 = $ 17.90, the required interest. 
 
 ORAL EXERCISE 
 
 State the interest at 6 % on : 
 
 1. 860 for 27 da. 11. I860 for 91 da. 
 
 2. 830 for 13 da. 12. 8420 for 87 da. 
 
 3. 820 for 171 da. 13. 8540 for 21 da. 
 
 4. 810 for 186 da. 14. 8660 for 37 da. 
 
 5. 815 .for 145 da. 15. 8750 for 56 da. 
 
 6. 812 for 179 da. 16. 83600 for 218 da. 
 
 7. 810 for 131 da. 17. 82000 for 183 da. 
 
 8. 8100 for 120 da. 18. 81200 for 155 da. 
 
 9. 8200 for 189 da. 19. 81800 for 181 da. 
 10. 8150 for 192 da. 20. 82400 for 218 da. 
 
 376. 81500 on interest for 24 da. at 8 % = 82000 (81500 4- 
 of itself) on interest for 24 da. at 6 %, or 81500 on interest for 
 32 da. (24 da. + J of itself) at 6 %. Hence, 
 
 377. If either the principal or the time is increased or decreased 
 by any fraction of itself, the interest is increased or decreased by 
 the same fraction. 
 
 378. Examples. 1. Find the interest on 8480 for 279 da. 
 at 71%. 
 
 SOLUTION. 1\ % is \ more than 6%. Increase the principal by \ of itself, and 
 the result is $600. Interchanging dollars and days, the problem is "Find the 
 interest on 8279 for 600 da." Pointing off one place in the new principal, the 
 result is 27.90, the required interest. 
 
 2. Find the interest on 82795.84 for 80 da. at 
 
 'fo 
 
 SOLUTION. 4% is less than 6% interest. 80 da. decreased by \ of itself 
 equals 60 da. The interest on $2795.84 for 60 da. = $27.96, the required result. 
 
INTEREST 305 
 
 ORAL EXERCISE 
 
 State the interest on : 
 
 1. #279.86 for 45 da. at 4 %. 6. $2400 for 39 da. at 5 %. 
 
 2. $478.65 for 45 da. at 4 %. 7. $2700 for 37 da. at 4 %. 
 
 3. $ 769.64 for 48 da. at 7J %. 8. 12400 for 87 da. at 4J %. 
 
 4. $217.49 for 80 da. at 4| %. 9. $ 1600 for 95 da. at 4 %.. 
 
 5. 1767.53 for 80 da. at 4J %. 10. $3200 for 59 da. at 4-| %. 
 
 THE Six PER CENT METHOD 
 
 379. This method is best adapted to finding the interest 
 when the time is one year, or more than one year. 
 
 ORAL EXERCISE 
 
 1. If the interest on 11 for 1 yr. at 6 % is 10.06, what is the 
 interest on $1 for 2 yr. ? for 3 yr. ? for 4 yr. ? for 6 yr. ? for 
 8 yr. ? for 10 yr. ? 
 
 2. If the interest on $1 for 1 yr. at 6% is 10.06, what is the 
 interest on $1 for 1 mo.? for 2 mo. ? for 3 mo. ? for 6 mo.? 
 for 10 mo. ? for 7 mo. ? for 8 mo. ? 
 
 3. What is the interest on $1 for 1 yr. 6 mo. at 6%? for 
 2 yr. 6 mo. ? for 3 yr. 4 mo. ? for 3 yr. 6 mo. ? for 4 yr. 8 
 mo. ? for 1 yr. 10 mo. ? for 5 yr. 6 mo. ? for 2 yr. 9 mo.? 
 
 4. What is the interest on 150 for 1 yr. at 6 % ? for 1 yr. 
 6 mo. ? for 2 yr. ? for 3 yr. 6 mo. ? for 2 yr. 8 mo. ? for 1 yr. 
 10 mo. ? for 2 yr. 6 mo. ? for 4 yr. 6 mo. ? for 1 yr. 9 mo. ? 
 
 5. If the interest on 1 for 1 mo. at 6 % is $0.005 (5 mills), 
 what is the interest for 1 da. ? for 2 da. ? for 3 da. ? for 4 da. ? 
 for 6 da. ? for 12 da. ? for 18 da. ? for 28 da. ? for 24 da. ? 
 
 6. What is the interest on $1 for 1 yr. 1 mo. 1 da. at 6% ? 
 for 2 yr. 3 mo. 3 da. ? for 1 yr. 10 mo. 6 da. ? for 4 yr. 4 mo. 
 24 da. ? for 1 yr. 5 mo. 12 da. ? for 2 yr. 1 mo. 1 da. ? 
 
 380. In the above exercise it is clear that : 
 
 10.06 = interest on $lfor I yr. at$%. 
 $0.005 = Interest on $lfor 1 mo. at 6 %. 
 $0.0001 = interest on $lfor 1 da. at 6 %. 
 
306 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 Find the interest on $1 at 6% for: 
 
 1. 1 yr. 4 mo. 12 da. 5. 2 yr. 6 mo. 6 da. 
 
 2. 1 yr. 8 mo. 18 da. 6. 3 yr. 4 mo. 9 da. 
 
 3. 1 yr. 7 mo. 24 da. 7. 5 yr. 3 mo. 3 da. 
 
 4. 1 yr. 9 mo. 27 da. 8. 4 yr. 8 mo. 4 da. 
 Find the interest at 6% on : 
 
 9. 1250 for 2 yr. 14. 1350 for 3 yr. 
 
 10. $400 for 5 yr. 15. 1450 for 2 yr. 3 mo. 
 
 11. 1700 for 4 yr. 16. $150 for 1 yr. 6 mo. 
 
 12. 8300 for 3 yr. 4 mo. 17. $50 for 1 yr. 2 mo. 6 da. 
 
 13. $500 for 4 yr. 2 mo. 18. $10' for 2 yr. 6 mo. 6 da. 
 381. Example. What is the interest on $600 for 2 yr. 8 mo. 
 
 15 da. at 6 % ? 
 
 SOLUTION. Find the $0.12 = int. on $1 for 2 yr. 
 interest on *1 for 2 yr.; ^ = -^ Qn fl for g mQ> 
 on .$1 for 8 mo. ; on 
 
 $1 for 15 da. The sum '^^ = lnt - on * for 15 da - 
 of these interest items $0.1625 = int. on $1 for the given time. 
 equals $0.1625, the in- (JQO x $0.1625 = $97.50, int. on $600 
 
 terest on *] ^ for the f g g 15 ^ ^ % 
 
 given time at 6%. Mul- 
 
 tiplying this interest by the given number of dollars, 600, the product is the 
 required interest, $97.50. Change to any other rate as in 362. 
 
 Sometimes it is shorter to find the interest on $ 1 for the given time at 
 any given rate, and multiply by the number of dollars in the principal. 
 Thus to find the interest on $400 for 2 yr. 6 mo. at 8%, take 400 times 20 j* 
 (2 x 8^ ); on $ 500 for 5 yr. 3 mo. at 4 %, take 500 times 21 ^ (5 x 8 ^ ; 
 on ^600 for 1 yr. 9 mo. at 4% take 600 times 7^; etc. 
 
 ORAL EXERCISE 
 
 Find the interest : 
 
 PRINCIPAL 
 
 TIME 
 
 RATE 
 
 PRINCIPAL 
 
 TIME 
 
 1. 
 
 $400 
 
 1 
 
 yr. 
 
 2 mo. 
 
 6% 
 
 7. 
 
 $840 
 
 1 
 
 yr. 
 
 6 
 
 mo. 
 
 2. 
 
 $500 
 
 2 
 
 yr- 
 
 4 mo. 
 
 6% 
 
 8. 
 
 $100 
 
 3 
 
 yr. 
 
 6 
 
 mo. 
 
 3. 
 
 $300 
 
 4 
 
 yr. 
 
 6 mo. 
 
 6% 
 
 9. 
 
 $960 
 
 4 
 
 yr. 
 
 2 
 
 mo. 
 
 4. 
 
 $250 
 
 1 
 
 yr. 
 
 8 mo. 
 
 6% 
 
 10. 
 
 $300 
 
 3 
 
 yr. 
 
 4 
 
 mo. 
 
 5. 
 
 $200 
 
 2 
 
 yr. 
 
 10 mo. 
 
 3% 
 
 11. 
 
 $240 
 
 2 
 
 yr. 
 
 6 
 
 mo. 
 
 6. 
 
 $300 
 
 1 
 
 yr. 
 
 11 mo. 
 
 6% 
 
 12. 
 
 $180 
 
 1 
 
 yr. 
 
 8 
 
 mo. 
 
 RATE 
 
 6% 
 5% 
 6% 
 3% 
 4% 
 6% 
 
L 
 
 
 382. This method employs a series of tables in which inter- 
 est computations are already worked out, and by the use of 
 which the interest may be found on any sum, at given rates, 
 for any time. 
 
 This method is used in banks, insurance offices, and kindred institutions, 
 and it greatly lessens the work of computing interest. Many different sys- 
 tems are published, but the section of an interest table given on page 308 
 will illustrate the general plan followed. 
 
 ORAL EXERCISE 
 
 1. What is the interest (use the table, page 308) on 1 8 for 
 5 da.? on $80? (10 x 18) ; on $800 ? on $8000? 
 
 2. What is the interest on $10 for 7 da.? on $100? on 
 $1000 ? on $10,000? on $70 for 5 da.? on $700 ? on $7000 ? 
 
 3. What is the interest on $4 for 11 mo. ? on $40 for the 
 same time? on $400? on $4000? on $50,000 for 7 mo. ? 
 
 383. Example. Find the interest on $9980 for 7 da. at 
 
 SOLUTION : By the table, $ 10.50 = interest on $ 9000. 
 1.05 = interest on $900. 
 
 .09 = interest on $ 80. 
 
 $11.64 = interest on 
 
WRITTEN EXERCISE 
 
 Using the table, find the interest on : 
 
 1. $8800 for 4 da. 5. $17,000 for 1 da. 
 
 2. $9600 for 5 da. 6. $29,000 for 1 da. 
 
 3. $7500 for 7 mo. 7. $71,000 for 7 da. 
 
 4. $8500 for 11 mo. 8. $87,000 for 11 da. 
 
 PROMISSORY NOTES 
 
 384. A written promise to pay a certain sum of money on 
 demand, or at a specified time, is called a promissory note. 
 
 the order of 
 
 
 JDollars 
 
 
 Value received 
 
INTEREST 
 
 309 
 
 Blank Indorsement 
 
 385. In the foregoing note Ellis B. Pitkin is the maker; 
 William B. Harris, the payee ; and $243.50, the face. The note 
 is negotiable ; that is, it may be transferred by the payee to 
 any other person by indorsement. 
 
 If the note were drawn payable to William B. Harris, or bearer, it would 
 be transferable by delivery and would be negotiable. If the words to the 
 order of were omitted, the note would not be transferable either by indorse- 
 ment or by delivery ; it would be payable to William B. Harris only, and 
 would be called a non-negotiable note. 
 
 386. If the payee should sell the foregoing note, he would 
 have to indorse it; that is, make it payable to the buyer by a 
 writing on the back of the instrument. This indorsement may 
 be made in either of the three ways shown in. the margin. 
 
 William B. Harris sold the note to O. D. Merrill and effected the transfer 
 by a blank indorsement. This is simply 
 William B. Harris's signature. It makes 
 the note payable to bearer. O. D. Merrill 
 sold the note to Andrew J. Lloyd and 
 effected the transfer by a full indorsement, 
 an indorsement which specifies the one to 
 whose order the note is made payable. By 
 indorsing the note both William B. 
 Harris and O. D. Merrill make themselves 
 responsible for its payment in case the 
 maker does not pay it. O. H. Briggs was 
 willing to buy the note without Andrew J. 
 Loyd's guarantee to pay it. The transfer 
 was effected by a qualified indorsement. 
 By this indorsement Andrew J. Lloyd avoids 
 the responsibility of an ordinary indorser. 
 
 The note just considered is a time note; 
 if the words On demand were substituted 
 for the words Two months after date the form 
 would be called a demand note. The note 
 is interest-bearing because it contains a 
 clause to that effect ; it would draw interest 
 after it became due without any interest 
 clause. A demand note, in which there is 
 no interest clause, draws interest after payment has been demanded. 
 
 Full Indorsement 
 
 Qualified Indorsement 
 
310 PRACTICAL BUSINESS ARITHMETIC 
 
 387. A note in which two or more persons jointly and 
 severally promise to pay is called a joint and several note; a 
 note in which two or more persons jointly promise to pay, a 
 joint note. 
 
 Rochester, MV s^*. .r 10 
 
 after date we jointly and severally promise to 
 
 / 
 
 pay totoi order of 
 
 *^4L^ 2&s^*?^^^^f "7s*-, . . Dollars 
 
 Payable at r^^ 
 Value received 
 
 No. 
 
 In a joint and several note, the holder may sue and collect of any one signer 
 without proceeding against the others, or he may sue all of them together. 
 In a joint note the signers must be sued jointly. The distinction between 
 a joint and a joint and several note has been .abolished by law in many of 
 the states. The above form is a joint and several note. If the words and 
 severally were omitted it would be a joint note. 
 
 The words value received in a note are equivalent to an acknowledgment 
 that there has been a consideration. Their insertion is usual and advisable, 
 but not legally required in all the states. 
 
 WRITTEN EXERCISE 
 
 Write interest-bearing notes as follows : 
 
 1. A demand note; amount, 1283.97 ; current date; payee, 
 C. H. Good; maker (your name); interest at 5J^. 
 
 2. A time note ; amount, $ 728.79 ; current date ; time, 90 da. ; 
 payee, Snow & Co.; maker (your name); interest at 3| Jo. 
 
 3. A joint note; amount, 11795.73; current date; time, 6 
 mo.; payee, Ellis & Co.; maker (your name), and Richard 
 Roe ; interest at 4| 56. Write a joint note under the same con- 
 ditions. 
 
 4. Find the amount (face plus interest) due 87 da. after date 
 in note No. 1 ; at the end of the time in note No. 2; at the 
 end of the time in note No. 3. 
 
INTEREST 311 
 
 EXACT INTEREST 
 
 388. Exact interest is simple interest for the exact number of 
 days on the basis of 365 da. in a common year, or 366 da. in a 
 leap year. 
 
 The United States Government takes exact interest, and its use is 
 growing among business men. In strict justice it is the only correct 
 method of computing interest. 
 
 389. The difference between the common year of 365 da. 
 and the commercial year of 360 da. is 5 da., or ^ of the com- 
 mon year. 
 
 If any sum were divided into 360 parts, each part would be larger than it 
 would be if the sum were divided into 365 parts. Thus, jfo ail( i sVo are 
 greater than jfo- and ^. It is therefore clear that exact interest is less than 
 ordinary interest. 
 
 390. To find the exact interest, compute interest in the usual 
 way for the commercial year, and from the interest thus obtained 
 subtract y^ of itself. 
 
 In many cases the work may be shortened by cancellation. 
 
 391. Example. Find the exact interest on 13285 for 35 da. 
 at 5%. 
 
 SOLUTION. 
 
 WRITTEN EXERCISE 
 Find the exact interest : 
 
 1. $734.50 for 124 da. at 6 %. 7. $1240.35 for 50 da. at 6%. 
 
 2. $420.60 for 99 da. at 4J%. 8. $1630.25 for 67 da. at 4%. 
 
 3. $965.50 for 82 da. at 3| %. 9. $150,000 for 28 da. at 6%. 
 
 4. $356.40 for 236 da. at 4%. 10. $100,000 for 135 da. at 5%. 
 
 5. $672.60 for 53 da. at 5|%. 11. $4653.28 for 182 da. at 4%. 
 
 6. $546.24 for 38 da. at 4| %. 12. $45,000 for 42 da. at 21%. 
 
 13. $3500 from July 17, 1907, to Nov. 26, 1907, at 3%; at 4|%. 
 
 14. $2315.89 from Mar. 11, 1907, to Sept. 1, 1907, at 6% ; at 2%. 
 
 15. $872.54 from Oct. 18, 1906, to Jan. 16, 1907, at 5 % ; at 7-| %. 
 
 16. 1006 6s. from Apr. 1, 1907, to Feb. 19, 1908, at 3 % ; at 2 % - 
 
312 PRACTICAL BUSINESS ARITHMETIC 
 
 PROBLEMS IN INTEREST 
 
 ORAL EXERCISE 
 
 1. If the principal is $ 100, the interest $ 12, and the time 2 
 yr., what is the rate ? 
 
 2. If the principal is $150, the interest $18, and the time 
 3 yr., what is the rate ? 
 
 3. If the principal is $ 200, the interest $ 24, and the rate 
 3 %, what is the time ? 
 
 4. If the principal is $160, the interest $12, and the rate 
 
 5 %, what is the time? 
 
 5. If the interest is $108, the rate 6%, and the time 3 yr., 
 what is the principal ? 
 
 6. If the interest is $42, the rate 3 %, and the time 3 yr. 
 
 6 mo., what is the principal ? 
 
 7. If the amount is $60, the rate 4%, and the time 5 yr., 
 what is the principal ? 
 
 8. When the cash price of an article is $ 25, what should the 
 sixty-day credit price be ? 
 
 9. When the sixty-day credit price of an article is $50.50, 
 what should the cash price be ? 
 
 10. When money is worth 5%, what cash offer will be 
 equivalent to a ninety-day credit of $101.25 ? 
 
 11. Which is the better and how much, a thirty-da}^ credit 
 offer of $ 100.50 or a cash offer of $ 98, money being worth 6 % ? 
 
 12. Which is the better and how much, a 60-da. credit offer 
 of $404 or a casli offer of $402, money being worth 6% ? 
 
 13. You offer a customer an article for $ 10 cash, or $ 10.40 
 on 4 mo. credit. If you consider the offers equal, how much is 
 money worth to you at the present time ? 
 
 14. One contractor offers to do a certain work for $ 1050 cash ; 
 another offers to do the same work for $ 1075, payable in 1 yr. 
 If money is worth 7J%, which is the better offer? how much 
 better ? 
 
INTEREST 313 
 
 WRITTEN EXERCISE 
 
 1. Which is the better for a tailor, to sell a suit for $65 cash, 
 or for $73.15 on 9 mo. time, money being worth 6% ? 
 
 2. Which is the better, to sell carpet at $1.50 per yard cash, 
 or at $1.68 per yard on 1 yr. time, money being worth 5% ? 
 
 3. Which is the more advantageous, to buy an article for 
 $58.50 cash or for $61.80 on 6 mo. time, money being worth 
 6% ? 
 
 4. A merchant paid $160 cash for 4 sewing machines. After 
 keeping them in stock 1 yr. 6 mo. he sold them for $190.80, 
 on one year's time without interest. If money is worth 6% what 
 was his gain or loss ? 
 
 5. An invoice of merchandise listed at $2500, on which trade 
 discounts of 20% and 10% were allowed, was purchased at 90 
 da. What was the actual cash value of the debt on the day 
 of the purchase, money being worth 5 % ? 
 
 6. A merchant bought 600 bbl. of flour at $7.50 per barrel. 
 Terms: one half on account, 3 mo.; one half on account, 6 mo. 
 At the end of 1 mo. he paid the cash value of the entire bill. 
 How much did he gain, money being worth 6%? 
 
 7. Sept. 8 you purchased of Edward Sprague & Son, at trade 
 discounts of 20% and 25%, an invoice of coffee listed at $2006. 
 Terms : 30 da. Sept. 20 you sent Edward Sprague & Son a 
 check for the actual cash value of the bill. What was the 
 amount of the check, money being worth 6%? 
 
 PERIODIC INTEREST 
 
 392. Periodic interest is simple interest on the principal 
 increased by the simple interest on each installment of interest 
 that was not paid when due. 
 
 As periodic interest can be legally enforced in only a few states, special 
 contracts should be made if it is to be collected. Where technically illegal, 
 periodic interest is often collected ; as, when a series of notes is given for 
 the interest on a note secured by a real-estate mortgage, such notes to draw 
 interest if not paid when due. 
 
314 PRACTICAL BUSINESS ARITHMETIC 
 
 393. Example. If payments of interest are due semiannually, 
 what is the interest on $1000 for 3 yr. at 6% ? 
 
 SOLUTION 
 
 $ 180 = interest on $ 1000 for 3 yr. at 6%. 
 
 $30 is the interest on $ ]000 for one semiannual period, 6 mo. 
 
 1st installment of interest, $ 30, was unpaid for 2 yr. 6 mo. 
 
 2d installment of interest, $ 30, was unpaid for 2 yr. 
 
 3d installment of interest, $ 30, was unpaid for 1 yr. 6 mo. 
 
 4th installment of interest, $ 30, was unpaid for 1 yr. 
 
 5th installment of interest, $ 30, was unpaid for 6 mo. 
 
 The sum of the periods for which interest was unpaid is 7 yr. 6 mo. 
 
 The interest on each $30 for the period it was unpaid is the same as 
 
 the interest on $30 for the sum of the periods. 
 13.50 = interest on $30 for 7 yr. 6 mo., at 6%. 
 $193.50 = the total interest due. 
 
 WRITTEN EXERCISE 
 
 1. If payments of interest are due annually, what is the 
 interest on $850 for 5 yr., at 8 % ? 
 
 2. If payments of interest are due quarterly, what is the 
 interest on $1380 for 2 yr. 6 mo., at 4%? 
 
 3. What is the difference between the simple interest and 
 periodic interest (payable annually) on $1800 for 6 yr. at 4%? 
 
 4. If payments of interest are due semiannually, what 
 amount should be paid in settlement of a debt of $1450 which 
 has run 5 yr. at 6%? 
 
 5. If payments of interest are due annually, what amount 
 will settle a debt of $1500 for 5 yr., at 6%, if the first install- 
 ment of interest was paid when due? 
 
 COMPOUND INTEREST 
 
 394. Compound interest is interest computed, at certain inter- 
 vals, on the sum of the principal and unpaid interest. 
 
 Interest may be compounded annually, semiannually, quarterly, or even 
 monthly. In most states the law does not sanction the collection of com- 
 pound interest, but if it is agreed upon by the parties, the taking of it does not 
 constitute usury. It is a general custom of savings banks to allow compound 
 interest. Compound interest is also used by life insurance companies. 
 
INTEREST 
 
 315 
 
 395. Example. What is the compound interest on $6000 
 for 4 yr., if the interest is compounded annually at 5%? 
 
 SOLUTION. $ 6000 = 1st principal. 
 
 300 = interest 1st year. 
 
 6300 = amount, or the principal the 2d year. 
 
 315 = interest 2d year. 
 
 6615 = amount, or the principal the 3d year. 
 
 330.75 = interest 3d year. 
 
 6945.75 = amount, or the principal the 4th year. 
 
 347.29 = interest 4th year. 
 
 7293.04 amount due at the end of the 4th year. 
 
 $ 7293.04 - $ 6000 = $ 1293.04, compound interest for 4 yr. 
 
 WRITTEN EXERCISE 
 
 1. If interest is compounded annually, what will be the 
 amount of 1600 for 5 yr. at 6 % ? 
 
 2. If interest is compounded semiannually, what will be the 
 compound interest on $ 1500 for 2 yr. 6 mo. at 4 % ? 
 
 3. A man deposited $750 in a savings bank Jan. 1, 1905, 
 and interest was added thereto every 6 mo. at the rate of 4 %. 
 No withdrawals having been made, what was the balance due 
 Jan. 1, 1907? 
 
 11 
 
 1.24337 
 
 1.31209 
 
 1.38423 
 
 1.45997 
 
 .53945 
 
 1.62285 
 
 1.71034 
 
 11 
 
 12 
 
 1.26824 
 
 .34489 
 
 1.42576 
 
 1.51107 
 
 .60103 
 
 1.69588 
 
 1.79586 
 
 12 
 
 13 
 
 1.29361 
 
 .37851 
 
 1.46853 
 
 1.56396 
 
 .66507 
 
 1.77220 
 
 1.88565 
 
 13 
 
 14 
 
 1.31948 
 
 .41297 
 
 1.51259 
 
 .61870 
 
 .73168 
 
 1.85194 
 
 1.97993 
 
 14 
 
 15 
 
 1.34587 
 
 .44830 
 
 1.55797 
 
 .67535 
 
 .80094 
 
 1.93528 
 
 2.07893 
 
 15 
 
 16 
 
 1.37279 
 
 .48451 
 
 1.60471 
 
 .73399 
 
 1.87298 
 
 2.02237 
 
 2.18287 
 
 16 
 
 17 
 
 1.40024 
 
 .52162 
 
 1.65285 
 
 .79468 
 
 1.94790 
 
 2.11338 
 
 2.29202 
 
 17 
 
 18 
 
 1.42825 
 
 .55966 
 
 1.70243 
 
 .85749 
 
 2.02582 
 
 2.20848 
 
 2.40662 
 
 18 
 
 19 
 
 1.45681 
 
 1.59865 
 
 1.75351 
 
 .92250 
 
 2.10685 
 
 2.30786 
 
 2.52695 
 
 19 
 
 20 
 
 1.48595 
 
 1.63862 
 
 1.80611 
 
 .98979 
 
 2.19112 
 
 2.41171 
 
 2.65330 
 
 20 
 
316 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 Refer to the table, page 315, and give rapid answers to the 
 following : 
 
 l. What is the amount of $1 for 12 yr. at 4% ? at 3% ? at 
 
 
 5%? at 4i%? at 2| 
 
 2. What is the amount of $1 for 18 yr. at 4|% ? at 
 at 2% ? at 3% ? at 2| % ? 
 
 3. What is the amount of $1 for 9 yr. at 5% ? at 4|% ? at 
 21% ? at 3|% ? at 3% ? at 4% ? 
 
 4. What is the amount of $1 for 20 yr. at 2% ? at 5% ? at 
 4|% ? at 3|% ? at 2|% ? at 3% ? 
 
 5. What is the amount of 1 10 for 10 yr. at 4 % ? for 20 yr. 
 at 2 % ? for 5 yr. at 5 % ? 
 
 6. What is the amount of 1100 for 5 yr. at 2% ? for 11 yr. 
 at 8J % ? for 19 yr. at 5 % ? 
 
 396. Example. What is the compound interest on $ 8000 
 for 10 yr., if interest is compounded annually at 5% ? 
 
 SOLUTION. $1.62889 = amount of $1 for 10 yr. at 5%. 
 
 8000 x $1.62889 = $13031.12, amount due in 10 yr. at 5%. 
 $13031.12 $8000 = $5031.12, the compound interest. 
 
 1. $7500 4% 5 yr. Annually 
 
 2. $2500 2% 12 yr. Annually 
 
 3. $5600 31% 20 yr. Annually 
 
 4. $3350 5% 10 yr. Semiannually 
 
 5. $2875 3% 17 yr. Annually 
 
 6. $4600 4% 15 yr. Semiannually 
 
INTEREST 
 
 317 
 
 SINKING FUNDS 
 
 397. A sinking fund is a sum of money set aside at regular 
 intervals for the payment of an existing or anticipated in- 
 debtedness. 
 
 The payment of a corporation or a public loan is sometimes facilitated 
 by regularly investing a certain sum in some form of security. The interest 
 from these investments from year to year constitutes a sinking fund which it 
 is planned shall accumulate to an amount sufficient to redeem the debt when 
 it falls due. 
 
 ORAL EXERCISE 
 
 1. In what time will any sum of money double itself at 4 % 
 simple interest ? at 3 % ? at 6 % ? at 4-* % ? 
 
 2. How long (approximately) will it take $1 to double it- 
 self at 3|%? compound interest, compounded annually? (See 
 table, page 315.) 
 
 3. How long (approximately) will it take any sum to double 
 itself at 4 J % compound interest, compounded annually ? at 5 % 
 compound interest, compounded annually ? 
 
 4. If you put $1 at compound interest to-day, $1 one year 
 from to-day, and so on for 20 yr., how much would you have 
 at the end of the twentieth year, interest being compounded 
 annually at 4J% ? (See table below.) 
 
 398. In the following table is shown the amount at the close 
 of a series of years of $1 invested at different rates of com- 
 pound interest at the beginning of each year. 
 
 COMPOUND INTEREST TABLE 
 
 YR. 
 
 2% 
 
 4% 
 
 44% 
 
 YR. 
 
 2% 
 
 4% 
 
 |% 
 
 1 
 
 1.020000 
 
 1.040000 
 
 1.045000 
 
 11 
 
 12.412089 
 
 14.025805 
 
 14.464031 
 
 2 
 
 2.060400 
 
 2.121600 
 
 2.137025 
 
 12 
 
 13.680331 
 
 15.626837 
 
 16.159913 
 
 3 
 
 3.121608 
 
 3.246464 
 
 3.278191 
 
 13 
 
 14.973938 
 
 17.291911 
 
 17.932109 
 
 4 
 
 4.204040 
 
 4.416322 
 
 4.470709 
 
 14 
 
 16.293416 
 
 19.023587 
 
 19.784054 
 
 5 
 
 5.308120 
 
 5.632975 
 
 5.716891 
 
 15 
 
 17.639285 
 
 20.824531 
 
 21.719336 
 
 6 
 
 6.434283 
 
 6.898294 
 
 7.019151 
 
 16 
 
 19.012070 
 
 22.697512 
 
 23.741706 
 
 7 
 
 7.582969 
 
 8.214226 
 
 8.380013 
 
 17 
 
 20.412312 
 
 24.645412 
 
 25.855083 
 
 8 
 
 8.754628 
 
 9.582795 
 
 9.802114 
 
 18 
 
 21.840558 
 
 26.671229 
 
 28.063562 
 
 9 
 
 9.949721 
 
 11.006107 
 
 11.288209 
 
 19 
 
 23.297369 
 
 28.778078 
 
 30.371432 
 
 10 
 
 11.168715 
 
 12.486351 
 
 12.841178 
 
 20 
 
 24.783317 
 
 30.969201 
 
 32.783136 
 
318 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. At the beginning of each year for 10 yr. a certain rail- 
 road company put aside out of the profits of the previous year 
 150,000 as a sinking fund. If this sum was invested at 4% 
 compound interest, compounded annually, what did it amount 
 to at the end of the tenth year ? 
 
 2. Jan. 1, 1907, a certain city borrowed $500,000 and agreed 
 to pay the principal and compound interest, compounded annu- 
 ally, at 4%, on Jan. 1, 1917. What sum must be invested in 
 securities, paying 4|% compound interest, compounded annu- 
 ally, on Jan. 1, 1907, and annually for 10 yr., in order to pay 
 the loan when it becomes due ? 
 
 3. On Dec. 31, 1907, a certain town borrowed $40,000 with 
 which to build a new high school. It was agreed that this 
 amount together with compound interest, compounded annu- 
 ally, at 4|%, should be paid on Dec. 31, 1912. What sum 
 must the town set aside and invest at 4-|-% compound interest, 
 compounded annually, on Jan. 1, 1905, and each year there- 
 after for 5 yr., in order to pay the debt when it becomes due ? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. What amount of interest (in United States money) at 6% 
 will accrue on a debt of < 84 12s. in 5 mo. 24 da.? 
 
 2. The yearly taxes on a house and lot which cost $12,500 
 are $162. How much should the house rent for per month 
 to clear 6% on the investment ? 
 
 3. A Chicago speculator bought 16,000 bu. of wheat at 85^, 
 and paid for it in 10 da. 46 da. from the date of purchase he 
 sold the wheat for 92^ per bushel, cash. If money was worth 
 4%, what did he gain? 
 
 4. A savings bank account was opened July 1, 1901, with a 
 deposit of $800. Interest was credited every 6 mo. at 4%. 
 No withdrawals or subsequent deposits having been made, what 
 was the balance of the account Jan. 1, 1907 ? 
 
INTEREST 319 
 
 5. The note on page 308 was not paid until May 27. How 
 much was due the holder of the note on that date ? 
 
 6. Jan. 1, 1905, B invested 124,000 in a manufacturing busi- 
 ness. July 1, 1907, he withdrew 133,000, which sum included 
 the original investment and the net gains. What average 
 yearly per cent of simple interest did the investment yield ? 
 
 7. Derby & Co. offer B the following terms : 2 / 10 , N / 30 . Jan. 1, 
 B bought a bill of goods amounting to $ 4000 which he paid Jan. 
 31. What rate of interest did he practically pay on the net 
 amount of the bill by not taking advantage of the cash offer ? 
 
 8. In a certain town the taxes are due Sept. 15 of each year, 
 and all taxes unpaid by Oct. 15 are subject to interest from the 
 date they are due, at 6%. The following taxes were paid on 
 the dates named: Oct. 18,168.40; Oct. 21,122.50; Oct. 25, 
 1132.75 ; Oct. 31, $98 ; Nov. 11, $176.80 ; Nov. 23, $326.30; 
 Dec. 2, $45 ; Dec. 16, $13.25 ; Dec. 29, $21. How much in- 
 terest was paid, the time being the exact number of days ? 
 
 9. Jan. 1, 1902, F bought a piece of city property for 
 $20,000, paid cash $4000, and gave a note and mortgage for 
 5 yr. without interest, to secure the balance. To cover the in- 
 terest, which it was agreed should be met quarterly, he gave 
 twenty notes for $240 each, one maturing every three months. 
 The first five installments of interest were paid when due, and the 
 balance of the mortgage and the interest were paid Jan. 1, 1907. 
 Find the final payment. 
 
 10. Lester B. Ford keeps his deposit with the Second National 
 Bank, and has left with the bank railroad stock valued at $1000 
 as collateral security for overdrafts, the bank charging 5 % on 
 all overdrafts that were not settled within 3 da. May 6 there 
 was an overdraft of $280 that was settled May 13; May 28, 
 $312.50, that was settled June 1; June 26, $156.75, that was 
 settled July 8 ; Aug. 1, $456.20, that was settled Aug. 11. How 
 much interest did Mr. Ford have to pay ? 
 
CHAPTER XXVI 
 
 BANK DISCOUNT 
 ORAL EXERCISE 
 
 1. What is meant by a promissory note ? by the face of a 
 note ? by the time ? by the maker ? by the payee ? 
 
 2. How would you word a promissory note for $600, dated 
 at your place to-da} 7 , payable in 60 da. at a bank in your place, 
 with interest at 5%, to C. B. Powell, signed by yourself? 
 
 3. What is meant by negotiable ? by indorsing a note ? 
 Illustrate a blank indorsement ; an indorsement in full ; a 
 qualified indorsement. 
 
 399. A commercial bank is an institution chartered by law to 
 receive and loan money, to facilitate the transmission of money 
 and the collection of negotiable paper, and, in some cases, to 
 furnish a circulating medium. 
 
 400. If the holder (owner) of a promissory note wishes to 
 use the money promised before it becomes due, a commercial 
 bank will usually buy the note, provided the holder can show 
 that it will be paid at maturity, that is, when it becomes due. 
 This is called discounting the note. 
 
 jjL^==- New Y*, //Z^gzsrs /# . M 
 
 -pay to 
 
BANK DISCOUNT 321 
 
 401. A commercial draft is now frequently used, instead of 
 the promissory note, as security for the payment of goods sold 
 on credit. Such a draft may be defined as a written order in 
 which one person directs another to pay a specified sum of 
 money to the order of himself or to a third person. 
 
 The circumstances under which the foregoing draft was drawn are as 
 follows: Geo. H. Catchpole sold Frank G. Hill goods amounting to $460.80. 
 Terms : 30-da. draft. The draft and an invoice were made out and sent 
 to Frank G. Hill by mail. Frank G. Hill accepted the draft, that is, signi- 
 fied his intention to pay it by writing the word accepted, the date, and his 
 name across the face. The draft was then returned to Geo. H. Catchpole, 
 who may discount it the same as lie would an ordinary promissory note. 
 
 The parties to a draft are the drawer, the drawee, and the payee. In the 
 foregoing draft, George II . Catchpole is both the drawer and the payee, 
 and Frank G. Hill is the drawee. 
 
 A draft payable after sight begins to mature from the date on which it is 
 accepted. An acceptance must, therefore, be dated in a draft payable after 
 sight, but it may or may not be dated in a draft payable after date. 
 
 Some states allow three days of grace for the payment of notes and other 
 negotiable paper. Days of grace are obsolete in so many of the states that 
 they are not considered in the exercises in this book. Some states provide 
 that when paper matures on Sunday or a legal holiday it must be paid the 
 day preceding such Sunday or legal holiday ; others provide that it must be 
 paid on the day following. To hold all interested parties, the laws of any 
 given state should always be observed. When the time of negotiable paper 
 is expressed in months, calendar months are used to determine the date of 
 maturity ; but when the time is expressed in days, the exact number of days 
 is used. Thus, a note payable 2 mo. after July 15 is due Sept. 15 ; but a 
 note payable 60 da. after July 15 is due Sept. 13. Paper payable 1 mo. 
 from May 31, Aug. 31, etc., is due Jan. 30, Sept. 30, etc. 
 
322 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 MATURITY TABLE 
 
 402. The time from the date of discount to the maturity of 
 paper is called the term of discount ; the whole sum specified to 
 be paid at maturity, the value, or amount, of the paper. 
 
 The term of discount is usually the exact number of days from the date of 
 discount to the date of maturity. Some banks, however, find the term of 
 discount by compound subtraction, and then reduce the time to days; e.g. 
 the term of discount on a note due May 6 and discounted Mar. 1 is counted 
 as 2 mo. 5 da., or 65 da. In this text the term of discount is the exact number 
 of days from the date of discount to the maturity of the paper. 
 
 403. The reduction made by a bank for advancing money on 
 negotiable paper not due is called bank 
 
 discount. The value of negotiable paper 
 at maturity, minus the bank discount, is 
 called the proceeds. 
 
 Bank discount is always the simple interest for 
 the term of discount on the whole sum specified to 
 be paid at maturity. 
 
 404. The accompanying maturity table 
 is sometimes used by bankers in finding 
 the maturity of notes and drafts. The 
 following examples illustrate its use. 
 
 405. Examples. 1. Find the maturity 
 of a note payable (#) 6 mo. from Apr. 27, 
 1906 ; (6) 6 mo. from Sept. 25, 1906. 
 
 SOLUTIONS, (a) Referring to the table, observe 
 that April is the 4th month; adding 4 and 6, the 
 result is 10, and the 10th month (see number on left) 
 is October. The note is therefore due Oct. 27, 1906. 
 
 (&) September is the 9th month. 9 + 6 = 15, and the 15th month (see number 
 oh right) is March of the next year. The note is therefore due Mar. 25, 1907. 
 
 2. Find the maturity of a note payable 90 da. from Jan. 18, 
 1907. 
 
 SOLUTION. 1 + 3 = 4, and the 4th month is April. If the note were pay- 
 able in 3 mo., it would be due Apr. 18. Referring to the table, note that 2 
 da. (1 da. + 1 da.) must be subtracted for January and March, and 2 da. added 
 for February. The note is therefore due Apr. 18. 
 
 After the student has become familiar with the principles of the table it will 
 not be found necessary to consult it. 
 
 1 
 
 Jan. 1 
 
 13 
 
 2 
 
 Feb. + 2 
 
 14 
 
 3 
 
 Mar. - 1 
 
 15 
 16 
 
 4 
 
 Apr. 
 
 5 
 
 May- 1 
 
 17 
 
 6 
 
 June 
 
 18 
 
 7 
 
 July - 1 
 
 19 
 
 8 
 
 Aug. - 1 
 
 20 
 
 9 
 
 Sept. 
 
 21 
 
 10 
 
 Oct. - 1 
 
 22 
 
 11 
 
 Nov. 
 
 23 
 
 12 
 
 Dec. - 1 
 
 24 
 
BANK DISCOUNT 323 
 
 ORAL EXERCISE 
 
 Find the maturity of each of the following notes : 
 
 DATE TIME DATE TIME 
 
 1. Apr. 6, 1906 30 da. 6. Jan. 30, 1907 30 da. 
 
 2. Oct. 6, 1907 3 mo. 7. Jan. 31, 1906 30 da. 
 
 3. Nov. 9, 1906 60 da. 8. May 10, 1907 90 da. 
 
 4. Jan. 31, 1907 1 mo. 9. June 19, 1907 60 da. 
 
 5. Sept. 18, 1906 90 da. 10. Nov. 15, 1907 30 da 
 
 Find the maturity of each of the following acceptances : 
 
 n TIME AFTER TIATW TIME AFTER 
 
 DATE DATE 
 
 11. Apr. 3 30 da. 14. Dec. 31 2 mo. 
 
 12. May 5 60 da. 15. Jan. 12 1 mo. 
 
 13. Jan. 29 1 mo. 16. Feb. 18 3 mo. 
 Find the maturity of each of the following acceptances: 
 
 DATE TIME AFTER DATE TIME AFTER 
 
 ACCEPTED SIGHT ACCEPTED SIGHT 
 
 17. Aug. 12 3 mo. 20. Apr. 25 60 da. 
 
 18. Sept. 18 2 mo. 21. May 17 3 mo. 
 
 19. Oct. 30 4 mo. 22. June 18 30 da. 
 
 WRITTEN EXERCISE 
 
 Find the maturity and the term of discount: 
 
 DATE TIME DISCOUNTED 
 
 1. Jan. 16, 1907 3 mo. Mar. 1 
 
 2. Jan. 31, 1907 1 mo. Feb. 3 
 
 3. Feb. 12, 1907 90 da. Mar. 2 
 
 4. Feb. 24, 1907 60 da. Apr. 1 
 
 . 5. Mar. 31, 1907 90 da. May 13 
 
 DATE OF DRAFT TIME AFTER DATE DATE ACCEPTED DATE DISCOUNTED 
 
 6. Feb. 7 60 da. Feb. 8 Feb. 9 
 
 7. Mar. 12 30 da. Mar. 12 Mar. 15 
 
 DATE OF DRAFT TIME AFTER SIGHT DATE ACCEPTED DATE DISCOUNTED 
 
 8. May 31 60 da. May 31 June 3 
 
 9. Mar. 17 90 da. Mar. 20 Mar. 21 
 
324 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 406. The following time table is frequently used by bankers 
 in finding the exact number of days between any two dates : 
 
 TABLE OF TIME 
 
 FROM ANY DAY 
 
 OF 
 
 To THE SAME DAY OF THE NEXT 
 
 Jan. 
 
 Feb. 
 
 Mar. 
 
 Apr. 
 
 May 
 
 June 
 
 151 
 120 
 92 
 61 
 31 
 365 
 335 
 304 
 273 
 243 
 212 
 182 
 
 July 
 
 Aug. 
 
 Sept. 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 JANUARY .... 
 FEBRUARY . . . 
 MARCH .... 
 APRIL 
 
 365 
 334 
 306 
 275 
 245 
 214 
 184 
 153 
 122 
 92 
 61 
 31 
 
 31 
 365 
 337 
 306 
 276 
 245 
 215 
 184 
 153 
 123 
 92 
 62 
 
 59 
 28 
 365 
 334 
 304 
 273 
 243 
 212 
 181 
 151 
 120 
 90 
 
 90 
 59 
 31 
 365 
 335 
 304 
 274 
 243 
 212 
 182 
 151 
 121 
 
 120 
 89 
 61 
 30 
 365 
 334 
 304 
 273 
 242 
 212 
 181 
 151 
 
 181 
 150 
 122 
 91 
 61 
 30 
 365 
 334 
 303 
 273 
 242 
 212 
 
 212 
 181 
 153 
 122 
 92 
 61 
 31 
 365 
 334 
 304 
 273 
 243 
 
 243 
 212 
 184 
 153 
 123 
 92 
 62 
 31 
 365 
 335 
 304 
 274 
 
 273 
 242 
 
 214 
 183 
 153 
 122 
 92 
 61 
 30 
 365 
 334 
 304 
 
 304 
 273 
 245 
 214 
 184 
 153 
 123 
 92 
 62 
 31 
 365 
 335 
 
 334 
 303 
 275 
 244 
 214 
 183 
 153 
 122 
 91 
 61 
 30 
 365 
 
 MAY 
 
 JUNE 
 
 JULY 
 
 AUGUST .... 
 SEPTEMBER . . . 
 OCTOBER .... 
 NOVEMBER . . . 
 DECEMBER . . . 
 
 The exact number of days from any day of any month to the correspond- 
 ing day of any other month, within a year, is found in the column of the 
 last month directly opposite the line of the first month. Thus, from June 
 6 to Sept. 6 is 92 da. ; from Apr. 1 to Oct. 1 is 183 da. ; from Aug. 26 to 
 Dec. 26 is 122 da. The exact number of days between any two dates is 
 found as in the following illustrations : 
 
 407. Examples. 1. How many days from Mar. 1 to May 11 ? 
 
 SOLUTION. From Mar. 1 to May 1 is 61 da. From May 1 to May 11 is 10 
 da. 61 da. -f 10 da. = 71 da., the required result. 
 
 2. How many days from July 26 to Oct. 6 ? 
 
 SOLUTION. From July 26 to Oct. 26 is 92 da. From Oct. 26 back to Oct. 6 
 is 20 da. 92 da. - 20 da. = 72 da., the required result. 
 
 ORAL EXERCISE 
 
 By the table find the exact number of days from : 
 
 1. July 8 to Sept. 8. 7. May 31 to Aug. 1. 
 
 2. Jan. 6 to Mar. 6. 8. 
 
 3. Jan. 23 to June 23. 9. 
 
 4. Feb. 13 to July 13. 10. 
 
 5. Mar. 11 to Sept. 11. 11. 
 
 6. Mar. 21 to Aug. 21. 12. 
 
 Feb. 23 to Sept. 23. 
 Mar. 24 to July 12. 
 May 11 to Aug. 31. 
 Aug. 15 to Dec. 10. 
 Nov. 25 to Mar. 25. 
 
BANK DISCOUNT 
 
 325 
 
 408. Examples, l. Find the proceeds of a note for 13000, 
 payable in 78 da., discounted at 6%. 
 
 SOLUTION. $0.013 = the rate for the term of discount. 
 3000 x $0.013 = $39, the bank discount. 
 $3000 - $39 = $2961, the proceeds. 
 
 2. A note for -16000 payable in 60 da. from May 10, 1907, 
 with interest at 6%, is discounted May 25, at 6%. Find the 
 maturity, the term of discount, the bank discount, and the 
 proceeds. 
 
 SOLUTION. July 9, 1907 = the maturity. 
 
 45 da. = the term of discount. 
 
 .$60 = the interest on the note for 60 da. 
 $6060 = the value of the note at maturity. 
 $ 45.45 = the bank discount. 
 $6014.55 = the proceeds. 
 
 409. The accompanying diagram illustrates *a convenient 
 outline for learning the proper 
 
 method of computing bank dis- 
 count. It will be observed that 
 the first problem is an interest- 
 bearing note, and the second 
 problem a non-interest-bearing 
 note. The items in black ink 
 are taken from the problem, and 
 the items in red ink are found 
 as previously explained. 
 
 &</. 
 
 f-303 
 f/.j-a. 
 
 WRITTEN EXERCISE 
 
 1. Assuming that the model note, page 9, was discounted 
 July 2, at 6%, find the bank discount and the proceeds. 
 
 2. Assuming that the model note, page 308, was discounted 
 Jan. 20, at 6%, find the bank discount and the proceeds. 
 
 3. Assuming that the model note, page 310, was discounted 
 Aug. 26, at 6 %, find the bank discount and the proceeds. 
 
 4. Assuming that the model draft, page 320, was discounted 
 May 15, at 6 % , find the bank discount and the proceeds. 
 
326 PRACTICAL BUSINESS ARITHMETIC 
 
 5. Assuming that the model draft, page 321, was discounted 
 April 12, at 6%, find the bank discount and the proceeds. 
 
 6. Find the proceeds of the following joint note: 
 895.40 BALTIMORE, MD., May 25, 1907. 
 
 Six months after date, for value received, we promise to pay 
 to the order of Ralph D. Gibson Eight Hundred Ninety-rive 
 -f^Q Dollars, at Exchange National Bank. 
 
 SETH M. BULLARD. 
 Discounted July 2, 1907, at 5%. ISAAC C. AV ATKINS. 
 
 7. Find the proceeds of the following joint and several note: 
 $ 1000.00 COLUMBUS. O.. May 1. 1907. 
 
 Three months after date we jointly and severally promise to 
 pay to the order of Wilson N. Burton One Thousand Dollars, 
 at Second National Bank, Columbus, O., with interest at 6%. 
 
 Value received. JOHN M. SELLERS. 
 
 Discounted June 2, 1907, at 6%. DANIEL W. SHELDON. 
 
 8. Find the proceeds of the following firm note: 
 81250.00 ST. Louis. Mo.. Aug. -20. 1907. 
 
 Ninety days after date we promise to pay to the order of 
 C. M. Courtwright Twelve Hundred Fifty Dollars, at the 
 National Bank of Redemption, with interest at 5%. 
 
 Value received. J. M. Cox & SON. 
 
 Discounted Sept. 1, 1907, at 6%. 
 
 9. Sept. 26 you sold R. M. Stein, Portland, Me., a bill of 
 hardware amounting to * 2-180, less 20 %, 25 %, and 10 % . Terms : 
 \ by 60-da. note with interest at 6 % ; \ on account 60 da. What 
 was the amount of the note which was this day received? 
 
 10. Oct. 12 you discounted at Union Bank, at 6%, R. M. 
 Stein's note received Sept. 26, the bank giving you credit for 
 the proceeds. If the bank charges -^ % for collecting out-of- 
 town paper, what was the amount of the proceeds credited ? 
 
 A small fee called collection and exchange is sometimes charged on 
 discounted paper payable out of town. The charge is by no means 
 uniform, being controlled largely by the size of the depositor's account and 
 the general custom of the banks in any given locality. 
 
BANK DISCOUNT 
 
 B27 
 
 11. The following is a part of a page from a bank's discount 
 register. Copy it, supplying all missing terms. The notes 
 were all discounted June 17. 
 
 So. 
 
 DATE <>K 
 PAIT.K 
 
 TIME 
 
 WIIEX 
 DIE 
 
 TERM OF 
 
 I)!-i <U NT 
 
 BATE OF 
 DISCOUNT 
 
 VALUE OF 
 PAPER 
 
 Disc. 
 
 COLL. & 
 Exce. 
 
 PROCEEDS 
 CREDITED 
 
 20 
 
 Apr. 25 
 
 3 mo. 
 
 
 
 
 6% 
 
 2000 
 
 00 
 
 
 
 
 
 
 
 21 
 
 May 1 
 
 3 mo. 
 
 
 
 
 6% 
 
 3500 
 
 00 
 
 
 
 3 
 
 50 
 
 
 
 2-2 
 
 Apr. 1 
 
 90 da. 
 
 
 
 
 6% 
 
 1500 
 
 00 
 
 
 
 
 
 
 
 23 
 
 Apr. 15 
 
 90 da. 
 
 
 
 
 6% 
 
 900 
 
 60 
 
 
 
 
 
 
 
 J4 
 
 June 15 
 
 30 da. 
 
 
 
 6% 
 
 378 
 
 90 
 
 
 
 
 38 
 
 
 
 12. Sept. 15 the First National Banb notifies you that your 
 bank account is overdrawn 1725.90. You immediately offer 
 for discount, at 6%, the following notes, the proceeds of which 
 are to be placed to your credit : E. M. Robinson's 30-day note 
 dated Sept. 1, for 300; C. E. Reardon's note payable 3 mo. 
 from July 25, with interest at 6 %, for $427.65; C. W. Allen's 
 60-day note dated Aug. 1, for 321.17; F. H. Clark's 60-day 
 note dated July 30, for 1500. What is your credit at the bank 
 after discounting the notes? 
 
 13. Apr. 6, 1907, Peter W. Berger has on deposit in the 
 First National Bank 523.87. He draws a check for $1176.45, 
 and then discounts the following notes at the bank, at 6%, 
 receiving credit for the proceeds. What was the balance of his 
 account after the notes were discounted and credited? 
 
 a. 
 
 8 346. 50 HARTFORD, CONN., Mar. 1, 1907. 
 
 Ninety days after date I promise to pay Peter W. Ber- 
 ger, or order, Three Hundred Forty-six -ffo Dollars, at First 
 National Bank, Hartford, Conn. 
 
 Value received. HENRY S. LANE. 
 
 b. 
 575.00 HARTFORD, CONN., Feb. 1, 1907. 
 
 Aug. 1, 1907, I promise to pay Peter W. Berger, or order, 
 Five Hundred Seventy-five Dollars, at Second National Bank, 
 Hartford, Conn. 
 
 Value received. SAMUEL D. SKIFF. 
 
328 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 14. July 18, C. B. Snow's bank balance is 1312.90. He dis- 
 counts at 6 % the following drafts, and then issues a check in 
 payment for 5 sewing machines at 175, less 20% and 25%. 
 What is the amount of his balance after issuing the check? 
 
 a. 
 
 ^L 19 
 
 sS^. 
 
 J^b^&s*.^j .*'/~ 
 
 'Dollar 
 
 Value receioed 
 
 flfr. 2, rPue 
 
 BANK LOANS 
 
 410. The foregoing exercises have reference to paper bought 
 or discounted by a bank. Money is frequently loaned upon 
 the notes of the borrower, indorsed by some one of known 
 financial ability, or secured by the deposit of stocks, bonds, 
 warehouse receipts, or other collaterals. These notes, if drawn 
 on time, are not interest-bearing, but the bank discounts them 
 by deducting from their face the interest for the full time. 
 
BANK DISCOUNT 329 
 
 411. Loans are sometimes made on call or demand notes ; that 
 is, on notes that can be called or demanded at any time after 
 they are made. These notes are interest-bearing and are drawn 
 for the exact sum loaned. 
 
 Call or demand loans generally bear a lower rate of interest than loans on 
 time. They are made principally to brokers and speculators, who use them 
 to pay for stocks ; but they are also made to merchants and others to some 
 exte.nt. Business men, however, generally prefer to borrow on time, for 
 they do not wish to be embarrassed by having the loans called in at an 
 unexpected time. Time loans are usually drawn for thirty, sixty, or ninety 
 days. If the borrower requires money for a longer period, the bank will 
 usually allow him to renew the note when it falls due. 
 
 WRITTEN EXERCISE 
 
 1. Jan. 7, 1907, E. L. Jennings & Co. desire to extend their 
 business, and for this purpose borrow money at 6 % of the First 
 National Bank of New York, on the following note. How 
 much will the bank place to the credit of E. L. Jennings & Co. ? 
 
 19 _ 
 
 fff Jate^tSZ/-f>romte to pay to 
 
 Value received 
 
 ^^7^^^y^f ^~V?^rx' 
 
 2. You gave the Union National Bank, of your city, your 
 note, for 11200, at 60 da., indorsed by Williams & Rogers. 
 How much cash will the bank advance you, if discount is 
 deducted at the rate of 6% 
 
 
 3. Howe & Rogers, Buffalo, N.Y., borrowed 112,000 of Mer- 
 chants National Bank on their demand note secured by 300 
 shares of Missouri Pacific Railway stock, at $50. If the rate 
 of interest was 21%, how much was required for settlement 
 39 da. after the loan was made ? 
 
330 PRACTICAL BUSINESS ARITHMETIC 
 
 4. Jan. 1, 1906, C. W. Allen & Co., brokers, borrowed of 
 First National Bank, Boston, Mass., $15,000 on the following 
 collateral note. How much was required for full settlement 
 of the loan 57 da. after it was made ? 
 
 Boston, Mn ^^-. 2. _ 19 _ 
 
 fnr value received, ~-tsz~ promise to pay to the order of 
 f^ at their banking house 
 
 ^r> - ------- - Dollars 
 
 As collateral security tor the payment of the note and all other liabilities to said bank, either absol 
 contingent, now existing or to be hereafter incurred, -44/T- have deposited with it : 
 
 Should the market value of the same decline, -^Ur&- promise to furnish satisfactory additional collateral on 
 demand, which may be made by a notice in writing, sent by mail or otherwise, to (T^^ residence or place of 
 business. On the nonperformance of either of the above promises -usr^ authorize the holder or holders 
 hereof to sell said collateral and any collaterals added to or substituted for the same, without notice, at public or 
 private sale, and at or before the maturity hereof, he or they giving -4*^d- credit for any balance of the net 
 proceeds of such sale remaining after paying all sums absolutely or contingently due and then or thereafter 
 payable from -<- to said holder or holders. And ~WZ- authorize said holder or holders, or any person in 
 his or their behalf, to purchase at any such sale. 
 
 FINDING THE FACE 
 
 412. Example. I wish to borrow $1980 of a bank. For 
 what sum must I issue a 60-cla. note to obtain the amount, dis- 
 count being at the rate of 6% ? 
 
 SOLUTION. Let the face of the note = $ 1 
 
 Then the bank discount = $0.01 
 And the proceeds = 80.99 
 
 But the proceeds = $ 1980 
 
 $1980 -$0.99 = 2000 
 
 /. the face of the note is 2000 x $1, or 2000. 
 
 WRITTEN EXERCISE 
 
 1. What must be the face of a 30-da. note in order that when 
 discounted at 6 % the proceeds will be 1 1990 ? Of a 60-da. note, 
 same conditions? 
 
 2. You wish to borrow 13940 cash. What must be the face 
 of a 90-da. note in order that when discounted at 6 % the pro- 
 ceeds will be the required sum? 
 
 ; 
 
BANK DISCOUNT 
 
 331 
 
 3. Oct. 15, J. M. King bought of you goods amounting to 
 13500, less 20% and 10%. Terms: cash. Not having the 
 money, he gave you his 60-da. note, dated Oct. 15, for an 
 amount equivalent to the cash value of the goods. What was 
 the face of the note, money being worth 6% ? 
 
 4. You purchased through W. D. Allen, an agent, 3000 Ib. 
 coffee at 33J^. Commission 3%; guaranty 2%. - You gave 
 Mr. Allen a 30-da. note, which when discounted at 6% for 
 its full term just covered the amount due. If the note bore 
 interest at 5%, what was its face? 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the proceeds of the following note, discounted 
 Feb. 2 at 5% ; collection charges |%. 
 
 12700.00 Los ANGELES, CAL., Dec. 27, 1906. 
 
 Mar. 27, 1907, we promise to pay to the order of F. M. Dun- 
 bar & Son Twenty- seven Hundred Dollars, at the Union Bank 
 of Los Angeles, with interest at 4 % . 
 
 Value received. GRAY & SALISBURY. 
 
 2. Copy the following discount memorandum, supplying all 
 missing terms : 
 
 FIRST NATIONAL BANK 
 
 Boston, Mass., 
 
 (L 
 
 10 
 
 ybrUrZ-O 
 
 2-e 
 20 
 2-0 
 
 /2-fV<&, 
 /* 
 
 /J" 
 
 t 
 
 tftf 
 
CHAPTER XXVII 
 
 PARTIAL PAYMENTS 
 THE UNITED STATES METHOD 
 ORAL EXERCISE 
 
 1. A note for $500 bears interest at 6%. What amount 
 would pay the note and interest at the end of 1 yr. ? 
 
 2. Suppose that a payment of $130 was made at the end of 
 1 yr. After the accrued interest has been paid, how much is 
 there left to apply to the face of the note ? 
 
 3. After the $100 has been applied to the face of the note, 
 what amount does the maker continue to keep? On what sum, 
 therefore, should he pay interest after the first year ? 
 
 4. The maker kept the remaining $400 another year. How 
 much interest was then due ? What was the total amount due ? 
 
 5. If a payment of $224 was made at this time, what amount 
 still remained unpaid ? If the balance of the note was paid 
 three years after it was issued, what was the amount of the 
 payment ? 
 
 413. Partial payments are payments in part of a note or bond. 
 Such payments may be made either before or after maturity. They 
 
 should be acknowledged by indorsement on the back of a note or bond. 
 Current forms for indorsing partial payments on notes are illustrated on 
 page 336. 
 
 414. The United States method of partial payments (as sug- 
 gested in problems 1-5 above) has been adopted by the Supreme 
 Court of the United States, and made the legal method in nearly 
 all the states. 
 
 This is the method ordinarily used by individuals when the time between 
 the date of the note and its payment is more than one year. 
 
 332 
 
PARTIAL PAYMENTS 
 
 333 
 
 415. Example. A note for 11200, dated Jan. 1, 1906, bear- 
 ing interest at 6%, had payments indorsed upon it as follows : 
 Mar. 1,1906, $212; July 1, 1906, 1 15; Sept. 1,1906,1515; 
 Nov. 1, 1906, $175. How much was due upon the note at final 
 settlement, Apr. 1, 1907 ? 
 
 SOLUTION 
 
 Face of note $1200. 
 
 Interest from Jan. 1, 1906, to Mar. 1, 1906 (2 mo.) ... 12. 
 
 Amount due Mar. 1, 1906 1212. 
 
 Payment Mar. 1, 1906 212. 
 
 New principal, or amount to draw interest after Mar. 1, 1906 . 1000. 
 
 Interest from Mar. 1, 1906, to July 1, 1906 (4 mo.) . . $20. 
 Interest exceeds the payment and the principal remains unaltered. 
 Interest from July 1, 1906, to Sept. 1, 1906 (2 mo.) . . $10. 
 
 Total interest due Sept. 1, 1906 . ~~ 30. 
 
 Amount due Sept. 1, 1906 
 
 Sum of the payments since July 1 ($15 -f$ 51 5) .... 
 New principal, or amount to draw interest after Sept. 1, 1906 
 Interest from Sept. 1, 1906, to Nov. 1, 1906 (2 mo.) 
 
 Amount due Nov. 1, 1906 
 
 Payment Nov. 1, 1906 
 
 New principal, or amount to draw interest after Nov. 1, 1906 . 330. 
 
 Interest from Nov. 1, 1906, to Apr. 1, 1907 (5 mo.) . . . 8.25 
 
 Amount due at settlement, Apr. 1, 1907 . ... . $338.25 
 
 It will be observed in the foregoing example that the United States method 
 provides : (1) that the payment must first be applied to discharge the accrued 
 interest ; (2) that the surplus, if any, after paying the interest may be used to 
 diminish the principal; and (3) that if any payment is less than the accrued 
 interest, the principal remains unaltered until some payment is made with which 
 the preceding neglected payment or payments is more than sufficient to discharge 
 the accrued interest, 
 
 CONDENSED FORM FOR WRITTEN WORK 
 
 1030. 
 530. 
 
 
 INTEREST 
 
 
 
 
 
 
 DATES 
 
 
 PER CENTS 
 
 
 INTERESTS ON 
 
 AMOUNTS OF 
 
 
 
 " 
 
 OF INTEREST 
 
 PRINCIPALS 
 
 PRINCIPALS 
 
 PRINCIPALS 
 
 PAYMENTS 
 
 
 
 
 
 
 
 Yr. 
 
 Mo. 
 
 Da. 
 
 Yr. 
 
 Mo. 
 
 Da. 
 
 
 
 
 
 
 1906 
 
 1 
 
 1 
 
 
 
 
 
 
 
 
 
 1906 
 
 3 
 
 1 
 
 
 2 
 
 
 
 $.01 
 
 $1200.00 
 
 $12.00 
 
 $1212.00 
 
 $212.00 
 
 1906 
 
 7 
 
 1 
 
 
 4 
 
 
 
 .02 
 
 1000.00 
 
 20.00 
 
 
 15.00 
 
 1906 
 
 9 
 
 1 
 
 
 2 
 
 
 
 .01 
 
 1000.00 
 
 10.00 
 
 1030.00 
 
 515.00 
 
 1906 
 
 11 
 
 1 
 
 
 2 
 
 
 
 .01 
 
 500.00 
 
 5.00 
 
 505.00 
 
 175.00 
 
 1907 
 
 4 
 
 1 
 
 
 5 
 
 
 
 .025 
 
 330.00 
 
 8.25 
 
 338.25 
 
 
 1 
 
 3 
 
 
 
 1 
 
 3 
 
 
 
 $.075 
 
 $338.25, balance due Apr. 1, 1907 
 
334 PRACTICAL BUSINESS ARITHMETIC 
 
 When there are many payments, the work may be simplified as shown in 
 the foregoing outline. First write the date and the face of the note and then 
 the dates and the amounts of the payments. Next find the interest periods 
 and the per cents of interest. Test the accuracy of the work to this point 
 
 (1) by finding the difference between the date of the note and the date 
 of settlement and comparing it with the sum of the interest periods ; and 
 
 (2) by comparing the sum of the per cents of interest with the interest on $1 
 for the full time as shown by the sum of the interest periods. Complete 
 the remainder of the work as suggested by the outline. 
 
 WRITTEN EXERCISE 
 
 1. Jan. 2, 1907, J. E. King & Co. borrowed of E. B. 
 Peterson & Bro. $1000 and gave in payment a note payable iij 
 6 mo., with interest at 5%. July 2, J. E. King & Co. made a 
 payment of $ 500 and issued a new note at 90 da., with interest 
 at 6 % for the balance due. What was the face of the new note? 
 
 2. Jan. 30, 1906, you sold Irwin & Co. 5 Eureka Elevator 
 Pumps at $475, less a trade discount of 16-|%. Terms: note 
 at 6 mo. with interest at 6 % . What was the amount of the 
 note ? At the maturity of the note Irwin & Co. paid you cash 
 $1000 and gave you a new note at 6 mo., with interest at 6% 
 for the balance due. What was the face of the new note? 
 Sept. 1, 1906, Irwin & Co. paid you $200, and Dec. 1, $300, on 
 their note of July 30. What was due on the note Feb. 9, 1907? 
 
 3. On the note below indorsements were made as follows: 
 May 1, 1906, $75; Sept. 2, 1906, $90; Oct. 2, 1906, $165; 
 Jan. 2, 1907, $125. 
 
 $825.40 OMAHA, NEB., Jan. 2, 1906. 
 
 Apr. 2, 1907, I promise to pay Wilson & Allen, or order, 
 Eight Hundred Twenty-five -^-fa Dollars, at their office, with 
 interest at 6 %. 
 
 Value received. JOHN D. AVERILL. 
 
 What was due at the maturity of the note ? 
 
 4. Find the amount due on each of the following notes July 
 1, 1907 : 
 
PARTIAL PAYMENTS 
 
 335 
 
 a. 
 
 Rochester, Jtf.., 
 
 the order 
 
 <^^^ "/ 
 
 ^k^ promise to pay to 
 
 Value received 
 
 I. 
 
 t/ie order f 
 
 
 to pay to 
 
 Value received 
 / 9),,* 
 
 s -s 
 
 paytotke order 
 
 6/ 
 date, for value received- 
 
 to 
 
 Collar, 
 
 - , with interest at the rate of^2^per centum 
 per annum during the said^^L^L&ZL^ and for such further time as the 
 said principal sum or any part thereof shall remain unpaid. 
 
336 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 *N V 
 
 N CM 
 X X 
 
PARTIAL PAYMENTS 337 
 
 THE MERCHANTS' METHOD 
 
 ORAL EXERCISE 
 
 1. A note for 1500 is dated July 1, 1906, payable in 1 yr. 
 with interest at 6%. If no payments have been made, what is 
 due on the note July 1, 1907 ? 
 
 2. A payment of $300 was indorsed on the note Jan. 1, 1907. 
 What was the amount of this payment at the time the note be- 
 came due ? 
 
 3. If the value of the note at maturity is $530 and the value 
 of the payment $309, what is the balance due ? 
 
 4. By the United States method what is the balance due at 
 maturity on the note described in problems 1 and 3 ? How 
 does this balance compare with the balance in problem 3 ? 
 
 416. The merchants' method is based on custom rather than 
 on legal authority. It is used by most banks and business men 
 on short-time notes and other obligations. 
 
 The principles of the merchants' method are suggested in problems 1-3. 
 This method provides that : (1) the face of the note shall draw interest to the 
 date of settlement; (2) interest shall be allowed on each payment from the 
 time it is made to the date of settlement. 
 
 417. Example. On a note for $600, dated May 13, 1907, pay- 
 able on demand, with interest at 6%, payments were made as 
 follows: June 28, 1907, $100; Aug. 28, 1907, $200. What was 
 due at settlement, Sept. 28, 1907? 
 
 SOLUTION 
 
 Face of note May 13, 1907 . $600.00 
 
 Interest from May 13, 1907, to Sept. 28, 1907 (4 mo. 15 da.) . . 13.50 
 
 Value of note Sept. 28, 1907, the date of settlement . . . $613.50 
 
 Payment June 28, 1907 $100.00 
 
 Interest on this payment from Aug. 28, 1907, to Sept. 28, 
 
 1907 (3 ino.) . . 1.50 
 
 Payment Aug. 28, 1907 200.00 
 
 Interest on this payment from Aug. 28, 1907, to Sept. 28, 
 
 1907 (1 mo.) 1.00 
 
 Value of the payments Sept. 28, 1907, the date of settlement . $302.50 
 
 Balance due Sept. 28, 1907, the date of settlement .... $311.00 
 
338 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 Some houses find the time by compound subtraction and some use the 
 exact number of days. In the following exercise find the difference in time 
 by compound subtraction in problems 1-2, and use the exact number of days 
 in problems 3-7. 
 
 WRITTEN EXERCISE 
 
 1. Solve problem a, page 335, by the merchants' method for 
 partial payments. Compare the results by the two methods. 
 
 2. On a note for 11200, dated Apr. 16, 1906, payable on de- 
 mand, with interest at 4| %, payments were made as follows: 
 June 15, 1907, 1500; July 18, 1907, $200. What was due at 
 settlement, Sept. 16, 1907 ? 
 
 3. June 15 you borrowed $25,000 at Traders' National Bank 
 on your demand note secured by a deposit of 300 shares of New 
 York, New Haven, and Hartford Railroad Stock at $170. June 
 27 you paid $5000, July 2, $10,000, and July 30, $5000. 
 Aug. 2 you paid the remainder of the note and interest, and 
 withdrew the collaterals. What was the amount of the last 
 payment, money being loaned at 4| % ? 
 
 4. The following is a partial page of the demand and loan 
 register of a large bank. Copy it, supplying the amount of 
 interest due Nov. 15, money being loaned at 4| %. 
 
 CHARLES W. SHERMAN 
 
 No. 
 
 DATE 
 LOANED 
 
 AMOUNT 
 LOANED 
 
 DATE OF 
 PAYMENT. 
 
 PART OF 
 LOAN 
 PAID 
 
 BALANCE 
 OF LOAN 
 
 INTER- 
 EST 
 
 COLLATERAL 
 
 VALUE on 
 COLLAT- 
 ERAL 
 
 347 
 
 Apr. 
 
 1 
 
 20,000 
 
 00 
 
 May 
 
 15 
 
 5,000 
 
 00 
 
 15,000 
 
 00 
 
 ??? 
 
 ?? 
 
 250 shares 
 
 
 
 
 
 
 
 
 July 
 
 1 
 
 5,000 00 
 
 10,00000;??? 
 
 ?? 
 
 Penn. R.R. 
 
 
 
 
 
 
 
 
 Sept. 
 
 1 
 
 6,000 00 
 
 4,000 
 
 00??? 
 
 ?? 
 
 Stock . . 
 
 31,250 
 
 00 
 
 
 
 
 
 
 Nov. 
 
 15 
 
 4,000 
 
 00 
 
 
 1??? 
 
 T? 
 
 
 
 
 The balance due by the merchants' method may be found in the manner 
 suggested by the above account. The interest is found on the face of the 
 note to the date of the first payment. The payment is deducted and the in- 
 terest found on the balance to the date of the second payment, and so on. 
 The results obtained by this process are exactly the same as the results ob- 
 tained by 416. 
 
PARTIAL PAYMENTS 339 
 
 5. Solve problem 4 by the United States method and com- 
 pare the result with the merchants' method. 
 
 6. Assuming that the collateral note, page 330, has the fol- 
 lowing payments indorsed on its back, find the amount due at 
 final settlement, Feb. 28, 1907. Indorsements: Jan. 15, 1907, 
 13000 ; Jan. 31, 1907, 15000 ; Feb. 5, 1907, $1000. 
 
 7. A collateral note dated at Philadelphia, Pa., July 10, 1907, 
 for $20,000 payable at the Quaker City National Bank is in- 
 dorsed as follows : Aug. 8, 1907, $3500 ; Sept. 12, 1907, 17500 ; 
 Nov. 19, 1907, 14000 ; Dec. 31, 1907, $5000. What was due 
 on the note Dec. 31, 1907, interest being at the rate of 4 % ? 
 
 To solve the problem copy and complete the following interest statement : 
 
 Philadelphia, _ ^>T^ 2-0 1 _ 19 
 
 To THE QUAKER CITY NATIONAL BANK, Dr. 
 
 To interest on demand loans, as follows: 
 
 $.,./?/? tftf-^ from ?//0 tn f/f _ , 2-& fkys, $ ? 
 
 $/^ ^7/7-^ from f /f to ?//2_ __cJ!^I_days f $ ? 
 
 $ ^^7^7/7 from ?// 2. to "//0 ? ? Jays, $ ? 
 
 ^ frnm ''/? / >n ' '/? ? _ ? .? A*ys, $ ? 
 
 Please send us the above interest on or \*Stw* 
 
 CASHIER 
 
 8. Make an interest statement, similar to the above, for 
 problem 6. 
 
 9. Make an interest statement, similar to the above, for 
 problem 3. 
 
 10. Bring to the class a canceled note on which partial pay- 
 ments are recorded. Find, by the United States method and by 
 the merchants' method, the amount required to cancel the note. 
 Which method is the better for the debtor? for the creditor? 
 
CHAPTER XXVIII 
 
 BANKERS' DAILY BALANCES 
 
 418. Some commercial banks and trust companies pay inter- 
 est on the daily balances of their depositors. 
 
 Whether interest shall be allowed on a depositor's account is usually 
 determined by the size of his daily balances. As a rule, no interest is 
 allowed on small balances subject to check. All balances not subject to 
 check usually draw interest. In an active account, that is, an account in which 
 the balance changes frequently, interest is seldom allowed except on an even 
 number of hundred dollars, and all parts of a hundred dollars are rejected. 
 
 The form of the book in which accounts with depositors are recorded 
 varies in different sections. What is known as the Boston individual ledger 
 (see form, page 38) is extensively used. Another form of depositors' ledger 
 is that shown in the example below. 
 
 419. Example. Verify the balance due on the following 
 account Mar. 1, 1907, interest settlements being made monthly 
 at 3%. 
 
 M. W. P^ARNHAM 
 
 EXPLANATION 
 
 DATE 
 
 F. 
 
 DEBIT 
 
 BALANCE 
 
 CREDIT 
 
 F. 
 
 DATE 
 
 Kxi'I.ANATION 
 
 
 1907 
 
 
 
 
 
 
 
 
 
 
 1907 
 
 
 
 
 
 
 
 
 
 1056 
 
 25 
 
 
 
 
 Jan. 
 
 1 
 
 
 
 
 
 
 
 
 1656 
 
 25 
 
 600 
 
 00 
 
 15 
 
 
 7 
 
 Currency 
 
 
 
 
 
 
 
 2556 
 
 25 
 
 900 
 
 00 
 
 15 
 
 
 11 
 
 N. Y. draft 
 
 Check 
 
 Jan. 
 
 15 
 
 14 
 
 510 
 
 00 
 
 2046 
 
 25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3746 
 
 25 
 
 1700 
 
 00 
 
 17 
 
 Jan. 
 
 22 
 
 N. Y. draft 
 
 Note 
 
 Jan. 
 
 25 
 
 16 
 
 210 
 
 00 
 
 3536 
 
 25 
 
 
 
 
 
 
 
 Check 
 
 
 28 
 
 16 
 
 500 
 
 00 
 
 3036 
 
 25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3042 
 
 08 
 
 5 
 
 83 
 
 17 
 
 Jan. 
 
 31 
 
 Interest 
 
 
 
 
 
 
 
 4042 
 
 08 
 
 1000 
 
 00 
 
 21 
 
 Feb. 
 
 8 
 
 N. Y. draft 
 
 Check 
 
 Feb. 
 
 15 
 
 20 
 
 500 
 
 00 
 
 3542 
 
 08 
 
 
 
 
 
 
 
 Check 
 
 
 22 
 
 22 
 
 1340 
 
 00 
 
 2202 
 
 08 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2209 
 
 49 
 
 7 
 
 41 
 
 23 
 
 Feb. 
 
 28 
 
 Interest 
 
 SOLUTION. The credit slip on page 341 shows a form used for recording the 
 daily balances. Only two money columns are used, one for hundreds and the 
 other for thousands. No interest is computed except on an even number of 
 hundred dollars, and all parts of a hundred dollars are rejected. 
 
 340 
 
BANKERS' DAILY BALANCES 
 
 341 
 
 Beginning with Jan. 1 the daily balance of M. W. Farnkam's account for 
 6 da. was $1056.25; record $1000 on the credit slip as shown in the margin. 
 A deposit of $600 was made Jan. 7, making the balance $1656.25 for the next 
 4 da.; record $1600 on the credit slip as shown in the margin. A deposit of 
 $900 on Jan. 11 made the balance $2556.25 
 for the next 4 da.; record $2500 on the 
 credit slip as shown in the margin. A with- 
 drawal of $ 510 on Jan. 15 left a balance of 
 $2046.25 for the next 7 da.; record $2000 
 on the credit slip as shown in the margin. 
 A deposit of $1700 on Jan. 22 made the 
 balance $3746.25 for the next 3 da.; record 
 $3700 on the credit slip as shown in the mar- 
 gin. A withdrawal of $210 on Jan. 25 left 
 a balance of $3536.25 for the next 3 da.; 
 record $3500 on the credit slip. A with- 
 drawal of $500 on Jan. 28 left a balance of 
 $3036.25 for the next 4 da. This records 
 the balance for each day in January. Add- 
 ing these balances the result is $70,000, and 
 the interest on this sum for 1 da. at 3% is 
 $ 5. 83. Adding $ 5. 83 to $ 3036. 25 gives the 
 balance to the credit of the depositor Feb. 1 
 as $3042.08. 
 
 Enter the daily balances for February as 
 shown in the margin. The result is found 
 to be $88,900, and the interest on this sum 
 for 1 da. at 3% is $7.41. $7.41 added to 
 the balance of the depositor's account Feb. 
 28 gives $ 2209.41 as the balance to his credit 
 beginning Mar. 1. 
 
 In practice the daily balances are usually 
 written as shown in the February column 
 of the accompanying credit slip. The total 
 is then found by multiplication and addi- 
 tion. Thus, the total of the February col- 
 umn is 7 x $3000 + 7 x $4000 + 7 x $3500 
 
 DAILY CREDIT BALANCES 
 
 M. W. Farnham 
 
 1907 
 
 JAN. 
 
 FEB. 
 
 1 
 
 1 
 
 
 3 
 
 
 2 
 
 1 
 
 
 
 
 3 
 
 1 
 
 
 
 
 4 
 
 1 
 
 
 
 
 5 
 
 1 
 
 
 
 
 6 
 
 1 
 
 
 
 
 7 
 
 1 
 
 6 
 
 
 
 8 
 
 1 
 
 6 
 
 4 
 
 
 9 
 
 1 
 
 6 
 
 
 
 10 
 
 1 
 
 6 
 
 
 
 11 
 
 2 
 
 5 
 
 
 
 12 
 
 2 
 
 5 
 
 
 
 13 
 
 2 
 
 5 
 
 
 
 14 
 
 2 
 
 5 
 
 
 
 15 
 
 2 
 
 
 8 
 
 5 
 
 16 
 
 2 
 
 
 
 
 17 
 
 2 
 
 
 
 
 18 
 
 2 
 
 
 
 
 19 
 
 2 
 
 
 
 
 20 
 
 2 
 
 
 
 
 21 
 
 2 
 
 
 
 
 22 
 
 3 
 
 7 
 
 2 
 
 2 
 
 23 
 
 3 
 
 7 
 
 
 
 24 
 
 3 
 
 7 
 
 
 
 25 
 
 3 
 
 5 
 
 
 
 26 
 
 3 
 
 5 
 
 
 
 27 
 
 3 
 
 5 
 
 
 
 28 
 
 3 
 
 
 
 
 29 
 
 3 
 
 
 
 
 30 
 
 3 
 
 
 
 
 31 
 
 3 
 
 
 
 
 Total 
 
 70 
 
 ~0~ 
 
 88 
 
 ~9~ 
 
 Interest 
 
 5 
 
 83 
 
 7 
 
 41 
 
 + 7 x 2200, or $88,900. 
 
 Some accountants also use the pure 
 interest method in finding the amount due. 
 Thus, the interest on $3000 for 7 da., plus the interest on $4000 for 7 da., plus 
 the interest on $3500 for 7 da., plus the interest on $2200 for 7 da. equals $7.41, 
 the same as by the first method. 
 
 In the examples which follow the student may use either of the three methods 
 suggested. 
 
342 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. The Rochester Trust and Safe Deposit Co. allows inter- 
 est to its depositors on daily balances at 3 % per annum, pay- 
 able quarterly. Find the cash balance of the following account 
 with Chas. M. Sherman, Apr. 1, 1907. Jan. 1, 1907, deposited 
 $1200; Jan. 12 drew out 1400; Jan. 30 deposited $800: 
 Jan. 31 drew out $400; Feb. 10 deposited $800; Feb. 25 
 drew out $100 ; Mar. 10 deposited $800 ; Mar. 20 drew out 
 $900 ; Mar. 25 deposited $300. 
 
 2. Mar. 1, 1907, Harvey & Smith's balance with the Fidelity 
 Trust Co. was $2246. During the month they made the follow- 
 ingdeposits: Mar. 3, $2500; Mar. 9, $1750; Mar. 24, $2645.75; 
 Mar. 28, $ 1310. 50 ; Mar. 30, $ 500. They also drew out by check 
 as follows: Mar. 4, $1050; Mar. 6, $2000; Mar. 8,' $720; 
 Mar. 12, $840.50 ; Mar. 16, $450 ; Mar. 19, $430 ; Mar. 23, 
 $1000 ; Mar. 26, $150 ; Mar. 29, $267. How much interest 
 should be credited at the end of the month, the rate being 3 % 
 per annum ? What was the balance of the account after the 
 interest was credited ? 
 
 3. Find the cash balance of the following account May 31, 
 1907, assuming that interest is allowed on daily balances at 3 % 
 and added to the account monthly. 
 
 A. S. OSBOBN 
 
 EXPLANATION 
 
 DATE 
 
 F. 
 
 DEBIT 
 
 BALANCE 
 
 CREDIT 
 
 F. 
 
 DATE 
 
 EXPLANATION 
 
 
 190T 
 
 
 
 
 
 
 
 
 
 
 1907 
 
 
 
 
 
 
 
 
 
 1200 
 
 00 
 
 1200 
 
 00 
 
 
 Mar. 
 
 1 
 
 N. Y. draft 
 
 Check 
 
 Mar. 
 
 12 
 
 
 100 
 
 00 
 
 1500 
 
 00 
 
 400 
 
 00 
 
 
 
 12 
 
 Currency 
 
 
 
 
 
 
 
 2000 
 
 00 
 
 500 
 
 00 
 
 
 
 25 
 
 Currency 
 
 Check 
 
 
 31 
 
 
 100 
 
 00 
 
 2400 
 
 
 500 
 
 00 
 
 
 
 31 
 
 N. Y. draft 
 
 
 
 
 
 
 
 *#** 
 
 *# 
 
 * 
 
 ** 
 
 
 
 31 
 
 Interest 
 
 
 
 
 
 
 
 **** 
 
 ** 
 
 700 
 
 00 
 
 
 Apr. 
 
 15 
 
 N. Y. draft 
 
 Note 
 
 Apr. 
 
 20 
 
 
 50 
 
 00 
 
 **** 
 
 ** 
 
 200 
 
 00 
 
 
 
 20 
 
 N. Y, draft 
 
 Check 
 
 
 30 
 
 
 1200 
 
 00 
 
 *#** 
 
 *# 
 
 * 
 
 ** 
 
 
 
 30 
 
 Interest 
 
 
 
 
 
 
 
 #*** 
 
 ** 
 
 250 
 
 00 
 
 
 May 
 
 10 
 
 Currency 
 
 Check 
 
 May 
 
 31 
 
 
 500 
 
 00 
 
 ***# 
 
 ** 
 
 # 
 
 ** 
 
 
 
 31 
 
 Interest 
 
CHAPTER XXIX 
 
 SAVINGS-BANK ACCOUNTS 
 
 420. A savings bank is an institution, chartered by the state, 
 in which savings or earnings are deposited and put to interest. 
 
 The deposits in a savings bank are practically payable on demand. Most 
 banks reserve the right to require notice of withdrawal from 30 to 60 da. 
 in advance ; but this right is seldom exercised. 
 
 The period of time which must elapse before dividends of interest are 
 declared is called the interest term. Dividends of interest are usually de- 
 clared semiannually ; but in some sections they are declared quarterly. The 
 stated days on which balances begin to draw interest are called interest days. 
 In some savings banks deposits begin to draw interest from the first of each 
 quarter ; in others, from the first of each month. 
 
 In nearly all savings banks, only such sums as have been on deposit for 
 the full time between the interest days draw interest. Thus, if the interest 
 days begin on the first of each quarter, only those sums that have been on 
 deposit for the full quarter draw interest. 
 
 421. Interest is computed on an even number of dollars, 
 and all fractions of a dollar are rejected. When interest is not 
 withdrawn it is placed to the credit of the depositor and draws 
 interest the same as any regular deposit. Savings banks there- 
 fore allow compound interest. 
 
 422. Examples. 1. In the Wildey Institution for Savings 
 the interest term is 6 mo. and the interest days are Jan. 1, 
 Apr. 1, July 1, and Oct. 1. Verify the balance due on the 
 following account Jan. 1, 1907, at 4%. 
 
 SOLUTION. The account was opened July 1, 1906, by a deposit of $500. 
 July 10 this sum was increased by a deposit of $10, making the balance $510; 
 Aug. 14 this sum was diminished by a withdrawal of $ 20, making the balance 
 $490; Oct. 4 this sum was diminished by a withdrawal of $200, making the 
 balance $ 290. The account was similarly increased and diminished until Dec. 
 31, when there was a balance of $300.75 due the depositor. 
 
 343 
 
344 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 i/ne riitdey Institution for Savings 
 
 in account with 
 
 DEPOSITS 
 
 INTEREST 
 
 PAYMENTS 
 
 BALANCE 
 
 2 
 
 2-rt 
 
 / 'ff 
 
 3 
 
 3 / 
 
 a f 
 
 The smallest balance for the first interest period, July 1 to Oct. 1, was 8490. 
 The interest on $490 for 3 mo. at 4% is $4.90. The smallest balance for the 
 second interest period, Oct. 1 to Jan. 1, was .$290. The interest on 8290 for 
 3 mo. at 4% is $2. 90. $4.90 plus $2.90 equals $7.80, the dividend of interest 
 due the depositor Jan. 1. Since this sum is not withdrawn, it is placed to the 
 credit of the depositor, making his balance $308.55. 
 
 2. In the Warren Institution for Savings interest dividends 
 are declared semiannually and the interest days are Jan. 1, 
 Apr. 1, July 1, and Oct. 1. Verify the balance due on the 
 following account Jan. 1, 1907, at 4%. 
 
 barren 3fostttution for 
 
 in account toi 
 
 DATE 
 
 DEPOSITS INTEREST PAYMENTS BALANCE 
 
 ,3 a >o 
 
 / a 
 
 / S) 
 
 - 
 
 - 
 
SAVINGS-BANK ACCOUNTS 
 
 345 
 
 SOLUTION. The smallest balance for the first interest period was $500 ; the 
 interest on $500 for 3 mo. at 4% is $5. The smallest balance for the second 
 interest period was $800; the interest on $800 for 3 mo. at 4% is $8. 
 $ 5 + $8 = $13, the total interest due the depositor July 1. $900 + $ 13 = $ 913. 
 This balance remained unchanged for the next 6 mo. The interest on $913 for 
 6 mo. at 4 % is $ 18.26. $ 913 + $ 18.26 = $ 931.26, the amount due the depositor 
 Jan. 1, 1907. 
 
 WRITTEN EXERCISE 
 
 1. Solve example 1 above, assuming that the interest days 
 are the first day of each month ; also example 2. 
 
 2. Copy the following account, supplying the missing 
 amounts. Interest at 4J % ; interest days, Jan. 1, Apr. 1, July 1, 
 and Oct. 1. 
 
 MANHATTAN SAVINGS BANK 
 IN ACCOUNT WITH Mr. Chas. B. Sherman 
 
 DATE 
 
 
 DEPOSTI 
 
 s 
 
 INTERES 
 
 T 
 
 PAY. MEM 
 
 s 
 
 BALANCI 
 
 l 
 
 1906 
 
 
 
 
 
 
 
 
 
 
 Jan. 
 Jan. 
 
 31 
 
 oOO 
 
 (JU 
 
 
 
 100 
 
 00 
 
 # * # 
 
 # # 
 
 Mar. 
 
 1 
 
 250 
 
 00 
 
 
 
 
 
 * * * 
 
 * * 
 
 May 
 May 
 July 
 
 6 
 31 
 
 1 
 
 100 
 
 00 
 
 # * 
 
 * * 
 
 60 
 
 00 
 
 * *.* 
 
 * * * 
 * * * 
 
 * * 
 * * 
 * * 
 
 3. Copy and complete the following account. Interest at 
 4% ; interest days, Jan. 1, Apr. 1, July 1, and Oct. 1. 
 
 FIDELITY SAVINGS BANK 
 IN ACCOUNT WITH Mr. Frank M. Ellery 
 
 DATE 
 
 DEPOSITS 
 
 INTEREST 
 
 PAYMENTS 
 
 BALANCE 
 
 1906 
 
 
 
 
 
 
 
 
 
 
 Jan. 
 
 1 
 
 300 
 
 00 
 
 
 
 
 
 * * 
 
 * * 
 
 Mar. 
 
 6 
 
 200 
 
 00 
 
 
 
 
 
 # # 
 
 * * 
 
 Mar. 
 
 30 
 
 
 
 
 
 125 
 
 00 
 
 * * 
 
 * 
 
 Apr. 
 
 17 
 
 165 
 
 50 
 
 
 
 
 
 * * 
 
 * 
 
 July 
 
 1 
 
 100 
 
 00 
 
 * # 
 
 * * 
 
 
 
 * * 
 
 * 
 
 Aug. 
 
 15 
 
 
 
 
 
 75 
 
 00 
 
 * * 
 
 * 
 
 Aug. 
 
 31 
 
 58 
 
 40 
 
 
 
 
 
 # * 
 
 * 
 
 Oct. 
 
 1 
 
 250 
 
 00 
 
 
 
 
 
 * * 
 
 * 
 
 Dec. 
 
 1 
 
 
 
 
 
 110 
 
 50 
 
 * * 
 
 * 
 
 1907 
 
 
 
 
 . 
 
 
 
 
 Jan. 
 
 1 
 
 
 
 * # j # # 1 
 
 
 
CHAPTER XXX 
 
 EXCHANGE 
 DOMESTIC EXCHANGE 
 
 ORAL EXERCISE 
 
 1. Mention some objections to sending actual money by 
 express. 
 
 2. If 50 sent by mail in a registered letter is lost, to what 
 extent are the postal authorities liable? 
 
 3. In what ways may you pay a debt at any distant point 
 without actually sending the money ? 
 
 423. The process of settling accounts at distant points with- 
 out actually sending the money is called exchange. 
 
 MONEY ORDERS 
 
 424. Money orders, as issued by post offices, express com- 
 panies, and banks are frequently used in making payments 
 at a distance. 
 
 425. A postal money order is a government order for the 
 payment of money, issued at one office and payable at another. 
 
 UNITED STATES POSTAL MONEY ORDER. 
 
 Boston (Bad Ba) Station), fa; T- 84449 
 
 JUl 26 1907 
 
 346 
 
EXCHANGE 
 
 347 
 
 The fees (rate of exchange) charged for postal money orders are : 
 For orders for sums not exceeding- 
 Over $30.00 to $ 40.00 15? 
 
 $2.50 
 
 3? 
 
 Over 2.50 to $ 5.00 of 
 Over 5.00 to 10.00 8? 
 Over 10.00 to 20.00 10 ? 
 Over 20.00 to 30.00 12? 
 
 Over 40.00 to 50.00 18? 
 
 Over 50.00 to 60.00 20? 
 
 Over 60.00 to 75.00 25? 
 
 Over 75.00 to 100.00 30? 
 
 The maximum amount for which a single postal money order may be 
 issued is <$ 100. When a larger sum is to be sent, additional orders must be 
 obtained. When an order is issued, the money is riot sent from one post 
 office to another. The transfer is merely a matter of bookkeeping, the 
 money being received by the government at one office and paid out at 
 another. If a postal money order is lost, a duplicate may be obtained from 
 the Post Office Department at Washington. 
 
 426. An express money order is an order for the payment of 
 money, issued by an express company and payable at any of its 
 agencies. 
 
 The fees charged for express money orders are the same as those for postal 
 money orders. The maximum amount for which a single express money 
 order may be issued is $50. A postal money order must not bear more 
 than one indorsement ; but an express money order may bear any number 
 of indorsements. 
 
 427. A bank money order (see form, page 348) is an order 
 for the payment of money issued by a bank and payable at 
 certain other banks in different parts of the country. 
 
 The charge for a bank money order is usually the same as that for a postal 
 money order. 
 
348 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 NOT OVER 
 
 FIFTY DOLLARS BOSTON MAS 
 
 428. A telegraphic money order is a telegram of an express 
 or telegraph company, at any given place, ordering the pay- 
 ment of money at another designated place. 
 
 THE UNION TELE.GRAPH CO. 
 
 INCORPORATED 
 
 23,000 OFFICES IN AMERICA 
 
 CABLE SERVICE TO ALL THE WORLD 
 
 ROBERT C. CLOWRY, President and General Manager 
 
 S E N D the following message subject to the 
 terms on back hereof, which are hereby agreed to. 
 
 The Union Telegraph Co. 
 
 Boston, Mass., July 27, 
 
 19 
 
 Rochester. N.Y. 
 
 Findable 
 
 Charles 
 
 Osgood 
 
 ten East Avenue 
 
 Fi chant 
 
 Findelkind 
 
 The Union 
 
 Telegraph 
 
 Co. 
 
 These telegrams are usually in cipher; that is, in a language not under- 
 stood by those who are unfamiliar with the system of abbreviations 
 (code) used. The sender and the receiver must each have a code. The 
 following code will illustrate the principle of telegraphing in cipher : 
 CODE WORD MEANING 
 
 Fichant One hundred dollars 
 
 Ficheron One thousand dollars 
 
 Findable Please pay of your city $ 
 
 Findelkind On production by him of positive evidence 
 
 of his personal identity. 
 
 The principle of a telegraphic money order is the same as that of a postal 
 money order; no money is transferred from one place to another. The 
 charge for an order is usually 1% of the amount to be transmitted plus 
 twice the rate for a single ten-word message. 
 
EXCHANGE 349 
 
 The following are the rates for a ten-word message from Boston to the 
 places named : 
 
 New York $0.25 Chicago $0.50 Galveston $0.75 
 
 Philadelphia $0.25 San Francisco $1.00 Rochester $0.35 
 
 ORAL EXERCISE 
 
 1. What was the total cost to the sender of the postal 
 money order, page 346? the express money order, page 347? 
 the telegraphic money order, page 348? the bank money order, 
 page 348 ? 
 
 2. What will be the total cost of a postal money order for 
 27f? 12.19? 15.28? 110.40? $18.90? 145.10? $35.89? $125 
 ($100 + $25)? $75.29? $49.82? $127.16? 
 
 3. What will be the total cost of an express money order for 
 $6.20? $28.80? $19.50? $27.95? $48.90? $65 ($50 +$15)? 
 $111? $37.59? $41.72? $65.59? $114? 
 
 4. What will be the total cost of a telegraphic money order 
 from Boston to New York for $50? $75? $100? $125? $150? 
 $200? $300? $400? $450? $500? from Boston to Phila- 
 delphia? from Boston to San Francisco? from Boston to 
 Chicago ? 
 
 5. Translate the following telegraphic money order : Find- 
 able F. J. Reed, 20 Park St. ficheron findelkind. How much 
 will it cost for such an order from Boston to Galveston? from 
 Boston to Chicago? from Rochester to Boston? 
 
 WRITTEN EXERCISE 
 
 1. Find the total cost of 5 postal money orders for the fol- 
 lowing amounts : $3.10; $8.19; $25.06; $18.50; $20. 
 
 2. Find the total cost of six express money orders for the 
 following amounts : $1.25; $10; $6.80; $16.25; $80; $19.50. 
 
 3. Find the total cost of the following telegraphic money 
 orders: one from Boston to New York for $50; one from 
 Boston to Philadelphia for $500; one from Boston to San 
 Francisco for $175; one from Boston to Galveston for $300; 
 one from Boston to Rochester for $250. 
 
350 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 CHECKS AND BANK DRAFTS 
 
 429. Business men usually keep their money on deposit with 
 a commercial bank or trust company and make most payments, 
 at home and at a distance, by check; that is, an order on a 
 bank from one of its depositors for the payment of money. 
 
 A check may be drawn for any amount so long as it does not exceed the 
 balance on deposit to the credit of the drawer. It may be drawn payable 
 to : (1) the order of a designated payee, in which case the payee must 
 indorse it before the money will be paid over; (2) the payee, or bearer, in 
 which case any one can collect it ; (3) " Cash," in which case any one can 
 
 collect it. 
 
 C.B. Sherman & Co. and E. II. 
 Robinson & Co. in the foregoing 
 check both reside in Boston. On 
 receiving the check, E. II. Rob- 
 inson & Co. indorse it and de- 
 posit it for credit with their 
 bank, say the National Shawmut 
 Bank. The First National Bank 
 and the National Shawmut 
 Bank, as well as each of the 
 other banks in the city, has 
 many depositors who draw 
 INTERIOR VIEW OF A CLEARING HOUSE. checks upon it which are de- 
 posited by the payees in various other city banks, and it also receives daily 
 for credit from its own depositors checks drawn upon various other city 
 banks. 
 
 Each bank therefore has a daily balance to settle or to be settled with 
 each of the other banks. To some it has payments to make and from 
 others it has payments to receive. If these balances were adjusted in 
 money, each bank would have to send a messenger to each of the debtor 
 
EXCHANGE 351 
 
 banks to present accounts and receive balances. This would be a risky 
 and laborious task. To facilitate the daily exchanges of items and settle- 
 ments of balances resulting from such exchanges there has been established 
 in every large city a central agency, called a clearing house. This agency 
 is an association of banks which pay the expense of conducting it in pro- 
 portion to the average amount of their clearings. 
 
 Suppose, for example, that the banks constituting a clearing house are 
 Nos. 1, 2, 3, and 4. No. 1 presents at the clearing house items against Nos. 
 2, 3, and 4, and Nos. 2, 3, and 4 present items against No. 1. So, likewise, 
 with No. 2 and each of the other banks. In the clearing house there are usually 
 two longitudinal columns contain ing as many desks as there are banks in the 
 association. At a given time a settling clerk from each bank takes his place 
 at his desk inside of one of the columns and a delivery clerk from each bank 
 takes his place outside the column. Each delivery clerk advances, one desk 
 at a time, and hands over to each settling clerk his exchange items against that 
 
 bank. After the circuit of the desks has ^__ 
 
 been completed each delivery clerk is at OC 
 
 the point from which he started, and each 
 
 settling clerk has on his desk the claims of 
 
 all of the other banks against his bank. 
 
 Each settling clerk then compares his 
 
 claims against other banks with those of 
 
 other banks against him and strikes a 
 
 balance. This balance may be in favor 
 
 of or against the clearing house. If No. 1 brought claims against Nos. 2, 3, 
 
 and 4 aggregating $211,000 and Nos. 2, 3, and 4 brought claims against 
 
 No. 1 aggregating $200,000, there is $11,000 due No. 1 from the clearing 
 
 house. But if No. 1 brought to the clearing house exchange items 
 
 aggregating $200,000 and took away exchange items aggregating $211,000, 
 
 there is $11,000 due the clearing house from No. 1. So, likewise, with 
 
 No. 2 and each of the other banks. When all of the exchanges have 
 
 been completed, the clearing house will have paid out the same amount 
 
 that it has received. 
 
 But all checks received by banks are not payable in the city. Suppose 
 that A. W. Palmer, of Chicago, 111., owes C. B. Andrews, of Westfield, 
 Mass., $500 and that the amount is paid by a check on the City National 
 Bank of Chicago. C. B. Andrews receives the check and offers it for credit at 
 the Farmers and Traders Bank of Westfield, Mass. The Westfield Bank has 
 no account with any Chicago bank, but it has with the First National Bank 
 of Boston, and the check is sent to that bank for credit. The First National 
 Bank wishes to increase its New York balance and the check is forwarded 
 to Chemical National Bank of New York for credit. Chemical National 
 Bank next mails the check to Commercial National Bank of Chicago, the 
 
352 PRACTICAL BUSINESS ARITHMETIC 
 
 bank with which it has regular dealings in that city. Commercial 
 National Bank sends the check to the clearing house and it is carried 
 to the City National Bank by a messenger from that bank. Thus, all of a 
 depositor's checks will in time be presented to the bank on which they are 
 drawn. When presented, they will be charged to the depositor, cancelled, and 
 later returned to him to be filed as receipts. 
 
 Banks frequently charge their depositors a small fee (rate of exchange) 
 for collecting out-of-town checks. This fee is rarely over ^%, but there is 
 no uniformity in the matter. Sometimes when a customer keeps a large 
 bank account, no charge whatever is made for the collection. 
 
 430. It often happens that a person will find it necessary to 
 make payment to one who does not care to take the risk of a 
 private check or to one who should not be called upon to pay 
 the cost of cashing a check. In such cases some other form of 
 instrument of transfer must be used. A very common and con- 
 venient method of making a remittance is by means of a check 
 of one banking institution upon another called a bank draft. 
 
 ^Boston, 
 
 traders ^National djanK 
 
 /- 
 
 y * 
 
 ^^ 
 
 Jo (3/iemical ^National 
 Jfeu, 
 
 
 Banks in the different cities frequently keep running accounts with each 
 other and make periodical settlements. At the time of drawing the above 
 draft Traders National Bank of Boston very likely has checks and drafts 
 drawn upon New York banks which it has received from its depositors. 
 These it sends to Chemical National Bank to cover the amount of the draft. 
 Corresponding transactions may also take place in New York. Chemical 
 National Bank may sell its draft on Traders National Bank and, to cover 
 the amount, remit checks and drafts on Boston banks which it has received 
 from its depositors. What is occurring between these two places is also 
 occurring between all manner of places ; but drafts upon New York banks 
 and other financial centers are the most used in making remittances. 
 
EXCHANGE 353 
 
 A bank draft is sometimes drawn payable to the one to whom it is to be 
 sent. It is better, however, to have it drawn payable to the purchaser who 
 may indorse it over to the person to whom it is to be sent. In this way 
 the name of the sender appears on the draft, and when canceled, the draft 
 will serve the purpose of a receipt. Banks usually sell drafts at a slight 
 premium on the face. This premium is called exchange. It varies somewhat 
 (see page 358), but is seldom more than ^%. 
 
 431. There are still other methods of transmitting funds 
 through the instrumentality of a bank. A depositor may ex- 
 change his own check for that of a cashier's check. The latter, 
 being a check of the cashier on his own bank, would pass among 
 strangers better than a depositor's check. 
 
 Boston, Mass., (^t^is /? 19 
 
 ^r f 
 
 NATIONAL SHAWMUT BANK 
 ) 
 
 the order of (^^*z^^~*7 X/^^Z-^^ $ 2 **/<& ^~ 
 
 ^ 
 
 Dollars 
 
 Cshier 
 
 Iii New York City these checks are occasionally used instead of the New 
 York draft. As New York exchange is in demand in all parts of the 
 country, the expediency of the course is apparent. 
 
 432. By depositing a sum of money in a bank a person may 
 receive a certificate, called a certificate of deposit. This will 
 direct the payment of the sum deposited to any person whom 
 the depositor may name. 
 
 on the return of this certificate properly indorsed. 
 
 The payee in a certificate of deposit will have no difficulty in getting the 
 certificate cashed or the amount credited to him by his bank. 
 
354 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. Assuming that the bank which cashed the check on 
 page 5 charged | % collection, what was the amount credited 
 to the depositor ? 
 
 2. Silas Long of New York deposited the following check. 
 The bank deducted -^ % for collection. How much was placed 
 to Silas Long's credit? 
 
 Union 33anfc 
 
 3. B deposited three out-of-town checks in his bank as fol- 
 lows : $300; |700; 1750. If the bank charged -^% collec- 
 tion, what amount was placed to B's credit? 
 
 4. Bring to the class a number of canceled checks and take 
 several of them and trace them from the time they were issued 
 until they were filed as receipts by the drawer. Show why a 
 canceled check is the best kind of a receipt for the payment of 
 money ? 
 
 5. How much did the bank draft on page 352 cost the pur- 
 chaser if the exchange was at ^ % premium ? 
 
 WRITTEN EXERCISE 
 
 1. Find the cost of a bank draft for $3958.75 at ^ % pre- 
 mium; of a bank draft for $679.80 at ^% premium; of a 
 bank draft for $768.54 at 50 J* per $1000 premium. 
 
 2. To cover the cost of a bank draft bought at -^% pre- 
 mium, I gave my bank a check for $250.25. What was the 
 face of the draft ? What was the rate of premium per $1000? 
 
EXCHANGE 
 
 355 
 
 3. Plow large a bank draft can be bought for $850.85, ex- 
 change being at -fa % premium ? 
 
 4. Find the proceeds of the accompanying deposit, ^% col- 
 lection and exchange being charged on the out-of-town checks. 
 
 THE UNION NATIONAL BANK 
 
 DEPOSITED BY 
 
 Boston, 
 
 L/L^< 
 
 Specie 
 Bills ... 
 Checks . . 
 
 /2-ff 
 
 g 
 
 
 When the receiving teller takes a 
 deposit from a customer, he classifies 
 the items on the deposit ticket, as 
 shown in the accompanying illustra- 
 tion. If the coin and bills passed in 
 count right, these items are checked (V) 
 on the deposit slip; if a check on a 
 clearing house bank is received, it is 
 marked with the number of that bank 
 in the clearing house; if a check on 
 the teller's bank is received, it is 
 marked "B"; if a check on an out-of- 
 town bank is received, it is marked 
 "X." 
 
 5. Write a bank draft using 
 the following data: your ad- 
 dress and the current date; drawer, Central National Bank; 
 drawee, Chemical National Bank, New York; amount, $711.94; 
 payee, C. E. Denison; cashier, your name. How large a check 
 will pay for the draft at ^ % premium? Write the draft. 
 
 6. Suppose that the members of the class whose surnames be- 
 gin with the letters from A to G inclusive have a deposit with 
 Traders National Bank ; that the members whose surnames 
 begin with the letters from H to N inclusive have a deposit 
 with City National Bank ; that the members whose surnames 
 begin with O to S inclusive have a deposit with First National 
 Bank; and that the members whose surnames begin with T to Z 
 inclusive have a deposit with Central Bank. Let each student 
 write a check on his bank in favor of one of his classmates, 
 and let this classmate indorse the check and deposit it with his 
 bank. Then form a clearing house, strike a balance between 
 the different banks, and have these balances adjusted by the 
 payment of school money. 
 
356 PRACTICAL BUSINESS ARITHMETIC 
 
 COMMERCIAL DRAFTS 
 
 433. Business men frequently employ the commercial draft 
 as an aid in the collection of accounts that are past due. 
 
 / 2.60.- 
 
 bf. 
 
 to the ort/er of 
 
 Value received and charge to account of 
 
 The above is a common form of draft used for collection purposes. 
 Edgar McMickle owes Wilbert, Closs & Co. $ 260.50. The amount is due, 
 and Wilbert, Closs & Co. draw a draft on Edgar McMickle and leave it with 
 their Springfield bank for collection. The Springfield bank forwards it to 
 its correspondent in Paterson and this bank sends it by messenger to Edgar 
 McMickle. When he pays the draft, the Paterson bank notifies the Spring- 
 field bank, and that bank deducts a small fee (collection and exchange) for 
 collecting the draft, and credits Wilbert, Closs & Co. for the proceeds. 
 
 434. It has been seen (page 321) that the time draft is fre- 
 quently used in connection with sales of merchandise. 
 
 t? / 
 
 ^ ?Pay to the order of 
 
 dollars 
 
 Value received and charge to account of 
 
 Jfo.^Z 
 
 Suppose Quincy, Bradley & Co. sell L. B. Wade & Co. a bill of merchan- 
 dise amounting to $500. Terms: 30-da. draft for the amount of the bill. 
 The draft, as above, and the bill in regular form would be drawn up and 
 
EXCHANGE 357 
 
 sent to L. B. Wade & Co. for acceptance. The object of drawing a time 
 draft in connection with sales of merchandise is twofold : (1) when ac- 
 cepted, the draft serves as a written contract; (2) since an acceptance is 
 negotiable, it may be discounted and cash realized upon it before maturity. 
 Such a draft is frequently left with a bank for collection instead of being 
 remitted with the bill. The bank will then first present the draft for accept- 
 ance and later for payment. 
 
 ORAL EXERCISE 
 
 1. If you exchange your check for a cashier's check, is there 
 any charge for the accommodation ? 
 
 2. If the sight draft on page 356 was collected by a bank 
 which charged \<J collection, how much was placed to the 
 credit of Wilbert, Gloss & Co.? 
 
 3. You deposited in Shawmut National Bank $5000, received 
 the certificate of deposit shown on page 353, and remitted it 
 to E. B. Stanton on account. Would there be any exchange ? 
 
 WRITTEN EXERCISE 
 
 1. The draft on page 356 was accepted July 17, and dis- 
 counted July 25. If the bank charged -^ % collection and 
 6 % interest, how much was placed to the credit of the drawers ? 
 
 2. Mar. 27 Wilson Bros., Chicago, 111., drew a 30-da. draft 
 on E. W. King, Toledo, O., in favor of themselves, payable 30 da. 
 after date, for 13500, and mailed it for acceptance. Apr. 1 the 
 draft was received accepted; Apr. 2 it was discounted at City 
 Bank. If the charges were ^ % collection and 6 % interest, 
 what amount was credited to Wilson Bros.? 
 
 3. Apr. 17 O. H. Brooks, Buffalo, N.Y., drew a sight draft 
 on Slocum & Co., Hartford, Conn., in favor of himself, for $391, 
 and left it with his bank (First National) for collection. First 
 National Bank sent the draft to its Hartford correspondent 
 (Commercial National), and 5 da. later informed O. H. Brooks 
 that the draft had been collected, and the amount, less ^ % col- 
 lection, placed to his credit. If O. H. Brooks's bank balance 
 was $ 758. 62 before the draft was drawn, what was it after the 
 draft was credited ? Write the draft and show the indorsements. 
 
358 PEACTICAL BUSINESS ARITHMETIC 
 
 4. Aug. 9 you sold C. D. Mead & Co., San Francisco, Cal., 
 39 mahogany sideboards at $ 162. 50, delivered the goods to the 
 Interstate Transportation Co., and received a through bill of 
 lading (receipt for the goods and an agreement to transport 
 and deliver them to the consignee or to his order). You then 
 drew a sight draft on C. D. Mead & Co. in favor of your bank, 
 attached the draft to the bill of lading, and left it with your 
 bank for collection. Your bank indorsed the draft and the bill 
 of lading and sent them to First National Bank of San Fran- 
 cisco for collection and credit. Aug. 23 you received advice 
 that the draft had been collected, and the amount, less | %, 
 placed to your credit. What was the amount credited ? 
 
 When First National Bank of San Francisco received the draft, it notified 
 C. D. Mead & Co. They paid the draft, and the bank gave them the bill of 
 lading. When goods are shipped in this manner, the transportation company 
 will not deliver the goods until the consignee presents the bill of lading. 
 
 FLUCTUATION OF RATES OF EXCHANGE 
 
 435. It has been seen that money orders always sell for more 
 than their face value, and that bank drafts frequently cost a 
 little more than their face value. When exchange costs its 
 face value, it is said to be at par : when it costs more than its 
 face value, it is said to be at a premium ; when it costs less than 
 its face value, it is said to be at a discount. 
 
 On bank drafts for small sums, say $ 500 or less, exchange is usually at 
 a uniform premium. This premium is to pay the banks for their trouble 
 and the expense of shipping money to the centers on which the drafts are 
 drawn, when balances at these points become low. But exchange on the 
 trade centers of the country may be at par at one time, at a premium at 
 another, and at a discount at still another. For example, during the late 
 fall months, when the grain crops begin to be sent East, New York is send- 
 ing a great many checks and drafts to the section of which Chicago is the 
 trade center. Exchange on New York is then very plentiful in Chicago, and 
 if a man in Chicago wished to buy a draft on New York for a large amount, 
 say $10,000 or more, the Chicago banks will sell it to him at a discount. 
 But if a man in New York at that time wished to buy a draft on Chicago 
 for $10,000, he would have to pay a premium, because the New York 
 banks would be anxious not to decrease their Chicago balances. 
 
EXCHANGE 359 
 
 Early in the spring, when New York importers and jobbers are sending 
 foreign and domestic manufactured goods for distribution in the West, a 
 great many checks and drafts are being sent from the West to New York, and 
 exchange is at a discount in New York and at a premium in Chicago. This 
 principle applies at any trade centers between which exchange operations go 
 on. Smaller places make their settlements in or through larger places, and 
 the main exchange transactions go on between the few leading cities, with 
 converging lines on New York. 
 
 The rate of exchange between two cities will never exceed the cost of 
 shipping actual money from one of the cities to the other, except in time of 
 panic or a financial unrest. Thus when the cost of sending money by express 
 from New York to Chicago is $5 per $ 10,000, the discount in New York or 
 the premium in Chicago will not greatly exceed Q% ($5 per $ 10,000). 
 To prevent the rates from going any higher the banks will arrange for the 
 shipment of actual money from New York to Chicago. 
 
 As a rule no charge is made for cashing bank drafts on the trade centers 
 of the country, like New Y r ork, Chicago, and Philadelphia. 
 
 436. It has been seen that banks frequently charge a small 
 fee for collecting paper payable out of town. 
 
 In some cases the rates of collection are more or less arbitrary ; in others 
 they are governed by trade movements, the same as rates of exchange. Jn 
 still others the clearing house association fixes the rate. 
 
 ORAL EXERCISE 
 
 Find the cost of the following bank drafts: 
 
 1. $18,500 at gV % discount ; at 40 j* per 1 1000 premium. 
 
 2. $ 516.90 at -^ % premium ; at 50 per $ 1000 discount. 
 
 3. $1600.80 at 75^ per $1000 premium ; at T ^ % discount. 
 
 4. A draft for $4000 was bought for $3998. Was ex- 
 change at a premium or at a discount, and what rate? 
 
 5. J. E. Smith & Co. drew at sight on E. M. Barrows for 
 $250 and made collection through their bank. If the bank 
 charged -$% for collection, for what amount did J. E. Smith 
 & Co. receive credit ? 
 
 6. During the late fall many checks and drafts are being 
 sent to the southern cities in payment for shipments of cotton. 
 At such times is exchange on New York likely to be at a dis- 
 count or at a premium in New Orleans ? in New York ? 
 
360 PRACTICAL BUSINESS ARITHMETIC 
 
 7. Frank M. Burton wishes to collect an account oi 70.58 
 and for this purpose draws the following draft and leaves it 
 with the National Express Co. for collection. If the express 
 company charges 25^ for collection, how much will it collect 
 of Fred W. Greenlaw ? how much will it pay Frank W. 
 Burton ? 
 
 _Pay to the 
 
 ' 
 
 order of_ 
 
 .Dollars 
 
 Value received and charge the same to account of 
 
 With current rate of Exchange 
 
 To_ 
 
 Wo. Jfe*^^Z^L^X 2fo0r \ 
 
 Note that the draft contains the clause " With current rate of Exchange." 
 This means that the drawee is requested to pay the face of the draft plus 
 the cost of exchange. Nearly all express companies have arrangements by 
 which they undertake the collection of notes and accounts. The process of 
 collecting is simple. The note or draft covering the amount of the account 
 is placed in a collection envelope furnished by the express company, and sent 
 to its destination. Tf collection cannot be made, notice is given with reasons 
 for refusal ; if collection is made, the money is sent back in the collection 
 envelope, and the amount, less collection charges, paid to the one for whom 
 the collection was undertaken. The charge varies with the distance. 
 
 WRITTEN EXERCISE 
 
 1. A bank draft for $15,000 was bought for $14,992.50. 
 Was exchange at a premium or at a discount, and what rate ? 
 At this rate find the cost of a draft for $17,121.98 ; a draft for 
 $12,929.75 ; a draft for $127,162.89. 
 
 2. I gave the American Express Co. an account of $178.50 
 for collection. If the collection charges were $ 2.50 per $1000, 
 how much did I receive from the company? At this rate what 
 should be the proceeds from the collection of three drafts with 
 amounts as follows : $125.60 ; $218.90 ; and $134.50 ? 
 
EXCHANGE 
 
 361 
 
 3. An agent sold for me 1000 T. hay at 117.50 per ton. 
 He paid $125 for cartage, 175 for storage, charged 2J^> com- 
 mission, and remitted the proceeds by a bank draft bought at 
 \<fo premium. What was the face of the draft? 
 
 4. A Boston commission merchant sold for his principal in 
 Chicago 27,518 Ib. leather at 25|^ per pound. If he charged a 
 commission of 4^%, how large a bank draft, bought at $ 1.50 
 per flOOO premium, should he remit to his principal? 
 
 5. Mar. 8 Edward Whitman & Co. drew a draft payable 
 30 da. after date on El wood & Spears for 375.98 and had it 
 discounted at City Bank. If the rate of collection was ^ % 
 and interest 5%, what were the proceeds of the draft? 
 
 6. Copy and complete the following letter of advice, 
 assuming that the rate of collection is \% on Nos. 720 and 
 716, and -fa % on Nos. 692 and 710. Check the results. 
 
 NATIONAL EXCHANGE BANK 
 
 ALBANY, N.Y., &&(>-. 12, 19 
 
 MR. &ka&. 1-i}-. f'fa'm.Lttom,, Cashier 
 7HcA^wunt^> cAat>i;&n>a,t Mdnfa 
 
 DEAR SIR, We credit your account this day for the proceeds of 
 collections as stated below. Respectfully yours, 
 L. H. PIERSON, Cashier 
 
 YOUR NO. 
 
 PAYER 
 
 AMOUNT 
 
 CHARGES 
 
 PROCEEDS 
 
 720 
 
 . e,. initu 
 
 soo 
 
 00 
 
 / 
 
 00 
 
 799 
 
 00 
 
 Yt6 
 
 10. . &wf 
 
 qoo 
 
 75 
 
 * 
 
 ** 
 
 *** 
 
 ** 
 
 6<?g 
 
 (H. <&. /Send ty (&&. 
 
 3750 
 
 50 
 
 * 
 
 ** 
 
 **** 
 
 ** 
 
 7/0 
 
 1&. &. Lo-ny ty / ! wi 
 
 37500 
 
 00 
 
 ** 
 
 ** 
 
 ***** 
 
 ** 
 
 ?*lb/ 
 
 25 
 
 ** 
 
 ** 
 
 ***** 
 
 ** 
 
 
 
 
 
 
 
 
362 PRACTICAL BUSINESS ARITHMETIC 
 
 FOREIGN EXCHANGE 
 
 FOREIGN MONEY 
 
 ORAL EXERCISE 
 
 1. Repeat the table for English money. (See Appendix 
 page 441) ; for French money ; for German money. 
 
 2. What is the value of a pound sterling in United States 
 money ? of a franc ? of a mark? 
 
 3. Express $4866.50 in English money; 100 in United 
 States money. Express $ 1930 in French money ; 1000 fr. in 
 United States money. Express $ 238 in German money; 
 10000 M. in United States money. 
 
 A pound sterling is commonly thought of as about $5; a shilling or a 
 mark as about 25 ^ ; a penny as about 2 ^ ; a franc or lira as about 20 ^ ; a 
 guilder as about 40 J*. In problems 4-6 use these approximations. 
 
 4. Express 1100 as English money ; as German money ; 
 as French money; 1500 guilders in United States money. 
 
 5. Express as United States money: 15; 8 5s. ; 25 
 10s.; 100 M.; 1500 M. ; 1750 M. ; 75 fr. ; 350 fr.; 200 fr. 
 
 6. A and B while abroad spent 3 wk. in Naples, Italy. If 
 their expenses here averaged 25 lire apiece per day, how much 
 was this in United States money for the 3 wk. ? 
 
 WRITTEN EXERCISE 
 
 1. Express as pounds and decimals of a pound : 25 6s. ; 
 150 15s. ; 200 10s. 6d.; 300 12s. M. 
 
 2. Reduce to United States money : 25 10s. ; 120 9s. 
 
 3. Reduce to United States money: 275 M.; 1500 M. 75 pf. ; 
 315 fr.; 725 fr.; 115 10s. Qd. Reduce $1250 to English 
 money ; to French money ; to German money. 
 
 4. In a recent year the funded debt of the German Empire 
 amounted to 2,733,500,000 M., of which 1,240,000,000 M. bore 
 interest at 3|% and 1,493,500,000 M. at 3%. Express in 
 United States money the interest on the funded debt for 1 yr. 
 
EXCHANGE 363 
 
 THE METRIC SYSTEM 
 
 437. The metric system is a system of measures having a 
 decimal scale of relation. It was invented by France, and is 
 now used in practical business in a large part of the civilized 
 world. It has been authorized by law in Great Britain and 
 the United States, but is not generally used in these countries 
 except in foreign trade and in scientific investigations. 
 
 The principal units of the system are the meter for length, the liter for 
 capacity, and the gram for weight. Stibmultiples and multiples of these 
 units are easily learned when the meaning of the prefixes is known. The 
 Latin prefixes, deci, centi, and milli mean respectively 0.1, 0.01, and 0.001 of 
 the unit. The Greek prefixes deca, hekto, kilo, and myria mean respectively, 
 10, 100, 1000, and 10,000 times the unit. 
 
 TABLE OF LENGTH 
 
 10 millimeters (mm.) = 1 centimeter (cm.) .01 meter. 
 
 10 centimeters = 1 decimeter (dm.) = .1 meter. 
 
 10 decimeters = 1 meter (m.) 1. meter. 
 
 10 meters = 1 dekameter (Dm.) = 10. meters. 
 
 10 dekameters = 1 hektometer (Hm.) = 100. meters. 
 
 10 hektometers = 1 kilometer (Km.) 1000. meters. 
 
 10 kilometers = 1 myriameter (Mm.) = 10,000. meters. 
 
 The units in common use are indicated by black-faced type. 
 TABLE OF SQUARE MEASURE 
 
 100 sq. millimeters =1 sq. centimeter (sq. cm.) .001 sq. meter. 
 
 100 sq. centimeters =1 sq. decimeter (sq. dm.) .01 sq. meter. 
 
 100 sq. decimeters =1 sq. meter (sq. m.) 1. sq. meter = 1 centare. 
 
 100 sq. meters =1 sq. dekameter (sq. Dm.) = 100. sq. meters = 1 are. 
 
 100 sq. dekameters =1 sq. hektometer (sq. Hm.)= 10,000. sq. meters =1 hectare. 
 
 100 sq. hektometers = lsq. kilometer (sq. Km.) 1,000,000. sq. meters. 
 
 100 sq. kilometers =1 sq. myriameter (sq. Mm.) =100,000,000. sq. meters. 
 
 The centare, are (a.), and hektare are common terms in land measure- 
 ments. 
 
 TABLE OF CUBIC MEASURE 
 
 1000 cu. millimeters := cu. centimeter (cu. cm.) .000001 cu. m. 
 
 1000 cu. centimeters = 1 cu. decimeter (cu. dm.) .001 cu. m. 
 
 1000 cu. decimeters = 1 cu. meter (cu. m.) 1. cu. m. 
 
 1000 cu. meters = 1 cu- dekameter (cu. Dm.) = 1000. cu. m. 
 
 1000 cu. dekameters == 1 on. hektometer (cu. Hm.) = 1,000,000. cu. m. 
 
 1000 cu. hektometers = 1 cu. kilometer (cu. Km.) 1,000,000,000. cu. m. 
 
 1000 cu. kilometers = 1 cu. myriameter (cu. Mm.) = 1,000,000,000,000. cu. m. 
 
 The cubic meter is also called a stere, a unit used in measuring wood. 
 
364 
 
 PKACTICAL BUSINESS ARITHMETIC 
 
 10 inilliliters (ml.) 
 10 centiliters 
 10 deciliters 
 10 liters 
 10 dekaliters 
 10 hektoliters 
 
 TABLE OF CAPACITY 
 = 1 centiliter (cl.) 
 = 1 deciliter (dt.) 
 = 1 liter (1.) 
 = 1 dekaliter (Dl.) 
 = 1 hektoliter (HI.) 
 = 1 kiloliter (Kl.) 
 
 A liter is the same as a cubic decimeter. 
 
 TABLE OF WEIGHT 
 10 milligrams (mg.) = 1 centigram (eg.) 
 
 10 centigrams 
 10 decigrams 
 10 grams 
 10 dekagrams 
 10 hektograms 
 10 kilograms 
 10 myriagrams 
 10 quintals 
 
 = 1 decigram (dg.) 
 = 1 gram (g.) 
 = 1 dekagram (Dg.) 
 = 1 hektogram (Hg.) 
 = 1 kilogram (Kg.) 
 = 1 myriagram (Mg.) 
 = 1 quintal (Q.) 
 = 1 tonneau (T.) 
 
 The tonneau is usually called a metric ton. 
 
 = .01 liter. 
 .1 liter. 
 = 1. liter. 
 = 10. liters. 
 = 100. liters. 
 = 1000. liters. 
 
 .01 gram. 
 
 1 
 
 gram. 
 
 1. 
 
 gram. 
 
 10. 
 
 grams. 
 
 100. 
 
 grams. 
 
 1000. 
 
 grams. 
 
 = 10,000. 
 
 grams. 
 
 = 100,000. 
 
 grams. 
 
 = 1,000,000. 
 
 grams. 
 
 TABLE OF APPROXIMATE VALUES 
 
 A meter 
 A kilometer 
 A square meter 
 An are 
 An hectare 
 A cubic meter 
 
 = 3Jft. or 1.1 yd. 
 
 = f mi. 
 
 = 1^ sq. rd. 
 
 = 4 sq. rd. 
 
 = 2JA. 
 
 = 1.3 cu. yd. 
 
 A stere = T 3 r cd. 
 
 A gram = 15^ gr. 
 
 A kilogram = 21 lb. av. 
 A liter = 1 qt. 
 
 An hektoliter = 2 bu. 
 A meti-ic ton = 2200 lb. 
 
 ORAL EXERCISE 
 
 1. Name the prefix which means 10,000 ; 0.001 ; 100 ; 0.01 ; 
 10; 0.1; 1000. 
 
 2. Read the following: 2.5m.; 72 mm.; 95.5 cm.; 
 302.05 km. Express 475.125 m. in millimeters ; in hek- 
 tometers. 
 
 3. Which of the divisions of the following scale are 
 millimeters? centimeters? 
 
 , 
 
 ! 2 
 
 
 y 
 
 
 4 
 
 
 5 
 
 
 6 
 
 
 7 
 
 
 8 
 
 
 y 
 
 
 10 
 
 imiini 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 decimeter 
 
EXCHANGE 365 
 
 4. A certain tower is 200 m. high; this is approximately 
 how many feet? 
 
 5. How many square meters in 1 a. ? how many ares in 
 5 Ha. ? in 25 Ha. ? 
 
 6. How many liters in 1 cu. m.? in 5 cu. m.? Find the 
 cost of 5 Kl. of milk at 5^ a liter ; at 4^ a liter. 
 
 7. Find the length of your schoolroom in meters; the 
 weight of any familiar object in kilograms. 
 
 8. Bought 1000 m. of cloth. How many yards was this ? 
 
 9. An importer bought 1000 1. of liquors at 80^ a liter. If 
 he sold it at $ 3.50 per gallon, did he gain or lose, and how much ? 
 
 10. The distance from Paris to Cologne is 510 Km.; from 
 Cologne to Mainz 150 Km. Express these distances in miles. 
 
 WRITTEN EXERCISE 
 
 1. At $75 an acre find the cost of 75 Ha. of land. 
 
 2. Find the cost of 175.75 m. of lace at 65^ a meter. 
 
 3. How many steres of wood in a pile 12 m. long, 1.5 m. 
 wide, and 3 m. high? How many cords? 
 
 4. A merchant bought cloth at 11.14 per meter, including 
 duties. For how much must he sell it per yard to gain 33|%? 
 
 5. I imported 1000 m. of silk (see duties, page 288) at 10 fr. 
 per meter and sold it at 3 per yard. Did I gain or lose and 
 how much, the silk being 1 yd. wide? 
 
 6. The distance between two places on a map is 15.5 cm. ; 
 this is 10-^00 of the actual distance. What is the actual dis- 
 tance in miles? 
 
 7. C bought cloth at f> 2 per meter, including duties, and 
 sold it by the yard at a gain of 25%. What was the selling 
 price per yard? 
 
 8. The speed rate of a certain express train is 64 Km. an 
 hour ; of a certain mail train, 48 Km. an hour. In a journey of 
 384 Km. what time will be saved by taking the express instead 
 of the mail train. 
 
366 PRACTICAL BUSINESS ARITHMETIC 
 
 FOREIGN MONEY ORDERS 
 
 438. Small sums are frequently sent from one country to 
 another by means of foreign money orders. 
 
 The international postal money order and the foreign express money order 
 or check are both extensively used for this purpose. These orders are 
 usually drawn payable in the money of the country on which they are issued. 
 They are similar in form to domestic money orders, but are issued on prac- 
 tically the same principle as the ordinary bank draft. 
 
 ORAL EXERCISE 
 
 1. D in Chicago wishes to send E in Havre, France, 780 fr. 
 At 19.5^ to the franc, how large an express money order (in 
 francs) can he buy ? 
 
 2. B in New York wishes to send $120 to C in Leipzig, 
 Germany. At 24^ to the mark, how large an express money 
 order (in marks) can he buy ? 
 
 3. At \/o premium find the cost of an international money 
 order, payable in Great Britain, for each of the following 
 amounts: $40; $50; 175; $100; $150; $200. 
 
 4. A in Boston bought an international money order for 
 $20 and sent it to a friend in Liverpool, England. At 1% 
 premium, what did the order cost? For how many pounds 
 sterling (approximately) was it issued ? 
 
 WRITTEN EXERCISE 
 
 1. I wish to send $100 to G in Holland. At 40| ^ to the 
 guilder, how large an express money order can I buy ? 
 
 2. I wish to send $50 to a friend in Scotland. At $4.87 to 
 the pound, how large an express money order can I buy ? 
 
 3. C in Chicago sent D in Geneva an express money order 
 for 256.41 fr. At 19.5^ to the franc, how much did the order 
 cost C ? 
 
 4. E in Philadelphia sent F in Naples an international postal 
 money order for 128.21 lira. At 19.5^ to the lira, how much 
 did the order cost E ? 
 
EXCHANGE 
 
 367 
 
 BILLS OF EXCHANGE 
 
 439. Drafts of a person or a bank in one country on a person 
 or a bank in another country are usually called bills of exchange. 
 
 ? 
 
 94.3K1 
 
 -//, JU1 10 1906 
 
 MESS 1 ?? liKOTOT, SUIPLKY A CO. 
 
 a 
 
 
 
 440. Bills of exchange may be divided into three classes: 
 (1) bankers' bills, which are drawn by one banker upon an- 
 other ; (2) commercial bills, which are drawn by one mer- 
 chant upon another ; (3) documentary bills, which are drawn 
 by one merchant upon another and secured by the assignment 
 and transfer of a bill of lading and policy of insurance covering 
 merchandise on its way to the market. 
 
 The foregoing form is a bankers' demand draft or check. 
 
 Bankers' bills of exchange are frequently issued in duplicate ; that is, in 
 sets of two of like tenor and amount. These bills are sometimes sent by 
 different mails; but more frequently the original is sent and the duplicate 
 is placed on file to be sent in case of necessity. Duplicate bills are so con- 
 ditioned that the payment of one of them cancels the other. The bankers' 
 sole bill of exchange is also used. This is preferred by many, inasmuch as 
 it may be more easily negotiated by the payee when he resides in a city other 
 than the one drawn upon. Commercial and documentary bills of exchange 
 are usually issued in duplicate. 
 
 441. The mint par of exchange is the actual value of the 
 pure metal in the monetary unit of one country expressed in 
 terms of another. 
 
368 PRACTICAL BUSINESS ARITHMETIC 
 
 The mint par of exchange is determined by dividing the weight of pure 
 gold in the monetary unit of one country by the weight of pure gold in the 
 monetary unit of another. Thus, the United States gold dollar contains 
 23.22 troy grains of pure gold and the English pound sterling, 113.0016 troy 
 grains. 113.0016 +-23.22 = 4.8665. Since there is 4.8665 times as much pure 
 gold in the pound sterling as in the gold dollar, the pound sterling is worth 
 4.8665 times $1, or $4.8665. The mint par of exchange is used mainly in 
 determining the values on which to compute customs duties. 
 
 442. The rate of exchange is the market value in one 
 country of the bills of exchange on another. 
 
 The price paid for bills of exchange fluctuates. When the United States 
 owes Great Britain exactly the same amount that Great Britain owes the 
 United States, the debts between these countries can be paid without the 
 transmission of money, and exchange is at par. But when Great Britain 
 owes the United States a greater amount than the United States owes 
 Great Britain, exchange in the United States is at a discount and in Great 
 Britain at a premium, and vice versa. The rates of premium or discount 
 are limited by the cost of shipping gold bullion from one country to another. 
 The cost of shipping gold from New York to London is about f %. There- 
 fore, when A in New York owes B in London, and A cannot buy a bill of 
 exchange on London for less than $4.88^ to $4.89, it is cheaper for him to 
 export gold. On the other hand, if D in London owes C in New York and 
 C cannot sell a draft on D for more than $4.83| to $4.84, it is cheaper for 
 him to import gold. The greater part of exchange is drawn on Great 
 Britain, France, Germany, Holland, Belgium, and Switzerland. Because 
 London is the financial center of the world, probably more foreign exchange 
 is drawn on Great Britain than on all the other countries combined. 
 
 443. Exchange on Great Britain is usually quoted at the 
 number of dollars to the pound sterling ; exchange on France, 
 Belgium, and Switzerland, at the number of francs to the dollar ; 
 exchange on Germany, at the number of cents to each four marks; 
 exchange on Holland, at the number of cents to each guilder. 
 
 The accompanying foreign exchange rates were quoted recently. 
 
 In Great Britain 3 da. of 60 Days Demand 
 
 grace are allowed on all bills K^ y ;Veich; m arkV.V.:V.V.V:.:.V 4 ^ *S8 
 drawn payable after sight, but France, francs 5 i<;% 5 .15 
 
 r J Belgium 5.18% 5.15% 
 
 drafts on Great Britain payable Switzerland, francs B-18% 5.15% 
 
 , . , , j v Holland, guilders 40 40% 
 
 at sight or on demand have no 
 
 grace. There are no days of grace allowed on any drafts drawn on Germany, 
 
 and nearly all Europe, excepting Holland, where 1 da. of grace is allowed. 
 
EXCHANGE 
 
 369 
 
 j. 6000 M. 
 k. 4000 M. 
 1. 12000 M. 
 
 WRITTEN EXERCISE 
 
 1. Using the foregoing table of quotations, or current quota- 
 tions clipped from any daily newspaper, find the cost of de- 
 mand drafts for each of the following amounts : 
 
 a. 100. d. 160 guilders. g. 200 M. 
 
 b. 1200. e. 240 guilders. h. 160 M. 
 
 c. 1800. /. 1200 guilders. i. 2000 M. 
 
 2. Find the cost of a 60-da. draft for each of the amounts 
 in problem 1. 
 
 WRITTEN EXERCISE 
 
 1. F. M. Cole & Co., importers, Boston, owe Richard Roe, 
 London, 525 10s., 6d., buy by check the draft illustrated on 
 page 367, and remit it in full of account. If exchange on 
 London is $4.87-J, what was the amount of the check ? 
 
 2. Jordan, Marsh & Co. wish to import a quantity of woolen 
 goods from Bradford, England. They make up an order and 
 inclose in payment the following draft which they buy by 
 check, at $4.85^. What was the amount of the check? 
 
 MESS9?BROW^f,SHIHLEY*CO. 
 
 ^q. 3497 
 
 3. 45 da. before the draft was due (problem 2) John Smith 
 & Co. sold it to Baring Bros, at 2% discount. How much 
 (in English money) did they receive ? Write the indorsements 
 which would appear on the back of the draft. 
 
370 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 4. D. M. Knowlton & Co. drew the following commercial 
 bill of exchange and sold it to Kidder, Peabody & Co. at 96|. 
 How much was received for it ? 
 
 Commercial bills of exchange are usually drawn by exporters against 
 funds abroad which have accumulated to their credit from sales previously 
 made. The exporter generally waits until the rates of exchange are high 
 and then draws the draft as above. 
 
 5. Aug. 1 T. H. Reed & Co., exporters, Minneapolis, Minn., 
 bought through their broker, 24,000 bu. No. 1 wheat at 84^ per 
 bushel and paid for same by check. What was the amount of 
 the check, the broker's commission being J^ per bushel ? 
 
 6. Aug. 2 the wheat was delivered and placed with City 
 Elevator for storage. The storage rates were |^ per bushel for 
 the first 10 da. or fraction thereof, and -faf per bushel for 
 each additional day thereafter. On Aug. 15 the wheat was 
 withdrawn from the City Elevator and delivered to the Soo 
 Freight Line for shipment to W. B. Radcliffe & Son, Liver- 
 pool. What was the amount of the storage bill ? 
 
 7. The wheat was sold to W. B. Radcliffe & Son at XI 12s. 
 2d. per quarter (8 bu. or 480 lb.). Make out the bill under 
 date of Aug. 15. 
 
 8. On Aug. 15 a through bill of lading in duplicate was re- 
 ceived from the Soo Freight Line. If the through freight rate 
 from Minneapolis to Liverpool was 2d. per hundredweight, 
 what was the amount of the freight bill ? 
 
EXCHANGE 
 
 371 
 
 9. Aug. 16, upon presentation of the bill of lading to the 
 Western Assurance Co., the goods were insured for 10% more 
 than their billed value and a certificate of insurance issued. 
 What was the amount of the premium, the rate being \\% ? 
 10. T. H. Reed & Co., drew the following draft on W. B. 
 Radcliffe & Son and attached it to the bill of lading and cer- 
 tificate of insurance. These documents, which constitute what 
 is called a documentary bill of exchange, were then offered for 
 sale and later sold to Kidder, Peabody & Co., at the rate of 
 $4.84| per pound. How much was received for the bill? 
 
 11. Aug. 17 Kidder, Peabody & Co. sold the draft to 
 American Express Co. at f4.84J. If the American Express 
 Co. paid by check, what was the amount of the check? 
 
 12. American Express Co. forwarded the bill to Provincial 
 Bank, Liverpool, for collection, and this bank presented the 
 draft to W. B. Radcliffe & Son for acceptance. Sept. 1 the 
 wheat arrived by steamer and as the draft was stamped "Sur- 
 render documents only upon payment of draft" W. B. Rad- 
 cliffe & Son had to pay the draft before they could get the docu- 
 ments or the goods. As the draft has 46 da. yet to run, the 
 bank allowed W. B. Radcliffe & Son 1% discount.. What was 
 the amount paid by W. B. Radcliffe & Son ? 
 
 Such drafts are frequently stamped " Surrender documents upon accept- 
 ance of the draft." In such cases the documents would be delivered to the 
 consignee upon the acceptance of the draft, and he could then obtain pos- 
 session of the goods. 
 
372 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 13. What was T. H. Reed & Co.'s net gain or loss on the 
 transactions in problems 5-10 ? 
 
 LETTERS OF CREDIT AND TRAVELER'S CHECKS 
 
 444. A traveler's letter of credit is an instrument issued by a 
 banker instructing his correspondents in specified places to pay 
 the holder funds in any amount not exceeding a specified sum. 
 
 CIRCULAR LETTER OF CREDIT. 
 
 MESS?fBROWN, S H i PLEYS Co. 
 
 ^^ 
 
 ^6^^<z^eU//u^ccA^ 
 fmcucms 
 e^tA^<^3^pC^ruc^^ / <^n^ 
 
 /u*^^ 
 
 s^^ 
 
EXCHANGE 
 
 373 
 
 The purchaser of a letter of credit is required to subscribe his name 
 upon the document as a means of identification later on. Other copies 
 of the signature are left and forwarded to the leading foreign banks 
 drawn upon. When the traveler desires funds, he presents his letter to the 
 proper bank at the place in which he is stopping. The letter itself always 
 specifies the banks that will honor the draft. When the letter is presented 
 to a foreign banker for payment, he draws a sight draft on the London 
 banker, which draft the traveler is required to sign. If the signatures on 
 the letter and on the draft are identical, the amount desired is promptly paid 
 and indorsed on the back of the letter. The indorsements on the back 
 of a letter show at all times the balance available for the traveler. The 
 bank making the last payment retains the letter to send to the drawee 
 in London. Letters of credit are usually drawn payable in pounds ster- 
 ling, but they are paid in the current money of the country in which 
 they are negotiated. Banks usually charge 1% commission for issuing 
 a letter of credit. 
 
 445. Another instrument frequently used by travelers is 
 what is called a traveler's check. 
 
 /////M//////////////M////'/' 
 
 AMERICAN EXPRESS COMPANY. 
 
 When a check is purchased, the buyer signs his name in the upper left- 
 hand corner. When he wishes funds, he presents his check to the cor- 
 respondent of the express company or bank and signs his name either 
 in the upper left-hand corner or on the back of the check. On the form 
 above, he would sign his name in the lower left-hand corner; but 
 on the form on page 374 he would sign his name on the back. The lat- 
 ter form is considered better because it is more difficult to forge an- 
 other's signature when there is no signature near at hand from which to 
 copy. 
 
 The terms of issue are cash for the face amount plus % commission. 
 
374 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 r Five PmmilH Stevlliig.oi- H* 
 the order of lite aUow 
 iidorxod with "" rtgunturi?. 
 
 ORAL EXERCISE 
 
 1. At $4.85 to the pound sterling plus 1% commission, what 
 did the letter of credit on page 372 cost? 
 
 2. At the same rate, find the cost of a letter of credit for 
 500; 1000. 
 
 3. At \/o commission, what will be the total cost of 10 
 checks like the sample on page 373? of 20 checks? of 25 
 checks ? 
 
 4. At $4.85 to the pound plus \ % commission, what was the 
 cost of a traveler's check on page 374 ? of a book of 10 checks 
 like the sample on page 374 ? 
 
 WRITTEN EXERCISE 
 
 1. On the letter of credit, page 372, the following payments 
 are recorded on the back : Aug. 31, 200 ; Sept. 9, 400 ; 
 Oct. 15, 250; Nov. 1, 100; Nov. 12, 200. The holder 
 returns to New York on Nov. 20 and presents the letter to 
 Brown Brothers & Co. for the refund. At $4.85 to the pound, 
 how much will Brown Brothers & Co. pay on the letter? 
 
 In this problem it is assumed that Brown Bros. & Co. refund 1 % commis- 
 sion on the unused portion of the letter. 
 
EXCHANGE 
 
 375 
 
 2. At 25^ per word and 1% of the amount, find the cost of 
 a twenty-one word cable money order from Boston to Paris for 
 25,000 fr. when exchange is quoted at 5.15|. 
 
 Money may be cabled from one country to another on the same principle 
 that it is telegraphed from one part of any country to another part. In a 
 cable message a charge is made for each word in the address of the one to 
 whom it is sent. 
 
 WRITTEN REVIEW EXERCISE 
 
 1. A broker sold for me a bill on Manchester, England, at 
 f 4.84J and charged \% brokerage. What was the face of the 
 bill, if the proceeds were $5218.50? 
 
 2. How much remains in the bank to the credit of H. B. 
 Claflin & Co. after the following check was issued ? 
 
 g)att ^ZtS^rf. /i /a 
 
 amnnnt, $ 
 
 3tjants Crust Company 
 
 to tfjc orfcer of 
 
 3. My agent in Brussels, Belgium, purchased for me carpet 
 amounting to 35,000 fr., and his commission was 5%. I re- 
 mitted him a draft to cover the cost of the carpet and the 
 commission for buying. If exchange was 5.15|, and I paid for 
 the draft by check, what was the amount of the check? 
 
 4. My agent in Rotterdam sold for me 525 kegs of tobacco, 
 each containing 50 lb., at ^ guilder per pound, and charged 
 me a commission of 4^%. I drew on him for the proceeds and 
 sold the draft to a broker at 40f . If the broker charged \% 
 for his services, what did I receive as proceeds of the draft ? 
 
EQUATIONS AND CASH BALANCE 
 CHAPTER XXXI 
 
 EQUATION OF ACCOUNTS 
 ORAL EXERCISE 
 
 1. How long will it take $ 5 to produce the same interest as 
 for 10 da. ? The use of 1 100 for 1 mo. is equivalent to 
 
 what sum for 2 mo. ? 
 
 2. If I have the use of 50 of A's money for 30 da., how 
 much of my money should he have the use of for 15 da. in 
 return for the accommodation ? 
 
 3. The interest on $40 for 2 mo. plus the interest on 140 for 
 4 mo. is equal to the interest on $80 for how many months ? 
 
 4. D owes E $100; $50 is due in 2 mo. and the balance in 
 4 mo. In how many months may the whole be paid without 
 loss to either party ? 
 
 5. On Apr. 1 I bought a bill of goods amounting to $200, 
 payable as follows: $100 in 3 mo. and the balance in 5 mo. 
 In how many months may the whole sum be equitably paid ? 
 
 6. A owes B $400 and pays $200 30 da. before the account 
 is due. How long after the account is due may B have in 
 which to pay the balance ? 
 
 446. The process of finding the date on which the settle- 
 ment of an account may be made without loss of interest to 
 either party is called equation of accounts. 
 
 Sometimes one or more of the items in a personal account are not paid at 
 maturity and the holder of the account suffers a loss ; sometimes one or 
 more of the items are paid before maturity and the holder of the account 
 realizes a gain. To equitably adjust these items of loss and gain, accounts 
 are equated. Retail accounts are not often equated ; but wholesale and 
 commission accounts are frequently equated, particularly foreign ones. 
 
 376 
 
EQUATIOK OF ACCOUNTS 
 
 377 
 
 447. The time that must elapse before several debts, due at 
 different times, may be equitably paid in one sum is called the 
 average term of credit; the date on which payment may be 
 equitably made, the average date of payment, the equated 
 date, or the due date. 
 
 448. Any assumed date of settlement with which the several 
 dates in the account are compared for the purpose of deter- 
 mining the actual due date is sometimes called the focal date. 
 
 The face value of each item should always be used in equating accounts. 
 Items not subject to a term of credit and interest-bearing notes are worth 
 their face value on the day they are dated. Items subject to a term of 
 credit and non-interest-bearing notes are not worth their face value until 
 maturity. 
 
 SIMPLE ACCOUNTS 
 
 ORAL EXERCISE 
 
 1. If I owe 1200 due Jan. 1 and $400 due Jan. 31, when 
 may both accounts be equitably paid in one sum? 
 
 SOLUTION. On Jan. 31, there is legally due $600 + $ 1 (the interest on $200 
 for 30 da.)- Since more than the face of the account is due, the equitable date 
 of settlement is before Jan. 31. It will take $600 one third as long as $200 to 
 produce $ 1 interest. ^ of 30 da. = 10 da. The whole account may therefore 
 be paid 10 da. before Jan. 31, or Jan. 21, without loss to either party. 
 
 2. You sold Baker, Taylor & Co. goods as follows : Apr. 20, 
 $ 600 ; Apr. 30, $ 600. How much is legally due on the ac- 
 count Apr. 30 ? On what day may the whole account, $ 1200, 
 be paid without interest ? 
 
 3. When is the following account due by equation? 
 
 A. B. COMER 
 
 1907 
 
 
 
 
 
 
 
 
 
 Sept. 
 
 1 
 
 To mdse. 
 
 300 
 
 
 
 
 
 
 
 21 
 
 To mdse. 
 
 300 
 
 
 
 
 
 
 4. Rowland & Hill bought goods of you as follows : Oct. 16, 
 Oct. 31, $ 800. How much was legally due on the ac- 
 count Oct. 31 ? On what date can the whole of the account, 
 $ 1200, be paid without interest ? 
 
378 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 449. Example. On what date may the total of the following 
 account be paid without interest ? 
 
 F. M. PRATT & Co. 
 
 1907 
 
 
 
 
 
 
 
 
 
 Jan. 
 
 1 
 
 To mdse. 20 da. 
 
 30 
 
 00 
 
 
 
 
 
 
 9 
 
 To mdse. 10 da. 
 
 120 
 
 
 
 
 
 
 
 15 
 
 To mdse. 15 da. 
 
 150 
 
 
 
 
 
 
 
 21 
 
 To mdse. 10 da. 
 
 300 
 
 
 
 
 
 
 
 26 
 
 To mdse. 10 da. 
 
 60 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 DATE 
 Jan. 1 
 
 AMOUNT 
 
 $30 
 
 DAYS 
 
 25 
 
 INTEREST 
 
 $.125 
 
 
 9 
 
 120 
 
 17 
 
 .34 
 
 
 15 
 
 150 
 
 11 
 
 .275 
 
 
 21 
 
 300 
 
 5 
 
 .25 
 
 
 26 
 
 60 
 
 
 
 
 SOLUTION. Take the latest date, 
 Jan. 26, as the focal date. If settle- 
 ment was made on Jan. 26, the 
 holder of the account might charge 
 interest on each item as shown in 
 the accompanying statement. 
 
 The holder loses $ 0. 1 1 per day 
 as long as the account remains un- 
 settled. If settlement was made 
 Jan. 26, the loss would be f 0.99, or 
 9 days' interest; therefore if the ac- 
 count were settled 9 da. before Jan. 
 26, the holder would lose nothing. 
 
 PROOF. The proof of the problem must show that the interest on the items 
 dated before Jan. 17, the equated date, is offset by the discount on the items 
 dated after Jan. 17. The following items are dated before Jan. 17 : 
 
 1.99 
 
 The amount of the account = $ 660. 
 The interest on $660 for 1 da. = $0.11. 
 $ 0.99 -f- $ 0.11 = 9, or the number of days. 
 Jan. 26 9 da. =Jan. 17, the equated date. 
 
 DATE 
 
 Jan. 1 to 17 
 
 9 to 17 
 
 15 to 17 
 
 INTEREST 
 PERIOD 
 
 16 da. 
 
 ITEM 
 $30 
 120 
 150 
 
 INTEREST 
 $.08 
 .16 
 .05 
 
 The following items are dated after Jan. 17 
 
 Total interest, $.29 
 
 DATE 
 
 Jan. 17 to 21 
 17 to 26 
 
 DISCOUNT 
 PERIOD 
 
 4 da. 
 9 
 
 ITEM 
 $ 300 
 60 
 
 DISCOUNT 
 $.20 
 .09 
 
 Total discount, $ .29 
 
 The proof shows that the equated date, Jan. 17, is correct. 
 
 Any rate of interest may be used in equating an account. As a matter 
 of convenience, always use 6 %. If items are subject to terms of credit, add 
 the time to the date of the items before beginning to equate. 
 
EQUATION OF ACCOUNTS 
 
 379 
 
 WRITTEN EXERCISE 
 
 In each of the following problems find the equated date and 
 prove the work. Assume that all the dates are in 1907 . 
 
 1. F. M. Drake, Dr. 
 
 Mar. 2, To mdse. . . f 120. 
 
 8, To mdse. . . 180. 
 11, To mdse. . . 60. 
 17, To mdse. . . 240. 
 
 23, To rndse. . . 150. 
 3, Geo. M. Barton, Dr. 
 Aug. 3, To mdse., 60 da. 1360. 
 
 6, To mdse., 30 da. 240. 
 
 11, To mdse., 30 da. 300. 
 
 19, To mdse., 30 da. 60. 
 
 24, To mdse., 30 da. 180. 
 5. Carter & Co., Dr. 
 
 May 5, To mdse. . . #180. 
 
 12, To mdse. . . 300. 
 
 16, To mdse. . . 230. 
 
 20, To mdse. . . 270. 
 
 23, To mdse. . . 360. 
 7. Brigham & Co., Dr. 
 
 Sept. 4, To mdse., 60 da. 1600. 
 
 9, To mdse., 60 da. 450. 
 
 12, To mdse., 60 da. 350. 
 
 17, To mdse., 60 da. 400. 
 22, To mdse., 30 da. 500. 
 
 30, To mdse., net, . 150. 
 9. Brown, Kerr & Co., Dr. 
 Oct. 1, To mdse., 3 mo. $210. 
 
 5, To mdse., 60 da. 840. 
 
 13, To mdse., 60 da. 720. 
 
 21, To mdse., 60 da. 660. 
 
 24, To mdse., 60 da. 540. 
 
 31, To rndse., net, . 300. 
 
 2. Louis M. Allen, Dr. 
 Apr. 3, To mdse. . . 1160. 
 9, To mdse. . . 250. 
 
 13, To mdse. . . 100. 
 
 19, To mdse. . . 280. 
 
 23, To mdse. . . 420. 
 4. Leon H. Hazelton, Dr. 
 June 6, To mdse. . . $200. 
 
 9, To mdse. . . 300. 
 
 14, To mdse. . . 400. 
 
 24, To mdse. . . 600. 
 
 27, To mdse. . . 330. 
 6. Lamson & Roe Co., Dr. 
 Dec. 1, To mdse., 3 mo. 1 294.20. 
 
 10, To mdse., 3 mo. 698.40. 
 
 20, To mdse., 60 da. 136.60. 
 
 24, To mdse., 60 da. 740.60. 
 28, To mdse., 60 da. 700.40. 
 
 8. D. H. Beckwith & Co. Dr. 
 Nov. 3, To mdse., 2 mo. 1 750.50. 
 8, To mdse., 2 mo. 432.25. 
 
 17, To mdse., net, 275.50. 
 
 22, To mdse., 2 mo. 210.50. 
 
 25, To mdse., 1 mo. 168.30. 
 
 28, To mdse., lino. 240.50. 
 10. D. M. Smith & Co., Dr. 
 
 July 3, To mdse. 
 8, To mdse. 
 11, To mdse. 
 16, To mdse. 
 25, To mdse. 
 29, To mdse. 
 
 1420.30. 
 325.70. 
 417.25. 
 186.24. 
 240.60. 
 126.84. 
 
380 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 COMPOUND ACCOUNTS 
 
 ORAL EXERCISE 
 
 l. The following is your account with John D. Foster. 
 
 Had no payment been made, when would the account have been due? 
 Since no payment was made until after maturity, you have /os/ the use 
 of $ 400 for how many days ? To offset this loss what should be the date of 
 an interest-bearing note given to cover the balance of the account? Jan. 
 16 30 da. = Dec. ?, the date of an interest-bearing note given to cover 
 the balance of the account. 
 
 2. The following is your account with Walter H. Wood. 
 WALTER H. WOOD 
 
 1907 
 
 Apr. 
 
 1 
 
 To mdse.,30da. 
 
 600 
 
 III 19 7 1 
 00 Apr. | 16 
 
 By Cash 
 
 300 
 
 00 
 
 Had no payment been made, when would the account have matured? 
 By the payment recorded you have gained the use of $300 for how many 
 days ? To offset this gain, you should allow Walter II . Wood to keep the 
 balance of the account how many days after maturity? May 1 + 15 da. 
 = May?, the date on which the balance is equitably due. 
 
 3. May 1 B sold C goods amounting to $ 500. Terms : 30 
 da. May 11 C made a payment of 1250 on account. On 
 what date is the balance of the account due ? 
 
 4. Find the date of an interest-bearing note given for the 
 balance of each of the following accounts, assuming that the 
 terms in each case are 30 da.; assuming that the terms are cash. 
 
 NAME 
 
 a. H. H. Howard 
 
 b. W. H. Lyman & Co. 
 
 c. R. H. Delaney & Son 
 
 DR. 
 
 Jan. 1, 1400 
 Jan. 1, 1 400 
 Jan. 1, 1400 
 
 CB. 
 
 Jan. 16, $ 300 
 Jan. 16, $ 100 
 Jan. 16, $ 200 
 
EQUATION OF ACCOUNTS 381 
 
 450. Examples. 1. Find the equated date for the following : 
 
 / L 
 
 44 * 
 
 24=0 
 
 /f 
 
 SOLUTION. Take as focal date the latest date in the account, Feb. 24. 
 
 DEBITS 
 
 DATE 
 Feb. 1 
 14 
 
 DATE 
 
 Feb. 18 
 24 
 
 ITEMS 
 
 $360 
 
 240 
 
 $600 
 
 ITEMS 
 $180 
 
 180 
 $360 
 
 CREDITS 
 
 INTEREST 
 PERIODS 
 
 23 da. 
 10 
 
 INTEREST 
 PERIODS 
 
 6 da. 
 
 
 INTEREST 
 $1.38 
 .40 
 
 $1.78 
 
 INTEREST 
 $.18 
 .00 
 $.18 
 
 $ 600 - $ 360 = $ 240, the balance of the account. $ 1.78 - $ .18 = $ 1.60, 
 the interest due the holder of the account on Feb. 24. The interest on $240 
 for 1 da. = $0.04. $ 1.60 -^ $0.04 = 40, the number of days. If the account 
 were settled Feb. 24 there would be interest for 40 da. due the holder of it. 
 Therefore the balance of the account is due 40 da. before Feb. 24. Feb. 24 
 40 da. = Jan. 15, the equated date. 
 
 PROOF. To prove the correctness of the above work it is necessary to show 
 that a payment of $ 240 on Feb. 24 will result in no loss of discount to either 
 party. This may be done by equatingthe account, using Jan. 15 as the focal date. 
 
 DEBITS 
 
 DATE 
 Jan. 15 to Feb. 1 
 
 15 to 
 
 14 
 
 DATE 
 
 Jan. 15 to Feb. 18 
 15 to 24 
 
 DISCOUNT 
 PERIODS 
 
 17 da. 
 30 
 
 CREDITS 
 
 DISCOUNT 
 PERIODS 
 
 34 da. 
 40 
 
 ITEMS 
 
 $360 
 
 240 
 
 $600 
 
 ITEMS 
 
 $180 
 
 180 
 
 $360 
 
 DISCOUNT 
 
 $1.02 
 1.20 
 
 $2.22 
 
 DISCOUNT 
 
 $1.02 
 
 1.20 
 
 $2.22 
 
 As there is no difference between the debit discount and the credit discount, 
 the account is proved to be due by equation on Jan. 15, 1907. 
 
382 PRACTICAL BUSINESS ARITHMETIC 
 
 2. Find the equated date for the following account : 
 
 Assume May 31 to be the date of settlement. 
 
 DATE 
 
 Apr. 1 
 24 
 30 
 
 
 DEBITS 
 
 TERM OF 
 CREDIT 
 
 MATURITY ITEM 
 
 60 da. 
 
 May 31 $660 
 
 30 
 
 24 360 
 
 10 
 
 10 280 
 
 $1300 
 
 CREDITS 
 
 DATE 
 
 May 2 
 20 
 
 ITEM 
 
 $330 
 
 300 
 
 $630 
 
 INTEKKST 
 PERIOD 
 
 29 da. 
 11 
 
 INTEREST 
 PERIOD 
 
 Oda. 
 
 21 
 
 INTEREST 
 
 $1.595 
 
 .55 
 $2.145 
 
 JJ 
 
 J 00 
 
 INTEREST 
 
 $.00 
 
 .42 
 
 .98 
 
 $ 1 .40 
 
 $ 1300 - $630 = $(570, the balance of the account. $ 2.145 - $ 1.40 = $0.745, 
 the interest due Watson & Moore on May 31. The interest on $670 for 1 da. = 
 $0.111. $0.745 -4- $0.11 = 6.6 or 7, the number of days. If the account were 
 settled May 31, Watson & Moore might deduct $0.75 from the balance of the ac- 
 count ; therefore the balance of the account is not due until 7 da. after May 31, 
 or June 7,1907. 
 
 PROOF. The maturity of each item is used in the proof. 
 
 DATE 
 
 May 31 to June 7 
 
 24 to 7 
 
 10 to 7 
 
 DATE 
 
 May 2 to June 7 
 20 to 7 
 
 DEBITS 
 
 INTEREST 
 PERIOD 
 
 7 da. 
 14 
 
 28 
 
 CREDITS 
 
 INTEREST 
 PERIOD 
 
 36 da. 
 18 
 
 ITEM 
 
 360 
 
 280 
 
 $1300 
 
 ITEM 
 
 $330 
 300 
 $630 
 
 INTEREST 
 
 S -77 
 .84 
 1.307 
 $2.917 
 
 INTEREST 
 $1.98 
 
 .90 
 
 $2.88 
 
 $2.917 - $2.88 = $0.037 ; as this is less than the interest on the balance of 
 the account for | da. the solution is probably correct. 
 
EQUATION OF ACCOUNTS 
 
 383 
 
 WRITTEN EXERCISE 
 
 Find the equated date and prove the work: 
 i. FRED L. UPSON 
 
 1907 
 
 
 
 
 11907 
 
 
 
 
 
 Jan. 
 
 10 
 
 To mdse. 
 
 360 
 
 Jan. 
 
 25 
 
 By cash 
 
 180 
 
 
 
 30 
 
 To mdse. 
 
 240 
 
 Feb. 
 
 12 
 
 By cash 
 
 120 
 
 
 2. 
 
 VINTON L. BROWN & Co. 
 
 1907 
 
 
 
 
 
 1907 
 
 
 
 
 
 Mar. 
 
 11 
 
 To mdse. 
 
 420 
 
 
 Mar. 
 
 27 
 
 By cash 
 
 540 
 
 
 
 23 
 
 To mdse. 
 
 300 
 
 
 
 31 
 
 By cash 
 
 180 
 
 
 Apr. 
 
 6 
 
 To mdse. 
 
 300 
 
 
 Apr. 
 
 24 
 
 By cash 
 
 300 
 
 
 
 20 
 
 To mdse. 
 
 120 
 
 
 
 
 
 
 
 3. 
 
 ANSON L. JAMES 
 
 1907 
 
 
 
 
 
 1907 
 
 
 
 
 
 Mar. 
 
 8 
 
 To mdse., 10 da. 
 
 240 
 
 60 
 
 Mar. 
 
 18 
 
 By cash 
 
 240 
 
 60 
 
 
 12 
 
 To mdse., 10 da. 
 
 180 
 
 30 
 
 
 24 
 
 By 30-da. note 
 
 
 
 
 19 
 
 To mdse., 10 da. 
 
 246 
 
 
 
 
 with interest 
 
 300 
 
 
 
 29 
 
 To mdse., 10 da. 
 
 381 
 
 24 
 
 
 31 
 
 By cash 
 
 257 
 
 54 
 
 The charge under Mar. 8 was paid when due, Mar. 18. 
 be omitted in equating the account. 
 
 4. MACGREGOR & Co. 
 
 Such items may 
 
 1907 
 
 
 
 
 
 1907 
 
 
 
 
 
 Apr. 
 
 7 
 
 To mdse., 10 da. 
 
 127 
 
 54 
 
 Apr. 
 
 17 
 
 By cash 
 
 127 
 
 54 
 
 
 25 
 
 To mdse. 
 
 218 
 
 99 
 
 
 30 
 
 By cash 
 
 100 
 
 
 May 
 
 6 
 
 To mdse., 10 da. 
 
 87 
 
 43 
 
 May 
 
 16 
 
 By cash 
 
 206 
 
 42 
 
 
 18 
 
 To mdse. 
 
 150 
 
 
 
 24 
 
 By mdse. 
 
 35 
 
 20 
 
 
 27 
 
 To mdse., 10 da. 
 
 86 
 
 45 
 
 
 
 
 
 
 5. 
 
 DAVID J. UPHAM 
 
 1907 
 
 
 
 
 
 1907 
 
 
 
 
 
 June 
 
 7 
 
 To mdse. 
 
 128 
 
 50 
 
 June 
 
 14 
 
 By cash 
 
 332 
 
 50 
 
 
 10 
 
 To mdse. 
 
 432 
 
 75 
 
 
 25 
 
 By mdse. 
 
 67 
 
 40 
 
 
 15 
 
 To mdse. 
 
 78 
 
 55 
 
 
 30 
 
 By cash 
 
 248 
 
 60 
 
 
 21 
 
 To mdse. 
 
 246 
 
 80 
 
 July 
 
 15 
 
 By cash 
 
 500 
 
 
 
 29 
 
 To mdse. 
 
 312 
 
 30 
 
 
 28 
 
 By mdse. 
 
 88 
 
 54 
 
 July 
 
 3 
 
 To mdse. 
 
 186 
 
 40 
 
 
 
 
 
 
 
 14 
 
 To mdse. 
 
 66 
 
 36 
 
 
 
 
 
 
384 
 
 PEACTICAL BUSINESS ARITHMETIC 
 
 ACCOUNT SALES 
 
 451. The method of averaging an account sales is practically 
 the same as the method of averaging an ordinary ledger ac- 
 count. The charges for freight, commission, guaranty, etc., 
 constitute the debits and the sales the credits of the account. 
 
 Commission and guaranty are sometimes considered due on the date of 
 the last sale, and sometimes on the average date of the sales. When goods 
 are sold promptly, commission and guaranty are generally considered due on 
 the date of the last sale ; when the sales are large and there are long intervals 
 between them, commission and guaranty are generally considered due on 
 the average due date of the sales. When goods are sold for cash, the ac- 
 count sales is seldom averaged. 
 
 WRITTEN EXERCISE 
 
 1. Equate the account sales on page 267, assuming that 
 both sales were made on 30 days' time, and that the commission 
 is due on the date of the last sale. 
 
 2. Copy and complete the following account sales. Consider 
 the commission as due on the date of the last sale. 
 
 for tl)e 
 
 , J&.JB., July 3. 
 Of Wentworth, Stratton & Co. 
 
 10 
 
 Indianapolis. Ind. 
 
 Commifigion 
 
 June 
 
 8 
 
 295 bbl. Roller Process Flour, 60da. $5.75 
 
 
 
 **** 
 
 ** 
 
 
 12 
 
 315 *' Old Grist Mill Flour, Cash 5.45 
 
 
 
 #*** 
 
 *# 
 
 July 
 
 1 
 
 305 " Roller Process Flour, 60 da. 5.671/2 
 
 
 
 **** 
 
 ** 
 
 
 3 
 
 285 " Old Grist Mill Flour, 30 da. 5.75 
 
 
 
 #**# 
 
 ** 
 
 June 
 
 12 
 
 (3Efrar0e 
 
 Freight and cartage 
 
 112 
 
 50 
 
 
 
 
 9 
 
 Insurance 
 
 60 
 
 
 
 
 July 
 
 3 
 
 Storage 
 
 30 
 
 
 
 
 
 3 
 
 Commission. 5% of sales 
 
 *** 
 
 ** 
 
 
 
 
 * 
 
 Net proceeds due by equation 
 
 
 
 ** 
 
 
 
 
 
 
 **** 
 
 ** 
 
 **** 
 
 ** 
 
CHAPTER XXXII 
 CASH BALANCE 
 
 ORAL EXERCISE 
 
 l. When is the balance of the following account due ? 
 JAMES B. SWEENEY 
 
 1907 
 
 Jan. 
 
 1 
 
 To mdse., 30 da. | 600 
 
 P907 
 an. 
 
 31 
 
 By cash 
 
 300 
 
 00 
 
 2. If no interest is charged on overdue balances, how much 
 will settle the account Feb. 28 ? 
 
 3. If interest at 6% is charged on all amounts not paid at 
 maturity, what is the cash balance of the above account Feb. 28 ? 
 
 4. Assuming that interest is charged on amounts not paid 
 at maturity, find the cash balance of the above account March 
 30, at 6%. 
 
 452. The amount due upon an account at any given time is 
 called the cash balance of an account. 
 
 When interest is not charged and discount is not allowed, the cash 
 balance is the difference between the sides of an account. When interest is 
 charged and discount is allowed, the cash balance is the difference between 
 the sides of an account after interest has been added to overdue items and 
 discount deducted from items not yet due. 
 
 Whether or not interest or discount is charged or allowed on ledger 
 accounts is determined by custom or agreement. It is customary for 
 wholesalers to charge interest on all overdue accounts. As a rule, retailers 
 do not charge interest on the items of an overdue account, but they fre- 
 quently close personal accounts at the end of the year and charge interest 
 on the balances brought down from the date of closing to the date of 
 settlement. 
 
 453. Example. What is the cash balance of the following 
 account Aug. 1, 1907, interest being charged on overdue 
 amounts at the rate of 6 % ? 
 
 385 
 
386 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 
 // /a 
 
 * /o 
 
 00 
 J 
 
 SOLUTION. 
 
 DEBITS 
 
 DATE 
 
 TERM OF 
 CREDIT 
 
 MATURITY 
 
 ITEM 
 
 l p> 
 
 June 1 
 
 30 da. 
 
 July 1 
 
 $900 
 
 31 da. 
 
 9 
 
 10 
 
 June 19 
 
 450 
 
 43 
 
 20 
 
 10 
 
 30 
 
 300 
 
 32 
 
 INTEREST 
 
 $4.65 
 3.23 
 1.60 
 
 $1650 
 
 CREDITS 
 
 DATE 
 June 30 
 July 10 
 18 
 
 ITEM 
 
 $600 
 
 300 
 
 150 
 
 $1050 
 
 INTEREST 
 PERIOD 
 
 32 da. 
 22 
 
 14 
 
 $9.48 
 
 $3.20 
 
 1.10 
 
 .35 
 
 $4.65 
 
 The debit footing and interest : $ 1650 + $9.48 = $ 1659.48 
 
 The credit footing and interest : $ 1050 + $ 4.65 = 81054.65 
 
 The balance due Aug. 1, 1907 = $ 604.83 
 
 WRITTEN EXERCISE 
 
 1. Find the cash balance due June 1, 1907, on problem 4, 
 page 383, money being worth 5 %. 
 
 2. Equate the following account and find the cash balance 
 due Aug. 1, 1907, money being worth 4|%. 
 
 FREDERICK T. LAWRENCE 
 
 1907 
 
 
 
 
 
 lyuT 
 
 
 
 
 
 May 
 
 4 
 
 To mdse., 60 da. 
 
 1360 
 
 
 May 
 
 14 
 
 By cash 
 
 360 
 
 
 
 17 
 
 To mdse. , 30 da. 
 
 720 
 
 
 June 
 
 10 
 
 By cash 
 
 300 
 
 
 
 26 
 
 To mdse., 60 da. 
 
 1080 
 
 
 
 21 
 
 By cash 
 
 420 
 
 
 To find the cash balance of an equated account : Equate the account. 
 Compute the interest on the balance of the account fr.om the equated date to the 
 date of settlement. Add the interest to the balance of the account and the result 
 is the cash balance due. 
 
CASH BALANCE 
 
 387 
 
 3-6. The following is a page from a sales ledger. Find the 
 cash balance due on each account Aug. 1, money being worth 6 % . 
 
 'f'7 
 
 
 
 
 
 
 /iff 7 
 
 
 
 
 
 
 ??t<zy 
 
 ^ 
 
 ~/s0->ms0&id~s./O'i}ets- 
 
 ^ 
 
 3 60 
 
 
 
 %Z^ 
 
 /# 
 
 ~&n/st>et^&' 
 
 ^ 
 
 360 
 
 
 
 
 '7 
 
 t? ft J> 
 
 J/6 
 
 7 20 
 
 
 
 
 '1 
 
 tt tt 
 
 ^ 
 
 J 00 
 
 
 
 
 Zt 
 
 n tt // 
 
 J*r 
 
 / <?<P0 
 
 
 
 z/ 
 
 // // 
 
 &/OJ 
 
 t/2.0 
 
 
 ^^^ 
 
 '000. 
 
 /fff 
 
 / 000 
 
 30 
 
 // / ft 
 
 /zoo 
 
 &J0 
 
 2.0 
 
 ' Z00 
 
DIVIDENDS AND INVESTMENTS 
 CHAPTER XXXIII 
 
 STOCKS AND BONDS 
 
 STOCKS 
 
 454. A corporation or stock company is an artificial person 
 created by law or under the authority of law for an association 
 of individuals. 
 
 Being a mere creature of law a corporation possesses only those properties 
 which its charter (the instrument which defines its rights and duties) confers 
 upon it. These are such as are best calculated to effect the object for which 
 it was created. Among the most important are legal immortality and power 
 to act as a single person. 
 
 455. The capital stock of a corporation is the amount con- 
 tributed by the stockholders to carry on the business. A share 
 is one of the equal parts into which the capital stock is divided. 
 
 Shares of $100 are the rule in most companies, although there are some 
 exceptions. Reading Railroad stock, for instance, is divided into shares of 
 $ 50 each. Mining companies rather more often use other amounts than 
 $100. 
 
 456. A stock certificate is an instrument signed usually by 
 the president and treasurer of the company specifying that the 
 holder is the owner of a certain number of shares of stock in 
 the corporation. A stockholder is a person who owns one or 
 more shares of stock. 
 
 Stockholders elect a few of their number to have general control of the 
 company. These constitute a board of directors, which is in turn controlled 
 by an executive committee. This executive committee is again controlled 
 by a capitalist, who holds more of the stock than any other person. The 
 average stockholder carries his stock merely for dividends and leaves the 
 burden of the management to the directors. 
 
STOCKS AND BONDS 
 
 389 
 
 457. A dividend is a sum paid to the stockholders out of the 
 net earnings of the company. An assessment is a sum levied 
 upon stockholders to make up losses or deficiencies. 
 
 The board of directors decide upon the rate of dividend, which is fre- 
 quently an even per cent on the face value of the slock of the corporation. 
 If fractions are used in these rates, they are usually halves or fourths. Any 
 portion of the profits remaining on hand after dividends have been declared 
 is usually credited to undivided profits, an account which is opened to receive 
 amounts set aside to be used in an emergency or in any manner which may 
 be determined by the directors. Some corporations, notably national banks, 
 carry a portion of the net profits to a surplus fund before declaring dividends. 
 This fund, with certain restrictions, may be used in practically the same 
 manner as the undivided profits account. 
 
 Shares of stock may be, and frequently are, non-assessable. 
 
 458. The two leading kinds of stock are preferred and common. 
 
 459. Preferred stock is stock which entitles the holder to a 
 fixed rate of dividend which must be paid before anything can 
 be divided among the stockholders. 
 
 ICORPOKATBD.VNDBR THE LAVS OF TBB COMMONWEALTH OF MASSACHUSETTS. 
 
 SHARES. $roo EACH. 
 
390 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 460. Common stock is stock which entitles the owner to an 
 equal proportionate share of the net earnings of the company 
 after the dividends on the preferred stock have been paid. 
 
 Preferred stock is usually bought for investment and common stock for 
 speculation. But many companies have no preferred stock, and their com- 
 mon stock is so steadily a dividend payer, and thus so valuable, that it is not 
 considered a speculative commodity. Preferred stock is usually given to 
 secure some obligation of the company or to meet some special demand for 
 capital when common stock may not be disposed of to advantage. 
 
 INCORPORATED UNDER THE LAWS OF THE COMMONWEALTH OF MASSACHUSETTS. 
 
 SHARES. $;oo EACH. 
 
 461. The par value is the face value of stocks; the market 
 value is the sum for which the stocks can be sold in the market. 
 
 462. If a company is prosperous and pays a higher rate of 
 dividend than the money could earn in other ways, a share may 
 sell for more than its face value. The stock is then said to be 
 above par, or at a premium. If the company is not prosperous 
 and pays a lower rate of dividend than could be earned on the 
 money in other ways, a share may sell for less than its face 
 value. The stock is then said to be below par, or at a discount. 
 
STOCKS AND BONDS 391 
 
 463. A stock broker is a person who negotiates sales of stock. 
 Brokerage is a commission charged by a stock broker for 
 buying and selling securities. 
 
 Stocks are usually bought and sold through stock brokers. Brokerage is 
 usually % of the par value of the stock; a charge is also made both for 
 buying and for selling. 
 
 464. When the price of stock is quoted at 97, 118f, 160-|, 
 it means that a share whose par value is $ 100 can be bought 
 for $97, 1118.75, $160.50. If a person buys stock through a 
 broker at 1601, it will cost him $160.50 + $0.121 brokerage, or 
 $160.62|; if he sells stock through a broker for 1601, he will 
 receive as proceeds $160.50 - $0.121, or $160.371. 
 
 Fractions in stock quotations are always halves, fourths, or eighths, and 
 fractions of a share cannot be purchased. The bulk of the transactions in 
 the stock exchange are in 100-share lots, although smaller lots are often 
 purchased for investment. 
 
 ORAL EXERCISE 
 
 1. Examine the certificate of stock, page 389. What is the 
 name of the company? From whom did the company get its 
 right to carry 011 business as a corporation ? 
 
 2. What is the entire capital stock of the company ? Into 
 how many shares is this divided ? What per cent of the entire 
 stock of the company does the holder of the certificate own? 
 
 3. What kind of stock is represented by the certificate ? 
 What is the difference between common and preferred stock? 
 
 4. What is the par value of each share ? If the market 
 value of each share is $160, what is the certificate worth? 
 
 5. What sum must be laid aside to provide for the divi- 
 dends on the preferred stock of the company, the rate being 6 % ? 
 How much of this sum will the holder of the certificate receive ? 
 
 6. Examine the stock certificate, page 390. What part of 
 the stock of the company is common stock ? 
 
 7. A 5% dividend on the common stock would require how 
 much money from the treasury of the company ? Of this sum 
 how much would George W. Putnam receive ? 
 
392 PRACTICAL BUSINESS ARITHMETIC 
 
 DIVIDENDS AND ASSESSMENTS 
 WRITTEN EXERCISE 
 
 Unless otherwise specified the par value of a share will be understood to 
 be $100. 
 
 1. A company with $3,500,000 capital declares an 8 % divi- 
 dend. What does the holder of 250 shares receive ? 
 
 2. B holds 450 shares of Pennsylvania Railroad stock. 
 When the company declares a dividend 1%%, how much will 
 he receive ? 
 
 3. What annual income is derived from investing $ 48,000 
 in Union Pacific Railroad stock at 120, if 2| % semiannual divi- 
 dends are declared ? 
 
 4. E. H. Rhodes holds 600 shares of Leliigli Valley Railroad 
 stock. If he received the following check as his annual divi- 
 dend, what was the rate ? 
 
 /9 
 
 Zfirst ^lationat SBank 
 
 | /J 
 
 QividendJfo. 
 
 '/reasurer 
 
 5. A company with 1,000,000 capital declares quarterly 
 dividends of \\%. What are the annual dividends? What is 
 the amount received annually by D, who owns 475 shares ? 
 
 6. A corporation with a capital of $125,000 loses $2500. 
 What per cent of his stock must each stockholder be assessed 
 to meet this loss? How much will it cost A, who owns 150 
 shares ? 
 
 7. A company with a capital of $ 750,000 declares a semi- 
 annual dividend of 3^%. How much money does it distribute 
 among its stockholders annually? What is the annual income 
 of a man who owns 200 shares ? 
 
STOCKS AND BONDS 393 
 
 8. If the Reading Railroad declares a semiannual dividend 
 of 2| % 011 a capital stock of $500,000,000, what amount is 
 annually distributed among the stockholders ? What is the 
 annual income to J. P. Morgan from this stock if he owns 
 7,500,000 shares having a par value of $50 each? 
 
 9. During a certain year a manufacturing concern with 
 a capital of % 750,000 earns 175,500 above all expenses. It 
 decides to save $15,500 of this for emergencies and to divide 
 the remainder in dividends. What is the rate ? What would 
 be the amount of A's dividend check if he owns 125 shares ? 
 
 10. The capital stock of the Gramercy Finance Company is 
 $1,500,000. The gross earnings of the company for a year are 
 $875,000 and the expenses $215,000. What even per cent of 
 dividend may be declared and what would be the amount of 
 undivided profits if 10 % of the net earnings are first set aside 
 as a surplus fund ? 
 
 11. A railway company has a capital of $3,500,000 and 
 declares dividends semiannually. During the period from 
 Jan. 1 to July 1 of a certain year the net earnings of the com- 
 pany were $191,000. Of this amount 10 % is carried to surplus 
 fund. What even rate per cent of dividend may be declared on 
 the balance and how much will be carried to undivided profits ? 
 
 12. A company with a capital stock of $500,000 gains during 
 a certain year $38,750. It decides to carry $5000 of the 
 profits to surplus fund and to declare an even per cent of 
 dividends on the remainder. What sum was divided among 
 the stockholders, and what sum was carried to undivided 
 profits account ? What was the annual income to F from this 
 stock if he owned 500 shares ? 
 
 13. During a certain year the gross earnings of a railroad 
 having a capital stock of $100,000,000 were $65,150,000, and 
 the operating expenses $45,150,000. If the company declared 
 a semiannual dividend of 3| % and carried the balance of the 
 net earnings to undivided profits account, how much was 
 divided among the stockholders ? How much was the working 
 capital of the company increased ? 
 
394 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 14. The capital stock of the National Shawmut Bank 
 is 8,000,000, and dividends are declared semiannually. 
 The profits of the bank for a certain six months are f 185,750. 
 10 % of this sum is carried to a surplus fund. The directors 
 then vote to declare a dividend of 3^ % and carry the balance 
 of the profits to undivided profits account. What amount was 
 carried to surplus fund account ? to dividend account ? to 
 undivided profits account ? 
 
 BUYING AND SELLING STOCK 
 
 465. The following is an abbreviated form of the stock 
 quotations for a certain day on the New York Stock Exchange: 
 
 TABLE OF SALES AND RANGE OF PRICES 
 
 Sales 
 
 Stocks 
 
 3 pen. 
 
 High. 
 
 Low. 
 
 Clos. 
 
 Net 
 Changes 
 
 100 
 
 Adams Express 
 
 243 
 
 243 
 
 243 
 
 243 
 
 + % 
 
 123,500 
 49,500 
 
 Amalgamated Copper 
 Am. Sugar Kef. 
 
 81 
 151 
 
 81% 
 152 
 
 79% 
 149% 
 
 79% 
 150 
 
 4-1 * 
 
 100 
 
 Am. Sugar Kef. pfd. 
 
 141 
 
 141 
 
 141 
 
 141 
 
 + 1 
 
 9,300 
 12,900 
 1,600 
 
 Baltimore & Ohio 
 Canadian Pacific 
 Delaware & Hudson 
 
 97% 
 135% 
 
 188 
 
 1355/8 
 
 188 
 
 97% 
 1341/4 
 186 
 
 971/4 
 1341/4 
 186 
 
 =i| 
 
 12,900 
 
 Del. Lak. & Western 
 
 388% 
 
 395 
 
 385 
 
 395 
 
 +10 8 
 
 1,200 
 
 General Klectric 
 
 1811/4 
 
 182 
 
 181% 
 
 181% 
 
 + % 
 
 500 
 
 Illinois Central 
 
 1501A 
 
 150% 
 
 149V 8 
 
 149% 
 
 -1 % 
 
 7,900 
 
 Manhattan Elevated 
 
 169% 
 
 169% 
 
 1673/4 
 
 167% 
 
 + 1 
 
 2,600 
 
 New York Central 
 
 136% 
 
 13C>3/4 
 
 135% 
 
 136 
 
 - y* 
 
 500 
 
 N.Y. N.H. &H. 
 
 201 
 
 202 
 
 2()13A 
 
 202 
 
 +2 
 
 63,700 
 
 Pennsylvania 
 
 137V 4 
 
 137% 
 
 136% 
 
 18<5% 
 
 % 
 
 4,700 
 
 Peoples Gas 
 
 
 109% 
 
 lOS 3 ^ 
 
 1083/4 
 
 + V4 
 
 85,700 
 
 Heading 
 
 75% 
 
 77 
 
 75l/ 
 
 753/ 8 
 
 ~~ ^ 
 
 100 
 
 Heading pfd. 
 
 88% 
 
 88 
 
 88% 
 
 88 
 
 1/4 
 
 33,800 
 
 Southern Pacific 
 
 6^% 
 
 OS 3/ s 
 
 66% 
 
 66% 
 
 1 % 
 
 303,700 
 
 Union Pacific 
 
 129% 
 
 130V 8 
 
 127% 
 
 128 
 
 % 
 
 
 Union Pacific pfd. 
 
 97 
 
 
 97 
 
 971/4 
 
 + % 
 
 43,100 
 
 United States Steel 
 
 27% 
 
 28 2 
 
 27 
 
 27 
 
 S /A 
 
 72,800 
 
 United States Steel pfd. 
 
 88 
 
 88% 
 
 871/4 
 
 871/4 
 
 % 
 
 100 
 
 Wells Fargo Express 
 
 235 
 
 235 
 
 235 
 
 235 
 
 +4 
 
 400 
 
 Western Union 
 
 92 
 
 923/ 8 
 
 92 
 
 92 
 
 - % 
 
 In the first column is shown the number of shares of stock sold ; in the 
 second, the name of the stock ; in the third, fourth, fifth, and sixth respec- 
 tively, the opening, highest, lowest, and closing prices of the day ; in the 
 last, the net charges between the closing price of yesterday and to-day. The 
 plus sign signifies an advance ; the minus sign a decline. Thus, on the day 
 given 123,500 shares of Amalgamated Copper stock were sold. The open- 
 ing price was $81 per share; the highest price for the day, $81.75; the 
 lowest, $79.62$; the closing, $79.75, which shows a decline of $1.12} from 
 the closing price of the preceding day. 
 
STOCKS AND BONDS 395 
 
 ORAL EXERCISE 
 
 1. Find in the table (page 394) three cases where a quotation 
 both for common stock and for preferred (pfd. stands for pre- 
 ferred) stock is given. Which is worth the more in each case ? 
 Under what circumstances may common stock sell for more 
 than preferred stock ? 
 
 2. What would 100 shares of American Sugar Refinery (com- 
 mon) cost if bought through a broker at the lowest price for 
 the day, brokerage being \% 
 
 9 
 
 3. What would the seller of the stock realize on the sale ? 
 
 SUGGESTION. The seller would receive the price for which it was sold 
 minus the brokerage, %. 
 
 4. State the cost, at the opening price in the table, of 100 
 shares of each of the following stocks, assuming that the trans- 
 actions take place through a broker who charges \% commis- 
 sion : Baltimore & Ohio ; Canadian Pacific ; General Electric ; 
 Manhattan Elevated ; New York Central ; Peoples Gas ; Wells, 
 Fargo Express; New York, New Haven and Hartford; Illinois 
 Central. 
 
 5. At the highest price in the table, state the amount re- 
 ceived from the sale of 100 shares of each of the following 
 stocks, assuming that they are sold through a broker who 
 charges \/ commission : Southern Pacific ; United States Steel 
 (preferred) ; Western Union Telegraph ; Reading (preferred) ; 
 American Sugar Refinery (common) ; Pennsylvania ; Amalga- 
 mated Copper ; Union Pacific (preferred ) ; Adams Express ; 
 Delaware, Lacka wanna and Western ; New York, New Haven, 
 and Hartford. 
 
 WRITTEN EXERCISE 
 
 Find the cost, at the dosing price in the table, of 2500 shares 
 of the folloiving stocks, including brokerage : 
 
 1. Canadian Pacific. 4. Pennsylvania. 
 
 2. Amalgamated Copper. 5. Manhattan Elevated. 
 
 3. American Sugar Refinery. 6. United States Steel (pref.). 
 
396 PRACTICAL BUSINESS ARITHMETIC 
 
 At the closing price for the day find the amount received from 
 the sale of 3500 shares of the following stocks sold through a broker : 
 
 7. Illinois Central. 11. Reading. 
 
 8. Western Union. 12. General Electric. 
 
 9. Southern Pacific. 13. Canadian Pacific. 
 
 10. Delaware and Hudson. 14. Amalgamated Copper. 
 
 466. Example. I bought 1000 shares Pennsylvania Railroad 
 stock, at the lowest price in the table, and sold the same at 
 140|. Allowing for brokerage both for buying and for selling, 
 did I gain or lose, and how much ? 
 
 SOLUTION. Since I bought through a broker, each share Iv.aiy 
 
 cost me $ 136.50 + $ 0.12$, or $ 136.62J ; and since I sold through 136. 62| 
 a broker the proceeds of each share sold was $ 140.50 $0.12$, <jj 3.75 
 or $140.37$. $ 140.37$ -f 188.62$ =$8.76, gained on each 
 share. Since $3.75 is gained on 1 share, 1000 times $3.75, or 
 
 . . , ., 
 
 $ 3750, is gained on 1000 shares. 
 
 In the following exercise it is understood that all sales and purchases are 
 made through a broker who charges a commission of $ % both for buying and 
 for selling. 
 
 WRITTEN EXERCISE 
 
 Find the gain or loss on oOO shares of each of the following 
 stocks bought at the opening price and sold at the price here given: 
 
 1. Pennsylvania, 141|. 7. Peoples Gas, 97|. 
 
 2. Western Union, 95. 8. New York Central, 132. 
 
 3. Illinois Central, 157. 9. Baltimore and Ohio, 98|. 
 
 4. General Electric, 195. 10. Manhattan Elevated, 170. 
 
 5. Canadian Pacific, 131. 11. Amalgamated Copper, 84 j. 
 
 6. Southern Pacific, 691. 12. United States Steel (pfd.),90|. 
 
 13-24. Find the gain or loss on 1000 shares of each of the 
 above stocks bought at the lowest price and sold at the highest 
 price in the table. 
 
 25. F bought 500 shares of Peoples Gas at the opening price 
 in the table and sold it so as to gain $750. What was the quoted 
 price when he sold it ? 
 
STOCKS AND BONDS 397 
 
 26. I bought some Western Union Telegraph stock at the 
 opening price in the table and sold it for 94J. If by so doing 
 I gained $ 4500, how many shares did I buy ? 
 
 27. I bought 2500 shares of General Electric at the lowest 
 price in the table, held it a year, received 5 % in dividends, and 
 then sold it at 183|. Did I gain or lose, and how much, money 
 being worth 4| % ? 
 
 28. I gave my broker orders to buy 1500 shares Amalga- 
 mated Copper and to sell 2500 shares Canadian Pacific. If he 
 buys at the lowest price in the table and sells at the highest 
 price, what balance will he put to my credit? 
 
 29. At the closing price in the table, find the total cost 
 of 500 shares American Sugar Refinery (preferred), 1500 
 shares General Electric, 1000 shares Manhattan Elevated, 
 100 shares Peoples Gas, 300 shares Delaware & Hudson, 
 and 500 shares Illinois Central. 
 
 BONDS 
 
 467. A negotiable bond is a very formal promissory note 
 issued by a government, railway, or industrial corporation for 
 borrowed money. 
 
 Bonds of corporation are generally issued in a series of like tenor and 
 amount, and bear interest payable annually, semiannually, or quarterly. A 
 bond is usually, though not invariably, issued for each $ 1000 borrowed. 
 
 The bonds of a business corporation are generally secured by a mortgage 
 upon its property (an agreement by which the owners of the bonds may sell 
 the property if the bonds and interest are not paid) ; but the bonds of a 
 government have no security other than the honor of the people. 
 
 The bonds of a business corporation with reference to their security are 
 of various kinds; the first-mortgage bonds usually stand highest, in that 
 they have a first lien on the property covered by the mortgage. Second- and 
 third-mortgage bonds take rank after the first. Debenture bonds are unse- 
 cured promises to pay ; they are similar in principle to the unsecured paper 
 of a merchant offered for discount. 
 
 468. With reference to the form of contract for the payment 
 of principal and interest there are two kinds of bonds : coupon 
 and registered. 
 
398 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 469. A coupon bond is a bond to which are attached interest 
 notes, or coupons, representing the interest due on the bond at 
 stated periods of payment. 
 
 The interest notes may be cut off from the bonds at maturity and the 
 amount of interest which they represent collected through a bank. If these 
 notes are not paid when due, they bear interest at the legal rate. 
 
STOCKS AND BONDS 399 
 
 470. A registered bond is a bond which has no separate con- 
 tract for the payment of the interest. Such a bond must be 
 recorded on the books of the corporation in the name of the 
 holder to whom the interest is sent. 
 
 Coupon bonds are usually drawn payable to bearer and may be transferred 
 by delivery or indorsement, or both. Registered bonds are always drawn 
 payable to some designated person and can be transferred only by assign- 
 ment and registry on the books of the corporation. 
 
 471. Bonds issued by the United States are called govern- 
 ment bonds or government securities ; bonds issued by a state, 
 state bonds or state securities ; bonds issued by a city, municipal 
 bonds or municipal securities. 
 
 The names of the different government bonds are usually derived from 
 the interest they bear and the time when they mature. Thus, " U. S. 2s, 
 1930 " are United States bonds bearing interest at 2% and maturing in 1930 ; 
 " U. S. 3s, 1908 " are United States bonds bearing 3% interest and maturing 
 in 1908; " U. S. 4s, 1925 " are United States bonds bearing 4% interest and 
 maturing in 1925. 
 
 472. Bonds, like preferred stock, pay a fixed income. 
 
 From the gross earnings of a company the operating expenses are first 
 deducted; from the net earnings are deducted all fixed charges, such as 
 interest on bonds; then the dividends on preferred stock are paid; and 
 finally out of the remainder dividends on the common stock are paid. 
 
 ORAL EXERCISE 
 
 1. Examine the bond on page 398. With reference to the 
 form of contract, what kind of a bond is it ? 
 
 2. How many interest notes (coupons) would be attached 
 to the full bond ? 
 
 3. When was the bond issued ? What date (of maturity) 
 should be written on each interest note ? 
 
 4. What is the face of the bond ? What rate of interest 
 does it bear ? What sum should be written on each interest 
 note? 
 
 5. How may coupon bonds be transferred ? registered 
 bonds ? 
 
400 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 6. If the bond on page 398 was quoted at 105| when it was 
 purchased, how much did it cost, including \% brokerage? 
 How much did the seller realize on it ? 
 
 7. Has the city or town in which you live any bonded in- 
 debtedness (indebtedness secured by bonds) ? If so, what are 
 these bonds called and what rate of interest do they pay ? 
 
 BUYING AND SELLING BONDS 
 
 473. Bonds, like stocks, are usually bought and sold 
 through brokers. 
 
 The broker's commission for buying and selling bonds is the same as for 
 buying and selling stocks. 
 
 474. The following table is an abbreviated form of the 
 sales, and opening, highest, lowest, and closing prices of bonds 
 traded in on the New York Exchange on a recent date. 
 
 TABLE or SALES AND RANGE OF PRICES 
 
 SALES 
 
 BONDS 
 
 OPEN. 
 
 HIGH. 
 
 Low. 
 
 CLOS. 
 
 $ 8000 
 
 Am Hide & Leather 6s 
 
 97 9 
 
 97% 
 
 97% 
 
 97% 
 
 241 000 
 
 Brooklyn Rapid Transit 4s . . 
 
 89? 
 
 89 i/o 
 
 89 
 
 891A 
 
 1,000 
 571,000 
 10,000 
 71,000 
 2,000 
 12,000 
 19 000 
 
 Chesapeake & Ohio 6s, 1911 
 Chicago, Burlington & (Juincy 4s . 
 Denver & Rio Grande 4s . . . . 
 Erie 4s 
 Illinois Central 4s, 1952 
 Lac ka wanna Steel 5s 
 Missouri Pacific 4s 
 
 110 
 
 1011/2 
 
 100% 
 
 IDS 
 108 
 
 1063/8 
 
 95 
 
 110 
 101% 
 100% 
 108V 8 
 IDS 
 
 10(534 
 
 '16 
 
 110 
 
 1013/g 
 
 99% 
 107% 
 107% 
 106% 
 95 
 
 110 
 101% 
 99% 
 1073/4 
 108 
 ,063/ 4 
 
 1,000 
 16,000 
 5000 
 
 National Starch 6s 
 Northern Pacific 1st mtg. 4s 
 Pennsylvania 4%s 
 
 85 
 
 105% 
 lOhS/. 
 
 85 
 106l/ 8 
 109 
 
 85 
 108% 
 
 85 
 105% 
 109 
 
 11 000 
 
 Seaboard Air Line 4s ... 
 
 COT/ 
 
 90 
 
 891/8 
 
 89 s /a 
 
 17,000 
 
 Seaboard Air Line 5s 
 
 103% 
 
 104% 
 
 104 
 
 101 8 
 
 87,000 
 1,000 
 5,000 
 
 Union Pacific 1st mtg. 4s 
 United States reg. 4s., 1907 
 United States coupon 4s 
 
 l053/ 4 
 104V 2 
 104V4 
 
 105% 
 104% 
 
 105% 
 104# 
 
 104 
 
 105% 
 104% 
 104i/ 4 
 
 In the first column is shown the par value of the bonds sold ; in the sec- 
 ond, the name of the bonds and the interest they bear ; in the third, fourth, 
 fifth, and sixth, respectively, the opening, highest, lowest, and closing prices 
 of the day. These prices are quoted at a rate per $ 100 of par value (amount 
 of the bond). Thus, on the day given $ 241,000 worth of Brooklyn Rapid 
 Transit bonds bearing 4% interest were sold. The opening price was 
 I 89.25 per $ 100 of par value, the highest price, $ 89.50, the lowest price, $ 89, 
 and the closing price, $ 89.25 per $ 100 of par value. 
 
STOCKS AND BONDS 401 
 
 475. Example. What is the cost of 150,000 (par value) 
 Chicago, Burlington & Quincy 4 % bonds at the highest price 
 quoted in the table (page 400) ? 
 
 SOLUTION. $100 of par value cost $101| + $0.12| brokerage, or $ 102. 
 
 . . $ 50,000 of par value will cost 500 times ($ 50,000 -=- $ 100) $ 102, or $ 51,000. 
 
 WRITTEN EXERCISE 
 
 1. What is the cost of $ 25,000 American Hide and Leather 
 bonds at the opening price in the table ? 
 
 2. I gave my broker orders to sell $10,000 Chesapeake and 
 Ohio 6 % bonds and buy $ 10,000 National Starch 6 % bonds. 
 If he sold at the highest price in the table and bought at the 
 lowest price, what balance should he place to my credit ? 
 
 3. Find the proceeds from the following sales : $ 1000 
 United States 4 % registered bonds at the opening price in the 
 table ; $ 5000 United States 4 % coupon bonds at the opening 
 price in the table ; $ 75,000 Chicago, Burlington & Quincy 
 4% bonds at the closing price in the table ; $10,000 Erie 4% 
 bonds at the lowest price in the table. 
 
 4. June 1, 1907, a certain city borrowed $ 250,000 with which 
 to build a new high school, and issued 4|% 10-yr. coupon 
 bonds as security. If these bonds sold (through a broker) at 
 101 J, how much was received by the city ? If A bought five 
 $ 1000 bonds, how much did they cost him ? If interest is 
 payable semiannually, what date (of maturity) should the last 
 interest note of each bond bear ? What will be the amount of 
 each interest note ? 
 
 5. Find the total cost of the following purchases : $ 20,000 
 Erie 4% bonds at the closing price in the table ; $ 2000 Illinois 
 Central 4 % bonds at the lowest price in the table ; $ 5000 
 Lackawanna Steel 5 % bonds at the lowest price in the table ; 
 $ 15,000 Missouri Pacific 4 % bonds at the opening price in the 
 table ; 1 10,000 Northern Pacific first-mortgage 4 % bonds at 
 the lowest price in the table ; $ 3000 Pennsylvania 4 J % bonds 
 at the opening price in the table. 
 
402 PRACTICAL BUSINESS ARITHMETIC 
 
 INCOMES AND INVESTMENTS 
 
 ORAL EXERCISE 
 
 1. A bought a 4 % United States bond at H9J. Not con- 
 sidering the question of the maturity of the bond, what rate of 
 income did he receive on his investment ? 
 
 SUGGESTION. $ 4 is what per cent of $ 120 ? 
 
 2. B bought 4 % bonds having a market value of 79J. 
 What rate per cent of interest did he receive 011 his invest- 
 ment ? 
 
 3. C bought 110,000 worth of 6% bonds quoted at 149|, 
 and $10,000 4|% bonds quoted at 112|. What rate of income 
 did he receive from both investments ? 
 
 4. D bought a Seaboard Air Line 4 % bond at the opening 
 price in the 'table, also a Seaboard Air Line 5% bond at the 
 opening price in the table. Interest being payable annually 
 in each case, which will yield the larger income ? 
 
 The rates of interest paid on bonds of high class security are very 
 much lower at the present time than they were a generation ago. For 
 example, in 1865 the National Government paid over 7% interest on 30% 
 of its debt, 6% on 10% of its debt, 5% on 55% of its debt, and 4% on 5% 
 of its debt. At the present time about one half of the United States bonds 
 pay only 2% interest; and the average rate of interest paid on railroad 
 bonds is about 4%. 
 
 476. As a general rule, a bond of undoubted security which 
 bears a high rate of interest commands so large a premium as 
 to reduce the actual return on the investment to the prevailing 
 rates on other investments of as good security. (See problem 
 4 in the foregoing exercise.) 
 
 477. At the maturity of a bond only its face value and the 
 interest accrued thereon are paid to the holder. In order to 
 command a high price, therefore, a bond must pay a good rate 
 of interest, be perfectly safe, and have a long period to run. 
 
 Thus, a 6 % third-mortgage bond having 10 yr. to run, or a 6% first- 
 mortgage bond having only 2 yr. to run, might not command as high a price 
 as a 3 % bond having a high class security and 30 yr. to run. 
 
STOCKS AND BONDS 403 
 
 WRITTEN EXERCISE 
 
 1. A bought a 5% bond quoted at 149|. What rate of 
 interest did he receive on the money invested ? 
 
 In the above and all similar problems the question of the maturity of the 
 bond is not considered, and it is assumed that the transaction was effected 
 through a broker who charged a commission of 1%. 
 
 2. F invested 42,600 in Lackawanna Steel 5% bonds at 
 the opening price in the table (page 400). What was his an- 
 nual income ? 
 
 3. Which gives the better income and how much, a 5% 
 bond bought at 79J or a 6 % bond bought at 119f ? 6 % stock 
 bought at 149J or 4 % stock bought at 112f ? 
 
 4. G invested $24,312.50 in Adams Express Company 
 stock at the closing price in the table on page 394. What 
 was his annual income from a 3| % quarterly dividend ? 
 
 5. H invested $ 79,025 in Delaware, Lackawanna & West- 
 ern Railroad stock at the closing price in the table, page 394. 
 What will be his annual income when the dividends are 4^% 
 quarterly ? 
 
 6. Which would be the more profitable as an investment, 
 to buy Missouri Pacific first-mortgage 4% bonds, due in 1925, 
 at 95|-, or Edison Electric Co. first-mortgage 5 % bonds, due in 
 1925, at 104$ % ? 
 
 7. When the current rate of interest is 4J%, what price 
 can I afford to pay for Chesapeake and Ohio 6 % first-mortgage 
 bonds ? (Give the nearest J in your answer.) 
 
 8. What sum must be invested in Illinois Central 4 % 
 bonds, at the opening price in the table, page 400, to realize an 
 annual income of I 2000 ? 
 
 SOLUTION. $4 = the income on $ 100 of the par value of the bonds. 
 $2000 -$4 = 500. 
 
 .-. bonds having a par value of 500 x $ 100 must be purchased. 
 But the cost is $ 108 + $ 0.121 O r $ 108. 12|. 
 .-. 500 x $108.12i or $54062.50 must be invested. 
 
404 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 9. What sum must be invested in Missouri Pacific 4 % 
 bonds at the closing price in the table, page 400, to realize an 
 annual income of $ 1500 ? 
 
 10. Using the closing price (with brokerage) in the 
 tables on pages 394 and 400, find which gives the better in- 
 come and how much : Illinois Central Railroad stock paying 
 6 % dividends or Denver & Rio Grande 4 % bonds ; General 
 Electric stock paying 8 % dividends or Lacka wanna Steel 5 % 
 bonds ; New York, New Haven & Hartford Railroad stock pay- 
 ing 8 % dividends or United States 4 % coupon bonds ; Man- 
 hattan Elevated Railroad stock paying 6| % dividends or Erie 
 4 % bonds. 
 
 STOCK EXCHANGES 
 
 478. Stock exchanges are associations organized for the pur- 
 pose of creating a regulated market for the buying and selling 
 of stocks and bonds. The principal stock market of the United 
 States is the New York Stock Exchange, an unincorporated 
 association of 1100 members. 
 
 There are stock exchanges in Chicago, Philadelphia, Boston, and other 
 
 large cities, but these are local 
 institutions and their dealings 
 are confined to local stocks. 
 The New York Stock Exchange 
 is a national institution which 
 deals with the securities of the 
 w r hole nation. 
 
 A membership in a stock ex- 
 change is called a "seat." The 
 price of a seat varies from 
 $10,000 to $20,000 on local 
 stock exchanges, to from 
 $30,000 to $75,000 on the New 
 INTERIOR OF A STOCK EXCHANGE. York stock Exchange. A stock 
 
 exchange always maintains a 
 
 uniform rate of commission. This, as has been seen, is usually |%, or $ 12.50 
 per 100 shares ; but as every purchase by a broker is usually followed by a 
 sale, the commission on one transaction both ways amounts to %, or $25 
 per 100 shares. 
 
STOCKS AND BONDS 
 
 405 
 
 479. The principal ways in which stocks are bought and sold 
 
 are as follows : " cash," that is, deliverable on the day of sale ; 
 " regular" that is, deliverable on the day following the sale ; 
 "at three days" that is, deliverable on the third day of the sale; 
 " buyer's option" that is, deliverable at the option of the buyer 
 at any time within the option period (from 4 to 60 days) ; 
 " seller s option" that is, deliverable at the option of the seller 
 any time within the option period. 
 
 By far the largest part of the sales are " regular." On " cash," " regular," 
 and " at three days " sales no interest is paid ; but on options over three 
 days, interest at the legal rate on the selling price of the stock is paid by 
 the buyer to the seller. To terminate an option of over three days, one 
 day's notice is required. 
 
 480. A margin is a sum of money deposited with a broker to 
 cover losses which he may sustain on behalf of his principal. 
 
 Stocks and bonds are frequently bought and sold on a margin. The 
 process may be illustrated in the following : 
 
 June 8, A. M. Greyson deposited with Richard Roe & Co., his brokers, 
 $ 4160, and instructed them to buy 400 shares of Atchison, Topeka and Santa 
 Fe Railroad stock whenever they could do so at 104. On the same day the 
 stock was bought in accordance with instructions. On June 14, pursuant 
 to instructions, Richard Roe & Co. sold the stock at 107 and sent A. M. 
 Greyson the following statement and a check for $5322.56. 
 
 New York,. 
 
 In account current with RICHARD ROE & CO. 
 
 jk*"* 
 
 7^-cA^c^A^U^i^. 
 
 J7 
 .yj 2.2- 
 
 DAYS INTEREST 
 
 37 
 
 (,0 
 
 By the above transactions A. M. Greyson has gained $1162.56. 
 
 The amount of margins demanded by a broker depends upon the charac- 
 ter of the stocks traded in. On stocks that have a good market 10% of the 
 market value is usually demanded ; on stocks that have little or no market 
 
406 PEACTICAL BUSINESS ARITHMETIC 
 
 20 % of the market value or more is often required. The broker, of course, 
 pays for the stock in full. In order to do this he is frequently obliged to 
 borrow money from a bank. This he may usually do by depositing 
 (hypothecating) stock as security (see page 328). 
 
 The speculators on the stock exchange may be divided into two classes : 
 bulls and bears. A bull is a speculator who buys stocks in the expectation 
 of selling them at a higher price. A bear, is a speculator who sells stocks 
 which he does not own, in the expectation that he can buy them at a lower 
 price before the date on which they must be delivered. A bull who has 
 bought is said to be "long" of stock; a bear who has sold is said to have 
 sold short," or to be "short" of stock. A bull works for advancing prices; 
 a bear for declining prices. A bull, when he sells at higher prices, is said 
 to have "realized" his profits; when at lower prices, to have "liquidated." 
 A bear, when he buys stock, is said to have "covered" no matter whether he 
 bought at a gain or at a loss. 
 
 WRITTEN EXERCISE 
 
 1. On June 25 I purchased through a broker 300 shares of 
 Amalgamated Copper at 87J b. 3 (buyer's option any time 
 within 3 da.). On June 28 the stock was delivered and, pur- 
 suant to my instructions, sold for 89 J cash. Did I gain or lose, 
 and how much ? 
 
 2. On Apr. 15 my broker purchased for me 500 shares 
 Delaware & Hudson at 172| regular. On April 16 he sold the 
 same at 174^ cash. What was my gain? 
 
 3. On Sept. 15 I bought, through a broker, 250 shares 
 Reading pfd. at 68| b. 30. On Sept. 25 my broker demanded 
 the stock and, in accordance with my instructions, sold it for 
 70 \ regular. Did I gain or lose, and how much? 
 
 4. On Dec. 1 D bought of me through C, his broker, 2000 
 shares of Missouri Pacific at 99 \ s. 60 (seller's option any time 
 within 60 da.). Dec. 17 C, pursuant to my instructions, de- 
 livered the stock which he had purchased for me on the 
 previous day at 96 regular. Did I gain or lose, and how much? 
 
 5. On June 27 I ordered my broker to sell "short" for me 
 500 shares Baltimore & Ohio at 105J s. 30. July 7 the stock 
 declined to 100J. I ordered my broker, at this price, to "cover 
 my short." Did I gain or lose, and how much ? 
 
STOCKS AND BONDS 
 
 407 
 
 6. Jan. 15 I deposited $4080 with my broker and instructed 
 him to buy 400 shares of Baltimore & Ohio whenever he could 
 do so at 102 regular. On the same day he bought the stock as 
 directed. On Feb. 27 I ordered him to sell, and he did so at 
 105| cash. What was my net gain? 
 
 7. May 25 a speculator sent his broker a margin of $ 2000 
 with which to buy 100 shares Metropolitan Street Railway at 
 165 regular. The broker invested as directed. On May 27 
 the stock rose to 170| and the broker was authorized to sell. 
 If he sold regular at this price, what was the speculator's gain ? 
 the broker's commission? 
 
 8. What is the balance due on the following account current : 
 
 M 
 
 New York,. 
 
 In account current with RICHARD ROE & CO. 
 
 DAYS INTEREST 
 
 PRODUCE EXCHANGES 
 
 481. Just as there are stock exchanges in many of the large 
 cities to supply a regular market for the purchase and sale of 
 securities, so there are produce exchanges (also called boards of 
 trade, chambers of commerce, etc.) to supply a regulated market 
 for the purchase and sale of farm crops. 
 
 Produce exchanges are important accessories of commerce. They 
 promote just and equitable principles of trade ; establish and maintain a 
 uniformity in commercial usages ; and acquire, preserve, and disseminate 
 valuable business information. The more important produce exchanges, 
 by inspecting and grading all of the important food products, protect the 
 public against fraud and adulterations. The cereals, for example, are 
 
408 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 inspected and graded according to their quality. There are usually four 
 grades of wheat and corn, five of barley, and three of oats and rye; No. i 
 wheat is the best quality; No. 4, the poorest; etc. 
 
 The principal produce exchange in the United States is the Chicago Board 
 of Trade. On the floors of this exchange are bought and sold a large part 
 of the cereals and the meat products of the Mississippi Valley and the 
 West. The association thus practically determines the price of these com- 
 modities, not only for the United States, but for the world. 
 
 Commodities are bought and sold on the exchanges for present or for 
 future delivery. Contracts for present delivery are called " cash " contracts ; 
 contracts for future delivery, " futures." Speculative trading in grain and 
 cotton is usually in "futures." 
 
 The established brokers' commissions for transactions on the Chicago 
 Board of Trade are as follows : for grain, \<f> per bushel; for pork, 2|^ per 
 barrel ; for lard and ribs, 2| $ per 100 Ib. 
 
 The lowest margins received are: on grain, $20 per 1000 bu.; on pork, 
 $125 per 250 bbl. ; on lard, $ 175 per 250 tierces ; on ribs, $125 per 50,000 Ib. 
 Of course the margins demanded are sometimes considerably higher than 
 the above figures. 
 
 OPEN. HIGH. Low. CLOSE. 
 
 Wheat July 
 
 Sept. 
 
 Dec. 
 Corn July 
 
 Sept. 
 
 Dec. 
 Oats July .. 
 
 Sept. .. 
 Pork Sept. .. 
 
 Oct. . . . 
 Lard Sept. .. 
 
 Oct. . . . 
 Eibs Sept. .. 
 
 Oct. 
 
 ..87 
 ..87 
 
 89% 
 
 In the accompanying table is 
 shown the opening, highest, lowest, 
 and closing prices of provisions for 
 a certain day on the Chicago Board 
 of Trade. 
 
 "Wheat July" signifies wheat 
 to be delivered in July ; " Wheat 
 Sept." wheat to be delivered in Sep- 
 tember; etc. The usual time for fu- 
 ture delivery is during the months of May, July, September, and December. 
 
 In the following exercise it is assumed that all transactions are effected 
 through a broker who charges the usual commission. 
 
 WRITTEN EXERCISE 
 
 1. What will it cost me to buy 5000 bu. September wheat 
 at the opening price in the table ? 
 
 2. C bought 6000 bu. July oats at 27^ per bushel and sold 
 the same at the closing price in the table. What was his net 
 gain ? 
 
 3. B bought 15,000 bu. July corn at the lowest price and 
 sold the same at the highest price in the table. Did he gain 
 or lose, and how much ? What per cent ? 
 
STOCKS AND BONDS 409 
 
 4. G bought 2250 tierces (765,000 Ib.) of October lard at 
 $ 7.26-J and sold the same at the closing price in the table. Did 
 he gain or lose, and how much ? 
 
 5. F bought 1500 bbl. of September pork at the opening 
 price and sold the same at the closing price in the table. Did 
 he gain or lose, and how much ? 
 
 6. D ordered his broker to sell 5000 bu. September corn and 
 buy 5000 bu. December corn. If the broker sold at the 
 highest price and bought at the lowest price in the table, what 
 amount should he remit D ? 
 
 7. A broker bought on his own account 10,000 bu. of each, 
 September wheat, December corn, and July oats, at the opening 
 price, and sold the same at the closing price in the table. Did 
 he gain or lose, and how much ? 
 
 8. H sold " short" 10,000 bu. September wheat at the 
 highest price in the table. September wheat subsequently 
 declined to 85 J and he bought at this price to "cover his 
 short." Did he gain or lose, and how much ? 
 
 9. June 27 I deposited with my broker a margin of $ 200 for 
 the purchase of 5000 bu. of September wheat at the lowest 
 price in the table. On July 25 I ordered him to sell. He 
 did so, receiving 89f ^ per bushel. How much should he pay 
 me in settlement ? 
 
 10. Aug. 5 I deposited with my broker $2500 as a margin for 
 the purchase of 5000 bbl. of October pork at the closing price 
 in the table. On Sept. 2 I ordered him to sell at 113.071. 
 He did so and remitted me a check for the amount due. 
 What was the amount of the check ? 
 
CHAPTER XXXIV 
 
 LIFE INSURANCE 
 
 482. Life insurance companies, like fire insurance companies 
 (page 274), are usually either stock companies or mutual com- 
 panies. 
 
 There are also assessment companies and fraternal beneficiary associa- 
 tions. These usually depend upon monthly assessments or "calls" to pay 
 death claims. They are required by law to hold but comparatively little, 
 if anything, as a fund from which to pay losses. 
 
 483. Insurance rates are always a certain price per $ 1000 of 
 insurance. They are payable annually, semiannually, or 
 quarterly in advance. 
 
 484. The four leading kinds of policies are : ordinary life, 
 limited life, endowment, and term. 
 
 485. An ordinary life policy, in consideration of premiums to 
 be paid during the life of the insured, guarantees to pay at his 
 death a stated sum of money. 
 
 486. A limited life policy, in consideration of premiums to 
 be paid for a fixed number of years, guarantees to pay a stated 
 sum of money at the death of the insured. 
 
 It will be observed that in an ordinary life policy the premiums are pay- 
 able during the life of the insured, while in a limited life policy they are 
 payable for a fixed number of years, when the policy becomes paid up (no 
 more premiums due). The premium is higher on the latter form of policy. 
 
 487. An endowment policy, in consideration of premiums 
 paid for a fixed number of years, guarantees to pay a stated 
 sum of money to the insured at a certain time or to the bene- 
 ficiary (one in whose favor the insurance is effected) in case of 
 prior death. 
 
 488. A term policy, in consideration of premiums paid for a 
 fixed time, guarantees to pay a stated sum of money if the 
 insured dies within the term of insurance. 
 
 410 
 
LIFE INSURANCE 
 
 411 
 
 Thus, a person may insure his life for a limited number of years only. 
 Since the company may never be called upon to pay the insurance, the 
 premiums on these policies are low. 
 
 489. The reserve is that part of the premiums of a policy, 
 with interest thereon, required by law to be set aside as a fund 
 to be used in payment of the policy when it falls due. 
 
 The legal rate of interest on reserve .funds varies slightly in different 
 states. The higher the rate of interest, the smaller the reserve required. 
 
 490. The surplus of an insurance company is the excess of 
 its assets (resources) over its liabilities. 
 
 This fund, with certain restrictions, may be used for such purposes as 
 the company deems best. After retaining a surplus large enough to pro- 
 vide for contingencies, companies which issue policies on the mutual or 
 participating plan divide the remainder of the surplus among such of its 
 policy holders as are entitled to share in it. This is practically a return of 
 an overcharge, but it is usually called the payment of a dividend. 
 
 491. Dividends may be used: (1) to reduce the next year's 
 premium ; (2) to purchase additional insurance, payable when 
 the policy matures ; (3) to shorten the time to run. 
 
 Dividends may also be left with the company, with the distinct under- 
 standing that there shall be no division of the same until the end of 
 a certain period. As the policyholder receives no benefit unless he 
 survives the selected period, it will be seen that the return should be some- 
 what larger. This plan is called semi-tontine, distribution period, accumu- 
 lated surplus, deferred dividend, etc. 
 
 492. If a policy is discontinued, the insured may secure an 
 equitable return for the reserve accumulated. 
 
 The insured usually has several options in this matter : (1) he may take 
 the cash value, or practically all of the reserve value of the policy ; (2) he 
 may take a paid-up policy for such an amount as its reserve value will pur- 
 chase ; (3) he may take extended insurance for the face of the policy for as 
 many years and days as its reserve value will purchase. 
 
 ANNUAL PREMIUM RATES FOR AN INSURANCE OF $1000 
 
 AGE 
 
 OIMMNAIIY 
 Lira 
 
 20- PAYMENT 
 
 LIFE 
 
 15-YKAR 
 
 ENDOWMENT 
 
 20-YEAR 
 
 ENDOWMENT 
 
 25 
 
 20.93 
 
 30.90 
 
 66.57 
 
 48.93 
 
 30 
 
 23.75 
 
 33.76 
 
 67.27 
 
 49.72 
 
 35 
 
 27.39 
 
 37.25 
 
 68.26 
 
 50.88 
 
 40 
 
 32. 16 
 
 41.60 
 
 69. 76 
 
 52.70 
 
 50 
 
 47.23 
 
 54.65 
 
 76.20 
 
 60.59 
 
412 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. What kind of a policy is that 011 page 413 ? Who is the 
 beneficiary? the insured? What is the annual premium? 
 
 2. Should the beneficiary die in 1912, to whom would the 
 policy be payable at the death of the insured in 1920 ? 
 
 3. Should the insured die after having paid one annual 
 premium, how much would his heirs receive ? 
 
 4. If the surplus earnings (dividends) on the policy amount 
 to $ 1200, at the end of 10 yr., how much cash (see page 414) 
 would the insured receive should he surrender the policy ? 
 
 5. Should the insured decide to discontinue paying premiums 
 after making five annual payments, how much ptaid-up in- 
 surance, exclusive of the surplus, might he receive ? 
 
 6. How large a sum may the insured borrow on the policy 
 after ten premiums have been paid ? 
 
 7. If the company secures interest in advance by deducting 
 it from the amount of the loan, and the insured should borrow 
 $4000 for one year at 5 %, what would be the amount of the 
 check which he would receive from the company ? 
 
 8. Had the insured taken out the policy when he was 
 twenty-five years of age, what would be the annual saving, 
 exclusive of interest, in the cost ? How much would he have 
 saved in 15 yr. ? in 20 yr. ? 
 
 9. If the insured should discontinue paying premiums after 
 5 yr. and take extended insurance, how much would the 
 beneficiary receive should the insured die in 1914? in 1919? 
 
 10. If the insured had taken a life policy (see rates, page 
 411) for the same amount, instead of an endowment policy, and 
 died after having paid ten full premiums, how much less would 
 his insurance have cost, exclusive of dividends and interest ? 
 
 11. If the insured should pay four full premiums on the 
 policy, take extended insurance, and die 5 yr. later, how much 
 would his beneficiary receive ? 
 
 12. If the insured discontinues making payments after seven 
 annual premiums had been paid, how much would he get in 
 cash at the end of 20 yr. from date of issue, if living ? 
 
LIFE INSURANCE 
 
 413 
 
 AGE 
 
 SUM INSURED 
 $/ '0,000 
 YEARLY PREMIUM 
 
 I n Consideration of the Application for this Policy, hereby made a part of this contracf, 
 
 The Penn Mutual Life Insurance Company of Philadelphia 
 
 insures thejife of WWWtQ ^.(dfcm?OU ~ r~^ 
 
 in the County of ff VOttfOl State of 
 
 ~ - Dollars, and promises 
 to pay at its Home Office, in the City of Philadelphia, unto ' ' " 
 
 executors, administrators, or assigns, the said sum insured on the 
 day of <^P&&&/ in the year nineteen hundred and--^^ 
 or if the said insured should die^before that time then to make said payment to 
 
 <TS .. * . ^* ,<*-* 0> . L. . f: .,.?.. ./) /) /? 
 
 ENDOWMENT 
 
 IN 2-0 YEARS 
 Regular 
 
 executors, administrators, or assigns, upon receipt of satisfactory proof of the death of the 
 insured, during the continuance in force of this Policy, upon the following conditions, namely : 
 payment in advance to the Company, at its Home Office, of the sum of 
 
 ^y/oo Dollars, at the date hereof, and of the 
 premium of ^^e.J^J^^^<^fe^^C^%:x^Dollars, 
 at or before three o'clock P.M., on the ^e^t^n^ day of v- /^^2^ x 
 
 in every year during the continuance of this contract, or until 
 
 %tt/&?z6y full years' premiums shall have been paid : 
 
 This Policy shall participate annually in the surplus earnings of the Company in accord- 
 ance with the regulations adopted by the Board of Trustees. 
 
 The extended insurance* paid-up insurance, and loan or cash surrender value privileges, 
 benefits, and conditions stated on the second page hereof form a part of this contract as fully 
 as if recited at length over the signatures hereto affixed. 
 
 In Witness Whereof, The Penn Mutual Life Insurance Company 
 
 of Philadelphia has caused this Policy to be signed by its President, Secretary, and 
 Actuary, attested by its Registrar, at its Home Office, in Philadelphia, Pennsylvania, the 
 day of <_x^<^/ / 19 07, 
 
 Secretary. 
 
 / J 
 
 Attest 
 
 President. 
 
 Actuary. 
 
414 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 Table of Extension, Paid-up, and Loan or Cash Values, provided 
 for by the Policy, if no indebtedness exists against it 
 
 AT 
 END OF 
 YEAR 
 
 TERM OF EXTENSION 
 FOR THIS POLICY 
 
 These Values are for $1 
 For this Policy multiply by /..(?..... 
 
 OOO Insurance 
 
 
 
 
 LOAN OR CASH 
 SURRENDER VALUES 
 
 END OF EXTENSION 
 
 ON SURRENDER 
 
 3d 
 
 //) Years ^^Days 
 
 $ 
 
 $ , 
 
 $ JTJ- 
 
 2- / 
 
 4th 
 
 /^ " J># " 
 
 
 ^/^ 
 
 / 2-t, 
 
 4-tr 
 
 5th 
 
 /J- " ' " 
 
 ^0 
 
 2. -7 f" 
 
 / ,# 
 
 2- / 
 
 6th 
 
 /^ " 
 
 /.B / 
 
 JLJJL 
 
 ^ /^ 
 
 < 
 
 7th 
 
 / 3 " 
 
 2~ / 
 
 3 <Tt 
 
 ZJ-& 
 
 3 J 
 
 8th 
 
 / 2- ' 
 
 z r 
 
 ^3 
 
 3 # (, 
 
 ^ 
 
 8th 
 
 // - 
 
 .1.J-& 
 
 ^^-7 
 
 lj- 
 
 10th 
 
 /n 
 
 ^2^0 
 
 
 2/1 & 7 
 
 / 
 
 llth 
 
 a 
 
 4^ a -7 
 
 
 */<J~ 
 
 p^ 
 
 12th 
 
 
 t 4- 2. 
 
 3 
 
 j2A 
 
 V f 
 
 13th 
 
 2 
 
 2.^ 
 
 F*- 
 
 .4-t / 
 
 2.P- 
 
 14th 
 
 ( 
 
 ftf 
 
 ^73 / 
 
 / t 
 
 ^TJ~ 
 
 15th 
 
 
 -7t/2- 
 
 7 *7 7 
 
 & *7 Z{ 
 
 <?t> 
 
 16th 
 
 sf 
 
 7 & f- 
 
 FZJ 
 
 >7JJ 
 
 7 7 
 
 17th 
 
 \3 
 
 
 Ff 
 
 -rat 
 
 
 18th 
 
 2. 
 
 #32- 
 
 & / J 
 
 f / 
 
 ^ / 
 
 19th 
 
 / 
 
 '&J-2. 
 
 '#J-t 
 
 &2F 
 
 7 / 
 
 20th 
 
 , 
 
 Afil 
 
 tt3&Ktutt 
 
 UUL& 
 
 & 
 
 
 
 
 y ? 
 
 
 
 
 
 
 
 
 
 Should any indebtedness exist it shall be deducted from the Cash Value of the Policy, 
 and the other values shall be diminished proportionately 
 
LIFE INSURANCE 415 
 
 WRITTEN EXERCISES 
 
 1. If the insured in the foregoing policy should die just be- 
 fore the twelfth payment was due, how much would the estate 
 receive above his total payments ? 
 
 2. Suppose that the insured in the foregoing policy survives 
 the endowment period, and the surplus earnings of the policy 
 amounted to $ 3500. What would be the difference between the 
 amount received and the amount paid, not reckoning interest ? 
 
 3. The insured in the foregoing policy took out a 110,000 
 20-payment life policy at the same time he procured his endow- 
 ment policy. The guaranteed cash value on the former was 
 $ 2557.80 at the end of 10 yr., and the dividends for this term 
 amounted to $83.22 per thousand. If the dividends on the 
 endowment policy for this period amounted to $ 127.83 per thou- 
 sand, which would have been the better investment, interest not 
 being considered, and how much ? 
 
 4. Assuming that the insured in the foregoing policy survived 
 the endowment period and that the dividends which amounted 
 to $350 per thousand were used to add to the value of the pol- 
 icy, how much less would he receive from the company than he 
 would from investing the amount of the premiums in a savings- 
 bank annually for 20 yr. at 4 % interest ? 
 
 5. What will be the first annual premium on a $15,000 ordi- 
 nary life policy for a man 50 yr. old ? 
 
 6. On his 25th birthday A took out a 20-yr. endowment 
 policy for $5000 : on his 35th birthday, a 15-yr. endow- 
 ment policy for $6000; on his 40th birthday, a 20-payment 
 life policy for $10,000. He died aged 43 yr., 6 mo. How 
 much more did his heirs receive (dividends excepted) than he 
 had paid the company ? 
 
 7. B at the age of 25 yr. took out a 20-payment life policy 
 for $5000. He died just before his twentieth payment became 
 due. The company allowed $87.50 per thousand in dividends 
 during this period, and these were used to reduce the annual 
 premium. How much more did his heirs receive than was paid 
 in premiums ? 
 
PARTITIVE PROPORTION, PARTNERSHIP, 
 AND STORAGE 
 
 CHAPTER XXXV 
 
 PARTITIVE PROPORTION AND PARTNERSHIP 
 PARTITIVE PROPORTION 
 
 ORAL EXERCISE 
 
 1. A fails in business owing D $500, E $1500, and F $2500. 
 If his resources are $1800, how much can he pay each of his 
 creditors ? 
 
 2. Two brothers, A and B, are engravers. A can earn $10 
 per day and B $5 per day. How much can they both earn in 
 a day ? What part of this amount can B earn ? A ? 
 
 3. They formed a partnership for one year and agreed to 
 divide the net profits in proportion to the earning capacity of 
 each. If the net profits for the year were $3600, what was the 
 share of each ? 
 
 4. C invests $3000, B $6000, arid A $9000 in a manufacturing 
 plant. The net profits for one year are $3600, and this sum is 
 shared in proportion to the amount of capital invested. What 
 amount does each receive as his share of the net profits ? 
 
 5. A certain street was paved at a cost of $3000. The prop- 
 erty owners on the street were A, who owned 200 ft. frontage, 
 B, who owned 400 ft. frontage, and C, who owned 600 ft. front- 
 age. If the cost of the paving was assessed on the property 
 owners in proportion to the frontage owned, how much did 
 each pay ? 
 
 493. The process of dividing a number into parts propor- 
 tional to several given numbers is called partitive proportion. 
 
 416 
 
PARTITIVE PROPORTION AND PARTNERSHIP 417 
 WRITTEN EXERCISE 
 
 1. Divide $42,770 among G, H, and I in proportion to ^, , 
 and -J, respectively. 
 
 SUGGESTION. , |, and % - |, j, and $, respectively. Therefore, |, $, and 
 | stand in the same relation to each other as f, f, and , or as 2, 4, and 1. 
 
 2. Divide the simple interest on f 72,000 for 1 yr. 7 mo. at 
 3J% among D, E, and F so that D's part will be twice E's part 
 and one half of F's part. 
 
 3. An inheritance of $75,000 was divided among 3 sons and 
 4 daughters, so that each daughter received ^ more than each 
 son. How much did each son receive ? each daughter ? 
 
 4. A, B, and C were partners in a business. A put in. 
 110,000, B 16000, and C $9000. Their net gain for a year was 
 $17,500, shared in proportion to the amount of capital invested. 
 What was each partner's share of the net gain ? 
 
 PARTNERSHIP 
 
 ORAL EXERCISE 
 
 1. I invested $ 500 in a business and during the first year 
 gained $1100. No withdrawals or subsequent investments 
 having been made, what was my present worth at the close of 
 the year ? 
 
 2. Jan. 1 M invested $ 7500 in a factory. July 1 he found 
 that his net loss was $ 1125. What was his present worth 
 July 1, no withdrawals or subsequent investments having been 
 made ? 
 
 3. Answer problem 1 assuming that there was a withdrawal 
 of $ 800 made during the year ; problem 2 assuming that there 
 was a subsequent investment of $ 1200 made on Mar. 1. 
 
 4. Apr. 1 B commenced business with a cash investment of 
 $ 1500 ; Jan. 1 of the next year his present worth was $ 1875. 
 What was his net gain or loss, no withdrawals or subsequent 
 investments having been made ? 
 
418 PRACTICAL BUSINESS ARITHMETIC 
 
 5. July 1 D began business investing 125,000; Jan. 1 of 
 the next year his net capital was $ 23,150. If no withdrawals 
 or subsequent investments were made, did he gain or lose, and 
 how much ? 
 
 6. Answer problem 4 assuming that there were withdrawals 
 amounting to $ 1000 ; problem 5 assuming that there was a 
 subsequent investment of $5000. 
 
 7. June 1 F began business with a capital of $ 1750. 
 During the 6 mo. following he lost $ 2750. What was the 
 condition of his business Dec. 1 ? 
 
 8. Z began business on July 1 with a capital of $ 2500. 
 6 mo. later his net insolvency was found to be $ 1250. What 
 was his net gain or loss ? 
 
 9. A's business was insolvent $ 1250 on Jan. 1. From 
 Jan. 1 to July 1 he gained $ 1750. What was the condition 
 of his business July 1 ? 
 
 10. G gained $ 3750 during a certain year. He then found 
 that his net capital was $1250. What was the condition of 
 his business at the beginning of the year ? 
 
 11. June 30, 1906, C's resources were I 7500 and his liabili- 
 ties $ 5000. June 30, 1907, his resources were $ 5000 and his 
 liabilities $ 7500. What was his net gain or loss during this 
 period ? 
 
 12. Were the conditions in problem 11 reversed for the year 
 stated, what would be the net gain or loss ? 
 
 13. What is meant by resources? liabilities? gain? loss? 
 
 14. What is meant by net gain? net loss? present worth? 
 net capital? net insolvency? 
 
 15. Read aloud the following, supplying the missing words: 
 The condition of the business at the beginning -f the 
 
 or the = the condition of the business at the 
 
 close ; and conversely, the condition of the business at the 
 
 close H- the or the = the condition of 
 
 the business at the beginning. 
 
PARTITIVE PROPORTION AND PARTNERSHIP 419 
 
 494. A partnership is an association of two or more persons 
 who have agreed to combine their labor, property, and skill, 
 or some of them, for the purpose of carrying on a common 
 business and sharing its gains and losses. 
 
 Partnerships may be formed by either an oral or a written agreement, and 
 in some cases by implication ; but all important partnerships should be 
 entered upon by an agreement in writing which definitely states all of the 
 conditions relating to the business. 
 
 495. The members of a partnership are called partners. 
 
 Partners may be divided into four classes: (1) Real, or ostensible, those 
 who are known to the world as partners and who in reality are such; 
 (2) nominal, those who are known to the world as partners but who have 
 no investment and receive no share of the gain ; (3) dormant, or silent, 
 those who are not known to the world but who nevertheless partake of the 
 benefits of the business and thereby become partners ; (4) limited, or 
 special, those whose liability is limited. 
 
 Nominal partners, like real, or ostensible, partners, are liable to third 
 parties for the debts of a business. Dormant partners are liable for the 
 debts of the business as soon as their partnership connections become known 
 to the world. 
 
 Ordinarily each partner is liable for all of the debts of the firm, but a 
 special partner's liability is limited usually to the amount which he con- 
 tributes to the firm's capital. 
 
 The method of forming a limited partnership is prescribed by statute. 
 This differs somewhat in the different states. Such a partnership must 
 usually have at least one member whose liability is not limited and who is 
 the manager of the business. 
 
 496. The capital of a partnership constitutes all the moneys 
 and other properties contributed by the different partners to 
 carry on the business. 
 
 GAINS AND LOSSES DIVIDED EQUALLY 
 
 497. The gains and losses of a business are divided among 
 the partners in accordance with the agreement or contract en- 
 tered into when the partnership was formed. If the partners 
 invest equal sums and contribute equally in work, the gains are 
 usually divided equally. 
 
420 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 l. Copy and complete the following ledger page : 
 
 30 
 
 Jo 
 
 , 7 cf? 
 
 !&4 
 
 t^Z^Si^^^^^i^ 
 
 ^W-**-d<^^-7-2-'*Z^ 
 
 J~006 
 
 ff 
 
 In solving problems 2-4 use ledger paper as above. 
 
 If the student is not familiar with simple accounts, pages 41-47 should 
 be reviewed. 
 
 2. Jan. 1, 1907, C. B. Johnson and B. H. Briggs engaged in 
 a partnership business, each investing $3750. July 1, 1907, 
 each partner withdrew $ 250. Jan. 1, 1908, their losses and 
 gains were as follows : 
 
 LOSSES GAINS 
 
 Expense $104.75 Merchandise $628.45 
 
 Merchandise Discounts 24.20 Interest and Discount 133.50 
 
 Real Estate 250.60 Stocks and Bonds 190.50 
 
 What was the present worth of each partner Jan. 1, 1908 ? 
 
PARTITIVE PROPORTION AND PARTNERSHIP 421 
 
 3. A, B, and C were partners for a year. Each invested 
 $9500 and during the continuance of the partnership each with- 
 drew $1000. The losses and gains at closing were as follows : 
 
 LOSSES GAINS 
 
 Merchandise Discounts $18.90 Merchandise $4375.80 
 
 Expense 650.00 Interest and Discount 90.14 
 
 What was the net capital of each at closing? 
 
 4. O, P, and Q are partners sharing the gains and losses in 
 equal proportions. O invested 18500, P 18200, and Q 18450. 
 During their first year the gains were as follows : merchandise, 
 16457.10 ; real estate, 1680.50 ; interest and discount, $29.90. 
 If the cost of conducting the business was $1920.50, what was 
 the present worth of each partner at the end of the year ? 
 
 GAINS AND LOSSES IRREGULARLY DIVIDED 
 
 498. Sometimes the gains are divided according to certain 
 arbitrary fractions which are riot in proportion to the amount 
 invested. In such cases the skill of a partner is frequently 
 considered as being equal to a certain amount of capital. In 
 some cases a certain amount is paid the heavier investor 
 before other division of the gains or losses is made. In still 
 other cases, a stated salary is paid to each partner before the 
 gains or losses of the business are divided. This salary varies 
 according to the ability of the several partners or according to 
 the time each devotes to the business. 
 
 WRITTEN EXERCISE 
 
 l. A and B entered into partnership, each investing $7500. 
 Because of the greater experience of A he was to be credited 
 with $1200 before any other division of the gains or losses. 
 The gains or losses were then to be divided equally. During 
 the first year the gains were as follows : merchandise, $4111.10 ; 
 real estate, $510. If the losses were $622.80, what was the 
 present worth of each at the end of the year? 
 
422 PRACTICAL BUSINESS ARITHMETIC 
 
 2. A and B entered into partnership, A investing $ 8000 and 
 B '$10,000. B doing no work, it was agreed that A should take 
 $ 2000 from the gains before dividing, and that the net gain or 
 loss should then be shared equally. The gains last year were 
 18900 and the losses 11400. What was the net gain of each? 
 
 3. C, D, and E entered into partnership Jan. 1, each in- 
 vesting $8500. The articles of agreement provided (1) that 
 C should devote all his time to the business and D and E only 
 a portion of their time ; (2) that if losses occurred, they should 
 be borne equally ; (3) that if gains were realized, C should 
 receive \ and D and E each ^. During the year the gains 
 were as follows: Merchandise, $8217.10; Stocks and Bonds, 
 $612.50; Interest, $492.92. If the expenses were $2217.80, 
 what was the present worth of each partner at the close of the 
 year ? 
 
 4. F and G entered into partnership, F investing $5000 and 
 G $7500. Because of the greater skill of F it was agreed that 
 he should be credited with $ 1500 a year before other division of 
 the gains or losses. Then if losses occurred, F was to bear | of 
 them and G ^ ; but if gains were realized, they were to be 
 divided equally. During the first year the gains of the firm 
 were as follows : Merchandise, $3129.50 ; Real Estate, $250 ; 
 Stocks and Bonds, $575; Interest, $130.50. If the cost of 
 conducting the business was $938.48 (exclusive of F's salary), 
 what was each partner's net capital at the close of the year ? 
 
 5. J, K, and L entered into partnership, J investing 
 $20,000, K $10,000, and L nothing. The articles of agreement 
 provided (1) that the gains or losses should be shared as 
 follows : J, f, K, ^, L, 2 3 o 5 (2) that the capital should be kept 
 intact ; (3) that before any division of the profits was made, J 
 should be credited with an annual salary of $1500. At the 
 end of a year the resources were found to be $65,250 and the 
 liabilities (not including J's salary), $16,750. What was each 
 partner's share of the net gain ? After the net gain was 
 credited, what was the net capital of each partner ? 
 
PARTITIVE PROPORTION AND PARTNERSHIP 423 
 
 GAINS AND LOSSES DIVIDED ACCORDING TO INVESTMENT 
 
 499. Sometimes the gains and losses are divided in propor- 
 tion to the amount invested ; that is, according to the princi- 
 ples of partitive proportion. 
 
 500. Example. A and B engaged in business, agreeing to 
 share the gains or bear the losses in proportion to the amount 
 of capital invested. A invested 12500 and B 13500. They 
 gained $1800. What was the share of each? 
 
 SOLUTION. $2500 + $ 3500 = $ 6000, the total capital. Since the total capital 
 is $6000 and A put in $2500, A's share is $$#, or T \, and B's share is ff{$, or 
 r 7 z . Therefore, A should receive T \ of $ 1800, or $750, and B should receive 
 & of $ 1800, or $ 1050. 
 
 ORAL EXERCISE 
 
 Find each mans gain or loss in each of the following problems : 
 INVESTMENT GAIN INVESTMENT Loss 
 
 1. A, $ 3000; B, 12000 $500 6. K,$2000; L,$4000 $120 
 
 2. C, 11000; D, 12000 $150 7. M,$1500; N, $2000 $700 
 
 3. E, $1200; F, $4800 $1200 8. O,$1000; P,$5000 $600 
 
 4. G,$1500; H, $4500 $1800 9. Q,$1500; R,$6000 $750 
 
 5. I, $1500; J, $7500 $1500 10. S, $1750; T,$3500 $600 
 
 WRITTEN EXERCISE 
 
 1. A, B, and C invested $2000, $3000, and $5000, respec- 
 tively, in a wholesale dry goods business. During the first year 
 the net profits were $4155.80. What was the share of each ? 
 
 2. D, E, and F invested $2500, $3250, and $3500, respec- 
 tively, in a manufacturing business. At the close of the first 
 year their profits were found to be $3774.37. What was the 
 share of each ? 
 
 3. G, H, and I formed a copartnership, G investing $3000, 
 H, $2000, and I, $1500. During the first six months their net 
 gain was $1829.10. How much was each man worth after his 
 share of the net gain had been carried to his account ? 
 
424 PRACTICAL BUSINESS ARITHMETIC 
 
 4. Copy and complete the following statement : 
 
PARTITIVE PROPORTION AND PARTNERSHIP 425 
 
 INTEREST ALLOWED AND CHARGED 
 
 501. The inequalities in investments and withdrawals are 
 frequently adjusted by allowing and charging interest upon 
 same. When interest is allowed and charged on investments 
 and withdrawals, the gains and losses are usually divided 
 equally. 
 
 502. Example. June 1, 1907, C. H. Dean and E. D. Snow 
 formed a partnership, C. H. Dean investing $5000 and E. D. 
 Snow $ 4000. They agreed that the gains and losses should be 
 divided equally, but that, owing to the unequal investments, 
 each partner should be allowed interest at 6 % on all sums 
 invested and charged interest at the same rate on all sums 
 withdrawn, said interest to be adjusted at the time of closing 
 the books. The profits for the first six months were $ 1050. 
 What was the net capital of each partner after the interest was 
 adjusted and the net gain carried to his account ? 
 
 C. H. DEAN 
 
 1906 
 Dec. 
 
 1 
 
 Net Capital 
 
 5540 
 
 00 
 
 1906 
 
 June 
 Dec. 
 
 1 
 1 
 1 
 
 Investment 
 Interest 
 \ Net Gain 
 
 Net Capital 
 
 5000 
 15 
 525 
 
 00 
 00 
 00 
 
 5540 
 
 00 
 
 5540 
 
 00 
 
 
 
 
 
 Dec. 
 
 1 
 
 5540 
 
 00 
 
 E. D. SNOW 
 
 1SI07 
 
 
 
 
 I 
 
 1907 
 
 
 
 
 
 Dec. 
 
 1 
 
 Interest 
 
 15 
 
 00 
 
 June 
 
 1 
 
 Investment 
 
 4000 
 
 00 
 
 
 1 
 
 Net Capital 
 
 4510 
 
 00 
 
 
 1 
 
 i Net Gain 
 
 525 
 
 00 
 
 
 
 
 4525 
 
 00 
 
 
 
 
 4525 
 
 00 
 
 
 
 
 
 ~l 
 
 Dec. 
 
 1 
 
 Net Capital 
 
 4510 
 
 00 
 
 SOLUTION. $ 5000 in 6 mo. will earn $ 150 interest. $ 4000 in 6 mo. will earn 
 
 $120 interest. S 150 + $ 120 -H 2 = $135, the average interest earned. 
 $ 150 - $ 135 = $ 15 ; that is, C. H. Dean's interest is $ 15 above the average. 
 $ 135 $ 120 = $ 15 ; that is, E. D. Snow's interest is $15 below the average. 
 Therefore to adjust the interest on the investments, credit C. H. Dean's ac- 
 count $ 15 and charge E. D. Snow's account $ 15. ^ of $ 1050 = $ 525, the net 
 gain of each. Credit each account with the net gain ; then C. II. Dean's net 
 capital is $5540 and E. D. Snow's net capital $4510. 
 
426 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. Copy and complete the following statement of conditions 
 
 QZ^zfys^^ 
 
 
 it 
 
 43 &S 
 
 2-0 &c*J 
 
 2-2. e>y 
 
 ? 2. Of 
 
 fo 
 
PARTITIVE PROPORTION AND PARTNERSHIP 427 
 
 2. W. H. Burgess and Otis Clapp began business July 1, 
 1906, the former investing 112,000 and the latter 110,000. 
 They agreed that the gains and losses should be divided equally, 
 but that, because of the inequality in the investments, interest 
 at 6 % should be allowed on investments and charged on with- 
 drawals. July 1, 1907, the firm's resources and liabilities 
 (partners' accounts excluded) were as follows : 
 
 RESOURCES LIABILITIES 
 
 Cash $4150.00 Accounts Pay. $7500. 
 
 Accounts Rec. 8150.60 Notes Pay. 4900. 
 
 Mdse. 18210.50 
 
 Notes Rec., on hand 4250.00 
 
 Street Railway Stock 3000.00 
 
 Store and Lot 5200.00 
 
 Office Fixtures 500.00 
 
 Make a statement, as in problem 1, showing the present con- 
 dition of the business. 
 
 3. Aug. 1, 1906, F. E. Greene and W. B. Linden formed a 
 partnership for the purpose of carrying on a manufacturing 
 business. F. E. Greene invested $8500 and W. B. Linden, 
 $10,750. It was agreed that interest at 6% should be allowed 
 and charged on investments and withdrawals and that the gains 
 and losses should be divided equally. At the close of the first 
 year the resources and liabilities (partners' accounts excluded) 
 were as follows : 
 
 RESOURCES LIABILITIES 
 
 Cash 12355.20 Notes Pay. $1158.25 
 
 Mdse. 5284.85 Accounts owed by the busi- 
 
 Notes Rec. 2840.00 ness 2100.00 
 
 Accounts owing the business 4170.50 
 Office Fixtures 450.00 
 
 Feb. 1, 1907, F. E. Greene withdrew $750 and W. B. Linden 
 $600. Make a statement showing the condition of the business 
 at the close of the year. 
 
 4. James B. Westfall and John L. Manning began a common 
 business on Sept. 1, 1906, the former investing $14,500 and 
 the latter $13,935. They agreed that interest at 6/0 should be 
 
428 PRACTICAL BUSINESS ARITHMETIC 
 
 allowed and charged on investments and withdrawals, respec- 
 tively, and that the gains and losses should be divided equally. 
 Sept. 1, 1907, a trial balance of their general ledger was as 
 
 follows : 
 
 DEBITS CREDITS 
 
 James B. Westfall $14500.00 
 
 John L. Manning 13935.00 
 
 Cash $13368.64 
 
 Merchandise 31664.00 20000.00 
 
 Office fixtures 510.50 
 
 Horse and wagon 405.00 
 
 Real estate 7000.00 
 
 Expense 445.80 
 
 Collection and exchange 12.20 
 
 Mdse. discounts 58.50 
 
 Accounts receivable 6852.84 
 
 Accounts payable 8864.75 
 
 Bills payable 3000.00 
 
 Interest and discount 17.73 
 
 $60317.48 $60317;48 
 
 The merchandise unsold was found to be worth 113,827.35 ; 
 the real estate, $7500 ; the office fixtures, 1500 ; the horses and 
 wagons, $ 400; and the expense items on hand, 102.50. There 
 was due on the merchandise account for freight, $138.50, and 
 on the expense account for telephone service, $25. Make a 
 statement showing the condition of the business Sept. 1, 1907. 
 (See model, page 431.) 
 
 GAINS AND LOSSES DIVIDED ACCORDING TO THE AVERAGE 
 
 INVESTMENT 
 
 503. That sum which, invested for a certain period, is 
 equivalent to two or more sums invested for different periods, 
 is called an average investment. The gains and losses of a 
 business are sometimes divided in proportion to the average 
 investment. 
 
 504. Example. April 1, 1906, A and B formed a partner- 
 ship and agreed to share the gains or losses according to aver- 
 age net investment. A furnished $10,000 of the capital and 
 
PARTITIVE PROPORTION AND PARTNERSHIP 429 
 
 B 17500. July 1 A withdrew 11500 and B $500. Apr. 1, 
 1907, their net gain was found to be 112,800. What was 
 the net gain of each partner? 
 
 SOLUTION 
 
 A had in $10,000 for 3 mo., when he withdrew $1500, leaving $8500 for the 
 remaining 9 mo. 
 
 B had in 87500 for 3 mo., when he withdrew $500, leaving $7000 for the 
 remaining 9 mo. 
 
 A's $10000 for 3 mo. = $30000 for 1 mo. 
 
 A's $8500 for 9 mo. = $76500 for 1 mo. 
 
 A's average net investment = $ 106500 for 1 mo. 
 
 B's $7500 for 3 mo. = $22500 for 1 mo. 
 
 B's $ 7000- for 9 mo. = $63000 for 1 mo. 
 
 B's average net investment = $85500 for 1 mo. 
 $ 106500 + $85500 = $192000, the firm's average net investment for 1 mo. 
 
 A's share is i|f^, or ^V 
 
 B's share is T W<&V or r 5 2 V 
 
 Therefore, A should receive T y* of $12800, or $7100. 
 
 And B should receive ^ of $12800, or $5700. 
 
 WRITTEN EXERCISE 
 
 1. Apr. 1 R and C formed a partnership for 1 yr., the 
 former investing $4500 and the latter 16000. They agreed 
 to share the gains and losses in proportion to the average net 
 investment. Aug. 1 R invested $1500, and C withdrew $1000. 
 On closing the books at the end of the year the net loss was 
 found to be $1290. What was each partner's present worth 
 after his account was charged with his share of the net loss ? 
 
 2. June 1, 1906, E and F formed a copartnership for the 
 purpose of carrying on a real estate business. E invested 
 $25,000 and F $15,000. They agreed to share the gains and 
 losses in proportion to the average net investment. Sept. 1, 
 
 1906, E withdrew $1000 and F $500. Dec. 1, 1906, each 
 withdrew $1000. Mar. 1, 1907, F invested $5000. June 1, 
 
 1907, the partnership was dissolved. After all resources were 
 converted into cash and all liabilities to outside parties paid, 
 the amount of cash in bank was $ 50,890. What amount was 
 due each partner? 
 
430 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Apr. 1, 1907, W. L. Cutter and O. M. Woodward formed 
 a copartnership for the purpose of carrying on a dry goods 
 business. W. L. Cutter invested 820,500 and O. M. Wood- 
 ward $18,500. They agreed to allow interest at 6% on 
 investments, charge interest at the same rate on withdrawals, 
 and divide the gains and losses equally. July 1, 1907, W. L. 
 Cutter withdrew 1 500. Oct. 1 O. M. Woodward withdrew 
 $1000 and W. L. Cutter $750. At the close of the year the 
 resources and liabilities, exclusive of partners' accounts, were 
 as follows : 
 
 RESOURCES LIABILITIES 
 Cash in bank $2130.60 Accounts owed by the busi- 
 Stocks and bonds on hand 6450.00 ness $7260.00 
 Goods in stock 16095.00 Notes payable unredeemed 1200.00 
 Notes receivable on hand 6150.00 
 Office fixtures on hand 500.00 
 Accounts owing the busi- 
 ness 12260.52 
 
 Make a statement showing the condition of the business 
 Apr. 1. 1908. 
 
 2. July 1, 1906, A. B. Curtis and B. H. Barton formed a 
 partnership and invested $ 7500, of which A. B. Curtis fur- 
 nished | and B. H. Barton, -|. Jan. 30, 1907, their resources 
 were as follows: merchandise, unsold, $2172.70; cash on 
 hand, $2823.96; real estate on hand, $3100; account against 
 James Noble, $840.10; account against A. H. Cook & Co., 
 $ 1156.84. On the same date their liabilities were as follows : 
 account in favor of D. M. Frost & Co., $218.60; account 
 in favor of J. B. Neal & Co., $385. During the year the 
 merchandise bought cost $6807.50 and the sales aggregated 
 $7154.90. The cost of carrying on the business was $530.10. 
 Make a statement (see page 424) showing the present condi- 
 tion of the business. Divide the net gain in proportion to the 
 investments. 
 
PARTITIVE PROPORTION AND PARTNERSHIP 431 
 3. Copy and complete the following statement of conditions: 
 
432 PRACTICAL BUSINESS ARITHMETIC 
 
 4. Jan. 1, 1906, C. H. Smith and W. W. Osgoodby formed 
 a copartnership for the purpose of carrying on a real estate 
 business. C. H. Smith invested 115,000 and VV. W. Osgoodby 
 % 10, 000. They agreed to share the gains and losses in pro- 
 portion to the average net investment. July 1, 1906, C. H. 
 Smith withdrew $1000 and W. W. Osgoodby $750. On clos- 
 ing the books at the end of the year the net gain was found to 
 be $8685. What was each partner's present worth after his 
 account was credited with his share of the net gain? 
 
 5. Frank M. Congdon, E. H. Robinson, and O. B. Moulton 
 are partners in a dry goods house under the firm name of 
 E. H. Robinson & Co. On commencing business Aug. 1, 1901, 
 Frank M. Congdon invested $17,500, E. H. Robinson $20,000, 
 and O. B. Moulton $12,000. The articles of agreement pro- 
 vided : (1) that each partner should be allowed interest at 6% 
 on investments and charged interest at the same rate on with- 
 drawals ; (2) that because of special skill and experience 
 Frank M. Congdon should be credited $1500 before any other 
 division of the gains and losses ; (3) that then the gains should 
 be divided equally. Aug. 1, 1908, the results of the year's 
 business were as follows : cost of merchandise purchased, 
 $81,240; value of merchandise on hand, $14,280.95; sales of 
 merchandise, $78,756; cost of real estate, $18,000; cost of 
 permanent improvements on real estate, $1200; present esti- 
 mated value of real estate, $25,000; notes in favor of the firm, 
 $11,500; interest accrued on these notes, $112; cost and pres- 
 ent value of horses and wagons, $ 1250 ; general expenses for 
 the year (exclusive of the amount due Congdon), $1800 ; trav- 
 eling expenses for the year, $1200; accounts owing the firm, 
 $20,160.90; cash on hand, $19,033.10; mortgage on the firm's 
 real estate, $12,000; interest accrued on the mortgage, $480; 
 notes outstanding, $3500; accounts owed by the firm, $11,260. 
 Show in proper statements the financial condition of the 
 partners. 
 
CHAPTER XXXVI 
 
 STORAGE 
 SIMPLE STORAGE 
 
 ORAL EXERCISE 
 
 1. I stored my piano in a warehouse from June 16 to Octo- 
 ber 1 at $1 per month or fraction thereof. What sum must I 
 pay in settlement ? 
 
 2. I rented a room in a storage warehouse from Sept. 1 to 
 Dec. 18 at 6.50 per month or fraction thereof. What amount 
 did I have to pay ? 
 
 3. What must I pay for the storage of 5000 bu. of wheat 
 stored from Dec. 3 to Apr. 15 at 4^ per bushel per month or 
 fraction thereof ? for the storage of 10,000 bu. of corn stored 
 from Dec. 1 to Mar. 1 at 3^ per bushel per month ? 
 
 505. Storage is a charge made for storing goods in a ware- 
 house. 
 
 506. The term of storage is the period of time for which a 
 certain rate is charged. 
 
 The term of storage is usually, though not invariably, 30 da. ; and in 
 estimating charges, a part of a term is counted the same as a full term. 
 
 507. The rates of storage are sometimes fixed by an agree- 
 ment between the contracting parties, sometimes by boards of 
 trade, chambers of commerce, or associations of warehousemen, 
 and sometimes by legislative enactment. 
 
 508. Simple storage is storage estimated at the time of the 
 withdrawal of the goods from the warehouse. 
 
 433 
 
434 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. Verify the following storage bill: 
 
 To Quincy Market Cold Storage and Warehouse Co., Dr 
 
 Main Office, 133 Commercial Street 
 
 FOR STORAGE 
 
 DATE 
 RECEIVED 
 
 QUANTITY 
 
 MERCHANDISE 
 
 STORAGE 
 LOT NO. 
 
 DATE 
 DELIVERED 
 
 QUANTITY 
 
 MO. 
 
 RATE 
 
 AMOUNT 
 
 $a&. 
 
 /-^ 
 
 22 
 
 -r^t. 
 
 tZ^f 
 
 z^T4^T 
 
 -^y^ 
 
 ^ 
 
 /^/7 
 
 ^^ 
 
 _^ 
 
 ^ 
 
 c2 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 'ti'W 
 
 ?(, 
 
 2^2 
 
 /*V7 
 
 
 
 
 
 
 
 
 
 
 
 (Lm 
 
 J 
 
 2 
 
 <P^( 
 
 /?-# 
 
 _ 
 
 ,?/ 
 
 _ 
 
 
 
 
 
 
 
 V 
 
 
 
 ^ 
 
 
 
 
 
 2. When were the eggs received for storage ? If there are 
 30 doz. in a case, how many dozen were received '? 
 
 3. Suppose the rate in the bill were 10^ per case per month 
 or fraction thereof for the first 3 mo., and 5^ per case per 
 month after the first 3 mo. What would this rate be for 4 mo. ? 
 for 1 mo. ? for 9 mo. ? for 10 mo. t for 11 mo. ? 
 
 4. Using the rate in the bill, find the storage on 150 cs. eggs 
 stored from July 1 to Jan. 14 ; on 500 cs. eggs stored from 
 July 3 to June 14 ; on 350 cs. eggs stored from June 14 to 
 Mar. 4 ; on 12,000 doz. eggs stored from June 14 to Nov. 18. 
 
 5. The storage rate on poultry is ^ ^ per pound per month. 
 Find the storage on 1000 lb. from Jan. 10 to Feb. 6 ; on 800 
 Ib. from Jan. 10 to Feb. 18 ; on 1200 lb. from Jan. 10 to May 
 27 ; 011 1600 lb. from Jan. 10 to July 3. 
 
 6. In a certain warehouse the rate of storage on cheese is 8 ^ 
 per 100 lb., for each month or fraction thereof. At that rate 
 find the storage on 1000 lb. cheese from May 3 to July 15 ; on 
 20,000 lb. from May 3 to Aug. 26 ; on 7500 lb. from May 3 to 
 Sept. 12 ; on 10,000 lb. from May 3 to Oct. 6 ; on 5 T. from 
 June 15 to Oct. 28 ; on 10 T. from June 15 to Nov. 17. 
 
STORAGE 
 
 435 
 
 509. Example. The following memorandum of flour stored 
 for you by the Central Storage Co. : received Nov. 1, 2000 bbl., 
 and Nov. 16, 3000 bbl. ; delivered Nov. 8, 1000 bbl., and Dec. 5, 
 4000 bbl. If the rate of storage was 5^ per barrel per month 
 or fraction thereof, what was the bill to render? 
 
 SOLUTION 
 
 RECEIPTS AND DELIVERIES 
 Nov. 1, received 2000 bbl. 
 Nov. 8, delivered 1000 bbl., which were in storage 
 
 1000 bbl., balance in storage 
 Nov. 16, received 3000 bbl. 
 
 4000 bbl., balance in storage 
 
 Dec. 5, delivered 4000 bbl., 1000 of which were in storage 34 da. 10 t 
 3000 of which were in storage 19 da. 5 ^ 
 Total storage, 
 
 TERM RATE STORAGE 
 
 7 da. 5 f $50 
 
 100 
 
 150 
 
 $ 300 
 
 WRITTEN EXERCISE 
 
 1. In a certain warehouse the storage charges on flour are 3 ^ 
 per barrel per month or fraction thereof. Nov. 1, I stored 500 
 bbl. ; Dec. 1, I withdrew 100 bbl. ; Jan. 1, I stored 600 bbl. ; 
 Mar. 1, I withdrew 1000 bbl. What was the storage on the first 
 withdrawal ? 400 bbl. of the second withdrawal was in storage 
 for how many months ? What was the total storage due Mar. 1 ? 
 
 2. How much is due on the following account? 
 
 ton, Mass.,, 
 
 Received from (/?. 
 
 
 .19. 
 
 
 DELIVERIES AND CHARGES 
 
 CREOITS 
 
 DATE 
 
 QUANTITY 
 
 MONTHS 
 
 RATE 
 
 AMOUNT 
 
 AMOUNT 
 
 DATE 
 
 REMARKS 
 
 ^ 
 
 3 
 
 J= 
 
 ^^ 
 
 MM* 
 
 / 
 
 ^^ 
 
 ^ 
 
 ? 7 
 
 //. 
 
 r^ 
 
 -&/- 
 
 ^ 
 
 ^^ 
 
 (2 
 
 
 /?**# 
 
 2- 
 
 ^^ 
 
 ? 
 
 
 
 
 /s2>it?^?j 
 
 /? /? 
 
 (^fsL^sif 
 
 
 
 
 'tori 
 
 
 ^ / 
 
 ? 7 
 
 ,, 
 
 
 
 
 
 
 7" 
 
 
 M# 
 
 ? 
 
 ^ ^ 
 
 , 
 
 ~ 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
436 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 3. The following is a memorandum of apples stored by you 
 for T. B. Welch & Co. : received Nov. 28, 5000 bbl., Dec. 15, 
 1000 bbl., and Dec. 18, 3000 bbl.; delivered Dec. 28,2000 bbl., 
 Feb. 1, 1000 bbl., and Feb. 10, 6000 bbl. Render a bill for 
 the storage, charges being 5^ per barrel per month or fraction 
 thereof. 
 
 4. Copy and complete the following bill : 
 
 To EASTERN COLD STORAGE CO., Dr. 
 
 28 to 44 North Street 
 
 FOR STORAGE 
 
 LOT 
 
 DATE 
 
 NO. 
 MONTH 
 
 ARTICLE 
 
 WEIGHT 
 
 RATE PER 
 
 100 LB. 
 
 EXTEN- 
 SION 
 
 AMOUNT 
 
 IN 
 
 OUT 
 
 7J&2 
 
 &PT. 
 
 'fl 
 
 -* 
 
 A. 
 
 4- 
 q. 
 
 ,? 
 
 / 
 
 2^?^^;2^Z2^ 
 
 /aaa/yj 
 
 /^/ 
 
 
 
 
 
 
 
 
 tffa. 
 
 , ? 
 
 /f7 /? f, f. 
 
 <J~0aa$ 
 
 JVt 
 
 
 
 
 
 
 
 
 ??7^ 
 
 ,4- 
 
 3J7> r 
 
 '7.4730-6 
 
 <?0 < 
 
 
 
 
 
 
 
 
 ytssujL 
 
 jjT 
 
 A-T/9 ff ,. 
 
 yj-004 
 
 tfrtfi 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 AVERAGE STORAGE 
 
 510. When there are frequent receipts and deliveries of 
 goods, it is customary for some warehouses to average the time 
 and charge a certain rate per month of thirty days. The 
 process is called average storage. 
 
 511. Example. The following is a memorandum of the re- 
 ceipts and deliveries of flour stored by the Eastern Storage Co. 
 for A. M. Briggs & Co. : received Apr. 10, 2000 bbl., and Apr. 
 30, 3000 bbl.; delivered May 8, 1000 bbl., and June 9, 4000 bbl. 
 The storage charge being 4J ^ per barrel per term of 30 da. 
 average storage, what was the amount of the bill to render ? 
 
 SOLUTION. The solution of this problem is clearly shown in the following 
 statement of account : 
 
STORAGE 
 
 437 
 
 ACCOUNT OF FLOUR KECEIVED AND DELIVERED BY 
 
 EASTEKN STORAGE CO., 
 For A. M. BRIGGS & CO. 
 
 DATE 
 
 KECEIPTS 
 
 DELIVERIES 
 
 BALANCE 
 
 TIME IN 
 STORAGE 
 
 QUANTITY IN 
 STORAGE FOR 1 DA. 
 
 1907 
 
 
 
 
 
 
 
 Apr. 
 
 10 
 30 
 
 2000 bbl. 
 3000 bbl. 
 
 
 2000 bbl. 
 5000 bbl. 
 
 20 da. 
 8 da. 
 
 40000 bbl. 
 40000 bbl. 
 
 May 
 June 
 
 8 
 9 
 
 
 1000 bbl. 
 4000 bbl. 
 
 4000 bbl. 
 0000 bbl. 
 
 32 da. 
 00 da. 
 
 128000 bbl. 
 00000 bbl. 
 
 5000 bbl. 
 
 5000 bbl. 
 
 30)208000 bbl. 
 
 Average storage for 1 mo. = 6933| bbl. 
 69331 bbl. at 4^ = $ 312, the amount of the bill to render. 
 
 WRITTEN EXERCISE 
 
 1. The Quincy Storage and Warehouse Co. received and 
 delivered on account of Boynton Travers & Co. sundry barrels 
 of apples as follows : received Dec. 1, 1906, 1000 bbl., Dec. 26, 
 2000 bbl.; delivered Feb. 1, 500 bbl., Mar. 1, 1000 bbl., 
 Mar. 15, 1100 bbl., Mar. 31, 400 bbl. If the charges were 
 6^ per barrel per term of 30 da. average storage, what was 
 the amount of the bill to render? 
 
 2. The Central Storage Warehouse Co. received and delivered 
 on account of A. S. Osborn & Co. sundry bushels of wheat as 
 follows : received Oct. 1, 17,600 bu., Nov. 15, 3600 bu., Dec. 18, 
 4200 bu., Dec. 27, 4320 bu.; delivered Oct. 31, 10,000 bu., 
 Dec. 4, 10,720 bu., Dec. 19, 4000 bu., Dec. 28, 5000 bu. If 
 the charges were 1| ^ per bushel per term of 30 da. average 
 storage, what was the amount of the bill to render ? 
 
 3. Metropolitan Storage Co. received and delivered on ac- 
 count of Chas. B. Sherman sundry barrels of flour as follows : 
 received Nov. 15, 1906, 1800 bbl., Nov. 30, 1000 bbl., Dec. 18, 
 600 bbl., Jan. 30, 3000 bbl. ; delivered Dec. 1, 1000 bbl., 
 Dec. 31, 1900 bbl., Jan. 31, 600 bbl., Feb. 5, 600 bbl., Apr. 30, 
 2300 bbl. If the charges were 5J^ per barrel per term of 30 
 da. average storage, what was the amount of the bill to render ? 
 
438 PRACTICAL BUSINESS ARITHMETIC 
 
 WRITTEN REVIEW EXERCISES 
 
 1. I bought wheat at $0.80 per bushel. Allowing 6% for 
 waste and incidentals and 2 % for storage, how much must I 
 receive per bushel for the wheat to realize a gain of 10.12 
 per bushel ? 
 
 2. A produce dealer bought 150 T. cabbage at $ 5.50 per ton. 
 He paid 90 f per ton for storage and then sold the cabbage at a 
 clear profit of 25%. How much did he receive per ton and 
 what was his gain ? 
 
 3. Nov. 1 a speculator bought 5000 bbl. apples at $2.25 per 
 barrel and put them in storage. Feb. 1 he withdrew them 
 from the storage warehouse. He had them sorted and repacked, 
 when he found that he had only 4600 bbl. of sound apples. 
 These he sold at $3.50 per barrel. If the storage charges 
 were 5^ per barrel per month or fraction thereof, and the 
 charges for repacking were $500, did he gain or lose, and how 
 much ? what per cent ? 
 
 4. Dec. 15, 1906, A. L. Farley bought 1000 bbl. flour at 
 $4 and placed it with the Union Warehouse Co. for storage. 
 Jan. 15 he bought 3000 bbl. flour at $4.15 and placed it with 
 the same warehouse company for storage. On Feb. 15 he with- 
 drew 2000 bbl. from storage and sold it at $5.85, on Mar. 25 
 he withdrew 1000 bbl. and sold it at $ 5.62^, on Apr. 1 he with- 
 drew 1000 bbl. and sold it at $ 5.87J. If the storage charges 
 were 5^ per barrel per month or fraction thereof, and cartage 
 and incidentals cost $ 100, did he gain or lose, and how much ? 
 
APPENDIX 
 
 TABLES OF MEASURES 
 
 MEASURES OF CAPACITY 
 
 Liquid Measure Dry Measure 
 
 4 gills = 1 pint 2 pints = 1 quart 
 
 2 pints = 1 quart 8 quarts = 1 peck 
 
 4 quarts = 1 gallon 4 pecks = 1 bushel 
 
 = 2:31 cubic inches =2150.42 cubic inches 
 
 Barrels and hogsheads vary in size ; but in estimating the capacity of tanks 
 and cisterns 31.5 gal. are considered a barrel, and 2 bbl., or 63. gal., a hogshead. 
 
 A heaped bushel, used for measuring apples, corn in the ear, etc., equals 
 2747.71 cu. in. A dry quart equals 67.2 cu. in., and a liquid quart 57.75 
 cu. in. 
 
 MEASURES OF WEIGHT 
 
 Avoirdupois Weight Troy Weight 
 
 16 ounces = 1 pound 24 grains = 1 pennyweight 
 
 100 pounds = 1 hundredweight 20 pennyweights = 1 ounce 
 
 2000 pounds = 1 ton 12 ounces = 1 pound 
 
 Apothecaries' Weight Comparative Weights 
 
 20 grains = 1 scruple 1 Ib. troy or apothecaries' = 5760 gr. 
 
 3 scruples 1 dram 1 oz. troy or apothecaries' = 480 gr. 
 
 8 drams 1 ounce 1 Ib. avoirdupois = 7000 gr. 
 
 12 ounces = 1 pound 1 oz. avoirdupois = 437^ gr. 
 
 The ton of 2000 Ib. is sometimes called a short ton. There is a ton of 2240 Ib. , 
 called a long ton, used in all customhouse business and in some wholesale trans- 
 actions in mining products. 
 
 In weighing diamonds, pearls, and other jewels, the unit generally employed 
 is the carat, equal to 3.2 troy grains. The term " carat" is also used to express 
 the number of parts in 24 that are pure gold. Thus, gold that is 14 carats fine 
 is || pure gold and \% alloy. 
 
 Miscellaneous Weights 
 
 1 keg of nails = 100 pounds 1 barrel of salt = 280 pounds 
 
 1 cental of grain = 100 pounds 1 barrel of flour =196 pounds 
 
 1 quintal of fish = 100 pounds 1 barrel of pork or beef = 200 pounds 
 
 A cubic foot of water contains 6 gal. and weighs 62 Ib., avoirdupois. 
 
 439 
 
440 
 
 PRACTICAL BUSINESS AEITHMETIC 
 
 MEASURES OF EXTENSION 
 
 Long Measure 
 
 12 inches = 1 foot 
 
 3 feet = 1 yard 
 
 5^ yards, or 16 feet = 1 rod 
 320 rods, or 5280 feet = 1 mile 
 
 Surveyors' Long Measure 
 
 7.92 inches = 1 link 
 
 25 links = 1 rod 
 
 4 rods, or 100 links = 1 chain 
 80 chains = 1 mile 
 
 City lots are usually measured by feet and decimal fractions of a foot ; farms, 
 by rods or chains. 
 
 Miscellaneous Long Measures 
 
 4 inches =1 hand 
 
 6 feet = 1 fathom 
 
 120 fathoms = 1 cable length 
 1.15 miles, nearly, = 1 knot, or 
 1 nautical or geographical mile 
 
 Square Measure 
 
 144 square inches = 1 square foot 
 9 square feet = 1 square yard 
 30J square yards = 1 square rod 
 160 square rods = 1 acre 
 640 acres = 1 mile 
 
 The hand is used in measuring the height of horses at the shoulder. The 
 fathom and cable length are used by sailors for measuring depths at sea. The 
 knot is used by sailors in measuring distances at sea. Three knots are frequently 
 called a league. 
 
 Surveyors' Square Measure 
 
 Cubic Measure 
 
 625 square links = 1 square rod 1728 cubic inches = 1 cubic foot 
 10 square rods 1 square chain 27 cubic feet = 1 cubic yard 
 10 square chains = 1 acre 
 
 640 acres = 1 square mile 
 
 36 square miles = 1 township 
 
 128 cubic feet = 1 cord 
 
 1 cubic yard = 1 load (of earth, etc.) 
 24| cubic feet = 1 perch 
 
 The square rod is sometimes called a perch. The word rood is sometimes 
 used to mean 40 sq. rd. or | A. In the government surveys, 1 sq. mi. is called 
 a section. 
 
 The perch of stone or masonry varies in different parts of the country ; but 
 it is usually considered as 1 rd. long, 1 ft. high, and 1 ft. thick, or 24| cu. ft. 
 
 Angular Measure 
 
 60 seconds = 1 minute 
 60 minutes = 1 degree 
 
 90 degrees = 1 right angle 
 360 degrees = 1 circumference 
 
 Angular (also called circular) measure is used principally in surveying, navi- 
 gation, and geography for measuring arcs of angles, for reckoning latitude and 
 longitude, for determining locations of places and vessels, and for computing 
 difference of time. 
 
 A minute of the earth's circumference is equal to a geographical mile. A 
 degree of the earth's circumference at the equator is therefore equal to about 
 69 statute miles. 
 
TABLES OF MEASURES 441 
 
 MEASURES OF TIME 
 
 60 seconds = 1 minute 12 months = 1 year 
 
 60 minutes = 1 hour 360 days = 1 commercial year 
 
 24 hours = 1 day 365 days = 1 common year 
 
 7 days = 1 week 366 days = 1 leap year 
 
 30 days = 1 commercial month 100 years = 1 century 
 
 September, April, June, and November have 30 da. each ; all of the other 
 months have 31 da. each, except February, which has 28 da. in a common year 
 and 29 da. in a leap year. 
 
 Centennial years that are divisible by 400 and other years that are divisible 
 by 4 are leap years. 
 
 In running trains across such a broad stretch of country as the United States, 
 it is highly important to have a uniform time over considerable territory. Rec- 
 ognizing this, in 1883, the railroad companies of the United States and Canada 
 adopted for their own convenience a system of standard time. This system 
 divides the United States into four time belts, each covering approximately 15 
 of longitude, 7^ of which are east and 7| c west of the governing meridian. The 
 region of eastern time lies approximately 7| each side of the 75th meridian, 
 and the time throughout this belt is the same as the local time of the 75th merid- 
 ian. Similarly, the regions of central, mountain, and Pacific time lie approxi- 
 mately 7| each side of the 90th, 105th, and 120th meridians, respectively, and 
 the time throughout each belt is determined by the local time of the governing 
 meridian of that belt. There is just one hour's difference between adjacent time 
 belts. Thus, when it is 11 o'clock A.M. by eastern time, it is 10 o'clock A.M. by 
 central time, 9 o'clock A.M. by mountain time, and 8 o'clock A.M. by Pacific time. 
 Since railroad companies change the time at important stations and termini, 
 regardless of the longitude of such stations and termini, the boundaries of the 
 time belts are quite irregular. 
 
 MEASURES OF VALUE 
 
 United States Money English Money 
 
 10 mills = 1 cent 4 farthings = 1 penny 
 
 10 cents = 1 dime 12 pence = 1 shilling 
 
 10 dimes = 1 dollar 20 shillings = 1 pound sterling 
 
 10 dollars = 1 eagle = $4.8665 
 
 The term " eagle " is seldom used in business. The mill is not a coin, but the 
 name is frequently used in some calculations. In Canada the units of money 
 are the same as in the United States. 1 far. = f|^ ; Id. = 2-fop ; Is. = 
 
 French Money German Money 
 
 100 centimes = 1 franc = $0.193 100 pfennigs = 1 mark = $0.238 
 
 MISCELLANEOUS MEASURES 
 
 Counting by 12 Counting Sheets of Paper 
 
 12 things = 1 dozen 24 sheets = 1 quire 
 
 12 dozen = 1 gross 20 quires = 1 ream 
 
 12 gross = 1 great gross = 480 sheets 
 
442 
 
 PRACTICAL BUSINESS ARITHMETIC 
 
 BUSINESS ABBREVIATIONS 
 
 A . . 
 
 . acre 
 
 Mar. . . 
 
 
 Apr. . 
 
 . April 
 
 mdse. 
 
 
 Aug. . 
 
 . August 
 
 Messrs. . 
 
 
 bbl. . 
 
 . barrel ; barrels 
 
 
 
 bdl. . 
 
 . bundle; bundles 
 
 mi. 
 
 . 
 
 bg. . 
 bkt. . 
 
 . bag; bags 
 . basket; baskets 
 
 min. . . 
 mo. . . 
 
 
 bl. . 
 
 . bale; bales 
 
 Mr. . . 
 
 . 
 
 bu. . 
 
 . bushel; bushels 
 
 Mrs. . . 
 
 . 
 
 bx. . 
 
 . box ; boxes 
 
 N. . . 
 
 
 cd. . 
 
 . cord; cords 
 
 No. . . 
 
 . 
 
 ch. . 
 
 . chain ; chains 
 
 Nov. . . 
 
 
 c.i.f. . 
 
 . carriage and insurance free 
 
 Oct. . . 
 
 . 
 
 Co. . 
 
 . company; county 
 
 oz. 
 
 . 
 
 c.o.d. . 
 
 . collect on delivery 
 
 p. ... 
 
 . 
 
 coll. . 
 
 . collection 
 
 pc. . . 
 
 
 Cr. . 
 
 . creditor; credit 
 
 per. . . 
 
 . 
 
 cs. 
 
 . case ; cases 
 
 per cent. 
 
 
 ct. 
 
 . cent ; cents ; centime 
 
 
 
 cu. ft. 
 
 . cubic foot ; cubic feet 
 
 pk. . . 
 
 . 
 
 cu. in. 
 
 . cubic inch ; cubic inches 
 
 pkg. . . 
 
 . 
 
 cu. yd. 
 
 . cubic yard ; cubic yards 
 
 pp. . . 
 
 . 
 
 cwt. . 
 
 . hundredweight 
 
 pr. . . 
 
 . 
 
 d. . . 
 
 . pence 
 
 pt. . . 
 
 . 
 
 da. . 
 
 . day; days 
 
 pwt. . . 
 
 
 Dec. . 
 
 . December 
 
 
 
 doz. . 
 
 . dozen; dozens 
 
 qr. . . 
 
 . 
 
 Dr. . 
 
 . debtor ; debit ; doctor 
 
 qt. . . 
 
 . 
 
 E. . . 
 
 . east 
 
 rd. . . 
 
 
 
 ea. 
 
 . each 
 
 rrn. . . 
 
 
 e.g. . 
 
 . exempli gratia, for ex- 
 
 Rm.(or M. 
 
 ) 
 
 
 ample 
 
 s. . . . 
 
 
 etc. . 
 
 . el ccetera, and so forth 
 
 S. . . . 
 
 
 far. . 
 
 . farthing ; farthings 
 
 sec. . . 
 
 . 
 
 Feb. . 
 
 . February 
 
 sq. ch. 
 
 , 
 
 f.o.b. . 
 
 . free on board 
 
 
 
 fr. . 
 
 . franc ; francs 
 
 sq. ft. . 
 
 . 
 
 ft. . 
 
 . foot; feet 
 
 sq. mi. . 
 
 . 
 
 gal. . 
 
 . gallon; gallons 
 
 
 
 
 . gill; gills 
 
 sq. rd. . 
 
 
 gr- 
 
 . grain ; grains 
 
 sq. yd. . 
 
 . 
 
 gro. . 
 
 . gross 
 
 
 
 hhd. . 
 
 . hogshead; hogsheads 
 
 T. . . . 
 
 
 hf. cht. 
 
 . half chest ; half chests 
 
 tb. . . 
 
 
 hr. . 
 
 . hour; hours 
 
 Tp. . . 
 
 
 i.e. 
 
 . id est, that is 
 
 viz. . . 
 
 , 
 
 in. 
 
 . inch; inches 
 
 via . . 
 
 . 
 
 Jan. . 
 
 . January 
 
 wk. . . 
 
 
 kg. . 
 
 . keg; kegs 
 
 wt. 
 
 , 
 
 1. . . 
 
 . link ; links 
 
 yd. . . 
 
 
 Ib. . 
 
 . pound; pounds 
 
 yr. . . 
 
 . 
 
 . March 
 
 merchandise 
 
 . Messieurs, Gentlemen ; 
 Sirs 
 
 mile; miles 
 
 minute; minutes 
 
 month ; months 
 
 Mister 
 
 Mistress 
 
 north 
 
 number 
 
 November 
 
 October 
 
 ounce; ounces 
 
 page 
 
 piece ; pieces 
 . by the ; by 
 . per centum, by the hun- 
 dred 
 
 . peck ; pecks 
 . package ; packages 
 
 pages 
 
 pair; pairs 
 . pint; pints 
 . pennyweight; penny- 
 weights 
 . quire; quires 
 . quart; quarts 
 . rod ; rods 
 
 ream ; reams 
 
 Reichsmark, Mark 
 
 shilling; shillings 
 . South 
 
 . second ; seconds 
 . square chain; square 
 
 chains 
 
 . square foot ; square feet 
 . square mile; square 
 
 miles 
 
 . square rod ; square rods 
 . square yard; square 
 yards 
 
 ton 
 
 . tub ; tubs 
 . township; townships 
 
 videlicet, namely ; to wit 
 . by way of 
 . week ; weeks 
 . weight; weigh 
 . yard; yards 
 
 year; years 
 
BUSINESS SYMBOLS AND ABBREVIATIONS 443 
 
 a /e account 
 / account sales 
 4- addition 
 ( )>~ aggregation 
 & and 
 
 and so on 
 
 @ at; to 
 c / care of 
 ? cent; cents 
 v/ check mark 
 
 degree 
 
 -r- division 
 $ dollar; dollars 
 
 BUSINESS SYMBOLS 
 
 = equal ; equals 
 ' foot; feet; 
 minutes 
 C hundred 
 
 inch ; inches ; seconds 
 x multiplication 
 # number, if written 
 before a figure; 
 pounds, if written 
 after a figure 
 
 1 1 one and one fourth 
 
 1 2 one and two fourths ; 
 
 one and one half 
 
 I 8 one and three 
 
 fourths 
 ^P per; by 
 % per cent ; 
 
 hundredth ; 
 hundredths 
 pounds sterling 
 
 since 
 subtraction 
 
 therefore 
 M thousand 
 Ye 5 shillings 6 pence ; 
 five sixths 
 
INDEX 
 
 Abbreviations, 442. 
 
 Above par, 390. 
 
 Abstract number, 50. 
 
 Account, 41. 
 
 Account current, 405, 407. 
 
 Account purchase, 267, 271. 
 
 Account sales, 267, 384. 
 
 Acute angle, 193. 
 
 Acute-angled triangle, 194. 
 
 Adding machine, 197. 
 
 Addition, 10, 88, 119, 184. 
 
 Ad valorem duty, 285, 289. 
 
 Agent, 266. 
 
 Aliquot parts, 150. 
 
 Altitude, 196. 
 
 Amount, 228, 322. 
 
 Angle, 193. 
 
 Angular measure, 440. 
 
 Apothecaries' weight, 439. 
 
 Approximations, 140. 
 
 Arabic numerals, 2. 
 
 Arc, 194. 
 
 Areas, 196. 
 
 Assessment, 389, 392. 
 
 At a discount, 358, 390. 
 
 At a premium, 358, 390. 
 
 At par, 358. 
 
 Average, 79. 
 
 Average clause, 278. 
 
 Average date of payment, 377. 
 
 Average investment, 428. 
 
 Average storage, 436. 
 
 Average term of credit, 377. 
 
 Avoirdupois weight, 439. 
 
 Bank discount, 320, 321. 
 
 Bank drafts, 350, 352. 
 
 Bank loans, 328. 
 
 Bank money order, 347. 
 
 Bankers' bills of exchange, 367, 369. 
 
 Bankers' daily balances, 340. 
 
 Banker's sixty -day method of interest, 
 
 297. 
 
 Banking, 294. 
 Base, 196, 228, 232. 
 Base line, 199. 
 
 Bear, 406. 
 
 Below par, 390. 
 
 Bill of lading, 358. 
 
 Bills, 39, 40, 59, 63, 100, 101, 128, 147, 
 157, 158, 160, 161, 162, 163, 164, 165, 
 166, 174, 179, 189, 192, 218, 244, 249, 
 250, 251, 259, 264, 265, 291, 292. 
 
 Bills and accounts, 160. 
 
 Bills of exchange, 367, 369, 370, 371. 
 
 Bins, 222. 
 
 Blank indorsement, 309. 
 
 Board foot, 215. 
 
 Bonds, 397, 398. 
 
 Brick work, 220. 
 
 Broker, 266. 
 
 Brokerage, 266, 391. 
 
 Bull, 406. 
 
 Bullion, 9. 
 
 Buying bonds, 400. 
 
 Buying by the hundred, 99. 
 
 Buying by the thousand, 99. 
 
 Buying by the ton, 102. 
 
 Buying on commission, 270. 
 
 Buying stocks, 394. 
 
 Calculation tables, 224. 
 
 Cancellation, 109. 
 
 Capacity, 221. 
 
 Capital, 419. 
 
 Capital stock, 388. 
 
 Carpeting, 209. 
 
 Cash account, 41. 
 
 Cash balance, 385. 
 
 Cashier's check, 353. 
 
 Certificate of deposit, 353. 
 
 Change memorandum, 172. 
 
 Charter, 388. 
 
 Checking results, 20, 32, 52, 57, 58, 67, 
 
 81, 82, 83. 
 Checks, 5, 20, 32, 52, 57, 58, 67, 350, 
 
 354, 375, 392. 
 Circle, 194. 
 Circumference, 194. 
 Cisterns, 223. 
 Clearing house, 350, 351. 
 Code, 348. 
 
 445 
 
446 
 
 INDEX 
 
 Co-insurance, 274. 
 
 Collateral note, 330. 
 
 Collection and exchange, 326, 356. 
 
 Commercial bank, 320, 340. 
 
 Commercial bills of exchange, 367, 370, 
 
 371. 
 
 Commercial discounts, 242. 
 Commercial drafts, 321, 356. 
 Commission, 266. 
 Commission merchant, 266. 
 Common accounts, 41. 
 Common denominator, 118. 
 Common divisor, 110. 
 Common fractions, 113. 
 Common stock, 390. 
 Comparative weights, 439. 
 Composite number, 107. 
 Compound accounts, 380. 
 Compound interest, 314, 343. 
 Concrete number, 50. 
 Consecutive numbers, 18. 
 Consignee, 266. 
 Consignment, 267. 
 Consignor, 266. 
 Conversion of fractions, 139. 
 C ,-d, 215. 
 Corporation, 388. 
 Corporation tax, 283. 
 Counting by 12, 441. 
 Counting sheets of paper, 441. 
 Coupon bond, 398. 
 Credit, 41. 
 Cube, 213. 
 Cubic measure, 440. 
 Customhouse, 285. 
 Customs duties, 285. 
 Cylinder, 219. 
 
 Day method of interest, 295. 
 Days of grace, 321. 
 Debit, 41. 
 Decimal, 85. 
 Decimal fractions, 85. 
 Decimal system, 3. 
 Decimal units, 85. 
 Demand note, 309, 329. 
 Denominate quantities, 181. 
 Denominator, 113. 
 Deposit slip, 355. 
 Depositors' ledger, 38. 
 Diameter, 194. 
 Difference, 328. 
 Discount series, 242, 245. 
 Distances, 193. 
 Dividend, 64, 389, 392, 411. 
 
 Division, 64, 69, 95, 98, 133, 187. 
 
 Divisor, 64. 
 
 Divisors, 110. 
 
 Documentary bill of exchange, 367, 
 
 371. 
 
 Domestic exchange, 346. 
 Drafts, 320, 321, 328, 356, 360. 
 Drawee, 321. 
 Drawer, 321. 
 Dry measure, 439. 
 Duties, 285. 
 
 Endowment policy, 410, 413, 414. 
 English money, 441. 
 Equated date, 377. 
 Equation of accounts, 376. 
 Equilateral triangle, 194. 
 Even number, 107. 
 Exact interest, 311. 
 Exchange, 346, 353. 
 Exchange quotations, 368. 
 Expense account, 43. 
 Exponent, 50. 
 
 Express money order, 347, 366. 
 Expressage, 178. 
 Extended insurance, 411. 
 
 Face, 309. 
 
 Factor, 50, 107. 
 
 Factoring, 108. 
 
 Final results, 117. 
 
 Finding the base, 232. 
 
 Finding the cost, 255. 
 
 Finding the difference between dates, 
 
 185. 
 
 Finding the gain or loss, 253. 
 Finding the percentage, 228. 
 Finding the per cent of gain or loss, 254. 
 Finding the rate, 230. 
 Fire insurance, 273. 
 Firm note, 326. 
 First-mortgage bonds, 397. 
 Five-eighths pitch, 205. 
 Flooring, 208. 
 
 Fluctuation of rates of exchange, 358. 
 Focal date, 377. 
 Foreign money, 362. 
 Foreign money orders, 366. 
 Fractional relations, 136. 
 Fractions, 85. 
 Free list, 285. 
 Freight bill, 179. 
 Freightage, 178. 
 French money, 441. 
 Full indorsement, 309. 
 
INDEX 
 
 447 
 
 Gain, 41. 
 
 Gain and loss, 252. 
 
 Gas meters, 101. 
 
 German money, 441. 
 
 Government bonds, 398. 
 
 Graphic representations, 138, 239, 241. 
 
 Greatest common divisor, 110. 
 
 Gross price, 243. 
 
 Gross weight, 38. 
 
 Grouping, 11, 14. 
 
 Guaranty, 266. 
 
 Heaped bushel, 221. 
 Holder, 320. 
 Horizontal addition, 24. 
 Hypotenuse, 202. 
 Hypothecating, 406. 
 
 Important per cents, 228. 
 Improper fraction, 114. 
 Incomes and investments, 402. 
 Indorsements, 309, 336. 
 Inheritance tax, 283. 
 Insurance, 273. 
 Insurance rates, 410. 
 Insurer, 274. 
 Interest, 294. 
 Interest days, 343. 
 Interest term, 343. 
 Interest-bearing note, 309. 
 International postal money orders, 
 
 366. 
 
 Invoice, 150. 
 Inward foreign entry, 293. 
 
 Joint and several note, 310, 326. 
 Joint note, 310, 326. 
 
 Key, 260. 
 
 Kinds of life insurance policies, 410. 
 
 Lateral surface, 219. 
 
 Least common denominator, 118. 
 
 Least common multiple, 112. 
 
 Letter of advice, 268, 361. 
 
 Letter of credit, 372. 
 
 Letter ordering goods, 175. 
 
 Liability, 41. 
 
 License fee, 280. 
 
 Life insurance, 410. 
 
 Life insurance companies, 410. 
 
 Like numbers, 7. 
 
 Limited life policy, 410. 
 
 Liquid measure, 339. 
 
 Listing goods for catalogues, 263. 
 
 Long measure, 440. 
 Loss, 41. 
 Lumber, 215. 
 
 Maker, 309. 
 
 Making change, 33. 
 
 Manifest, 286. 
 
 Margins, 405, 408. 
 
 Marine insurance, 278. 
 
 Market value, 390. 
 
 Marking goods, 260. 
 
 Masonry, 220. 
 
 Maturity, 320. 
 
 Maturity table, 322. 
 
 Measures of capacity, 439. 
 
 Measures of extension, 440. 
 
 Measures of time, 441. 
 
 Measures of value, 441. 
 
 Measures of weight, 439. 
 
 Merchandise account, 442. 
 
 Merchants' method of partial pav- 
 
 ments, 337. 
 Metric system, 363. 
 Mint par of exchange, 367. 
 Miscellaneous measures, 440, 441. 
 Miscellaneous weights, 439. 
 Mixed numbers, 114. 
 Model figures, 19, 21, 22, 23. 
 Money orders, 346. 
 Mortgage note, 335. 
 Multiple, 50. 
 Multiplication, 50, 55, 57, 59, 60, 61, 
 
 92, 127, 132, 187. 
 Multiplying machine, 55. 
 Municipal bonds, 398. 
 Mutual insurance company, 274. 
 
 Negotiable, 309. 
 
 Net capital, 41. 
 
 Net gain, 41. 
 
 Net insolvency, 41. 
 
 Net loss, 41. 
 
 Net price, 243. 
 
 Net weight, 39. 
 
 Notation, 2, 86. 
 
 Notes, 9, 308, 310, 330, 335. 
 
 Numeration, 2, 86. 
 
 Numeration table, 4, 86. 
 
 Numerator, 113. 
 
 Obtuse angle, 193. 
 Obtuse-angled triangle, 194. 
 Odd number, 197. 
 One-fourth pitch, 204. 
 One-half pitch, 204. 
 
448 
 
 INDEX 
 
 Open policy, 274. 
 Orders of units, 3. 
 Ordinary life policy, 410. 
 
 Paid-up policy, 411. 
 
 Painting, 207. 
 
 Papering, 211. 
 
 Par value, 390. 
 
 Parenthesis, 31. 
 
 Partial payments, 322. 
 
 Partitive proportion, 416. 
 
 Partners, 419. 
 
 Partnership, 417. 
 
 Pay rolls, 80, 172, 173, 176, 177, 
 
 226. 
 
 Pay-roll memorandum, 173. 
 Payee, 309, 321. 
 Per cent, 86, 227. 
 Per cents of decrease, 235. 
 Per cents of increase, 234. 
 Percentage, 227. 
 Perch, 220. 
 Perimeter, 194. 
 Periodic interest, 313. 
 Periods, 4. 
 
 Perpendicular lines, 193. 
 Personal accounts, 42. 
 Pitch of roof, 204. 
 Place value, 3. 
 Plane surface, 193. 
 Plastering, 206. 
 Policy, 274. 
 Poll tax, 280. 
 Port of delivery, 285. 
 Port of entry, 285. 
 Postal information, 72. 
 Postal money order, 346. 
 Power, 51. 
 
 Practical measurements, 193. 
 Preferred stock, 389. 
 Premium, 274. 
 Present worth, 41. 
 Prime number, 107. 
 Principal, 266, 294. 
 Principal meridian, 199. 
 Problems in interest, 312. 
 Proceeds, 322. 
 Promissory notes, 9, 308, 310, 335, 329, 
 
 330. 
 
 Properties of 9, 81. 
 Properties of 11, 82. 
 Property insurance, 273. 
 Property tax, 280. 
 Proprietary account, 243. 
 Public lands, 199. 
 
 Qualified indorsement, 309. 
 Quotient, 64. 
 
 Radical sign, 200. 
 
 Radius, 194. 
 
 Ranges, 199. 
 
 Rate, 228, 294. 
 
 Rate of exchange, 347, 352, 358, 368. 
 
 Reading decimals, 86. 
 
 Rectangle, 193. 
 
 Rectangular solids, 213. 
 
 Reduction, 115, 116, 117, 118, 182, 183. 
 
 Reference method of interest, 307. 
 
 Registered bond, 399. 
 
 Remainder, 64. 
 
 Repeaters, 260. 
 
 Reserve, 411. 
 
 Resource, 41. 
 
 Review of the common tables, 181. 
 
 Right angle, 193. 
 
 Right-angled triangle, 194. . 
 
 Roman numerals, 6. 
 
 Roofing, 203. 
 
 Savings bank, 343. 
 
 Savings-bank accounts, 343. 
 
 Scalene triangle, 194. 
 
 Second-mortgage bonds, 397. 
 
 Section, 199. 
 
 Selling by the hundred, 99. 
 
 Selling by the thousand, 99. 
 
 Selling by the ton, 102. 
 
 Selling on commission, 268. 
 
 Separatrix, 3. 
 
 Share, 388. 
 
 Shipment, 267. 
 
 Shipping invoice, 269. 
 
 Short methods, 55, 69, 120, 130. 
 
 Sight draft, 356. 
 
 Similar fractions, 118. 
 
 Simple accounts, 377. 
 
 Simple interest, 295. 
 
 Simple storage, 433. 
 
 Sinking fund, 317. 
 
 Six per cent method of interest, 305. 
 
 Sixteen to one, 130. 
 
 Solids, 213. 
 
 Solution of problems, 142. 
 
 Specific duty, 285. 
 
 Square, 193, 203. 
 
 Square measure, 440. 
 
 Square root, 200. 
 
 Standard time, 441. 
 
 State bonds, 398. 
 
 Statements, 45, 46, 170, 171, 258, 339. 
 
 
INDEX 
 
 449 
 
 Statutory weights of the bushel, 190. 
 
 Stock broker, 391. 
 
 Stock certificates, 388, 389, 390. 
 
 Stock company, 388. 
 
 Stock exchanges, 404. 
 
 Stock insurance company, 274. 
 
 Stockholder, 388. 
 
 Stocks and bonds, 388. 
 
 Stone work, 220. 
 
 Storage, 443. 
 
 Stricken bushel, 221. 
 
 Subtraction, 31, 90, 124, 184. 
 
 Surface, 193. 
 
 Surplus, 411. 
 
 Surveyors' long measure, 440. 
 
 Surveyors' square measure, 440. 
 
 Table of aliquot parts, 152. 
 Table of bond quotations, 400. 
 Table of common measures, 439. 
 Table ol compound interest, 315, 
 
 317. 
 
 Table of foreign coins, 287. 
 Table of important per cents, 228. 
 Table of insurance rates, 276* 411. 
 Table of simple interest, 308. 
 Table of stock quotations, 394. 
 Table of time, 324. 
 Table of twelfths, 262. 
 Tables of metric measures, 363. 
 Tare, 38. 
 Tariff, 285. 
 Tax rate, 281. 
 Tax table, 284. 
 Taxes, 280. 
 
 Telegrams, 176, 348. 
 
 Telegraphic money order, 348. 
 
 Telegraphic rates, 349. 
 
 Term of discount, 322. 
 
 Term of storage, 433. 
 
 Term policy, 410. 
 
 Terms of a fraction, 114. 
 
 Tests of divisibility, 108. 
 
 Third-mortgage bonds, 397. 
 
 Time note, 309. 
 
 Time sheets, 76, 77, 78, 80, 149, 172, 
 
 173, 176, 177, 226. 
 Time slip, 177. 
 Township, 199. 
 Trade discount, 242. 
 Traveler's check, 373, 374. 
 Triangle, 194. 
 Troy weight, 439. 
 
 Underwriter, 274. 
 Unit, 7. 
 
 Unit fraction, 115. 
 United States coins, 8. 
 United States method of partial pay- 
 ment, 332. 
 United States money, 8, 9, 441. 
 
 Valued policy, 274. 
 
 Values of foreign coins, 287. 
 
 Vinculum, 31. 
 
 Warehousing, 287. 
 Weigh tickets, 102, 106. 
 Wood, 215. 
 
UNIVERSITY OF CALIFORNIA LIBRARY 
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