I "I '' i t 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 1 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 1 4 2 2 5 7 2 6 3 4 3 8 1 7 7 6 1 1 1 1 7 7 1 2 3 3 6 2 2 4 2 2 4 3 4 2 1 1 1 2 2 2 3 5 1 8 3 2 2 3 1 3 8 6 2 4 1 5 1 2 3 2 4 1 2 4 4 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 BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. 23Sep'54GH 48-195-41$ . (,<- > LD 21-100w-ll, 1 49(B7146sl6)476 tfl V "**-*' YC 22367 QA 103 THE UNIVERSITY OF CALIFORNIA LIBRARY ;:'::;:?;:; '.: : . :':',