UC-NRLF 
 
 $B 55 bMfl 
 
 CONCISE 
 
 BUSINESS 
 
 ARITHMETIC 
 
 MOORE 
 
 and: 
 
 MINER 
 
 GINN AND COMPANY 
 
^. 
 
 GIFT OF 
 
Digitized by the Internet Archive 
 
 in 2007 with funding from 
 
 IVIicrosoft Corporation 
 
 http://www.archive.org/details/concisebusinessaOOmoorrich 
 
MOORE AND MINER SERIES 
 
 CONCISE BUSINESS 
 ARITHMETIC 
 
 BY 
 
 JOHN H. MOORE 
 
 u 
 AND 
 
 GEORGE W. MINER 
 
 GINN AND COMPANY 
 
 BOSTON - NEW YORK • CHICAGO • LONDON 
 ATLANTA • DALLAS • COLUMBUS • SAN FRANCISCO 
 

 EDUC. 
 
 ENTEUED AT STATIONERS HALL 
 
 COPYRIGHT, 1915, BY GEORGE W. MINER 
 
 Practical Business Arithmetic 
 copyright, 1906, by john h. moore and george w. miner 
 
 copyright, 1915, BY GEORGE W. SIINER 
 
 ALL RIGHTS RESERVED 
 
 fgftc gtftengum jgregg 
 
 GINN AND COMPANY- PRO- 
 PRIETORS • UOSTON • U.S.A. 
 
PREFACE 
 
 The " Concise Business Arithmetic " has been prepared to meet 
 the needs of those schools that have short courses in business 
 arithmetic. It emphasizes fundamental processes and those sub- 
 jects that are commonly used in the business world. The aver- 
 age student needs all the drill he can get to acquire accuracy 
 and facility in the handling of numbers. 
 
 This book is made up of twenty chapters selected from the 
 " Practical Business Arithmetic " (Revised) and retains the fea- 
 tures of that volume that have been so highly commended by 
 teachers, namely: the presentation of each subject in a logical 
 order; the selection of problems that appeal to the needs and 
 the interest of the student and of the community as well ; the 
 omission of complex and useless problems and the inclusion of 
 such material as will meet the needs of persons who have time 
 for only a brief study of business arithmetic ; a plan of grad- 
 ing and grouping problems which aids the student in acquiring 
 facility and in advancmg his educational equipment ; the inclu- 
 sion of an amount of work that will contribute to real efficiency ; 
 the development of subjects inductively and the omission of set 
 rules ; the unusual amount of work in the different chapters. 
 
 The text includes the computation of loss and gain on the 
 sellmg price, tests on a time limit, additional work on graphs, 
 statistical matter based on the latest census, and an appendix 
 on the varied uses of the adding machine. 
 
 As this work is based on the " Practical Business Arithmetic," 
 of which the late John H. Moore was the senior author, it seems 
 proper to retain his name in the first place on the title-page of 
 this volume, the actual preparation of which has necessarily been 
 entirely in the hands of the junior author of the Moore and 
 Miner textbooks. 
 
 iii 
 
 459906 
 
iv CONCISE BUSINESS ARITHMETIC 
 
 Grateful acknowledgment for helpful service is due to 
 Dr. David Eugene Smith, Professor of Mathematics, Teachers 
 College, Columbia University, New York ; to Mr. George Abbot 
 of Brown Bros. & Co., Boston ; to Mr. H. T. Smith, assistant 
 cashier of the Shawmut National Bank, Boston, for valuable 
 assistance on the chapters on interest and banking ; to Mr. Wm. 
 B. Medlicott, Lecturer on Property Insurance at Harvard Uni- 
 versity, for his work on the chapter on property insurance ; to 
 Mr. Montgomery Rollins of Boston, author of " Money and 
 Investments"; to Mr. Harold T. Sibley of Chicago for sug- 
 gestions on the chapter on stocks and bonds ; to Mr. Alexander 
 H. Sproul of the State Normal School, Salem, Massachusetts, 
 and to Mr. C. D. McGregor of Des Moines, Iowa. 
 
 GEORGE W. MINER 
 
CONTENTS 
 
 FUNDAMENTAL PROCESSES 
 
 CHAPTER PAGE 
 
 I. Introduction 1 
 
 11. Addition 2 
 
 III. Subtraction 23 
 
 IV. Multiplication 36 
 
 V. Division 52 
 
 VI. Checking Results 71 
 
 FRACTIONS 
 
 VII. Decimal Fractions 75 
 
 VIII. Factors, Divisors, and Multiples ....... 95 
 
 IX. Common Fractions 101 
 
 X. Aliquot Parts 138 
 
 XL Bills and Accounts 150 
 
 DENOMINATE NUMBERS 
 
 XII. Denominate Quantities 169 
 
 PERCENTAGE AND ITS APPLICATIONS 
 
 XIII. Percentage 175 
 
 XIV. Commercial Discounts 188 
 
 XV. Gain and Loss . 196 
 
 XVI. Marking Goods 204 
 
 XVII. Property Insurance 209 
 
 INTEREST AND BANKING 
 
 XVIIL Interest 216 
 
 XIX. Bank Discount 230 
 
 XX. Domestic Exchange , , , 242 
 
 V 
 
vi CONCISE BUSINESS ARITHMETIC 
 
 DIVIDENDS AND INVESTMENTS 
 
 CHAPTER PAGE 
 
 XXI. Stocks and Bonds 256 
 
 APPENDIX A 
 
 Adding Machines . 273 
 
 APPENDIX B 
 
 Tables of Measures 275 
 
 Business Abbreviations 278 
 
 Business Symbols 279 
 
 INDEX . 281 
 
CONCISE BUSINESS ARITHMETIC 
 
 FUNDAMENTAL PROCESSES 
 
 CHAPTER I 
 
 INTRODUCTION 
 
 1. The student who is prepared to study business arithmetic 
 must be familiar with the ordinary symbols used in the state- 
 ment or the solution of problems; he must have the ability to 
 read and to write numbers with facility; he must know the 
 fundamentals, and he must be able to perform ordinary opera- 
 tions in United States money, and in both common and decimal 
 fractions. 
 
 2. In this course in business arithmetic one learns many 
 simple methods for handling numbers and solving problems, 
 and the adaptation of arithmetic to important business operations ; 
 he also acquires skill, rapidity, and accuracy, and he learns how 
 to prove his own work, thus developing self-reliance. Because 
 arithmetic deals with the problems of the home as well as the 
 business office, the study of its practical and everyday features 
 increases one's knowledge of the usages, the phraseology, and 
 the literature of business and commerce. 
 
 3. Much attention is given, in the text, to the fundamental 
 processes, for these are at the foundation of all arithmetic. One 
 must acquire a high degree of accuracy and speed in the hand- 
 ling of these fundamentals if he is to achieve any marked degree 
 of success in his subsequent work. 
 
 The text contains an unusual amount of material for the studei t's work, 
 and portions of it may be omitted, at the discretion of the instructor, if the 
 advancement of the class warrants it. 
 
 1 
 
CHAPTER II 
 
 ADDITION 
 ORAL EXERCISE 
 
 1. Find the sum of 1, 2, 3, 7, 5, 9, 4, 8, and 6. 
 
 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. 
 
 4. Only like numbers can he added. 
 
 5. 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 
 S 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. 
 
 322815813551342 
 
 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 
 
 1 
 
 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 
 
 862242243421112 
 2235 18322313 862 
 415123241244 987 
 
ADDITION 3 
 
 6. 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. 
 
 7. 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. 
 
 8. The following list contains all possible groups of two 
 figures each. 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of each of the following groups: 
 ab cde f gbij klmno 
 1. 112241334314247 
 1312 15232673567 
 
 2. 8 
 
 9 
 
 8 
 
 5 
 
 6 
 
 4 
 
 5 
 
 5 
 
 7 
 
 1 
 
 5 
 
 6 
 
 6 
 
 8 
 
 9 
 
 9 
 
 9 
 
 8 
 
 5 
 
 1 
 
 4 
 
 3 
 
 4 
 
 2 
 
 8 
 
 6 
 
 6 
 
 9 
 
 6 
 
 1 
 
 3. 8 
 
 7 
 
 7 
 
 4 
 
 9 
 
 7 
 
 6 
 
 7 
 
 5 
 
 3 
 
 2 
 
 4 
 
 5 
 
 7 
 
 6 
 
 2 
 
 3 
 
 5 
 
 8 
 
 3 
 
 8 
 
 7 
 
 9 
 
 9 
 
 8 
 
 9 
 
 9 
 
 8 
 
 4 
 
 2 
 
 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. 
 
CONCISE BUSINESS ARITHMETIC 
 
 
 
 
 
 
 ORAL 
 
 EXERCISE 
 
 
 
 
 
 
 Name the 
 
 swm 
 
 in each i 
 
 ?/ ^^6 
 
 ; 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 tlie 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 iii the exercise on page 2 by 
 groups of two figures each. 
 
 9. 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 G 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 Q^, 
 
 ORAL EXERCISE 
 
 Pronounce at sight the sum of each of the following groups : 
 1.27 48 59 77 58 52 59 75 95 84 39 59 84 76 91 
 786878869765988 
 
 2. 75 
 
 59 
 
 77 
 
 88 
 
 74 
 
 23 
 
 24 
 
 44 
 
 89 
 
 78 
 
 67 
 
 37 
 
 m 
 
 58 68 
 
 _8 
 
 9 
 
 9 
 
 5 
 
 6 
 
 8 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 7 
 
 7 
 
 4 5 
 
 3. 37 
 
 49 
 
 38 
 
 37 
 
 45 
 
 95 
 
 98 
 
 87 
 
 54 
 
 72. 
 
 63 
 
 42 
 
 73 
 
 97 88 
 
 _5 
 
 _8 
 
 7 
 
 6 
 
 9 
 
 8 
 
 7 
 
 7 
 
 9 
 
 9 
 
 8 
 
 9 
 
 ^ 
 
 5 ^ 
 
ADDITION 5 
 
 10. 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 : 
 abode fghi jklmno 
 1. 12 17 12 16 11 12 18 16 17 11 19 13 18 12 17 
 15 17 12 13 14 11 18 12 18 19 15 13 12 14 19 
 
 2.13 
 
 11 
 
 15 
 
 19 
 
 14 
 
 19 
 
 17 
 
 15 
 
 13 
 
 19 
 
 16 
 
 14 
 
 18 
 
 18 
 
 12 
 
 18 
 
 16 
 
 16 
 
 14 
 
 15 
 
 16 
 
 16 
 
 13 
 
 11 
 
 18 
 
 14 
 
 14 
 
 11 
 
 15 
 
 19 
 
 3.11 
 
 17 
 
 12 
 
 17 
 
 15 
 
 15 
 
 12 
 
 18 
 
 16 
 
 14 
 
 19 
 
 14 
 
 19 
 
 17 
 
 11 
 
 11 
 
 14 
 
 13 
 
 13 
 
 17 
 
 15 
 
 17 
 
 16 
 
 16 
 
 13 
 
 19 
 
 18 
 
 13 
 
 11 
 
 15 
 
 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. 
 
 11. Numbers between 10 and 20 may be combined with num- 
 bers above 20 in practically the same manner as in § 10 
 
 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 each of the following groups: 
 1. 25 48 59 87 91 75 86 75 48 78 57 89 37 m 75 
 17 17 16 14 18 18 19 12 16 13 16 14 17 18 14 
 
 I 
 
 2.29 
 
 47 
 
 83 
 
 92 
 
 36 
 
 54 
 
 59 
 
 78 
 
 67 
 
 92 
 
 77 
 
 86 
 
 53 
 
 78 
 
 85 
 
 13 
 
 14 
 
 19 
 
 14 
 
 19 
 
 13 
 
 18 
 
 15 
 
 13 
 
 13 
 
 19 
 
 19 
 
 17 
 
 14 
 
 14 
 
 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 
 
64, 
 
 71, 8, 85. 
 
 14. 
 
 8's from 10 to 138. 
 
 15. 
 
 7's from 19 to 152. 
 
 16. 
 
 6's from 20 to 128. 
 
 17. 
 
 6's from 15 to 111. 
 
 18. 
 
 9's from 12 to 102. 
 
 19. 
 
 8's from 17 to 113. 
 
 20. 
 
 7's from 24 to 108. 
 
 21. 
 
 6's from 27 to 117. 
 
 22. 
 
 4's from 19 to 183. 
 
 23. 
 
 ll's from 14 to 102. 
 
 24. 
 
 12's from 17 to 161. 
 
 25. 
 
 13's from 17 to 121. 
 
 6 CONCISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. Count by 7's from 1 to 85. 
 Solution. 8, 15, 22, 9, 36, 43, 50, 7, 
 
 Count hy : 
 
 2. 2's from 39 to b^, 
 
 3. 5's from 11 to 86. 
 
 4. 6's from 15 to 63. 
 
 5. 5's from 2 to 107. 
 
 6. 7's from 11 to 60. 
 
 7. 8's from 25 to 89. 
 
 8. 9's from 31 to 112. 
 
 9. 8's from 32 to 192. 
 
 10. 7's from 18 to 102. 
 
 11. 6's from 72 to 126. 
 
 12. 9's from 10 to 136. 
 
 13. 9's from 17 to 152. 
 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. 
 
 12. 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. 
 
 1. 419811318145178 
 131223173314414 
 332175631941641 
 
ADDITION 7 
 
 2. 161412111176981 
 412122911666555 
 925231187811117 
 
 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 
 
 
 5 
 
 8 
 
 3 
 
 3 
 
 7 
 
 5 
 
 5 
 
 5 
 
 8 
 
 8 
 
 5 
 
 4 
 
 5 
 
 7 
 
 3 
 
 
 3 
 
 2 
 
 2 
 
 8 
 
 9 
 
 7 
 
 5 
 
 9 
 
 9 
 
 6 
 
 5 
 
 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. 
 
8 CONCISE BUSINESS ARITHMETIC 
 
 
 
 
 
 ( 
 
 ORAL 
 
 EXERCISE 
 
 
 
 
 
 
 1-15. Turn to the 
 
 exercise 
 
 ! on page 2 and find the 
 
 sum of 
 
 the 
 
 numbers 
 
 given. 
 
 
 
 
 
 
 
 
 
 Name results on 
 
 ly, and make \ 
 
 groups of three figures each. 
 
 Thus, in 
 
 problem 1, say 
 
 9, 23, 37, 
 
 ^^. 
 
 
 
 
 
 
 
 
 Add from the bottom up and check the work by adding from the top down. 
 
 Find the Bum in each of the 
 
 following problems: 
 
 
 
 
 16. 
 
 17. 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 24. 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 1 
 
 3 1 
 
 4 
 
 2 
 
 2 
 
 2 
 
 4 4 5 
 
 1 
 
 2 
 
 9 
 
 5 
 
 4 
 
 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 
 
 18 8 
 
 9 
 
 2 
 
 8 
 
 
 
 1 
 
 2 
 
 4 1 
 
 4 
 
 6 
 
 4 
 
 5 
 
 8 3 2 
 
 
 
 3 
 
 
 
 
 
 6 
 
 2 
 
 2 3 
 
 8 
 
 1 
 
 1 
 
 2 
 
 17 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 
 
 18 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 12 
 
 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 
 
 3 
 
 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 
 
 12 3 
 
 9 
 
 1 
 
 2 
 
 5 
 
 2 
 
 1 
 
 3 4 
 
 4 
 
 4 
 
 1 
 
 7 
 
 7 10 
 
 
 
 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 12 
 
 1 
 
 5 
 
 7 
 
 1 
 
 1 
 
ADDITION 
 
 9 
 
 13. 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 in each of the following problems^ taking advan- 
 tage of groups of 10 and 20 wherever possible : 
 
 1. 2. 3. 4. 
 
 6 
 4 
 
 1 21 71 
 9j 8J 3j 
 71 41 5' 
 3J 6j 5. 
 
 2 7 7 
 
 J 9 2 
 
 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 525343 78 259 
 
 554325 5 4 789 
 
 56785 56 321 
 
 79874 02 581 
 
 431236 9 7 525 
 
 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 
 
 3J 8 
 
 71 
 
 2 
 
 1 
 
 6 
 
 91 1 
 
 6 5 
 
 2 4 4 
 
 6 
 
 2-2 422393 
 
 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 
 
 2 
 
 31 
 
 91 
 
 2 
 
 8 
 
 4 
 
 9 
 
 ■ 9j 
 
 7j 
 
 9J 
 
 7 
 
 9 
 
 Q 6 6 
 
 7 7 5 
 
 7 8 6 
 
 9 7 
 
 8 7 
 
 6 2 7 6 
 
 9 8 9 7 
 
 5 9 9 4 
 
 6 9 2 9 
 
 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 
 634768672 
 6 84898858 
 8 67455 236 
 
10 CONCISE BUSINESS ARITHMETIC 
 
 14. 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 
 91215182124273033363942454851 
 
 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 Q^ 70 75 80 
 
 11 16 21 26 31 36 41 46 51 ^ 61 m 71 76 81 
 
 12 17 22 27 32 37 42 41 52 57 62 67 72 77 82 
 
 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 
 14192429343944495459 64697479 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 3^ 
 
 14 17 20 23 26 29 32 35 38 41 44 47 50 53 m 
 
 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 
 1720232629323538414447505356 59 
 
 15. When a figure is repeated several times the sum may be 
 found by multiplication. 
 
ADDITION 11 
 
 ORAL EXERCISE 
 
 ^y inspection find the sum of : 
 
 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 
 
 434537 8 8 15 6 T 8 15 13 9 
 
 97453757 15 687 14 13 8 
 
 984597 5 9 15 12 7 8 15 13 8 
 
 989598 6 98 12 77 14 79 
 
 989988698 12 78 15 78 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 3 
 
 7 
 
 4 
 
 2 
 
 7 
 
 5 
 
 12 
 
 2 
 
 4 
 
 6 
 
 8 
 
 9 
 
 8 
 
 5 
 
 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 
 
 16. 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. 
 
 / Z ^ 4^ur ^ y <^ f ^ 
 
 17. 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. 
 
 18. 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 
 
 CB 
 
12 
 
 CONCISE BUSINESS ARITHMETIC 
 
 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 
 
 19. 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. 
 
 20. 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. • 
 
 21. 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 two processes agree, the work may be assumed to be correct. 
 
 22. Example. Find the sum of 54,669, 15,218, 36,425, 
 45,325, and 68,619. 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 (h). 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 (6), the result, 220,256, is assumed to be correct, 
 addition should be carefully checked. 
 
 (J) 
 
 54669 
 
 (a) 
 
 19 
 
 15218 
 
 36 
 
 28 
 
 36425 
 
 12 
 
 21 
 
 45325 
 
 21 
 
 12 
 
 68619 
 
 28 
 
 36 
 
 220256 
 
 19 
 
 220256 
 
 
 220256 
 
 med to be correct. All work in 
 
ADDITION 13 
 
 WRITTEN EXERCISE 
 
 See how many times the following numbers can he written in 
 one minute. Write each number in form for vertical addition. 
 
 1. 426579. 3. ^7983.21. 5. 170812.34. 
 
 2. 123987. 4. $4080.91. 6. $41182.50. 
 
 Thus, in repeating the number in problem 1 write it as follows: 
 
 ^ z ^ ^ 7 
 
 ^ 
 
 A^ z C ^ 7 
 
 f 
 
 A^ Z ^ S- 7 
 
 ^ 
 
 ^^ Z / JT 7 
 
 f 
 
 <ii^. 
 
 
 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. 
 
 23. 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. 
 
 24. 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 sayyhwr hundred dollars, thirty-seven; in calling 
 $25.11 say twenty-Jive dollars, eleven; in calling $1573.86 say fifteen hundred 
 seventy-three dollars, eighty-six; in calling $5.31 sajfive 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, $84.98, 
 $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, 
 tlOO.85, $310.60, $80.90, $399.80, $412.60. 
 
14 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Copy, find the sum, and check : 
 
 1. 2. 3. 
 
 "f (^ fJi^<^^Z/ "^^^ Z4^Z^^4^.f2 ^Z /J~/ 6 Z /.^// 
 
 yJ^cTiiyJ^.j-^ / ZJ' f z-/ ii\c7^ / 2 (^ z/ ^/.Cy 
 
 3yft2Z(if./y Z / y y ZoJ.c^ Z/3 /A^yZ.c^S 
 
 CyZ / Z3^.23 y / 3 / A^z C.o^ /^(^ Z / ^/.c^y 
 
 A^z/z^/ z.A^s / z^y z/ z.^C f6^ry^r.c^3 
 
 / ZA^y Z / Z.J-A^ / 3 Z / C^Z./ y / Z^ZA^y Z.A^Z 
 
 / ZJ^Zf i^A^.y ^ Z/ A/r y /^ 2 /.A^^ y>r^<r63r.^r 
 
 2 / y y z / 6.J~A^ 3 / ^/ zs'f.c? (^ z/A^/z<^z.^y 
 
 ^ yz 3 A^ (>y.A^r z / / A^zc? /.j-r ry ^yrA^y.<i / 
 
 ZA^^^^zy.//^ 3 / y^z^y.6y / z C z^yy/^ 
 
 ^£j£^;_Z^y^^^^^^^/_^ 3j£/__C2_^^jyf^ 
 
 4. 5. 6. 
 
 ^/ z Cy z<^/^j- >^/ zy^Z^^.A^f' ^/ zj-/ ^ za^.^^ 
 
 ^3y.zC y^/ 2c? A^y.y z y z/ z ^ ^.^^ 
 
 / Z.y / / Z (^ (23'^.A^Z ^//2^^.v/4^ 
 
 y.Cy 2/<iA//A^.yy /j~cp^6Pc7t2.yr 
 
 C/Zy /^ (r6.^2 / C / ^y.fz / y C y z / ^.3V 
 
 J-// / C^.yJ' 7 2 / A^ C.^A^ 2Ayc^ / z<2'6.zs 
 
 y/z.yr / z.yj- / zyn3.C^ 
 
 yz./AZ /z^.yz / z<^A<yz 
 
 <r^^.rC z/A^C'^/ /\^/ z <^ yz.(zy 
 
 / /,^6 3 2<^AZ3:y/ / C f Z / C Z.(2A^ 
 
 yzdf.A^z ^2C^.(2/ /y2/.y^ 
 
 (>y2^.y^ 3(p(Z/.yr' a^/ i^.ys 
 
 /Zyyr./if yj-.(pi (^yz/.y^ 
 
 /lA^.Ci? /.fZ /A^.ys 
 
ADDITION 15 
 
 7. 8. 9. 
 
 Z3 Z~y /^./ ^ / (i f Zf./^-' / CP / ^ ^ Zy.6<P 
 
 /ZsjrCr.3^ ^y^zl/.A^z yz/z^^^.y^^ 
 
 zz 'yf^z.yr / ^ z (^4^^j^.A^y 3 tf fj/^^j<i 
 
 z C (P^JrA<f^ /^z/^j~y.fz /f4^/yz.^j' 
 
 zz i!^ ^f /.3y yz/:zA^ ^ j./r^r f//^f3<r.j-^ 
 
 r3 ^ z.A^^ CfZA^/^.ZA^ /z^/z.^cp 
 
 VZ i^ tJ ^.y^ ^Z./ z (^ y.rA^ /i A^ / Z.yj- 
 
 rzf^A^.33r J y zf z.zc^ / ^ / Cf / 2./^z 
 
 3 j-fA^rz.z-c? / z ^ A^^.o c^ yj~/(r.fs 
 
 yf6o:cP(p yZA^^.<^f / (^ Z / f.yj' 
 
 r CJ~2 /.^<^ J ^ c? A^yr.4A(^ / A^ / yj-Z /./Za/^ 
 
 yjTA^j y /.uT^ (^ f ^/ / ^.j-z / / z / A^f o.yS 
 
 / (P / 6 rz3.z^ y z / zos:/ / 6f<ry^.Cz 
 
 fZ^^^AJ./Z- <^ Z-/ ^y (^.dP / y Za^ / J r.yj' 
 
 A^r3 <(.f ^ yA^ / 6 zy. ^3 / z ^ A^z/,zt 
 
 fZyr^y.A^^ C Z / Z-/^A^.y^ 2-/ y ZZ/.Ca^ 
 
 ZC 2^rz.yA^ (2>y/zr.Co CfZ/^y^ 
 
 / Z (^ / Z f.A^J- / O / Z <Z / (i.J'y Z / / / ^fA^.JZ/ 
 
 f (^ rj~Z./ y y f Z ^ / y.Zf yyy.yA^^.^y 
 
 /vy/z./f^ / z-/ 2^ z.C (p yZ/Z(^-y3 
 
 Zj- / y z C.r(^ / ^ / A^ZyX^- z^/ 3 zy./A^ 
 
 ^ii3~3z.^^ z^/C^y.^A^ yj'yytJ.yC 
 
 z z (^ / A^.yz^ Cyjyr.y^r / C / z C.^y 
 
 V ^ z zrA^.zo y (Z / Z-^.yZ y Z / Z.a^S 
 
 yy^^z.o^ (^yj'A^.ry zyyzZy,/r 
 
 C ^ ocrz.6>^ / z C y ^ z,^.j~A^ / <^y ZA^y.yc? 
 
 /z<i/ZJ~.Cs 3z/6/^.yo /^fZA^.i^yr 
 
 3 yj-r^ ^A^ /J>Z3 C y. y^ Zj£j_Z^C^Z^ 
 
16 CONCISE BUSINESS ARITHMETIC 
 
 25. 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. 
 
 26. Example. Find the sum of 83, 72, 89. _„ 
 
 oo 
 
 Solution. Beginning at the bottom and adding up, think of 89 and rro 
 
 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, 24Ji^ 
 
 89 
 244 
 
 ORAL EXERCISE 
 
 By inspection give the sum of each of the folloiving 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 
 251829562743673472754639472539 
 
 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 Qb 25 48 57 45 31 65 39 64 34 43 82 25 
 75213431392167698787^25419831 
 
 HORIZONTAL ADDITION 
 
 27. In some kinds of invoicing and 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. 
 
 28. 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 17 
 
 WRITTEN EXERCISE 
 
 Copy and add the following numhers 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, m, 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. 1525, 5025^ 1684, 3142^ ggss^ igw 2312, iQis, 6480, 4010. 
 
 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" ; ^ 2.08 may be written 2«8. 
 
 13. 1525, 893, 488, 2184, 1635^ 1846, 291*, 44^0, 6290, 8460, 4050. 
 
 14. 76'5, 8497, 6705, 9574^ 6863, 5221, 1325^ 4218, 6095, 80i3, 90^2. 
 
 29. 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 . 
 hundred twenty words per minute. Nothing should be written by the 
 students until all of the numbers of a problem have been called by the 
 instructor; then one student may be sent to the blackboard and required 
 to write the numbers from memory. If the numbers are correctly written, 
 the instructor may require another student to give the sum of them with- 
 out using pen or pencil. The numbers may be written on the board in 
 either vertical or horizontal order, as the instructor may direct. 
 
18 
 
 CONCISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 From the instructor's dictation find mentally the sum of each of 
 the following problems : 
 
 1. 6, 9, 8, 4, 8, 6. 15. 
 
 2. 14, 17, 20, 5, 9. 16. 
 
 3. 24, 17, 16, 9, 5. 17. 
 
 4. 5, 6, 7, 1, 3, 8. 18. 
 
 5. 6, 2, 8, 1, 7, 4. 19. 
 
 6. 364, 436, 657, 25. 20. 
 
 7. 438, 212, 750, 64. 21. 
 
 8. 859, 441, 769, 71. 22. 
 
 9. 2140, 3160, 4000. 23. 
 
 10. 200, 415, 600, 95. 24. 
 
 11. 857, 643, 237, 500. 25. 
 
 12. S 4150, $4050, $850. 26. 
 
 13. $5.15, $2.15, $6.70. 27. 
 
 14. $167.14, $232.86, $9. 28. 
 
 147, 253, 179, 121. 
 423, 517, 81, 49. 
 255, 45, 89, 121. 
 25, 65, 27, 133. 
 $48, $32, $138. 
 $135, $275, $418. 
 $23, $67, $281. 
 $284, $36, $245. 
 133, 167, 29, 61. 
 2319, 1681, 2335. 
 3310, 2790, 1565. 
 2740, 1365, 2135. 
 2273, 1237, 1145. 
 1432, 1058, 1210. 
 
 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 froin 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 
 
ADDITION 
 
 19 
 
 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 
 
 6948 
 
 23 
 
 
 
 76 
 
 95 
 
 87 
 
 14 
 
 2150 
 
 49 
 
 172 
 
 93 
 
 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 op Clerks' Daily Sales 
 
 Names of Cleeks 
 
 Monday 
 
 TtTESDAY 
 
 Wednesday 
 
 Thuesday 
 
 Feiday 
 
 Satuedat 
 
 Total 
 FOE 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 
 
 61 
 
 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 Benton 
 
 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. 0. Beck 
 
 127 
 
 16 
 
 95 
 
 27 
 
 114 
 
 82 
 
 162 
 
 15 
 
 102 
 
 15 
 
 112 
 
 61 
 
 
 
 L. 0. Avery 
 
 214 
 
 91 
 
 218 
 
 46 
 
 920 
 
 41 
 
 172 
 
 14 
 
 155 
 
 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 
 
 00 
 
 116 
 
 84 
 
 117 411 
 
 200 
 
 60 
 
 
 
 E. 0. Burrill 
 
 84 
 
 90 
 
 90 
 
 10 
 
 116 
 
 80 
 
 114 
 
 30 
 
 65 
 
 20 
 
 300 
 
 75 
 
 
 
 Total 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6. On the page following are a number of inventory exten- 
 sions ; find the footing of each. 
 
20 CONCISE BUSINESS AEITHMETIC 
 
 Each column should be added in approximately three minutes. 
 
 a. 
 
 I. 
 
 c. 
 
 d. 
 
 $1628.45 
 
 $1743.19 
 
 $2065.32 
 
 $1156.78 
 
 176.22 
 
 78.91 
 
 145.55 
 
 11.69 
 
 453.26 
 
 1011.45 
 
 28.49 
 
 189.24 
 
 1102.65 
 
 125.60 
 
 217.86 
 
 338.54 
 
 45.22 
 
 101.25 
 
 207.41 
 
 24.75 
 
 143.51 
 
 74.24 
 
 1078.44 
 
 8.95 
 
 55.68 
 
 212.35 
 
 45.60 
 
 1250.05 
 
 425.70 
 
 338.90 
 
 256.85 
 
 74.33 
 
 119.45 
 
 227.83 
 
 194.61 
 
 258.97 
 
 7.15 
 
 46.21 
 
 112.45 
 
 364.20 
 
 89.52 
 
 117.25 
 
 34.65 
 
 126.70 
 
 48.75 
 
 57.81 
 
 133.27 
 
 82.56 
 
 170.25 
 
 9.11 
 
 24.13 
 
 219.63 
 
 613.81 
 
 764.35 
 
 495.34 
 
 360.42 
 
 1203.05 
 
 88.75 
 
 6.17 
 
 24.45 
 
 327.16 
 
 401.19 
 
 98.75 
 
 175.26 
 
 654.32 
 
 1145.22 
 
 856.21 
 
 1364.12 
 
 108.17 
 
 366.18 
 
 1408.95 
 
 374.11 
 
 75.45 
 
 201.13 
 
 376.23 
 
 211.06 
 
 9.58 
 
 64.33 
 
 112.50 
 
 21.08 
 
 142.53 
 
 8.78 
 
 56.40 
 
 312.74 
 
 189.70 
 
 89.56 
 
 76.50 
 
 118.44 
 
 20.65 
 
 192.35 
 
 244.56 
 
 94.65 
 
 673.13 
 
 98.75 
 
 339.54 
 
 951.15 
 
 120.06 
 
 320.16 
 
 87.40 
 
 73.07 
 
 65.34 
 
 135.20 
 
 467.80 
 
 239.15 
 
 753.25 
 
 ■ 846.18 
 
 515.05 
 
 1856.22 
 
 371.10 
 
 1904.76 
 
 287.01 
 
 475.02 
 
 69.16 
 
 128.44 
 
 301.04 
 
 602.13 
 
 231.06 
 
 473.08 
 
 1654.23 
 
 342.50 
 
 503.44 
 
 95.16 
 
 270.15 
 
 89.65 
 
 78.42 
 
 143.65 
 
 69.40 
 
 439.20 
 
 250.21 
 
 54.30 
 
 355.11 
 
 175.06 
 
 2859.89 
 
 1756.84 
 
 742.13 
 
 1914.56 
 
ADBITIOK 21 
 
 WRITTEN EXERCISE 
 
 Each of these groups should be added in approximately one minute. 
 
 1. 2. 3. 
 
 6,354,276,742 6,917,408,583 8,632,714,509 
 
 5,116,433,854 5,880,734,112 6,875,352,272 
 
 8,446,750,284 6,538,922,553 8,539,168,753 
 
 2,141,991,648 7,543,276,445 8,335,674,912 
 
 4.653.752.816 6,441,819,263 5,321,841,174 
 
 3.256.851.539 2,574,438,911 2,435,627,819 
 
 5.462.175.255 4,156,717,549 1,546,721,973 
 6,435,621,953 1,817,908,667 5,167,534,217 
 4,717,880,945 6,745,243,517 4,576,819,054 
 5,601,523,764 3,546,798,212 4,151,762,492 
 
 4. 5. 6. 
 
 2,334,515,637 5,432,317,892 6,453,615,809 
 
 5.734.516.772 6,534,317,865 4,576,879,253 
 
 7.354.618.227 4,531,841,962 2,432,653,274 
 3,542,618,906 3,132,341,264 7,819,457,836 
 5,115,616,874 4,651,272,335 ' 1,918,776,425 
 
 7.175.437.256 3,256,728,143 5,327,731,224 
 
 1.735.273.540 1,830,925,165 4,532,551,243 
 
 8.134.556.773 2,543,175,213 6,231,605,228 
 3,115,617,221 3,413,214,605 7,615,257,818 
 3,255,617,711 5,443,216,448 5,663,338,119 
 
 7. 8. 9. 
 
 4.334.561.228 3,653,212,716 4,176,234,562 
 1,765,371,442 7,661,823,394 5,934,736,548 
 9,717,632,461 5,749,287,716 6,254,817,259 
 5,616,727,640 3,264,723,445 1,218,735,143 
 
 2.615.431.817 2,845,367,621 7,342,235,907 
 4,256,713,332 4,256,443,486 6,543,217,194 
 3,078,395,668 7,254,563,823 2,546,718,911 
 7,845,446,772 9,117,224,383 3,664,293,189 
 8,250,114,337 1,493,786,332 9,226,847,821 
 
22 CONCISE BCrSlKESS AKITHMETIC 
 
 A WRITTEN REVIEW TEST 
 
 Write the following problems from dictation^ and tTien complete 
 the work. Time, approximately^ thirty minutes, including the dicta- 
 tion. Add the following : 
 
 1. 2. 
 
 23,418 17,546 28,356 43,572 
 
 43,621 23,811 32,718 21,471 
 
 71,892 32,264 10,918 37,509 
 
 22,457 31,542 27,354 42,311 
 
 34,256 45,623 45,612 20,175 
 
 41,243 54,819 33,452 75,604 
 
 44,172 22,716 31,174 70,219 
 
 34,523 45,613 44,530 28,332 
 
 31,113 41,414 45,517 37,743 
 
 20,125 13,064 50,197 22,508 
 
 62,157 93,845 29,875 45,612 
 
 In problems 3 and 4 add by columns and then by lines, and check 
 the work by adding the vertical and horizontal totals. 
 
 542 
 
 236 
 
 ? 
 
 123 
 
 235 
 
 ? 
 
 437 
 
 653 
 
 ? 
 
 947 
 
 834 
 
 ? 
 
 572 
 
 246 
 
 ? 
 
 174 
 
 215 
 
 ? 
 
 445 
 
 354 
 
 ? 
 
 313 
 
 208 
 
 ? 
 
 236 
 
 716 
 
 ? 
 
 364 
 
 312 
 
 ? 
 
 423 
 
 394 
 
 ? 
 
 252 
 
 733 
 
 ? 
 
 347 
 
 616 
 
 ? 
 
 243 
 
 317 
 
 ? 
 
 455 
 
 494 
 
 ? 
 
 203 
 
 406 
 
 ? 
 
 337 
 
 651 
 
 ? 
 
 543 
 
 392 
 
 ? 
 
 453 
 
 283 
 
 ? 
 
 527 
 
 618 
 
 ? 
 
 624 
 
 912 
 
 ? 
 
 624 
 
 483 
 
 ? 
 
 538 
 
 496 
 
 ? 
 
 713 
 
 626 
 
 ? 
 
 712 
 
 324 
 
 ? 
 
 235 
 
 439 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
CHAPTER III 
 
 SUBTRACTION 
 ORAL EXERCISE 
 
 State the number that^ added to the smaller number^ makes the 
 larger 07ie in each of the following : 
 
 1. 344567889999887 
 
 
 1 
 
 2 
 
 1 
 
 3 
 
 2 
 
 3 
 
 3 
 
 2 
 
 3 
 
 1 
 
 6 
 
 4 
 
 4 
 
 1 
 
 2 
 
 2. 
 
 12 
 
 11 
 
 12 
 
 11 
 
 12 
 
 11 
 
 12 
 
 11 
 
 10 
 
 11 
 
 10 
 
 11 
 
 10 
 
 12 
 
 10 
 
 
 _9 
 
 2 
 
 3 
 
 9 
 
 8 
 
 3 
 
 4 
 
 _8 
 
 4 
 
 _7 
 
 6 
 
 4 
 
 7 
 
 5 
 
 3 
 
 3. 
 
 18 
 
 17 
 
 16 
 
 17 
 
 16 
 
 15 
 
 14 
 
 15 
 
 14 
 
 13 
 
 13 
 
 16 
 
 15 
 
 14 
 
 13 
 
 
 9 
 
 8 
 
 7 
 
 9 
 
 8 
 
 6 
 
 9 
 
 7 
 
 8 
 
 4 
 
 j; 
 
 9 
 
 8 
 
 5 
 
 9 
 
 4. 
 
 13 
 
 14 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 18 
 
 19 
 
 19 
 
 19 
 
 19 
 
 18 
 
 18 
 
 17 
 
 
 11 
 
 12 
 
 11 
 
 13 
 
 12 
 
 13 
 
 13 
 
 12 
 
 13 
 
 11 
 
 16 
 
 14 
 
 14 
 
 11 
 
 12 
 
 5. 
 
 22 
 
 21 
 
 22 
 
 21 
 
 22 
 
 21 
 
 22 
 
 21 
 
 20 
 
 21 
 
 20 
 
 21 
 
 20 
 
 22 
 
 20 
 
 
 19 
 
 12 
 
 13 
 
 19 
 
 18 
 
 13 
 
 14 
 
 18 
 
 14 
 
 17 
 
 16 
 
 14 
 
 17 
 
 15 
 
 13 
 
 6. 
 
 38 
 
 27 
 
 26 
 
 37 
 
 26 
 
 35 
 
 44 
 
 25 
 
 34 
 
 53 
 
 43 
 
 36 
 
 45 
 
 54 
 
 73 
 
 
 29 
 
 18 
 
 17 
 
 29 
 
 18 
 
 26 
 
 39 
 
 17 
 
 28 
 
 44 
 
 37 
 
 29 
 
 38 
 
 45 
 
 69 
 
 7. 
 
 42 
 
 51 
 
 72 
 
 81 
 
 92 
 
 71 
 
 32 
 
 41 
 
 70 
 
 61 
 
 90 
 
 81 
 
 30 
 
 62 
 
 50 
 
 
 39 
 
 42 
 
 63 
 
 79 
 
 88 
 
 63 
 
 24 
 
 38 
 
 64 
 
 57 
 
 86 
 
 74 
 
 27 
 
 55 
 
 47 
 
 30. 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. 
 
 23 
 
24 
 
 CONCISE BUSINESS ARITHMETIC 
 
 31. Examples, l. Find the difference between 849 and 162. 
 
 Solution. 2 from 9 leaves 7. 6 cannot be subtracted from 4, but 6 qaq 
 from 14 leaves 8. Since 1 of the 8 hundreds has been taken, there are but -| /»n 
 
 7 hundreds remaining. 1 from 7 leaves 6. 
 
 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 j " 1 and 4 + 2 = 7," and write 2. 4824 
 
 Check. 2422 + 4824 = 7246. • "2422 
 
 ORAL EXERCISE 
 
 1. 16+ 23 + ? = 54? 7. 
 
 2. 27 + 14 + ?=72? 8. 
 
 3. 17 + 36 + ? =62? 9. 
 
 4. 19 + 17 + 12 + ? =57? 10. 
 
 5. 25 + 14 + 11+? = 75? 11. 
 
 6. 18 + 17 + 16 + ? = 70? 12. 
 
 16 + 18 + 16=25 + ? 
 72 + 17 + 11 = 37 + ? 
 
 14 + 18 + 38 = 42 + ? 
 12 + 16 + 12 + 14+?: 
 
 75? 
 
 16 + 15 + 19 + 15+? = 93? 
 18 + 17 + 15 + 29+? = 98? 
 
 WRITTEN EXERCISE 
 
 1. Without copying the individual problems, find quickly 
 the sum of the twenty differences in the following: 
 
 12140.50 
 
 $4157.50 
 
 $5000.24 
 
 $9000.72 
 
 $3145.62 
 
 714.23 
 
 1236.80 
 
 249.17 
 
 1246.18 
 
 2000.79 
 
 $5500.89 
 
 $1624.14 
 
 $1985.72 
 
 $1379.54 - 
 
 $1742.18 
 
 2799.14 
 
 957.80 
 
 645.92 
 
 923.18 
 
 842.16 
 
 19275.17 
 
 $2446.80 
 
 $3169.14 
 
 $3156.19 
 
 $4756.83 
 
 842.99 
 
 1321.44 
 
 874.36 
 
 1400.72 
 
 2738.44 
 
 17514.85 
 
 $7291.80 
 
 $1756.92 
 
 $8721.13 
 
 $1872.14 
 
 721.92 
 
 1642.95 
 
 •921.74 
 
 2049.79 
 
 742.12 
 
SUBTRACTION 
 
 25 
 
 2. Copy the following table and show (a) the total exports 
 for each year given; (5) the excess of exports for each year 
 given ; (tf) the total exports and imports for the ten years ; 
 (c?) the total excess -of exports for the ten years. Check. 
 
 Imports axd Exports ix the United States for Ten Years 
 
 Year End- 
 
 Exports 
 
 Total 
 Exports 
 
 Imports 
 
 Excess of 
 
 ixu June 30 
 
 
 
 Exports 
 
 
 Domestic 
 
 Foreign 
 
 
 
 
 1904 
 
 $1435170 017 
 
 $25 648 254 
 
 
 .$991090 978 
 
 
 1905 
 
 1 491 744 641 
 
 26 817 025 
 
 
 1117 513 071 
 
 
 1906 
 
 1 717 953 382 
 
 25 911 118 
 
 
 1 226 562 446 
 
 
 1907 
 
 1 853 718 034 
 
 27 133 044 
 
 
 1 434 421 425 
 
 
 1908 
 
 1 834 786 357 
 
 25 986 357 
 
 
 1 194 341 792 
 
 
 1909 
 
 1 638 355 593 
 
 24 655 51i 
 
 
 1311920 224 
 
 
 1910 
 
 1 710 083 998 
 
 34 900 722 
 
 
 1556 947 430 
 
 
 1911 
 
 2 013 549 025 
 
 35 771 174 
 
 
 1 527 226 105 
 
 
 1912 
 
 2 170 319 828 
 
 34 002 581 
 
 
 1 653 264 934 
 
 
 1913 
 
 2 428 506 358 
 
 37 377 791 
 
 
 1 812 978 234 
 
 
 Total 
 
 
 
 
 
 
 Under the term domestic exports are included exports of merchandise, 
 the growth, produce, or manufacture of the United States ; under foreign 
 exports are included articles of merchandise previously imported into the 
 United States and subsequently reexported. Under the term imports are 
 included imports of all merchandise of whatever origin received into the 
 United States. 
 
 32. 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 7^^ and tenders $1 in 
 payment, the mental process of the clerk in making the change is as follows : 
 "74^2^ + 1/^ + 25jz^ = $1"; the customer should receive as change a 1-cent 
 piece and a quarter of a dollar. 
 
 Change may 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. 
 In the following 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 S 1 for each of the following purchases : 17/; 24/; 31/; 
 38/; 45/; 52/; 59/; m pf ', 73/; 80/; 87/; 18/; 25/. 
 
26 COKCISE BUSINESS ARITHMETIC 
 
 2. Name the coins and the amount of change to be given 
 from $2 for each of the following purchases: 11.19; f 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 each 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 
 
 $3.23; $5.17; $4.24 
 
 $3.66; $5.73; $4.80 
 
 $3.60; $4.53; $2.46 
 
 $9.42; $3.67; $1.93. 
 
 $3.86; $7.70; $2.44; $8.37; $5.30 
 
 $3.31; $8.38; $2.45; $6.52; $4.59 
 
 $3.87; $2.88; $7.81; $9.74; $5.67 
 
 $3.29; $8.32; $7.25; $2.18; $7.49 
 
 33. 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. 
 
 34. 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 ? 
 
 rrTQ A 
 
 Solution. Arrange the numbers as shown in the margin. Dio ^. 
 
 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. gg 
 
 Four (2 carried + 1 + 1) and one are 6 ; write 1. 121 
 
 Check. 197 + 121 + 98 + 162 = 678. 
 
 197 A. 
 
 WRITTEN EXERCISE 
 
 Find the amount each person has remaining on deposit: 
 
 1. A. Deposit, 1900; checks, 1210, $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 
 
 27 
 
 5. E. Deposit, $967; checks, $192, 1102, |11T, $128,1146. 
 
 6. F. Deposit, 1998; checks, $119, $117, 1105, $123,1173. 
 
 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 : 
 
 $148.90 + $149.75 + $421.77 = 
 118.60+ 172.12+ ???.?? = 
 242.30+ ???.??+ 210.96 = 
 ???.??+ 168.72+ 130.41 = 
 
 ? ? ? 
 
 ? ? ? 
 
 ? ? ? 
 
 ? ? 9 
 
 ? ? 
 ?? 
 
 ?? 
 ? ? 
 
 9 ? 
 
 $718.95 + $698.75 + $978.60 =$?? ? ?. 
 
 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. (/ + z + A should equal g.) 
 
 Face of Paper 
 
 Discount 
 
 Coll. & Excu. 
 
 Proceeds 
 
 729 
 
 U 
 
 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 
 
 3 
 
 78 
 
 
 38 
 
 f 
 
 
 9 
 
 
 h 
 
 
 i 
 
 
 J 
 
 
 35. 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 when two 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. 
 
 CB 
 
28 CONCISE BUSINESS ARITHMETIC 
 
 36. Since numbers are read from left to right, in finding the 
 complement of a number, begin at the left to subtract. 
 
 37. 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. 
 
 38. 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 f 100.00 
 leaves 2 ; 5 from 9 leaves 4 ; 2 from 10 leaves 8. Or 77 ^9 
 
 (b) 7 and 2 are 9 ; 7 and 2 are 9 ; 6 and 4 are 9 ; 2 and 8 are ' 
 
 10. $22.48. $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 
 
 Find the total of each group of numbers, then find the difference 
 between the two totals: 
 
 1. (24 26 32 30 35 25) - (18 13 19 12 20 30). 
 
 2. (13 27 45 25 21 19) - (15 14 21 32 18 22). 
 
 3. (11 29 35 15 24 16) - (27 13 18 22 25 20). 
 
 4. (17 14 29 32 22 26) - (23 13 16 24 20 16). 
 
 5. (45 25 30 40 32 18) - (25 35 33 17 20 30). 
 
 6. (34 24 35 30 15 32) - (21 39 14 15 11 30). 
 
 7. (15 25 33 27 14 36) - (13 30 16 14 20 16). 
 
 8. (14 16 30 10 40 50) - (11 19 18 12 20 30). 
 
 9. (19 10 11 20 30 32) - (15 11 14 30 32 18). 
 ,10. (33 17 22 11 17 50) - (21 19 31 12 17 40). 
 
 11. (25 30 15 40 15 20) - (15 16 19 21 29 30). 
 
 12. (17 23 25 26 15 44) - (24 20 26 27 13 20). 
 
 13. (11 39 52 18 10 20) - (12 18 40 22 28 12). 
 
 14. (35 15 27 23 34 16) - (21 17 12 42 13 15). 
 
 15. (22 18 34 26 60 10) - (35 15 20 11 19 31). 
 
 16. (33 17 22 18 40 60) - (14 26 23 17 40 12). 
 

 
 SUBTEACTION 
 
 29 
 
 
 
 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. 
 
 11.25, $0.75, $2.18 
 
 $20 
 
 2. 
 
 27^, 23^, 14^ 
 
 12 
 
 15. 
 
 il.50, 12.70,11.18 
 
 $20 
 
 3. 
 
 45^, 55^, 13^ 
 
 15 
 
 16. 
 
 $4.60, $1.40, $2.13 
 
 $20 
 
 4. 
 
 64^, 16^, 87^ 
 
 15 
 
 17. 
 
 $1.50, $1.20, $2.30 
 
 $10 
 
 5. 
 
 23^, 14^, 27^ 
 
 $2 
 
 18. 
 
 $3.17, $4.11,14.98 
 
 $50 
 
 6. 
 
 63.^, 17^, 59iZf 
 
 $5 
 
 19. 
 
 $4.25, $0.75, $3.18 
 
 $20 
 
 7. 
 
 49^, 84^, 37^ 
 
 f5 
 
 20. 
 
 $1.29, $2.17, $1.50 
 
 $20 
 
 8. 
 
 78^, 42^, 67^ 
 
 $5 
 
 21. 
 
 $1.64, $1.66, $2.50 
 
 $20 
 
 9. 
 
 52^, 69^, 885^ 
 
 15 
 
 22. 
 
 $1.59, $23.41, $118 
 
 $200 
 
 10. 
 
 75^, 86^, 54^ 
 
 15 
 
 23. 
 
 $24.17, $20.83, $15 
 
 $100 
 
 11. 
 
 89^, 46^, 72^ 
 
 15 
 
 24. 
 
 $11.48, $10.52, $50 
 
 $100 
 
 12. 
 
 76^, 54^, 29^ 
 
 $5 
 
 25. 
 
 $18.91, $12.09, $45 
 
 $100 
 
 13. 
 
 75^, 25^, 89^ 
 
 810 
 
 26. 
 
 $21.27, $2.73, $50.50 
 
 $100 
 
 39. 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) 4- 822 (the complement of the 
 subtrahend), and so on. 
 
 40. This principle makes it a simple matter to find the dif- 
 ference between a subtrahend and several minuends. 
 
 41. 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), gig 299 311 
 
 16, 17; 17-10 = 7. 9, 13, 16; 16-10=6. 
 
 2. 9, 17, 26; 26-10=16; that is, 6 and 1 +-*<Q +^^Q +^^^ 
 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 =676 =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. 
 
30 
 
 CONCISE BUSINESS ARITHMETIC 
 
 42. Example. The following problem shows a concrete appli- 
 cation of the foregoing principle : 
 
 Depositors' Ledger 
 
 Solution. Here is a 
 depositors' ledger. TJie 
 data in the first three 
 columns being given, it 
 is required to find the 
 new balance. 
 
 Depositor 
 
 Balance 
 
 Checks 
 
 Deposits 
 
 A 
 B 
 C 
 
 ^74 
 $86 
 192 
 
 $25 
 $11 
 $79 
 
 $86 
 $99 
 $81 
 
 Balance 
 
 $135 
 
 $174 
 $ 94 
 
 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 new balances^ the total old balance^ the total checks^ the 
 total deposits^ the total new balances^ and cheek the work: 
 
 1. 2. 
 
 Dbpositok 
 
 Bal. 
 
 Checks 
 
 Deposits 
 
 Bal. 
 
 A 
 
 $758 
 
 $128 
 
 $ 421 
 
 a 
 
 B 
 
 921 
 
 154 
 
 175 
 
 h 
 
 c 
 
 934 
 
 214 
 
 122 
 
 c 
 
 D 
 
 862 
 
 162 
 
 218 
 
 d 
 
 E 
 
 478 
 
 187 
 
 126 
 
 e 
 
 F 
 
 921 
 
 215 
 
 124 
 
 f 
 
 G 
 
 756 
 
 157 
 
 137 
 
 9 
 
 H 
 
 864 
 
 128 
 
 142 
 
 h 
 
 I 
 
 926 
 
 214 
 
 121 
 
 i 
 
 J 
 
 752 
 
 221 
 
 124 
 
 J 
 
 K 
 
 878 
 
 162 
 
 218 
 
 k 
 
 
 / 
 
 m 
 
 n 
 
 
 
 Depositor 
 
 Bal. 
 
 Checks 
 
 Deposits 
 
 Bal. 
 
 A 
 
 $428 
 
 $125 
 
 $ 718 
 
 a. 
 
 B 
 
 726 
 
 128 
 
 296 
 
 h 
 
 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 
 
 H 
 
 837 
 
 316 
 
 176 
 
 h 
 
 I 
 
 493 
 
 121 
 
 219 
 
 i 
 
 J 
 
 862 
 
 128 
 
 188 
 
 J 
 
 K 
 
 925 
 
 125 
 
 211 
 
 k 
 
 
 I 
 
 m 
 
 n 
 
 
 
 43. 48 — 29 = 48 + 1 (30, the next higher order of units than 
 29, - 29) - 30, or 19 ; 128 - 59 = 128 -f- 1 - 60, or 69. 
 
 44. 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 
 
SUBTEACTION 
 
 31 
 
 of merchandise ; the net weight is the difference between the gross weight 
 and the tare. 
 
 45. 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. 
 
 332-19 337-18 335-18 949 # 
 
 Solution. The numbers 
 would be written on the bill 
 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 lb. 
 
 WRITTEN EXERCISE 
 
 Oofy the following hills. Verify the net weights given and supply 
 all missing terms. 
 
 1. 
 
 Chicago, III 
 
 '.-^^^/ Z, 
 
 yi(r.<i,<i ^ r< ^. 
 
 
 JO. 
 
 Bought of PHIUP ARMOUR & CO. 
 
 Terms 
 
 J/t/^^l^^-d^^^^^^'-r^ 
 
 7<?- /'^ 
 
 — /^4- y/-/^ 
 
 lA^ <±t 
 
 J^ 
 
 A. 
 
 ^^>^- 
 
 7^^^^Z^^>^^^^^^^,^ 
 
 ^J.2.-C^ VZf-70 ^Z^- C<J- 
 
 ^2.^-/:^ z^^.^-v^ A^z^-ya 2.AJLL — 'Jtl 
 
 ^il 
 
 7^-L^^^ ry^A;-7.^'2^y^ ^^ 
 
 H4- 
 
 7^ 
 
 U»X>--7n </i/2.-'T/ ^/^-«^^ 
 
 »***■ ^^^ 3 oj 
 
 2A 
 
 JUL 
 
32 
 
 CONCISE BUSINESS ARITHMETIC 
 
 2. 
 
 Chicago^ IIL, July 20, 19 
 
 Messrs. A. M. THOMPSON & CO. 
 
 Rochester, N.Y. 
 
 Bought of Nelson, Morris & Co* 
 
 Terms 50 da 
 
 tubs Lard 
 72-17 70-14 
 69-14 71-14 
 71-15 70-16 
 
 *#* 
 
 casks Shoulders 
 421-65 426-70 
 424-72 422-64 
 427-72 421-60 #**# 
 
 casks Hams 
 
 409-72 412-70 
 414-71 410-73 
 412-70 416-71 *### 
 
 $0.13 
 
 14 
 
 .18 
 
 43 
 
 299 
 
 368 
 
 29 
 
 32 
 
 28 
 
 **# 
 
 #* 
 
 3. The gross weights and tares of 6 casks of shoulders are 
 as follows : 428 - 68, 419 - 70, 423 - 63, 432 - 72, 436 - 69, 
 484 - 65 lb. 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 lb. 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 lb. Find the 
 total net weight. 
 
SUBTRACTION 
 
 33 
 
 WRITTEN EXERCISE 
 
 Co'py each of the following examples; complete the work, and 
 check the result. Time, approximately, thirty minutes. Face of 
 paper, minus discount and collection and exchange, equals proceeds. 
 
 Face of Paper 
 
 Discount 
 
 Coll. and Exch. 
 
 Proceeds 
 
 1. $376.25 
 
 $3.76 
 
 $0.38 
 
 ? 
 
 255.78 
 
 1.28 
 
 0.26 
 
 ? 
 
 176.44 
 
 1.76 
 
 
 ? 
 
 259.86 
 
 2.60 
 
 0.26 
 
 ? 
 
 492.71 
 
 2.46 
 
 0.49 
 
 ? 
 
 149.52 
 
 0.75 
 
 0.15 
 
 ? 
 
 643.15 
 
 6.43 
 
 0.64 
 
 ? 
 
 319.21 
 
 0.80 
 ? 
 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 Face of Paper 
 
 Discount 
 
 Coll. and Exch. 
 
 Proceeds 
 
 2. $186.73 
 
 $1.87 
 
 $0.19 
 
 ? 
 
 237.50 
 
 2.38 
 
 0.24 
 
 ? 
 
 412.88 
 
 4.13 
 
 
 ? 
 
 337.95 
 
 3.38 
 
 0.34 
 
 ? 
 
 360.90 
 
 . 0.90 
 
 
 ? 
 
 245.91 
 
 1.23 
 
 0.25 
 
 ? 
 
 307.55 
 
 3.08 
 
 0.31 
 
 ? 
 
 250.40 
 
 3.76 
 
 0.25 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 Face of Paper 
 
 Discount 
 
 Coll. and Exch. 
 
 Proceeds 
 
 3. $421.95 
 
 $2.11 
 
 $0.42 
 
 ? 
 
 112.70 
 
 1.13 
 
 0.11 
 
 ? 
 
 324.50 
 
 1.62 
 
 
 ? 
 
 245.60 
 
 2.46 
 
 0.25 
 
 ? 
 
 194.75 
 
 0.92 
 
 0.19 
 
 ? 
 
 217.50 
 
 1.09 
 
 0.22 
 
 ? 
 
 311.59 
 
 3.12 
 
 0.31 
 
 ? 
 
 289.72 
 
 1.45 
 
 0.29 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
34 
 
 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Copy each of the following examples ; find the new balance^ the total 
 old balance, the total checks, the total deposits, and check the work : 
 
 1. 
 
 Name Bal. Checks Deposits Bal. 
 
 Name Bal. Checks Deposits Bal. 
 
 A 
 
 $516 
 
 $423 
 
 $313 
 
 ? 
 
 A 
 
 $309 
 
 $423 
 
 $267 
 
 ? 
 
 B 
 
 203 
 
 507 
 
 398 
 
 ? 
 
 B 
 
 476 
 
 379 
 
 112 
 
 ? 
 
 C 
 
 195 
 
 461 
 
 412 
 
 ? 
 
 C 
 
 277 
 
 407 
 
 321 
 
 ? 
 
 D 
 
 204 
 
 165 
 
 
 ? 
 
 D 
 
 255 
 
 
 126 
 
 ? 
 
 E 
 
 335 
 
 515 
 
 296 
 
 ? 
 
 E 
 
 167 
 
 217 
 
 178 
 
 ? 
 
 F 
 
 411 
 
 309 
 
 156 
 
 ? 
 
 F 
 
 213 
 
 453 
 
 329 
 
 ? 
 
 G 
 
 135 
 
 257 
 
 145 
 
 ? 
 
 G 
 
 208 
 
 196 
 
 114 
 
 ? 
 
 H 
 
 
 295 
 
 512 
 
 ? 
 
 H 
 
 126 
 
 240 
 
 114 
 
 ? 
 
 I 
 
 500 
 
 316 
 
 104 
 
 ? 
 
 I 
 
 255 
 
 153 
 
 
 ? 
 
 J 
 
 450 
 
 225 
 
 117 
 
 ? 
 
 J 
 
 
 212 
 
 317 
 
 ? 
 
 K 
 
 650 
 
 751 
 
 211 
 
 ? 
 
 K 
 
 455 
 
 235 
 
 103 
 
 ? 
 
 L 
 
 512 
 
 337 
 
 206 
 
 ? 
 
 L 
 
 275 
 
 230 
 
 115 
 
 ? 
 
 M 
 
 242 
 
 176 
 
 105 
 
 ? 
 
 M 
 
 315 
 
 275 
 
 144 
 
 ? 
 
 
 ? 
 
 ? 
 3. 
 
 ? 
 
 ? 
 
 
 ? 
 
 ? 
 
 4. 
 
 ? 
 
 ? 
 
 Name 
 
 ; Bal. 
 
 Checks Deposits Bal. 
 
 Name 
 
 : Bal. 
 
 Checks Deposits 
 
 Bai 
 
 A 
 
 $311 
 
 $242 
 
 $301 
 
 ? 
 
 A 
 
 $267 
 
 $133 
 
 $145 
 
 ? 
 
 B 
 
 235 
 
 115 
 
 118 
 
 ? 
 
 B 
 
 
 247 
 
 315 
 
 ? 
 
 C 
 
 178 
 
 
 212 
 
 ? 
 
 C 
 
 256 
 
 119 
 
 228 
 
 ? 
 
 D 
 
 142 
 
 188 
 
 206 
 
 ? 
 
 D 
 
 116 
 
 
 
 177 
 
 ? 
 
 E 
 
 
 268 
 
 315 
 
 ? 
 
 E 
 
 215 
 
 411 
 
 196 
 
 ? 
 
 F 
 
 447 
 
 397 
 
 109 
 
 ? 
 
 F 
 
 423 
 
 375 
 
 116 
 
 ? 
 
 G 
 
 214 
 
 375 
 
 226 
 
 ? 
 
 G 
 
 198 
 
 213 
 
 132 
 
 ? 
 
 H 
 
 154 
 
 106 
 
 
 ? 
 
 H 
 
 245 
 
 157 
 
 109 
 
 ? 
 
 I 
 
 256 
 
 400 
 
 144 
 
 ? 
 
 I 
 
 233 
 
 334 
 
 168 
 
 ? 
 
 J 
 
 512 
 
 613 
 
 199 
 
 ? 
 
 J 
 
 443 
 
 337 
 
 155 
 
 ? 
 
 K 
 
 245 
 
 237 
 
 155 
 
 ? 
 
 K 
 
 704 
 
 856 
 
 266 
 
 ? 
 
 L 
 
 146 
 
 
 114 
 
 ? 
 
 L 
 
 231 
 
 250 
 
 119 
 
 ? 
 
 M 
 
 565 
 
 743 
 
 248 
 
 ? 
 
 M 
 
 178 
 
 252 
 
 107 
 
 ? 
 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
SUBTRACTION 35 
 
 A WRITTEN REVIEW TEST 
 
 Write problems 1 and 2 from dictation^ and then complete the 
 work, Time^ approximately^ forty minutes^ including the dictation. 
 
 1. Add the following and check the results : 
 
 3412 4571 
 
 6243 8132 
 
 1729 2642 
 
 4572 7235 
 
 2643 6254 
 
 3414 8149 
 
 7145 6127 
 
 3328 2170 
 
 5331 4262 
 
 3473 1208 
 
 2. Find the new balance, the total old balance, the total 
 checks, the total deposits, and check the work : 
 
 3582 
 
 ? 
 
 2738 
 
 ? 
 
 9810 
 
 ? 
 
 1345 
 
 ? 
 
 4165 
 
 ? 
 
 3542 
 
 ? 
 
 4713 
 
 ? 
 
 2312 
 
 ? 
 
 1745 
 
 ? 
 
 8052 
 
 ? 
 
 ? 
 
 ? 
 
 AME 
 
 Balance 
 
 Checks 
 
 Deposits 
 
 Bala 
 
 A 
 
 $235 
 
 $142 
 
 $217 
 
 ? 
 
 B 
 
 312 
 
 254 
 
 122 
 
 ? 
 
 G 
 
 288 
 
 •300 
 
 212 
 
 ? 
 
 D 
 
 542 
 
 250 
 
 106 
 
 ? 
 
 E 
 
 
 350 
 
 500 
 
 ? 
 
 F 
 
 600 
 
 325 
 
 
 ? 
 
 G 
 
 750 
 
 
 252 
 
 ? 
 
 H 
 
 219 
 
 200 
 
 151 
 
 ? 
 
 I 
 
 224 
 
 100 
 
 216 
 
 ? 
 
 J 
 
 116 
 
 330 
 
 214 
 
 ? 
 
 K 
 
 255 
 
 225 
 
 110 
 
 . ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 3. The text, page 14, problem 4. 
 
 4. The text, page 14, problem 5. 
 
 5. The text, page 14, problem 6. 
 
CHAPTER IV 
 
 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 + 2-1-8 + 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? 
 
 46. In problems 7 and 8 it is seen that the multiplier is 
 always an abstract number ; and tlie multiplicand and product are 
 like numbers. 
 
 47. Three 5's are equal to five 3's ; $3 multiplied by 5 is 
 equal to $5 multiplied by 3 ; 4 trees multiplied by 125 is equal 
 to 125 trees multiplied by 4. 
 
 48. It is therefore seen that the product is not affected by 
 changing the order of the factors regarded as abstract numbers. 
 
 49. 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. 
 
 50. 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^, 5 used four times as a factor 
 is written 5*, and 6 used^ye times as a factor is written 6^. 
 
MULTIPLICATION 37 
 
 51. 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 8 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 lb. crackers at 
 8^; 9 lb. coffee at 34^; 7 lb. tea at 57^; 11 lb. beef at 17^; 
 120 lb. sugar at 4^; 134 lb. 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^; 8 yd. at $1.08; 7 yd. at f 1.01; 5 yd. at 11.35. 
 
 6. Beginning at count by 9's to 81 ; by lO'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. 
 
38 CONCISE BUSINESS ARITHMETIC 
 
 52. Examples, i. Find the cost of 2150 lb. at 5^. 
 
 Solution. Since 1 lb. costs 5^, 2150 lb. will cost 2150 times ^ 21.50 
 6f; but 2150 times 5^ is equal to 5 times 2150)2^. 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 45 4.Q 
 
 lowest order of units of the multiplier ; in fact, in "TqTZ 00^ 
 
 some multiplications there is a decided advantage ^q^ ^ n^, 
 
 in beginning with the highest order. The arrange- . 
 
 ment of work for both methods is shown in the 10oU4 lUoUi 
 
 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 73 and 74.) 
 
 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 ^M)0 9c c a 
 
 the product of any number multiplied by is 0, the occa ^ ^1 Ort 
 
 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 $11 per ton. 
 
 2. Find the cost of 175 lb. 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 $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 f 4.50 per pair, and 
 8 pr. of boots at $3.50 per pair? 
 
MULTIPLICATION 39 
 
 7. What must be paid for handling 12 loads of freight at 
 $2.25 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. Qheek the results by comparing the 
 sum of the line products with the sum of the multiplicands multi- 
 plied by one of the multipliers. 
 
 1. 2. 3. 
 
 15x211=? 9x1475=? 12 x $16.50=? 
 
 15x346=? 9x2618=? 12 x $27.75=? 
 
 15x318=? 9x1575=? 12 x $14.95=? 
 
 15 X 721 = ? 9 X 1792 = ? 12 x $29.86= ? 
 
 15x936=? 9x4936=? 12 x $49.88=? 
 
 15x849=? 9x7289=? 12 x $39.62= ? 
 
 15x218= ? 9x8728=_?, 12 x $86.99 = ? 
 
 15 X ? = ? 9 x ? = ? 12 X ? = ? 
 
40 CONCISE BUSINESS ARITHMETIC 
 
 4. 5. 6. 
 
 12x192=? 98x2178=? 16 xf 18.10=? 
 
 12x721=? 98x1692=? 16 x 17.20=? 
 
 12 X 836 = ? 98 X 2536 = ? 16 x 21.40 = ? 
 
 12x456=?^ 98x2892= ? 16 x 25.85 = ? 
 
 12 X ? = ? 98 X ? = ? 16 X ? = ? 
 
 Problems such as the above are very helpful. They aiford a variety of 
 work and suggest a simple method by which the student may test the cor- 
 rectness of his results. The instructor should add as many more problems 
 as circumstances require. 
 
 7. A produce dealer bought 2145 bu. of potatoes at 83/ a 
 bushel, and sold them at S1.05 a bushel. What did he gain ? 
 
 8. A drover bought 125 head of cattle at $15.75 per head. 
 He sold 65 head at $23.40, 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 $1.35 per bushel and 
 12 bu. of potatoes at 84/ per bushel. He sold the apples at 40/ 
 a peck and the potatoes at 25/ a peck. What did he gain ? 
 
 10. A bought 1247 bbl. of apples at $3.10 per barrel. After 
 holding them for three months he sold them at $4.80 per barrel. 
 If he paid $74.82 for storage, and his loss by decay was 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 13^ 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 
 18^ per pound. 
 
MULTIPLICATION 41 
 
 SHORT METHODS IK MULTIPLICATION 
 
 53. There are many short methods in multiplication, but of 
 these only a few are practical, either because they apply generally 
 to problems that in themselves are not practical or because they 
 have been supplanted by the elaborate use of tables and mechani- 
 cal devices. A great many practical and helpful tables are in 
 use for figuring pay rolls, interest, discount, and the like. These 
 tables are great time savers. 
 
 54. The machines that are used for adding, subtracting, multi- 
 plying, dividing, and for setting forth results in interest and dis- 
 count are now in such common use that a chapter is devoted to 
 then* consideration in Appendix A at the close of this volume. 
 These machines are found in business offices, especially where 
 extensive operations are to be performed. Both in accuracy and 
 in the saving of time they are most valuable. 
 
 55. The short methods given herewith have a wide applica- 
 tion. They are not dependent upon formal rules, and are sug- 
 gestive of 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 4x59 X 100? 
 
 6. Give a short method for multiplying an integer by any 
 number of lO's, lOO's, or lOOO's. 
 
42 COKCISE BUSINESS ARITHMETIC 
 
 7. Multiply 270 by 300. 
 
 Solution. In the accompanying illustration "70 =27 X 10 
 
 it will be seen that 270 x 300 = 27 x 3 x 1000 300 = 3 X 100 
 
 ^'^ ^^'^^^- 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 $0.70? $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 . 
 
 (5) 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. 
 
 56. In the above exercise it is clear that 
 
 Annexing a cipher to an integer multiplies the integer hy 10; 
 and 
 
 Removing the decimal point one place to the right multiplies 
 the number hy 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 : 
 
 650 yd. silk at $1.20. 
 140 bu. beans at $3.50. 
 500 bu. beans at $2.50. 
 240 gro. jet buttons at $3. 
 500 doz. half hose at $5.50. 
 800 yd. taffeta silk at $1.20. 
 
 a. 
 
 750 lb. coffee at 30)^. 
 
 fl- 
 
 h. 
 
 500 lb. cocoa at 40^. 
 
 h. 
 
 c. 
 
 650 lb. chocolate at 50^. 
 
 i. 
 
 d. 
 
 300 bbl. lump salt at $3. 
 
 J- 
 
 e. 
 
 200 bbl. oatmeal at $4.50. 
 
 k. 
 
 /. 
 
 170 bx. wool soap at $3. 
 
 I 
 
MULTIPLICATION 43 
 
 57. 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. 
 
 58. Examples, l. Multiply 123 by 99. 
 
 Solution. 9D 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 
 by 100 and then by 4 ctnd subtract the results. The product is 580 
 
 13,920. Check by retracing the steps in the process. 13920 
 
 12300 
 
 14500 
 
 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 il.04. 
 
 2994 bu. millet at 97^. 998 bbl. apples at 11.05. 
 
 1112 bu. wheat at 97^. 893 bkt. peaches at 11.05. 
 
 2160 bu. millet at 96^. 993 bu. clover seed at f 3.35. 
 
 Multiplication by 11 and Multiples op 11 
 59. Example. Multiply 237 by 11. 
 
 Solution. To multiply by 11 is to multiply by 10 + 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; 14.95; $9.62; 14.41; $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. 
 
44 CONCISE BUSINESS ARITHMETIC 
 
 60. Examples, i. Multiply 46 by 22. 
 
 Solution. 22 is 11 times 2. Multiply 46 by 11 and by 2, as fol- 
 
 lows : 2x6 = 12; write 2 and carry 1. 4 + 6 = 10 ; 2 x 10 + 1 (car- "*" 
 
 ried) = 21 ; write 1 and carry 2. 2x4 + 2 (carried) = 10 ; write 10. 22 
 
 The result is 1012. 1012 
 
 2. Find the cost of 122 bu. of potatoes at 66 j^ per bu. 
 
 Solution. 6x2 = 12; write 2 and carry 1. 2 + 2 = 4;6x4 -iqq 
 + 1 (carried) = 25 ; write 5 and carry 2. l+2=3;6x3 + 2 
 
 (carried) = 20 ; write Oand carry 2. 0x1+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 lb. coffee at 42^. 115 bu. rye at 99^. 
 
 14 doz. eggs at 21^. 215 bu. peas at 77^. 
 
 64 lb. cheese at 22^. 344 bu. oats at 44^. 
 
 33 bu. carrots at 56^. 300 bu. grain at 85^. 
 
 11 bu. potatoes at 85^. 115 bu. barley at 88^. 
 
 88 bu. wheat at 88/. 400 bbl. apples at {|3.25. 
 
 2. Find the total cost of : 
 
 77 bu. peaches at $1.85. 820 bu. rye at 88^. 
 
 151 bu. corn at 66^, 327 bu. oats at 33^. 
 
 265 bu. onions at 80^. 314 bu. peas at 66^. 
 
 135 bu. apples at 82^. 110 bu. pears at $1.66. 
 
 241 bu. turnips at 44^. 880 bu. barley at $ 1.17. 
 
 112 bu. tomatoes at 55^. 100 bu. quinces at 11.60. 
 
 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 32j^, at once see that the result will be a little more than ^63.00 
 (210 times 30^); this will do away with such absurd results as $6752, 
 $675.20, 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 
 
 Tenns Cash 
 
 45 
 
 
 15 
 25 
 31 
 55 
 212 
 
 cs. Horse-radish 
 lb. Huyler*s Cocoa 
 gal. N. 0. Molasses 
 lb. Japan Tea 
 u Raisins 
 
 $0.66 
 .44 
 .63 
 .48 
 .11 
 
 
 
 
 
 MULTIPLICATIOlSr BY 25, 50, AND 75 
 
 61. Annexing two ciphers to an integer multiplies it by 100. 
 Removing the decimal point two jjlaces to the right multiplies 
 the decimal by 100. 
 
 62. Example. Multiply 76 by 100. 
 
 Solution. 76 x 100 = 7600. (Annexing the two ciphers gives the required 
 result without the necessity for a written solution.) 
 
 63. Example. Multiply 148 by 25. 
 
 Solution. 148 x 100 = 14,800. 14,800 -- 4 = 3700. 
 
 Hence, to multiply an integer by 25, annex two ciphers to the multiplicand 
 and then divide by 4. 
 
 64. Example. Multiply 278 by 50. 
 
 Solution. 278 x 100 = 27,800. 27,800 - 2 = 13,900. 
 
 Hence, to multiply an integer by 50, annex two ciphers to the multiplicand 
 and then divide by 2. 
 
 65. Example. Multiply 48 by 75. 
 
 Solution. 48 x 100 = 4800. 4800 ^ 4 = 1200 ; 3 x 1200 = 3600. 
 Hence, to multiply an integer by 75, annex two ciphers to the multiplicand, 
 divide that product by 4, and then multiply by 3. 
 
46 
 
 CONCISE BUSINESS AEITHMETIC 
 
 
 ORAL EXERCISE 
 
 
 
 State the product of: 
 
 
 
 
 • 
 
 1. 36 X 25. 
 
 8. 
 
 48 X 50. 
 
 15. 
 
 64 X 75. 
 
 2. 27x50. 
 
 9. 
 
 52 X 75. 
 
 16. 
 
 63 X 25. 
 
 3. 28x75. 
 
 10. 
 
 67 X 50. 
 
 17. 
 
 69 X 25. 
 
 4. 97x25. 
 
 11. 
 
 89 X 50. 
 
 18. 
 
 56 X 75. 
 
 5. 248 X 25. 
 
 12. 
 
 186 X 50. 
 
 19. 
 
 240 X 75, 
 
 6. 126x50. 
 
 13. 
 
 146 X 25. 
 
 20. 
 
 184 X 75. 
 
 7. 164x25. 
 
 14. 
 
 204 X 50. 
 
 21. 
 
 144 X 75. 
 
 WRITTEN EXERCISE 
 
 In the following problems make all the extensions mentally, 
 1. Find the total cost of : 
 
 42 lb. cocoa at 40 /. 
 45 lb. cocoa at 50/. 
 50 lb. cofPee at 28/. 
 25 lb. raisins at 15/. 
 23 lb. tea at 40/. 
 
 2. Find the total cost of : 
 36 yd. wash silk at 25/. 
 25 doz. whalebones at 92/. 
 97 yd. cloth at 75/. 
 25 gro. buttons at 35/. 
 29 yd. gunner's duck at 19/. 
 
 27 bx. salt at 50/. 
 23 lb. coffee at 25/. 
 21 lb. candy at 75/. 
 33 lb. chocolate at 50/. 
 85 lb. Oolong tea at 45/. 
 
 87 yd. flannel at 50/. 
 21 yd. cottonade at 18/. 
 25 yd. denim at 19/. 
 17 yd. dress goods at 50/ 
 23 yd. cheviot at 21/. 
 
 Multiplication by an Even Number of Hundreds 
 
 66. Example. Multiply 468 by 300. 
 
 Solution. 468 x 100 = 46,800 ; 46,800 x 3 = 140,400. 
 
 Hence, to multiply an integer by an even number of hundreds, annex two 
 ciphers to the multiplicand and then multiply by the significant figure in the 
 multiplier. 
 
 67. The value of many short methods is that they enable 
 one to write results quickly without performing the mechanical 
 operations. 
 
MULTIPLICATION 47 
 
 68. Many short methods in multiphcation are not practical 
 because they require one to remember so many things, or they 
 apply to so few numbers that it is impossible for an ordinary 
 person to remember them. The short methods given in this 
 text are practical. 
 
 ORAL EXERCISE 
 
 Find the product of: 
 
 1. 234 X 200. 7. 753 x 300. 13. 964 x 200. 
 
 2. 175 X 600. 8. 845 x 400. 14. 554 x 300. 
 
 3. 335 X 800. 9. 453 x 200. 15. 181 x 700. 
 
 4. 216 X 900. 10. 256 x 400. 16. 312 x 800. 
 
 5. 648x100. ^ 11. 145x800. 17. 237x600. 
 
 6. 452 X 500. 12. 333 x 700. 18. 122 x 900. 
 
 Multiplication by Numbers from 101 to 109 Inclusive 
 
 69. Examples, l. Find the cost of 64 bu. of wheat at i 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=f64; 64 bu. at 2^ = 11.28; $64 + $1.28 = $65.28. 
 
 2. Find tlie cost of 251 bu. of barley at $1.04. 
 
 Solution. 4 x 51 = 204 ; write 04 in the product and cany 2. 251 
 
 4x2 + 2 (carried) + 1 (the right-hand figure of the multiplicand) -i qa 
 
 = 11 ; write 1 and carry 1. 1 x 25 + 1 (carried) = 26 ; write 26. 
 The result is $261.04. 
 
 261.04 
 
 70. Similarly multiply by such numbers as 201, 302, and 405. 
 
 71. Example. Find the cost of 124 bu. of beans at I 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 ; 9 O'^ 
 
 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. 
 
48 
 
 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the value of: 
 
 1. 215 T. coal at $6.05. 
 
 2. 224 bu. rye at 11.02. 
 
 3. 215 bu. wheat at $1.02. 
 
 4. 318 bu. barley at f 1.05. 
 
 5. 124 bbl. apples at 12.05. 
 
 6. 116 bbl. onions at 11.08. 
 
 8. 302 bu. peas at 74 ^, 
 
 9. 104 bu. corn at 89 ^. 
 
 10. 103 bu. beets at 85 ^. 
 
 11. 205 bu. turnips at 54 ^. 
 
 12. 215 bu. pears at $1.05. 
 
 13. 411 bu. plums at $1.08. 
 
 7. 232 bbl. potatoes at $2.05. 14. 206 bu. parsnips at 93^. 
 
 Miscellaneous Short Methods 
 
 72. 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. 
 
 73. Example. 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 
 
 147084 147084 
 
 357 
 412 
 1428 
 4284 
 
 74. Example. Multiply 214 by 756. 
 
 Solution. 56 is 8 times 7. 7 x 214 = 1498, which we write as 
 the first partial product. 8 x 1498 = 11,984, which we write as the 
 second partial product. The sum (161,784) of these partial products 
 is the entire product. 
 
 Check as in problem 1. (See also pages 73 and 74.) 
 
 214 
 
 756 
 
 1498 
 
 11984 
 161784 
 
 WRITTEN EXERCISE 
 
 Find the product of: 
 
 1. 319 X 248. 3. 728 x 287. 
 
 2. 927 X 279. 4. 848 x 369. 
 
 The above short methods are practical in a limited num- 
 ber of problems. 
 
MULTIPLICATION 
 
 49 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Use 6 as a multiplier for each column. Check. (See 
 page 39.) 
 
 a. 
 
 h. 
 
 c. 
 
 d. 
 
 e. 
 
 m 
 
 74 
 
 39 
 
 126 
 
 215 
 
 48 
 
 63 
 
 58 
 
 232 
 
 175 
 
 73 
 
 52 
 
 82 
 
 311 
 
 243 
 
 49 
 
 65 
 
 72 
 
 135 
 
 223 
 
 45 
 
 55 
 
 85 
 
 144 
 
 183 
 
 (6^ 
 
 47 
 
 19 
 
 225 
 
 253 
 
 11 
 
 88 
 
 92 
 
 245 
 
 127 
 
 2. Use 8 as a multiplier for each column. Check. 
 
 3. I bought 15 A. of land at $275 per acre and laid it out in 
 100 city lots. After expending S6750 for grading and taxes, 
 $257 for ornamental trees, and $250 for advertising, I sold 
 15 lots at $625 each, 35 lots at $415 each, and exchanged the 
 remainder 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 : 
 
 RocLester, N.Y., July 26, 
 
 Mr. F. C. GORHAM 
 
 120 Spring Street, City 
 
 Bouglit of C. E. Ferguson fe? Son 
 Terms 30 da. 
 
 19 
 
 37 bu. 
 
 Oats 
 
 JO. 40 
 
 50 u 
 
 Corn 
 
 .67 
 
 76 u 
 
 Wheat 
 
 1.02 
 
 75 u 
 
 Rye 
 
 1.04 
 
 95 u 
 
 Beans 
 
 4.00 
 
 16 u 
 
 Clover Seed 
 
 3.50 
 
 26 a 
 
 Millet 
 
 .99 
 
50 
 
 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN REVIEW 
 
 Copy these examples ; add the checks in the Checks in Detail columii 
 and enter the totals in the Total Checks column ; find the new balance, the 
 total old balance, the total checks, the total deposits, and check the work. 
 
 
 
 Checks in 
 
 Total 
 
 
 
 Name 
 
 Balancb 
 
 Detail 
 
 $180.55 
 
 Checks 
 
 Deposits 
 
 Balance 
 
 A 
 
 $313.25 
 
 211.15 
 165.43 
 
 208.19 
 
 ? 
 
 $278.40 
 
 ? 
 
 B 
 
 285.67 
 
 100.55 
 145.97 
 
 ? 
 
 327.44 
 
 ? 
 
 C 
 
 186.53 
 
 200.12 
 
 45.67 
 
 118.95 
 
 ? 
 
 198.45 
 
 ? 
 
 D 
 
 276.65 
 
 205.18 
 
 ? 
 
 210.50 
 
 ? 
 
 E 
 
 
 612 40 
 
 ? 
 
 918.75 
 
 ? 
 
 xu 
 
 
 64.25 
 
 F 
 
 347.85 
 
 103 86 
 
 ? 
 ? 
 
 
 ? 
 
 X; 
 
 6.84 
 ? 
 
 
 
 ? 
 
 ? 
 
 ? 
 
 
 
 2. 
 
 
 
 
 
 
 Checks in 
 
 Total 
 
 
 
 Name 
 
 Balance 
 
 Detail 
 
 Checks 
 
 Deposits 
 
 Balance 
 
 A 
 
 $195.63 
 
 $214.70 
 
 71.20 
 
 8.50 
 
 ? 
 
 $174.25 
 
 ? 
 
 B 
 
 98.40 
 
 102.45 
 
 74.65 
 
 123.52 
 
 ? 
 
 115.68 
 
 ? 
 
 C 
 
 153.30 
 
 10.55 
 75.20 
 55.34 
 
 ? 
 
 89.48 
 
 ? 
 
 D 
 
 386.54 
 
 7.35 
 172.38 
 ? 
 
 ? 
 ? 
 
 275.40 
 
 ? 
 
 
 ? 
 
 ? 
 
 ? 
 
MULTIPLICATION 51 
 
 A WRITTEN REVIEW TEST 
 
 Write the following problems from dictation^ and complete the 
 work. Time, approximately, forty minutes, including the dictation. 
 Mental extensions only, 
 
 1. Write in one column, and find the total value : 
 
 78 yd. at 11/ . 55 yd. at 55/ 
 
 69 yd. at 25/ 91 yd. at 50/ 
 
 60 yd. at 85/ 89 yd. at 99/ 
 
 45 yd. at 98/ 75 yd. at 90/ 
 
 37 yd. at 97/ 76 yd. at 70/ 
 
 112 yd. at 99/ 125 yd. at 98/ 
 
 2. Write in one column, and find the total value : 
 
 76 yd. at Sl.lO 82 yd. at S1.05 
 
 55 yd. at $1.06 ' 65 yd. at S1.20 
 
 108 yd. at Sl.ll 130 yd. at $1.09 
 
 b^ yd. at $1.25 83 yd. at $1.50 
 
 88 yd. at $1.04 97 yd. at $1.03 
 
 67 yd. at $1.02 137 yd. at $1.01 
 
 3. Write in one column ; use 11 as the multiplier, and check 
 the results : 
 
 49, 16, 34, 78, 57, 73, 85, 94, 59, 64, 56, 81. 
 
 4. Write in one column; use 6 as the multiplier, and check 
 the results : 
 
 125, 212, 350, 175, 162, 224, 319, 452, 133, 145, 121, 142. 
 
 5. Write in one column ; use 8 as the multiplier, and check 
 the results : 
 
 45, 75, 62, 29, 76, 61, 19, 34, 85, 92, 27, 77. 
 
 6. Write in one column ; square each number, and total the 
 products : 
 
 25, 55, 15, 45, 75, 35, * 85, 65, 95. 
 
 7. The text, page 49, problem 3, in the Written Review 
 Exercise. 
 
CHAPTER V 
 
 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 $11 
 contained in $187 ? What is Jj of $187 ? 
 
 3. What is the product of 9 times 12 ft.? How many times 
 is 12 ft. contained in 216 ft.? What is J^ of 225 ft.? 
 
 4. When one factor and the product are given, how is the 
 other factor found ? 
 
 75. The process of finding either factor when the product 
 and the other factor are given is called division. 
 
 76. The known product is called the dividend; the known 
 factor, the divisor; the unknown factor, when found, the 
 quotient. 
 
 77. 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. 
 
 78. Since 6 times 7 ft. = 42 ft., 42 ft. -5- 7 ft. = 6, and 
 42 ft. ^ 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 thgit there are two kinds of division: 42 ft. -4- 7 ft. = 
 6 is sometimes called measuring, because 42 ft. is measured by 7 ft. ; 42 ft. -^ 
 6 = 7 ft. is sometimes called partition, because 42 ft. is divided into 6 equal 
 parts. 
 
 62 
 
DIVISIOK 53 
 
 ORAL EXERCISE 
 
 1. Divide by 2 : 18, 32, 78, 450, 642, 964, 893. 
 
 2. Divide by 3 : 27, 67, 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, 96, 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. -^ 8 ft. = ? 
 
 2. $25 -i- 5 = ? 129.75 -- 5 = ? 1129.78 -- 9 = ? 13.40 -- 
 4 = ? 
 
 3. 126 yd. -4- 3 yd. = ? 1125-^25 = ? 16.25 -^ $1.25 = ? 
 
 4. If 9 T. of coal cost $49.50, what is the cost per ton? 
 
 Solution. $49.50 -f- 9 = $5 ; subtracting 9 times |5, the re- $5.50 
 
 suit is $4.50 undivided; $4.50 h- 9 = $0.50. Therefore the a\WJorT7i 
 
 quotient is $5.50. y;*4y.^U 
 
 5. At $ 1. 75 a yard, how many yards can be bought for $ 35 ? 
 
 Solution. The divisor contains cents and it is therefore 20 
 
 better to first change both dividend and divisor to cents. It is 
 
 found that $35 would buy 20 times as many yards as $1.75 , or -^ 
 
 20 yd. 
 
 6. If 5 T. of coal cost $31.25, what is the cost per ton? 
 
 7. At $ 2.50 per yard how many yards can be bought for $ 550 ? 
 
 ORAL EXERCISE 
 
 1. How many weeks in 98 da. ? 
 
 2. What is ^^ of 2250 bbl. of apples? Jg? i? ^\? 
 
 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? 
 
54 CONCISE 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 $21, 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, 7 can be subtracted 
 from that number 7 times. 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 lb. of tea at 70^ per pound? 
 
 18. A clothier pays $96 for a dozen overcoats. At how 
 much apiece must he 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? 
 
DIYISIOK 55 
 
 79. Examples, i. Divide 4285 by 126. 
 
 Complete Operation Required Work 
 
 34^lg Mjl^ 
 
 126)4285 126)4285 
 
 378 =3 times 126 378 
 
 505 undivided 505 
 
 604 =4 times 126 604 
 
 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 f 2 remaining." 
 
 2. A farmer received $283.25 in payment for 275 bu. of wheat. 
 How much was received per bushel for the wheat? 
 
 $1.03 
 
 Solution. $283.75 -- 275 = $1 and §8.25 undivided. 275)$283.25 
 $8.25 -J- 275 = $0.03. $1.03 per bushel was therefore re- eync 
 
 ceived for the wheat. — • 
 
 Check. 275 times $1.03 = §283.25. ° -^^ 
 
 8 25 
 
 80. Work in division may be abridged by omitting the 
 partial products and writing only the partial dividends. 
 
 81. Example. Divide S614.80 by 232. 
 
 Solution. Omit writing the products; subtract mentally and write the 
 remainder only : 2 x 232 = 464 ; 464 subtracted from 614 
 equals 150 ; omit the writing of the 464. Proceed as follows : 
 
 2 times 2 plus = 4; 2 times 3 plus 5 =11. 2 ti mes 2 + 1 = 5, 232) S 614.80 
 
 and 5 plu s 1 = 6. Bring down 8. 6 times 2 p lus 6 = 18 ; 150 8 
 
 6 times 3 plus 1 = 19, and 19 + 1 = 20 ; 6 times 2 plus 2 = 14, 1160 
 
 and 14 plus 1 = 15. Bring down and proceed as before. 00 
 
 WRITTEN EXERCISE ' 
 
 1. Find the cost of 8800 lb. of oats at 45/ per bushel of 32 lb. 
 
 2. How many automobiles, at $650 each, can be purchased 
 for 84,225,000? 
 
 3. By^ what number must 8656 be multiplied to make the 
 product 8,223,200? 
 
 S2.65 
 
56 
 
 CONCISE BUSINESS AEITHMETIC 
 
 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 $3040, 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 lb. 
 at $ 6.50 per ton. He retailed the same at $ 8.25 per short ton of 
 20001b. What was the total gain ? 
 
 11. In a recent year there were produced in the United States 
 730,627,000 bu. of wheat on 45,814,000 A. What was the yield 
 per A. ? What was the total yield worth at 90/ 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 Hecent Year 
 
 State 
 
 Yield in Bushels 
 
 Farm Price 
 PER Bushel 
 
 Farm Valuation 
 
 Illinois 
 
 Iowa 
 
 Nebraska 
 
 Missouri 
 
 Indiana 
 
 Kansas 
 
 426 320 000 
 
 ? 
 
 ? 
 
 ? 
 199 364 000 
 174 225 000 
 
 62^ 
 
 62^ 
 62j? 
 62)? 
 62ji 
 
 264 318 400 
 267 853 020 
 113 221920 
 151 220 480 
 
 ? 
 
 ? 
 
 
 Total 
 
 ? 
 
 m<f' 
 
 p 
 
 
 13-15. Make and solve three self -checking problems in division. 
 
BIYISIOK 57 
 
 SHORT METHODS IN DIVISIOK 
 
 Powers and Multiples of 10 
 
 oral exercise 
 
 1. How many times is 10 contained in 50 ? 100 in 800? 
 1000 in 9000? 
 
 2. Cutting 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 lO's in any number may be found by 
 cutting off the units' figure ; the number of lOO's by cutting 
 
 off the and figures ; the number of by cutting 
 
 off the hundreds' and tens' and units' figures. 
 
 h. In 4561 there are 456 tens and 1 unit, or 456 J^ tens ; 45 
 
 and 61 units, or 45^^^^ hundreds ; and thousands and 
 
 561 units, or 4^^q6_L- thousands. 
 
 6. How many times is $0.10 contained in f 1 ? fO.Ol in 
 fl? $0,001 in $1? 
 
 7. What is Jo of $1? -jloof^l? lAoofll? 
 
 8. Read aloud, supplying the missing words: 10.60 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 -f- 10. e, $271-5-100. ^. 2140 lb. ^ 100. 
 
 h. 1531-^100. / $519.50-10. j. 3145 lb. -^ 100. 
 
 c. 16351 -f- 1000. ^.$84.50-100. A?. 3416 ft. -!- 1000. 
 
 d, 311219-10000. h, $2150-1000. I. 1279 posts -^ 100. 
 
 11. Read aloud, supplying the missing amounts : 
 a. 6400-1600 = ; 640-^10 = . 
 
 h. 27000-5-9000 = ; 2700^900= ; 270-^90 = 
 
 ; 27 --9= . 
 
 18801 -- 90 = --9; 214200 -^ 700 = 2142 
 
58 CONCISE BUSINESS ARITHMETIC 
 
 12. Ho\^ 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 ^il^ 
 
 digits in the right of tlie dividend, thus dividing both dividend 4|00^13I23 
 and divisor by 100. 4 is contained in 13 tliree times witli a ' -j ^ 
 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. Eead aloud, supplying the missing amounts : 1611 -j- 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 -f- 400. h. 63571-^3000. 
 
 h. 9647^40. g. 84199-^700. Z. 16657^4000. 
 
 c, 6551 --50. h. 64137-800. m. 36119-^6000. 
 
 (f. 4273^70. i. 45117-^900. n, 18177-5-9000. 
 
 e. 8197 -f- 90. j, 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 Buffalo? 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 
 
 59 
 
 4. How many miles between Montrose and each station 
 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 2j^ 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. 
 
 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 and 49 and then of 283 and 9, or 292. 
 
 CB 
 
 
 
 
 "zn 
 
 
 NORTH 
 
 Ip 
 
 
 1 
 
 AND 
 WEST BOUND 
 
 1^ 
 
 bCJ5 
 
 s 
 
 
 73 
 
 93 
 
 
 New York 
 
 
 
 
 
 Grand Cent. Sta Lv. 
 
 121110 
 
 6t01 
 
 4 
 
 125th St. Sta " 
 
 12A23 
 
 6,*,13 
 
 5 
 
 138th St. Sta " 
 
 
 6.15 
 
 7 
 
 High Bridge " 
 
 < 
 
 6.21 
 
 8 
 
 Morris Heights " 
 
 6.25 
 
 10 
 
 Kings Bridge " 
 
 
 6.29 
 
 11 
 
 Spuyten Duyvil " 
 
 Jii 
 
 6.33 
 
 1« 
 
 Riverdale " 
 
 « 
 
 
 14 
 
 Mt. St. Vincent " 
 
 r% 
 
 
 15 
 
 Ludlow " 
 
 
 
 16 
 
 Yonkers " 
 
 12 46 
 
 6.43 
 
 18 
 
 Glenwood '• 
 
 
 6.46 
 
 20 
 
 Hastings-on-Hudson " 
 
 
 6.52 
 
 21 
 
 Dobbs' Ferry " 
 
 Ardsley- on -Hudson " 
 
 
 6.59 
 
 22 
 
 
 7.01 
 
 23 
 
 Irvington " 
 
 
 7.05 
 
 26 
 
 Tarrytown " 
 
 1.09 
 
 7.12 
 
 30 
 
 Scarborough " 
 
 
 7.19 
 
 31 
 
 Ossining •' 
 
 1.25 
 
 7.25 
 
 35 
 
 Croton-on-Hudson . " 
 
 
 7.31 
 
 37 
 
 Oscawana " 
 
 
 7..34 
 
 38 
 
 Crugers " 
 
 
 7.37 
 
 ;«) 
 
 Montrose " 
 
 
 7.41 
 
 42 
 
 Peekskill «* 
 
 1.47 
 
 7.49 
 
 47 
 
 Highlands " 
 
 
 7.59 
 
 50 
 
 Garrison " 
 
 % 
 
 8.06 
 
 53 
 
 Cold Spring " 
 
 X 
 
 8.12 
 
 56 
 
 Storm King ♦' 
 
 
 8.16 
 
 58 
 
 Dutchess June " 
 
 
 8.21 
 
 59 
 
 Fishkill Landing " 
 
 2.24 
 
 8.27 
 
 63 
 
 Chelsea " 
 
 2.31 
 
 8.34 
 
 65 
 
 New Hamburg " 
 
 
 8.40 
 
 69 
 
 Camelot " 
 
 
 8,46 
 
 74 
 
 Poughkeepsie Ar. 
 
 2.53 
 
 8A55 
 
 74 
 
 80 
 
 84 
 
 89 
 
 95 
 
 99 
 
 105 
 
 109 
 
 111 
 
 115 
 
 Poughkeepsie Lv. 
 
 Hyde Park " 
 
 Staatsburgh " 
 
 Rhineclitf (Rh'b'k).. " 
 
 Barrytown " 
 
 Tivoli " 
 
 Gerraantown " 
 
 Linlithgo " 
 
 Greendale " 
 
 Hudson " 
 
 3.05 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4.47 
 
 
 119 
 122 
 125 
 
 Stockport " 
 
 Newton Hook " 
 
 Stuyvesant " 
 
 
 
 
 
 
 
 131 
 135 
 142 
 143 
 
 Schodack Landing.. " 
 
 Castleton " 
 
 Rensselaer " 
 
 Albany Ar. 
 
 
 
 
 
 
 
 5.50 
 
 
 149 
 
 Troy.„ " 
 
 6^ 
 
 
 238 
 
 [Jtica Ar. 
 
 8/)40 
 
 
 291 
 
 Syracuse " 
 
 9.55 
 
 
 371 Rochester " 
 
 11.38 
 
 
 440 Buffalo " 
 
 U15 
 
 
 463 Niagara Falls Ar. 
 
 ?r^^ 
 
 
 464 1 Suspension Bridge " 
 
 2520 
 
 
60 CONCISE 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 by 11 each of the following numbers: 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. 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the total cost of the articles in problem 3 of the 
 oral exercise, page 42. Fmd the total of the products in the 
 oral exercise, page 46. 
 
 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 save $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? 
 
 4. 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. 
 
 5. In a recent year there were produced on 37,917,000 A. 
 in the United States 1,418,337,000 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? 
 
DIVISION 
 
 61 
 
 6. Without copying find (a) the total number of railway 
 employees in the United States in 1910 and (h) the total num- 
 ber per one hundred miles of hue in the same year. 
 
 Railway Employees in the United States 
 
 
 1910 
 
 1911 
 
 Class 
 
 Total 
 Number 
 
 Number 
 
 PER 
 
 100 Ml. 
 
 Average 
 Daily 
 Wages 
 
 Total 
 Number 
 
 Number 
 
 PER 
 
 100 Mi. 
 
 Average 
 Daily 
 Wages 
 
 General officers 
 
 5.476 
 
 2 
 
 $13.27 
 
 5,628 
 
 2 
 
 $12.99 
 
 Other officers 
 
 9,392 
 
 4 
 
 6.22 
 
 10,196 
 
 4 
 
 6.27 
 
 General office clerks 
 
 76,329 
 
 32 
 
 2.40 
 
 76,513 
 
 31 
 
 2.49 
 
 Station agents 
 
 37,379 
 
 16 
 
 2.12 
 
 38,277 
 
 16 
 
 2.17 
 
 Other station men 
 
 153,104 
 
 64 
 
 1.84 
 
 153,117 
 
 62 
 
 1.89 
 
 Engineers 
 
 64,691 
 
 27 
 
 4.55 
 
 63,390 
 
 26 
 
 4.79 
 
 Firemen 
 
 68,321 
 
 28 
 
 2.74 
 
 66,376 
 
 27 
 
 2.94 
 
 Conductors 
 
 48,682 
 
 20 
 
 3.91 
 
 48,200 
 
 20 
 
 4.16 
 
 Other trainmen 
 
 136,938 
 
 57 
 
 2.69 
 
 133,221 
 
 64 
 
 2.88 
 
 Machinists 
 
 55,193 
 
 23 
 
 3.08 
 
 55,207 
 
 22 
 
 3.14 
 
 Carpenters 
 
 68,085 
 
 28 
 
 2.51 
 
 65,989 
 
 27 
 
 2.54 
 
 Other shopmen 
 
 225,196 
 
 94 
 
 2.18 
 
 226,785 
 
 92 
 
 2.24 
 
 Section foremen 
 
 44,207 
 
 18 
 
 1.99 
 
 44,466 
 
 18 
 
 2.07 
 
 Other trackmen 
 
 378,955 
 
 157 
 
 1.47 
 
 363,028 
 
 147 
 
 1.50 
 
 All other employees 
 
 229,806 
 
 95 
 
 2.01 
 
 227,779 
 
 93 
 
 2.08 
 
 7. Without copying find (a) the total number of railway 
 employees in the United States in 1911 and (5) the total num- 
 ber per one hundred miles of line in the same year. 
 
 8. Find the total salaries paid to railway employees in 1910 ; 
 in 1911. 
 
 9. Find the average daily wages paid to railway employees 
 in 1910; in 1911. 
 
 10. In a recent year four leading railway systems had out- 
 standing bonds as follows : 
 
 a. 8761,963,000. c. $1,096,773,410. 
 
 b. $576,300,000. d. $428,649,000. 
 Find the average amount of the bonds outstanding. 
 
62 CONCISE BUSINESS AEITHMETIC 
 
 WRITTEN REVIEW 
 
 In these problems divide across, and then add the dividend column 
 and the quotient column. Check : divide the total of the dividend 
 column by the divisor, and this quotient should equal the sum of the 
 
 individual quotients. Time, approximately, fifteen minutes, 
 
 1. 2. 3. 
 
 36-^4 = ? 45-^5 = ? m^Q^'i 
 
 48-f-4 = ? 75-5-5 = ? 72-f-6 = ? 
 
 56-f-4 = ? 95-5-5 = ? 84-^6 = ? 
 
 24-^4 = ? Q^-^b^"^ 78-5-6 = ? 
 
 84-4-4 = ? 35-f-5 = ? 48-f-6 = ? 
 
 44-4-4 = ? 55-4-5 = ? 36-5-6 = ? 
 
 64-4-4 = ? 15-5-5 = ? 54-4-6 = ? 
 
 76^4 = ? ^-^^=^1 1?-^?.=Z 
 
 ? -4-4 = ? ? -4-5 = ? ? -^6 = ? 
 
 4. 5. 6. 
 
 98-5-7 = ? 88-4-2 = ? . 48-4-3 = ? 
 
 84-4-7 = ? 76-^2 = ? 54-5-3 = ? 
 
 63-4-7 = ? 58-5-2 = ? 69-4-3 = ? 
 
 49-5-7 = ? 64-4-2 = ? 72-4-3 = ? 
 
 91-4-7 = ? 82-4-2 = ? 84^3 = ? 
 
 56-5-7 = ? 94-2 = ? 93-4-3 = ? 
 
 77-5-7 = ? 52-^2 = ? 87-4-3 = ? 
 
 42-4-7 = ? Ii-^? = ? ^^5=Z 
 
 ?-5-7 = ? ?-5-2 = ? ?^3 = ? 
 
 7. 8. 9. 
 
 126-5-2 = ? 144-5-4 = ? 129-4-3 = ? 
 
 152^2 = ? 124-4-4 = ? 114-4-3 = ? 
 
 134-4-2 = ? 152-4-4 = ? 108-5-3 = ? 
 
 168-^2 = ? 148-5-4 = ? 147-5-3 = ? 
 
 184^2 = ? 176-5-4 = ? 189-4-3 = ? 
 
 156-4-2 = ? 184-5-4 = ? 165-5-3 = ? 
 
 172^2 = ? 136-5-4 = ? 195-4-3 = ? 
 
 138-4-2 = ? l^-^i = Z 138-5-3 = ? 
 
 ? -4-2 = ? ? -5-4 = ? ? -*-3 = ? 
 
DIVISION. U.S. POSTAL SERVICE 63 
 
 82. 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-, second-, third-, 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; for a postal 
 card, 1 / ; for a reply postal card, 2 /. Written or typewritten 
 matter is of the first class, whether sealed or unsealed. 
 
 Second-class matter mcludes 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. 
 
 Third-class matter mcludes books and catalogues (weighing 
 8 oz. or less), circulars, pamphlets, proof sheets and manuscript 
 copy accompanying tlie same, and engravings. The rate is 1/ 
 for each 2 oz. or fraction thereof. The limit of weight is 4 lb. 
 
 All postal matter of the first, second, or third class may be 
 registered at the rate of 10/ for each package in addition to the 
 regular rates of postage. 
 
 The rates on special delivery letters are 10 / per letter in addition 
 to the regular postage. Any matter on which a special delivery 
 stamp is affixed is entitled to special delivery within certain limits. 
 
 Foreign rates of postage are as follows : letters, 5/ per ounce for 
 the first ounce, and 3 / for each additional ounce. (Double rate 
 is charged at delivery office for any deficiency in prepayment.) 
 Postal cards, 2/ each; newspapers and other printed matter, 
 1/ for 2 oz. 
 
 Some foreign countries, as Germany and Great Britain, come 
 under the letter rate of 2 / per ounce. 
 
 All fourth-class matter is now included in the domestic parcel 
 post, by a law which became effective January 1, 1913. The fol- 
 lowing are some of the principal features of this law : 
 
 The country is divided into zones, the rate of postage being dependent on 
 the zone where the parcel is to be delivered. The zone center is the point 
 of mailing. Regular postage stamps are used on parcel-post packages. 
 
64 
 
 CONCISE BUSIKESS AEITHMETIC 
 
 Parcels weighing 4 oz. or less are mailable at the rate of 1^ for each 
 ounce or fraction of an ounce, regardless of distance. Parcels weighing 
 more than 4 oz. are mailable at the pound rates shown in the table, a 
 fraction of a pound being considered as a full pound. 
 
 Books and catalogues weighing in excess of 8 oz. may be sent by parcel post. 
 
 The weight limit for zones 1 and 2 is 50 lb. ; for all the other zones, 20 lb. 
 
 The local rate applies to parcels to be delivered at the office of mailing, 
 or on a rural route starting from that office. 
 
 A parcel may be insured against loss to the amount of its actual value 
 not exceeding $50. 
 
 A special delivery of a parcel will be made on the payment of an addi- 
 tional 10 f, at the mailing office. 
 
 In the table, the rates are complete up to 11 lb. From this point on only 
 illustrative weights and rates are given ; omissions are indicated by stars. 
 
 The local post office can furnish a parcel-post map of the United States 
 showing the regions included in the different zones. 
 
 
 50 mi. 
 
 50- 
 150 mi. 
 
 150- 
 SOOmi. 
 
 300- 
 600 mi. 
 
 600- 
 lOOOmi. 
 
 1000- 
 1400 mi. 
 
 1400- 
 1800 mi. 
 
 All over 
 1800 mi. 
 
 
 First Zone 
 
 Second 
 Zone 
 Rate 
 
 Third 
 Zone 
 Rate 
 
 Fourth 
 Zone 
 Rate 
 
 Fifth 
 Zone 
 Rate 
 
 Sixth 
 Zone 
 Rate 
 
 Seventh 
 Zone 
 Rate 
 
 Eighth 
 
 Weight 
 
 Local 
 Rate 
 
 Zone 
 Rate 
 
 Zone 
 Rate 
 
 lib. 
 
 $0.05 
 
 $0.05 
 
 $0.05 
 
 $0.06 
 
 $0.07 
 
 $0.08 
 
 $0.09 
 
 $0.11 
 
 $0.12 
 
 21b. 
 
 .06 
 
 .06 
 
 .06 
 
 .08 
 
 .11 
 
 .14 
 
 .17 
 
 .21 
 
 .24 
 
 31b. 
 
 .06 
 
 .07 
 
 .07 
 
 .la 
 
 .15 
 
 .20 
 
 .25 
 
 .31 
 
 .36 
 
 41b. 
 
 .07 
 
 .08 
 
 .08 
 
 .12 
 
 .19 
 
 .26 
 
 .33 
 
 .41 
 
 .48 
 
 51b. 
 
 .07 
 
 .09 
 
 .09 
 
 .14 
 
 .23 
 
 .32 
 
 .41 
 
 .51 
 
 .60 
 
 61b. 
 
 .08 
 
 .10 
 
 .10 
 
 .16 
 
 .27 
 
 .38 
 
 .49 
 
 .61 
 
 .72 
 
 71b. 
 
 .08 
 
 .11 
 
 .11 
 
 .18 
 
 .31 
 
 .44 
 
 .57 
 
 .71 
 
 .84 
 
 81b. 
 
 .09 
 
 .12 
 
 .12 
 
 .20 
 
 .35 
 
 .50 
 
 .65 
 
 .81 
 
 .96 
 
 91b. 
 
 .09 
 
 .13 
 
 .13 
 
 .22 
 
 .39 
 
 .56 
 
 .73 
 
 .91 
 
 1.08 
 
 101b. 
 
 .10 
 
 .14 
 
 .14 
 
 .24 
 
 .43 
 
 .62 
 
 .81 
 
 1.01 
 
 1.20 
 
 111b. 
 
 .10 
 
 .15 
 
 .15 
 
 .26 
 
 .47 
 
 .68 
 
 .89 
 
 1.11 
 
 1.32 
 
 * * * 
 
 * * * 
 
 * * * 
 
 * * * 
 
 * * * 
 
 « « « 
 
 * * * 
 
 * * * 
 
 « « « 
 
 * * * 
 
 151b. 
 
 .12 
 
 .19 
 
 .19 
 
 .34 
 
 .63 
 
 .92 
 
 1.21 
 
 1.51 
 
 1.80 
 
 » * * 
 
 * * * 
 
 * * * 
 
 * * ^ 
 
 « « « 
 
 * * * 
 
 * * * 
 
 * * * 
 
 « « « 
 
 « « « 
 
 201b. 
 
 .15 
 
 .24 
 
 .24 
 
 .44 
 
 .83 
 
 1.22 
 
 1.61 
 
 2.01 
 
 2.40 
 
 « « « 
 
 * * * 
 
 * * * 
 
 * * * 
 
 
 
 
 
 
 
 301b. 
 
 .20 
 
 .34 
 
 .34 
 
 
 
 
 
 
 
 « « « 
 
 « « « 
 
 « « « 
 
 « « « 
 
 
 
 
 
 
 
 401b. 
 
 .25 
 
 .44 
 
 .44 
 
 
 
 
 
 
 
 « « « 
 
 * * * 
 
 * * * 
 
 * * * 
 
 
 
 
 
 
 
 501b. 
 
 .30 
 
 .54 
 
 .54 
 
 
 
 
 
 
 
DIVISION. U. S. POSTAL SERVICE 65 
 
 ORAL EXERCISE 
 
 1. What is the postage on a letter weighing i- oz. ? 4| oz. ? 
 11 oz. ? 3J oz. ? 2^ oz. ? 41 oz. ? 
 
 2. What will be the cost of postage on the following articles at 
 your post office to points within the United States : an ordinary- 
 letter weighing 2| oz. ; a registered letter weighing 1^ oz. ; a 
 bundle of papers weighing 10 oz. ? 
 
 3. Find the total cost of postage on the following to points 
 within the United States: a special delivery letter weighing 1^ oz.; 
 some printers' proofs weighing 18 oz. ; some separate matter for 
 the printer weighing 12 oz. ; a pamphlet weighing 6 oz. 
 
 4. Use a zone map and find the cost of mailing each of the 
 following articles : 
 
 Article Weight Destination 
 
 A pair of opera glasses 2 lb. 8 oz. Kansas City, Mo. 
 
 A pair of ladies' gloves 6 oz. Indianapolis, Ind. 
 
 A copy of Star-Land 1 lb. 8 oz. Macon, Ga. 
 
 A copy of Whittier's Poems 1 lb. 12 oz. Pittsburgh, Pa. 
 
 A copy of Lowell's Poems 1 lb. 10 oz. Denver, Colo. 
 
 A box of merchandise 3 lb. 8 oz. Chicago, 111. 
 A box containing a pair of 
 
 shoes 3 lb. 6 oz. Austin, Tex. 
 
 A piece of hardware 6 lb. 9 oz, Detroit, Mich. 
 
 5. A publisher sends 20,000 copies of his magazine by mail. 
 If each magazine and wrapper weighs 14i oz. and the total 
 number is weighed at the post office in bulk, what will the 
 publisher have to pay for postage ? 
 
 6. A subscriber mailed two copies of the above magazine to a 
 friend. What was the cost for postage ? 
 
 7. 25,000 copies of a monthly magazine weighing 14J oz. were 
 sent by mail. What was the cost to the publisher for postage ? 
 
 8. Find the total cost for mailing the following: printers' 
 proof weighing 18^ oz. ; manuscript and printers' proof in one 
 package, weighing 28 i- oz. ; a special delivery letter, weighing | oz. 
 
66 CONCISE BUSINESS ARITHMETIC 
 
 PKICE LISTS AND INVENTORIES 
 
 Price Lists 
 
 These price lists are to he used in making out the inventories 
 which are found on the four pages following : 
 
 Article 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 Bedsteads 
 
 $6.25 
 
 $8.50 
 
 $11.75 
 
 $5.25 
 
 $14.50 
 
 Bookcases 
 
 42.00 
 
 38.00 
 
 25.00 
 
 35.00 
 
 32.00 
 
 Bureaus 
 
 18.60 
 
 27.25 
 
 22.50 
 
 16.50 
 
 34.20 
 
 Cabinets : 
 
 
 
 
 
 
 China 
 
 22.00 
 
 20.00 
 
 27.50 
 
 32.50 
 
 37.50 
 
 Medicine 
 
 2.25 
 
 1.75 
 
 2.50 
 
 3.25 
 
 2.75 
 
 Music 
 
 10.00 
 
 11.00 
 
 9.00 
 
 8.60 
 
 10.50 
 
 Parlor 
 
 25.50 
 
 21.50 
 
 25.00 
 
 36.50 
 
 38.00 
 
 Chairs: 
 
 
 
 
 
 
 Easy 
 
 12.50 
 
 10.50 
 
 15.00 
 
 22.25 
 
 18.50 
 
 Morris 
 
 10.50 
 
 12.25 
 
 12.00 
 
 9.75 
 
 8.25 
 
 Piano 
 
 5.00 
 
 6.50 
 
 7.25 
 
 9.00 
 
 12.00 
 
 Typewriter 
 
 3.50 
 
 4.50 
 
 4.00 
 
 5.60 
 
 6.00 
 
 Cheval Mirrors 
 
 20.00 
 
 17.25 
 
 18.50 
 
 16.50 
 
 21.25 
 
 Chiffoniers 
 
 24.00 
 
 18.20 
 
 31.75 
 
 27.50 
 
 40.00 
 
 Davenports 
 
 62.50 
 
 50.00 
 
 60.00 
 
 45.50 
 
 37.50 
 
 Desks: 
 
 
 
 
 
 
 Flat-top 
 
 21.20 
 
 17.60 
 
 16.80 
 
 22.30 
 
 18.60 
 
 Roll-top 
 
 23.50 
 
 21.25 
 
 25.50 
 
 27.25 
 
 30.50 
 
 Typewriter 
 
 11.25 
 
 12.25^ 
 
 14.25 
 
 10.25 
 
 13.25 
 
 Dinner Trays 
 
 5.50 
 
 6.25 
 
 7.25 
 
 6.26 
 
 8.25 
 
 Footrests 
 
 1.75 
 
 1.50 
 
 1.60 
 
 2.00 
 
 2.25 
 
 Hall Racks 
 
 14.25 
 
 13.50 
 
 17.25 
 
 18.50 
 
 12.25 
 
 Lounges 
 
 25.00 
 
 17.50 
 
 21.50 
 
 32.00 
 
 23.50 
 
 Mattresses 
 
 11.40 
 
 12.50 
 
 13.25 
 
 17.50 
 
 21.00 
 
 Ottomans 
 
 5.25 
 
 4.50 
 
 4.25 
 
 6.50 
 
 4.75 
 
 Parlor Suites 
 
 63.00 
 
 52.50 
 
 75.00 
 
 67.50 
 
 62.50 
 
 Pillows 
 
 2.50 
 
 3.00 
 
 3.50 
 
 2.00 
 
 3.25 
 
 Sideboards 
 
 60.00 
 
 50.00 
 
 45.00 
 
 37.50 
 
 72.50 
 
 Tables : 
 
 
 
 
 
 
 Dining 
 
 21.50 
 
 17.50 
 
 22.60 
 
 24.50 
 
 25.00 
 
 Dressing 
 
 37.50 
 
 32.25 
 
 21.50 
 
 35.25 
 
 24.75 
 
 Serving 
 
 13.50 
 
 11.00 
 
 14.50 
 
 10.50 
 
 12.25 
 
 Work 
 
 10.00 
 
 9.25 
 
 9.00 
 
 10.25 
 
 11.00 
 
 Wardrobes 
 
 20.50 
 
 25.25 
 
 15.50 
 
 21.76 
 
 25.00 
 
 Washstands 
 
 6.00 
 
 7.50 
 
 5.50 
 
 8.00 
 
 10.50 
 
 Each inventory may be worked out Jive times, using the above price lists. 
 This work may be done by copying the data and making the extensions, or by 
 making the extensions only and then totaling each inventory. 
 
WEITTEN EEVIEW 
 
 67 
 
 7 Bureaus 
 19 Bedsteads 
 
 12 Chiffoniers 
 
 5 Dressing Tables 
 21 Washstands 
 
 8 Mattresses 
 23 Pillows 
 
 6 Bookcases 
 
 3 Davenports 
 
 13 Lounges 
 
 17 Easy Chairs 
 
 7 Morris Chairs 
 5 Parlor Suites 
 
 8 Music Cabinets 
 
 12 Piano Chairs 
 15 Parlor Cabinets 
 
 5 Sideboards 
 
 13 Dining Tables 
 
 8 China Cabinets 
 
 4 Serving Tables 
 
 9 Work Tables 
 12 Dinner Trays 
 
 4 Medicine Cabinets 
 
 8 Wardrobes 
 
 11 Cheval Mirrors 
 15 Ottomans 
 
 12 Footrests 
 
 5 Hall Racks 
 
 6 Roll-top Desks 
 3 Flat-top Desks 
 
 9 Typewriter Desks 
 8 Typewriter Chairs 
 
 IirVENTOKIES 
 
 2. 
 
 8 Bureaus 
 
 17 Bedsteads 
 
 15 Chiffoniers • 
 
 3 Dressing Tables 
 
 18 Washstands 
 
 11 Mattresses 
 21 Pillows 
 
 5 Bookcases 
 
 4 Davenports 
 
 12 Lounges 
 
 20 Easy Chairs 
 
 3 Morris Chairs 
 
 6 Parlor Suites 
 
 10 Music Cabinets 
 
 11 Piano Chairs 
 
 21 Parlor Cabinets 
 2 Sideboards 
 
 16 Dining Tables 
 
 5 China Cabinets 
 
 6 Serving Tables 
 
 7 Work Tables 
 15 Dinner Trays 
 
 8 Medicine Cabinets 
 
 5 Wardrobes 
 
 14 Cheval Mirrors 
 
 12 Ottomans 
 
 17 Footrests 
 
 7 Hall Racks 
 
 4 Roll-top Desks 
 2 Flat-top Desks 
 
 10 Typewriter Desks 
 
 6 Typewriter Chairs 
 
68 
 
 CONCISE BUSINESS ARITHMETIC 
 
 3. 
 
 8 Bureaus 
 
 15 Bedsteads 
 14 Cliiffoniers 
 
 4 Dressing Tables 
 19 Washstands 
 
 12 Mattresses 
 
 18 Pillows 
 
 8 Bookcases 
 
 5 Davenports 
 
 16 Lounges 
 22 Easy Chairs 
 
 6 Morris Chairs 
 
 7 Parlor Suites 
 
 11 Music Cabinets 
 14 Piano Chairs 
 
 12 Parlor Cabinets 
 
 6 Sideboards 
 
 10 Dining Tables 
 
 7 China Cabinets 
 
 6 Serving Tables 
 
 8 Work Tables 
 
 11 Dinner Trays 
 
 7 Medicine Cabinets 
 
 9 Wardrobes 
 
 13 Cheval Mirrors 
 
 19 Ottomans 
 
 12 Footrests 
 
 6 Hall Racks 
 
 8 Roll-top Desks 
 4 Flat-top Desks 
 
 14 Typewriter Desks 
 10 Typewriter Chairs 
 
 4. 
 
 9 Bureaus 
 13 Bedsteads 
 
 11 Chiffoniers 
 
 7 Dressing Tables 
 
 17 Washstands 
 9 Mattresses 
 
 23 Pillows 
 
 6 Bookcases 
 
 . 3 Davenports 
 21 Lounges 
 
 18 Easy Chairs 
 
 9 Morris Chairs 
 4 Parlor Suites 
 9 Music Cabinets 
 
 13 Piano Chairs 
 18 Parlor Cabinets 
 
 4 Sideboards 
 
 12 Dining Tables 
 9 China Cabinets 
 
 5 Serving Tables 
 11 Work Tables 
 
 14 Dinner Trays 
 
 5 Medicine Cabinets 
 
 7 Wardrobes 
 
 17 Cheval Mirrors 
 
 15 Ottomans 
 
 18 Footrests 
 
 3 Hall Racks 
 
 5 Roll-top Desks 
 
 6 Flat-top Desks 
 
 11 Typewriter Desks 
 
 7 Typewriter Chairs 
 
WRITTEN REVIEW 
 
 69 
 
 12 Bureaus 
 23 Bedsteads 
 
 13 Chiffoniers 
 
 8 Dressing Tables 
 
 16 Washstands 
 
 14 Mattresses 
 22 Pillows 
 
 4 Bookcases 
 4 Davenports 
 
 17 Lounges 
 
 14 Easy Chairs 
 12 Morris Chairs 
 
 10 Parlor Suites 
 14 Music Cabinets 
 17 Piano Chairs 
 22 Parlor Cabinets 
 
 7 Sideboards 
 14 Dining Tables 
 
 4 China Cabinets 
 
 11 Serving Tables 
 
 5 Work Tables 
 
 19 Dinner Trays 
 
 6 Medicine Cabinets 
 
 12 Wardrobes 
 
 20 Cheval Mirrors 
 
 11 Ottomans 
 
 21 Footrests 
 
 4 Hall Racks 
 
 12 Roll-top Desks 
 
 5 Flat-top Desks 
 
 13 Typewriter Desks 
 12 Typewriter Chairs 
 
 14 Bureaus 
 21 Bedsteads 
 
 16 Chiffoniers 
 
 11 Dressing Tables 
 
 14 Washstands 
 
 15 Mattresses 
 
 17 Pillows 
 
 7 Bookcases 
 
 7 Davenports 
 19 Lounges 
 
 25 Easy Chairs 
 
 11 Morris Chairs 
 9 Parlor Suites 
 
 12 Music Cabinets 
 21 Piano Chairs 
 
 16 Parlor Cabinets 
 9 Sideboards 
 
 18 Dining Tables 
 
 6 China Cabinets 
 9 Serving Tables 
 
 10 Work Tables 
 
 13 Dinner Trays 
 
 10 Medicine Cabinets 
 
 15 Wardrobes 
 
 16 Cheval Mirrors 
 
 19 Ottomans 
 
 14 Footrests 
 
 8 Hall Racks 
 
 9 Roll-top Desks 
 8 Flat-top Desks 
 
 7 Typewriter Desks 
 
 15 Typewriter Chairs 
 
70 
 
 CONCISE BUSINESS AEITHMETIC 
 
 19 Bureaus 
 
 21 Bedsteads 
 11 Chiffoniers 
 
 9 Dressing Tables 
 
 15 Washstands 
 
 11 Mattresses 
 24 Pillows 
 
 9 Bookcases 
 6 Davenports 
 
 22 Lounges 
 
 12 Easy Chairs 
 
 8 Morris Chairs 
 
 9 Parlor Suites 
 14 Music Cabinets 
 
 9 Piano Chairs 
 17 Parlor Cabinets 
 
 3 Sideboards 
 
 13 Dining Tables 
 
 4 China Cabinets 
 11 Serving Tables 
 13 Work Tables 
 24 Dinner Trays 
 
 6 Medicine Cabinets 
 
 13 Wardrobes 
 
 14 Cheval Mirrors 
 
 6 Ottomans 
 
 8 Footrests 
 11 Hall Racks 
 
 3 Roll-top Desks 
 
 7 Flat-top Desks 
 
 16 Typewriter Desks 
 
 9 Typewriter Chairs 
 
 8. 
 
 17 Bureaus 
 
 20 Bedsteads 
 16 Chiffoniers 
 
 6 Dressing Tables 
 
 21 Washstands 
 
 15 Mattresses 
 25 Pillows 
 10 Bookcases 
 
 2 Davenports 
 
 16 Lounges 
 
 8 Easy Chairs 
 13 Morris Chairs 
 
 3 Parlor Suites 
 10 Music Cabinets 
 
 7 Piano Chairs 
 
 22 Parlor Cabinets 
 5 Sideboards 
 
 9 Dining Tables 
 
 10 China Cabinets 
 7 Serving Tables 
 
 17 Work Tables 
 21 Dinner Trays 
 
 9 Medicine Cabinets 
 
 11 Wardrobes 
 
 18 Cheval Mirrors 
 9 Ottomans 
 
 10 Footrests 
 
 12 Hall Racks 
 
 2 Roll-top Desks 
 9 Flat-top Desks 
 
 10 Typewriter Desks 
 
 11 Typewriter Chairs 
 
CHAPTER yi 
 
 CHECKING RESULTS 
 
 83. 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. 
 
 84. 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 38. 
 
 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 
 
 85. Any number of lO's is equal to the same number of 9's 
 plus the same number of units ; any number of lOO's is equal 
 to the same number of 99's plus the same number of units; 
 any number of lOOO'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. 
 
 86. 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 -1-70 + 6. 
 
 71 
 
72 CONCISE BUSINESS ARITHMETIC 
 
 87. The excess of 9's in any power of 10 or in any multiple 
 of a power of 10 is the saijie as the significant figure (unless that 
 figure is 9, then there is no excess) 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. 
 
 88. 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. 
 
 PKOPERTipS OF 11 
 
 89. Any number of lO's is equal to the same number of ll's 
 minus the same number of units; any number of lOO's is equal 
 to the same number of 99's plus the same number of units ; any 
 number of lOOO's is equal to the same number of lOOl's minus 
 the same number of units ; and so on. 
 
 Thus, 40 = four ll's - 4; 500 = five 99's + 5; 7000 = seven lOOl's - 7. 
 
 90. 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, 102 or 100 = nine ll's + 1 ; 10^ or 1000 = ninety-one ll's - 1 ; 10* 
 or 10,000 = nine hundred nine ll's+ 1. 
 
 91. 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^^ + r=^) ; the excess of ll's in 2473 is 9 (3 + 4 + 11 - 7T2 = 9) j 
 the excess of Xl's in 14,206 is 5. 
 
CHECKING RESULTS 73 
 
 Checking Addition and Subtraction 
 
 92. Examples, i. By casting out the 9's, show that the 
 sum of 935, 651, 782, and 465 is 2833. 
 
 Solution. The sum of the digits in 935 is 17 ; but since 17 935 = 8 
 contains 9, find the sum of the digits in 17 and the result, 8, is the (?ci _ o 
 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. 
 
 Sol ution. 8-4 + 6-0 = 10, the excess of ll's in 648. 648=10 
 
 7-1 +2 -0=8, the excess of ll's in 217. 12 (11+1) -5+ 917= 8 
 
 4 — = 11; but 11 contains 11, hence, the excess of ll's in 451 
 
 is 0. 8 - 8 + 6 - = 6, the excess of ll's in 688. Since 648 is 451= 
 
 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. 
 
 93. 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 12, and subtraction as 
 explained on page 24. 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 
 
 94. Examples, i. 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 qc _ c 
 
 is a multiple of 9 + 5 and 64 a multiple of 9 + 1, the product of /> < ~~ i 
 
 64 X 95 should be a multiple of 9 plus (1x6). 1 x 5 or 5 equals ^^ ~ i 
 
 the excess of 9's in 6080 ; hence, the work is probably correct. 6080 = 6 
 
74 CONCISE BUSINESS ARITHMETIC 
 
 2. By casting out the ll's show that the product of 46 x 95 
 is 4370. 
 
 SomxioN. The excess of ll's in 95 is 7, and in 46, 2. Since 95 — 7 
 
 95 is a multiple of 11 + 7 and 46 a multiple of 11 + 2, the prod- 4fi — 9 
 
 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 4370 = 3 
 11 + 3, the work is probably correct. 
 
 95. 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-- 521. 
 
 2. X)etermine 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 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 VII 
 
 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; 3.5 ft.; 27.5 1b.; .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 ? 
 
 5. In the accompanying S) 
 diagram what part of J. is ^ ? 
 What part of jB is (7? What 
 part of G is D? 
 
 6. What part of A is (7? 
 What part of ^ is D? b a 
 
 7. If ^ is a cubic inch, what is ^? (7? 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 y^^? one hun- 
 dredth besides -^-^ ? one thousandth besides y^^'^ ^ 
 
 96. Units expressed by figures at the right of the decimal 
 point are called decimal units. 
 
 97. A number containing one or more decimal units is 
 called a decimal fraction or a decimal. 
 
 CB 
 
 76 
 
76 COKCISE BUSIKESS 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 hundredths? 
 
 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 ? 
 
 98. 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 sia: hundred Jive thousandths; in reading 
 600.005 say six hundred and Jive thousandths. 
 
 99. '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 
 
 
 
 "• 
 
 f 
 
 
 ' 
 
 
 
 " "* 
 
 
 
 ^ 
 
 ' 
 
 OQ 
 
 
 
 
 CO 
 
 
 
 
 
 
 
 
 
 
 tS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Ti 
 
 80 
 
 Orders : ^ 
 
 i 
 
 05 
 
 1 
 
 1 
 
 1 
 
 a 
 
 09 
 
 -a 
 
 
 « 
 
 i 
 
 s 1 
 
 1 
 
 73 
 
 CO 
 
 
 
 1 
 
 1 
 
 if 
 
 W 
 
 1 
 
 >? 
 
 a 
 
 
 1 
 
 1 
 
 
 g 
 
 ii 
 
 
 e 
 
 1 
 
 11 
 
 9 
 
 8 
 
 7, 
 
 6 
 
 5 
 
 4, 
 
 3 
 
 2 
 
 1 
 
 . 2 
 
 3 
 
 4 
 
 5 
 
 6 7 
 
 100. Hundredths are frequently referred to as per cent, a 
 phrase originally meaning hy the hundred, 
 
 101. The symbol % stands for hundredths and is read j^^r cent. 
 Thus 45% = .45 ; 48% of a number = .48 of it. 
 
DECIMAL FRACTIONS 77 
 
 ORAL EXERCISE 
 
 Read : 
 
 1. 0.073. 5. 532.002. 9. 31.08%. 
 
 2. 0.00073. 6. 60.0625. lo. 126.75%. 
 
 3. 3004.025. 7. 63.3125. li. 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. 
 
 h. 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 lb. 
 
 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. 
 
78 CONCISE BUSINESS ARITHMETIC 
 
 5. Four million ten thousand ninety-seven ten-millionths ; 
 four million ten thousand and ninety-seven ten-millionths; 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. 
 
 102. 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 he annexed to or omitted from the right 
 of any number without changing its value, 
 
 ORAL EXERCISE 
 
 Read the following (a) as printed and (5) 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. 
 
 103. 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, 256 12 
 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 79 
 
 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 8436.14 .92 9270.54 ? 
 
 .72 8435.96 9.26 75.86 ? 
 
 14178.21 7926.11 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 I 
 
 ? ? ? ? ? 
 
 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. 
 
80 CONCISE 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 hundredths 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 ? 
 
 104. 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 ^ 1 9Q 
 
 as the subtrahend ; hence suppose decimal orders to be annexed ' 
 
 until the right-hand figure is of the same order, then subtract as o.L^i 
 
 in integers and place the decimal point in the remainder directly under the 
 decimal points in the numbers subtracted. 
 
 WRITTEN EXERCISE 
 
 Find the difference between^ 
 
 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 81 
 
 12. From the sum of two hundred fifty-seven thousandths 
 and eight and one hundred twenty -six millionths take the sum 
 of live 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 §5265.90 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. 
 
82 CONCISE 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 89.375 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 167.50 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. 
 
 h. 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 2400x80.06 with 100x24x80.06 or with 
 24 X ^Q. 
 
 21. Compare 3000 x 612.251 with 1000 x 3 x 612.251, or with 
 3 X 612251. 
 
DECIMAL FRACTIONS 83 
 
 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. oj. 24 
 
 The result is 2125. 24 times 2125 equals 51,000, the ■ -^^ TKFTT 
 
 required product. ^^^^ ^250 
 
 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 multiplyiug a decimal by any 
 number of lO's, lOO's, lOOO's, etc. 
 
 24. Find the cost of : 
 
 a, 500 lb. at 18^. d, 600 lb. at 29)^. g, 900 lb. at 34^. 
 h, 150 lb. at 14^. e, 300 lb. at 41^. h, 700 lb. at 51^. 
 c. 200 lb. at 26/^. /. 400 lb. at 121^. i. 1400 lb. at 5^. 
 
 105. Examples, l. Multiply 41.127 by 4. 
 
 Solution. 41.127 is equal to 41,127 thousandths. 41,127 thou- 41.127 
 sandths multiplied by 4 equals 164,508 thousandths, or 164.508. That 4 
 
 is, thousandths multiplied by a whole number must equal thousandths. 164.508 
 
 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 i nA g rtQ 
 
 point in the product two places to the left, the result is 1.64508. -L.O^OUo 
 
 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 hundredths 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 ? 
 
84 
 
 CONCISE BUSINESS ARITHMETIC 
 
 3. What are 400 bbl. of apples worth at $2.12 per barrel? 
 at il.27l per barrel? 
 
 4. I bought 60 lb. of sugar at $0,041 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 ? 
 
 WRITTEN EXERCISES 
 
 Find the product of : 
 
 1. 3.121 X 152. 4. 12.14 X 265. 7. 2.531 x 31000. 
 
 2. 3121 X .152. 5. 9.004 x .021. 8. .1724 x 18000. 
 
 3. 31.21 X 15.2. 6. .3121 X .0152. 9. .15539 x 2002. 
 
 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 Price 
 PER Bushel 
 
 Farm Valuation 
 
 North Dakota 
 Kansas 
 Minnesota 
 South Dakota 
 
 143,820,000 
 92,290,000 
 67,038,000 
 52,185,000 
 
 92.4^ 
 
 92 A f 
 92 A f 
 92 A ^ 
 
 ? 
 ? 
 ? 
 ? 
 
 Total 
 
 ? 
 
 ? 
 
 ? 
 
 13-15. Make and solve three self-checking problems in multi- 
 plication of decimals. 
 
DECIMAL FRACTIONS 85 
 
 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, $6.40, 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^ 
 
 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 correct 
 
 106. 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. 
 
 107. It has been seen that multiplying both dividend and 
 divisor by the same number does not change the quotient. 
 
 108. Therefore, to divide decimals when the divisor is not an 
 
 integer : 
 
 Multiply both dividend and divisor by the power of 10 that 
 will make the divisor an integer^ and divide a% in United States 
 money. 
 
86 
 
 CONCISE BUSINESS ARITHMETIC 
 
 109. Divide 0.3375 by 0.45. 
 .3375 ^ .45 = 33.75 -- 45. 33.75 -^ 45 = .7, with a remainder of 
 2.25. 2.25 -J- 45 = .05. The quotient is therefore .75. 45TsTT^ 
 
 Observe that the divisor may always be made an integer if the ^1 \ 
 
 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 
 
 75 
 
 2 25 
 
 2 25 
 
 places in the dividend, annex decimal ciphers and continue the division 
 as far as is desired. 
 
 ORAL EXERCISE 
 
 
 Divide : 
 
 
 
 
 1. Ibyl. 
 
 19. 
 
 33 by .11. 
 
 
 2. Iby.l. 
 
 20. 
 
 33 by 110. 
 
 
 3. IbylO. 
 
 21. 
 
 .33 by .11. 
 
 
 4. .Iby.l. 
 
 22. 
 
 3.3 by 1.1. 
 
 
 5. 1 by .01. 
 
 23. 
 
 .0001 by 1. 
 
 
 6. 1 by 100. 
 
 24. 
 
 33 by .011. 
 
 
 7. 1 by .001. 
 
 25. 
 
 33 by 1100. 
 
 
 8. .10 by .10. 
 
 26. 
 
 .0001 by .1. 
 
 
 9. .01 by .01. 
 
 27. 
 
 3300 by .11. 
 
 
 10. 1 by 1000. 
 
 28. 
 
 330 by .011. 
 
 
 11. 1 by .0001. 
 
 29. 
 
 33 by .0011. 
 
 
 12. 1 by 10,000. 
 
 30. 
 
 33 by 11000. 
 
 
 13. 1 by .00001. 
 
 31. 
 
 .0001 by .01. 
 
 
 14. .001 by .001. 
 
 32. 
 
 .033 by .011. 
 
 
 15. 1 by 100,000. 
 
 33. 
 
 .0001 by .001. 
 
 
 16. 1 by .000001. 
 
 34. 
 
 .0033 by .0011. 
 
 
 17. .0001 by .0001. 
 
 35. 
 
 .0001 by .0001. 
 
 
 18. .00001 by .00001. 
 
 36. 
 
 .0001 by .00001. 
 
 
 WRITTEN EXERCISE 
 
 
 
 Divide : 
 
 
 
 1. 
 
 5842 by .046. 6. 2200 by .44. 
 
 
 11. 16 by .0064. 
 
 2. 
 
 2.592 by .108. 7. 231.6 by 579. 
 
 
 12. 1.86 by 31,000. 
 
 3. 
 
 1.750 by 8750. 8. 950 by 19,000. 
 
 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. 
 
L>EC1MAL FKACTIONS 
 
 87 
 
 Find the sum 
 
 of the quotients : 
 
 
 16. 
 
 17. 
 
 18. 
 
 8.1-^.9. 
 
 72-^8. 
 
 125^250. 
 
 81-f-.09. 
 
 72 -.8. 
 
 12.5-2.5. 
 
 8.1 -.09. 
 
 7.2 -.8. 
 
 1.25^2.5. 
 
 .81 -V- 900. 
 
 72 -.08. 
 
 12.5^250. 
 
 .0081-9. 
 
 .72 -.08. 
 
 125 ^ 2500. 
 
 8.1^900. 
 
 72 --.008. 
 
 .125^.025. 
 
 810 -.009. 
 
 72-8000. 
 
 12500 -.25. 
 
 .0081^9000. 
 
 72-^.0008. 
 
 125-^25000. 
 
 81000 -.009. 
 
 .072 -f- .008. 
 
 12500 -.025. 
 
 81-^.000009. 
 
 72 -J-. 00008. 
 
 125 ^ 250000. 
 
 8100 - 90000. 
 
 .0072-^.0008. 
 
 .125 -f-. 00025. 
 
 .00081-5-90000. 
 
 .00072 -f- .00008. 
 
 12500 ^ .0025. 
 
 19. 
 
 20. 
 
 21. 
 
 8.8-4-2.2. 
 
 17^68. 
 
 36^.072. 
 
 .88 -5- .22. 
 
 1.7 -f- 6.8. 
 
 3.6^.072. 
 
 88 -f-. 0022. 
 
 .17-^.68. 
 
 .36^.072. 
 
 8.8 -i- 2200. 
 
 1.7-^680. 
 
 360^.072. 
 
 880-^2200. 
 
 170^680. 
 
 .036 H- .072. 
 
 8.8-^2.200. 
 
 .017^.068. 
 
 ' 3.6^72000. 
 
 880^.2200. 
 
 1.7-^68000. 
 
 36 ^ 720000. 
 
 8800 -f- 2200. 
 
 1700 -- 6800. 
 
 360 -.00072. 
 
 880-^22000., 
 
 1700 - 68000. 
 
 3600 --.0072. 
 
 880-^.0002^ 
 
 .0017^.0068. 
 
 .0036^.0072. 
 
 88000-^.0022. 
 
 .00017^.00068. 
 
 3.6^.000072. 
 
 88000 -J-. 00022. 
 
 .000017^.000068. 
 
 .00036^.00072. 
 
 22. The proc 
 
 luct 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? 
 
88 
 
 CONCISE 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 Price 
 PER Bushel 
 
 Farm Valuation 
 
 Illinois 
 Iowa 
 
 Wisconsin 
 Minnesota 
 
 ? 
 ? 
 ? 
 ? 
 
 31^ 
 31^ 
 31^ 
 31^ 
 
 54,818,000 
 58,811,000 
 27,119,000 
 31,926,000 
 
 
 Total 
 
 ? 
 
 31^ 
 
 ? 
 
 
 26-28. Make and solve three self -checking problems in 
 division of decimals. 
 
 DIVIDING BY POWERS AND MULTIPLES OE 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 
 withl; .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 -j- .7 with the quotient of 
 
 .7 with the quotient of 
 
 28 X 10 -f- .7 X 10 ; the quotient of 28 
 280 -^ 7. 
 
 6. Compare the quotient of 16.4-5-40 with the quotient of 
 16.4 -5- 10 -7-40-^10; the quotient of 16.4 ^ 40 with the quotient 
 of 1.64 -f- 4. What is the quotient of 56.77 divided by 7000? 
 
 .00811 
 
 Solution. Eemoving the decimal point three places to the 
 
 left and dropping the ciphers of the divisor is equivalent to dividing 
 
 both dividend and divisor by 1000 and does not change the value 7^.05677 
 of the quotient. 
 
DECIMAL FEACTIONS 89 
 
 Buying and Selling by the Hundred 
 oral exercise 
 
 1. Compare 460 ^ 100 x $2 with 4.60 x f 2. 
 
 2. Find the cost of 450 lb. of guano at $4 per cwt. 
 
 3. Find the cost of 600 lb. of wire nails at 34^ per cwt. 
 
 4. Find the cost of 4950 paving stones at 18 per C. 
 
 Solution. C stands for 100. 4950 paving stones are 49.5 times 4y.O 
 
 100 paving stones. Since 1 hundred paving stones cost $8, 49.5 8 
 
 hundred paving stones will cost 49.5 times ^8, or $396. 396^ 
 
 WRITTEN EXERCISE 
 
 Find the cost : 
 
 
 
 
 
 Quantity 
 
 Price per 
 Hundredweight 
 
 
 Quantity 
 
 Price per 
 Hundredweight 
 
 1. 450 1b. 
 
 55^ 
 
 5. 
 
 1600 lb. 
 
 71^ 
 
 2. 510 1b. 
 
 77^ 
 
 6. 
 
 2600 lb. 
 
 15>> 
 
 3. 640 1b. 
 
 60^ 
 
 7. 
 
 4900 lb. 
 
 "JOp 
 
 4. 330 1b. 
 
 5Q^ 
 
 8. 
 
 3100 lb. 
 
 88j* 
 
 Buying and Selling by the Thousand 
 
 ORAL exercise 
 
 1. Compare 3500 -v- 1000 x 19 with 3.500 x $9. 
 
 2. Compare 12200 -- 1000 x $5 with 12.2 x 15. 
 
 3. Find the cost of 7150 feet of lumber at $11 per M. 
 
 Solution. M stands for thousand. 7150 feet are 7.15 times 7.15 
 
 1000 feet. Since 1 thousand feet of lumber cost $11, 7.15 thousand 11 
 
 feet will cost 7.15 times $11, or $78.65. 78^65 
 
 Mnd the cost of: 
 
 4. 8500 tiles at $8 per M ; at 8 9 per M. 
 
 5. 4500 bricks at $6 per M ; at 17 per M, 
 
 6. 7500 shingles at 812 per M ; at 814 per M. 
 
 7. 3200 ft. lumber at 814 per M ; at 812 per M. 
 
 8. 15,000 ft. lumber at 811 per M ; at 812 per M. 
 
 9. 12,000 ft. lumber at 816 per M ; at 815 per M. 
 
90 CONCISE BUSINESS ARITHMETIC 
 
 Buying and Selling by the Ton of 2000 Pounds 
 oral exercise 
 
 1. Compare 8000 -f- 2000 x 8 with 8000^1000 x 4. 
 
 2. Compare 7000 -v- 2000 x 18 with 7x9. 
 
 3. Find the cost of 4250 lb. coal at S8 per ton. 
 
 Solution. 4250 lb. is 4.25 times 1000 lb. If the cost of 2 thou- 4.25 
 sand pounds is |8, the cost of 1 thousand pounds is $4. Since A 
 
 17.00 
 
 1 thousand pounds of coal cost $4, 4.25 thousand pounds will cost 
 4.25 times |4, or $17. 
 
 WRITTEN EXERCISE 
 
 1. At S9 per ton, find the cost of the hay in the following 
 weigh ticket. Also find the cost at S8.75 per ton. 
 
 SCALES OF E. H. ROBINSON & CO. 
 
 ^ y/OO ^°^^ of x yr^^ y r>. 
 
 From ^,,C^A/^^i^^/^^ To ^/jJ. .TJtT^^ ST^^ 
 
 Gross weight ^^//^ lb. 
 Tare / <r ^ ^ Ih. 
 
 Net weight Z-f^jTO^ lb. . . ^^ 
 
 Weigher 
 
 2. At S 7.50 per ton find the cost of the coal in the following 
 weigh ticket. Also find the cost at S6.95 per ton. 
 
 WELLINGTON -WILD COAL CO, 
 
 126 Main Street. Rochester, N. Y. 
 
 3^ ^ //^^r^-y;^..i^-^ t^yf^A-iT^.^ ^~Y?^^y 
 Teamster y/7.^^r7,y?^.^7^^, Receioed by C.lYl.. \\.yCn H /r\. h< m ^ 
 
DECIMAL FRACTIONS 91 
 
 3. What will 8650 lb. of hay cost at $12 per ton? 
 
 4. Find the cost of 2150 lb. of coal at $6 per ton. 
 
 5. At 132 per ton, what is the cost of 26,480 lb. of 
 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 lb. 
 net, at $5.20 per ton. 
 
 8. Find the total cost of : 5265 lb. hard coal at $8.40 per ton ; 
 12,200 lb. soft coal at $3 per ton; 8275 lb. cannel coal at $11.75 
 per ton; 34,160 lb. egg coal at $6.20 per ton; 12,275 lb. nut 
 coal at $5.75 per ton; 8753 lb. grate coal at $5.80 per ton; 
 24,160 lb. 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, 6160, 6410, 6370, 
 6410, 6570, .6480, 6240, 6370, 6430, 6480, 6300, 7400, 7580, 
 7620, 7240, 7110, 7220, 7420, 7480, 6390, 6100, 6250, 6250, 
 6900, 6270, 6280, 6290, 6270, 6390, 6420, 6120, 6120, 6200, 
 6300, 6120, 6430, 6430, 8100, 6100, 6200, 6310, 6204, 6160, 
 6170, 6240, 6390, 6140, 6240, 7190, 7240, 7140, 7200, 6340, 
 8420, 6310, 7420, 6120 lb. net. Find the cost at $5.87J 
 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 ? 
 
 CB 
 
92 CONCISE BUSINESS ARITHMETIC 
 
 5. What number is that which is 165 times as great as 
 82.5? 
 
 6. If 450 bbl. of beef sold for $5872.50, what was the 
 selHng 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. An article was sold for $22.50 ; if i of the cost was lost, 
 what was the loss ? 
 
 9. Wood costing $3.50 per cord is sold for $4.10 per cord. 
 How many cords must be handled to gain $240 ? 
 
 10. Fmd the cost of 8 bbl. of pork weighing 280, 281, 286, 
 290, 285, 277, 285, and 290 lb. net, at $8.50 per hundred 
 pounds. 
 
 11. A flock of 200 sheep was bought for $700. Ten of the 
 sheep died, and the remainder of the flock was sold at $3.95 per 
 head. What was the gain or loss ? 
 
 12. If the actual cost of the necessities of life for one person, 
 in a given year, amounted to $81.45, and 10 yr. later, owing to 
 the advance in prices, the same necessities cost $108.60, what 
 was the fractional increase in the cost of living ? 
 
 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. The following were the transactions of a merchant for 
 1 mo.: merchandise on hand July 1, $3378.50, sold for cash, 
 $2374.20; bought for cash, $1945. 35; sold on account, $2276.30; 
 bought on account, $876.40 ; on hand July 31, $2056.35. Ex- 
 penses for the month, $284.25. What was the net gain for 
 the month? 
 
 15. The following were the transactions of a merchant for 
 1 mo.: merchandise on hand January 1, $8120.90; bought for 
 cash, $3265.90; bought on account, $2845.10; sold for cash, 
 $5157.65; sold on account, $4218.25; on hand January 31, 
 $7253.25. The sale to Jas. S. Greet, on account, cannot be 
 collected, $51.20. What was the net gain for the month? 
 
DECIMAL FRACTIONS 93 
 
 16. What is the total freight on 12,250 lb. of hardware at 
 $.65 per hundredweight and 15,670 lb. of hardware at 1.60 
 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 f 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 lb. net, at 5|^ 
 per pound ? 
 
 19. A received 11088 from the sale of his barley crop. If he 
 received 10.85 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 manufacturing pay roll shows that 40 hands are em- 
 ployed at S1.45 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 134,350.65. 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 (6) 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 
 
 165.42 
 
 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 
 
 18.641 
 
94 
 
 CONCISE BUSINESS ARITHMETIC 
 
 A REVIEW TEST 
 
 Without copying, find the quotients and the sum of the quotients, 
 in each problem. Time, approximately, forty minutes. 
 
 In these problems the quotient in each division is apparent at a glance, 
 hence the attention is fixed on placing the decimal point. 
 
 1. 
 
 
 2. 
 
 3. 
 
 12.5^5 
 
 96 -f- .4 
 
 3.9 -5- .3 
 
 1.25 -^ .5 
 
 .96- 
 
 -.004 
 
 39-f-.03 
 
 .125-^.5 
 
 9.6- 
 
 -4 
 
 3.9 -4- .003 
 
 .125-^.05 
 
 .96- 
 
 -.04 
 
 .0039-^.003 
 
 .0125-^5 
 
 9.6- 
 
 -.04 
 
 .039 -4- .0003 
 
 125 -f- .5 
 
 960 -5- .4 
 
 390^.3 
 
 12.5-^.05 
 
 .096 ^ .04 
 
 3.9-4-3 
 
 .0125-^.005 
 
 960 -^ .004 
 
 390 -i- .03 
 
 12.5-^.005 
 
 9.6 -5- .04 
 
 39 -5- .003 
 
 4. 
 
 5. 
 
 6. 
 
 .0065-^1.3 
 
 .69 H- 23 
 
 .085-5- .17 
 
 6.5 -^ 1.3 
 
 690 -^ 2.3 
 
 .85 -5- .017 
 
 .65-^.13 
 
 6.9 -i- 23 
 
 8.5 -4- .017 
 
 65 H- .013 
 
 6.9 -^ 2.3 
 
 .85-^.0017 
 
 6.5-^130 
 
 .69 -H 230 
 
 85^.17 
 
 65-1-130 
 
 .0069 -^ .23 
 
 .085-1- .0017 
 
 6.5-^1300 
 
 6.9 -f- 230 
 
 8.5^1.7 
 
 .65-5-13 
 
 .069-^.0023 
 
 85-5-1700 
 
 6500^130 
 
 690-5-2300 
 
 8.5-5-170 
 
 7. 
 
 8. 
 
 9. 
 
 5.7 -f- .19 
 
 75-^.25 
 
 55 -f. 1.1 
 
 57^.019 
 
 75 -f- 2.5 
 
 550-5-1.1 
 
 570-^1.9 
 
 .75-^2.5 
 
 .055-5-110 
 
 57^190 
 
 7.5-4-250 
 
 5.5 -f- 110 
 
 .0057-1-1.9 
 
 .75 -5- .25 
 
 55^110 
 
 5.7-^190 
 
 75^.025 
 
 .055^.011 
 
 57^.19 
 
 .75 ^ 250 
 
 550 -5- .11 
 
 .57 -f- 190 
 
 7.5 -4- .025 
 
 550 -5- 1100 
 
CHAPTER VIII 
 
 FACTORS, DIVISORS, AND MULTIPLES 
 
 FACTOES 
 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. 
 
 110. 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 ? 
 
 96 
 
96 COKCISE BUSIKESS ARITHMETIC 
 
 Tests of Divisibility of Numbers 
 
 111. A number is divisible by: 
 
 1. Two, when it is even, that is, 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. Fioe, 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: 
 
 1. 184. 5. 6984. 9. 51625. 13. 14128. 
 
 2. 2781. 6. 2750. 10. 83870. 14. 66438. 
 
 3. 1449. 7. 8975. ii. 13599. 15. 31284. 
 
 4. 638172. 8. 71168. 12. 123125. 16. 17375. 
 
 Factoring 
 
 112. Factoring is the process of separating a number into its 
 factors. 
 
 113. Example. Find the prime factors of 780. 
 
 Solution. Since the number ends in a cipher, divide it by the prime 
 
 factor 6 ; 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. 
 
 .lo 
 
 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. 
 
 5 
 
 2 
 2 
 3 
 
 780 
 
 156 
 
 78 
 
 39 
 
FACTORS, DIVISORS, AND MULTIPLES 97 
 
 Cancellation 
 oral exercise 
 1. (4xl5)-f-(4x3) = 15-f-3. Why? 
 
 2. Divide 2x5x7 by 5x2; 8x7x5 by 5x2x7. 
 3 3x7x8 ^ ^ 5x2x8x3 ^ ^ 2x9x7x5 ^.> 
 7x3 ' 2x8x3 ' 5x7x2x3' 
 
 4. What effect on the quotient has rejecting equal factors 
 in both dividend and divisor ? 
 
 114. Cancellation is the process of shortening computations 
 by rejecting or canceling equal factors from both dividend and 
 divisor. 
 
 115. Example. Divide the product of 6, 8, 12, 32, and 84 by 
 the product of 3, 4, 6, and 24. 
 
 2 2 2 4 28 
 
 6xgx;2x32x?4 
 
 ^^^^^^^ = 2x2x2x4x28=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 
 
 1. 14x21x48^7x21x6 = ? 
 
 2. 128 X 48 X 88 -V- 64 X 24 X 4 = ? 
 
 3. Divide 128 x 18 x 36 by 64 x 18 x 12. 
 ^ 12 X 16x24 X 8x92x28 ^ y 
 
 6 X 8 X 23 X 7 
 
98 CONCISE 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 $2.75 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 bushels 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 lb. of evaporated apricots is $1.47. 
 At that rate how much freight should be paid on 7350 lb. 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. 
 
 116. 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. 
 
 117. 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 (j*) 
 twice in all the numbers and the factor 3 once 24= 2x2x2x3 
 in all the numbers. None of the other factors 84 =2x^x3x7 
 occur in all the numbers; hence, 2 x 2 x 3, or ^_^ __ ^ ^ „ ^ „ 
 12, is the greatest common divisor of 24, 84, ^"^^ = lX^Xoy.6X i 
 and 252, 
 
FACTORS, DIVISORS, AND MULTIPLES 99 
 
 (b) The common prime factors of two or more given ('5\ 
 
 numbers may be found by dividing the numbers by their 9^24 — 84—2^2 
 
 prime factors successively until the quotients contain no ^rr^^ ~r: 
 
 common factor, as shown in the margin. Z ^IZ — 41 — Izb 
 
 Ever since decimal fractions came into quite gen- -^ — 
 
 eral use the subject of greatest common divisor has "^ * •^-*- 
 
 been stripped of most of its practical value. When fractions like i||^ 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 -ff^ to its 
 lowest terms? iff? ^%\? ^\%? ^^V? 2%? 
 
 WRITTEN EXERCISE 
 
 Find the greatest common divisor of: 
 
 1. 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? 
 
5)14 
 
 21 
 
 42 
 
 3)7 
 
 21 
 
 21 
 
 7)7 
 
 7 
 
 7 
 
 100 CONCISE BUSINESS ARITHMETIC 
 
 118, 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 each of the given numbers. 
 
 119. Example. Find the 1. c. m. of 28, 42, and 84. 
 
 Solutions, (a) Resolve each of the numbers into (^) 
 
 its prime factors. The factor 2 occurs twice in 28 and 98 = 2x2x7 
 
 in 84, the factor 3 occurs once in 42 and 84, the factor 7 .^ ^ ^ - 
 
 A*} — ^ y o y 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 = 2 X 2 X 3 X 7 
 
 (6) Arrange the numbers in a horizontal line and divide 
 by any prime factor that will exactly divide any two of \^) 
 
 them. Divide the numbers in the resulting quotient by any 2) 28 42 84 
 prime factor that will divide any two of them, and so con- 
 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 l.c.m. 2x2x3x7 
 = 84, the L c. m. Ill 
 
 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. 6, 42, 84, 168, 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 IX 
 
 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 : ^, f , |, |, 1, ^, 1 
 
 8. Complete the following statement : Such parts of a unit 
 as .5, .25, J, |, etc., are called . 
 
 120. Common fractions are expressed by two numbers, one 
 written above and one below a short horizontal line. 
 
 121. The number written above the line is called the 
 numerator of the fraction, and the number written below, 
 the denominator of the fraction. 
 
 122. 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. 
 
 101 
 
":I02 ^ dONCISE BUSINESS ARITHMETIC 
 
 ' '' 1^3.' 'It 1^ td'^ar that the greater the number of equal parts into 
 which a unit is divided, the smaller is each part ; and the fewer 
 equal parts into which a unit is divided, the greater the size of 
 each part. Hence, 
 
 Cf two fractions having the same denominator^ the one having 
 the greater numerator expresses the greater value; and 
 
 Of two fractions having the same numerator^ the one having the 
 smaller denominator expresses the greater value, 
 
 124. The terms of a fraction are the numerator and denomi- 
 nator. 
 
 125. A unit fraction is a fraction whose numerator is one. 
 
 Thus \, \, \, and J^ are unit fractions. \ in. is read one third of an inch. 
 
 126. An improper fraction is a fraction whose numerator 
 is equal to or greater than its denominator. 
 
 Thus, I, f, and ^/. are improper fractions. The value of an improper 
 fraction is always equal to or greater than one. 
 
 127. A mixed number is the sum of a whole number and 
 a fraction. 
 
 Thus, 2\ and 4|, 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 : |, -jL h h h i6' 6' h 2V' 2V' ih' 
 
 3. Read aloud the following fractions in the order of their 
 size, the smallest first : |, |, J, f , 1 |, -j^, A, f, 1 Jg , f . 
 
 4. Read aloud the following: J mi.; |T.; 21^ yd.; ij^'S 
 cu. ft.; 275f A.; 250^5^ lb.; X IS^^^ ; <£ 2711 ; ^^^ sq. ft. 
 
 5. Of all the cotton produced in the United States in a recent 
 year the principal cotton-growing states contributed approxi- 
 mately as follows : North Carolina, ^^^ ; South Carolina, ^ ; 
 Georgia, I ; Oklahoma and Indian Territory, Jg^ ; Alabama, I ; 
 Mississippi, -Jg ; Louisiana, -^^ ; Texas, ^ ; Arkansas, Jy ; Ten- 
 nessee, ^^g. Name the principal cotton-growing states, in the 
 order of production, for that year. 
 
u 
 
 ^ 
 
 '^A 
 
 ^1 
 
 yA 
 
 yA 
 
 ^ 
 
 W\ 
 
 ^^ 
 
 
 'm^ 
 
 
 m$ 
 
 
 ^ 
 
 
 'Mmm. 
 
 
 w/Mim 
 
 1 
 
 yMW/Mmmm. 
 
 1 
 
 COMMON FRACTIONS 103 
 
 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 i| ? how 
 many halves in ^^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' 1 to twelfths; J; i; J; §; f; f- 
 
 8. Name three fractions equal in value to |^ ; to | ; to |. 
 
 128. It has been seen that multiplying or dividing both terms 
 of a fraction hy the same number does not change the value of the 
 fraction. 
 
 129. A fraction is reduced to higher terms when the given 
 numerator and denominator are expressed in larger numbers. 
 
 ORAL EXERCISE 
 
 1. Reduce to twelfths : ^, |, |. 
 
 2. Reduce to sixteenths : |, \, J, f . 
 
 3. Reduce to twentieths : |, -|, -f^, |, f . 
 
 4. Reduce to twenty-fourths : |, |, |, -^, f , f . 
 
 5. Reduce to thirty-seconds : J, f , f , |, yV^ yV^ -^6' tV* 
 
 6. Reduce to one-hundredths : |, J, f , -j^, 2V ^' \' A* 
 
 7. Reduce | and f to fractions having the denominator 24. 
 
104 CONCISE BUSINESS ARITHMETIC 
 
 To Lowest Terms 
 
 ORAL EXERCISE 
 
 1. ^ equals how many thirds? 1| equals how many halves? 
 
 2. Name the largest possible unit frac- 
 tion. Why is this the largest possible 
 unit fraction? 
 
 3. Change -^^ *^ *^^ largest possible 
 
 unit fraction; y8_; _2^_.; _5_o_. J^2^. Express -l| in its simplest 
 form. Reduce ^^q to its lowest terms. 
 
 130. A fraction is reduced to its lowest terms when the 
 numerator and denominator are changed to numbers that are 
 mutually prime. 
 
 131. Example. Reduce -^^^ 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 
 16 and 18 ; dividing both terms by 2, the result is |. 
 
 1% — 11 
 
 ORAL EXERCISE 
 
 1. Reduce to fifteenths : ^, -|, |, |. 
 
 2. Reduce to eighths : ^\, -|-, |, if, 1|, |. 
 
 3. Reduce to fiftieths : |-, |, j%%, -^, -/g, J^. 
 
 4. Change to twentieths : ^ -^^ |, |, l -^%, f . 
 
 5. Reduce to lowest terms : ^g, y^^, ^^^ ||, -^^, f . 
 
 WRITTEN EXERCISE 
 
 1. Reduce to sixteenths : IJ^, ^|^, |, f|, f , J|§. 
 
 2. Reduce to lowest terms: -^^^^ cu. ft., -^^-^ A., ^^^^-^ T. 
 
 3. Reduce to lowest terms: J|§ mi., £l|f, fff^ lb., |f mi. 
 
 4. Reduce to three-hundred-twentieths : | mi., ^ mi., Jg mi. 
 
 5. Reduce to their simplest common fractional form : |^f|^ T., 
 hin T., ^ A., l|^ A., IIJ sq. mi., f |f sq. mi., §|^ mi. 
 
COMMON FRACTIONS 105 
 
 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 1|? in If? in 3J? 
 
 4. Express as fourths : 6J, 12|, 13, 87, 61^, 281 
 
 5. Express as eighths : 15, 12, lOJ, 1^, 2|, If, 9J. 
 
 6. Express as halves : 27, 14, 301 1711 1821, 249. 
 
 WRITTEN EXERCISE 
 
 Reduce to improper fractions : 
 
 1. 
 2. 
 
 83J. 
 
 4. 666|. 
 
 7. 266jV. 
 
 10. 
 
 3150f. 
 
 166|. 
 
 5. 180^. 
 
 8. 319^5. 
 
 11. 
 
 16251. 
 
 333J. 
 
 6. 212Jj. 
 
 9. 146ii. 
 
 12. 
 
 2150,^ 
 
 Improper Fractions to Integers or Mixed Numbers 
 oral exercise 
 
 1. How many pecks in 240 qt. ? ^|^ = ? ^^ = ? 
 
 2. Change to integers : 1|^, 1|^, ^^-, 2_8_8., A|5JI, l||iL. 
 
 3. Express 28 J as fourths ; express ^\^ as a mixed number. 
 
 4. Change to mixed numbers: ^{^, ij^, 1|^, -Ifl, ^. 
 
 5. What is the value of: ^-^ lb.? ^^-^- lb.? 1|^ bu.? ^fk p^.? 
 ^^ ft.? ^-if A.? 11^ mi.? ^5_(i lb.? 1|| sq, ft.? 
 
 written exercise 
 Reduce to integers or mixed numbers: 
 1. fit mi. 4. 
 
 3 95.55. T 6 
 
 132. When expressing final results reduce all proper frac- 
 tions to their lowest terms and all improper fractions to 
 integers or mixed numbers. 
 
 ^¥A. 
 
 7. 241 a lb. 
 
 im T. 
 
 8. -1111 CU. ft. 
 
 ffl*T. 
 
 9. ^V^sq. mi 
 
106 CONCISE BUSINESS AKITHMETIG 
 
 To Least Common Denominator 
 
 ORAL EXERCISE 
 
 1. How many pounds in 1 T. 500 lb. ? 5 T. + 1000 lb. = ? lb. 
 6 T. 1000 lb. = ? T. 
 
 2. How must numbers be expressed before they can be 
 added or subtracted? 
 
 ^* 2— ?> 2+8 — - 17 16' 1 16 — 16' 3—6' 36 — - 
 
 4. What kind of fractions can be added or subtracted? 
 
 5. Express | as sixteenths. Add | and -f^ ; J and -f^ ; | 
 and |. 
 
 6. Express J as eighths. Subtract -| and | ; J and -f^ ; | 
 and Jg . 
 
 133. 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. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 WRITTEN EXERCISE 
 
 Change to fractions having the least common denominator: 
 
 ^' h 32' H' ^- h h 12' Z2' ^' 12' 9' ¥' i^* 
 
 2- f ' A' 2V 6. |, f , 3^, ^V 10. iJ, ^, i ^f . 
 
 3. h h I' i- 7. |, -5^^, ^2, If 11. ^Vo' I' I'e^' f • 
 *• I' 9' iV 3- S- iV A' 12' }• ^2- 61% tV 3V' ^2* 
 
 Change the fractions to form for addition or subtraction: 
 
 13. 31^,7^5. 14. 134Jj,112^. 15. 6126,^,178^. 
 
 h\- 
 
 6. 
 
 -l-f 
 
 11. 
 
 f f 
 
 16. 
 
 h i> i- 
 
 hk- 
 
 7. 
 
 I'f- 
 
 12. 
 
 i iV 
 
 17. 
 
 !' r \ 
 
 h\- 
 
 8. 
 
 if 
 
 13. 
 
 iiV 
 
 18. 
 
 i' i' A- 
 
 I'i- 
 
 9. 
 
 if 
 
 14. 
 
 I'tV 
 
 19. 
 
 i h f • 
 
 I'A- 
 
 10. 
 
 if 
 
 15. 
 
 iiV 
 
 20. 
 
 i' 1' ^e- 
 
COMMON FRACTIONS 107 
 
 ADDITION 
 
 134. It has been seen that only like numbers and parts of 
 like units can he added. 
 
 
 
 RAL EXERCISE 
 
 State the sum of: 
 
 
 1- h h 1- 
 
 7, 2|, 3|, 12J, 19J. 
 
 2- i 1. \- 
 
 8. 5J, 121, 7^, loj. 
 
 3- h f f 
 
 9. 7J, 2|, 8i, H, 2|. 
 
 *• ^v ^-v A- 
 
 10. 2J, 5|, 8f 12J, lOf. 
 
 5- i i f > i I- 
 
 11. IJ, 10|, 161, 181, 121. 
 
 *• iV' iV iV i%- 
 
 12. 5J., 2-/5, 1^, 8^, 3f,. 
 
 ^^ horizontal addition find the sum of : 
 
 13. 2 pieces of gingham containing 41^ and 43^ 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, 51^ equals 51 J, 54^ equals 54| (54|), and 
 523 equals 52|. 
 
 14. 4 pc. stripe containing A2\ 38^ 40^, and 49 yd. 
 
 15. 3 pc. fancy plaid containing 42^, 40^, and 41 yd. 
 
 16. 4 pc. duck containing 48i, 47^, 46^, and 40^ yd. 
 
 17. 2 pc. monument cotton containing 54^ and 55^ yd. 
 
 18. 4 pc. dress silk containing 32^, 342, 353^ and 322 yd. 
 
 135. Examples, l. Find the sum of |- and |. 
 
 Solution, | and | are not similar fractions ; 1. c. m. of 8 and 5 = 40 
 
 hence, make them similar by reducing them to X=3-^*-2 16- 
 
 equivalent fractions having a least common de- 35 1 6^^ 5 1^ 111 
 
 nominator. | = f^ and | = i|. H+H=H 40 +10 = 40 = -^57 
 
 = m- 
 
 2. Find the sum of m\, 34|, 52f . 
 
 Solution. By inspection determine the least common 564 = 8 
 denominator of the given fractions ; then make the frac- 0^1 __ 3 
 tions similar and add them, as shown in the margin. .^ . 
 
 The result is 1 2^, which added to the sum of the into- 4 ~ _ 
 
 gers equals 143^, the required result. -^"^^ A f f ~ -^ A* 
 
 CB 
 
108 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the sum of: 
 
 
 
 1- ^6.1- 
 
 7. 
 
 12f, 172^. 
 
 2- .1^6' II- 
 
 8. 
 
 8i 1. \l 2Tf 
 
 3. 2J,17J. 
 
 9. 
 
 52|, 591, 57|, 52^. 
 
 4. 12|,19^. 
 
 10. 
 
 60|, 18|, 21,^5, 142jV. 
 
 5. m,in. 
 
 11. 
 
 204, 121, 18^, 92J, 75f. 
 
 6. 21 4f , 25J5. 
 
 12. 
 
 140f, 2601, 1451, 216J, 890| 
 
 13. A carpet dealer sold at different times 125| yd., 272 J 
 yd., 1691 yd., 186f yd., 2411 yd., 265| yd., 296| yd., and 
 314|- yd. of Axminster 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 
 $1 per yard. If the pieces contained 42^, 432, 442, 473^ 441^ 452^ 
 403, 462^ 451^ 42, 471, 482, 493^ 491, 402, 403, 502, 493, 472, 483, 493^ 
 451, 402, 452^ 442^ 473^ 462^ 411^ 513^ 423, 532^ 572^ 531^ 511^ 483, 472, 
 401, 452, 452, 403, 401, 453, 472, 481, 511, 522, 572, 513, 502, 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. 1. -f- 1 = 1|.. Observe that the numerator of the sum is 
 equal to the sum of the denominators in the given fractions. 
 
 2. ^ -{- 1 = ? Give a short method for adding any two sim- 
 ple fractions whose numerators are 1. 
 
 3. ^ -f- 1- = 11^. 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. I + I = ? Give a short method for adding any two frac- 
 tions whose numerators are alike. 
 
 5. Find the sum of J, \^ and \' 
 
 Solution, i + i = 1^2 ; t^j + i = M) the required result 
 
COMMON FRACTIONS 
 
 109 
 
 ORAL EXERCISE 
 
 State the sum of: 
 
 1. 
 
 h\' 
 
 7. 
 
 hh 
 
 13. 
 
 hh 
 
 19. 
 
 ^^f 
 
 2. 
 
 h h 
 
 8. 
 
 hh 
 
 14. 
 
 hh 
 
 20. 
 
 f A- 
 
 3. 
 
 hh 
 
 9. 
 
 hh 
 
 15. 
 
 hh 
 
 21. 
 
 hhi 
 
 4. 
 
 hh 
 
 10. 
 
 hh 
 
 16. 
 
 hh 
 
 22. 
 
 hhi 
 
 5. 
 
 hi- 
 
 11. 
 
 hh 
 
 17. 
 
 h h 
 
 23. 
 
 hh^ 
 
 6. 
 
 h h 
 
 12. 
 
 hh 
 
 18. 
 
 hh 
 
 24. 
 
 hhi 
 
 136. 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. 
 
 137. Example. Find the sum of -f^, |, |^ and l. 
 
 Solution. By inspection determine that the least common denominator is 
 16. Then mentally reduce each fraction to 16ths and add as in whole numbers. 
 Thus, 5, 7, 19, fl, m. 
 
 
 
 
 
 ORAL EXERCISE 
 
 
 
 
 
 Find the 
 
 sum of: 
 
 
 
 
 
 
 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 * 
 
 1 
 
 i 
 
 f 
 
 i 
 
 1 
 
 i 
 
 i 
 
 1 
 
 i 
 
 f 
 
 i 
 
 i 
 
 i 
 
 i 
 
 i 
 
 f 
 
 i 
 
 i 
 
 i 
 
 * 
 
 1 
 
 6 
 
 -^ 
 
 i 
 
 i 
 
 * 
 
 i 
 
 i 
 
 J 
 
 i 
 
 1 
 
 i 
 
 A 
 
 i 
 
 i 
 
 i 
 
 i 
 
 1 
 
 A 
 
 1 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 i 
 
 * 
 
 f 
 
 i 
 
 i 
 
 1 
 
 i 
 
 J 
 
 i 
 
 i 
 
 1 
 
 1 
 
 1 
 
 f 
 
 i 
 
 i 
 
 f 
 
 i 
 
 1 
 
 i 
 
 i 
 
 1 
 
 1 
 
 t 
 
 1 
 
 1 
 
 f 
 
 i 
 
 1 
 
 J 
 
 t 
 
 i 
 
 i 
 
 i 
 
 i 
 
 i 
 
 f 
 
 2^ 
 
 i 
 
 4 
 
 1 
 
 ^ 
 
 1 
 
 f 
 
 i 
 
 1 
 
 i 
 
 t 
 
 i 
 
 f 
 
 i 
 
 '^ 
 
 tV 
 
 f 
 
 i 
 
 f 
 
 f 
 
 f 
 
 i 
 
 1^ 
 
 i 
 
 A 
 
 ^ 
 
 f 
 
 1 
 
 i\ 
 
 1 
 
 i 
 
 i 
 
 A 
 
 i 
 
 A 
 
 ^ 
 
 i 
 
 f 
 
 iJ 
 
 A 
 
 * 
 
 i 
 
 ^ 
 
110 CONCISE BUSINESS ARITHMETIC 
 
 Exercises similar to the foregoing should be continued until the student 
 can name the successive results in the addition without hesitation. 
 
 138. 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. 
 
 139. Example. Find the sum of 2^ 54, and 3^. 
 
 ^ 
 
 Solution. By inspection determine that the least common denomi- ni 
 nator of the fractions is 8. Mentally find the sum of the fractions and ^ 
 the result is 14. Add this result to the integers and the entire sum is 114. fi^ 
 
 ORAL EXERCISE 
 
 State the sum of , 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 2J 
 
 H 
 
 H 
 
 H 
 
 14i 
 
 6| 
 
 4i 
 
 2| 
 
 3^ 
 
 14} 
 
 ?i 
 
 2J 
 
 H 
 
 ^ 
 
 I7f : 
 
 13J 
 
 'i 
 
 16| 
 
 iH 
 
 16f 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 9f 
 
 ^ 
 
 n 
 
 If 
 
 8* 
 
 4i 
 
 5i 
 
 H 
 
 4* 
 
 4J 
 
 10^ 
 
 4i 
 
 ^ 
 
 6J 
 
 S| 
 
 2i 
 
 2f 
 
 5f 
 
 2| 
 
 If 
 
 13i 
 
 iij 
 
 7^ 
 
 6| 
 
 2tV 
 
 4i 
 
 4i 
 
 6f 
 
 6t 
 
 7f 
 
 lOi 
 
 12tV 
 
 8A 
 
 13| 
 
 4t% 
 
 3f 
 
 6i 
 
 2* 
 
 3i% 
 
 12J 
 
 21. 
 
 22. 
 
 23. 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 28. 
 
 29. 
 
 30. 
 
 4J 
 
 H 
 
 ^ 
 
 H 
 
 8i 
 
 4| 
 
 5| 
 
 H 
 
 4^ 
 
 4^ 
 
 5i 
 
 6| 
 
 ^ 
 
 If 
 
 6| 
 
 2^ 
 
 IJ 
 
 H 
 
 2i 
 
 H 
 
 3| 
 
 5f 
 
 ^ 
 
 2f 
 
 H 
 
 4* 
 
 n 
 
 7f 
 
 6f 
 
 9| 
 
 H 
 
 5f 
 
 7| 
 
 6| 
 
 2# 
 
 3i 
 
 ^ 
 
 5* 
 
 6^ 
 
 7| 
 
 H 
 
 ^ 
 
 li 
 
 n 
 
 4 
 
 ^ 
 
 n 
 
 2f 
 
 9f 
 
 8f 
 
 4i 
 
 ^ 
 
 2f 
 
 2f 
 
 5i 
 
 H 
 
 H 
 
 n 
 
 4i 
 
 2J 
 
 ^ 
 
 ^ 
 
 8iV 
 
 8f 
 
 2i 
 
 H 
 
 2f 
 
 n 
 
 3^ 
 
 H 
 
 H 
 
 2i^ 
 
 8A 
 
 13f 
 
 5,^ 
 
 3i 
 
 12J 
 
 15f 
 
 9t^ 
 
 12J 
 
 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 
 
 111 
 
 
 
 WRITTEN I 
 
 SXERCISE 
 
 
 
 Copy i 
 
 or write from 
 
 dictation and find the 
 
 sum of: 
 
 
 1. 
 
 2. 
 
 3. 
 
 4. 
 
 5. 
 
 6. 
 
 1649J 
 
 1672f 
 
 14361 
 
 21101 
 
 6214J 
 
 12141 
 
 43721 
 
 14851 
 
 1390f 
 
 16401 
 
 1745J 
 
 2167| 
 
 8431| 
 
 16351 
 
 24151 
 
 36801 
 
 3146f 
 
 31591 
 
 5132J 
 
 12641 
 
 18671 
 
 4590| 
 
 18641 
 
 9275J 
 
 16541 
 
 1269f 
 
 16391 
 
 2169f 
 
 2839| 
 
 7215f 
 
 18311 
 
 1748J 
 
 4136f 
 
 8432f 
 
 6241J 
 
 52611 
 
 1831| 
 
 1936| 
 
 1652J 
 
 40411 
 
 4036| 
 
 7215f 
 
 14621 
 
 54131 
 
 31161 
 
 6542f 
 
 8130^ 
 
 5144f 
 
 1851^ 
 
 2114jV 
 
 1439^0 
 
 18621 
 
 2148^ 
 
 6257f 
 
 111^2 
 
 8. 
 
 2243/^ 
 9. 
 
 3246 1 
 10. 
 
 1439^^ 
 
 2186^^2 
 
 7. 
 
 u. 
 
 12. 
 
 91241 
 
 72491 
 
 16491 
 
 75291 
 
 7365^ 
 
 28141- 
 
 2716^ 
 
 2724| 
 
 27241 
 
 62141 
 
 26141 
 
 29101 
 
 2514J 
 
 86921 
 
 86951 
 
 18251 
 
 15831 
 
 2817i 
 
 29671 
 
 2476J 
 
 15651 
 
 8614| 
 
 16951 
 
 2714J 
 
 2964J 
 
 86951 
 
 2724-1 
 
 9215f 
 
 17621 
 
 2913| 
 
 6875J 
 
 62141 
 
 86191 
 
 6719f 
 
 1875| 
 
 2874f 
 
 8875f 
 
 72411 
 
 2924f 
 
 8516^ 
 
 1629J 
 
 26191 
 
 26581 
 
 86141 
 
 65291 
 
 75281 
 
 7214| 
 
 1472^ 
 
 8425| 
 
 4725^ 
 
 85921 
 
 7216| 
 
 25101 
 
 2615f 
 
 8273| 
 
 1649^ 
 
 27251 
 
 67291 
 
 2625f 
 
 1813| 
 
 1782f 
 
 12861 
 
 8647| 
 
 3514| 
 
 8614J 
 
 19621- 
 
 8695^ 
 
 6248| 
 
 8725f 
 
 1686f 
 
 2729^ 
 
 1862J 
 
 24721 
 
 12861 
 
 6219| 
 
 1725J 
 
 28161 
 
 1759J 
 
 62731 
 
 8537f 
 
 84131 
 
 2538f 
 
 28141 
 
 2864| 
 
 9685f 
 
 6982J 
 
 7226f 
 
 17581 
 
 2716| 
 
 1624J 
 
 968511 
 
 3685^ 
 
 18251 
 
 27521 
 
 17621 
 
 1729J 
 
 1925-/2 
 
 2614f 
 
 4725-1 
 
 21141 
 
 18751 
 
 1805| 
 
 4212^2 
 
 8796| 
 
 2816| 
 
 2216J 
 
 2614| 
 
 17211 
 
 2729J^ 
 
 1592| 
 
 2519^ 
 
 18721 
 
 2075J 
 
 1465| 
 
112 
 
 COKCISE BUSINESS AEITHMETIO 
 
 SUBTRACTION 
 
 ORAL EXERCISE 
 
 1. 172 A. - 154 A. = ? |-f = ? Ibu. -3pk. = ? 
 
 2. Find the difference between J and J ; ^ and ^; | and ^; 
 f and f . 
 
 140. It is clear that onl^ like numbers and parts of like units 
 can he subtracted. 
 
 141. Examples, i. Find the difference between J and -f^. 
 
 Solution. The given fractions must be reduced to equivalent fractions having 
 a least common denominator. The least common denominator is 24. | = f| and 
 h = \l' l\-\l = \h ^^^ required result. 
 
 2. From 211 take 171 
 
 Solution. Change the given fractions to similar fractions as in example 1. 
 ^ cannot be subtracted from f , hence 1 is taken from 21 and mentally united 
 to I, making f. | from | leaves |, and 17 from 20 leaves 3, The required result 
 is therefore 3|. 
 
 ORAL EXERCISE 
 
 
 
 Find the value of: 
 
 
 
 1. 2|-J. 5. 4f-l|. 
 
 9. 
 
 30- 
 
 2. 2f-i. 6. 6f-4^j. 
 
 10. 
 
 45- 
 
 3. 31 -|. 7. 1\~^-,. 
 
 11. 
 
 lli 
 
 4. 7|-1|. 8. 12^-6^. 
 
 12. 
 
 70| 
 
 16f. 
 -61. 
 -20J. 
 
 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 
 
 Opening 
 
 Highest 
 
 Lowest 
 
 Closing 
 
 July 
 September 
 
 87f)^ 
 
 90|^ 
 
 881^ 
 
 90f^ 
 87)^ 
 
 92^^ 
 87|)^ 
 
 13. What was the difference between the highest and the 
 lowest price of July wheat ? of September wheat ? 
 
 14. What was the difference between the opening and the 
 closing price of September wheat ? of July wheat ? 
 
COMMON FRACTIONS 113 
 
 13. 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. llf= ^0.015 ; 1000 times ^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. 39-111, 5. I651-4I3V. 9. l-i-i- 
 
 2. 85-213. 6. 245f-17^g. 10. i-^\-i. 
 
 3. 168 -15f. 7. 177|-17fg. 11. 2i + lf-1^2- 
 
 4. 264j9g_131i. 8. 2150- 121 1|. 12. 251 -8|- 151. 
 
 142. When the numerators of any two fractions are alike, the 
 subtraction may be performed as in the following examples. 
 
 143. Examples. 1. From | take l. 2. From | take f . 
 
 Solutions. 1. 9 — 7=2, the new numerator. 9 x 7 = 63, the new denomi- 
 nator. Therefore, the required result is ^^. 2. 8 — 5 x 3 = 0, the new numer- 
 ator. 8 X 5 = 40, the new denominator. Therefore, ^^ is the required result. 
 
 State the value of: 
 
 
 
 
 
 1- J-J- 
 
 8- i-f 
 
 15. 
 
 *-f 
 
 22. 
 
 f-f 
 
 2- i-h 
 
 9- i-i- 
 
 16. 
 
 l-f 
 
 23. 
 
 J-f 
 
 3- J-J. 
 
 10. i-1. 
 
 17. 
 
 !-«• 
 
 24. 
 
 l-f- 
 
 *• i-h 
 
 11. i-1. 
 
 18. 
 
 l-f 
 
 25. 
 
 121 -6|. 
 
 5- i-h 
 
 la. l-f 
 
 19. 
 
 t-f 
 
 26. 
 
 13 J - 21. 
 
 6- i-h 
 
 13. l-\. 
 
 20. 
 
 l-f 
 
 27. 
 
 ^H-H- 
 
 •>■ i-f 
 
 14. l-f 
 
 21. 
 
 f-i 
 
 28. 
 
 16f-12f, 
 
114 CONCISE BUSINESS AEITHMETIC 
 
 MULTIPLICATION 
 
 ORAL EXERCISE 
 
 1. 12 times 2 A. are how many acres? 12 times 2 fifths (|) 
 are how many fifths ? ^^- — ? 
 
 2. 32 mi. divided by 4 equals how many miles? \ of 32 mi. 
 equals how many miles? Multiplying by ^, ^, ^, and |-, 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 ? 
 
 144. Example. Multiply | by 248. 
 
 {a) 
 
 Solutions, (a) 248 times 3 eighths = 744 eighths | x 248 = -^4^= 93 
 = i|i = 93;but, 
 
 (6) If the multiplication is indicated as in the "■*■ 
 
 margin, the work may be shortened by cancellation. %^P times o __ gg 
 
 145. 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 
 
 ORAL EXERCISE 
 
 1. If 1 yd. of cloth costs 87^/ (f|), what will 16 yd. cost? 
 48 yd.? 128 yd.? 72 yd.? 
 
 2. When oats cost 33i/ (fi) a bushel, how much must be 
 paid for 29 bu.? for 36 bu.? for 129 bu.? 
 
 3. A boy earns 75^ (S|) 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 $720 a year, what is the rent 
 for J yr.? for \ yr.? for \ yr.? for ^ jr.? for J yr.? 
 
 5. A ship is worth $48,000. What is | of the ship 
 worth ? ^g of the ship ? | of the ship ? ^ of the ship ? ^ of 
 the ship? 
 
COMMON FRACTIONS 115 
 
 WRITTEN EXERCISE 
 
 Find the product of : 
 
 1. 98 X |. 7. J of 95. 13. 784 x f . 19. f of 2420. 
 
 2. 80 X f . 8. f of 25. 14. 459 x \, 20. | of 2500. 
 
 3. 50 X 2V 9- I of 88. 15. 400 X iV 21. I of 3240. 
 
 4. 97 X ^, 10. ^9g of 51. 16. 510 X iV 22. f of 5117. 
 
 5. 92xiV 11. 2^0^99. 17. 990 XsV 23. ^ of 7254. 
 
 6. 188 X 6^1. 12. -j^g of 77. 18. 800 x if. 24. ^ of 1024. 
 
 146. Example. MultiDly 25 by 4|. 
 
 25 
 Solution. | of 25 = ^{- or 9|. Write f as shown in the margin, 
 
 and carry 9 to the product of the integers. 4 x 25 + 9 = 109. There- 
 fore, 25 multiplied by 4f = 109|. 109| 
 
 147. Therefore, to find the product of a mixed number 
 and a whole number, multiply the integer and the fraction sepor 
 rately and find the sum of the products, 
 
 ORAL EXERCISE 
 
 Find the cost of: 
 
 1. 15f lb. of fish at 9^. 6. 6| bu. turnips at 32^. 
 
 2. 7f yd. of cloth at 83. 7. 12 J bu. of oats at 39^. 
 
 3. 16 lb. of beef at 12 1 ^. 8. l^ yd. of calico at 4^. 
 
 4. l^ lb. of sugar at 5^. 9. ^^ yd. of ribbon at 20 )Z^. 
 
 5. 12 yd. of cloth at 11^^. 10. 8J- gal. of molasses at 40^. 
 
 WRITTEN EXERCISE 
 
 1. A merchant bought 24 pc. of English serge, containing 52, 
 472, 501, 483,- 49, 513, 47^ 482^ 453^ 491^ 522, 502, 51^, 50, 52, 53i, 
 523, 473^ 481, 512, 513^ 482, 49, and 53 yd., at $1,121 per yard, and 
 sold it all at S1.35 per yard. What did he gain ? 
 
 2. I bought 25 pc. taffeta silk, contaming 42^, 40^, 43, 44^ 
 
 45, 412, 43^ 461^ 472^ 44^ 452^ 491^ 471^ 451^ 46^ 44^ 433^ 40, 41^, 
 
 46, 47, 402, 451, 42, and 47^ yd., at 871/ per yard, and sold 
 the first 15 pc. at S1.05 and the remainder at Sl.lO. What 
 did I gain? 
 
116 
 
 CONCISE BUSINESS ARITHMETIC 
 
 3. A merchant bought 25 pc. of striped denim containing 
 411, 411, 422^ 432^ 421, 442^ 431^ 402^ 421, 453^ 42i, 402, 412, 473^ 
 451, 411, 432^ 472^ 443^ 423, 432, 391, 421, 482, and 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 : 
 
 Little Falls, NV., {U^^-^^^'r^ tq 
 
 Te..s ^^^^^/"^ ^^ ^' The Eureka Mills 
 
 ^ 
 
 A-X-r^-p^ ^-^^-^^y-^f^.^i^^^r:^^ 
 
 l.^^'^J'T^^ 
 
 AC/' AC2/ A^jT' 4^/7 4^/ 2.//^Uc^. S^%<\ 
 
 r \J2^^ ~:^7^^i^^.,^^^:^^^-/>r^ ..^i^^^^^^^ 
 
 ^2.' AC/ .ic7-' ^^"^ A^2. dZZ. 
 
 LO. 
 
 
 ^^'^^^T'^^ 
 
 4^/ Jf 4^ 4L/. A^O 
 
 -%i 
 
 148. The expressions |^ of |^ and ^ X f have the same meaning ; 
 hence the sign of multiplication may be read of, or multiplied hy^ 
 when it immediately follows a fraction. 
 
 149. Examples. 1. Multiply | by |. 
 
 Solution. To multiply f by | is to find f of f . 
 
 Let the line ^JF in the accompanying diagram represent a unit divided into 
 5 equal parts. ad p n f T7 
 
 Then ^D will represent |. Sub- ^ ^ C D E F 
 
 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 y of ^ 
 equals ^^. Since | of ^ is J^, ^ of f is ^^. But | of f is 2 times | of f ; there- 
 fore f of I equals y^. 
 
 2. Find the product of 2i, |, and -^j. 
 
 Solution. Reduce the mixed number 2\ to an im- 2 
 
 proper fraction and obtain ^. Cancel, and there remains 5 4 7 14 
 
 in the numerators 2 times 7, and in the denominators 15, Tj^'g.^ Tc ~ i~c 
 
 from which obtain the fraction \^. r r 
 
COMMON FRACTIONS 
 
 117 
 
 150. 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 in | rd. ? feet in | rd. ? 
 
 2. When barley is worth 25^^ per bushel, what is the value 
 of Ibu.? 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. 
 
 WRITTEN EXERCISE 
 Reduce to their simplest form : 
 
 1. I of I off 3. 7^x25xf. 5. 50x^xT|. 
 
 2. fof|of2J. 4. 3fx 41x20. 6. l|x4J-x8f. 
 
 7. A saves 89.75 per week and B | as much. How much 
 more will A have than B at the end of a year ? 
 
 8. A merchant bought a piece of cloth containing 43|^ yd. 
 at $1.50 per yard. He sold | of it at f 1.62 J a yard, and the re- 
 mainder at f 1.37 J 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 
 
 Opening 
 
 Highest 
 
 Lowest 
 
 Closing 
 
 July 
 September 
 
 661/ 
 651/ 
 
 65|/ 
 64J/ 
 
 661/ 
 65^/ 
 
 64J/ 
 641/ 
 
 65|/ 
 64f/ 
 
 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? 
 
118 CONCISE BUSIKESS 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 approximate 
 weight of a silver dollar ? If silver coins are -f^ pure, approxi- 
 mately how much pure silver in 10 silver dollars? 
 
 Short Methods in Multiplication 
 
 151. When mixed numbers are large, they maybe multiplied 
 as shown in the following example. 
 
 152. Example. Multiply 2551 by 24f. 
 
 2551 
 
 Solution. Multiply the fractions together 24I 
 
 and obtain ^5, which write as shown in the ^^ 2 - - 
 
 margin. Multiply the integer in the multi- T^ ~ 5" 3 
 
 plicand by the fraction in the multiplier and 102 = |^ of 265 
 
 obtain 102. Multiply the fraction in the mul- 8 =24 times ^ 
 
 tiplicand by the integer in the multiplier and 1020 1 
 
 obtain 8. Multiply the integers together and tj i = 24 times 255 
 
 add the partial products. The result is ^ 
 
 6230^. 6230^2^ = 24f times 255J 
 
 WRITTEN EXERCISE 
 
 Multiply : 
 
 1. 975Jbyl8J. 3. 720Jby21|. 5. 512^ by 161. 
 
 2. 876|by21|. 4. 445iby46|. 6. 450^^ by 20|. 
 
COMMON FRACTIONS 119 
 
 SQUARING NUMBERS ENDING IN J OR .5 
 
 153. Examples, i. Multiply 9J by 9i. 
 
 Solution. | of ^ = J, which write as shown in the margin. ^ 9i 
 
 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 5 
 multiplier. 9 x 10 = 90. Then, 9^ x 9J = 901. 
 
 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 .5 = .25, 8 x 9 = 72. 
 Therefore, 8. 5 tons of coal at § 8.50 per ton will cost $ 72.25. 72.25 
 
 3. Find the cost of 75 A. of land at $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 ne 
 
 8.5 
 8.5 
 
 5625 
 
 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. 11 by 11 6. 6 J by 61 ii. 131 by ISJ. 16. 161 by 161. 
 
 2. 21 by 21 7. 7.5 by 7.5. 12. 141 by 141. 17. 171 by 171. 
 
 3. 31 by 31. 8. 8.5 by 8.5. 13. 151 by 151 is. 18 J by 18^. 
 
 4. 4^ by 41 9. 9.5 by 9.5. 14. 11.5 by 11.5. 19. 195 by 195. 
 
 5. 51 by 51. 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 lb. of tea at 85 f. 55 lb. tea at 55 ^. 
 
 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 Qtb^, 750 lb. cream codfish at 7J^. 
 
 4 J cs. baking powder at $ 4.50. 3 J cs. baking powder at $ 3.50. 
 
120 CONCISE BUSINESS ARITHMETIC 
 
 MULTIPLICATION OF ANY NUMBERS ENDING IN |^ OR .5 
 
 154. Examples, l. Multiply 7^ by 6|. 
 
 Solution. | of the integer in the multiplicand plus ^ of the integer gl 
 
 in the multiplier is equal to ^ of 6 + 7, or 0^, which added to ^ of ^ r-l 
 
 equals 6|. Write f as shown in the margin, and carry 6. 6x7+ 6 j-^ 
 
 = 48. Therefore, 7| x 6| = 48|. ^^f 
 
 2. Multiply 7i by 9J. 
 
 7J- 
 
 Solution. | of 7 + 9 = 8, with no remainder. ^ of | = ^, which ^^ 
 
 write as shown in the margin, and carry 8. 7x9 + 8 = 71. There- 2 
 
 fore, 7^ X 9| = 71|. 71^ 
 
 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 is an odd num- 
 ber^ write f {.75 or 75) in the product. Multiply the integers and to the product 
 add \ of their sum. 
 
 Multiple/ : 
 
 ORAL EXERCISE 
 
 
 1- 3|by7i. 
 
 2. 4|by6J. 
 
 3. 16Jby4^. 
 
 4. 17Jby2J. 
 
 5. 141 by 61 
 
 6. 21Jby9J. 
 
 7. 3.5 by 8.5, 
 
 8. 7.5 by 6.5, 
 
 9. 5.6 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 $8.50. 8.5 T. coal at $9.50. 
 
 2.5 T. hay at $17.50. 16.5 T. hay at $11.50. 
 
 15.5 cd. wood at $3.50. 14.5 cd. wood at $5.50. 
 
 2. Find the total cost of : 
 
 45 bu. beans at $2.50. 350 bu. wheat at $1.05. 
 
 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 121 
 
 DIVISION 
 
 ORAL EXERCISE 
 
 1. 8A. -4-4 = ? Sninths (|)-f-4? 
 
 2. If 2 lb. of cofPee costs |0.66| (If), what will 1 lb. cost? 
 Divide | by 2. What is the effect of dividing the numerator 
 of a fraction ? 
 
 3. i + 2 = ? Joft=? 
 
 4. Because ^-h2 = ^ of |, therefore, | -=- 5 = ^ of ^, or 
 ixi. ixi = ? 
 
 5. What is the quotient of 1 -5- 5 ? of-|-^8? ofi-T-2? 
 
 6. Because |- -f- 5 = ^ of J, therefore | -f- 5 = 2 times J of ^. 
 That is, f ^ 5 = I of |, or I X f | x l = ? 
 
 7. How much is 1^5? f-3? 7l(-Y.)^8? 31^6? 
 
 8. What is the effect of multiplying the denominator of a 
 fraction ? 
 
 155. In the above exercise it is clear that 
 
 Dividing the numerator of a fraction hy 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-r-4. 4. |-^12. 7. ■35^-^4. 10. f-f-9. 13. 1-^19. 
 
 2. j%-Sr2. 5. f-^12. 8. iV^^- ^^- i-^^' ^*- A"^^- 
 3.1^^5. 6. ^9_^3. 9. -A ^7. 12.^^5. 15. ^V^ 5- 
 
 156. 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, 7\OQ,7 
 28|-7 = 4f ^ 8 
 
 2. Divide 261 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| ONOfiT" 
 
 to an improper fraction and the result is f . f -^ 8 = ^^. Therefore, ^ 2 
 20^ - 8 = 3^. 
 
122 CONCISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 Divide : 
 
 1. 161 by 4. 5. 32f by 4. 9. 21^ by 8. 13. 8^ by 5. 
 
 2. 18| by 9. 6. 271 by 7. lo. 24^ by 6. 14. 14f by 7. 
 
 3. 25| by 2. 7. 19| by 9. ii. 45f by 5. 15. Ill by 9. 
 
 4. 171 by 8. 8. 20f by 10. 12. 40| by 10. 16. 261 by 10. 
 
 ORAL EXERCISE 
 
 1. How many eighths in one ? 1 -*- 1 = ? 
 
 2. What is the value of: Ih-J^? ^--1? 11-^1? 
 125-^^2? 250-^? 
 
 3. Read aloud the following, supplying the missing word: 
 To divide an integer hy a unit fraction^ multiply the integer by 
 the of the fraction. 
 
 4. What is the value of 25 -i- 1 ? 2.5-^1? 7.5^ |? 25.5^ 
 _L? 54^1? 48^1? 29^-1? 21^1? 
 
 5. If B^ in the accompanying dia- 
 grahi, is 1, what is (7? How many 
 blocks like OinBl 1 h- i = ? 
 
 6. If A is 1, what is ^ ? J. is how 
 many times B ? That is, A^B=? 
 1-4-1 = ? 
 
 7. If 1^1 = 1(11), then 2-1 = ? 
 
 8. What is the value of 4 -J- f ? 5-4-|? 12-4-|? 15-4-f? 
 
 9. Read aloud the following, supplying the missing words : 
 
 If JL is 1, -S is , and C is . If B is contained in 
 
 -4 I (1 J) times, it is contained in (7 l of | times or times. 
 
 That is, i-5-| = J X I = . 
 
 10. What is the value of 1-^^? fH-|? f-^f? f^f? 
 
 157. The reciprocal of a fraction is 1 divided by that fraction. 
 Thus, the reciprocal of | is 1 -,- 1, or |. That is, the reciprocal of a fraction 
 
 is the fraction inverted. 
 
 158. Reciprocal numbers, as we use the terms in arithmetic, 
 are numbers whose product is 1. 
 
 Thus, 4 and \, % and |, \ and 6, | and |, are reciprocal numbers, because 
 their product is equal to 1. 
 
COMMON FRACTIONS 
 
 123 
 
 159. It has been seen that the brief method for dividing a 
 fraction or an integer by a fraction is to multiply the dividend 
 hy 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 
 
 7. 
 
 fbyf. 
 
 8. 
 
 4f by f . 
 
 9. 
 
 ^by|. 
 
 LO. 
 
 6| by 11 
 
 1- ibyf. 
 
 2. 7|byi. 
 
 3. 95 by f . 
 
 4. 88byf. 
 
 5. 16by|. 11. 160 by 41 
 
 6. 151 by f 12. 250 by 3f . 
 
 . 160. Examples, i. 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 ^^a and i|6.. Reject the common denominators 
 and divide as in whole numbers. 
 
 2. Divide Q^ 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 5^|. Or, 
 
 Reduce both the dividend and divisor to sixths, obtain- 
 ing as a result ^ and ^. Reject the common denomi- 
 nator and divide as in simple numbers. 
 
 Divide: 
 
 1. 2701 by 121 
 
 2. 508iby30|. 
 
 3. 1431^ by 201. 
 
 CB 
 
 WRITTEN EXERCISE 
 
 13. 
 14. 
 15. 
 16. 
 17. 
 18. 
 
 ibyf 
 fbyf 
 169 by 4|. 
 640 by 5|. 
 625 by 831 
 920f by 73. 
 
 48f)2190 
 
 _3 3_ 
 
 146) 6570(45 
 584 
 730 
 730 
 
 121)651 
 
 _6 6_ 
 
 74)393(5fi 
 
 370 
 
 23 
 
 9621 by 31J. 
 650f by 261 
 1680J by 451. 
 
 7. 7552by78f. 
 
 8. 470|byl7|. 
 
 9. 10541 by 168f 
 
124 CONCISE BUSINESS ARITHMETIC 
 
 FRACTIONAL RELATIONS 
 
 ORAL EXERCISE 
 
 ^^ 1. If / in the accompanying diagram is 
 
 ^^2 1, what is e? d? c? b? a? 
 
 ^^L 2. What part of e is /? aid? oi c? of 
 
 ^^b^ h? of a? What part of 6 is 1? of 5? of 4 ? 
 
 ^^B^j^ ' 3. What part of a is e? d? c? b? What 
 ^•^ part of 6 is 2? 3? 4? 5? 
 
 4. What part of d is/? What part of 5 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 (|) 
 is 1 eighth (J)? 
 
 6. What part of | is ^? 
 
 Solution, f and | are similar fractions ; hence they may be compared in 
 the same manner as concrete integral numbers. 2 is | of 3 ; therefore, | is | of 
 f ; or, 
 
 f is I off. | = fxf = f. 
 
 7. f is what part of If (|) ? of 2|? of 5^? 
 
 8. ^ is what part of ^ ? ' 
 
 Solution. ^ = f . | is ^ of f , therefore, | = J of ^ ; or, 
 
 iisiofi. i=ix^=i. 
 
 161. 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| da. ? 
 
 3. If B can do a piece of work in 1^ da., what part of it 
 can he do in 1 da. ? in 2 da. ? in 6 da. ? in 5 J da. ? in 6 J da. ? 
 
COMMOK FEACTIONS 125 
 
 4. What part of 100 is 331? I2i ? 6Gf ? 8i ? 25? 75? 
 125? 16f? 831? G2|-? 22| ? 9^^-? 56 ^ ? 6f? 
 
 5. What part of SI is 331/? 66|/? 25/? 75/? 16f/? 
 81/? 6f/? 31/? 6|/? 62^/? 871/? 371/? 142/? 
 
 6. What part of 1000 is 125? 166|? 666f ? 625? 3331? 
 
 7. Whatpartof S10isS3.331? S1.25? $1.66|? S8.33i? 
 $2.50? $6.25? $6.66f ? 
 
 WRITTEN EXERCISE 
 
 1. A man asked for a horse | more than it cost, but finally 
 reduced the price -J^^. He gained $ 26. What was the cost of 
 the horse ? the price asked ? the selling price ? 
 
 2. A had 1 of his money invested in bonds, -f^ in bank stock, 
 and the remainder, 81980, on deposit in the First National Bank. 
 How much was invested in bonds ? in bank stock ? 
 
 3. A man left his estate to his- four sons. To the first son he 
 gave 1 of the estate ; to the second, 1 of the remainder ; to the 
 third, ^ of the estate ; to the fourth son, $1556. What was the 
 value of the estate ? 
 
 4. A merchant reduced the marked price of a machine 1, and 
 then sold it so that he gained ^ of the first cost. If he gained 
 $ 8, what was the first cost of the machine, and the marked price 
 before any reduction was made ? 
 
 5. A man placed a house and lot in the hands of a real estate 
 agent to be sold at such a price that he, the owner, might realize 
 $5985, after paying the agent 2V of the selling price of the 
 property. For how much was the property sold? 
 
 6. A farmer had three bins containing wheat, rye, and oats 
 respectively. The quantity of oats was three times that of the 
 wheat, and the rye was one haK of the quantity of the oats. If 
 the value of the oats at 35/ per bushel was $1155, how many 
 bushels of each kind of grain did the farmer have ? If the 
 wheat was worth 95/ per bushel, and the rye 67^/ per bushel, 
 what was the value of the entire lot of grain ? 
 
126 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. The square in the margin represents the 
 total population of the state of New York (state 
 census of 1910), and the shaded area represents 
 the urban (city) population. If the rural (coun- 
 try) population is 1,800,000, what is the entire 
 population of the state ? the urban population ? 
 
 2. In a recent year the population of Massachusetts was in 
 round numbers 3,360,000, and there were fourteen persons living 
 in the cities of the state to each person living in the country. 
 Represent this graphically as in problem 1, and find the city 
 population and the country population for the state. 
 
 A 
 B 
 
 c 
 
 D 
 E 
 F 
 
 1 1 1 r 
 
 12 3 4 
 
 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 1910) 
 is 2,537,167, and the rural population, 629,957. Represent this 
 .graphically and find the urban population. 
 
COMMON FEACTIOKS 127 
 
 CONVERSIOK 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. 
 
 162. A decimal may be written as a common fraction. 
 
 163. Examples, l. Reduce .0625 to a common fraction. 
 
 SoLUTiox. .0625 means yf ^ ; but yf §f^ may be 625 ^^ 5 _ J 
 
 expressed in simpler form. Dividing both terms of T0^0()¥ So 1^ 
 
 the fraction by 625, the result is ^. 
 
 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. 1.66f. 10. 0.00561 14. 126.1875. 
 
 3. 0.0016. 7. 0.4375. ii. 181.875. 15. 175.0625. 
 
 4. 0.5625. 8. 0.125. 12. 171.245. 16. 172.0075. 
 
 164. A common fraction may be written as a decimal. 
 
 165. Example. Reduce f to a decimal. 
 
 Solution, f equals i 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 : J, ^, |, \, |, J, f , i, |, |, 
 
 13 5 7 JL _i .3- 1 JL 
 
 1^' ^' ^' t' 16' 12' 16' 9' 11- 
 
 2. Reduce to common fractions : .5, .25, .50, .75, .331, .66|, 
 .16f, .121 .6, .4, .60, .40, .2, .831-, .20, .08J, .375, .125, .371 
 .87f .875, .0625, .111 m^. 
 
 WRITTEN EXERCISE 
 
 Reduce to equivalent decimals : 
 
 1. f 3. ^j. 5. ^j. 7. :^\. 9. ^^. 11. 21f. 
 
 2. ^. 4. I'j. 6. ii 8. 2V. 10. 6,^. 12. 165^. 
 
128 CONCISE BUSINESS ARITHMETIC 
 
 THE SOLUTION OF PROBLEMS 
 
 166. 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. 
 
 167. 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. 
 
 168. 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 ; 9f % of 1290 bu. is equal to approximately ^V of 1290 bu. ; etc. 
 
 169. 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 f yd. ; 45 waistcoats will require 45 times f f yd. 
 15 5 
 
 3. r^ = 75 ; that is 75 yd. of flannel are required in making 45 
 
 waistcoats. 
 
 4. 1^ yd. = f yd. ; || yd. = | yd. ; therefore the work is probably correct. 
 
 170. 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 the instructor. 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 129 
 
 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 88, what will 5 T. cost? 
 
 Suggestion. $20; since 2 T. cost $8, 5 T., which are 2| times 2 T., will 
 cost 2 i times $8, or $20. 
 
 2. 24 is 1^ of what number ? f of what number ? -f^ of what 
 number ? 
 
 3. 220 is ^ less than what number? 450 is J less than 
 what number ? 
 
 4. A, having spent ^ of his money, finds he has 884 left. 
 How much had he at first ? 
 
 5. 1124 is i more than what sum of money? fSOO 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 J 
 above cost. If he received 8275, 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 8240, what was the cost 
 and what was his loss ? 
 
 9. -^Q 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 8 300 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 ^ more than the cost. If the selling price was 8720, 
 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 8750 for the sale of the car- 
 peting, what was the cost of same, and what was his loss ? 
 
130 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 In the following problems give both analysis and computation. 
 
 1. If I lb. of tea cost 21^, what will 9^ lb. cost ? 
 
 Computation Analysis 
 
 9| = J^ 9| = V- ; 91 is therefore 19 times i If | lb. cost 
 
 19 X 21 j? = $ 3.99 2i f, 9i lb. will cost 19 times 21 f, or |3.99. 
 
 2. If I of a pound of tea cost 42 ^, what will 35| lb. cost ? 
 
 3. If a drain can be dug in IT 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 f 0.621- per day earn as much 
 as 4 men at $2.25 each per day will earn in 45| da.? 
 
 5. A spends 872 per week or | of his income ; B saves 
 848 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 bu. of wheat are required to make 23 bbl. of 
 flour, how many bushels will he required to make 50 bbl. of 
 flour ? 117 bbl. of flour ? 259 bbl. of flour ? 
 
 ORAL REVIEW EXERCISE 
 
 1. .05x6x0x21 = ? 
 
 2. $0.75 is what part of $3? 
 
 3. What is the sum of ^, |, ^, and -^ ? 
 
 4. Find the value of .45 + (.25 x 5) -.04. 
 
 5. 60 is f of what number? |? f ? -f? f ? 
 
 6. At 25^ a yard, what will 2|^ yd. of cloth cost? 
 
 7. y is 1^ of what number? | is | of what number? 
 
 8. If I of an acre of land costs $75, what will 50 A. cost ? 
 
 9. If I of a number is 84, what is 5 times the same number ? 
 
 10. The dividend is 4^ and the quotient is 6|; 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 131 
 
 13. How much will 4 carpenters earn in 10 da. at the 
 rate of $2.25 each per day? 
 
 14. At $4.50 per cord, what will be the cost of 4 J cd. 
 of wood ? of 61 cd. ? of 121 cd. ? of 71 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 J 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 J 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 lb. to a ton, find the cost of 5| T. of 
 steel at 1^^^ per pound. 
 
 3. When flour is sold at $6.02 per barrel of 196 lb., what 
 should be paid for 5b^ lb. ? 
 
 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 1^ da. 
 If they join in the completion of the work, how long will it 
 take them? 
 
132 CO:^^CISE BUSINESS ARITHMETIC 
 
 7. How much will 7 men earn in 6 da., working 10 hr. per 
 day, at 25 ^ per Lour? 
 
 8. At $2.50 per day of 8 hr., how much should a man 
 receive for 11 J hours' work ? 
 
 9. A boy works 4 J 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 i of a day, earns 
 $0.87|. How much will the two together earn in 40 J 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 $3.75 per day? 
 
 13. In one year the cotton produced in the United States 
 approximated 14,000,000 bales of 500 lb. each. If Texas 
 produced ^ of the crop, Georgia i. South Carolina i, and Ala- 
 bama 1, what was the value of the cotton produced in each 
 state, at 101/ per pound ? 
 
 14. In one year the value of the cotton crop (including the 
 seed) in Texas was 1188,000,000. The value of the cotton seed 
 was 125,000,000. The value of the cotton was what fraction 
 of the total value ? The value of the seed was what fraction 
 of the total value ? (Express decimally, using three places.) 
 
 15. In one day 14,310 beef cattle were received at the Union 
 Stock Yards, in Chicago. If |- of the number were of an average 
 weight of 1056 lb. and sold for $6.80 per hundred pounds, and if 
 the remainder were of an average weight of 1192 lb. and sold at 
 $6.95 per hundred pounds, what was the total value of the cattle ? 
 
 16. In one year the approximate production of sugar in the 
 United States (including Hawaii and Porto Rico) was as follows : 
 beet sugar, 1,240,000,000 lb.; cane sugar, 1,108,000 short tons. 
 If the beet sugar was worth I^^q/ per pound, and the cane 
 sugar ly^Q-/ per pound, what was the total value of the crop? 
 (The price is based on the export value of refined sugar.) 
 
COMMOK i^EACTIONS 
 
 133 
 
 GKAPHIC OUTLINE 
 
 A comparison of the money value of the wheat crop, and the fire losses 
 paid bj insurance companies, in the United States, 1890 to 1899 inclusive. 
 ,- -value of wheat crop. value of fire losses. 
 
 
 1890 
 
 1891 
 
 1892 
 
 1893 
 
 1894 
 
 1895 
 
 1896 
 
 1897 
 
 1898 
 
 1899 
 
 800 million dollars 
 
 
 
 
 
 
 
 
 
 
 
 700 million dollars 
 
 
 
 
 
 
 
 
 
 
 
 GOO million dollars 
 
 
 
 
 
 
 
 
 
 
 
 500 million dollars 
 
 
 A 
 
 
 
 
 
 
 
 
 
 400 million dollars 
 
 
 /\ 
 
 
 
 
 
 t\ 
 
 
 
 
 300 milUon dollars 
 
 i 
 
 
 \ 
 \ 
 \ 
 
 \ 
 
 
 
 . / 
 
 1 X 
 
 
 \ 
 
 
 •"" 
 
 
 200 million dollars 
 
 
 
 \ 
 
 ___„ 
 
 ./' 
 
 
 
 
 
 
 100 million dollars 
 
 
 
 
 
 
 
 1 
 
 
 , . 
 
 
 WRITTEN EXERCISE 
 
 1. The figures below give the value of the wheat crop, and the 
 fire losses paid by fire msurance companies, in the United States, 
 for the years 1890 to 1899 inclusive. (See Graphic Outline.) 
 
 Farm Val. of Wheat Fire Losses 
 
 1890 $334,773,678 $108,993,792 
 
 1891 513,473,711 143,764,967 
 
 1892 322,111,881 151,516,098 
 
 1893 213,171,381 167,544,370 
 
 1894 225,902,025 140,006,484 
 
 1895 237,938,998 142,110,233 
 
 1896 310,602,593 118,737,420 
 
 1897 428,547,121 116,254,575 
 
 1898 392,770,320 130,593,505 
 
 1899 319,545,259 153,597,830 
 
134 CONCISE BUSINESS ARITHMETIC 
 
 2. Make a graphic outline comparing the wheat crop, and the 
 fire losses paid by the fire insurance companies, in the United 
 States, for the years 1880 to 1889 inclusive. 
 
 
 Farm Val. of Wheat 
 
 Fire Losses 
 
 1880 
 
 $474,201,850 
 
 $74,643,400 
 
 1881 
 
 456,880,427 
 
 81,280,900 
 
 1882 - 
 
 445,602,123 
 
 84,505,024 
 
 1883 
 
 883,649,272 
 
 100,149,228 
 
 1884 
 
 830,862,260 
 
 110,008,611 
 
 1885 
 
 275,320,390 
 
 102,813,796 
 
 1886 
 
 314,226,020 
 
 104,924,750 
 
 1887 
 
 810,612,960 
 
 120,283,055 
 
 1888 
 
 385,248,030 
 
 110,885,665 
 
 1889 
 
 342,491,707 
 
 123,046,833 
 
 3. Make a graphic outline comparing the wheat crop, the cotton 
 crop, and the fire losses paid by* the fire insurance companies, in 
 the United States, for the years 1900 to 1909 inclusive. 
 
 
 Farm Yal. of Wheat 
 
 Farm Val. of Cotton 
 
 Fire Losses 
 
 1900 
 
 $323,515,177 
 
 $515,828,431 
 
 $160,929,805 
 
 1901 
 
 467,350,156 
 
 439,166,710 
 
 165,817,810 
 
 1902 
 
 422,224,117 
 
 501,897,135 
 
 161,087,040 
 
 1903 
 
 443,024,826 
 
 660,549,230 
 
 145,302,155 
 
 1904 
 
 510,489,874 
 
 652,031,626 
 
 229,198,050 
 
 1905 
 
 518,372,727 
 
 632,298,332 
 
 165,221,650 
 
 1906 
 
 490,332,760 
 
 721,647,237 
 
 518,611,800 
 
 1907 
 
 554,437,000 
 
 700,956,011 
 
 215,084,709 
 
 1908 
 
 616,826,000 
 
 681,230,956 
 
 217,885,850 
 
 1909 
 
 730,046,000 
 
 812,089,833 
 
 188,705,150 
 
 Use a dotted line to represent the cotton crop. 
 
 The figures representing the fire losses do not include the cost of main- 
 taining fire departments, nor the losses sustained by the interruption of 
 business. 
 
 The United States exceeds all other countries in losses by fire. A large 
 per cent of these losses are due to carelessness. 
 
commo:n^ feactions 135 
 
 ORAL REVIEW EXERCISE 
 
 1. f of 36 is what part of 81 ? 
 
 2. Multiply 126 by 101; 92 by 102. 
 
 3. Divide 41 by 2| ; 3| by 21. 
 
 4. Find the cost of each of the following : 
 
 a, 35 bu. of seed at 35/ per busheL 
 h, 65 A. of land at S65 per acre. 
 c, 45 yd. of cloth at 45/ per yard 
 
 5. Divide I by A; |byf; f by |. 
 
 6. Multiply 36 by I ; 49 by f ; 55 by J^. 
 
 7. What is the square of 15 ? of 1.5 ? of 11 ? 
 
 8. 64x| = ? 64^^ = ? i + i + J=? 
 
 9. How many yards of cloth can be bought for $25 at 121/ 
 per yard ? 
 
 10. If it costs $7.50 to harvest 61 A. of com, what will it 
 cost to harvest 65 A. ? 
 
 11. An agent received $7.20 for collecting a debt, and the 
 merchant received $232.80. What was the total debt? 
 
 12. C and D received $ 21.75 for work done jointly. If C does 
 only half as much work as D, how should the money be divided ? 
 
 13. If a lot of articles were bought at the rate of 3 for 2/ and 
 sold at the rate of 2 for 3 /, how many must be sold to gain $ 5 ? 
 
 14. A and B received $34 for work done jointly. If A can 
 do as much work in 8 da. as B can do in 9 da., how should the 
 money be divided ? 
 
 15. Name the results quickly : 
 
 a. A can do a piece of work in 4 da., and B in 5 da. If they 
 work together, in how many days will they finish the task ? 
 
 h. F can do a piece of work in 31 da., and G in 5 da. If they 
 work together, in how many days will they finish the task ? 
 
 c, C can do a piece of work in 2 da., D in 3 da., and E in 4 da. 
 If they work together, in how many days will they finish the task ? 
 
 d. H and J together can do a piece of work in 20 da. If H 
 alone can do the work in 30 da., in how many days can J alone 
 do the work ? 
 
136 CONCISE BUSINESS ARITHMETIC 
 
 written exercise 
 Problems of the Farm 
 
 1. If 15 sheep consume 5785 lb. of dry fodder in a year, what 
 is the cost per sheep if the fodder is worth S8.50 per ton ? 
 
 2. If eggs are worth 24/ per dozen, what is the difference 
 in the value of two hens, in a year, if one lays 180 eggs and the 
 other lays 96 eggs ? 
 
 3. An apple tree produced 9i bu. of apples, 61- bu. of which 
 graded as " firsts " and the remainder as " seconds." What frac- 
 tional part of the yield were firsts, and what fractional part were 
 seconds ? 
 
 4. The apple tree referred to in Ex. 3 was sprayed the year 
 following, and that year it produced 10 i bu. of which 9^ bu. 
 were firsts and the remainder seconds. What fractional part of 
 the yield were firsts ? What part were seconds ? 
 
 5. If the apples referred to in Exs. 3 and 4 were sold at S1.20 
 per bushel for firsts and 70/ a bushel for seconds, what was the 
 value of the spraying ? 
 
 6. It is estimated that a quail in one year eats 28/ worth 
 of grain and saves $1.68 worth of grain by destroying insects 
 and weeds. What is the value of a pair of quails to the farmer 
 annually, not counting the value of the brood ? 
 
 7. An undrained field produced 24 bu. of grain per acre, and 
 after being drained it produced 33 bu. per acre. What was the 
 fractional increase ? What was the value of the increase if the 
 grain sold for 55i-/ per bushel ? 
 
 8. A flock of hens averaged 78 eggs each per year. What 
 would be the value to the farmer of introducing a better breed 
 of hens that would produce 120 eggs each per year, if he kept 
 a flock of 40 hens, and received 24/ per dozen for the eggs ? 
 
 9. If 6 A. of unfertilized land produced 275 bu. of corn, and 
 if fertilized, it would have produced 350 bu., what would the 
 farmer have gained by fertilizing the land if the corn was sold 
 for 68/ per bushel, and the fertilizer cost S 24 per ton, and 400 lb. 
 were used on each acre ? 
 
COMMON FRACTIONS l37 
 
 WRITTEN REVIEW TEST 
 (Time, approximately, forty minutes) 
 
 1. A, B, and C hire a pasture for $ 81. A puts in 6 cows for 
 4 mo. ; B, 6 cows for 6 mo. ; and C, 6 cows for 5 mo. "What sum 
 should each pay ? 
 
 2. A man owned |- of a tract of land ; he sold |- of his share 
 for $14,504.46. At that rate, what was the value of his original 
 share ? What was the whole tract worth ? 
 
 3. The owner of a house received a net yearly income from 
 rental of S408.90, after paying the following : insurance, $64.20 ; 
 taxes, $74.50 ; repairs, $28.40. What was the monthly rental? 
 
 4. A man drew i of his money from the bank and then paid 
 bills of the following amounts: $12.50, $18.25, and $7.50; he 
 then had left in cash $11.75. What sum had he in the bank 
 before drawing the check ? 
 
 5. A man placed a mortgage on his house and lot for $2967. 
 The lot cost $2720 ; the improvements, $260.50; and the dwell- 
 ing, $5920.50. The mortgage was what fractional part of the 
 total value of the property ? 
 
 6. At the end of a season a dealer sold a machine for $64, 
 after reducing the marked price ^. If he still gained ^- of the 
 cost, what was the first cost? The marked price was what 
 fraction above the cost price ? 
 
 7. From dictation, write results for the following: -^ of 
 25J; J of 26J; i of 361 ; i of I71 ; 1 of 42|; | of 28J; ^\ of 
 221 . 1 of 641 ; 1 of 50 1; J^ of 35t ; J^ of 501. 
 
 8. A merchant closed his business under the following con- 
 ditions: resources, $22,455.20; liabihties, $33,682.80. What 
 fractional part of his debts can he pay ? If he owes James S. 
 Brown $202.50, how much will Brown receive in settlement? 
 
 9. A, B, and C are partners in a mercantile business in 
 which A has invested $9180 ; B, $6120 ; and C, $3060. At the 
 end of 1 yr. they divided a gain of $3060.90. If each partner 
 received of the gain according to his fractional part of the 
 investment, how much did each receive ? 
 
CHAPTER X 
 
 ALIQUOT PARTS 
 
 171. An aliquot part of a number is a part that is 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 $l? in |J? in S^? in |1? 
 
 2. What aliquot part of $1 is 25^? 50^? 6|^? 121^? 
 
 3. Read aloud the following, supplying the missing terms : 
 16x50)2^ = 16x|i^iof$16r 16x25y = 16x$i = ^ofil6; 
 
 16xl2l^=16x$ = of 116; 16x61^=16x8 
 
 = of $16. 
 
 4. Give a short method for finding the cost when the quan- 
 tity is given and the price is 50^; 25^; 12^^ ; 6^^. 
 
 5. What is the cost of 160 yd. of dress goods at $1? at 50^? 
 at 25^? at 121^? at 6^^? 
 
 6. How many cents in $1? in $1? in $^-^? in $^^5? in $|? 
 in$^? in$Jo? 
 
 7. What aliquot part of $1 is 331^? 16f^? 8^^? 62^? 
 14f^? 20^? 10^? 
 
 8. Read aloud the following, supplying the missing terms : 
 
 140xl4f^ = 140 X i| = | of $140; 90 x 6|^ = 90 x $ 
 
 = of 890; 90x20^ = 90x8 = of 890. 
 
 9. Read aloud the following, supplying tlie missing terms : 
 
 240 X 33iy = 240 X 8 = | of 8240 ; 240 x 16f = 240 x 
 
 8J = of 8240; 240x12^^ = 240x8 = of 8 240. 
 
 10. Give a short method for finding the cost when the quan- 
 tity is given and the price is 33 J ^ ; 16|^; 81^; 6f^; 14f^. 
 
 11. Find the cost of 960 yd. of cloth at 33J^; at 16|^; at Sy. 
 
 138 
 
ALIQUOT PARTS 139 
 
 ORAL EXERCISE 
 
 State the cost of: 
 
 1. 240 1b. tea at 50/; at 331^; at 25^. 
 
 2. 3601b. coffee at 331^; at 25^; at 20^; at 12J^. 
 
 3. 720 gal. cider at 6^^; at 6|^; at 10^; at 12|-^. 
 
 4. 2400 doz. eggs at 12^^; at 16|^; at 20^; at 25^. 
 
 5. 2400 yd. prints at SJ^; at 6|^ ; at 6|^; at 121^. 
 
 6. 960 yd. cotton at 61^; at 81^; at6fj^; at 10^; at 121^. 
 
 7. 2040 yd. plaids at 50^; at 331^; at25j^; at 20^; at 16f ^. 
 
 8. 480 1b. lard at 81^; at6J^; at 121)^; at 16|^; at 10^. 
 
 9. 3600 lb. raisins at 12|-^; atl6|^; at 20^; at 25^; at 33^^. 
 
 10. 480 yd. lining at 81^; at6|^; at 10^; at 121^; at6|^. 
 
 11. 4200 yd. Silesia at W; at 20)^ ; at 12^^: at 16f ^ ; at 14f ^. 
 
 12. 1500 yd. plaids at $1; at 50^; at 33ij^; at 25^; at 20^. 
 
 13. 420 yd. stripe at 10^; atl2i^; at 14|y ; at 16f ^; at 25ji^. 
 
 14. 120 yd. gingham at 8i^; at6|/; at6|^; at loV; at 121^. 
 
 15. 1240 yd. wash silk at 25^; at 50^; at 331 ^; at 20^. 
 
 16. At the rate of 3 for 50^, what will 27 handkerchiefs 
 cost? 
 
 17. At 33i^ per half dozen, what will 12 doz. handkerchiefs 
 cost? 17 doz.? 25 doz.? 7 J 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 121 yd. of silk at 96 ^ per yard? 
 Suggestion. The cost of 12| yd. at 9Qj^ = 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 11.72 per yard. 
 Suggestion. The cost of 25 yd. at$ 1.72 (172^) = the cost of 172 yd. at 2bf, 
 
 3. Find the cost of : 
 
 a, 25 yd. at 16^. e. 6J lb. at 32^. e. 25 yd. at 84^. 
 
 b, 12|^ yd. at 48^. d. 12Jlb.at80^. /. 121 yd. at 11.75. 
 
140 
 
 COKCISE BUSIKESS AEITHMETIC 
 
 Table of Aliquot Parts 
 
 Nos. 
 
 I's 
 
 i's 
 
 Fs 
 
 tVs 
 
 fs 
 
 •rs 
 
 tV's 
 
 I'^'S 
 
 i's 
 
 Iter's 
 
 1 
 
 .50 
 
 .25 
 
 .121 
 
 .061 
 
 .331 
 
 .161 
 
 .081 
 
 .061 
 
 .20 
 
 .10 
 
 10 
 
 5. 
 
 n 
 
 H 
 
 .62^ 
 
 H 
 
 If 
 
 .83^ 
 
 .66f 
 
 2. 
 
 1. 
 
 100 
 
 50. 
 
 25. 
 
 m 
 
 n 
 
 33^ 
 
 16f 
 
 8^ 
 
 6f 
 
 20. 
 
 10. 
 
 1000 
 
 500. 
 
 250. 
 
 125. 
 
 62^ 
 
 333^ 
 
 166|- 
 
 83^ 
 
 66f 
 
 200. 
 
 100. 
 
 WRITTEN EXERCISE 
 
 In the three problems following make all the extensions mentally/. 
 
 1. Without copying, find quickly the total cost of : 
 84 lb. tea at 50^. 6J lb. tea at 64^. 
 
 75 lb. tea at 331^. 25 lb. cocoa at 52^. 
 
 72 lb. cofPee at 25^. 121 lb. cocoa at 48^. 
 
 84 lb. coffee at 331^. . 860 lb. codfish at 6|^. 
 
 25 lb. coffee at 28 j2^. 66 lb. crackers at 8^^. 
 
 88 lb. candy at 121 jz^. 25 lb. chocolate at 36^. 
 
 24 lb. tapioca at 6J^. 25 cs. horseradish at 64^. 
 
 2. Without copying, find quickly the total cost of : 
 
 25 yd. silk at 84^. 
 12| yd. silk at dQfl. 
 750 pc. lace at 6f ^. 
 112 yd. ticking at 6Jj^. 
 210 yd. plaids at 33^^. 
 128 gro. buttons at 12^^. 
 68 yd. lansdowne at 50^. 
 
 77 yd. duck at 14f ^. 
 
 6| gro. buttons at 32^. 
 
 155 yd. cheviot at 20)^. 
 
 96 yd. gingham at 8^^. 
 
 84 yd. shirting at 121 ^. 
 
 25 doz. spools thread at 25^. 
 
 168 yd. striped denim at S^ ^. 
 
 3. Without copying, find quickly the total cost of 
 
 25 bu. corn at 64^. 
 25 bu. corn at $0.72. 
 121 bu. oats at $0.36. 
 25 bu. beans at $2.80. 
 121 bu. wheat at $1.04. 
 12Jbu. millet at $1.24. 
 25 bu. clover seed at $3.60. 
 50 bu. clover seed at $3.75. 
 
 25 bu. corn at $0.84. 
 25 bu. corn at $0.44. 
 25 bu. oats ^t $0.35. 
 12Jbu. rye at $1.04. 
 6Jbu. wheat at $1.20. 
 6Jbu. wheat at $1.12. 
 25 bu. timothy seed at $2.40. 
 50 bu. timothy seed at $2.75. 
 
ALIQUOT PAETS 141 
 
 ORAL EXERCISE 
 
 1. Multiply by 10: 4; 15; .07 ; 8^; $1.12; 124.60; $12,125. 
 
 2. Multiply by 100: 3; 17; .09; 12^; $1.64; $21.17. 
 
 3. Multiply by 1000: 7; 29; .19; 15^; $1.75; $23.72. 
 
 4. What aliquot part of $10 is $2.50 ? Find the cost of 16 
 articles at $10 each; at $2.50 each. 
 
 5. Find the cost of 84 bu. of wheat at $1.25. 
 
 Solution. $1.25 is I of $10. 84bu. at $10 = $840; ^ of $840 = $106. 
 
 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^; $1.66|. 
 
 8. Find the cost of 168 yd. of cloth at $1.25; at $2.50; 
 at $3,331; at $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 121; by6i; by 331; by 81. 
 
 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? 166|? 200? 100? 831? 66|? 
 
 14. Formulate a short method for multiplying a number 
 by 250. 
 
 Solution. Since 250 = ■^°^°-^, 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 IJ ; by 121; by 125; by 621 
 
 18. Multiply 240 by 31; by 1|; by 331; by 16f ; by 338f 
 
142 CONCISE 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, I 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 lb. sugar at 21^. 
 
 Solution. 2^^ is I of 10^. The cost of 440 lb. at 10^ = $44 ; but the price is 
 2Jj^, 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 1 ,^. 
 
 Solution. 1^^ = | of 10^ ; hence, point off one place in the quantity and take 
 I of the result. 
 
 23. Give a short method for finding the cost when the quan- 
 tity is given and the price is 2^^; S^f^ ; IJ^. 
 
 24. Find the cost of 160 lb. at 2^; at l^^; at 2^; 
 at 1|^. Also of 240 lb. at each of these prices. 
 
 25. Find the cost of 2400 lb. at 2i ^; at 1^^; at 3^^; 
 at 1|^. Also of 360 lb. at each of these prices. 
 
 ORAL EXERCISE 
 Bt/ inspection find the cost of : 
 
 1. 25 lb. tea at 54^. 16. 1\ yd. silk at 88f^. 
 
 2. 25 lb. tea at 331^. 17. 64 pc. lace at $1.25. 
 
 3. 125 lb. tea at 64^. is. 125 yd. silk at 11.12. 
 
 4. 6^ A. land at $112. 19. 1250 bbl. beef at $24. 
 
 5. 25 T. coal at $8.40. 20. 78 yd. velvet at $2.50. 
 
 6. 25 T. coal at $5.20. 21. 2^ bu. potatoes at 96^. 
 
 7. 18 T. coal at $6.25. 22. 640 bu. apples at 871^. 
 
 8. 164 A. land at $25. 23. 840 yd. prints at 16f ^. 
 
 9. 72 T. coal at $6.25. 24, 121 bu. potatoes at 64^. 
 
 10. 250 yd. silk at 88 ^. 25. 84 bookcases at $12.50. 
 
 11. 250 yd. silk at 96^. 26. 810 bbl. pork at $12.50. 
 
 12. 25 pc. lace at $6.60. 27. 125 yd. crepon at $3.60. 
 
 13. 250 yd. silk at $1.12. 28. 12^ yd. cheviot at $1.04. 
 
 14. 192 A. land at $12.50. 29. 24 oak sideboards at $125. 
 
 15. 165 gro. buttons at 33^^. 30. 12^ yd. gunner's duck at 48 A 
 
ALIQUOT PARTS .143 
 
 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 lb. at 10 /. 2500 lb. at 64 1 24 lb. at 11 ^. 
 
 310 lb. at 20 ^. 1600 lb. at 25 ^. 48 lb. at 2i ^. 
 
 100 lb. at 14 ^. 1893 lb. at 31 ^. 21 lb. at 96 ^. 
 
 1000 lb. at 27 ^. 2500 lb. at 14 ^. 125 lb. at 24^. 
 
 1000 lb. at 41 i. 1400 lb. at 25 ^. 192 lb. at 31 ^. 
 
 1250 lb. at 44 ^. ' 1250 lb. at 88 ^. 88 lb. at 121 f, 
 
 2. Without copying, find the total cost of : 
 
 88 yd. at 1 1 /. 174 yd. at 10 p. 24 yd. at 12 ^. 
 
 72 yd. at 31 ^. 123 yd. at 11 ^. 78 yd. at 3J ^. 
 
 104 yd. at 2i ^. 127 yd. at 11 ^. 165 yd. at 20 ^. 
 
 480 yd. at 61 ^. ' 246 yd. at 25/. 114 yd. at 6f /. 
 
 360 yd. at 81 ^. 1712 y^j. at 10 /. 1280 yd. at 6^ /. 
 
 121 yd. at 11 /. 178^ yd. at 10 /. 192 yd. at 331/. 
 
 3. Copy and find the total cost of : 
 
 450 lb. at 11 /. 249 lb. at 25 /. 6J lb. at 88 /. 
 
 820 lb. at 11 /. 240 lb. at 31 /. 92 lb. at 21 /. 
 
 1200 lb. at 41 /. 200 lb. at 3| /. 121 lb. at 24 /. 
 
 1400 lb. at 61 /. 450 lb. at 6f /. 18 lb. at 41 /. 
 
 7961 lb. at 50 ^. 791 ib. at 40 /. 125 lb. at 18 /. 
 
 1293 lb. at 30 ^. 78i lb. at 50 /. 648 lb. at 61 /. 
 
 1480 lb. at 40 /. 750 lb. at 331 ^. 1900 lb. at 4 1 /. 
 
 4. Copy and find the total cost of : 
 
 750 gal. at 81 /. 99 gal. at 30 /. 360 gal. at 5 /. 
 
 488 gal. at 6| /. 60 gal. at 6| /. 625 gal. at 64 /. 
 
 640 gal. at 61 /. 50 gal. at 76 /. 810 gal. at IJ /. 
 
 194 gal. at 50 /. 25 gal. at 74 /. 920 gal. at 21 /. 
 
 176 gal. at 25 /. 121 gal. at 88 /. 165 gal. at 6| /. 
 
 280 gal. at 121 ^. 79 gal. at 331 ^. 240 gal. at 621 ^. 
 
 720 gal. at 331 ^. 20 gal. at $1.79. 666 gal. at 66| /. 
 
 366 gal. at 16f ^. 6J gal. at $1.96. 1680 gal. at 16|/. 
 
144 CONCISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. How much less than il is 75^? what fractional part 
 of f 1 less? 
 
 2. Find the cost of 144 pc. of lace at 15 P per piece. 
 
 Solution. At $ 1 per piece the cost would be f 144 ; but the cost is not 1 1 
 but J less than $ 1. Deducting J 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 J of itself = $ 930, the 
 required result. 
 
 4. Formulate a rule for multiplying a number by .75; by 
 7|; by 75; by 750. 
 
 5. How much more than $1 is $1.12|? What fractional 
 part of fl more? 
 
 6. Find the cost of 84 yd. of silk at |1.16| per yard. 
 
 Solution. At $ 1 per yard, the cost would be $84 ; but $1.16| 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|; 
 $1.33i; $11.25; f 112.50. 
 
 8. How much less than $1 is 87|^^? what fractional 
 part of f 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 87^ yd. at 64^ with the cost of 
 64 yd. at 87^^. 
 
 ORAL EXERCISE 
 
 State the cost of: 
 
 1. 24 yd. at 15^. 7. 87^ yd. at $2.88. 13. 270 yd. at 111^. 
 
 2. 75 yd. at 24^. a 25 yd. at 4^. 14. 144 yd. at 11^^. 
 
 3. 192 yd. at 871^. 9. 28yd.at75^. 15. Iliyd.atl8^. 
 
 4. 240 yd. at 83^^. lo. 27 yd. at 75^. 16. 1125 yd. at 64^. 
 
 5. 871 yd. at $2.48. u. 75 yd. at 84^. 17. 1125 yd. at 32 f^. 
 
 6. 176 yd. at 11.121 12. 75 yd. at 16)z^. 18. 1125 yd. at 48 )Z^. 
 
ALIQUOT PARTS 
 
 145 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the total of the costs called for in problems 1-15 in 
 the oral exercise at the top of page 139. 
 
 2. Find the total cost of the items in the oral exercise at the 
 bottom of page 142; of the items in the oral exercise at the 
 bottom of page 144. 
 
 3. Find the total cost of : 
 84 yd. at 7^. 98 yd. at 9^. 
 
 1121 yd. at 5^. 79 yd. at 11^. 
 
 112|- yd. at 6^. 17 yd. at 16^. 
 
 4. Find the total cost of : 
 71 yd. at 22^. 85 yd. at 30^. 
 31 yd. at U^, 17 yd. at 25^. 
 82 yd. at 88^. 121 yd. at 39^. 
 71 yd. at 72^. 250 yd. at 64^. 
 
 5. Find the total cost of : 
 192 lb. at 31^. 167 lb. at 12J^. 
 3841b. at 61^. 184 lb. at 371^. 
 3781b. at 6|^. 2164 lb. at 2i^. 
 1491b. at 61^. 1369 lb. at 21^. 
 
 6. Copy and find the amount of the following bills, less 3 % : 
 
 a, 
 
 Kochester, N.Y., Aug. 2, 19 
 
 Mr. C. G. Garlic 
 
 North Rose, N.Y. 
 
 To Smith, Perkins & Co., Dr. 
 
 Terms : cash, less 3 %. 
 
 72yd. at 75^. 
 87 J yd. at 88^. 
 320 yd. at 11^. 
 
 30 yd. at 7^^. 
 24 yd. at SJ^. 
 56 yd. at 83^^. 
 124 yd. at 11.121 
 
 1151f lb. at 10^. 
 17211 lb. at 15^. 
 29111 lb. at 33 J ^. 
 2706 1b. at 331^. 
 
 330 lb. Granulated Sugar 
 
 6|<? 
 
 32 ' 
 
 ' Butter 
 
 22^ 
 
 64 ' 
 
 ' Cheese 
 
 16|^ 
 
 75 ' 
 
 ' Young Hyson Tea 
 
 24;^ 
 
 155 ' 
 
 ' Dried Apples 
 
 Sf 
 
 300 ' 
 
 < Brown Sugar 
 
 ^\f 
 
 60 * 
 
 ' Oolong Tea 
 
 h\f 
 
 125 ' 
 
 ' Rio Coffee 
 
 28^ 
 
 250 ' 
 
 ' Mocha Coffee 
 
 24 j^ 
 
146 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Buffalo, N.Y., Aug. 5, 19 
 Mr. George A. Collier 
 
 Savannah, N.Y. 
 
 Bought of George H. Buell & Co. 
 
 Terms: cash, less ,^%. 
 
 72 pr. Boys' Hose 12 1^ 
 
 18 doz. Linen Handkerchiefs 2.50 
 
 18 " Lace Handkerchiefs 3.33^ 
 
 78 yd. Silk Velvet 3.33^ 
 
 75 pc. Black Ribbon 28^ 
 
 347 yd. Pontiac Seersucker Q\^ 
 
 186 " Washington Cambric 12^^ 
 
 ORAL EXERCISE 
 
 1. At 33^ ^ per pound, how many pounds of coffee can be 
 bought for $12? 
 
 Solution. .33^ = $ | ; 3 pounds can be bought for $ 1 ; then, 12 x 3 lb. 
 = 36 lb., 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^^; 6f ^; 
 16|^. 
 
 4. Formulate a short method for dividing any number by 
 125. 
 
 Solution. 125 is I 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, 
 i\t — T^' Therefore, multiply by 8 and move the decimal point three 
 places to the left. 
 
 5. Give a short method for dividing by 6J. 
 
 Solution. Q\ = r^oi 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 
 
 147 
 
 6. Give a short method for dividing a number by 12J ; by 
 16|; by 83J ; by 6| ; by 66f ; by 333J; 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 1144? for $192? for $240? for |780? for $1260? 
 for $360? for $1350? for $810? 
 
 9. At $7.50 per dozen, how many dozen men's gloves can 
 be bought for $1440? 
 
 Solution. $7.50 + ^ of itself = -$10. To divide by 10 is to point off one 
 place to the left. $ 1440 -f i of itself = $1920 ; $ 1920 -r- $ 10 = 192, the number 
 of dozen. 
 
 10. State a short method for dividing a number by 7 J ; by 
 75; by 750. 
 
 ORAL EXERCISE 
 
 Find the quantity : 
 
 
 Price per 
 
 
 Price PER 
 
 Cost 
 
 Yard 
 
 Cost 
 
 Pound 
 
 1. $65 
 
 331^ 
 
 7. $75 
 
 6|^ 
 
 2. $250 
 
 25^ 
 
 8. $12 
 
 If^ 
 
 3. $120 
 
 6^^ 
 
 9. $25 
 
 m^ 
 
 4. $215 
 
 ^^ 
 
 10. $38 
 
 -^¥ 
 
 5. $126 
 
 12|^ 
 
 11. $125 
 
 fl.25 
 
 6. $125 
 
 20^ 
 
 12. $420 
 
 ISi*' 
 
 WRITTEN EXERCISE 
 
 Find the quantity : 
 
 
 
 Price per 
 
 
 
 Price per 
 
 
 Cost 
 
 Yard 
 
 
 Cost 
 
 Bushel 
 
 1. 
 
 $570.00 
 
 75^ 
 
 6. 
 
 $1721.00 
 
 33jy 
 
 2. 
 
 $612.00 
 
 13^ 
 
 7. 
 
 $1842.50 
 
 26^ 
 
 3. 
 
 $274.50 
 
 H^ 
 
 8. 
 
 $1785.00 
 
 Sl^fl 
 
 4. 
 
 $281.50 
 
 12|^ 
 
 9. 
 
 $2142.00 
 
 33|^ 
 
 5. 
 
 $864.50 
 
 12|^ 
 
 10. 
 
 $2720.50 
 
 16|^ 
 
148 
 
 CONCISE BUSINESS AEITHMETIG 
 
 REVIEW EXERCISE 
 
 This exercise may be used in a number of different ways, some of which 
 are suggested below. 
 
 1. One student may make the oral extension, using the first quantity, 
 60 yd., by each price in column 1 ; a second student may use the same 
 quantity and make the extension by each price in column 2, and so on for 
 the ten lists. 
 
 2. Each student in the class may take the same quantity and make the 
 extension by each price in column 1, and foot the extensions. Compare 
 results. Such an exercise should occupy one minute. This work may be 
 continued for ten or fifteen minutes daily, as the instructor desires, a different 
 quantity being used for each minute. 
 
 1 
 
 s 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 50/ 
 
 25/ 
 
 66f/ 
 
 60/ 
 
 25/ 
 
 61/ 
 
 50/ 
 
 75/ 
 
 $1.50 
 
 $1.33J 
 
 20/ 
 
 62J/ 
 
 6|/ 
 
 87i/ 
 
 20/ 
 
 16f/ 
 
 90/ 
 
 8J/ 
 
 $1.25 
 
 $1.66§ 
 
 12i/ 
 
 33J/ 
 
 75/ 
 
 sn/ 
 
 60/ 
 
 30/ 
 
 10/ 
 
 371/ 
 
 $1.12i 
 
 $1.20 
 
 161/ 
 
 30/ 
 
 8J/ 
 
 6J/ 
 
 121/ 
 
 66f/ 
 
 e2i/ 
 
 80/ 
 
 $1.10 
 
 $1.16§ 
 
 90/ 
 
 10/ 
 
 40/ 
 
 80/ 
 
 331/ 
 
 6|/ 
 
 40/ 
 
 871/ 
 
 $1.75 
 
 $1.30 
 
 1. Find the cost of 
 
 a. 60 jd. 
 80 yd. 
 40 yd. 
 
 h. 72 yd. 
 50 yd. 
 44 yd. 
 
 2. Find the cost of : 
 
 a. 24 yd. 
 16 yd. 
 32 yd. 
 
 h. 78 yd. 
 69 yd. 
 81yd. 
 
 3. Find the cost of 
 
 a, 100 yd. 
 120 yd. 
 150 yd. 
 
 5. 108 yd. 
 135 yd. 
 144 yd. 
 
 90 yd. 
 20 yd. 
 25 yd. 
 
 e. 12 yd. 
 36 yd. 
 42 yd. 
 
 160 yd. 
 180 yd. 
 128 yd. 
 
 d. 75 yd. 
 84 yd. 
 54 yd. 
 
 d. 92 yd. 
 21yd. 
 46 yd. 
 
 d. 200 yd. 
 240 yd. 
 300 yd. 
 
 e. 48 yd. 
 96 yd. 
 64 yd. 
 
 e. 15 yd. 
 18 yd. 
 10 yd. 
 
 e. 320 yd. 
 400 yd. 
 860 yd. 
 
ALIQUOT PAETS 
 
 WRITTEN REVIEW EXERCISE 
 
 149 
 
 Name 
 
 Quan- 
 tity 
 
 PRICE.S 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Boucle Stripe 
 
 yd- 
 
 $0.10i 
 
 $0.11 
 
 $0.10 
 
 $0,111 
 
 $0.12 
 
 $0.12^ 
 
 Dress Silks 
 
 yd- 
 
 1.20 
 
 1.25 
 
 1.331 
 
 1.371 
 
 1.40 
 
 1.50 
 
 English Serge 
 
 yd- 
 
 1.331 
 
 1.30 
 
 1.35 
 
 1.25 
 
 1.37i 
 
 1.45 
 
 Fancy Gingham 
 
 yd. 
 
 .061 
 
 .06 
 
 .061 
 
 .07 
 
 .07^ 
 
 .071 
 
 Fancy Plaids 
 
 yd. 
 
 .311 
 
 .32 
 
 .33^ 
 
 .35 
 
 .34 
 
 .37i 
 
 Gunner's Duck 
 
 yd. 
 
 .14 
 
 .15 
 
 .IH 
 
 .16 
 
 .17 
 
 .17i 
 
 Percale Shirting 
 
 yd. 
 
 .07 
 
 .07^ 
 
 .08 
 
 .08^ 
 
 .09 
 
 .09^ 
 
 Scotch Cheviot 
 
 yd. 
 
 .39 
 
 .40 
 
 .37i 
 
 .45 
 
 .44 
 
 .48 
 
 Taffeta Silk 
 
 yd. 
 
 .871 
 
 .85 
 
 .90 
 
 .88 
 
 .921 
 
 .95 
 
 Wash Silk 
 
 yd. 
 
 .30 
 
 .37i 
 
 .40 
 
 .35 
 
 .42 
 
 .4H 
 
 Prepare each of the following invoices in correct form, omit the 
 heading, and find the value hy each price list. 
 
 5. 
 
 22 yd. Boucle Stripe 
 27 yd. English Serge 
 56 yd. Percale Shu^ing 
 48 yd. Wash Silk 
 
 2. 72 yd. Dress Silk 
 104 yd. Scotch Cheviot 
 64 yd. Taffeta Silk 
 60 yd. Gunner's Duck 
 
 36 yd. Fancy Gingham 
 88 yd. Scotch Cheviot 
 92 yd. Wash Silk 
 20 yd. Boucle Stripe 
 80 yd. Gunner's Duck 
 
 4. 96 yd. Fancy Plaids 
 36 yd. English Serge 
 100 yd. Taffeta Silk 
 70 yd. Percale Shirting 
 90 yd. Wash Silk 
 
 72 yd. Boucle Stripe 
 56 yd. Wash Silk 
 50 yd. Fancy Plaids 
 80 yd. Dress Silk 
 70 yd. Gunner's Duck 
 
 6. 84 yd. Taffeta Silk 
 QQ yd. Fancy Gingham 
 84 yd. Scotch Cheviot 
 ^Q yd. EngHsh Serge 
 45 yd. Percale Shirting 
 
CHAPTER XI 
 
 BILLS AND ACCOUNTS 
 BILLS 
 
 172. 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 
 hill; 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 hill or an invoice. 
 
 173. 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 da. Telephone, Main 167 
 
 3 
 
 10 
 5 
 
 bbl. Rolled Oats $6.25 
 
 " Gold Medal Flour 6.50 
 
 bx. Wool Soap 3.10 
 
 18 
 65 
 15 
 
 75 
 
 00 
 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 
 
 151 
 
 2. Groceries 
 
 Boston, Mass., Nov. 12, 19 
 
 Messrs. E. 0. Sherman & Co. 
 
 Charlestown, Mass. 
 
 Bought of S. S. PIERCE COMPANY 
 
 Terms 50 da.; 5fo 10 da. 
 
 10 Red Label Hams 146 lb. $0.,23 $33.58 
 20 mats Java Coffee 1500 ^ .25 375.00 
 
 12 6-lb. tins Mustard 72 " .36 25.92 
 15 6-lb. tins Cocoa 90 " .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. 
 
 3. 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 $1.33 J. 
 
 ^ew york. 
 
 
 19- 
 
 bought of J^/ie Eureka jrtareiL 
 
 e. 
 
 ompanif 
 
 ZS 
 
152 
 
 CONCISE BUSINESS ARITHMETIC 
 
 4. Wholesale Dry Goods 
 
 ^ >o CHICAGO. /^Z^^^4^. Ar; 10 
 
 Bought of MARSHALL FIELD & CO. 
 
 Franklin Street and Fifth Avenue 
 
 j^i. ^J ^/' ^^^ ^o' ^s.'- s-gg. 
 
 JJLJL 
 
 J-2:. 
 
 ^ 
 
 3 Z^ ^^^ JA/'- 3e?' ^O' 
 
 J6^ 
 
 ^ 
 
 2^ 
 
 ^ 
 
 /^^ 
 
 1J=. 
 
 
 ^o Jf ^Z. ^o ¥^i. ^o 
 ¥'i. ^/ ACi. ^/ <^^ iA3 
 
 A^jT ^^{ ZA/ 
 
 ZJL 
 
 /3X 
 
 ±2^ 
 
 !/ ^3 %^2. 4^V ^S Jf 
 
 /^7 
 
 L2=. 
 
 ' y/ •» Zl /I U-/0 ZAO //..^ ^Of^ 
 
 ¥f t J // 2^ 
 
 /rC^TJL 
 
 ^2. ¥0 4^ ^O ^J 3^^ 
 ^/ ^3 ^C ^^ ¥^ ^^^ 
 
 jik 
 
 j^ 
 
 ^ 
 
 /.^^ 
 
 X 
 
 -fo^^^r^y^^ 
 
 l^y^Z^ii^-p^.^1^4^^^^ 
 
 37 ¥/ 3f^ A^/ ^ 37 4<a 
 
 Z^^ // i 
 
 JLJL 
 
 /^/ 
 
 ~i^<^rc//Arl^.^t?-7^7:6- 
 
 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. Manufactueer'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 188) are allowed are arranged as shown in this bill. 
 
BILLS AND ACCOUNTS 
 
 JQetogorlt, Oct. 10, 19 
 
 JHessrs. J. E. Whiting & Co. 
 
 Boston, Mass. 
 
 25ougf)t of S^o^n^on 25tD^., ^on$ a Co. 
 
 Ccrmfi Net 30 da. 
 
 153 
 
 721 
 
 n 
 
 doz. Neckwear 
 
 $4.50 
 
 6 
 
 75 
 
 
 
 1026 
 
 1 
 
 2 
 
 
 27.00 
 
 13 
 
 50 
 
 
 
 1025 
 
 n 
 
 
 27.50 
 
 41 
 
 25 
 
 
 
 1020 
 
 3 
 4 
 
 
 9.00 
 
 6 
 
 75 
 
 
 
 923 
 
 2| 
 
 
 18-00 
 
 45 
 
 00 
 
 
 
 1015 
 
 n 
 
 
 24.00 
 
 42 
 
 00 
 
 
 
 
 155 
 
 25 
 
 
 
 
 Less 255 
 
 
 3 
 
 11 
 
 152 
 
 14 
 
 
 
 1 
 
 
 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. 
 
 BOSTON,. 
 
 M^.AA^ ^ .U . c^^^^^f^^^ 
 
 6r^Z ^ Z3, 19 . 
 
 Ar^^. 
 
 '.^n^f^l^^:^-?^. 
 
 Bought of E. M. PRAY, SONS & CO. 
 
 AT^ Manufacturers of Fine Furniture 
 
 TERMS //C^Jff.^-r^^ 
 
 AJIL 
 
 . ^ 
 
 '^^^.^l.d^^jr^^^YT-r^j'^^ 
 
 JJli 
 
 /2-3 
 
 7^- 
 
 
 A2^ 
 
 JJL 
 
 ^ 
 
 79fayA^fr7^^sz^^^X^^^^. 
 
 Z^ 
 
 ^ 
 
 '>ry-7^y7.^f:7^2^. 
 
 f y^^ /7^ 
 
 /7^ 
 
 >r:T^^^ 
 
 /a^ 
 
 ZAA 
 
 s^ 
 
 'J37 
 
 ^^^^ U^S-t ^yA 
 
 J^ 
 
 /o 
 
 ' J^ ± 
 
 ?^ 
 
154 
 
 CONCISE BUSINESS ARITHMETIC 
 
 7. Wholesale Coal 
 F. H. OSBORN & CO. 
 
 SHIPPERS OF 
 
 Anthracite, Bituminous, and Gas Coal 
 
 Sold 
 
 Temi£ 
 
 ana 
 
 Boston,. 
 
 .19_ 
 
 /^ Z ^^^^^^^V./Tg7^--^4^ ^^^^^ 
 
 '?^'7 rn n ^-V^^^^ 
 
 A^^So_ 
 
 lA^J2j2jtl!^^:=t^ 
 
 jjll 
 
 Ay 
 
 z^ . 
 
 ta^CPC 
 
 >r7-t^~£^ 
 
 jJH 
 
 vu 
 
 T-fyoo ^^^ ^.^^^J? 
 
 JA^ 
 
 l^ 
 
 7-^/ 
 
 ^^ 
 
 "/fe^ ^.^o^/-e.^-^^2''PC^^C''-y^ ^.^y?.^ 
 
 -^^=^n 4 7^^.re^ 
 
 ^^^r^ 
 
 The above is the form of bill generally used for wholesale transactions 
 in coal. It is called a receipted bill, and shows that the coal has been paid for. 
 
 8. Retail Coal 
 
 CermB- 
 
 
 T 
 
 JL 
 
 2 -T;^777^ <7^-A<:^;>^r7VJ^'-^^^^;>.g:7^ 
 
 ^j^ff-z/^Ao i<jj>^- ^/l^ Faaff#- ^^ 
 
 J=^ 
 
 2^ 
 
 IjL 
 
 2. -i>r?~x:?^^ ■^^^<f'^yy^^..^y-z^yL 
 
 /^JS'fP- 2/A^(7 (,a^o-2./A^^ /-^g^/^# /i^- 
 
 2.^ 
 
 J-g 
 
 ^o 
 
 /^^r</<~^ 
 
 ^m^^^l^^Z- 
 
 ^^-/.(/^U \ 
 
BILLS AKD ACCOUNTS 
 
 155 
 
 The foregoing bill shows a 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 
 
 t/joston, Nov. 6, f9 
 
 ^^ THE WENTWORTH = STRATTON CO. 
 
 Rochester. N.Y. 
 
 bought of (Osgood, fJ^ raver &* C^on 
 
 %/erms 60 da. net; 2% 10 da. 
 
 25 
 
 Dinner 
 
 Set, 130 pieces; viz. : 
 
 1 doz. 
 
 Plates. 8 in. 
 
 1 " 
 
 7 .. 
 
 1 " 
 
 6 " 
 
 1 •• 
 
 7 •• (deep) 
 
 1 '* Fruit Saucers, 4 in. 
 
 1 " 
 
 [ndividual Butters 
 
 1/12 doz. Covered Dishes. 8 i 
 
 1/12 ' 
 
 ' Casseroles, 8 in. 
 
 1/4 • 
 
 ' Dishes, 8 in. 
 
 1/12 ' 
 
 10 " 
 
 1/3 2 • 
 
 12 " 
 
 1/12 • 
 
 14 *• 
 
 1/6 * 
 
 • Bakers, 8 in. 
 
 1/12 ' 
 
 ' Sauce Boats 
 
 1/12 • 
 
 ' Pickles 
 
 1/12 • 
 
 ' Bowls 
 
 1/12 ' 
 
 Sugars 
 
 1/12 ' 
 
 Creams 
 
 1 
 
 Handled Teas 
 
 1/2 • 
 
 Coffees 
 
 1/12 ' 
 
 • Pitchers 
 
 1/12 • 
 
 ' Covered Butters and 
 
 
 Drainers 
 
 more Di 
 
 nner Sets as above 
 
 Crates 
 
 
 
 1 
 
 88 
 
 
 
 
 
 1 
 
 63 
 
 
 
 
 
 1 
 
 38 
 
 
 
 
 
 1 
 
 63 
 75 
 50 
 
 
 
 
 $12.00 
 
 1 
 
 00 
 
 
 
 
 13.50 
 
 1 
 
 13 
 
 
 
 
 2.50 
 
 
 63 
 
 
 
 
 4.50 
 
 
 38 
 
 
 
 
 7.50 
 
 
 63 
 
 
 
 
 10.50 
 
 
 88 
 
 
 
 
 4.50 
 
 
 75 
 
 
 
 
 4.00 
 
 
 33 
 
 
 
 
 3.00 
 
 
 25 
 
 
 
 
 2.00 
 
 
 17 
 
 
 
 
 6.00 
 
 
 50 
 
 
 
 
 2.79 
 
 2 
 
 23 
 00 
 
 
 
 
 2.33 
 
 1 
 
 17 
 
 
 
 
 6.00 
 
 
 50 
 
 
 
 
 9.00 
 
 
 75 
 
 19 
 
 07 
 
 
 19.07 
 
 
 
 476 
 
 495 
 
 7 
 
 75 
 82 
 50 
 
 
 
 
 
 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. 
 
 CB 
 
156 CONCISE BUSINESS AKITHMETIC 
 
 10. Lumber 
 Jhe 7{. w^. ^ickford 60. 
 
 SBosfon, >^Atass,, C t . 8 , /9 
 
 Sold to L . A . Hammond & Co . 
 
 Paterson, N.J. 
 
 ^erms Pgt . net cash; bal. in 5 da. less I2' 
 
 23,289 ft. 1 X 2j #1 N. C. Ceili 
 
 ng 
 
 $18.50 $430.85 
 
 3,520 " " 2 " " " 
 
 
 17.00 59.84 
 
 10,307 " i X 2l 1 " " " 
 
 
 13.50 139.14 
 
 1,690 " " 2 " " " 
 
 
 12.50 21.13 
 $650.96 
 
 Less freight (45,200 lb. 
 
 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 150. Increase the price of 
 each article 25;^ and then copy and find the amount of the bill. 
 
 2. Study the first model bill, page 151, 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 151, and then copy and 
 find the amount of it at the following prices : porcelain knobs 
 #8, $1,121; #16,^1.25; steelyards #64, $11; #17, $8.33J; 
 jack-planes #14, $6; #21, 16.25; #48, $6.75. 
 
BILLS AND ACCOUNTS 157 
 
 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 lb. raw mixed coffee at 
 29^; 25 lb. raw Pan-American coffee at 19/; 5 cartons Fowle's 
 entire-wheat flour at 39|/; |^bbl. Franklin Mills flour at $6.75; 
 J 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 $9.75, 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 152. 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, 521, 58^ 62, 38, 49, 51, 54, and 46^ yd., at 7| / ; 10 pc. 
 fine wool cheviot containing 58^, 42, 49, 51, 442, 45^ 43, 412^ 39, 
 and 42 yd., at $1.12J; 5 pc. cashmere containing 49^, 40^, 48^, 
 491, 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 153. 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. Omit the discount. 
 
 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 $1.66|; 15 
 pc. #1371 at $1,331; 15 pc. #624 at $4.371 ; 12 pc. #909 at 
 $L87l; 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 
 
158 CONCISE BUSINESS ARITHMETIC 
 
 10. Study the second model bill on page 153. Increase the 
 price of the articles marked 65 and 396, 25^ each, and diminish 
 the price of the other articles i2|^ 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; 21 #94 china closets at $2T.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. Terras: 30 da. The prices 
 are free on board Boston, and the shipper prepaid the freight, 
 134.50. Write the bill. 
 
 12. Study the first model bill on page 154. 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 154, 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 154. Make the price of the coal $6. 66 J. 
 
 16. Study the model bill on page 155. 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 doz. handled teas at 
 $1.85. Terms: 30 da. Cost of crate used in packing, $2; 
 cartage, 75/. Write the bill. 
 
BILLS AND ACCOUNTS 
 
 159 
 
 PAY ROLLS 
 
 PAY ROLL For th>. wi.^V ^nHin g ^-^^A^A /^ Tg 
 
 Y d^ a/r/^ . 
 
 ..£^ 
 
 >2^g^ 
 
 Ai 
 
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 ^m^ 
 
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 21. 
 
 ,:22^£.>d=^ 
 
 ^^£. 
 
 ij^-^^^ 
 
 ^■^/ 
 
 Z^ 
 
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 2^-. 
 
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 £^ 
 
 ^a^^Tf^ ^ ^-^^^^YYrf^KVr^ 
 
 W^.f,Z^2A^. 
 
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 2-/-^ 
 
 m^s7'4f7'^r7 ^fi /^fP"^ 
 
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 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 j^ay 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 160. 
 
 No 
 
 Bills 
 
 Coins 
 
 
 $20 
 
 $10 
 
 $5 
 
 $2 
 
 $1 
 
 mf 
 
 ^f 
 
 10^ 
 
 hf 
 
 \f 
 
 1 
 2 
 3 
 4 
 5 
 6 
 7 
 8 
 9 
 10 
 
 1 
 
 1 
 
 1 
 
 ■■■ 
 
 
 1 
 1 
 
 1 
 
 1 
 1 
 2 
 
 1 
 
 1 
 1 
 
 1 
 1 
 
 1 
 - 1 
 
 1 
 
 1 
 
 1 
 1 
 
 1 
 
 1 
 1 
 
 1 
 1 
 
 1 
 
 2 
 2 
 
 1 
 
 1 
 1 
 1 
 
 1 
 1 
 
 3 
 
 4 
 
 2 
 
 
 2 
 
 
 
 7 
 
 5 
 
 6 
 
 5 
 
 6 
 
 5 
 
 9 
 
160 
 
 CONCISE BUSINESS ARITHMETIC 
 
 FIRST NATIONAL BANK 
 
 Westfield, Mass. 
 
 PAY-ROLL MEMORANDUM 
 
 NELSON y CO. 
 
 require the following: 
 
 When the amount of the j)ay 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 
 memorandum. 
 
 * 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 bookkeeper can make a very accurate estimate 
 
 Pennies 'f 
 
 Nickels ^ 
 
 Dimes ^ 
 
 Quarters ....... t/" 
 
 Halves ^ 
 
 Dollars ^ 
 
 a's . 7 
 
 5's ^ 
 
 lo's 7 
 
 20's Z 
 
 / 
 
 3 
 S 
 
 /sy-/^ 
 
 Co 
 oo 
 
 ao 
 
 4^ oa^ 
 
 
 PAY ROLL 
 
 
 For the 
 
 week ending- 
 
 
 
 ?Ur^ 
 
 ^ 
 
 
 
 
 
 _I9 
 
 
 — 
 
 
 NAME 
 
 Time in hours 
 
 Tot.l 
 time 
 
 Rate 
 
 per 
 
 Amount 
 advanced 
 
 Amount 
 due 
 
 Bills and silver necessary 
 
 
 
 M 
 
 T 
 
 w 
 
 T 
 
 F 
 
 s 
 
 $20 
 
 $10 
 
 $5 
 
 P 
 
 V 
 
 50c 
 
 25c 
 
 lOc 
 
 5c 
 
 Ic 
 
 
 / 
 
 i^J^^^^. 
 
 <? 
 
 ^ 
 
 a 
 
 ^ 
 
 ^ 
 
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 r-^ 
 
 
 
 
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 ?. 
 
 
 
 
 
 
 
 
 7 
 
 
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 -72 
 
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 WRITTEN EXERCISE 
 
 1. Study the model pay roll, page 159, and find the amount of 
 it at the following wages per hour: #1, 18/ ; #2, 21|/; #3, 25/; 
 #4,35/; #5,331/; #6,35/; #7,37i^; #8,35/; #9, 27^/; 
 #10, 18|/. Make a change memorandum. 
 
BILLS AND ACCOUNTS 
 
 161 
 
 2. Study the model pay roll on page 160, and then find the 
 amount of it at the following wages per hour: #1, 50^; #2, 45^; 
 #3, 331^; #4, 35^; #5, 27|-^; #6, 371^; #7, 25^; #8, 331 J^; #9, 
 44|^; #10,22f^; #ll,22f^; #12, 14f ^; #13,121^; #14,30)^. 
 
 3. Make a pay roll memorandum from problem 2. 
 
 WRITTEN REVIEW EXERCISE 
 
 1. Find the amount of each of the following bills : 
 
 New York^ May 31, /p 
 
 ATessrs. Gray, Salisbury & Co. 
 
 Rochester, N.Y. 
 
 Bought of y. E. PAGE, SONS & CO. 
 
 Terms 
 
 ; net, 
 
 60 da.; 2% 10 da. 
 
 
 
 
 
 
 
 Cask 
 
 Pieces 
 
 Dksceiption op Aeticlbs 
 
 Yds. 
 
 Price 
 
 Items 
 
 Amount 
 
 #364 
 
 10 
 
 Velveteen 
 421 40 40 46 38i 
 40 42 42 41 39 
 
 
 25^ 
 
 
 
 
 
 #359 
 
 12 
 
 Corduroy 
 
 36 381 392 42 412 392 
 
 37 37 41 45 41 40i 
 
 
 66f^ 
 
 
 
 
 
 #371 
 
 15 
 
 Gray Homespun 
 39 38 35 42 41 
 45 39 41 34 37 
 41 40 41 38 423 
 
 
 83 J ^ 
 
 
 
 
 
 #360 
 
 6 
 
 Storm Serge 
 40 421 43 42 39 421 
 
 
 44^ 
 
 
 
 
 
 #373 
 
 24 
 
 Fine English Serge 
 42 38 42 42 402 421 
 40 39 40 41 401 43 
 
 42 42 382 38 4I 42 
 
 43 44 41 40 371 37 
 
 
 1.371 
 
 
 
 
 
 #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 
 
 
 33i 
 
 
 
 
 
162 CONCISE BUSINESS AEITHMETIC 
 
 2. Make out a bill for the following order. Bill the English 
 breakfast tea at 41 J^ ; Finest oolong tea at 65^; Young Hyson 
 tea at 97^^; Choice Japan tea at 59^; Orinda kaughphy at 
 11.90; raw Java coffee at 30^^; gluten flour at 30^ a carton 
 and 87.75 per barrel. Assume that half a chest of tea weighs 
 75 lb., and a mat of coffee 70 lb. 
 
 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 $10.25 ; 750 yd. matting at 55^ ; 225 yd. lin- 
 oleum at 271^; 25 Turkish rugs 81 x 12 at $21.75; 25 Persian 
 rugs6 x9at $12.25; 12 Persian rugs 7 x 11 at $16.25; 10 rolls, 
 each containing 150 yards, Brussels carpeting at $2.25 ; 275 yd. 
 Moquette carpeting at $1.75. Find the amount of the bill. 
 
BILLS AND ACCOUNTS 
 
 163 
 
 
 TIME SLIP 
 
 
 
 TIME SLIP 
 
 
 
 Friday, 4/26, 19 
 
 — 
 
 Saturday, 4/27, 19— 
 
 
 IN 
 
 OUT 
 
 IN 
 
 OUT 
 
 
 IN 
 
 OUT 
 
 IN 
 
 OUT 
 
 1 
 
 751 
 
 1201 
 
 1256 
 
 502 
 
 1 
 
 753 
 
 1200 
 
 1258 
 
 502 
 
 2 
 
 747 
 
 1202 
 
 1247 
 
 503 
 
 2 
 
 757 
 
 1204 
 
 1259 
 
 501 
 
 3 
 
 744 
 
 1204 
 
 1254 
 
 504 
 
 3 
 
 753 
 
 1200 
 
 1256 
 
 504 
 
 4 
 
 751 
 
 1205 
 
 1255 
 
 501 
 
 4 
 
 755 
 
 1202 
 
 1254 
 
 502 
 
 5 
 
 753 
 
 1206 
 
 1259 
 
 505 
 
 5 
 
 749 
 
 1201 
 
 1257 
 
 504 
 
 6 
 
 751 
 
 1202 
 
 1259 
 
 503 
 
 6 
 
 828 
 
 1203 
 
 1255 
 
 503 
 
 7 
 
 859 
 
 1201 
 
 1254 
 
 502 
 
 7 
 
 755 
 
 1202 
 
 1253 
 
 501 
 
 8 
 
 756 
 
 1202 
 
 1250 
 
 501 
 
 8 
 
 857 
 
 1201 
 
 1254 
 
 502 
 
 9 
 
 757 
 
 1201 
 
 1259 
 
 502 
 
 9 
 
 758 
 
 1202 
 
 1258 
 
 504 
 
 The above slips show a record of time for 9 employees for 2 da. in a 
 large printing establishment. The records are made by a large mechani- 
 cal timekeeper, and at convenient periods are copied in the pay-roll book. 
 Fractions are recorded to the nearest i of an hour. The above record is 
 based on an eight-hour day, from 8 to 12 a.m., and 1 to 5 p.m. If a record 
 is made before the hour for beginning work, either in the morning or at 
 noon, it is not counted in the regular time, but if an employee is late, his 
 record for time begins at the nearest multiple of ten after the record is 
 made. For instance, if an employee rang in at 8:42 a.m., his time for the 
 morning would begin at 8:50. In the above slip for Friday, No. 1 rang 
 in at 7:51 and left at 12:01; he rang in at 12:56 and rang out at 5:02; 
 time, 8 hr. 
 
 4. Copy the following pay roll, enter the time for Friday and 
 Saturday (from the above slips), find the amount of the pay roll ; 
 make a change memorandum and a pay-roll memorandum. 
 
 
 PAY ROLL 
 
 
 For the Wee 
 
 K Ending 
 
 April 
 
 27, 
 
 19— 
 
 No. 
 
 Name 
 
 Number of Hours' 
 Work Each Day 
 
 Total 
 No. OF 
 
 Wages 
 
 PER 
 
 Total 
 
 Remarks 
 
 
 
 M. 
 
 T. 
 
 W. 
 
 T. 
 
 F. 
 
 S. 
 
 Hours 
 
 Hour 
 
 
 
 1 
 
 A. B. Comer 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 
 55^^ 
 
 
 
 
 2 
 
 W. D. Ball 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 
 A^^ 
 
 
 
 
 3 
 
 A. M. Snow 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 
 U^f 
 
 
 
 
 4 
 
 R. 0. Mark 
 
 8 
 
 8 
 
 8 
 
 8 
 
 
 
 
 334)? 
 
 
 
 
 5 
 
 Miss Mary Cane 
 
 8 
 
 7| 
 
 8 
 
 8 
 
 
 
 
 33^,? 
 
 
 
 
 6 
 
 Miss Ellen Kyle 
 
 8 
 
 7^ 
 
 8 
 
 8 
 
 
 
 
 35^ 
 
 
 
 
 7 
 
 D. M. Garson 
 
 8 
 
 I:- 
 
 8 
 
 8 
 
 
 
 
 S6ft 
 
 
 
 
 8 
 
 S. D. Lane 
 
 8 
 
 n 
 
 n 
 
 8 
 
 
 
 
 25/ 
 
 
 
 
 9 
 
 Miss Cora Knapp 
 
 8 
 
 8 
 
 n 
 
 8 
 
 
 
 
 221/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
164 
 
 CONCISE BUSINESS AEITHMETIC 
 
 EXPKESSAGE AND EREIGHTAGE 
 
 These express rates went into effect February 1, 1914, in con- 
 formity with the order of the Interstate Commerce Commission : 
 
 Bktween New York 
 
 Between New York 
 
 Between New York 
 
 AND Chicago 
 
 AND New Orleans 
 
 AND Denver 
 
 1st class 2d class 
 
 1st class 
 
 2d class 
 
 1st ela^ts 
 
 2d class 
 
 51b. 31/ 
 
 31/ 
 
 41/ 
 
 41/ 
 
 47/ 
 
 47/ 
 
 6 33 
 
 32 
 
 46 
 
 46 
 
 53 
 
 53 
 
 7 35 
 
 32 
 
 50 
 
 48 
 
 58 
 
 57 
 
 8 38 
 
 32 
 
 54 
 
 48 
 
 64 
 
 57 
 
 9 40 
 
 32 
 
 59 
 
 48 
 
 69 
 
 57 
 
 10 42 
 
 32 
 
 63 
 
 48 
 
 75 
 
 57 
 
 15 53 
 
 40 
 
 84 
 
 63 
 
 1.02 
 
 77 
 
 20 64 
 
 48 
 
 1.06 
 
 80 
 
 1.30 
 
 98 
 
 25 75 
 
 57 
 
 1.27 
 
 96 
 
 1.57 
 
 1.18 
 
 Between Chicago 
 
 Between Chicago 
 
 Between Chicago 
 
 AND Boston 
 
 AND Galveston 
 
 AND Portland, Ore. 
 
 1st class 2d class 
 
 1st class 
 
 2d class 
 
 1st class 
 
 2d class 
 
 5 lb. 31/ 
 
 31/ 
 
 39/ 
 
 39/ 
 
 63/ 
 
 63/ 
 
 6 34 
 
 33 
 
 43 
 
 43 
 
 72 
 
 72 
 
 7 36 
 
 33 
 
 47 
 
 45 
 
 81 
 
 80 
 
 8 38 
 
 33 
 
 51 
 
 45 
 
 89 
 
 80 
 
 9 41 
 
 33 
 
 55 
 
 45 
 
 98 
 
 80 
 
 10 43 
 
 33 
 
 59 
 
 45 
 
 1.06 
 
 80 
 
 15 54 
 
 41 
 
 78 
 
 59 
 
 1.50 
 
 1.13 
 
 20 Q6 
 
 50 
 
 98 
 
 74 
 
 1.93 
 
 1.45 
 
 25 77 
 
 58 
 
 1.17 
 
 88 
 
 2.36 
 
 1.77 
 
 Under the new system the country is divided into blocks, each block 
 covering a certain designated territory, and fixed rates are made for certain 
 weights and distances, not as under the old system, at so much per pound. 
 
 The tables given herewith suggest the manner in which charges are 
 made for given amounts to certain points. 
 
 First-class matter includes all merchandise ; second-class matter applies 
 to food and drink, and these terms are elaborated and explained in the 
 instructions to express agents. On small packages the difference in charges 
 for first-class matter or second-class matter is very slight (sometimes the 
 same), but for large packages and long distances the difference is marked. 
 
BILLS ANB ACCOUKTS 
 
 165 
 
 WRITTEN EXERCISE 
 
 1. Find the total cost of sending the following packages 
 
 10 lb. first class from New York to Chicago. 
 5 lb. second class from Chicago to Boston. 
 15 lb. first class from Chicago to Galveston. 
 20 lb. second class from New York to Denver. 
 10 lb. first class from New York to New Orleans. 
 
 2. Find the total cost of sending the following packages 
 
 15 lb. first class from Chicago to Galveston. 
 
 25 lb. second class from Chicago to Portland, Ore. 
 
 7 lb. second class from Boston to Chicago. 
 
 9 lb. first class from Chicago to New York. 
 10 lb. first class from Galveston to Chicago. 
 
 3. Find the amount of the following freight bill : 
 
 Date of W. B.AU^^/^ig W. B. No. ^Cyf Albany y N.Y.A^cOyZo/^ 
 
 To The Interstate Transportation Company, Dr, 
 
 For Transportation frorn^^t:^iit^:mo ^^-^^-2:1^^7^^ 
 
 
 Weight 
 
 
 > / / /^ ZjT^ 
 
 Advance charges 
 Received paymen. 
 
 No. CarJ//A^J- 
 
 Freight Agent 
 
 
 /J- 
 
 P ? 
 
 Bulky goods are generally sent by freight. The articles are divided, 
 according to quantity and character, into different classes and are subject 
 to different rates. All railroads follow some official classification. All 
 official classifications divide freight into six different classes. 
 
 Such bulky articles as furniture, uncased, is subject to a classification 
 called double first-class. There is so much unoccupied space that the first- 
 class rate is doubled. 
 
166 
 
 CONCISE 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 lb. are charged 
 as 100 lb., irrespective of weight. 
 
 BOSTON & ALBANY EAILEOAD 
 
 Local Freight Tariff between 
 
 BOSTON, MASS. 
 
 Stations 
 
 So. Framingham 
 Westboro . . 
 Worcester . . 
 Webster . . . 
 Palmer . . . 
 
 Rate peb 100 Lb. 
 
 Classes 
 
 2 3 4 5 6 
 
 6f 
 
 If 
 
 9f 
 
 10^ 
 
 5^ 
 
 98 
 108 
 146 
 150 
 202 
 
 Stations 
 
 Springfield 
 Westfield 
 Athol . . 
 Pittsfield 
 Albany . 
 
 Rate per 100 Lb. 
 
 Classes 
 
 28^ 
 35j? 
 
 20 20^ 
 25^120^ 
 23^ 
 
 23^ 
 25^ 
 
 4 5 6 
 
 IW 
 
 12)^ lOj* 
 
 11^ 
 11J2J 
 12J^ 
 
 4. Using the table, find the amount of freight to charge on 
 27,500 lb. sixth-class matter, from Boston to Pittsfield. 
 
 5. Using the above table, find the amount of freight to 
 charge on 27,290 lb. sixth-class matter and 890 lb. first-class 
 matter from Boston to Albany ; to Westfield. 
 
 6. Using the above table, find the amount of freight to 
 charge on 14,790 lb. fifth-class matter and 2170 lb. second-class 
 matter from Boston to Palmer; to Worcester; to Pittsfield; 
 to Springfield. 
 
 7. Using the above table, find the amount of freight to 
 charge on 75 lb. first-class matter, 125 lb. second-class matter, 
 1250 lb. third-class matter, 7290 lb. fourth-class matter, 21,490 
 lb. fifth-class matter, and 64,640 lb. sixth-class matter from 
 Boston to South Framingham ; to Westboro ; to Webster ; to 
 Springfield ; to Athol ; to Albany. 
 
BILLS AND ACCOUNTS 167 
 
 ORAL REVIEW EXERCISE 
 
 Each problem on pages 167 and 168 should he completed in 
 approximately four minutes. Without copying^ find the cost of: 
 
 1. 
 
 2. 
 
 3. 
 
 32 yd. at 61/ 
 
 176 yd. at 121/ 
 
 149 yd. at 25/ 
 
 240 yd. at 81.121- 
 
 177 yd. at 50/ 
 
 150 yd. at $1,331 
 
 25 yd. at S2.50^ 
 
 210 yd. at 28f / 
 
 120 yd. at $1.25 
 
 19 yd. at 4J/ 
 
 291 yd. at 33^/ 
 
 169 yd. at 11/ 
 
 57 yd. at66|/ 
 
 104 yd. at 21/ 
 
 162 yd. at 121/ 
 
 36 yd. at 31/ 
 
 98 yd. at 7/ 
 
 48 yd. at 61/ 
 
 241 yd. at 8/ 
 
 90 yd. at 6f / 
 
 331 yd. at 9/ 
 
 190 yd. at 25/ 
 
 45 yd. at S 1.331 
 
 174 yd. at 30/ 
 
 75 yd. at 28/ 
 
 45 yd. at 45/ 
 
 291 yd. at 3/. ' 
 
 75 yd. at 12 1/ 
 
 706 yd. at 331/ 
 
 117 yd. at 9/ 
 
 42 yd. at 21/ 
 
 221 yd. at 8/ 
 
 18 yd. at 31/ 
 
 246 yd. at 11/ 
 
 146 yd. at 11/ 
 
 1821 yd. at 10/ 
 
 48 yd. at 101/ 
 
 74 yd. at 12i / 
 
 179 yd. at 20/ 
 
 28 yd. at 6/ 
 
 78 yd. at 25/ 
 
 64 yd. at 121/ 
 
 144 yd. at 121/ 
 
 44 yd. at $1.25 
 
 167 yd. at 50/ 
 
 4. 
 
 33 yd. at 331/ 
 
 5. 
 
 48 yd. at S 1.50 
 
 6. 
 
 688 yd. at Sl.lO 
 
 96 yd. at 371/ 
 
 36 yd. at $1.25 
 
 521 yd. at 10/ 
 
 129 yd. at 11/ 
 
 55 yd. at 11/ 
 
 156 yd. at 25/ 
 
 75 yd. at IJ/ 
 
 143 yd. at 50/ 
 
 85 yd. at 85/ 
 
 75 yd. at 75/ 
 
 36 yd. at 70/ 
 
 144 yd. at 16f / 
 
 27 yd. at 80/ 
 
 55 yd. at 55/ 
 
 34 yd. at 90/ 
 
 73 yd. at 1^ / 
 
 95 yd. at 30/ 
 
 125 yd. at 20/ 
 
 Qb yd. at 65/ 
 
 112 yd. at 142/ 
 
 53 yd. at 25/ 
 
 94 yd. at 331/ 
 
 47 yd. at 331/ 
 
 29 yd. at 66f / 
 
 63 yd. at 111/ 
 
 53 yd. at 331/ 
 
 99 yd. at 25/ 
 
 139 yd. at 50/ 
 
 17 yd. at 66f / 
 
 88 yd. at 371/ 
 
 64 yd. at 621/ 
 
 104 yd. at 121 / 
 
 176 yd. at 12 1/ 
 
 98 yd. at 16|/ 
 
 80 yd. at 6f / 
 
 25 yd. at 25/ 
 
 225 yd. at 25/ 
 
 77 yd. at 30/ 
 
 88 yd. at 9 Jj/ 
 
 67 yd. at 331/ 
 
 99 yd. at 40/ 
 
 57 yd. at 50/ 
 
168 CONCISE BUSINESS ARITHMETIC 
 
 7. 
 
 8. 
 
 9. 
 
 128 yd. at 11/ 
 
 219 yd. at 11/ 
 
 65 yd. at 80/ 
 
 73 yd. at 60/ 
 
 85 yd. at 30/ 
 
 83 yd. at 40/ 
 
 76 yd. at 60/ 
 
 94 yd. at 25/ 
 
 145 yd. at 11/ 
 
 177 yd. at 11/ 
 
 89 yd. at 11/ 
 
 63 yd. at 11/ 
 
 72 yd. at 11/ 
 
 28 yd. at 2|/ 
 
 151yd. at 33 1/ 
 
 270 yd. at 111/ 
 
 112 yd. at 61/ 
 
 49 yd. at 75/ 
 
 36 yd. 'at 11/ 
 
 191yd. at 50/ 
 
 124 yd. atSl.25 
 
 185 yd. at 25/ 
 
 781 yd. at 10/ 
 
 180 yd. at 121/ 
 
 225 yd. at 20/ 
 
 306 yd. at 331/ 
 
 360 yd. at 371/ 
 
 39 yd. atSl.331 
 
 122 yd. at 21/ 
 
 24 yd. at S 1.121 
 
 49 yd. at 66f/ 
 
 32 yd. at si. 75 
 
 165 yd. at 6f/ 
 
 42 yd. at S 2.50 
 
 92 yd. at 121/ 
 
 175 yd. at 8/ 
 
 25 yd. at $1.10. 
 
 224 yd. at 7/ 
 
 171yd. at 11/ 
 
 22 yd. at 61/. 
 
 240 yd. at 21/ 
 
 132^ yd. at 10/ 
 
 125 yd. at 36/ 
 
 276 yd. at 11/ 
 
 110 yd. at 25/ 
 
 108 yd. at 9/ 
 
 68 yd. at 8/ 
 
 51yd. at 121/ 
 
 216 yd. at 121/ 
 
 125 yd. at 12/ 
 
 301yd. at 25/ 
 
 10. 
 
 11. 
 
 12. 
 
 62 yd. at 41/ 
 
 144 yd. at 871/ 
 
 97 yd. at 30/ 
 
 189 yd. at 111/ 
 
 25 yd. at S 1.62 
 
 36 yd. atS1.16f 
 
 78 yd. at 40/ 
 
 14 yd. at S 1.14 2 
 
 225 yd. at 8/ 
 
 334 yd. at 7/ 
 
 612 yd. at 6/ 
 
 1431 yd. at 4/ 
 
 255 yd. at 5/ 
 
 1171yd. at 10/ 
 
 65 yd. at 101/ 
 
 78 yd. at 11 / 
 
 45 yd. at 11/ 
 
 15 yd. at If/ 
 
 118 yd. at 11/ 
 
 155 yd. at 12/ 
 
 235 yd. at 20/ 
 
 187 yd. at 25/ 
 
 247 yd. at 50/ 
 
 66 yd. at 331/ 
 
 88 yd. at 331/ 
 
 92 yd. at 121-/ 
 
 48 yd. at 121/ 
 
 96 yd. at 371/ 
 
 65 yd. atl6f/ 
 
 84 yd. at 121/ 
 
 :051yd. at 10/ 
 
 37 yd. at 101/ 
 
 165 yd. at 25/ 
 
 232 yd. at 11/ 
 
 42 yd. atSL25 
 
 192 yd. at 121/ 
 
 36 yd. at S 1.331 
 
 24 yd. atS1.66| 
 
 145 yd. at 5/ 
 
 256 yd. at 6/ 
 
 178 yd. at 7/ 
 
 231yd. at 8/ 
 
 143 yd. at 9/ 
 
 321yd. at 11/ 
 
 148 yd. at 16f/ 
 
 64 yd. at S1.25 
 
 24 yd. atSl.871 
 
 121yd. at 25/ 
 
 61yd. at SI. 331 
 
 36ydoatS1.66f 
 
 1101 yd, at 10/ 
 
a. 
 
 16 
 
 h. 
 
 24 yr. 
 
 c. 
 
 64 hr. 
 
 d. 
 
 12 men 
 
 e. 
 
 15 desks 
 
 DENOMINATE NUMBERS 
 CHAPTER XII 
 
 DENOMINATE QUANTITIES 
 REVIEW OF THE COMMON TABLES * 
 
 ORAL EXERCISE 
 
 1. Which of the following numbers are concrete ? which are 
 abstract? which are denominate? 
 
 /. 150 k. 36 min. 
 
 ^. 21 yd. L 5 yd. 2 ft. 
 
 h. 65 A. m. 3 yr. 4 mo. 
 
 i. 17 books n. 10 T. 75 lb. 
 
 y. 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 B. 
 
170 COKCISE BUSINESS ARITHMETIC 
 
 EEDUCTION 
 
 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.? J ft.? { ft.? 
 
 7. Reduce 5 bu. to pecks ; to quarts ; to pints. 
 
 Reduction Descending 
 174. Example. Reduce 4 T. 75 lb. to ounces. 
 
 Solution. Since 1 T. = 2000 lb., 4 T. = 4 times 2000 
 2000 lb. = 8000 lb.; and with the 75 lb. added this = 4 
 
 8075 lb. Since 1 lb. = 16 oz., 8075 lb. = 8075 times 16 oz. oQ-rr 
 = 129,200 oz., the required result. ^ n 
 
 8075 times 16 oz. = 16 times 8075 oz.; therefore 8075 — 
 
 times 16 oz. is found as shown in the margin. 129^00, No, 01 OZ. 
 
 WRITTEN EXERCISE 
 
 Reduce : 
 
 1. 115' 6'' to inches. 5. 3| rd. to feet. 
 
 2. 12 bu. 4 qt. to pecks. 6. IJ T. to ounces. 
 
 3. «£ 16 158. 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. I mi. to feet. 4. ^ yd. to inches. 
 
 2. .75 cd. to cubic feet. 5. .375 mi. to feet. 
 
 3. -Ill A. to square feet. 6. -^^ hr. to seconds. 
 
DENOMINATE QUANTITIES 171 
 
 Reduction Ascending 
 
 175. Example. Express 176 qt. dry measure in higher de- 
 nominations. ^_^ o r»r. ^^1 
 
 176 -f- 8 = 22, or 22 pk. 
 
 Solution. Since 8 qt. = 1 pk., divide by 8 90_t,4._c; /i 
 and obtain as a result 22 pk. Since4pk. = lbu., * ^ ~ *^ ^^^ ^ ^®" 
 
 divide by 4 and obtain as a result 5 bu. 2 pk. mamder 01 2, 
 
 or 5 bu. 2 pk. 
 
 WRITTEN EXERCISE 
 
 Reduce to higher denominationB : 
 
 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. li. 145,152 cu. in. 
 
 4. 2000 sq. in. 8. 27,900 lb. 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.? J in.? 
 
 4. What decimal part of an acre is 16 rd.? 40 rd.? 
 
 5. What part of 35 bu. is 7 bu.? of IJ bu. is J bu.? 
 
 WRITTEN EXERCISE 
 
 1. Reduce 1| in. to the fraction of a foot ; of a yard. 
 
 2. Reduce 10«. ^d. to the fraction of a pound sterling. 
 
 Solution. There are 12d. in a shilling and 20s. 10s.and9(^. = 129c?. 
 
 in a pound sterling, or 240d!. a-j 940^ 
 
 To find what fractional part of a pound sterling cq't-* 
 
 10s. and 9d. are, use the following statement : 2^^ 0" ~ '*^oiO^ 
 
 10s. M. = \2M. £\ = 240d. Therefore, 10s. 9d.= Or ^£.5375 
 m of a £, or £.5375. 
 
 3. Reduce 4 yd. IJ ft. to the decimal of a rod. 
 
 4. Reduce 10s. Gc?. 2 far. to the decimal of a pound sterling. 
 
 5. Reduce 5 T. 721 lb. to tons and decimal of a ton; 6 T. 
 1750 lb.; 12 T. 290 lb.; 29,240 lb.; 28,390 lb. 
 
 6. Find the cost of 1750 lb. of coal at $6.25 per ton; of 
 2170 lb.; of 690 lb.; of 1360 lb.; of 3240 lb.; of 32590 lb. 
 
172 
 
 CONCISE BUSINESS ARITHMETIC 
 
 ADDITION AND SUBTRACTION 
 
 
 ORAL 
 
 EXERCISE 
 
 
 
 State the sum 
 
 Of: 
 
 
 
 
 
 1. 
 
 2. 
 
 
 3. 
 
 
 4. 
 
 12 ft. 1 in. 
 
 5 lb. 8 oz. 
 
 
 15 rd. 5 ft. 
 
 10 mi. 8 rd. 
 
 6 3 
 
 6 3 
 
 
 17 2 
 
 8 
 
 40 
 
 State the difference between : 
 
 
 
 
 
 5. 
 
 6. 
 
 
 7. 
 
 
 8. 
 
 90 mi. 300 rd. 
 
 75 rd. 121 J 
 
 ft. 
 
 30 yd. 2 ft. 
 
 44 bu. 3 pk. 
 
 75 120 
 
 26 41 
 
 — 
 
 17 n 
 
 29 
 
 1 
 
 
 WRITTEN EXERCISE 
 
 
 
 Find the sum 
 
 of: 
 
 
 
 
 
 1. 
 
 2. 
 
 
 3. 
 
 
 4. 
 
 £140 6s. 
 
 £139 5s. 
 
 84 T. 75 lb. 
 
 279 T 
 
 . 840 lb. 
 
 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. 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 was the gain or the loss in 
 English money ? in United States money ? 
 
DENOMINATE QUANTITIES 173 
 
 MULTIPLICATION AND DIVISION 
 
 ORAL EXERCISE 
 
 Multiply: Divide: 
 
 1. 3 ft. by 6. 7. 27 yd. by 9. 
 
 2. IJ mi. by 8. 8. 225 ft. by 71 ft. 
 
 3. 9 lb. 4 oz. by 2. 9. 48 ft. 6 in. by 2. 
 
 4. 18 lb. 1 oz. by 9. 10. 540 yd. by 18 yd. 
 
 5. 17 yd. 2 in. by 9. 11. 164 lb. 12 oz by 4. 
 
 6. 19 gal. 1 qt. by 3. 12. 640 mi. 160 rd. by 20. 
 176. Examples, l. How much hay in 8 stacks each contain- 
 ing 5 T. 760 lb. ? 
 
 Solution. 8 times 760 lb. = 6080 lb. = 3 T. 80 lb. ; 5 x. 760 lb. 
 ■write 80 in place of pounds and carry 3. 8 times 5 T. = ^ 
 
 40 T. ; 40 T. + 3 T. carried = 43 T. The required result 
 
 is therefore 43 T. 80 lb. 43 T. 80 lb. 
 
 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 15s. 
 
 3^ of £ 87 10s. ^V of £ 87 = £ 1 with an undivided re- ^0 \£ ^7 IQ^ 
 
 mainder of £ 37 ; write £ 1 in the quotient and add -^ 
 
 £ 37 to the next lower denomination ; £ 37 10s. = 750s. -^-^ of 750s. = 15s. 
 
 3. At 10 s. Qid. per yard, how many yards can be bought for 
 X 15 15s. ? 
 
 Solution. The dividend and 
 divisor are concrete numbers; 
 
 therefore reduce them to the <£ 15 15s. = 3780a. 
 
 same denomination before divid- lOs. 6c?. = 126c?. 
 
 ing. £15 15s. = 2,imd., 10s. 6d 3739^ ^ i^Qd. = 30, no. of yd. 
 
 = VIM. 3780(?. - 126c?. = 30 ; 
 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 lb. of 
 pepper ? 
 
 3. Find the cost of 3 T. of bran at 30^ per hundredweight; 
 of 5 T. at 50 ^ per hundredweight. 
 
174 CONCISE 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 lb. cost ? 6400 
 lb.? 3600 lb.? 
 
 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 ^ 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 8 f^ 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 ^ ; what was my gain or loss ? 
 
 10. I bought 3|- bu. of apples at f 1.00 per bu. and sold 
 them at 50 ^ a peck. What was my gain ? 
 
 11. I sold 4 J cd. of wood for $27 and thereby lost $9 on 
 the cost. What was the cost per cord ? 
 
 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 f 1.10 per pennyweight. 
 
 2. I bought 3 J A. of city land at $125 an acre and sold it 
 at 50 ^ 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 21 bu. at $4 
 per bushel and retailed them at 15^ a quart. Did I gain or 
 lose and how much ? 
 
 9. From a farm of 375 A. I sold 25| A. What is the re- 
 mainder worth at $125 per acre ? 
 
PERCENTAGE AND ITS APPLICATIONS 
 CHAPTER XIII 
 
 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 J % . 
 
 2. Read each of the following in three ways : •^, J, ^, J, gV' 
 h h h h h 2 % 21%, 125%, 6J%, 81%, 66|%, 250%, 375%. 
 
 3. 50 % of a number is .50 or ^ of the number. What is 
 50% of $600? 25%? 121-%? io%? 40%? 20%? 75%? 
 
 177. Per cent is a common name for hundredths. 
 
 178. The symbol % may be read hundredths ov per cent. 
 
 179. 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. .142. 6. .28f 8. .0075. 10. .2. 
 Express as decimal fractions : 
 
 11. 20%. 13. 72%. 15. 1%. 17. 125%. 19. ^%. 
 
 12. 45%. 14. 18%. 16. \%. 18. 250%. 20. 375%. 
 Express as common fractions : 
 
 21. 1%. 23. 21%. 25. 1331%. 27. 871%. 29. 1%. 
 
 22. 2%. 24. 3i%. 26. 266|%. 28. 1121%. 30. 175%. 
 Express as per cents : 
 
 31. \. 33. Jj. 35. 1\. 37. f. 39. f. 
 
 32. 1 34. ^^. 36. 2f. 38. IJ. 40. •^. 
 
 175 
 
176 
 
 CONCISE BUSINESS AEITHMETIC 
 
 Important Per Cents and their Fractional Equivalents 
 
 Pee 
 
 Cent 
 
 Fractional 
 
 Value 
 
 Per 
 
 Cent 
 
 Fractional 
 Value 
 
 Pee 
 
 Cent 
 
 Fractional 
 Value 
 
 Per 
 
 Cent 
 
 Fractional 
 Value 
 
 121% 
 
 25% 
 
 371% 
 
 50% 
 
 621% 
 
 1 
 I 
 
 f 
 
 1. 
 
 i 
 
 75% 
 
 100% 
 
 16f% 
 
 33|% 
 
 06f% 
 
 
 831% 
 20 % 
 40% 
 G0% 
 80% 
 
 f 
 1 
 
 1 
 
 6i% 
 
 6f% 
 
 81% 
 
 111% 
 
 14r/o 
 
 i 
 
 180. The terms used 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 ; the percentage, the result obtained by taking a 
 certain per cent of the base. 
 
 In the expression *' 12% of 1 50 is $ 6," $ 50 is the base, 12 %, the rate, and 
 $ 6, the percentage. 
 
 181. The base plus the percentage is sometimes called the 
 amount ; the base minus the percentage, the difference. 
 
 FINDING THE PERCENTAGE 
 
 182. Example. What is 15 % of $ 660 ? 
 
 Solution. 15% of a number equals .15 of it. .15 of ^660 = 
 $ 99, the required result. 
 
 $660 
 .15 
 
 $99.00 
 
 183. Obviously, the product of the base and rate equals the 
 percentage. 
 
 The base may be either concrete or abstract. The rate is always abstract. 
 The percentage is always of the same name as the base. 
 
 ORAL EXERCISE 
 
 1. What aliquot part of 1 is .121 ? .25 ? -.50 ? .16| ? .331 ? 
 .20? .06J? .06f? .081? .111? .142? 371%? 621 %? 66f % ? 
 
 2. Formulate a short method for finding 12|^ % of a number. 
 Solution. 12| % = .12| = \ ; hence, to find 12| % of a number, divide by 8. 
 
 3. State a short method for finding 25% of a number; 
 50%; 16|%; 33^%; 20%; 6^ % ; 6|% ; 8J % ; 111%. 
 
PERCENTAGE 177 
 
 To guard against absurd answers in exercises of this character estimate 
 the results in advance as explained on pages 44 and 128. 
 
 4. Find 50% of 960. Also 25%; 371%; 121%; 62i%; 
 75%; 16f%; 331%; 66|%; 831%; 20%; 40%; 60%; 6i%. 
 
 5. By inspection find : 
 
 a, 50% of 1792. e, 25% of 8 1729. ^. 66f % of 2460. 
 
 h. 371% of $320. /. 6f% of 16600. j. 331% of 2793. 
 
 c. 121% of 1880. g, 61% of 3296. h. 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% ? 21 % ? 11% ? 31% ? If % ? 
 
 3. Formulate a short method for finding 1 J % of a number. 
 
 Solution. 1^% 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 ; 2 J % ; 
 3l%;lf%. 
 
 5. By inspection find : 
 
 a. 5% of 720. d, 1|% of 1840. g. 31% of $3900. 
 
 h. 21% of 840. e. If % of $366. h. 1| % of 120 mi. 
 
 c. 31% of 1560. /. 21% of $720. L 1\% of 1632 A. 
 
 ORAL EXERCISE 
 
 1. Compare 24% of $25 with 25%, of $24; 24% 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 864,800, 
 
178 CONCISE 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 J % 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 f 756, B $1250, 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 33J % 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; 3J% 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 179 
 
 184. Example. 135.50 is what per cent of f 284? 
 Solutions, a. ^35.50 is ^W^^^ or | of {a) 
 
 $284. $284 is 100% of itself; hence, ' -AAMr = i = 121^ 
 
 $35.50, which is \ of $284, must be | of 
 
 100%, or 12^<%. Or, C^) 
 
 6. Since the product of the base and __J^5 = 12J % 
 
 the rate is the percentage, the quotient 284)35.50 
 
 obtained by dividing the percentage by the base is the rate. 
 
 185. Obviously, thQ 'percentage divided hy the base equaU the 
 rate, 
 
 ORAL EXERCISE 
 
 What per cent of: 
 
 
 
 
 1. 95 is 19? 
 
 
 7. 
 
 1.6 is .008? 
 
 2. 4.8 is 1.2? 
 
 
 8. 
 
 1 yd. is 1 ft. ? 
 
 3. $35is$17i? 
 
 
 9. 
 
 2 da. are 8 hr. ? 
 
 4. 225 A. are 75 A. 
 
 ? 
 
 10. 
 
 4T. are 3000 lb.? 
 
 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 17500 and sold it for $8700. 
 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^ 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 ? 
 
180 CONCISE BUSINESS AKITHMETIC 
 
 FINDING THE BASE 
 ORAL EXERCISE 
 
 1. What is 5% of 240 bu. ? 
 
 2. 12 bu. is 5 % of how many bushels ? 
 
 3. 160 is8% of whatnuraber? 4%? 2% ? 1% ? |% ? 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 ? 
 
 186. Example. 37.5 is 25% of what number? 
 
 Solution. 25% or I of the number = 37.5 
 . •. the number = 37.5 -^ ^ = 150. 
 
 187. Obviously, the quotient of the percentage divided hy 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? 
 
PERCEKTAGE 181 
 
 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 $5400, what is the number? 
 
 188. 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 -f- 1.30 = $ 3000. 
 
 2. What number increased by 33 J % of itself equals 180? 
 
 Solution, f of the number = 180 
 
 . •. the number = 180 s- f = 135. 
 
 G|% of itself is 480? 
 125% of itself is 900? 
 371% of itself is 440? 
 11-1% of itself is 300? 
 14f% of itself is 328? 
 200% of itself is 2700? 
 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 $6.75. If 
 his gain was 12^%, what did the oranges cost him? 
 
 
 
 
 ORAL EXERCISE 
 
 What number increased hy: 
 
 
 1. 
 
 10% 
 
 of itself is 
 
 220? 
 
 8. 
 
 2. 
 
 25% 
 
 of itself is 
 
 125? 
 
 9. 
 
 3. 
 
 50% 
 
 of itself is 
 
 300? 
 
 10. 
 
 4. 
 
 75% 
 
 of itself is 
 
 700? 
 
 11. 
 
 5. 
 
 6i% 
 
 of itself is 
 
 170? 
 
 12. 
 
 6. 
 
 12^^ 
 
 9 of itself i 
 
 s 180? 
 
 13. 
 
 7. 
 
 66i^ 
 
 '0 of itself is 135? 
 
 14. 
 
 3. My savings for March increased 331% over February. If 
 my savings for March were $84.36, what were my savings for 
 February and March? 
 
182 COKCISE BUSINESS AKITHMETIC 
 
 PER CENTS OF DECREASE 
 
 ORAL EXERCISE 
 
 1. "What per cent of a number is left after taking away 
 33^% of it ? What fractional part? 
 
 2. If I 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? 
 
 189. Examples, l. A man sold a horse for $332, thereby 
 losing IT %, 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. | of the number = $ 375. 
 
 . •. the number = $ 375 ^ | = $ 500. 
 
 ORAL EXERCISE 
 
 What number diminished by: 
 
 1. ^ % of itself equals 75 ? 4. -J of itself equals 750 ? 
 
 2. 81% of itself equals 440? 5. J% of itself equals 99.5? 
 
 3. 6f % of itself equals 280? 6. 1% of itself equals 49.5? 
 
 WRITTEN EXERCISE 
 
 1. Of what number is 9581.88 77 % ? 
 
 2. A merchant sold 1200 bu. of potatoes for $640, which 
 was 16|^ % 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 23 J % 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 1 6 per barrel, and 
 by so doing lost 16f %. If he paid $309.60 for the apples, 
 how many barrels did he buy ? 
 
PEECENTAGE 
 
 183 
 
 ORAL REVIEW EXERCISE 
 
 1. By inspection find 12| % of the following numbers : 
 
 a. 1872. e. 12464. i. $1688. m. 124.72. 
 
 h. 648 bu. /. 2696 A. j. 2072 A. n. $168.48. 
 
 t?. 1264 A. ^. 1624 ft. A:. 11,464 mi. o. $176.24. 
 
 d. 960 mi. h, 1832 mi. I. 37,128 mi. p. $2184.32. 
 
 2. By inspection find 10 % of each of the above numbers ; 
 25%; 125%; 20%. 
 
 3. State the missing term in each of the following : 
 
 No. 
 
 Base 
 
 Kate 
 
 Pkbckntagk 
 
 No. 
 
 Babe 
 
 Bate 
 
 Percentage 
 
 a. 
 
 $600 
 
 n% 
 
 ? 
 
 /• 
 
 966 
 
 16f% 
 
 ? 
 
 b. 
 
 $650 
 
 ? 
 
 $39 
 
 ff- 
 
 ? 
 
 8i% 
 
 15 bu. 
 
 c. 
 
 ? 
 
 4% 
 
 $18 
 
 h. 
 
 1275 
 
 61% 
 
 ? 
 
 d. 
 
 900 
 
 ? 
 
 720 
 
 i. 
 
 ? 
 
 6i% 
 
 21 mi. 
 
 e. 
 
 ? 
 
 4% 
 
 20 
 
 J- 
 
 400 
 
 ? 
 
 600 
 
 4. By inspection find 10 % of each of the following : 
 
 a, $264. d. $840. g. $232. j, $2448. 
 
 5. $920. e, $750. A. $144. k. $1432. 
 
 (?. $720. /. $364. ^. $288. ?. $3624. 
 
 5. By inspection find 1^ % of each of the above numbersj 
 
 lf%; 1000%; 125%; 166f% 
 
 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 bQ 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? 
 
184 CONCISE BUSINESS ARITHMETIC 
 
 5. 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? 
 
 6. In a recent year 191,571,750 lb. of fish were landed in 
 Boston and Gloucester, and of this quantity 103,460,410 lb. 
 were landed m Gloucester and 88,111,340 in Boston. What 
 per cent of the total was furnished by each city? (Correct 
 to the nearest .01.) 
 
 7. A owned property valued at $12,000 from which he 
 received a yearly rental of S 960. If he paid taxes amounting 
 to $160, msurance $75.50, and made repairs amounting to 
 $184.50, what per cent net income did he receive? 
 
 8. 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? 
 
 9. A landowner rented a field to a tenant and was to 
 receive as rent 16|% 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 gram for the same 
 price per bushel, how much did he receive ? 
 
 10. In a single year the cost of the cotton yarn used in the 
 manufacture of hosiery and knit goods in the state of New York, 
 in round numbers, was $13,825,000; in the state of Illinois, 
 $1,550,000. The cost of the cotton yarn used in Illinois was 
 what per cent less than the cost of the cotton yarn used in 
 New York, in a year? (Correct to the nearest .01.) 
 
 11. 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 $10,000,000,000. Draw parallel lines making 
 a comparison of the personal property and the 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 185 
 
 12. 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? 
 
 13. 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 $ 263.06, and 
 the average net profit for each employer was $ 2273. What per 
 cent greater was the income of each employer than of each em- 
 ployee? (Correct to the nearest .01.) 
 
 14. The population of three 
 
 Ti I I I I I I I I I I 1 I I I h M I I I I I I I I I H I 
 
 cities during a certain year is 
 Aw^^a^^^^^^^a^m^m^^ illustrated by the accompany- 
 Bmamma^m^m^^^^^^m ing lines, which are drawn on 
 
 CH^HHHVHHHiHH^H a scalc of 12,500 inhabitants 
 
 to each -|- 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 ? 
 
 15. The annual coal production in the United States, Great 
 Britain, Germany, and France 
 
 for a certain year is illustrated h 1 1 1 1 1 1 1 1 1 1 1 1 1 1 li 1 1 1 1 1 1 1 1 1 1 1 itT 
 
 in the accompanying rectan- United states 
 e^les, drawn on the scale of 
 
 °^ ' ^ ^^^ , , GreatBritain 
 
 50,000,000 short tons to each —i— 
 ^ of an inch. During that Germajj^ 
 year, how many tons did the jYanc© 
 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 200,000,000 short tons. Illustrate graph- 
 ically the world's coal production for that year. What was the 
 world's approximate production this year? 
 
186 CONCISE BUSINESS AKITHMETIC 
 
 A REVIEW EXERCISE 
 
 Illustrate the following problems by the use of graphs. Graph forms 
 are given on pages 126, 133. Use the form suggested by the instructor. 
 
 1. Illustrate graphically problem 25, page 88. Use the even 
 number of thousands for each month. 
 
 2. In a recent year the railway mileage, single-track, of the 
 world was as follows : America, 325,000 mi. ; Europe, 200,000 mi. ; 
 Asia, 63,000 mi.; Africa, 23,000 mi.; Australia, 19,000 mi. Illus- 
 trate graphically, showing the total mileage, and the relation 
 that each country bears to the total. 
 
 3. In a recent year there were enrolled in the schools and col- 
 leges of the United States 20,000,000 students, grouped accord- 
 ing to ages as follows: 5 yr., 400,000; 6 to 9 yr., 6,200,000; 
 10 to 14 yr., 9,000,000; 15 to 17 yr., 3,000,000; 18 to 20 yr., 
 1,000,000 ; 21 to 24 yr., 400,000. Illustrate graphically. Each 
 group is what per cent of the total ? 
 
 4. The number of cattle, other than milch cows, on farms and 
 ranches in the United States, as reported by the decennial cen- 
 suses, for the years named were as follows: 1870, 13,500,000; 
 1880, 22,500,000 ; 1890, 33,500,000 ; 1900, 50,000,000 ; 1910, 
 41,000,000. Illustrate graphically. What do these figures sug- 
 gest regarding the cost of living as applied to beef ? 
 
 5. The following figures represent the latest estimates of the 
 wealth of the nations named. The figures given represent bil- 
 lions of dollars: United States, 130 ; Great Britain and Ireland, 
 80; France, 65; Germany, 60; Eussia, 40; Austria-Hungary, 25; 
 Italy, 20; Belgium, 9; Spain, 5-|-; Netherlands, 5; Portugal, 21. 
 Switzerland, 2i. Illustrate graphically. 
 
 6. In a recent year the cities of the United States which 
 had a population of over 100,000 expended $100,000,000 in 
 various school expenses, according to the following geographical 
 divisions: North Atlantic Division, $54,000,000; North Cen- 
 tral Division, $30,000,000; South Atlantic Division, $2,700,- 
 000; South Central Division, $3,000,000; Western Division, 
 $10,300,000. lUustrate graphically. 
 
PERCENTAGE 187 
 
 A WRITTEN REVIEW TEST 
 (Time, approximately, forty minutes) 
 
 1. A gardener planted 1 qt. of corn and harvested 5 bu. What 
 per cent of the planting was the harvest ? 
 
 2. A bookkeeper made an investment on which he lost 15%. 
 If the sum returned to him was S 1912.50, what was the 
 investment ? 
 
 3. A piece of cloth, unfinished, cost 6/ per yard. It costs 
 .75/ per yard to bleach it, and then it sells for 7|/ per yard. 
 The selling price is what per cent advance over the total cost ? 
 
 4. A merchant paid the following bills less the discounts 
 named: $85.50 less 2%; $141.50 less 3%; $117.95 less 1%; 
 $225.40 less li% ; $47.50 less 2^ %. What was the total sum 
 paid ? What was the total discount allowed ? 
 
 5. On Monday a man deposited in the bank $184.96. On 
 Wednesday he deposited a sum 121% greater than the deposit 
 of Monday ; he then drew a check for 50 % of his total deposit. 
 What was the amount of the check ? 
 
 6. A merchant's sales increased the second month of his 
 business 25% over the first month; the third month they in- 
 creased 20% over the second month; the fourth month they 
 decreased 10% from the sales of the third month. What were 
 the sales for each month if they were $ 3240 for the fourth month ? 
 
 7. A farmer used 1200 lb. of potato fertilizer per acre, on a 
 16-acre field of potatoes. The fertilizer cost $24,125 per ton, 
 less 5% for cash payment. If the unfertilized land produced 
 60 bu. of potatoes per acre, and the fertilized land produced 
 150 bu. per acre, what per cent of increase was realized by 
 using the fertilizer if the potatoes sold for 80/ per bushel? 
 
 8. A man bought a piece of land, and at the end of the first 
 year it had increased in value 25% ; at the end of the second 
 year it had increased an additional 8 % in value ; at the end of 
 the third year it had increased an additional 5% in value. 
 What did he pay for the property if at the end of the third 
 year it was worth $2551.50? 
 
CHAPTER XIV 
 
 COMMERCIAL DISCOUNTS 
 ORAL EXERCISE 
 
 1. A set of Scott's works is marked $12. If I buy it at this 
 price, less 16|%, what does it cost me? 
 
 2. I buy 890 worth of goods on 30 da. time, or 5% off for 
 cash. What cash payment will settle the bill ? 
 
 3. I owe B 8600, due in 30 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 ? 
 
 190. 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 
 ^/aof ov 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 Vio, ^/so, or 2 % 10 da., net 30 da. 
 
 191. Manufacturers, jobbers, and wholesale dealers usually 
 have printed price lists for tlieir 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. 
 
 192. 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 %. 
 
 188 
 
COMMERCIAL DISCOUNTS 189 
 
 193. 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 %. 
 
 194. 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 PEICE 
 
 195. Example. The list price of a dozen pairs of shoes is 
 $45. 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 j\ of $36 = $3.60, the second discount. 
 $36 - $3.60 = $32.40, the net selUng price. 
 
 
 
 
 ORAL EXERCISE 
 
 
 
 Find the net price : 
 
 
 
 
 
 List 
 
 Trade 
 
 List Trade 
 
 
 List Trade 
 
 
 Pkice 
 
 Discount ] 
 
 Price Discount 
 
 
 Price Discounts 
 
 1. 
 
 $4: 
 
 25% 8. 
 
 $6 40% 
 
 15. 
 
 $4 25% and 331% 
 
 2. 
 
 $15 
 
 20 % 9. 
 
 $4 121% 
 
 16. 
 
 $30 331% and 25% 
 
 3. 
 
 190 
 
 331 % 10. 
 
 $24 81% 
 
 17. 
 
 $35 20% and 25% 
 
 4. 
 
 120 
 
 10 % < 11. 
 
 $42 16f% 
 
 18. 
 
 $45 20% andl6f% 
 
 5. 
 
 150 
 
 50% 12. 
 
 $35 20% 
 
 19. 
 
 $50 20% and 25% 
 
 6. 
 
 12.50 20% 13. 
 
 $100 25% 
 
 20. 
 
 $100 20% and 10% 
 
 7. 
 
 $^.50 16f % 14. 
 
 $720 331% 
 
 21. 
 
 $600 161% 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 $5Q ? 
 
190 
 
 CONCISE BUSINESS ARITHMETIC 
 
 WRITTEN EXERCISE 
 
 Find the net price 
 
 Gross Gross 
 
 Selling Price Trade Discounts Selling Price 
 
 1. $3360 
 
 2. $3510 
 
 3. $4500 
 
 25 % and 10 % 
 331 % and 20 % 
 20 % and 16f % 
 
 Trade Discounts 
 
 4. $2500 20%, 10%, and 5% 
 
 5. $5400 25 %, 20 %, and 10 % 
 
 6. $3960 33^%, 20%,andl6f% 
 
 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. 
 
 m^i^ 
 
 Chicago, 111.. JAU^/ / (^ 19 
 
 0, yr^r^::^^^^ ^>^L^^^-r7-7^^^ 
 
 Bought of GEORGE W. MUNSON & CO. 
 
 Terms. 
 
 J-rm -X^ o<^^^ ^^ Md^fT-T-^J-^l^/i,^ 
 
 2-(?C> 
 
 ^ /^<^7^^. 
 
 _/4^ 
 
 ^. 
 
 6^J2: 
 
 ^^^^ ^^^ 
 
 ZJj^ 
 
 ^ 
 
 1^. 
 
 ^^^^^^ /^y!i 
 
 AA 
 
 ^ 
 
 2=^ 
 
 4^ 
 
 2^ 
 
 /^^y. Y/^tz^A-f^ 
 
 ■j£it: 
 
 ^^ ^ .<£<^ XJ - yC 
 
 JC 
 
 :y^^^ /d^A^. 
 
 ^£i 
 
 2J3 
 
 4^ 
 
COMMEKCIAL BISCOUKTS 191 
 
 10. One firm offers a piano for §400, subject to discounts of 
 20% and 20% ; another offers tlie 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; 7 J doz. 
 mortise locks, #271, at $4.25; 25 doz. pocket knives, #27, at 
 $7.50; and If doz. cheese knives at $8.25. Discount: 25^,10^. 
 
 h. You bought 41|^' of 2" extra strong iron pipe at 70^; 
 94J' of 11'^ extra strong iron pipe at 31J^; 153J' of I" iron 
 pipe at 61^; 88^' of ^" iron pipe at 7f ^. Discount: 25^, lO^fc. 
 
 c. You bought 25 kitchen tables at $ 3. 25 ; 25 dining-room 
 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: 16|%, 5%. 
 
 FINDING A SINGLE RATE OF DISCOUNT EQUIVALENT 
 TO A DISCOUNT SERIES 
 
 196. Example. What single rate of discount is equivalent 
 to a discount series of 25 %, 33i %, and 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 _^ (331 % of 75 % ) 
 price, equals 55%, the single rate of discount .50 
 
 equivalent to the given discount series. 05 TlO ^ of 50 ^ ^ 
 
 A single discount equivalent to a discount 
 
 series may often be determined mentally (see 
 
 .45 
 
 197, 198). 100 % - 45 % = 55 % 
 
192 CONCISE BUSINESS ARITHMETIC 
 
 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 for the buyer 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 J%, 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 $ 1026 was re- 
 quired 3 da. after the date of the bill, what was the list price 
 of the goods sold ? 
 
 197. 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, 
 
 198. 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 will be the equivalent single discount. 
 
 When two separate discounts cannot be reduced to a single discount 
 mentally, proceed as in §196 ; when they can, proceed as in §198. 
 
COMMERCIAL DISCOUNTS 193 
 
 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. 8^% and 24%. 
 
 3. 30% and 30%. 19. 20% and 5%. 35. 8j%and36%. 
 
 4. 40% and 40%. 20. 40% and 5%. 36. 35%andl0%. 
 
 5. 50% and 50%. 21. 25% and 30%. 37. 20%andl2|%. 
 
 6. 20%andl0%. 22. 25% and 40%. 38. 40%andl2i%. 
 
 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. 33J%andl5%. 
 
 14. 60% and 20%. 30. 60% and 15%. 46. 66-|%andl5%. 
 
 15. 25% and 10%. 31. 25% and 331%. 47. 111% and 18%. 
 
 16. 35% and 40%. 32. 45% and 33^%. 48. 36% and 111%. 
 
 199. When a discount series consists of three separate rates, 
 the first two may be combined as in § 198 and then the result 
 and the third may be combined in the same manner. 
 
 200. 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 th^ 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%, 331%, and 10%. 12. 20%, 20%, and 25%. 
 
194 CONCISE BUSINESS ARITHMETIC 
 
 201. "When it is not desirable to show the separate discounts, 
 the net selling price may be found as shown in the following 
 example. 
 
 202. Example. A mahogany sideboard listed at $175 is 
 sold subject to trade discounts of 20% and 25%. Find the 
 net cost to the purchaser. 
 
 Solution. By inspectioii determine that a 100 % 40 % = GO % 
 
 discount of 40% is equivalent to a series of 25% aC) cf of 1^17 'i 11>10'i 
 
 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. $400, less 20 % and 25 %. 5. flOOO, less 50 % and 50%. 
 
 2. 1300, 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%, 33^%, 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 33^% and 8%. The terms offered by both 
 firms are ^/jo, Vso- ^^^ accept the better offer and pay cash. 
 How much does the lumber cost you? 
 
COMMERCIAL DISCOUNTS 195 
 
 WRITTEN REVIEW TEST 
 (Time, approximately, forty minutes) 
 
 1. If goods are bought 25% below the list price and sold at 
 the list price, what is the advance per cent over the cost ? 
 
 2. If goods are bought 20 % below the list price and sold at 
 the list price, what is the advance per cent over the cost ? 
 
 3. If goods are bought 10 % below the list price and sold at 10 % 
 above the list price, what is the advance per cent over the cost ? 
 
 4. If goods are bought at 20% and 12|% below the list 
 price, and sold at 10% below the list price, what is the advance 
 per cent over the cost ? 
 
 5. A hardware dealer bought a machine listed at S24, less 
 16 J % and 10%, and sold it at the list price. At what per cent 
 above cost did he mark the selling price ? 
 
 6. A jobber wished to buy at such a discount from the manu- 
 facturer's list price that he could make an advance of 25% over 
 cost, and still sell at the manufacturer's list price. What would 
 the jobber pay for $1000 worth of goods ? 
 
 7. A gentleman wished to buy a carriage. One dealer offered 
 him a discount of 33^% and 10% from the hst price, and an- 
 other dealer offered him 20%, 10%, and 10% from the list price. 
 If the hst price is $450, what will be the cost of the carriage if 
 it is bought at the better discount ? 
 
 8. Aug. 5, you buy of Gray, Salisbury & Son, New York 
 City, 4000 lb. raisins at 16/, less trade discounts of 25%, 20%, 
 and 10%. Terms: Vio» Vso- You pay cash for freight $3.20. 
 If you pay the bill Aug. 7, what will the raisins cost you ? 
 
 9. You desire to buy 200 lb. nutmeg. You find that S. S. 
 Pierce Co., of your city, offer this article at 75/ per lb., less a 
 discount of 25%, and that Smith, Perkins & Co., New York 
 City, offer it at 70/ per lb., less discounts of 15% and 10%. 
 The freight from New York to your city on a package of this 
 kiod is $1.50. The terms offered by both firms are: Vio? Vso* 
 You accept the better offer and pay cash. How much does 
 the nutmeg cost you? 
 
CHAPTER XV 
 
 GAIN AND LOSS 
 ORAL EXERCISE 
 
 1. What is 33|% of $660? How much is gained on goods 
 bought for $900 and sold at a profit of 331% ? 
 
 2. What per cent greater is $75 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% of 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 8|^%; a gain of 10%; a gain of 1J%; a gain 
 of 1|%; a gain of 21%; a gain of 31%. 
 
 7. State a brief method for finding a loss of 11^%; a loss 
 of 121% ; a loss of 14f % ; a loss of 16f % ; a loss of 20% ; a loss 
 of 25% ; a loss of 9^^ % ; a loss of 371%. 
 
 8. State a brief method for finding a gain of 33 J%; a gain 
 of 22|%; a gain of 50% ; a gain of 66|%; a gain of 75 %. 
 
 203. 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. 
 
 196 
 
GAIN AND LOSS 
 
 197 
 
 FINDING THE GAIN OR LOSS 
 
 ORAL EXERCISE 
 
 By inspection find the gain or loss : 
 
 Per Cent 
 Cost of Gain 
 
 Per Cent 
 Cost of Loss 
 
 1. $2900 50% 
 
 2. $1600 75% 
 
 3. $5600 28^% 
 
 4. $2700 331% 
 
 5. $2400 371% 
 
 6. $1400 42f% 
 
 7. $3200 621% 
 
 8. $2100 66|% 
 
 9. $1500 10% 
 
 10. $1600 1|% 
 
 11. $3000 1|% 
 
 12. $4800 21% 
 
 13. $3600 31% 
 
 14. $3200 6J% 
 
 15. $4500 6f% 
 
 16. $8400 81% 
 25-48. Find the selling price in each of 
 
 WRITTEN EXERCISE 
 
 Per Cent 
 Cost of Gain 
 
 17. $7500 20% 
 
 18. $1400 25% 
 
 19. $2200 9J-^-% 
 
 20. $8100 111% 
 
 21. $6400 12|% 
 
 22. $2800 14f% 
 
 23. $9600 16|% 
 
 24. $3600 22|% 
 the above problems. 
 
 1. An importation of silks invoiced at £ 40 10«. 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 331 % . 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 331 % . What was his gain, and how 
 much did he realize from the sale of the three kinds of 
 material ? 
 
198 CONCISE 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 
 
 
 ^_„ Selling 
 C^^^ Price 
 
 Selling 
 Price 
 
 Gain 
 
 1. 
 
 $100 
 
 $10 
 
 7. 
 
 $60 
 
 $15 
 
 13. 
 
 $80 $90 
 
 19. 
 
 $300 
 
 $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 
 
 18. 
 
 $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 199 
 
 FINDING THE COST 
 
 ORAL EXERCISE 
 
 JBy inspection find the cost : 
 Loss Rate of Loss 
 
 1. 
 
 1150 
 
 10% 
 
 2. 
 
 $100 
 
 li% 
 
 3. 
 
 1200 
 
 11% 
 
 4. 
 
 $450 
 
 ^% 
 
 5. 
 
 1220 
 
 6|% 
 
 6. 
 
 1115 
 
 81% 
 
 
 Selling 
 
 Rate 
 
 
 Price 
 
 OF Gain 
 
 13. 
 
 $1050 
 
 5% 
 
 14. 
 
 $2040 
 
 2% 
 
 15. 
 
 $3600 
 
 20% 
 
 16. 
 
 $1400 
 
 16|% 
 
 17. 
 
 $1800 
 
 12^% 
 
 18. 
 
 $2400 
 
 38* % 
 
 
 Gain Rate of Gadt 
 
 7. 
 
 $35 
 
 20% 
 
 8. 
 
 $79 
 
 25% 
 
 9. 
 
 $12 
 
 iH% 
 
 10. 
 
 $19 
 
 16|% 
 
 11. 
 
 $44 
 
 22|% 
 
 12. 
 
 $15 
 
 331% 
 
 
 Selling 
 
 Rate 
 
 
 Price 
 
 OF Loss 
 
 19. 
 
 $950 
 
 6% 
 
 20. 
 
 $900 
 
 50% 
 
 21. 
 
 $150 
 
 H% 
 
 22. 
 
 $550 
 
 16|% 
 
 23. 
 
 $240 
 
 38J% 
 
 24. 
 
 $490 
 
 22|% 
 
 25. A man bought a machine for S 240.48. For how much 
 must he sell it to gain 12^ % ? 
 
 26. B sold a farm for S2400, thereby losing 25%. For how 
 much should he have sold it to have gained .10% ? 
 
 27. By selling a piano at $400 a dealer realizes a gain of 
 33^%. 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 16f % above cost. What is 
 the cost of an article that he has marked $21.70? 
 
200 CONCISE BUSINESS ARITHMETIC 
 
 4. An owner of real estate sold 2 city lots for 812,000 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 $645.15, 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 $-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 33J%, and the retailer to the consumer at a gain of 
 25%. If the average gain was 8 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: Vio, Vso- ^'- H. Clark & Co. 
 paid cash. Find the cash payment. 
 
GAIN AND LOSS 201 
 
 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: Vio» Vso- 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 12.50 per barrel. Terms : Vio, Vso- You paid cash. 
 Find the amount of your payment. 
 
 8. May 15 you sold F. E. Kedmond the apples bought in 
 problem 7, at |4 a barrel. Terms: Vio? Vso* 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 f 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 J%. 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 lb. 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 331% 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. 
 
202 CONCISE BUSINESS AEITHMETIC 
 
 FINDING THE PER CENT OF GAIN OR LOSS 
 ON THE SELLING PRICE 
 
 ORAL EXERCISE 
 
 1. An article cost S80 and it is sold for $100. What is the 
 sum gained ? The gain is what per cent of the cost ? of the 
 selling price ? 
 
 2. An article costs $60 and it is sold for $75. What is the 
 sum gamed? The gain is what per cent of the cost? of the 
 selling price ? 
 
 3. An article is sold for $ 90. If the gain on the selling price 
 is 331 %, what was the cost, and what is the gain per cent on 
 the cost price ? 
 
 204. Find by inspection the gam per cent on the selling price : 
 
 Cost 
 
 Selling Price 
 
 Cost 
 
 Selling Price 
 
 a, $20 
 
 $30 
 
 /. $120 
 
 $150 
 
 b. $30 
 
 $40 
 
 g. $125 
 
 $150 
 
 c. $45 
 
 $60 
 
 k $140 
 
 $160 
 
 d. $60 
 
 $75 
 
 I $150 
 
 $175 
 
 e. $50 
 
 $60 
 
 y. $160 
 
 $180 
 
 This principle may be applied effectively when goods have been marked 
 by a merchant at a certain per cent on the advance of the cost, and then 
 marked down to sell at cost. 
 
 205. If an article that costs $ 1 is marked to sell at $ 1.10, what 
 per cent of reduction will restore the original cost price ? 
 
 Suggestion. It is evident that a reduction of 10 % on the selling price 
 will not restore the original marking of $ 1. 
 
 206. Find by inspection the per cent of reduction that must 
 be made to reduce the marked price to the cost price. 
 
 Cost Marked Price Cost Marked Price 
 
 a. $1.00 $1.25 d. $1.50 $1.80 
 
 b. $1.25 $1.50 e, $2.00 $2.50 
 
 c. $1.60 $2.00 /. $3.00 $4.00 
 
 207. Business men are continually dealing with the problem 
 of overhead charges; that is, the cost of doing business. Overhead 
 
GAIN AND LOSS 203 
 
 charges include such expenses as employees' salaries, rent, insur- 
 ance, taxes, light and heat, postage, advertising, depreciation, 
 telephone, and many others. To the invoice charges there must 
 be added a certain per cent to cover the cost of doing business. 
 208. The followmg principle applies to subsequent problems: 
 Divide the invoice cost plus the freight by 100 % minus the over- 
 head charges plus the per cent of profit (100 % — charges + profits) ; 
 the result will be the selling price. (This statement is based on 
 reckoning the overhead expenses and the gain as a per cent of 
 the selling price.) 
 
 WRITTEN EXERCISE 
 
 1. An article was invoiced at $33.50; freight charges, S1.50. 
 If the overhead charges amounted to 15 % and the gain to 10 %, 
 what was the selling price ? 
 
 Solution. 15% + 10% = 25%. 
 
 100% -25% =75%. 
 
 $33.50 + $ 1.50 = $35, the cost. 
 
 $35 -T- .75 = $46.67, the selling price. 
 Proof. 25% of $46.67 = $11.67, overhead charges and gain. 
 
 $46.67- $11.67 = $35, the cost. 
 
 2. A merchant sold goods amounting to $ 22,500. If the over- 
 head charges amounted to 18 % and the profits to 8 %, what was 
 the invoice price of the goods if the freight amounted to $ 350 ? 
 
 3. A merchant marked a lot of goods 331 ^ above cost, but as 
 he was unable to sell them at the marked price, he decided to reduce 
 the marking to cost. "What per cent reduction must be made ? 
 
 4. A machine was invoiced at $53.50; freight charges, $3.50. 
 If the overhead charges of the business amounted to 20 %, and 
 the gain to 10 %, what must be the selling price of the goods ? 
 
 5. An invoice of merchandise amounted to $1204.50; freight 
 charges, $ 10.50. If the overhead charges amounted to 1 7J % and 
 the gain to 7J %, what must be the selling price ? 
 
 6. A merchant marked a lot of goods at 25 % above cost, but 
 as the goods did not sell at the marked price, he reduced it 25 %, 
 and announced that he was selling at cost. What per cent rep- 
 resents the amount of his error? If the goods thus marked 
 cost $1760.48, what did the merchant lose by his blunder? 
 
CHAPTER XYI 
 
 MARKING GOODS 
 
 209. 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. 
 
 210. 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. 
 
 211. 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. 
 
 212. The following illustrates the method of marking goods 
 by letters : 
 
 Cost Key Selling-price Key 
 
 REPUBLICAN" PERTHAMBOY 
 
 1234567 8 90 1234567890 
 
 Repeaters : S and Z Repeaters : W and D 
 
 204 
 
\_fUru_\ 
 
 First Cost 
 
 OF 
 
 Article Freight 
 
 Gain 
 
 Loss 
 
 
 First Cost 
 
 OF 
 
 Article 
 
 Freight 
 
 Gain 
 
 1. 12.50 10% 
 
 20% 
 
 
 5. 
 
 116.00 
 
 H% 
 
 37|% 
 
 2. $1.00 10% 
 
 20% 
 
 
 6. 
 
 $40.00 
 
 6% 
 
 16|% 
 
 3. .50 
 
 33^% 
 
 
 7. 
 
 1 3.60 
 
 nfo 
 
 
 4. 14.80 20% 
 
 
 25% 
 
 8. 
 
 $24.00 
 
 
 
 MAEKING GOODS 205 
 
 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 
 
 213. Using the keys given in § 212^ write the cost and the selling 
 price in each of the following problems : 
 
 Loss 
 
 10% 
 
 214. Using the following keg, write the cost and the selling price in 
 each of the followiiig problems : 
 
 Cost Key Selling-price Key 
 
 rL1JhHCDJ"+ T±unE3miui# 
 
 1234567890 1234567890 
 
 Repeaters: Q C^ 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% 13. $18.00 10% 25% 
 
 11. $30.00 6|% 25% 14. $12.00 5% 331% 
 
 215. 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 
 T5 to Tz inclusive, should be memorized. 
 
206 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Table op Twelfths 
 
 Twelfths 
 
 Simplest 
 
 Decimal 
 
 Twelfths 
 
 Simplest 
 
 Decimal 
 
 
 Form 
 
 Value 
 
 
 Form 
 
 Vaute 
 
 A 
 
 
 $.08^ 
 
 A 
 
 
 $.581 
 
 A 
 
 J 
 
 .16! 
 
 A 
 
 f 
 
 .6Gf 
 
 A 
 
 i 
 
 .25 
 
 A 
 
 f 
 
 .75 
 
 A 
 
 i 
 
 .331 
 
 a 
 
 t 
 
 .83^ 
 
 A 
 
 
 .411 
 
 H 
 
 
 .911 
 
 A 
 
 i 
 
 .50 
 
 a 
 
 1 
 
 1.00 
 
 216. 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^^, $1.58|, practically $1.58. 
 
 ORAL EXERCISE 
 fState the cost per article when the cost per dozen articles is 
 
 1. 
 
 $25.00. 
 
 7. 
 
 $7.00. 
 
 13. $23.20. 
 
 19. 
 
 $9.00. 
 
 2. 
 
 $37.00. 
 
 8. 
 
 $3.60. 
 
 14. $19.20. 
 
 20. 
 
 $7.00. 
 
 3. 
 
 $42.00. 
 
 9. 
 
 $2.40. 
 
 15. $66.60. 
 
 21. 
 
 $5.00. 
 
 4. 
 
 $64.00. 
 
 10. 
 
 $5.60. 
 
 16. $38.00. 
 
 22. 
 
 $7.50. 
 
 5. 
 
 $80.00. 
 
 11. 
 
 $3.40. 
 
 17. $17.00. 
 
 23. 
 
 $8.40. 
 
 6. 
 
 $13.00. 
 
 12. 
 
 $13.20. 
 
 ORAL 
 
 18. $11.00. 
 
 EXERCISE 
 
 24. 
 
 $17.50. 
 
 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 % ? 
 
 3. Note books costing $1.60 per dozen must be retailed 
 at what price each to gain 121% ? 
 
 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% ? 
 
MAEKING GOODS 207 
 
 6. Envelopes bought at $2 per M must be sold at what 
 price per package of 25 to gaiu 100%? 
 
 7. Pickles bought at $1.80 per dozen bottles must be sold 
 at what price per bottle to gain 33 J % ? 
 
 8. Mustard costing $14.40 per gross packages must be re- 
 tailed at what price per package to gain 20% ? to gain 50 % ? 
 
 LISTING GOODS FOR CATALOGUES 
 
 217. In listing goods for catalogues dealers generally mark 
 them so that they may allow a discount on the goods and still 
 realize a profit. 
 
 218. 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 = $30. 
 
 .% the catalogue price = §30 -f- .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 33^ % 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 J % and allow for a 20 % loss 
 through bad debts. What will be your asking price per 
 dozen? 
 
208 
 
 CONCISE 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 
 
 Mv. Edgar C. Townsend 
 
 Rochester, N.Y. 
 
 Bought of WELLS, FOWLER & CO. 
 
 Terms Net SO da. 
 
 #721 
 #924 
 
 50 
 25 
 
 18.00 
 12.00 
 
 Oak Bookcases 
 Gentlemen *s Chiffoniers 
 
 Less IO5J 
 
 WRITTEN REVIEW EXERCISE 
 
 400 
 300 
 
 700 
 70 
 
 630 
 
 1. Using the word importance^ with repeaters s and w^ for 
 the buying key, and the words huy for cash^ with repeaters t 
 and w, 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 & WYCKOPP 
 
 Holyoke, Mass. 
 
 Bought of C. E. Stevens & Co. 
 
 Terms Net 30 da. 
 
 100 
 25 
 
 50 
 
 gro. Pens |0.80 
 
 «» Lead Pencils 5.20 
 
 pkg. Record Cards .40 
 
 Less 12 1/251 
 
 80 
 80 
 20 
 
 180 
 22 
 
 50 
 
 157 
 
 50 
 
CHAPTER XYII 
 
 PROPERTY INSURANCE 
 riEE INSURANCE 
 
 ORAL EXERCISE 
 
 1. One hundred persons have property valued at S 500,000. 
 They pay into a common fund 60/ per S 100 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 fire in the same year ? 
 
 3. Suppose the losses to this property by fire for a year amount 
 to S2500. What portion of the common fund will remain on 
 hand as a surplus ? (No interest.) 
 
 4. If this surplus is divided among the hundred 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 distribute 
 the fund in problem 1 called ? 
 
 219. Insurance is a contract whereby for a stipulated con- 
 sideration one party agrees to indemnify another for the loss or 
 damage on a specified subject by specified perils, according to 
 certain prescribed terms and conditions. 
 
 The best-known forms of property insurance are fire insurance and 
 marine insurance. 
 
 There are also property-insurance companies which insure against loss 
 due to steam-boiler explosions, failure of crops, death of live stock, burglary, 
 injury to business by strikes among employees, and numerous other hazards. 
 
 220. Fire insurance is insurance against loss of property or 
 
 damage to it by fire. 
 
 A contract of fire insurance frequently covers loss by lightning or tornado. 
 It also covers damage resulting from or consequent on a fire, such as the loss 
 
210 CONCISE BUSINESS ARITHMETIC 
 
 resulting from water applied for the purpose of extinguishing flames, 
 also, for the loss when such destruction has been ordered by the proper 
 authorities. 
 
 221. The insurer, also 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 to be paid by the insured. The policy is the 
 written contract between the insurer and the insured. 
 
 222. Fire insurance is usually conducted under the joint stock 
 or the mutual plan. 
 
 In a joint stock company capital is subscribed, paid for, and owned by- 
 persons called stockholders, who share in the gains and are liable, to the 
 extent of their subscriptions, for all the losses. 
 
 A mutual insurance company is one in which all the policy holders share 
 the gains and bear the losses in proportion to the amount of the premiums 
 they pay to that particular company, and their fire funds consist of the 
 reserve earnings and the results of investments. 
 
 223. Policies of insurance are of various kinds. The ordinary 
 policy is a contract of indemnity, that is, a contract in which the 
 amount paid in case of loss does not exceed a certain specified 
 sum ; this sum is determined by evidence after the loss occurs. 
 A valued policy is one that states in advance the amount to be 
 paid in case of loss. 
 
 Further subdivisions of policies are as follows : specific^ one that covers 
 a particular kind of property, as a single building ; blanket, one that covers 
 several items of property, as a group of buildings and the contents ; Jixed, 
 one that covers property at some particular defined location ; floating, one 
 that covers specified property while in transit or in various defined locali- 
 ties ; open, one which, while it affixes the extreme limit of the amount and 
 duration of the risk, is yet open to secure endorsements granting insurance 
 in various amounts and places at any time and for any period that may be 
 agreed upon at the time of the endorsement ; this policy is used largely to 
 protect such stocks as grain in elevators or as the contents of warehouses, 
 and the records are usually kept in a book known as an open policy book. 
 
 224. The standard forms of contract used in fire insurance 
 
 policies are prescribed by the state. 
 
 These forms not only define the maximum amount and the term for 
 which the company is liable but also the consideration paid by the insured. 
 
PKOPERTY INSURANCE 211 
 
 the conditions under which the contract will become void, the methods 
 to be followed in the settlement of a loss, and the procedure to effect the 
 cancellation of the contract. 
 
 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 in- 
 demnify 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 $3000, the sum stated in the policy. 
 
 225. Average and co-insurance clauses. "Where a number of 
 detached properties are insured under one policy, it is customary 
 to attach what is known as an average clause which specifies that 
 the amount of insurance covering any one particular piece of 
 property shall bear such proportion to the total amount of insur- 
 ance on the whole as the value of that special piece of property 
 bears to the value of all of the properties so covered. 
 
 226. Many fire-insurance policies contain what is known as a 
 co-insurance, or a reduced-rate, clause. Under this clause the 
 insured party agrees to keep his property insured for a certain 
 percentage of its value ; failing to do this, the company or com- 
 panies insuring him are liable only for that proportion of a loss 
 which the amount they insure bears to the specified percentage 
 of the sound value of the property covered. 
 
 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 $0000 insurance. Should a loss occur, the company will pay 
 only three fourths (f ^^^) of the amount of such loss. 
 
 227. The rate in fire insurance is the amount to be paid to 
 secure S 100 of indemnity for one year. 
 
 The rate is based on the character of the risk ; the greater the likeli- 
 hood of fire the higher the rate. 
 
 When policies are written for a period of more than one year, a reduc- 
 tion is usually made in figuring the premium. Illustrations : on city dwell- 
 ings the premium for five years is charged for four times the annual rate ; 
 if written for three years, for two and one-half times the annual rate. 
 
 Rates are expressed by the number of cents charged for $ 100 of insurance. 
 When over $1 per hundred, the rate is often stated in dollars and cents. 
 
 Short rates are those used for a term of less than one year ; they are 
 proportionately higher than the annual rates. 
 
212 CO]^CISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. What is the cost of S6500 insurance at 80/ per SlOO? 
 
 2. What is the premium on a S 4000 policy at S1.50 per SlOO ? 
 
 3. What is the cost of S6000 insurance at 75/ per SlOO ? 
 
 4. B insures a S6000 bam for | value at 50/ per SlOO. 
 What quarterly premium should he pay ? 
 
 5. A insures a S6000 house for | value, at 50/ per SlOO. 
 What is the semiannual premium ? 
 
 6. Goods worth S3000 are insured for |- value. If the 
 annual premium is S 30, what is the rate ? 
 
 7. I insure S 2400 worth of merchandise for | of its value at 
 60/ per SlOO. What premium must I pay? 
 
 8. I insure a stock of goods worth S8000 for S6000 at 2%. 
 The goods become damaged by fire to the extent of S3000. 
 Under an ordinary policy how much can I recover ? What will 
 be my net loss, premium included ? 
 
 9. A brick schoolhouse is insured at 50/ per SlOO, the 
 annual premium is S50, and the face of the policy | of the 
 value of the building. What is the value of the building? 
 
 
 
 
 ORAL EXERCISE 
 
 
 
 
 ^ta 
 
 te the premium in each of the following problems : 
 
 
 
 
 Facb 
 
 
 Face 
 
 
 
 
 
 OF POLICT 
 
 Rate 
 
 OF Policy 
 
 
 Rate 
 
 
 1. 
 
 S1600 
 
 mo 
 
 3. S3500 
 
 Sl.lO 
 
 per 
 
 SlOO 
 
 2. 
 
 $1000 
 
 ii% 
 
 4. $5000 
 
 S1.20 
 
 per 
 
 SlOO 
 
 State the face of the policy in each of the following problems : 
 Premium Rate Premium Rate 
 
 5. S9 2% 7. S 13.50 S1.35 per SlOO 
 
 6. S15 11% 8. S24.00 S1.60 per SlOO 
 
 State the rate of insurance in each of the following problems : 
 
 Face 
 
 
 Face 
 
 
 OF Policy 
 
 Premium 
 
 OF Policy 
 
 Premium 
 
 9. SI 700 
 
 S 25.50 
 
 11. S3200 
 
 $130.00 
 
 10. $1850 
 
 $37.00 
 
 12. $6500 
 
 $40.00 
 
PEOPEETY iNSiTRAjSTCE ^13 
 
 228. The following is an extract from a tariff, or rate, book for 
 the properties shown on the map which follows this schedule. 
 
 MAIN STREET, SOUTH SIDE 
 
 No. Flat Rate 80% Ratk 
 
 189 John Smith & Co. 
 
 Frame carriage factory $1.75 c $1.23 c 
 
 Contents 1.75 c 1.23 c 
 
 193 John Smith 
 
 Frame dwelling $0.25 a 
 
 197 Frame stable (private) 1.00 a 
 
 199 William Brown 
 
 Frame store and dwelling $0.40 c $0.28 c 
 
 Contents of grocery store 0.40 c 0.28 c 
 
 Contents of dwelling 0.40 a 0.28 c 
 
 203-205 James Robinson 
 
 Brick mercantile building $0.70 a $0.50 a 
 Robinson & Co. 
 
 Department store $0.70 c $0.50 c 
 
 Offices second and third floors 0.70 c 0.50 c 
 
 STATE STREET, KORTH SIDE 
 
 244 James Green 
 
 Brick store and dwelling $0.25 a $0.17^ a 
 National Butter Co. 0.25 c 0.17^ c 
 Dwelling 0.25 c 
 
 248 Thomas White 
 
 Frame stable $1.00 c $0.70 c 
 
 White's Livery . 1.00 c 0.70 c 
 
 252 Thomas White 
 
 Frame dwelling and contents $0.25 a $0.17^ a 
 
 256 Town of Jonesville 
 
 Brick high school $0.50 a $0.35 a 
 
 Contents . 0.50 a 0.35 a 
 
 258 Samuel Parker 
 
 Brick dwelling $0.17 a $0.12 a 
 
 260 . State Street Baptist Society 
 
 Brick church building $0.50 a $0.35 a 
 
 Organ and other contents 0.50 a 0.35 a 
 
 The letter a after the rate indicates that the insurance on this property can 
 be written for more than one year ; that is, at two and one-half times the rate, 
 for a three-year policy, and at four times the rate, for a five-year policy. 
 
 The letter c after the rate indicates that the insurance on this property can 
 be written for one year, or for a number of years, at yearly rates. 
 
 The city block, page 214, contains properties insured under the above 
 schedule of rates. 
 
214 
 
 CONCISE BUSINESS AEITHMETIC 
 
 J 
 
 Diagram op a City Block 
 
 Main Street 
 
 103 197 199 
 
 244 248 262 256 
 
 State Street 
 
 n [ 
 
 r 
 
 WRITTEN EXERCISE 
 
 These problems apply to tlie properties shown on the above 
 diagram ; also to the tariff of rates in the preceding schedule. 
 The flat rate is used unless the co-insurance clause is mentioned. 
 
 1. The frame carriage factory at 189 Main Street is worth 
 $7000. The contents are worth $8000 ; both are insured at -f 
 of their value. What is the amount of the annual premium ? 
 
 2. The frame dwelling at 193 Main Street is worth $ 3400, and 
 the contents, $1200. The frame stable owned by the same party 
 at 197 Main Street is worth $1500, and the contents, $1100. 
 All of this property is insured for 1 yr. at a | valuation. What 
 is the annual premium ? What will it cost to insure it for 3 yr. ? 
 
 3. The store and dwelling at 199 Main Street are worth $4800. 
 The contents of the store are worth $2400, and of the dwelling, 
 $800. What will it cost to insure the property for 1 yr.? 
 
 4. The brick mercantile building at 203—205 Main Street is 
 worth $20,000. The contents of the first floor are worth $4500, 
 and of the second Eind third floors, $ 7500. All are insured at a 
 75% valuation for 1 yr. What is the amount of the premium? 
 A fire occurs, and the building and the contents are damaged to the 
 extent of $4500. If the policies contained an 80% co-insurance 
 clause, how much will the insuring company have to pay ? 
 
PKOPEllTY mSURAi^CE 215 
 
 5. Suppose that the buildmg described in problem 4 was 
 insured in Company A for $ 18,000 at the tariff rate, and the con- 
 tents in Company B for S 10,000 at a rate of 75/; that each 
 company had an 80 % co-insurance clause attached to its policy ; 
 that the building was damaged to the extent of $ 3000, and the 
 contents, $ 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 contents? (Premium included in each case, but 
 no interest.) 
 
 6. The brick church at 260 State Street is worth $10,000, 
 and the contents, $3500. The property is insured for 1 yr. 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 wholly destroyed by fire ? 
 
 7. If the brick school building at 256 State Street is worth 
 $15,000 and the contents are worth $7500, what will it cost 
 under the term rule to insure it for 5 yr. for 80 % of its value ? 
 
 8. For insuring the frame buildings at 252 and 248 State 
 Street, and the contents of each for ^ of their value, the owner 
 pays an annual premium of $ 22.50. If the frame stable and the 
 contents are worth |- of the frame dwelliug and the contents, what 
 is the value of each building, includiug the contents ? 
 
 9. The brick store and the dwelliug at 244 State Street are 
 worth $15,000 ; the property is insured in three companies for ^ 
 of its value. Company A carries i of the line at the tariff rate ; 
 Company B, | of the line at a 50 / rate ; Company C, the re- 
 mainder of the line at a 66| / rate. What is the total premium 
 paid ? The building is damaged by fire to the amount of $6000. 
 What amount will each company pay ? 
 
 10. I insured a block of buildings in the ^tna Insurance 
 Company for $75,000 at an annual rate of 75/. The ^tna 
 afterwards reinsured $15,000 of its liability under my policy in 
 the Continental Insurance Company at 75/, and $20,000 in the 
 German American Insurance Company at the same rate. The 
 buildmg was damaged by fire $ 20,000. What was the net loss 
 pf each of the three companies ? 
 
INTEREST AND BANKING 
 CHAPTER XYIII 
 
 INTEREST 
 ORAL EXERCISE 
 
 1. A borrows $100 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 ? ~ 
 
 229. 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 may 
 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. 
 
 230. 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. 
 
 216 
 
INTEREST 217 
 
 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 II 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 ^ of .001 ? What is 
 the interest on 11200 for 1 da. at 6 % ? on $180 ? on $1500 ? 
 
 6. State a short method for finding the interest on any 
 principal for 1 da. at 6 % . 
 
 231. 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 6^0- 
 
 ORAL EXERCISE 
 
 1. Find the interest on each of the following for 6 da. at 6%. 
 a. $250. e. $560. i. $678. m, $290. q. $890. 
 h. $870. /. $435. j, $320. n. $150. r. $750. 
 
 c, $358. g. $430. k. $100. o. $325. s. $580. 
 
 d. $350. h, $470. I $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 tlie interest on each of the following for 1 da. at 6%. 
 a. $360. e. $660. i. $600. m. $480. q. $840. 
 5. $450. /. $900. j. $180. n. $780. r. $200. 
 c. $300. g. $540. h. $720. o. $400. s. $330. 
 6?. $420. h. $240. Z. $500. ^. $120. t, $960. 
 
 4. Find the interest on each of the above amounts for 
 3 da. at 6 % ; for 2 da. 
 
218 CONCISE BUSINESS ARITHMETIC 
 
 232. Example. Find the interest on $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. ^94 30 -=- 6 = S4 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- ■-* =$4.05 
 
 ened. 
 
 WRITTEN EXERCISE 
 
 f 
 
 At 6^0 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 93 da. 
 
 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 72 da. 
 
 11. 
 
 $178.45 40 da. 
 
 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, 
 \ of 80)^, or 40 <P, is the interest for 6 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 
 I of itself equals the interest at 8%. 
 
 4. State a short method for changing 6% interest to 7% 
 interest; to 5% ; to 9% ; to 71% ; to 41%. 
 
 5. If the interest at 6% is $120, what is the interest at 7%? 
 at 5%? at 8%? at 4% ? at 7i%? at 41% ? 
 
INTEREST 219 
 
 233. In the foregoing exercise it is clear that 6 % interest in- 
 creased by ^ of itself equals 9 % interest; hy \ of itself 8 % interest; 
 ^y \ of itself 7\^o interest; hy \ of itself 7% interest; also that 
 
 6ffo interest decreased hy i of itself equals 4 (fo interest; hy \of 
 itself 41 % interest; hy J of itself 5% interest; also that 
 
 6% interest divided hy 2 equals 3% interest; hy 3^ 2(fo inter- 
 est; hy 6, 1% interest; hy 4, i| % interest, 
 
 6 % interest multiplied by 2 equals 12 % interest. 
 
 6 % interest is clianged 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 numher of days^ find the interest on : 
 
 1. $2500 from Sept. 18, 1915, to Feb. 6, 1916, at 9%; at 
 ^%', Sit 4:%; at 3%. 
 
 2. $1700 from Nov. 20, 1915, to Jan. 16, 1916, at 8% ; at 
 21% ; at 51%; at 31%; at 4%. 
 
 3. $ 2750 from Dec. 16, 1915, to Jan. 17, 1916, at 7 % ; at 2 % ; 
 at 4 % ; at 5 % ; at 1 % ; at 10 %. 
 
 4. 16250 from Dec. 18, 1915, to Feb. 6, 1916, at 71%; 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. 
 
 CB 
 
220 CONCISE 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. 
 
 h. 60 da. plus ^^2" ^^ 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 
 bb 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 ^b da. ; for 55 da. ; for 75 da. ; for 
 70 da. ; i^ 40 da. ; for 45 da. 
 
 234. 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<^o* 
 
 235. Examples, l. Find the interest on $1950 for 20 da. 
 at 6%. 
 
 Solution. Removing the decimal point two places to the left $19.50 
 gives the interest for CO da. 20 da. is \ of 60 da. \oi% 19.50 = ~^6~50 
 $6.50. • ' 
 
 2. What is the interest on $8400.68 for 75 days ? 
 
 Solution. Removing the decimal point two $84.0068 
 places to the left gives the interest for 60 da. ^-j ^/%^ «- 
 
 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 221 
 
 2. Find the total amount of interest at 6% on: 
 
 $ 1600 for 60 da. $ 1600 for 40 da. 1 2800 for 75 da. 
 
 i 1600 for 55 da. $ 2800 for 60 da. $ 2800 for 80 da. 
 
 1 1600 for 50 da. $ 2800 for 65 da. $ 2800 for 90 da. 
 
 $ 1600 for 45 da. $ 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. 1 8575.65 for 70 da. 
 $ 1800.72 for 20 da. $ 720.18 for 10 da. 8 6282.40 for 15 da. 
 $ 1200.64 for 15 da. $ 440.70 for 40 da. f 1460. 84 for 65 da. 
 f 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. 1 432.65 for 15 da. 
 
 $ 3240.64 for 70 da. $ 6400.00 for 45 da. $ 832.30 for 10 da. 
 
 $4125.18 for 45 da. $ 1200.45 for 30 da. $ 926.17 for 20 da. 
 
 ORAL EXERCISE 
 
 1. What is the interest on i 215 for 6 da. at 6 % ? on $ 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 ^ of itself equals 5 da. ; 6 da. minus of 
 
 itself equals 4 da. 
 
 h. 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. 
 
 236. In the above exercise it is clear that removing the 
 decimal point in the principal three places to the left gives the 
 interest for 6 da, at 6<fo* 
 
222 CONCISE BUSINESS ARITHMETIC 
 
 237. Example. What is the interest on $420 for 8 da. at 
 6%? 
 
 $.420 
 .140 
 
 Solution. Removing the decimal point three places to the left gives 
 the interest for 6 da., or $0.42. Since 8 da. is 6 da. plus -} of itself, 
 $0.42 increased by ^ of itself, or $0.56 is the required interest. In the $.5t) 
 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 : 
 
 $800 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 Ida. $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 223 
 
 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 100 da. 
 
 6. If the interest on f 1 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 $18.90? 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? 
 
 238. 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 600 da. at 6(^o > ol^o that any sum of money will double itself 
 in 6000 da. at 6%. 
 
 WRITTEN EXERCISE 
 
 Find the interest at 6(fo 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 Ida. 
 
 3. $912 for 2000 da. 7. $8400.50 for 400 da. 11. $17890 for 10 da. 
 
 4. $316 for 1500 da. a $7500.79for 1500da.l2. $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. ? 
 
 239. Example. Find the interest on $375 for 48 da. at 6 %. 
 
 SoLDTioy. 37 J J? 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 
 
224 CONCISE BUSINESS AKITHMETIC 
 
 WRITTEN EXERCISE 
 
 1. Find the total amount of interest at 6 % on: 
 
 $750 for 6 da. 1750 for 36 da. ^750 for 60 da. 
 
 1750 for 12 da. t750 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. 
 
 240. 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 f, or $1.70. 
 
 2. What is the interest on $6000 for 49 da. at 6^? on $300? 
 on $240? on $3000? on $1800? on $840? on $600? 
 
 3. State the interest at 6^ on: 
 
 a. $600 for 19 da. e, $6000 for 37 da. L $ 900 for 17 da. 
 
 b. $300 for 37 da. /. $3000 for 43 da. J. $1500 for 40 da. 
 
 c. $240 for 43 da. ^. $2400 for 67 da. L $ 600 for 139 da. 
 
 d. $180 for 27 da. h, $1800 for 89 da. L $ 300 for 179 da. 
 
 241. 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. 
 
7. 
 
 7 da. 
 
 13. 
 
 86 da. 
 
 19. 
 
 17 da. 
 
 8. 
 
 22 da. 
 
 14. 
 
 55 da. 
 
 20. 
 
 25 da. 
 
 9. 
 
 11 da. 
 
 15. 
 
 84 da. 
 
 21. 
 
 85 da. 
 
 10. 
 
 63 da. 
 
 16. 
 
 14 da. 
 
 22. 
 
 89 da. 
 
 11. 
 
 37 da. 
 
 17. 
 
 97 da. 
 
 23. 
 
 19 da. 
 
 12. 
 
 23 da. 
 
 18. 
 
 99 da. 
 
 24. 
 
 29 da. 
 
 INTEREST 225 
 
 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. 
 
 2. 67 da. 
 
 3. 27 da. 
 
 4. 13 da. 
 
 5. 72 da. 
 
 6. 43 da. 
 
 242. Examples, l. Find llie interest on $840 for 31 da. at 
 6%. 
 
 SoLUTiox. 31 da. = 30 da. + 1 da. The interest for CO da. is '^ 
 
 $8.40 and for 30 da. ^ of this sum or $4.20. The interest for 6 da. is $4.20 
 $0.84 and for 1 da. | of this sum or $0.14. Adding $4.20 and $0.14 .14 
 
 the result is the required interest, or $4.34. S4~34 
 
 2. What is the interest on $2500 for 121 da. at 6 % ? 
 
 Solution. 121 da. = 2 x 60 da. + 1 da. The interest for 60 da. ^^^-^Q 
 
 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. a of this sum, or $0.42. Adding $50 and 42 
 
 $0.42 the result is §50.42, the required interest. ^rr^ .^^ 
 
 WRITTEN EXERCISE 
 
 Find the interest : 
 
 
 
 
 
 
 Principal 
 
 Time 
 
 Rate 
 
 Principal 
 
 Time 
 
 Rate 
 
 1. $420 
 
 3 mo. 
 
 6% 
 
 11. 
 
 $450 
 
 4 mo. 
 
 H% 
 
 2. $650 
 
 4 mo. 
 
 5% 
 
 12. 
 
 $600 
 
 2 mo. 
 
 6% 
 
 3. $360 
 
 92 da. 
 
 4% 
 
 13. 
 
 $720 
 
 8 mo. 
 
 8% 
 
 4. $250 
 
 30 da. 
 
 3% 
 
 14. 
 
 $840 
 
 2 mo. 
 
 Hfo 
 
 5. $380 
 
 24 da. 
 
 7% 
 
 15. 
 
 $120 
 
 7 mo. 
 
 6% 
 
 6. $900 
 
 55 da. 
 
 6% 
 
 16. 
 
 $280 
 
 9 mo. 
 
 H% 
 
 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. 
 
 n% 
 
 10. $270 
 
 11 da. 
 
 1% 
 
 20. 
 
 $560.17 
 
 27 da. 
 
 6% 
 
226 CONCISE BUSINESS ARITHMETIC 
 
 243. It has been observed that 6 times $800 = 800 times $6 ; 
 that 0.01 of 1715 = 715 times 10.01 ; etc. Hence, 
 
 244. The principal in dollars and the time in days may he 
 interchanged without affecting the amount of interest. 
 
 245. Example. Find the interest on $600 for 179 da. at 6 %. 
 
 Solution. |600 for 179 da. = $179 for 600 da. ; ^ of the principal equals 
 the interest for 600 da. \ ^ ol^ 179 = f 17.90, the required interest. 
 
 $360 for 91 da. 
 $420 for 87 da. 
 $540 for 21 da. 
 $660 for 37 da. 
 $750 for 56 da. 
 $3600 for 218 da. 
 $2000 for 183 da. 
 $1200 for 155 da. 
 $1800 for 181 da. 
 $2400 for 218 da. 
 
 of itself) on interest for 24 da. at 6 %, or $1500 on interest for 
 32 da. (24 da. + J of itself) at 6 %. Hence, 
 
 247. If either the principal or the time is increased or decreased 
 hy any fraction of itself the interest is increased or decreased by 
 the same fraction. 
 
 248. Examples, l. Find the interest on $ 480 for 279 da. 
 at 71 %. 
 
 Solution. 7| % 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 $279 for 600 da." Pointing off one place in the new principal, the 
 result is $27.90, the required interest. 
 
 2. Find the interest on $2795.84 for 80 da. at 41%. 
 
 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. 
 
 ORAL 
 
 EXERCISE 
 
 State the interest at 6 % on : 
 
 
 1. $60 for 27 da. 
 
 11. 
 
 2. $30 for 13 da. 
 
 12. 
 
 3. $20 for 171 da. 
 
 13. 
 
 4. $10 for 186 da. 
 
 14. 
 
 5. $15 for 145 da. 
 
 15. 
 
 6. $12 for 179 da. 
 
 16. 
 
 7. $10 for 131 da. 
 
 17. 
 
 8. $100 for 120 da. 
 
 18. 
 
 9. $200 for 189 da. 
 
 19. 
 
 10. $150 for 192 da. 
 
 20. 
 
 246. $1500 on interest for 24" da. at 
 
INTEREST 227 
 
 ORAL EXERCISE 
 
 State the interest on : 
 
 1. $279.86 for 45 da. at 4 %. 6. 12400 for 39 da. at 5 %. 
 
 2. $478.65 for 45 da. at 4%. 7. 12700 for 37 da. at 4 %. 
 
 3. $769.64for 48 da. at 71 %. 8. $2400 for 87 da. at 41 %. 
 
 4. $217.49 for 80 da. at 41 %. 9. $1600 for 95 da. at 41 %. 
 
 5. $767.53 for 80 da. at 41 %. lo. . $3200 for 59 da. at ^ %. 
 
 The Six Per Cent Method 
 
 249. 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 $1 for 1 yr. at 6 % is $0.06, 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 $0.06, 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 $50 for 1 yr. at 6 % ? for 1 jt. 
 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. ? 
 
 250. In the above exercise it is clear that : 
 
 $0.06 = interest on^l for 1 yr. at^%. 
 $0,005 = interest on $lforl mo, at 6 %. 
 $0.0001 = interest on $lforl da, at 6 %. 
 
228 CONCISE BUSINESS AEITHMETIC 
 
 ORAL EXERCISE 
 Find the interest on $1 at 6 (Jo 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. $250 for 2 yr. i4. 8350 for 3 yr. 
 
 10. $400 for 5 yr. 15. $450 for 2 yr. 3 mo. 
 
 11. $700 for 4 yr. 16. $150 for 1 yr. 6 mo. 
 
 12. $300 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. 
 251. 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 for2 yr.; q^ ^ -^^^ ^^ ^^ ^^^ g ^^^ 
 
 on |1 for 8 mo.; on ^^^r • ^n-i «• w i 
 
 $1 for 15 da. The sum '^^^^ = 1"^. on $1 for 15 da. 
 
 of these interest items $0.1625 = int. on $1 for the given time, 
 equals $0.1625, the in- 600 X $0.1625 = $97.50, int. on $600 
 
 terest on ^1 Jor the ^^^ ^ yr. 8 mo. 15 da. at 6 %. 
 
 given time ate %. Mul- "^ ' 
 
 tiplying this interest by the given number of dollars, 600, the product is the 
 required interest, $97.50. 
 
 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. mo. at 8%, take 400 times 2{)^ 
 (2^ X 8^) ; on $500 for 5 yr. 3 mo. at 4%, take 500 times 21;^ (5J x 8^) ; 
 on $600 for 1 yr. mo. at 4% take 000 times 7 ti etc. 
 
 
 
 ORAL EXERCISE 
 
 
 
 Find the interest: 
 
 
 
 
 
 Principal 
 
 Time 
 
 Rate 
 
 Principal 
 
 TnMtE 
 
 Rate 
 
 1. $400 
 
 1 yr. 2 mo. 
 
 6% 
 
 7. $840 
 
 1 yr. 6 mo. 
 
 6% 
 
 2. $500 
 
 2 yr. 4 mo. 
 
 6% 
 
 8. $100 
 
 3 yr. 6 mo. 
 
 bfo 
 
 3. $300 
 
 4 yr. 6 mo. 
 
 6% 
 
 9. $960 
 
 4 yr. 2 mo. 
 
 6% 
 
 4. $250 
 
 1 yr. 8 mo. 
 
 6% 
 
 10. $300 
 
 3 yr. 4 mo. 
 
 8% 
 
 5. $200 
 
 2 yr. 10 mo. 
 
 3% 
 
 11. $240 
 
 2 yr. 6 mo. 
 
 4% 
 
 6. $300 
 
 1 yr. 11 mo. 
 
 6% 
 
 12. $180 
 
 1 yr. 8 mo. 
 
 6% 
 
INTEREST 229 
 
 WRITTEN EXERCISE 
 
 Find the interest : 
 
 1. Principal, $74.90; time, 6 mo. 15 da. ; rate, 4 %. 
 
 2. Principal, $986.00; time, 11 mo. 28 da.; rate, 41%. 
 
 3. Principal, 11900.00; time, 10 mo. 28 da.; rate, 6%. 
 
 4. Principal, $87.55; time, 4 yr. 5 mo. 6 da.; rate, 6%. 
 
 5. Principal, $735.00; time, 4 yr. 4 mo. 4 da.; rate, 6%. 
 
 6. Principal, $609.50; time, 2 yr. 7 mo. 6 da.; rate, 6%. 
 
 7. Principal, $875.40; time, 1 yr. 2 mo. 21 da.; rate, 4^%. 
 
 8. Principal, $1124.75; time, 1 yr. 5 mo. 14 da.; rate, 6%. 
 
 9. Principal, $1245.00 ; time, 3 yr. 6 mo. 23 da.; rate, 6%. 
 10. Principal, $1570.00; time, 1 yr. 9 mo. 25 da.; rate, 5%. 
 
CHAPTER XIX 
 
 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 S600, dated 
 at your place to-day, 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. 
 
 252. 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. 
 
 253. 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. 
 
 230 
 
BANK DISCOUNT 231 
 
 254. 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 he would an ordinary promissory note. 
 
 The parties to a draft are the drawer, the drawee, and the payee. In the 
 foregoing draft Geo. H. 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. 
 
 SBu/faio. jr.y., (^^^^k^^. ^, f9 — 
 
 ^^/ ^ ^^ 
 
 '^ y^^ ^-v!^^..^^^^ "^y/^t ^:=^Q)oUara 
 
 to tieeount of 
 
 '3^ 
 
 ^z^^^Z^^*^ 
 
 ^ 
 
 \ ~r<;6f^^^ ^y^^r^^J^^^^^^ 
 
 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 June 30, Sept. 30, etc. 
 
232 
 
 CONCISE BUSINESS ARITHMETIC 
 
 255. 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. 
 
 256. The reduction made by a bank for advancing money on 
 negotiable paper not due is called bank m* 
 
 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. 
 
 257. The accompanying maturity table 
 is sometimes used by bankers in finding 
 the maturity of notes and drafts. The 
 following examples illustrate its use. 
 
 258. Examples, l. Find the maturity 
 of a note payable (a) 6 mo. from Apr. 27, 
 1915; (5) 6 mo. from Sept. 25, 1915. 
 
 Solutions, (a) Refen-ing 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, 1915. 
 
 (6) September is the 9th month. 9 + = 15, and the 15th month (see number 
 on right) is March of the next year. The note is therefore due Mar. 25, 1916. 
 
 2. Find the maturity of a note payable 90 da. from Jan. 18, 
 
 1916. 
 
 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 
 6 
 
 May-1 
 
 17 
 18 
 19 
 
 June 
 
 7 
 
 July - 1 
 
 8 
 
 Aug. - 1 
 
 20 
 21 
 22 
 
 9 
 
 Sept. 
 
 10 
 
 Oct. - 1 
 
 11 
 
 Nov. 
 
 23 
 
 12 
 
 Dec. - 1 
 
 24 
 
BANK DISCOUKT 
 
 233 
 
 ORAL EXERCISE 
 Find the maturity of each of the following notes : 
 Date Time 
 
 1. Apr. 6, 1915 30 da. 
 
 2. Oct. 6, 1916 3 mo. 
 
 3. Nov. 9, 1915 60 da. 
 
 4. Jan. 31, 1916 1 mo. 
 
 5. Sept. 18, 1915 90 da. 
 
 Find the maturity of each of the following acceptances : 
 
 Datf- ^'^® AFTER J. Time after 
 
 ^^^^ Date ^^^^ Date 
 
 11. Apr. 3 30 da. 14. Dec. 31 2 mo. 
 
 12. May 5 60 da. 15. Jan. 12 
 
 13. Jan. 20 1 mo. 16. Feb. 18 
 Find the maturity of each of the following acceptances 
 
 Date 
 
 6. Jan. 30, 1916 
 
 7. Jan. 31, 1915 
 
 8. May 10, 1916 
 
 9. June 19, 1916 
 10. Nov. 15, 1916 
 
 Time 
 30 da. 
 30 da. 
 90 da. 
 60 da. 
 30 da. 
 
 1 mo. 
 
 3 mo. 
 
 17. 
 18. 
 19. 
 
 Date 
 Accepted 
 
 Aug. 12 
 Sept. 18 
 Oct. 30 
 
 Time after 
 Sight 
 
 3 mo. 
 2 mo. 
 
 4 mo. 
 
 20. 
 21. 
 22. 
 
 Date 
 Accepted 
 
 Apr. 25 
 May 17 
 June 18 
 
 Time after 
 Sight 
 
 60 da. 
 
 3 mo. 
 
 30 da. 
 
 WRITTEN EXERCISE 
 
 Find the maturity and the term of discount 
 Date 
 
 1. Jan. 16, 1916 
 
 2. Jan. 31, 1916 
 
 3. Feb. 12, 1916 
 
 4. Feb. 24, 1916 
 
 5. Mar. 31, 1916 
 
 Date of Draft Time after Date 
 
 6. Feb. 7 60 da. 
 
 7. Mar. 12 30 da. 
 Date of Draft Time after Sight 
 
 8. May 31 60 da. 
 
 9. Mar. 17 90 da. 
 
 Time 
 
 Discounted 
 
 3 mo. 
 
 Mar. 1 
 
 1 mo. 
 
 Feb. 3 
 
 90 da. 
 
 Mar. 2 
 
 60 da. 
 
 Apr. 1 
 
 90 da. 
 
 May 13 
 
 Date Accepted 
 
 Date Discounted 
 
 Feb. 8 
 
 Feb. 9 
 
 Mar. 12 
 
 Mar. 15 
 
 Date Accepted 
 
 Date Discounted 
 
 May 31 
 
 June 3 
 
 Mar. 20 
 
 Mar. 21 
 
234 
 
 CONCISE BUSINESS ARITHMETIC 
 
 259. 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 
 
 
 To THE Same Day of the Next 
 
 OF 
 
 Jan. 
 
 Feb. 
 31 
 
 Mar. 
 59 
 
 Apr. 
 
 90 
 
 May 
 120 
 
 Jane 
 151 
 
 July 
 181 
 
 Aug. 
 212 
 
 Sept. 
 
 Oct. 
 
 Nov. 
 
 Dec. 
 
 January .... 
 
 365 
 
 243 
 
 273 
 
 304 
 
 334 
 
 Febkuary 
 
 
 
 
 334 
 
 365 
 
 28 
 
 59 
 
 89 
 
 120 
 
 150 
 
 181 
 
 212 
 
 242 
 
 273 
 
 303 
 
 March . 
 
 
 
 
 306 
 
 337 
 
 365 
 
 31 
 
 61 
 
 92 
 
 122 
 
 153 
 
 184 
 
 214 
 
 245 
 
 275 
 
 April . . 
 
 
 
 
 275 
 
 306 
 
 334 
 
 365 
 
 30 
 
 61 
 
 91 
 
 122 
 
 153 
 
 183 
 
 214 
 
 244 
 
 May . . 
 
 
 
 
 245 
 
 276 
 
 304 
 
 335 
 
 365 
 
 31 
 
 61 
 
 92 
 
 123 
 
 153 
 
 184 
 
 214 
 
 June . . . 
 
 
 
 
 214 
 
 245 
 
 273 
 
 304 
 
 334 
 
 365 
 
 30 
 
 61 
 
 92 
 
 122 
 
 153 
 
 183 
 
 July . . 
 
 
 
 
 184 
 
 215 
 
 243 
 
 274 
 
 304 
 
 335 
 
 365 
 
 31 
 
 62 
 
 92 
 
 123 
 
 153 
 
 August . 
 
 
 
 
 153 
 
 184 
 
 212 
 
 243 
 
 273 
 
 304 
 
 334 
 
 365 
 
 31 
 
 61 
 
 92 
 
 122 
 
 September 
 
 
 
 
 122 
 
 153 
 
 181 
 
 212 
 
 242 
 
 273 
 
 303 
 
 334 
 
 365 
 
 30 
 
 61 
 
 91 
 
 October . 
 
 
 
 
 92 
 
 123 
 
 151 
 
 182 
 
 212 
 
 243 
 
 273 
 
 304 
 
 335 
 
 365 
 
 31 
 
 61 
 
 November 
 
 
 
 
 61 
 
 92 
 
 120 
 
 151 
 
 181 
 
 212 
 
 242 
 
 273 
 
 304 
 
 334 
 
 365 
 
 30 
 
 December 
 
 
 
 
 31 
 
 62 
 
 90 
 
 121 
 
 151 
 
 182 
 
 212 
 
 243 
 
 274 
 
 304 
 
 335 
 
 365 
 
 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 dateSj leap 
 years excepted, is found as in the following illustrations : 
 
 260. Examples, l. 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. + 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 
 
 Bt/ the table find the exact number of days from : 
 
 1. July 8 to Sept. 8. 
 
 2. Jan. 6 to Mar. 6. 
 
 3. Jan. 23 to June 23. 
 
 4. Feb. 13 to July 13. 
 
 5. Mar. 11 to Sept. 11. 
 
 6. Mar. 21 to Aug. 21. 
 
 7. May 31 to Aug. 1. 
 
 8. Feb. 23 to Sept. 23. 
 
 9. Mar. 24 to July 12. 
 
 10. May 11 to Aug. 31. 
 
 11. Aug. 15 to Dec. 10. 
 
 12. Nov. 25 to Mar. 25. 
 
BANK DISCOUNT 
 
 235 
 
 261. Examples, l. Find the proceeds of a note for S3000, 
 
 payable in 78 da., discounted at 6 %. 
 
 Solution. 78 da. = the term of discount. 
 $ 39 = the bank discount. 
 $3000 — $39 = $2961, the proceeds. 
 
 2. A note for S6000, payable in 60 da. from May 10, 1915, 
 with interest at 6 %, is discounted May 25, at 6 %. Find the 
 maturity, tlie term of discount, the bank discount, and the 
 proceeds. 
 
 Solution. July 9, 1915 = the maturity. 
 
 45 da. = tlie term of discount. 
 
 $60 = the interest on the note for 60 da. 
 $6060 = tlie value of the note at maturity. 
 $45.45 = the bank discount. 
 $6014.55 = the proceeds. 
 
 262. 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. 
 
 ^^^<t^y»t-o-^.-a>'»t>e^*g^ 
 
 
 
 ^<^tUS^<«^ 
 
 /J 
 
 f303 
 //.S2. 
 
 <3o. 
 
 
 
 ■«r (rfC.fi 
 
 WRITTEN EXERCISE 
 
 1. Assuming that the model draft, page 252, was discounted 
 July 20, at 6%, find the bank discount and the proceeds. 
 
 2. Assuming that the model draft, page 230, was discounted 
 May 30, at 6 %, find the bank discount and the proceeds. 
 
 3. Assuming that the model draft, page 231, was discounted 
 April 26, at 6 %, find the bank discount and the proceeds. 
 
 4. Assuming that the model draft, page 230, wa.s discounted 
 May 15, at 6%, find the bank discount and the proceeds. 
 
236 CONCISE BUSINESS AKITHMETIC 
 
 5. Assuming that the model draft, page 231, 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, 1915. 
 
 Six months after date, for value received, we promise to pay- 
 to the order of Ralph D. Gibson Eight Hundred Ninety-five 
 ^Yo Dollars, at Exchange National Bank. 
 
 Seth M. Bullard. 
 Discounted July 2, 1915, at 5%. Isaac C. Watkins. 
 
 7. Find the proceeds of the following joint and several note: 
 11000.00 Columbus, O., May 1, 1915. 
 
 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, 1915, at G %. Daniel W. Sheldon. 
 
 8. Find the proceeds of the following firm note: 
 $1250.00 St. Louis, Mo., Aug. 20, 1915. 
 
 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, 1915, at 6 %. 
 
 9. Sept. 26 you sold R. M. Stein, Portland, Me., a bill of 
 hardware amounting to ^2480, 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 
 
 237 
 
 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. 
 
 No. 
 
 Date of 
 
 Time 
 
 When 
 
 Teem op 
 
 Rate of 
 
 Value of 
 
 Disc. 
 
 Coll. & 
 
 Peoceeds 
 
 Papee 
 
 Dub 
 
 Discount 
 
 Discount 
 
 Papke 
 
 EXCH. 
 
 Ceeditbd 
 
 20 
 
 Apr. 25 
 
 3 mo. 
 
 
 
 
 6 7o 
 
 2000 
 
 00 
 
 
 
 
 
 
 
 21 
 
 May 1 
 
 3 mo. 
 
 
 
 
 6% 
 
 3500 
 
 00 
 
 
 
 3 
 
 50 
 
 
 
 22 
 
 Apr. 1 
 
 90 da. 
 
 
 
 
 6% 
 
 1500 
 
 00 
 
 
 
 
 
 
 
 23 
 
 Apr. 15 
 
 90 da. 
 
 
 
 
 6% 
 
 900 
 
 60 
 
 
 
 
 
 
 
 24 
 
 June 15 
 
 30 da. 
 
 
 
 
 6% 
 
 378 
 
 90 
 
 
 
 
 38 
 
 
 
 12. Sept. 15 your balance in the First National Bank was 
 $1725.90. You immediately offered for discount, at 6%, the fol- 
 lowing notes, the proceeds of which were to be placed to your 
 credit : E. M. Robinson's 30-day note dated Sept. 1, for S 300 ; 
 C. E. Reardon's note payable 3 mo. from July 25, with interest 
 at 6%, for S 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 was your credit at the bank after discounting the 
 notes ? 
 
 13. April 6, 1915, 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. 
 f 346. 50 Hartford, Conn., Mar. 1, 1915. 
 
 Ninety days after date I promise to pay Peter W. Ber- 
 ger, or order. Three Hundred Forty-six -^^^ Dollars, at First 
 National Bank, Hartford, Conn. 
 
 Value received. Henry S. Lake. 
 
 6. 
 $575.00 Hartford, Conn., Feb. 1, 1915. 
 
 Aug. 1, 1915, 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. 
 
238 
 
 CONCISE BUSINESS ARITHMETIC 
 
 14. July 18, C. B. Snow's bank balance is S312.90. He dis- 
 counts at 6% the following drafts, and then issues a check in 
 payment for 5 sewing machines at S75, less 20% and 25%. 
 What is the amount of liis balance after issuing the check ? 
 
 a. 
 
 $.im^ ^ 
 
 IMan 
 
 tNio.J^Sl'i 
 
 T^Jfrr T;^^ 
 
 /..-^.-fp-r^J-^ 
 
 S^fLGJtrrr 
 
 Rochester, tNl^Y., Jlf ^ ^f /^, /9 
 
 ^^<^^^^^!!^.<?-.-^7gz::^?cz^^gfk- ■^- - 'Pntj to the order of 
 
 ."Dollar 
 
 Ko.M^T>Ui 
 
 -T^-^g^ 
 
 ^^^'tr-r^y 
 
 BANK LOANS 
 
 263. The foregoing exercises have references 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 239 
 
 264. 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 investors, who use 
 them to pay for stocks ; but they are also made to merchants and others to 
 some extent. 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, 1915, 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. ? 
 
 ^.fTP^^-^ J^ewYorA, Jlr^^^. /, 79 
 
 ■ ' /^c^.^?^ ^^Z^^'*:fC'i ^ ^^^ n ffff- date ^-U^T^ promlae to pay to 
 
 tAe order o f ^-X^<^.<£^ X/^,^..-'??^?^ .^- 7? 7, ^"7^ V ^ ~- " 
 
 -^'^^k^^^n/t^.^^^.d^^^'y^,^ — : g)n//^^ 
 
 at ^^L:Ji^^^^-T>^.^f7..'^^<i^^ -^^f>- f^.^^y - 
 
 Value received 
 
 2. You gave the Union National Bank, of your city, your 
 note for S1200, 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 $12,000 of 
 Merchants National Bank on their demand note secured by 300 
 shares of Missouri Pacific Railway stock at S50. If the rate 
 of interest was 2i%, how much was required for settlement 
 39 da. after the loan was made? 
 
240 CONCISE BUSINESS ARITHMETIC 
 
 4. Jan. 2, 1915, C. W. Allen & Co., brokers, borrowed of 
 First National Bank, Boston, Mass., S 15,000 on the following 
 collateral note. How much was required for full settlement 
 of the loan 57 da. after it was made ? 
 
 $ /.f^^/7^ Eoslon, Mass. , J^^g2>^^^. Z, / 9 
 
 ., C y^^..'t^c.£^^^^^..'i:^.''7^^^ for value receioed, ^-JV^- prombe to pay to the order of 
 
 r: ^ i:^^^<^ <^ /)^.^^^^-t^^^ at their banking home 
 
 -^./-^^ 
 
 As collateral security for the payment of the note and all other liabilities to said bank, either absolute or 
 contingent, now existing or to be hereafter incurred, -<'</%- have deposited with it : 
 
 Should the market value of the same decline, -Cert- promise to furnish satisfactory additional collateral on 
 demand, which may be made by a notice in writing, sent by mail or otherwise, to ^P-t^--r-' residence or place of 
 business. On the nonperformance of either of the above promises -tt/~t^ 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 -«-'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 ~<crt- authorize said holder or holders, or any person iix 
 his or their behalf, to purchase at any such sale. ^^ >-a / ^ ^rp»*N 
 
 FINDING THE FACE 
 
 265. Example. I wish to borrow $1980 of a bank. For 
 what sum must I issue a 60-da. note to obtain the amount, 
 discount being at the rate of 6 % ? 
 
 Solution. Let the face of the note = $ 1 
 
 Then the bank discount = $0.01 
 And the proceeds = $0.99 
 
 But the proceeds - % 1980 
 
 1 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 S1990 ? of a 60-da. note, 
 same conditions ? 
 
 2. You wish to borrow S 3940 cash. What must be the face 
 of a 90-da. note in order that when discounted at 6% the 
 proceeds will be the required sum ? 
 
BAXK DISCOUNT 
 
 241 
 
 A WRITTEN REVIEW TEST 
 
 (Time, approximately, forty minutes) 
 
 Co]py each of the following problems ; complete the worh^ and 
 check the result. 
 
 When a certain number of days is written in the Discount column, compute 
 the discount at 6% for the given time. When Jg.% is written in the Collection 
 and Exchange column, compute the collection on the face of the paper. 
 
 When copying the problem do not copy the number of days in the dis- 
 count column, nor the ■^■^% in the collection and exchange column, but com- 
 pute the discount or the collection and enter the result in the required column. 
 
 Face of Paper 
 
 1. S856.40 
 442.50 
 365.30 
 297.45 
 175.40 
 217.50 
 246.30 
 
 Discount 
 
 S3.56 
 2.21 
 
 60 da. 
 2.97 
 1.75 
 2.18 
 
 soda. 
 
 Coll. & Exch. 
 
 $0.36 
 0.44 
 0.37 
 
 0.18 
 
 Proceeds 
 ? 
 ? 
 ? 
 ? 
 ? 
 ? 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 Face of Paper 
 
 Discount 
 
 Coll. & Exch. 
 
 Pkoceuus 
 
 2. S325.65 
 
 S1.63 
 
 $0.33 
 
 ? 
 
 150.60 
 
 90 da. 
 
 0.15 
 
 ? 
 
 327.85 
 
 3.28 
 
 0.33 
 
 ? 
 
 180.96 
 
 60 da. 
 
 tV% 
 
 ? 
 
 313.46 
 
 3.13 
 
 0.31 
 
 ? 
 
 286.32 
 
 1.43 
 
 0.29 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 ? 
 
 Face of Paper 
 
 Discount 
 
 Coll. & Exch. 
 
 Proceeds 
 
 3. S422.50 
 
 30 da. 
 
 tV% 
 
 ? 
 
 384.20 
 
 S3.84 
 
 $0.38 
 
 ? 
 
 519.40 
 
 5.19 
 
 0.52 
 
 ? 
 
 280.50 
 
 90 da. 
 
 0.28 
 
 ? 
 
 375.90 
 245.32 
 
 1.25 
 2.45 
 
 
 ? 
 ? 
 
 .tV% 
 
CHAPTER XX 
 
 EXCHANGE 
 DOMESTIC EXCHANGE 
 
 ORAL EXERCISE 
 
 1. Mention some objections to sending actual money by 
 express. 
 
 2. If S50 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? 
 
 266. The process of settling accounts at distant points with- 
 out actually sending the money is called exchange. 
 
 Money Orders 
 
 267. Money orders, as issued by post offices, express com- 
 panies, and banks are frequently used in making payments at 
 a distance. 
 
 268. A postal money order is a government order for the 
 payment of money, issued at one office and payable at another. 
 
 61596 Westfield, Sta.1,Mass. 
 
 3746 
 
 United States Postal Money Order 
 
 XA 
 
 DOLLARS / _^ 
 
 -^yV CENT. 
 
 PAY AMOUNT STATED ABOVE TO ORI 
 " IF ISSUED WITHIN THE COI 
 
 POSTMASTER 
 
 UNITED STATES, ALASKA EXCEPTED 
 
 OF PATEE NAMED 
 NENTAL UNITED : 
 
 JHIBTm ATS /ROM DATE OF ISai 
 
 RECEIVED PAYMENT: 
 
 FACSIMILE. OF NO VALUE 
 
 Westfield, Sta. 1 , Mass. 3746 
 
 61596 «:=ii--. 
 
 "" """" Coupon for Paytngr Office 
 
 J THIS MONEY ORDER IS NOT GOOD 
 
 5 FOR MORE THAN LARGEST AMOUNT 
 
 I INDICATED ON LEFT-HAND MARGIN 
 
 Z OF THE ORDER AND ANY ALTERA- 
 
 < TION OR CRAaURE RENDERS IT VOID 
 
 242 
 
EXCHANGE 243 
 
 The fees (rate of exchange) charged for postal money orders are : 
 
 For orders for sums 
 
 Not exceeding $2.50 Zf Over $30.00 to .$40.00 \hf 
 
 Over $2.50 to 5.00 hf Over 40.00 to 50.00 \%f 
 
 Over 5.00 to 10.00 8^ Over 50.00 to 60.00 20)* 
 
 Over 10.00 to 20.00 10^ Over 60.00 to 75.00 25)? 
 
 Over 20.00 to 30.00 VI f Over 75.00 to 100.00 Z^f 
 
 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 not 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. 
 
 269. An express money order is an order for the payment 
 of money issued by an express company and payable at any 
 of its agencies. 
 
 if.mf/;. 
 When G^untersigned 
 
 BYAOENTATPOINT OF ISSUE 
 
 Ber TO THE ORDER llF ^^:^^^~;^fe^^^.>.<^;;^^^ a t'^^^/^^,...;^^ . >^^^^^ 
 The Sum of /Z^^<i<>^^7^^.^^-^ //cm, -^ Dollars 
 
 GOOO FOR MORC THAN THE HJGMC3T PRiNTtD M>MtCJNAL AHOUHT. IN NO CASE TO EXCEED I 
 
 """CT^^^^^^^^J/ AecNT <:::^>c^i^Sr<x_ 
 
 '""i^^^7'-^S^e<;^^^^ State op /'/f^^,^^^ name oi- »EM«»e« /-"i^-) 
 
 .TE \le^y ^/, ,9 ^^Z^r^^^^04^-^^v 
 
 ^ / Axr ERASURE.ALTCRATION.DEFACEMENTORMUtnATIONOFTHIS ORDCRRENOERS rrvOIO. / 
 
 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. 
 
 270. A bank money order (see form, page 244) 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. 
 
244 
 
 CONCISE BUSINESS ARITHMETIC 
 
 CAPITAL 
 
 1 
 
 MONEY ORDER 
 NOT OVER 
 
 Fl F"TV DOL-UARS 
 
 Boston Mas 
 
 The N 
 
 TO ANV BANK NAMED 
 ONTHE BACKOrTHlS DRAPT 
 
 ANK 
 
 271. 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 TELEGRAPH CO. 
 
 INCORPORATED 
 
 23.000 OFFICES IN AMERICA 
 
 CABLE SERVICE TO ALL THE WORLD 
 
 ROBERT C. CLOWRY, President and General Manager 
 
 w t iM U the following message subject 
 terms on back hereof, which are hereby agreed 
 
 "YO The Union Telegraph Co, 
 
 to the \ 
 sedto. ^ 
 
 Boston. Mass.. July 27, 
 
 19 
 
 Rochester, N.Y, 
 
 Findahle 
 Findelkind 
 
 Charles 
 
 Osgood 
 
 ten 
 
 East 
 
 Avenue 
 
 Fi chant 
 
 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 
 
 Fickant One hundred dollars 
 
 Ficheron One thousand dollars 
 
 Findable Please pay of your city I . 
 
 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 245 
 
 The following are the rates for a ten-word message from Boston to the 
 places named : 
 
 New York $0.30 Chicago -10.50 Galveston $0.75 
 
 Philadelphia $0.35 San Francisco 11.00 Rochester $0.40 
 
 ORAL EXERCISE 
 
 1. What was the total cost to the sender of the postal 
 money order, page 242? the express money order, page 243? 
 the telegraphic money order, page 244? the bank money order, 
 page 244? 
 
 2. What will be the total cost of a postal money order for 
 27^? $2.19? 85.28? 810.40? 818.90? 845.10? 835.89? 8125 
 (1100 + 825)? 875.29? 849.82? 8127.16? 
 
 3. What will be the total cost of an express money order for 
 86.20? 828.80? 819.50? 827.95? 848.90? 865 (850+815)? 
 8111? 837.59? 841.72? $65.59? 8114? 
 
 4. What will be the total cost of a telegraphic money order 
 from Boston to New York for 850? 875? 8100? 8125? 8150? 
 8200? 8300? 8400? 8450? 8500? 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 Farh St. jicheron 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 : 83.10; 88.19; 825.06; 818.50; 820. 
 
 2. Find the total cost of six express money orders for the 
 following amounts : 81.25; 810; 86.80; 816.25; 880; 819.50. 
 
 3. Find the total cost of the following telegraphic money 
 orders: one from Boston to New York for 850; one from 
 Boston to Philadelphia for 8500; one from Boston to San 
 Francisco for 8175; one from Boston to Galveston for 8300; 
 one from Boston to Rochester for 8250. 
 
246 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Checks and Baxk Drafts 
 
 272. 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. 
 
 go^ton, a^aisf^., 
 
 ^^7, 19 — ^o./J'/ 
 
 ^ap to tjc order of^CT^Jj 
 
 T^.^7^^^:^^^.<^^^ ^^\^ 
 
 
 1= aDoIIarjg 
 
 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. H. Robinson & Co. in the 
 foregoing check both reside 
 in Boston. On receiving the 
 check E. H. Robinson & Co. 
 indorse it and deposit it for 
 credit with their bank, say 
 the National Shawmut Bank. 
 The First National Bank or 
 the National Shawmut Bank, 
 as well as each of the other 
 banks in the city, has many 
 depositors who draw checks 
 upon it which are deposited 
 by the payees in various other city banks ; 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 
 
 Interior View or a Clearing House 
 
EXCHAIS^GE 247 
 
 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 containing 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 
 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 
 
248 CONCISE 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, canceled, 
 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 ^i^%, 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. 
 
 273. 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 bank 
 draft, a check of one banking institution upon another. 
 
 Boston, ^ass.^JU c^ / ( ^J9 J/o..^Z^ 
 
 Uraders >J\ationat ^Jjank 
 
 ^aif to the ort/er of ^~ W.~^. . ~^ ^^^^^-g -^^^^T^ ^A^^^M 
 
 Jo CAemlcal J/ationai 38ank\ ~;^^^'^^-r^y^^^ 
 
 J/ew York j ^ ^«*>'-'' 
 
 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 many other places ; but drafts upon New York banks 
 and other financial centers are the most used in making remittances. 
 
EXCHANGE 249 
 
 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 some- 
 what (see page 254), but is seldom more than ■^-^%. 
 
 274. 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. 
 
 National Shawtmut Bank 
 
 Boston, Mass., J^^^^//, 19 No.di2^£/ 
 
 ]^«^the order oi ~^..^.^<^^^S^^/\y/^^ 
 
 
 In New York City, cashier's 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. 
 
 275. 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. 
 
 ^:Jj2J2J2Jr- SBoaton. -M^.,, (l^^^ /r fO J^o.Z^f 
 
 ^^P^^ ^jyational SLaivmut 38ank 
 
 payahte to the orcUf n f ^'~^./'^.'^^^^^^C^^^^^^<y7S^^ - 
 
 on the return of this certificate properlif indorsed. 
 
 C^r^ ,.> ^ y r^^4 ::^--^^ ^ ^ 
 
 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. 
 
250 CONCISE BUSINESS ARITHMETIC 
 
 ORAL EXERCISE 
 
 1. Assuming that the bank which cashed the check on 
 page 5 charged i % collection, what was the amount credited 
 to the depositor? 
 
 2. Silas Long of New York deposited the following check. 
 The bank deducted yL. % for collection. How much was placed 
 to Silas Long's credit ? 
 
 Cljt ^niott Bank 
 
 150jgton, 0^agiEi., xvv^-g^^-^ i 9 /i5o._^ 
 
 l^ar to ti^e otDet of 
 
 CjJ^^^^^r^Ah^^^^^^c/'T^-re^ /y^^. 
 
 <^'f^yh. 
 
 3. B deposited three out-of-town checks in his bank, as fol- 
 lows: S300; $700; S750. If the bank charged J^% 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 receipt for the payment of 
 money ? 
 
 5. How much did the bank draft on page 248 cost the pur- 
 chaser if the exchange was at J^ % premium ? 
 
 WRITTEN EXERCISE 
 
 1. Find the cost of a bank draft for S 3958.75 at yV % Pre- 
 mium; of a bank draft for $679.80 at gV^ premium; of a 
 bank draft for $768.54 at 50/ per $1000 premium. 
 
 2. To cover the cost of a bank draft bought at J^ % premium, 
 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 
 
 251 
 
 3. How large a bank draft can be bought for $850.85, ex- 
 change being at Jg-% premium? 
 
 4. Find the proceeds of the accompanying deposit, J^^ col- 
 lection and exchange being charged on the out-of-town checks. 
 
 "When the receiving teller takes a 
 deposit from a customer, he classi- 
 fies 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 
 (►^) 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." 
 
 THE UNION NATIONAL BANK 
 
 DEPOSITED BY 
 
 Boston, 
 
 c^Cf^ 
 
 cv^. y, /c 
 
 Specie 
 
 Bills .... ^^.^ 
 
 Checks . . -xdyLiz.<6i^4^^ . >K/ 
 
 2,^ 
 
 2^ 
 
 i^J / 7-7 
 
 JS\ 
 
 rd t^^ 
 
 - / / /f ^^J/ 
 
 ^(r^<1^AfrJk^\ 
 
 fCjSJl. 
 
 / zr? 
 
 ^/L 
 
 
 5. AVrite 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 J^- % premium ? Write the check. 
 
 6. Suppose that the members of the class whose surnames 
 begin 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 ai 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. 
 
252 CONCISE BUSINESS ARITHMETIC 
 
 Commercial Drafts 
 
 276. Business men frequently employ the commercial draft 
 as an aid in the collection of accounts that are past due. 
 
 / 2/^^.^^ --^c^^^.^^,^^.^^ ■ 9, 1Q 
 
 r^^-^T^^ 
 
 •^A^^..<U 
 
 U^^^^b^^,^!^^^ • ^qy to the order of 
 
 Value received and ckarye to account of 
 
 ■Jo. (^-^..f'^l^F^y^'^/^ .^/'J/ y^ /7 y^ 
 
 -^ 
 
 The above is a common form of draft used for collection purposes. 
 Edgar McMickle owes Wilbert, Gloss & 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. 
 
 277. It has been seen (page 231) that the time draft is fre- 
 quently used in connection with sales of merchandise. 
 
 :'^::^'^^-^^^ .g?^-^,.^^ ^,^^^..-^.^}^:Zf:?^7t'^ ^^y to the order of 
 
 Value received and charge to account of 
 
 Jo^ ^-^."M^^^^ ;^7^ ^ , ^ . ^^ 
 
 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 di*awn up and 
 
EXCHANGE 253 
 
 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 252 was collected by a bank 
 which charged J% collection, how much was placed to the 
 credit of Wilbert, Closs & Co.? 
 
 3. You deposited in Shawmut National Bank $5000, received 
 the certificate of deposit shown on page 249, and remitted it 
 to E. B. Stanton on account. Would there be any exchange ? 
 
 WRITTEN EXERCISE 
 
 1. The draft on page 252 was accepted July 17, and dis- 
 counted July 25. If the bank charged J^ % 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 §3500, and mailed it for acceptance. Apr. 1 the 
 draft was received accepted; Apr. 2 it was discounted at City 
 Bank. If the charges were gV % collection and 6 % interest, 
 what amount was credited to AVilson 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. 
 
254 CONCISE BUSINESS ARITHMETIC 
 
 4. Aug. 9 you sold C. D. Mead & Co., San Francisco, Cal., 
 39 mahogany sideboards at i 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 
 
 278. 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 255 
 
 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 all 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 ji^ % (| 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 York, Chicago, and Philadelphia. 
 
 279. 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. In 
 still others the clearing house association fixes the rate. 
 
 ORAL EXERCISE 
 
 Find the cost of the following hank drafts: 
 
 1. 8 18,500 at 2V % discount ; at 40 ^ per $ 1000 premium. 
 
 2. $ 516.90 at Jq % premium ; at 50 ^ per $ 1000 discount. 
 
 3. 81600.80 at 75^ per 81000 premium ; at -^^ % discount. 
 
 4. A draft for $4000 was bought for 8 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 
 8250 and made collection through their bank. If the bank 
 charged ^L ^ 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 ? 
 
DIVIDENDS AND INVESTMENTS 
 CHAPTER XXI 
 
 STOCKS AND BONDS 
 STOCKS 
 
 280. A corporation, or stock company, is an association of indi- 
 viduals organized under the laws of a particular state into a 
 body which is by law given the rights and powers and civil 
 liabihties of a person. 
 
 Being a mere creature of law a corporation possesses only those proper- 
 ties 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 is legal continuous 
 existence, irrespective of that of the individuals composing it. 
 
 281. The capital stock of a corporation represents the interest 
 of the individuals who compose the corporate body in the prop- 
 erty and profits of the corporation. 
 
 The capital stock is divided into a definite number of shares. It is not 
 necessary to give these shares a par value, but it is customary to do so. 
 The usual par value of a share is SIOO. However, any amount may be the 
 par value. 
 
 282. A stock certificate is a legal instrument which evidences 
 that the holder owns a certain number of shares of stock in the 
 corporation or association issuing the certificates. A stockholder 
 is a person who owns one or more shares of stock. 
 
 The certificate bears the seal of the corporation and is signed by officers 
 (usually the president and the treasurer or their representatives) authorized 
 by the by-laws to sign stock certificates. 
 
 Stockholders elect a few of their number to have general control of the 
 company. The stockholders thus elected constitute the board of directors. 
 This board may delegate its powers to several of its members called an 
 executive committee. The control of a corporation is vested in its board 
 of directors. 
 
 266 
 
STOCKS AND BONDS 
 
 257 
 
 283. A dividend is a sum of money paid by a corporation to 
 its stockholders, each share participating equally. An assess- 
 ment is an amount per share which stockholders are called upon 
 to pay to make up losses or deficiencies. 
 
 The board of directors decide upon the rate of dividend, which usually 
 means the rate per annum on the face value of the stock, but it may also be 
 expressed as a certain amount in dollars and cents per share. 
 
 Shares of stock may be non-assessable. 
 
 284. A company may divide its stock into two or more classes; 
 the usual division is preferred and common. 
 
 285. Preferred stock is stock which is entitled, out of profits, 
 to a preferential dividend at a fixed rate. In case a company 
 is dissolved, its preferred stock usually has a preferential claim 
 against the assets of the company up to the par value of the 
 preferred stock outstanding. 
 
 The prior rights of preferred stocks over common usually make them 
 safer investments, but stocks are not necessarily safe because preferred. 
 
258 
 
 CONCISE BUSINESS ARITHMETIC 
 
 286. Common stock is the stock wliich has the right to the 
 equity in the earnings and the income of the hquidation in the 
 assets of a corporation after the claims of all prior security 
 issues (bonds, notes, preferred stock, etc.) have been satisfied. 
 
 287. 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. 
 
 288. If a company is prosperous and pays a higher rate of 
 dividend than the money could earn with no greater risk in the 
 general money market, a share may sell for more than its face 
 value ; it is then said to be above par^ or at a premium. If the com- 
 pany pays a lower rate of dividend than could be obtained at no 
 greater risk in the general money market, a share may sell for 
 less than its face value ; it is then helow par^ or at a discount 
 
 289. A stock broker is a person who buys and sells stocks for 
 other persons on commission. 
 
 Stocks are usually bought and sold through stock brokers. The broker's 
 commission is usually ^% of the par value of the stock, or 12^^ per share. 
 A charge is made for either buying or selling. 
 
STOCKS AND BONDS 259 
 
 290. When the price of stock is quoted at 97, 118|, 1601 
 it means that a share whose par value is $100 can be bought 
 for $97, $118.75, $160.50. If a person buys stock through a 
 broker at 1601, it will cost him $160.50 + $0,121 brokerage, or 
 $160,621; if he sells stock through a broker for 1601, he will 
 receive as proceeds $160.50 - $0,121, or $160,371, per share. 
 
 On the New York Stock Exchange quotations are expressed in dollars 
 and eighths of a dollar. 
 
 In some other cities quotations are expressed in dollars, in eighths of a 
 dollar, and in sixteenths of a dollar. When stocks are quoted at less than 
 $1 per share, fluctuations are sometimes expressed in cents. 
 
 The bulk of transactions in the stock exchanges is in round lots. In 
 New York round lots are 100 shares or some multiple thereof ; in Boston, 
 50 shares or some multiple thereof. In these cities any other number of 
 shares than the ones named for each would be called odd lots. In Chicago 
 no distinction is made between round and odd lots. Fractional shares of 
 stock which are occasionally in the market are called scrip. 
 
 ORAL EXERCISE 
 
 1. Examine the certificate of stock, page 257. What is the 
 name of the company ? From whom did the company get its 
 right to carry on 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 dividends 
 on the preferred stock of the company, the rate being 6 % ? How 
 much of this sum will the holder of the certificate receive ? 
 
 6. Examme the stock certificate, page 258. 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 ? 
 
260 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Dividends and Assessments 
 written exercise 
 
 Unless otherwise specified, the par value of a share will be understood 
 to be .1100. 
 
 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 Lehigh Valley Railroad stock. When 
 the company declares a dividend of 7J%, 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 
 dividends are declared ? 
 
 4. E. H. Rhodes holds 600 shares of Lehigh Valley Rail- 
 road stock. If he received the following check as his annual 
 dividend, what was the rate ? 
 
 ^.^^S^ay to /■/JjLfe- 
 
 K/Ae 3'irst >^ational SBank 
 
 i 
 
 J/o.A2=lZ 
 
 -/^ /g ?^ — 
 
 a>ioi€Und J{o.A^ 
 
 reasurer 
 
 5. A company with $1,000,000 capital declares quarterly 
 dividends of 1^%. 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 
 annually among its stockholders ? What is the annual income 
 of a man who owns 200 shares ? 
 
STOCKS AND BONDS 261 
 
 8. If the Pennsylvania Railroad declares a semiannual divi- 
 dend of 21% on 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 $75,500 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 
 $375,000 and the expenses $215,000. What even per cent of 
 dividend may be declared and what would be the amount of un- 
 divided profits if 10% of the net earnings are first set aside as a 
 surplus fund ? (An even per cent is a per cent without a fraction.) 
 
 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 3J % 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 ? 
 
262 
 
 CONCISE BUSINESS ARITHMETIC 
 
 14. The capital stock of the First National Bank is $ 3,000,000, 
 and dividends are declared semiannually. The profits of the 
 bank for a certain six months are $185,750. Of this sum 10% is 
 carried to a surplus fund. The directors then vote to declare a 
 semiannual 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 
 
 291. The following is an abbreviated form of the stock quo- 
 tations for a certain day on the New York Stock Exchange : 
 
 
 Table op Sales and 
 
 Range 
 
 OF Prices 
 
 
 Sales 
 
 Stocks 
 
 Open. 
 
 High. 
 
 Low. 
 
 Clos. 
 
 Net Change 
 
 2,600 
 
 Am. Sugar. . . . 
 
 lOOi 
 
 100^ 
 
 99i- 
 
 99f 
 
 -f 
 
 200 
 
 Am. Sugar (pfd.) . 
 
 110 
 
 llOi 
 
 109i 
 
 109i 
 
 -i 
 
 10,200 
 
 Atchison .... 
 
 95^ 
 
 95i 
 
 91f 
 
 92 
 
 -H 
 
 300 
 
 Atchison (pfd.) . . 
 
 100 
 
 100 
 
 100 
 
 100 
 
 
 900 
 
 At. Coast Line . . 
 
 121i 
 
 120 
 
 116 
 
 116 
 
 -^ 
 
 13,600 
 
 Baltimore & 0. . . 
 
 m 
 
 88f 
 
 87i 
 
 88 
 
 -i 
 
 600 
 
 Baltimore &0. (pfd.) 
 
 80i 
 
 81 
 
 80i 
 
 80i 
 
 -i 
 
 147,100 
 
 Canadian Pacific . . 
 
 1931- 
 
 200f 
 
 1881 
 
 1891 
 
 -Si 
 
 20,200 
 
 Chic. M. & St. P. . 
 
 98| 
 
 98i 
 
 94i 
 
 95 
 
 -3f 
 
 300 
 
 Chic. M.& St. P. (pfd.) 
 
 13 7f 
 
 135 
 
 134| 
 
 1341 
 
 -2 
 
 200 
 
 General Chem. (pfd.) 
 
 108 
 
 109 
 
 108i 
 
 109 
 
 + 1 
 
 2,500 
 
 General Electric . . 
 
 144 
 
 144 
 
 141 
 
 141 
 
 -3 
 
 15,600 
 
 Gt. Northern (pfd.) . 
 
 122 
 
 1211- 
 
 119 
 
 im 
 
 -H 
 
 1,600 
 
 Illinois Central . . 
 
 110 
 
 110 
 
 107i 
 
 107| 
 
 -2f 
 
 59,800 
 
 Lehigh Valley . . 
 
 136i 
 
 136^ 
 
 132ir 
 
 134f 
 
 -If 
 
 650 
 
 Louisville & Nash. . 
 
 135f 
 
 135i 
 
 131i 
 
 131ir 
 
 -4i 
 
 2,100 
 
 Nat'l Biscuit . . . 
 
 131 
 
 130i 
 
 125 
 
 125 
 
 -5 
 
 100 
 
 Nat'l Biscuit (pfd.) . 
 
 123 
 
 1231 
 
 1231- 
 
 1231 
 
 + 1 
 
 69,200 
 
 South. Pacific . . . 
 
 92|r 
 
 91i 
 
 86i 
 
 87i 
 
 -^ 
 
 300 
 
 South. Pacific (pfd.) . 
 
 lOOi" 
 
 97i 
 
 97i 
 
 97i 
 
 -21 
 
 210,100 
 
 Union Pacific . . . 
 
 154i 
 
 154J 
 
 1481 
 
 1491 
 
 -4 
 
 400 
 
 Union Pacific (pfd.) . 
 
 82i 
 
 82^ 
 
 82 
 
 82 
 
 -i 
 
 390,100 
 
 U.S. Steel .... 
 
 58i 
 
 58f 
 
 56 
 
 56f 
 
 -2f 
 
 4,200 
 
 U.S. Steel (pfd.) . . 
 
 109 
 
 109i 
 
 107i 
 
 107i 
 
 -li 
 
 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, the highest, the lowest, and the closing prices of the day; 
 in the last, the net changes betw:een the closing price of yesterday and to-day. 
 Thus, 2600 shares of American Sugar stock were sold. The opening price 
 was $100.50 per share; the highest price $100.50; the lowest, $99.25 ; the 
 closing, $99.75, w^hich shows a decline of 75^ from the preceding day. 
 
STOCKS AKD BOKDS 263 
 
 ORAL EXERCISE 
 
 1. Find in the table (page 262) three cases where a quo- 
 tation both for common stock and for preferred (^pfd, stands 
 for preferred) stock of the same company is given. Which is 
 worth the more in each case ? The par value of all shares is 
 $100. 
 
 If the profits of a concern are so great that a large per cent may be paid 
 on the common stock, after paying the fixed rate on the preferred stock, 
 then the common stock may sell for a higher figure than the preferred. 
 
 2. What would 100 shares of American Sugar (common) cost 
 if bought through a broker at the lowest price for the day, 
 brokerage being |^%. 
 
 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, i%. 
 
 4. State the cost, at the opening price in the table, of 100 
 shares each of the following stocks, assuming that the transac- 
 tions take place through a broker who charges ^ % commission : 
 Baltimore & Ohio ; Canadian Pacific ; General Electric ; Lehigh 
 Valley. (Base the calculations on the common stock.) 
 
 5. At the highest price in the table, state the amount that 
 would be received from the sale of 100 shares of each of the 
 following stocks, assuming that they were sold through a broker 
 who charged 1% commission: Southern Pacific; U.S. Steel (pre- 
 ferred) ; Great Northern (preferred) ; National Biscuit ; Ameri- 
 can Sugar (preferred) ; Atchison ; General Chemical (preferred) ; 
 Illinois Central; Union Pacific. (If preferred is not named, 
 common stock is referred to.) 
 
 WRITTEN EXERCISE 
 
 Find the coat, at the closing price in the table, of 2500 shares of 
 the following stocks, inclvding brokerage : 
 
 1. Canadian Pacific. 4. Baltimore & Ohio (pfd.). 
 
 2. American Sugar (pfd.). 5. Atlantic Coast Line. 
 
 3. National Biscuit (pfd.). 6. United States Steel (pfd.). 
 
264 CONCISE BUSINESS AEITHMETIC 
 
 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. Atchison (pfd.). 
 
 8. Louisville & Nashville. 12. General Electric. 
 
 9. Southern Pacific. 13. Southern Pacific (pfd.). 
 10. Lehigh Valley. 14. Great Northern (pfd.). 
 
 292. Example. I bought 1000 shares Chicago, Milwaukee, & 
 St. Paul preferred stock, at the lowest price in the table, and 
 sold the same at 140 i-. Allowing for brokerage both for buying 
 
 and selling, did I gain or lose, and how much ? 
 
 S140 37I- 
 SoLUTiON. Since I bought through a broker, each share * 2 
 
 cost me ^ 134.871 +. $0.12^, or $ 135 ; and since I sold through 12>b.00 
 
 a broker, the proceeds of each share sold was $140.50 — $0.12i, $ 5.371 
 
 or $140.37|. $140,371 - $135.00 = $5.37|, gain on each 1000 
 
 share. Since $5.37^ is gained on each share, 1000 times ■ ^ ^ 
 
 $5.37^, or $5375, is gained on 1000 shares. ^o61b. 
 
 In the following exercise it is understood that all sales and jDurchases are 
 made through a broker, who charges a commission of ^% both for buying 
 and for selling. 
 
 WRITTEN EXERCISE 
 
 Find the gain or loss on 500 shares of each of the following stocks 
 bought at the opening price and sold at the price here given : 
 
 1. Illinois Central, 108|. 5. American Sugar (pfd.), 103. 
 
 2. General Electric, 147|. 6. National Biscuit, 1341. 
 
 3. Southern Pacific (pfd.), 89. 7. Baltimore & Ohio, 90f . 
 
 4. General Chemical (pfd.), 110. 8. Canadian Pacific, 2001. 
 
 9. United States Steel (pfd.), 112^. 
 
 10. Atlantic Coast Line, 115|. 
 
 11. Great Northern (pfd.), 125. 
 
 12. National Biscuit (pfd.), 126J. 
 
 13-24. Find the gain or the 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. John R. West bought 400 shares of United States Steel, 
 (common) at the opening price in the table and sold it so as to 
 gain S300. What was the quoted price when he sold it? 
 
STOCKS AND BONDS 265 
 
 26. I bought some United States Steel (preferred) at the 
 opening price in the table and sold it for 112i. If I gained 
 $650 by the transaction, how many shares did I buy? 
 
 27. I bought 2500 shares of General Electric at the lowest 
 price in the table, held it for a year, received 5 % in dividends, 
 and then sold it at 139|^. If money was worth 41 %, did I gain 
 or lose, and how much ? 
 
 The interest is to be computed on the cost of the stock, the dividend on 
 the par value. 
 
 28. I gave my broker orders to buy 1500 shares of Atchison 
 (preferred) and to sell 2000 shares of Canadian Pacific. If he 
 bought at the lowest price in the table and sold at the highest 
 price, what balance will he put to my credit ? 
 
 BONDS 
 
 293. A bond is an instrument by which a government, a 
 municipality, or a corporation contracts and agrees to pay a 
 specified sum of money on a given date, at a specified rate of 
 interest. — Rollins. 
 
 Bonds are generally issued at a face vailue of $ 1000 ; less frequently, of 
 $500 ; occasionally, of $100. All bonds of the same issue usually have the 
 same rights and security. 
 
 Bonds, the payment of which depends only on the unsecured credit of 
 the issuing company, are called debenture bonds; those that have their pay- 
 ment secured by a mortgage on the property of the issuing corporation 
 are called mortgage bonds; those that are secured by a deposit with a trustee 
 of collateral are called collateral trust bonds ; those that provide that the 
 interest on them shall be paid only if earned are called income bonds. 
 
 Bonds of a national government are called government bonds; of a state, 
 a city, a town, or other municipal organization, municipal bonds. 
 
 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. 
 
 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. 
 
266 
 
 CONCISE BUSINESS ARITHMETIC 
 
 294. With reference to the form of contract for the payment 
 of principal and interest there are two kinds of bonds: coupon 
 and registered. 
 
 295. 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. 
 
STOCKS AND BONDS 267 
 
 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. 
 
 296. 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 by check. 
 
 Coupon bonds may be made payable either to bearer or registered as to 
 principal only (the first custom prevails generally), and may be transferred 
 by delivery or indorsement accordingly. Registered bonds are always 
 drawn payable to some designated person and can be transferred only by 
 assignment and registry on the books of the corporation. 
 
 ORAL EXERCISE 
 
 1. Examine the bond on page 266. 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 ? 
 
 All bonds are bought and sold « and interest " ; that is, interest should be 
 reckoned on the par value from the date of the last interest payment to the 
 date of the purchase or sale, at the rate which the bond pays. 
 
 6. If the bond on page 266 was quoted at 105|- when it was 
 purchased, how much did it cost, mcluding ^ % brokerage ? 
 How much did the seller realize on it, if sold Aug. 1. 1915 ? 
 
 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 ? 
 
 8. What is the difference in the meaning of government bond 
 and municipal bond ? Upon what authority does the government 
 issue bonds ? Upon what authority does a town or a city issue 
 bonds ? Must the bond issue be approved by the state in which 
 the town or the city is located ? 
 
268 CONCISE BUSINESS ARITHMETIC 
 
 The Use of Bond Tables 
 
 297. The use of tables for finding the interest on notes, 
 bonds, etc., is common among bankers and brokers. No interest 
 tables are illustrated in this connection because they are too 
 extended and complex for a textbook. 
 
 Referring to the bond table, page 269, the per cents at the top of 
 the table represent the income on the face of a bond at one of 
 the given rates, and the per cents given in the column at the left 
 represent the income that will be realized when a bond is bought 
 at a certain market price. This table is for a bond maturing 20 
 yr. from date, with interest payable semiannually. 
 
 298. Example. What will be the net income on a 5 % bond 
 bought at 97.53? 
 
 Solution. In the column headed 5% find the price named, 97.53, then fol- 
 low this line to the left and note that in the Ter Cent per Annum column 5.20 
 is given; the net income on the price paid for the bond, 97.53, will be 6.2%. 
 
 ORAL EXERCISE 
 
 Mefer to the table and find the cost of: 
 
 1. A 6 % bond that will net 6J %. 
 
 2. A 3 % bond that will net 5 %. 
 
 3. A 41 % bond that will net 4.8 %. 
 
 4. A 4 % bond that will net 6^ %. 
 
 5. A man purchased 4 bonds, as follows : a 3 % bond that 
 would net 4.6 % ; a 4^^ % bond that would net 4 % ; a 5 % bond 
 that would net 4i^ %. What did he pay for each bond ? 
 
 Refer to the table and find the net income of: 
 
 6. A 5% bond that willcost $91.15. 
 
 7. A 7% bond that will cost $125.10. 
 
 8. A 3% bond that will cost $79.95. 
 
 9. A 6 % bond that will cost $106.02. 
 
 10. A man purchased 5 bonds each of which netted him 5 % 
 income. If the bonds which he bought yielded, on the face 
 value, the following rate of income, what did he pay for each 
 one: 4%, 3^%, 5%, 6 %, and 7% ? 
 
STOCKS AND BONDS 
 
 269 
 
 A BOND TABLE 
 20-YEAR. Interest Payable semiannually 
 
 Per CE>rT 
 PER Annum 
 
 3% 
 
 H% 
 
 4% 
 
 ^7o 
 
 5% 
 
 6% 
 
 7% 
 
 3.70 
 
 90.17 
 
 97.19 
 
 104.21 
 
 111.24 
 
 118.26 
 
 132.30 
 
 146.35 
 
 31 
 
 89.51 
 
 96.50 
 
 103.50 
 
 110.49 ■ 
 
 117.48 
 
 131.46 
 
 145.44 
 
 3.80 
 
 88.86 
 
 95.82 
 
 102.78 
 
 109.74 
 
 116.70 
 
 130.63 
 
 144.55 
 
 3^ 
 
 87.90 
 
 94.81 
 
 101.73 
 
 108.64 
 
 115.56 
 
 129.39 
 
 143.22 
 
 3.90 
 
 87.58 
 
 94.48 
 
 101.38 
 
 108.28 
 
 115.18 
 
 128.98 
 
 142.78 
 
 4. 
 
 86.32 
 
 93.16 
 
 100.00 
 
 106.84 
 
 113.68 
 
 127.36 
 
 141.03 
 
 4.10 
 
 85.09 
 
 91.86 
 
 98.64 
 
 105.42 
 
 112.20 
 
 125.76 
 
 139.32 
 
 •4i 
 
 84.78 
 
 91.54 
 
 98.31 
 
 105.07 
 
 111.84 
 
 125.37 
 
 138.90 
 
 4.20 
 
 83.87 
 
 90.59 
 
 97.31 
 
 104.03 
 
 110.75 
 
 124.19 
 
 137.63 
 
 4i 
 
 83.27 
 
 89.96 
 
 96.65 
 
 103.35 
 
 110.04 
 
 123.42 
 
 136.80 
 
 4.30 
 
 82.68 
 
 89.34 
 
 96.00 
 
 102.60 
 
 109.33 
 
 122.65 
 
 135.98 
 
 4| 
 
 81.80 
 
 88.42 
 
 95.04 
 
 101.65 
 
 108.27 
 
 121.51 
 
 134.75 
 
 4.40 
 
 81.51 
 
 88.11 
 
 94.72 
 
 101.32 
 
 107.93 
 
 121.14 
 
 134.35 
 
 4i 
 
 80.35 
 
 86.90 
 
 93.45 
 
 100.00 
 
 106.55 
 
 119.65 
 
 132.74 
 
 4.60 
 
 79.22 
 
 85.72 
 
 92.21 
 
 98.70 
 
 105.19 
 
 118.18 
 
 131.16 
 
 # 
 
 78.94 
 
 85.42 
 
 91.90 
 
 98.38 
 
 104.86 
 
 117.82 
 
 130.77 
 
 4.70 
 
 78.11 
 
 84.55 
 
 90.99 
 
 97.43 
 
 103.86 
 
 116.74 
 
 129.61 
 
 4i 
 
 77.57 
 
 83.98 
 
 90.39 
 
 96.80 
 
 103.20 
 
 116.02 
 
 128.84 
 
 4.80 
 
 77.02 
 
 83.40 
 
 89.79 
 
 96.17 
 
 102.55 
 
 115.32 
 
 128.08 
 
 4i 
 
 76.22 
 
 82.56 
 
 88.90 
 
 95.24 
 
 101.59 
 
 114.27 
 
 126.95 
 
 4.90 
 
 75.95 
 
 82.28 
 
 88.61 
 
 94.94 
 
 101.27 
 
 113.92 
 
 126.58 
 
 5. 
 
 74.90 
 
 81.17 
 
 87.45 
 
 93.72 
 
 100.00 
 
 112.55 
 
 125.10 
 
 5.10 
 
 73.86 
 
 80.09 
 
 86.31 
 
 92.53 
 
 98.76 
 
 111.20 
 
 123.65 
 
 5i 
 
 73.61 
 
 79.82 
 
 86.03 
 
 92.24 
 
 98.45 
 
 110.87 
 
 123.29 
 
 5.20 
 
 72.85 
 
 79.02 
 
 85.19 
 
 91.36 
 
 97.53 
 
 109.87 
 
 122.22 
 
 5i 
 
 72.34 
 
 78.49 
 
 84.64 
 
 90.78 
 
 96.93 
 
 109.22 
 
 121.51 
 
 5.30 
 
 71.85 
 
 77.97 
 
 84.09 
 
 90.21 
 
 96.33 
 
 108.57 
 
 120.81 
 
 5f 
 
 71.11 
 
 77.19 
 
 83.27 
 
 89.36 
 
 95.44 
 
 107.60 
 
 119.77 
 
 6.40 
 
 70.87 
 
 76.94 
 
 83.01 
 
 89.07 
 
 95.14 
 
 107.28 
 
 119.42 
 
 51 
 
 69.90 
 
 75.92 
 
 81.94 
 
 87.96 
 
 93.98 
 
 106.02 
 
 118.06 
 
 ^ 
 
 68.72 
 
 74.68 
 
 80.64 
 
 86.59 
 
 92.55 
 
 104.47 
 
 116.38 
 
 51 
 
 67.57 
 
 73.46 
 
 79.36 
 
 85.26 
 
 91.15 
 
 102.95 
 
 114.74 
 
 5i 
 
 66.43 
 
 72.27 
 
 78.11 
 
 83.95 
 
 89.78 
 
 101.46 
 
 113.13 
 
 6. 
 
 65.33 
 
 71.11 
 
 76.89 
 
 82.66 
 
 88.44 
 
 100.00 * 
 
 111.56 
 
 6i 
 
 64.25 
 
 69.97 
 
 75.69 
 
 81.41 
 
 87.13 
 
 98.57 
 
 110.01 
 
 6i 
 
 63.19 
 
 68.85 
 
 74.51 
 
 80.18 
 
 85.84 
 
 97.17 
 
 108.50 
 
 6f 
 
 62.15 
 
 67.76 
 
 73.36 
 
 78.07 
 
 84.58 
 
 95.79 
 
 107.01 
 
 6i 
 
 61.14 
 
 66.69 
 
 72.24 
 
 77.79 
 
 83.34 
 
 94.45 
 
 105.55 
 
 6f 
 
 60.14 
 
 65.64 
 
 71.14 
 
 76.64 
 
 82.13 
 
 93.13 
 
 104.12 
 
 6t 
 
 59.17 
 
 64.62 
 
 70.06 
 
 75.50 
 
 80.95 
 
 91.83 
 
 102.72 
 
 ^ 
 
 58.22 
 
 63.61 
 
 69.00 
 
 74.39 
 
 79.78 
 
 90.57 
 
 101.35 
 
 7. 
 
 57.29 
 
 62.63 
 
 67.97 
 
 73.31 
 
 78.64 
 
 89.32 
 
 100.00 
 
270 
 
 COKCISE BUSINESS AEITHMETIC 
 
 Buying and Selling Bonds 
 
 299. Bonds are generally bought and sold through invest- 
 ment bankers or private bankers. 
 
 The commission for buying and selling bonds is the same as 
 for buying and selling stocks. 
 
 300. The following table is an abbreviated form of the sales, 
 and the opening, highest, lowest, and closing prices of bonds 
 traded in on the New York Exchange on a recent date. 
 
 Table of Sales and Range of Prices 
 
 Sales 
 
 Bonds 
 
 Open. 
 
 High. 
 
 Low. 
 
 Clos. 
 
 Net Change 
 
 5,000 
 
 Am. Hide & Leather 
 
 
 
 
 
 
 
 6s 
 
 103^- 
 
 103^ 
 
 103 
 
 104 
 
 + f 
 
 8,000 
 
 Brooklyn Rapid Tran- 
 
 
 
 
 
 
 
 sit con, 6s . . . . 
 
 103 
 
 103 
 
 102f- 
 
 103 
 
 
 6,000 
 
 Cliesapeake & Ohio 5s 
 
 106i 
 
 107i 
 
 1061 
 
 107i 
 
 + 1 
 
 81,000 
 
 Chicago, Burlington & 
 
 
 
 
 
 
 
 Quincy 4s . . . 
 
 931 
 
 931- 
 
 92| 
 
 92| 
 
 -1 
 
 15,000 
 
 Erie 1st con. 4s . . 
 
 85| 
 
 8of 
 
 85 
 
 85 
 
 -f 
 
 1,000 
 
 Illinois Central 4s . . 
 
 93 .V 
 
 93i 
 
 93i 
 
 93i 
 
 
 11,000 
 
 Lehigh Valley con. 4^8 
 
 99f 
 
 99i 
 
 m 
 
 99i 
 
 -f 
 
 1,000 
 
 Louisville & Nashville 
 
 
 
 
 
 
 
 gold 5s .... 
 
 103 
 
 110 
 
 110 
 
 110 
 
 + 2 
 
 2,000 
 
 Manhattan Ry.con,43 
 
 92 
 
 92i 
 
 91f 
 
 91i 
 
 -i 
 
 8,000 
 
 Missouri Pacific 4s . 
 
 59 
 
 57 
 
 56 
 
 56 
 
 -2 
 
 24,000 
 
 N.Y. Central & Hud- 
 
 
 
 
 
 
 
 son River 4s 1934 . 
 
 m 
 
 91| 
 
 89i 
 
 90 
 
 -n 
 
 35,000 
 
 Reading general 4s . 
 
 94f 
 
 95 
 
 94i 
 
 941 
 
 -i 
 
 1,000 
 
 Standard Gas 6s . . 
 
 89f 
 
 89f- 
 
 89i- 
 
 89 
 
 -1- 
 
 4,000 
 
 Texas Pacific 1st 5s . 
 
 102 
 
 102^ 
 
 101| 
 
 1021 
 
 + i 
 
 62,000 
 
 Union Pacific 1st 4s . 
 
 97i 
 
 971 
 
 97i 
 
 96f 
 
 -f 
 
 196,000 
 
 United Steel 5s . . 
 
 102i 
 
 1021- 
 
 102i 
 
 1011 
 
 -f 
 
 18,000 
 
 Wabash 1st 5s . . . 
 
 1031 
 
 104 
 
 103i 
 
 1021 
 
 -1 
 
 8,000 
 
 West Shore 4s . . . 
 
 93f 
 
 94 
 
 -93f 
 
 93.V 
 
 -i 
 
 In the first column is shown the par value of the bonds sold ; in the 
 second, the name of the bonds and the interest they bear; in the third, 
 fourth, fifth, and sixth, respectively, the oj^ening, highest, lovrest, and 
 closing prices of the day. In the last column. Net Change, the net changes 
 between the closing prices of the given day and the closing prices of the 
 day preceding. Thus, on the day given, $8000 worth of Brooklyn Rapid 
 Transit bonds bearing 5 % interest were sold. The opening price was $ 103 
 per $ 100 of par value ; the highest price, $ 103 ; the lowest price, $ 102.62J ; 
 the closing price, $ 103 ; there was no change between the closing price of 
 the day given and the day preceding. 
 
STOCKS AND BONDS 271 
 
 301. Example. What is the cost of S 50,000 (par value) 
 Chicago, BurUngton & Quincy 4 % bonds at the highest price 
 quoted in the table (page 270) ? 
 
 Solution. $100 of par value cost $93| + $0.12^ brokerage, or $94. 
 
 .-. $50,000 of par value w^ill cost 500, i.e., ($50,000-7- $100) times $94, or$47,000. 
 
 WRITTEN EXERCISE 
 
 (Omit the interest in solving these problems) 
 
 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 S 10,000 Chesapeake & 
 Ohio 5 % bonds and buy $10,000 Texas Pacific 1st 5 % 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 these sales : $1000 United Steel 5 % 
 bonds at the opening price in the table; $5000 Illinois Central 
 4 % bonds at the opening price in the table ; $ 75,000 Chicago, 
 Burlington & Quincy 4 ^o bonds at the closing price in the table ; 
 $10,000 Erie 4% bonds at the lowest price in the table. 
 
 4. June 1, 1915, a certain city borrowed $ 250,000 with which 
 to build a new high school, and issued 41 % 10-yr. coupon bonds 
 as security. If these bonds sold (through a broker) at 101 1-, 
 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 Louis- 
 ville & Nashville 5 % bonds at the lowest price in the table ; 
 $15,000 Missouri Pacific 4 % bonds at the opening price in the 
 table; $10,000 Manhattan Railway 4 % bonds at the lowest price 
 in the table ; $3000 West Shore 4 % bonds at the opening price 
 in the table. 
 
APPENDIX A 
 
 ADDING MACHINES 
 
 Machines or mechanical devices for performing arithmetical calculations are 
 now commonly used in business offices ; in banks, factories, insurance offices, 
 and wholesale and retail houses they may be 
 regarded as indispensable. 
 
 A machine will list and add figures in one 
 fifth or one sixth of the time in which the 
 work can be done by a person using a 
 pen or a pencil, and with an accuracy 
 that a person cannot equal. The 
 operations of subtraction, multi- 
 plication, division, and trade 
 discount may be as readily per- 
 formed as those in addition. 
 
 The machine writes figures 
 as rapidly as a typewriter, and 
 as legibly ; figures are recorded 
 by simply touching the keys. 
 The figures written down are 
 added automatically, and at any 
 time, by the mere operation of a 
 handle, will be recorded without 
 the possibility of an error, the 
 absolutely correct total. When 
 an item is incorrectly put 
 into the keyboard, it may, 
 before pulling the handle, be 
 corrected. 
 
 Machines are of 
 different sizes, and 
 some machines have 
 paper carriages simi- 
 lar to the carriage 
 on a typewriter ; on 
 these carriages, if 
 desired, results are 
 printed and carbon 
 copies made. Ma- 
 chines may be 
 furnished wit'.i 
 an electric drive, 
 thus avoiding the 
 handle pull. 
 
 273 
 
274 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Machines can be equipped for adding dollars and cents; feet and inches; 
 dozens and gross ; hours and minutes ; tons and hundred weights ; pounds and 
 bushels; grains and penny- 
 weights; English pounds, shil- 
 lings, and pence, or any other 
 kind of foreign money ; dates and 
 amounts ; or any kind of figures. 
 Machines may be equipped 
 with the unlimited split device 
 for dividing the keyboard into 
 two or more sections, for listing 
 and adding two or more sets of 
 figures at one operation. Thus 
 they may also be equipped with 
 devices for automatically listing 
 and adding across the sheet or 
 form in two or more columns. 
 There is a duplex adding machine 
 with two sets of wheels, to accumulate two 
 separate totals at the same time. With a ma- 
 chine of this type, totals of groups of items 
 may be secured and a grand total of the 
 group totals accumulated at the same time. 
 Adding-subtracting machines add debits, 
 subtract credits, and automatically compute 
 the difference and print it. There are special 
 adding machines for handling monthly 
 statements and for ledger posting and cost 
 accounting ; a pay-roll machine that, with one operation, prints the employees' 
 numbers and the amount of pay on the pay-roll sheet and pay envelopes. 
 
 The following are some of the uses of these 
 machines in offices : proving daily postings ; daily 
 ledger balance ; daily cash balance ; daily reca- 
 pitulation of sales (as cash, credit, C.O.D., etc.) ; 
 checking invoices and freight bills; figuring 
 discounts; computing commissions; summary 
 of day's receipts and disbursements; figuring 
 estimates; making out pay envelopes; 
 analysis of outstanding accounts ; analy- 
 sis of accounts payable ; balancing petty 
 cash account; footing ledger accounts 
 before taking the trial balance ; taking 
 off the trial-balance figures (debits and 
 credits); reconciling cashbook balance 
 with bank balance, listing the number 
 and the amount of each outstanding 
 check ; making monthly statements giv- 
 ing month, date, total of debits, total of 
 credits, balance and special terms ; compiling statements of cost of production ; 
 footing inventories and calculating extensions ; posting customers' ledger. 
 The cuts show various types of calculating machines. 
 
APPENDIX B 
 
 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 
 
 = 231 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 lb. troy or apothecaries' = 5760 gr. 
 
 3 scruples = 1 dram 1 oz. troy or apothecaries' = 480 gr. 
 
 8 drams = 1 ounce 1 lb. avoirdupois = 7000 gr. 
 
 12 ounces = 1 pound 1 oz. avoirdupois = 437^ gr. 
 
 The ton of 2000 lb. is sometimes called a short ton. There is a ton of 2240 lb. , 
 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 II 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 about 7| gal. and weighs 62^ lb., avoirdupois. 
 
 276 
 
276 
 
 CONCISE BUSIKESS ARITHMETIC 
 
 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 
 
 City lots are usually measured by feet and decimal fractions of a foot ; farms, 
 by rods or chains. 
 
 Surveyors* Long Measure 
 
 7.92 inches = 1 link 
 
 25 links = 1 rod 
 
 4 rods, or 100 links = 1 chain 
 80 chains = 1 mile 
 
 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 
 30^ square yards = 1 square rod 
 160 square rods = 1 acre 
 640 acres = 1 square 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 
 
 625 square links = 1 square rod 
 16 square rods = 1 square chain 
 10 square chains = 1 acre 
 
 640 acres = 1 square mile 
 
 36 square miles = 1 township 
 
 Cubic Measure 
 
 1728 cubic inches = 1 cubic foot 
 27 cubic feet = 1 cubic yard 
 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 li 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 277 
 
 MEASURES OF TIME 
 
 60 seconds = 1 inimite 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 raih'oad companies of tlie 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^° 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. = |§^ ; Id. = 2,^^^^ ; Is. = 24^ f. 
 
 French Money German Money 
 
 100 centimes = 1 franc = 1 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 
 
278 
 
 CONCISE BUSINESS ARITHMETIC 
 
 BUSINESS ABBREVIATIONS 
 
 A . . 
 
 . acre 
 
 Mar. . . 
 
 . March 
 
 Apr. . 
 
 . April 
 
 I^Idse. . 
 
 . merchandise 
 
 Aug. . 
 
 . August 
 
 Messrs. . 
 
 . Messieurs, Gentlemen ; 
 
 bbl. . 
 
 . barrel; barrels 
 
 
 Sirs 
 
 bdl. . 
 
 . bundle; bundles 
 
 mi. . . 
 
 . mile; miles 
 
 bg. . 
 
 . bag; bags 
 
 . basket; baskets 
 
 min. . . 
 
 . minute; minutes 
 
 bkt. . 
 
 mo. . . 
 
 . month ; mouths 
 
 bl. . 
 
 . bale; bales 
 
 Mr. . . 
 
 . Mister 
 
 bu. . 
 
 . bushel; bushels 
 
 Mrs. . . 
 
 . Mistress 
 
 bx. . 
 
 . box; boxes 
 
 N. . . 
 
 . north 
 
 cd. . 
 
 . cord; cords 
 
 No. . . 
 
 . number 
 
 ch. . 
 
 . chain ; chains 
 
 Nov. . . 
 
 . November 
 
 c.i.f. . 
 
 . carriage and insurance free 
 
 Oct. . . 
 
 . October 
 
 Co. . 
 
 . company; county 
 
 oz. . . 
 
 . ounce; ounces 
 
 C.O.D. 
 
 . collect on delivery 
 
 p. . . . 
 
 . page 
 
 Coll. . 
 
 . collection 
 
 pc. . . 
 
 . piece; pieces 
 
 Cr. . 
 
 . creditor; credit 
 
 per. . . 
 
 . by the ; by 
 
 CS. 
 
 . case; cases 
 
 per cent. 
 
 . per centum, by the hun- 
 
 ct. . 
 
 . cent; cents; centime 
 
 
 dred 
 
 cu. ft. 
 
 . cubic foot ; cubic feet 
 
 pk. . . 
 
 . peck; pecks 
 
 cu. in. 
 
 . cubic inch ; cubic inches 
 
 pkg. . . 
 
 . package; packages 
 
 cu. yd. 
 
 . cubic yard ; cubic yards 
 
 pp. . . 
 
 . pages 
 
 cwt. . 
 
 . hundredweight 
 
 pr. . . 
 
 . pair; pairs 
 
 d. . . 
 
 . pence 
 
 pt. . 
 
 . pint; pints 
 
 da. . 
 
 . day; days 
 
 pwt. . . 
 
 . pennyweight; penny- 
 
 Dec. . 
 
 . December 
 
 
 weights 
 
 doz. . 
 
 . dozen; dozens 
 
 qr. . . 
 
 . quire; quires 
 
 Dr. . 
 
 . debtor; debit; doctor 
 
 qt. . . 
 
 . quart; quarts 
 
 E. . . 
 
 . east 
 
 rd. . 
 
 . rod ; rods 
 
 ea. 
 
 . each 
 
 rm. . 
 
 . ream ; reams 
 
 e.g. . 
 
 . exempli gratia, for ex- 
 
 Rm.(or B 
 
 I.) Reichsmark, Mark 
 
 
 ample 
 
 s. . . 
 
 . shilling; shillings 
 
 etc. . 
 
 . et ccetera, and so forth 
 
 S. . . 
 
 . South 
 
 far. . 
 
 . farthing; farthings 
 
 sec. . 
 
 . second; seconds 
 
 Feb. . 
 
 . February 
 
 sq. ch. 
 
 . square chain; square 
 
 f.o.b. . 
 
 . free on board 
 
 
 chains 
 
 fr. . 
 
 . franc; francs 
 
 sq. ft. . 
 
 . square foot; square feet 
 
 ft. . 
 
 . foot; feet 
 
 sq. mi. 
 
 . square mile; square 
 
 gal. . 
 
 . gallon; gallons 
 
 
 miles 
 
 gi- • 
 
 . gill; gills 
 
 sq. rd. 
 
 . . square rod; square rods 
 
 gr. . 
 
 . grain ; grains 
 
 sq. yd. 
 
 . . square yard; square 
 
 gi-o. . 
 
 . gross 
 
 . hogshead; hogsheads 
 
 
 yards 
 
 hlid. . 
 
 T. . , 
 
 . . ton 
 
 hf. cht. 
 
 . half chest ; half chests 
 
 tb. . 
 
 . . tub; tubs 
 
 hr. . 
 
 . hour; hours 
 
 Tp. . 
 
 . . township; townships 
 
 i.e. 
 
 . id est, that is 
 
 viz. . 
 
 . . videlicet, namely ; to wit 
 
 in. 
 
 . inch; inches 
 
 via . 
 
 . . by way of 
 
 Jan. . 
 
 . January 
 
 wk. . 
 
 . . week; weeks 
 
 kg. . 
 
 . keg; kegs 
 
 wt. . 
 
 . . weight; weigh 
 
 1. . . 
 
 . link ; links 
 
 yd. . 
 
 . . yard; yards 
 
 lb. . 
 
 . pound; pounds 
 
 yr. . 
 
 . . year; years. 
 
BUSINESS SYMBOLS AND ABBREVIATIONS 279 
 
 «/<j account 
 
 «/s account sales 
 
 + addition 
 ( ) ~ aggregation 
 
 & and 
 
 and so on 
 
 @ at; to 
 
 c/o care of 
 
 ^ cent; cents 
 
 y/ check mark 
 
 ° degree 
 
 -h division 
 
 $ dollar; dollars 
 
 BUSINESS SYMBOLS 
 
 = equal; equals 
 ' foot; feet; 
 
 minutes 
 C hundred 
 
 " inch ; inches ; seconds 
 X multiplication 
 ;J^ number, if written 
 
 before a figure; 
 pounds, if written 
 
 after a figure 
 1^ one and one fourth 
 V one and two fourths ; 
 
 one and one half 
 
 1^ one and three 
 
 fourths 
 ^ per; by 
 % per cent ; 
 
 hundredth ; 
 hundredths 
 £ pounds sterling 
 
 since 
 — subtraction 
 
 therefore 
 M thousand 
 Ye 5 shillings 6 pence ; 
 five sixths 
 
INDEX 
 
 Abbreviations, 278 
 Above par, 258 
 Abstract number, 36 
 Adding machines, 273 
 Addition, 2, 78, 107, 172 
 Aliquot parts, 138 
 Amount, 176, 232 
 Angular measure, 276 
 Apothecaries' weight, 275 
 Assessment, 257, 260 
 At a discount, 254, 258 
 At par, 254 
 
 At a premium, 254, 258 
 Average clause, 211 
 Avoirdupois weight, 275 
 
 Bank discount, 230, 231 
 
 Bank drafts, 246, 248 
 
 Bank loans, 238 
 
 Bank money order, 243 
 
 Banker's sixty-day method of interest, 
 
 219 
 Banking, 216 
 Base, 176, 180 
 Below par, 258 
 Bill of lading, 254 
 Bills, 31, 32, 45, 49, 116, 145, 146, 150, 
 
 151, 152, 153, 154, 155, 156, 161, 165, 
 
 190, 208 
 Bills and accounts, 150 
 Blanket policy, 210 
 Bond table, 269 
 Bonds, 265, 266 
 Buying bonds, 270 
 Buying by the hundred, 89 
 Buying by the thousand, 89 
 Buying by the ton, 90 
 Buying stocks, 262 
 
 Cable length, 276 
 Cancellation, 97 
 Capital stock, 256 
 Carat, 275 
 Cashier's check, 249 
 Certificate of deposit, 249 
 Change memorandum, 159 
 Charter, 256 
 
 Checking results, 12, 24, 38, 43, 44, 55, 
 
 71 72 73 
 Checks, 246, 250, 260 
 Clearing house, 246, 247 
 Code, 244 
 Co-insurance, 211 
 Collateral note, 240 
 Collateral trust bond, 265 
 Collection and exchange, 236, 252 
 Commercial bank, 230 
 Commercial discounts, 188 
 Commercial drafts, 231, 252 
 Common denominator, 106 
 Common divisor, 98 
 Common fractions, 101 
 Common stock, 258 
 Comparative weights, 275 
 Complement, 27 
 Composite number, 95 
 Concrete number, 36 
 Consecutive numbers, 10 
 Conversion of fractions, 127 
 Corporation, 256 
 Counting by 12, 277 
 Counting sheets of paper, 277 
 Coupon bond, 266 
 Cubic measure, 276 
 
 Day method of interest, 217 
 
 Days of grace, 231 
 
 Debenture bonds, 265 
 
 Decimal, 75 
 
 Decimal fractions, 75 
 
 Decimal units, 75 
 
 Demand note, 239 
 
 Denominate quantities, 169 
 
 Denominator, 101 
 
 Deposit slip, 251 
 
 Depositors' ledger, 30, 34, 35, 50 
 
 Difference, 176 
 
 Discount series, 188, 191 
 
 Dividend, 52, 257, 260 
 
 Division, 52, 57, 85, 88, 121, 173 
 
 Divisor, 52 
 
 Divisors, 98 
 
 Domestic exchange, 242 
 
 Drafts, 230, 231, 238, 252 
 
 281 
 
282 
 
 CONCISE BUSINESS ARITHMETIC 
 
 Drawee, 231 
 Drawer, 231 
 Dry measure, 275 
 
 English money, 277 
 Even number, 95 
 Exchange, 242, 249 
 Exponent, 36 
 Express money order, 243 
 Expressage, 164 
 
 Factor, 36, 95 
 
 Factoring, 96 
 
 Fathom, 276 
 
 Final results, 105 
 
 Finding the base, 180 
 
 Finding the cost, 199 
 
 Finding the gain or loss, 197 
 
 Finding the per cent of gain or loss, 
 
 198 
 Finding the percentage, 176 
 Finding the rate, 178 
 Fire insurance, 209 
 Fire losses, 133, 134 
 Firm note, 236 
 Fixed policy, 210 
 Floating policy, 210 
 Fluctuation of rates of exchange, 254 
 Fractional relations, 124 
 Fractions, 75 
 Freight bill, 165 
 Freightage, 164 
 French money, 277 
 
 Gain and loss, 196 
 
 Gain or loss on selling price, 202 
 
 German money, 277 
 
 Government bonds, 265 
 
 Graphic representations, 126, 133, 185 
 
 Greatest common divisor, 98 
 
 Gross price, 189 
 
 Gross weight, 30 
 
 Grouping, 3, 6 
 
 Hand, 276 
 Heaped bushel, 275 
 Holder, 230 
 Horizontal addition, 16 
 
 Important per cents, 176 
 Improper fraction, 102 
 Income bond, 265 
 Insurance, 209 
 Insurance rates, 213 
 Insurer, 210 
 
 Interest, 216 
 Invoice, 150 
 
 Joint and several note, 236 
 Joint note, 236 
 
 Key, 204 
 Knot, 276 
 
 League, 276 
 
 Least common denominator, 106 
 
 Least common multiple, 100 
 
 Letter ordering goods, 162 
 
 Liquid measure, 275 
 
 Listing goods for catalogues, 207 
 
 Long measure, 276 
 
 Long ton, 275 
 
 Making change, 25 
 
 Market value, 258 
 
 Marking goods, 204 
 
 Maturity, 230 
 
 Maturity table, 232 
 
 Measures of capacity, 275 
 
 Measures of extension, 276 
 
 Measures of time, 277 
 
 Measures of value, 277 
 
 Measures of weight, 275 
 
 Miscellaneous measures, 277 
 
 Miscellaneous weights, 275 
 
 Mixed numbers, 102 
 
 Model figures, 11, 13, 14, 15 
 
 Money orders, 242 
 
 Mortgage bonds, 265 
 
 Multiple, 36 
 
 Multiplication, 36, 41, 43, 45, 46, 4T 
 
 82, 114, 120, 173 
 Municipal bonds, 265 
 Mutual insurance company, 210 
 
 Net price, 189 
 Net weight, 31 
 Notation, 76 
 Notes, 239, 240 
 Numeration, 76 
 Numeration table, 76 
 Numerator, 101 
 
 Odd number, 95 
 Open policy, 210 
 Ordinary policy, 210 
 
 Par value, 258 
 Parcel post, 63 
 Parenthesis, 23 
 Pay rolls, 159, 160, 163 
 
IKDEX 
 
 28a 
 
 Payee, 231 
 
 Pay-roll inemorandum, 160 
 
 Per cent, 76, 175 
 
 Per cents of decrease, 182 
 
 Per cents of increase, 181 
 
 Percentage, 175 
 
 Perch, 276 
 
 Policy, 210 
 
 Postal money order, 242 
 
 Postal service, 63 
 
 Power, 37 
 
 Preferred stock, 257 
 
 Premium, 210 
 
 Prime number, 95 
 
 Principal, 216 
 
 Proceeds, 232 
 
 Promissory notes, 239, 240 
 
 Properties of 9, 71 
 
 Properties of 11, 72 
 
 Property insurance, 209 
 
 Quotient, 52 
 
 Rate, 176, 211, 216 
 
 Rate of exchange, 243, 248, 254 . 
 
 Reading decimals, 76 
 
 Reduction, 103, 104, 105, 106, 170, 171 
 
 Registered bond, 267 
 
 Remainder, 52 
 
 Repeaters, 204 
 
 Review of the common tables, 169 
 
 Review tests, 22, 35, 51, 94, 137, 187, 
 
 195, 241 
 Rood, 276 
 
 Scrip, 259 
 
 Section, 276 
 
 Selling by the hundred, 89 
 
 Selling by the thousand, 89 
 
 Selling by the ton, 90 
 
 Share, 256 
 
 Short methods, 41, 57, 108, 118 
 
 Short ton, 275 
 
 Sight draft, 252 
 
 Similar fractions, 106 
 
 Simple interest, 217 
 
 Six per cent method of interest, 227 
 
 Sixteen to one, 118 
 
 Solution of problems, 128 
 
 Specific policy, 210 
 
 Square measure, 276 
 
 Standard time, 277 
 
 Stock broker, 258 
 
 Stock certificates, 256, 257, 258 
 
 Stock company, 256 
 
 Stock insurance company, 210 
 
 Stockholder, 256 
 
 Stocks and bonds, 256 
 
 Subtraction, 23, 80, 112, 172 
 
 Surveyors' long measure, 276 
 
 Surveyors' sqiiare measure, 276 
 
 Table of aliquot parts, 140 
 
 Table of bond quotations, 270 
 
 Table of common measures, 275 
 
 Table of .important per cents, 176 
 
 Table of insurance rates, 213 
 
 Table of stock quotations, 262 
 
 Table of time, 234 
 
 Table of twelfths, 206 
 
 Tare, 30 
 
 Tariff, or rate, book, 213 
 
 Telegram, 244 
 
 Telegraphic money order, 244 
 
 Telegraphic rates, 245 
 
 Term of discount, 232 
 
 Terms of a fraction, 102 
 
 Tests of divisibility, 96 
 
 Time sheets, 159, 160, 163 
 
 Time slip, 163 
 
 Trade discount, 188 
 
 Troy weight, 275 
 
 Underwriter, 210 
 Unit fraction, 102 
 United States money, 277 
 
 Value, 232 
 Valued policy, 210 
 Vinculum, 23 
 
 Weigh tickets, 90 
 
 CB 
 
YC 45042