IN MEMORIAM 
 Johlr'Swett 
 
FRENCH'S MATHEMATICAL SEHffi$v \V , 
 
 MENTAL ARITHMETIC; 
 
 COMBINING A 
 
 COMPLETE SYSTEM OF RAPID COMPUTATIONS, 
 
 CORRECT LOGIC OF THE SOLUTIONS OF PROBLEMS, 
 AND THE ANALYSES OF PROCESSES. 
 
 BY 
 
 JOHN H. FRENCH, LL.D. 
 
 Mental Arithmetic is tht Logic of the Common School. 
 
 NEW YORK : 
 HARPER & BROTHERS, PUBLISHERS, 
 
 FRANKLIN SQUARE. 
 1872. 
 
1C -N DEP 
 
 PUBLISHERS' NOTICE 
 
 FRENCH'S ARITHMETICS. 
 
 This Series consists of Five Books, vis. : 
 
 I. FIRST LESSONS IN NUMBERS. 
 II. ELEMENTARY ARITHMETIC. 
 
 III. MENTAL ARITHMETIC. 
 
 IV. COMMON SCHOOL ARITHMETIC. 
 
 V. ACADEMIC ARITHMETIC. (In prep* 
 
 Tho Publishers present this Scries of Text-Books to American 
 Teachers, fully believing that they contain many new ar 
 able features that will especially commend them to t! 
 wants of the age. 
 
 Tin- plan i' -r the Scries, and for each book embraced in it, was 
 fully matured before any one of the Series was completed ; and as 
 it is baaed upon true philosophical principles, there is a hannmiv. 
 a fitness, and a real progreoriveneM in the books that an n<>t 
 found iu any other Scries of Arithmetics published. 
 
 Entered according to Act of Congrea*, In the year 1870, bj 
 
 HARPER & BROTHERS, 
 In the Office of the Librarian of Congress at Washington. 
 

 PREFACE. 
 
 T3REVIOUS to the introduction of tbc study of Mental 
 Arithmetic into American schools, pupils were seldom 
 required to give reasons for processes of computation ; and 
 few teachers could be found, who could give any reason for 
 an arithmetical process other than u The rule says so." The 
 publication of Warren Colburn's First Lessons, in 1826, 
 marked the beginning of an era of progress in the art of 
 teaching. The use of that book turned the attention of 
 teachers to two facts, viz: 1st. That for every arithmetical 
 process there is a reason ; and 2d. That it is quite as im- 
 portant that pupils learn the why as the how. 
 
 The general principle that reformers go to extremes, found 
 no exception in the case of the introduction of the study 
 of Mental Arithmetic into our schools. The chief aim of 
 some teachers of this subject seems to have been, to see how 
 much a child could be made to say, in solving a problem, 
 rather. than to cultivate his power to combine numbers, and 
 his ability to explain processes and state reasons clearly, con- 
 cisely, and understandingly. By this class of teachers, much 
 talking has been regarded as indispensable to good scholar- 
 ship in this subject. But, within the past ten years, many 
 prominent educators in different sections of the country have 
 had sufficient independence to question the value of the dis- 
 cipline resulting from lengthy solutions, recited from memo- 
 
 541815 
 
.IV PREFACE. 
 
 >';( ippmnja -and to test the comparative value of tlirsc with 
 ' concise processes, which appeal constantly to the reason 
 understanding of the learners. It is scarcely needless t 
 mark that. win n v.r these testa have been made, they have 
 .ted in favor of concise methods of solution. 
 
 The objects for which children should study Mental Arith- 
 metic are two, namely : First. To acquire accuracy ;. 
 ity in combinations; and Second. To acquire the 
 
 .<on correctly. The attainment of this BCCOT. will 
 
 give them the ability to combine a process \\iih a reason, and 
 \ra\ statements adapted to the solution of prob- 
 lems, which shall IT i rrcct. In th- i 
 aration of thi- work these I :s have )>een kept 
 stantly in view. The attention of teachers and parents is 
 especially invited to the following general plan and di>tin 
 features of the work : 
 
 <. m r;il Plan. The book is divided into * 
 ten, the first one of which is devoted to combinations in 
 integers 'in which no result exceeds 100, and is called a 1 
 
 irse in Integers; the second chapter is a Second Course in 
 Integers, and embraces combinations in which the roults do 
 not exceed 1,000; the third chapter is devoted to United 
 States Money ; the fourth to Compound Numbers ; the fifth to 
 Fractions; the sixth to Converse Operations in the funda- 
 mental rules, and in the reductions of Compound Numbers 
 and Fractions; the seventh to the five general case 
 centage, and their special applications to Insurance- Commis- 
 sion, Profit and Loss, Stocks, Taxes, Interest, and Discount ; 
 and the eighth to Miscellaneous Review Problems, 
 
 The First Course in Integers is designed especially for chil- 
 dren who have had no previous instruction in Mental Arith- 
 metic. Beginning at the Second Course in Integers, 
 the order of subjects is the same as that in the Common School 
 
PREFACE. V 
 
 Arithmetic ; and, from this place to the end of the book, the 
 two works can be used together, the same subject in the two 
 books being studied at the same time. This arrangement has 
 received the approval of many of the best teachers in the land. 
 
 I>rill on Combinations. The Addition, Subtrac- 
 tion, Multiplication, and Division tables are omitted. Thor- 
 ough drills in the exercises given on pages 15, 17 to 22, 27, 
 30 to 35, 41, 51, and 52 will make pupils accurate and rapid 
 in every possible combination of numbers. 
 
 Problems. These are all new, and being prepared from 
 material gathered from the various departments of actual 
 business life, are, in numerous instances, the medium of in- 
 struction in the usages of business, and the uses of business 
 terms and expressions. 
 
 Illustrations. The cuts and diagrams, all of which were 
 designed and engraved especially for this work, possess the 
 superior artistic merit which has been conceded to the illus- 
 trations in the other works of this Series. 
 
 Manual. A manual occupies the last ten pages of the 
 work. The first three pages of this Manual contain hints and 
 suggestions to teachers, references to which are made in the 
 body of the work ; and the last seven pages present methods 
 of solving the different classes of problems found in the book, 
 and arc embraced together under the head 
 
 Methods. All methods for the solution of problems 
 being omitted from the body of the work, are here placed 
 together, and are referred to after the problems to which 
 they apply. These Methods are intended as models, to be 
 varied at the discretion of the teacher. They are logical and 
 progressive, while they avoid all useless verbiage and repe- 
 tition. 
 
 The arrangement of the subjects, the manner in which they 
 are presented, and the methods for the solution of problems, 
 
vi P B J 
 
 have constant reference to the healthful development of the 
 mental powers of the learner, conducting him, in an i 
 ruj)tcd progress, from the easy to the difficult ; pr 
 him but one new difficulty at once, and giving him 
 pra.-tiei- to enable him to ma.-U-r that difficulty li l\>:-< 
 ing it. 
 
 :idently belii-vcd that tin- nbundaiit ]>ra( : 
 combinations, in connection with the solution of the great 
 number of easy problems given in the First Course in In- 
 tegers, can not fail to make children in combinations 
 of numlxTs: while the very large number of well graded 
 
 DM in the wor'.,. mgp in the pr 
 
 afTiirs Ofltts will atlord th- pmeti .-ipline tl 
 
 them to compute rapidly, and reason logically axd 
 -cly. 
 
$ 
 ' ^ 
 
 CHAPTER I. 
 
 FIRST COURSE IN INTEGERS. 
 
 SECTION I. 
 
 DEFINITIONS 
 
 A Unit is a single thing, or one, of any kind : as, one apple, 
 one bushel, one dozen. 
 
 A Number is a unit, or a collection of units. 
 
 A Concrete Number is a number applied to some object ; 
 as, four men, ten gallons, fifty quires. 
 
 An Abstract Number is a number not applied to any 
 object ; as, four, ten, fifty. 
 
 An Integer is a number the units of which are whole or 
 undivided. Integers are also called Whole Numbers. 
 
 The use of numbers in estimating quantities and values in 
 the practical affairs of life, is the Art of Computation ; 
 and a proper classification and arrangement of the definitions, 
 principles, and rules used in computations, is the Science of 
 Numbers. Hence, 
 
 Arithmetic is the science of numbers, and the art of com- 
 putation. 
 
 In writing numbers for computations, ten characters, called 
 Figures, are used. 
 
 The figure 0, called cipher or naught, denotes nothing, or the 
 absence of number. The other figures represent the first nine 
 integers, and are sometimes called digits. 
 
8 
 
 FIRST COURSE IX INTEGERS. 
 
 The t nrc^- 
 
 3, 4, 5, 6, 7, 8, 9, 
 \ naught, one, two, three, four, Jive, tix, wren, eight, nine. 
 
 To express numbers greater than 9, two or more of the ten 
 figures must be combined. 
 .livery ten one* taken together are called a ten. 
 
 Ten is written 10 
 
 i-. or twenty, are written 90 
 
 8 tens, or thirty, " SO 
 
 4 tens, or forty, 40 
 
 5 tens, or fifty, 
 
 C tens, or sixty, CO 
 
 ns, or seventy, 70 
 
 8 tens, or eighty, SO 
 
 9 tens, or inn * 4 90 
 
 Whon two figures an ritt n together to express a number, 
 the Irft-h.ind figure expresses ten*, and th ri-ht-hand figure 
 one*. Thus, 
 
 Fourteen consists of 1 ten and 4 ones, written 14 
 
 ity-threc 
 Thin 
 
 " 
 
 Fifty -nine 
 Sixty-seven 
 Seventy-eight " 
 Eighty-one " 
 
 Ninety 
 
 1. "\Vrite in words the following numbers: 
 89, 91, 17, 40. 
 
 2. Write in words 61. 08. 
 
 3. How many are expressed by each of the foil. 
 numbers : 63, 72, 9, 56, 43, 25, 10. 
 
 Write in words 73, 55, 18, 85, 32, 90, 27, 20. 
 5. Express by figures the following numbers: thirty, 
 eleven, twenty-six, lifty-1. 
 
 2 tens 
 
 .. 
 
 3 ones. 
 
 t 
 
 fft 
 
 :j tens 
 
 
 6 ones, 
 
 . 
 
 1 S6 
 
 4 tens 
 
 H 
 
 5 ones. 
 
 . 
 
 ' 45 
 
 5 tens 
 
 u 
 
 9 ones, 
 
 i 
 
 59 
 
 tens 
 
 H 
 
 7 ones. 
 
 i 
 
 
 7 tens 
 
 H 
 
 S ones. 
 
 
 78 
 
 8 tens 
 
 a 
 
 1 one, 
 
 i 
 
 81 
 
 
 U 
 
 ones, 
 
 
 90 
 
DEFINITIONS AND NOTATION. 9 
 
 6. Express by figures eighty-seven, thirty-four, nine- 
 teen, seventy-two. 
 
 7. Express by figures forty-one, eight, sixty-four, ninety- 
 nine. 
 
 Every 10 tens taken together are called a hundred. 
 
 10 tens are one hundred, -written 100 
 
 20 tens are two hundred, " 200 
 
 30 tens are three hundred, " 300 
 
 40 tens are four hundred, * 400 
 
 50 tens are five hundred, " 500 
 
 60 tens are six hundred, " 600 
 
 70 tens are seven hundred, u 700 
 
 80 tens are eight hundred, " 800 
 
 90 tens are nine hundred, " 900 
 
 When three figures are written together to express a number, 
 
 the left-hand figure expresses hundreds, the middle figure tens, 
 
 and the right-hand figure ones. Thus, 
 
 172 is one hundred seventy-two, or 1 hundred 7 tens and 2 ones. 
 
 863 " eight hundred sixty-three, " 8 hundreds 6 tens " 3 ones. 
 
 351 " three hundred fifty-one, " 3 hundreds 5 tens " lone. 
 
 408 " four hundred eight, " 4 hundreds tens " 8 ones. 
 
 619 " five hundred nineteen, " 5 hundreds 1 ten * 9 ones. 
 
 8. Write in words the following numbers: 100, 700, 
 
 520, 9GO, 340, 210, 470. (Sec Manual, page 171.) 
 
 9. Write in words 444, 591, 716, 343, 434, 2G8. 
 
 10. How many arc expressed by each of the following 
 numbers : 254, 309, 207, 702, 506, 104, 999 ? 
 
 11. Express by figures the following numbers : two 
 hundred, seven hundred sixty, three hundred seven- 
 teen, four hundred fifty-nine. 
 
 1,1. Express by figures three hundred seventy-four, one 
 hundred eight, five hundred two, three hundred 
 seven, seven hundred three, three hundred seventy, 
 seven hundred thirty, nine hundred ninety-nine. 
 
10 FIRST CO U BSE IX INTEGERS. 
 
 In writing numbers, every 10 hundreds taken together are 
 called a thousand. Thousands are writtr 11 t! 
 
 One thousand, 1,000 Five thousand, 5,000 
 
 Two thousand, ~'/>00 
 
 Thivr thousand, 3,000 
 
 Four thousand, 4,000 
 
 Six thousand, 6,000 
 
 Bem thousand, 7,OOO 
 
 Eight thousand, 8,000 
 
 Nine thousand, P,000. 
 
 When four figures are written top-tin T to express a number. 
 :":-h:uid iL'im- expresses thoutand*, and the other three 
 res express hundred*, tent, and 0/s. Thus, 
 8,000 is eiuht thousand, 
 5,400 is live thousind four hund: 
 'J..1W) is two thousand five luindred siv 
 1,644 is one thousand six li ur, 
 
 :hnv thousand seven hui 
 O/.'-l iiousund nine hundred forty-two, 
 
 " i.- time thousand four hundred five, 
 4,096 is four thousand ninety-six, 
 7,010 is seven thousand 
 6,000 is six thousand nine. 
 
 15. Write in words the following numbers: 4,000; 6,200; 
 2,500; 5,100; 2,460; 4,620; 5,910. 
 
 in words 8,123; 3,434; 7,090; 1,050. 
 
 16. Write in words 3,091 ; 4,082; 2,075; 6,204; 3,708; 
 4,070; 9,030; 9,999. 
 
 : . IAJMVSS l.y liirures six tliousand. live thousand three 
 hundred, two tliousand one luindred thirty, eight 
 tliousand three hundred twenty-!: 
 
 .press by TILTH res four thousand fifty, seven thou- 
 sand two, nine thousand >' thousand 
 two hundred seven. 
 
ADDITION. 
 
 11 
 
 SECTION II. 
 
 1. Prom 1 and 1 to 10 and 10. 
 
 (See Manual, page 171.) 
 
 .7. In this picture of a picnic party, is a group of boys, 
 3 of whom arc standing, and 2 are sitting. How 
 many boys are in the group ? Methods, page IM. 
 
 2. How many trees are 1 tree and 2 trees ? Method*, page *7 '4. 
 
 3. 1 girl and 1 girl are how many girls ? 
 
 4. One boy and four boys are how many beys 2 
 
 5. How many men are 4 men and 2 men ? 
 
 G. How many children are 6 children and 2 children ? 
 7. Jane bought two peaches for 5 cents, and some pea- 
 nuts for 1 cent. How many cents did she pay out ? 
 
12 FIRST COURSE IX INTEGERS. 
 
 8. Alice bought a pr-ar for 1 cent, and a bun 
 grapes for 7 rants. How many cents di 
 
 9. 2 balls and 7 balls are how many balls ? 
 
 10. 9 girls and 1 boy are in the same class. II>\\ 
 pupils an- in the class? 
 
 11. William's father pave him 8 marbles, and In- found 1. 
 I low many marbles had he tlien? 
 
 1 :. Bob rt paid in cent- fr I 
 
 il. How many cents did hi 
 cost him ? 
 IS. I low many books arc 9 books and 2 books? 
 
 Mire-books, and 5 book- without pic- 
 tures. How many books has B 
 
 iarles }>aid 1 cents for an orange, ; 
 a leinMii. How much did he pay for b- 
 
 i liree roses are on one bush, and six on an 
 How many roses are there on both bushes ? 
 
 /.. I lit hard has 3 rabbits, and Thomas has 3. How 
 many rabbits have th<- two h. 
 
 /v. Manila's muff cost \\ dollars, and IHT fur cape 7 
 dollars. How much did both of them cost? 
 
 ire are 8 whi lack ones. 
 
 How many sheep are in the pastu: 
 
 you pay '> nuts for figs, and 9 cents for ra 
 how many cents do you pay out ? 
 . .'. Hiram found 5 e^rs in one nest, and 4 in an 
 
 How many eggs did lie find? 
 
 ;??. A hunter shot t< n pL'.-ons. an( l two quails. How 
 many birds did he shoot ? M,-th<> t i*. r 
 
 'ora had 1 shells, and her brother gave her 4 more. 
 How many shells had she then ? 
 
ADDITION. 13 
 
 24. If a ball costs 6 cents, and a top 4 cents, how much 
 do both cost ? 
 
 25. A chandler sold 4 boxes of candles to one grocer, 
 and 7 boxes to another. How many boxes did he sell 
 to both ? 
 
 26. Sarah is 9 years old, and her brother Joseph is 4 
 years older. How old is Joseph ? 
 
 27. Fanny's silk dress cost 10 dollars, and her bonnet 4 
 dollars. How much did both cost ? 
 
 28. A hotel keeper buys 4 loaves of brown bread, and 8 
 loaves of white bread, every day. How many loaves 
 of bread does he buy daily ? 
 
 How many are 
 
 29. 5 lilies and 5 lilies ? 
 
 30. 4 cherries and 5 cherries ? 
 
 31. 5 cherries and 4 cherries ? 
 
 32. 6 pears and 5 pears ? 
 
 33. 5 pears and 6 pears ? 
 
 34. 5 days and 7 days ? 
 
 35. 7 days and 5 days ? 
 
 30. 10 minutes and 5 minutes ? 
 
 37. 5 weeks and 9 weeks ? 
 
 38. 9 weeks and 5 weeks ? 
 
 In each of the preceding problems we have united or put 
 together two numbers to form one larger number. 
 
 Addition is the process of uniting two or more numbers 
 to form one number. 
 
 The Amount or Sum is the result obtained by Addition. 
 
 The *Parts are the numbers which are united to form the 
 sum. 
 
 The Siffn of Addition., made thus, + , is called Plus; 
 and when written between numbers, it signifies that they are to 
 be added. 
 
 The Siffn of Equality > made thus, =, when written be- 
 tween numbers or sets of numbers, signifies that they are equal 
 to each other. Thus, 5 + 3 + 9 = 17 is read, " 5 plus 3 plus 
 9 equals 17," or " the sum of 5, 3, and 9 is 17." 
 
 A number with the sign $ before it expresses dollars. Thus, 
 $72 is read "72 dollars." 
 
14: FIRST COUBSE IN INTEGERS. 
 
 .*'/. IIo'.v many sheep are 7 sheep + 3 sh 
 40. 5 cows -f 7 cows are how many cows ? 
 ,} 1. 4 horses + 7 horses = how many horses ? 
 42. What is the sum of $7 -f $7 ? Of $7 + $9 ? 
 4S. 8 robins + 7 robins = how many robins ? 
 44. How man ;o 7 wrens + 10 wrennf 
 
 ; ". An upholsterer made the scats for G mal. 
 
 chairs, and 6 rosewood chairs. How many chair 
 
 seats did IK- mak 
 
 \ dairy-man bought 7 large milk-pans, and r. 
 
 ones. How many milk-pans did he buy ? 
 ;,. Mary has pinks, and Clara has C. How many 
 
 pinks have the two girls? 
 
 48. A grocer sold 5 bushels of sweet apples, a: . 
 
 f sour ones. How many bushels of both 1. 
 did lu- | 
 
 ; . How many quarts of milk will it take to fill a 
 i;-<|iiart pan and an S-<juart pail? 
 
 50. A sold a bracelet for $7, and a lock 
 
 $7. 1I..\\ much did 
 
 .:/. If it tak-s 7 yards fora dress for Jo and s 
 
 >r one f> P, how many yards will it 
 
 thf t\vo dresses? 
 
 .:.'. ( > millinrr mad.- 1> !>.!. 
 
 How many bonnets did she make ii 
 two 
 
 53. 1 sold nine plows one day, and .- 
 II..\v many plows did I sell in the two d 
 
 . \ hoy pitliered Is of appl-s in the forenoon, 
 
 and S Imshels in the afternoon. How many bush- 
 els did he gather in all day? 
 
ADDITION. 15 
 
 55. If you go 8 miles east, and I go 9 miles west from 
 this school-house, how far apart will we be ? 
 
 56. A horse-dealer bought 9 black horses, and 9 bay 
 ones. How many horses did he buy? 
 
 57. A book-keeper wrote 9 pages of entries in the fore- 
 noon, and 10 pages in the afternoon. How many 
 pages did he write in the day ? 
 
 58. I paid an agent $10 for insuring my dwelling- 
 house, and $10 for insuring my furniture. How 
 much did my insurance cost me ? 
 
 59. Add 1 to 1, 2, 3, 4, 5, 6, 7, 8, 9, .and 10, in this manner: 1 
 and 1 are 2, 2 and 1 arc 3, 3 and 1 are 4, and so on. 
 
 (See Manual, page 171.) 
 GO. Add 2 to 1, 2, 3, 4, and so on to 19 inclusive. 
 
 61. Add 3 to 1, 2, 3, 4, and so on to 10 inclusive. 
 
 62. Add 4 to each number from 1 to 10 inclusive. 
 
 63. Add 5 to each number from 1 to 10 inclusive. 
 
 64. In the same manner, add to 1, 2> 3, 4, and so on to 10 
 inclusive. 
 
 65. In the same manner, add 7 to 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. 
 
 66. Add 8 to 1, 2, 3, 4, 5, G, 7, 8, 9, 10. 
 
 67. Add 9 to 1, 2, 3, 4, 5, G, 7, 8, 9, 10. 
 
 68. Add 10 to each number from 1 to 10 inclusive. 
 
 2. Addition, from 1 and 11 to 10 and 99- 
 
 GO. A blacksmith shod 13 horses one day, and 4 horses 
 the next. How many horses did he shoe in the two 
 days? 
 
 70. The third day he shod 5 horses. How many horses 
 did he shoe in the three days ? 
 
 71. Alfred bought a knife for 45 cents, and sold it so as 
 to gain 5 cents. How much did he get for it ? 
 
16 FIRST COURSE IN INTEGERS. 
 
 , .. Twcnt y-five children were in their seats when school 
 opened in the morning, und three afterward came 
 in. How many children were in school that d; 
 
 73. What is the sum of $01 and 
 
 74. My father is 38 years old. How old will 1 
 
 paper-han^vr used 8 rolls of paper for a bedroom, 
 and Ml mils for a parlor. How many rolls of pap. T 
 did he use for tin- two rooms? 
 
 ?'<'. If I pay *\i 1 f.T a (-at, and $6 for a hat, how much 
 do I pay tor both? 
 
 milk-man who had 18 cows, b<>ii_'';; " BfcOra H\v 
 many cows had he th 
 
 ; ?. \ boy tied a string 10 yards long to a k 
 yards long. How long was the who 
 
 7ft Two fishermen caught 43 shad and 7 p' 
 
 one haul of a seine. How many fish did they catch ? 
 
 id I and 87. Add 5 and 69. 
 ,<?/. What is the sura of 6 nncl 89? Of 7 and 84 ? 
 
 ^ .'. II. nnan's frrandfailn-r was 73 years old 8 years ago. 
 How old is he now? 
 
 v -.'. Chi a ferry-lat were -1(5 peiitlrnicii and 10 ladies. 
 How many passengers were on board ? 
 
 84. Th- 1 Brew <f the boat consisted of 8 men. How 
 many persons were on board ? 
 
 .A fann.-r paid $54 for a grain drill, and $9 f.>r a 
 plow. I low much did he pay for both ? 
 
 86. A laborer who had $50 in the savinirs-hauk, dcpos- 
 d $8 more. How much money had he then n 
 deposit ? 
 
ADDITION. 17 
 
 S7. There were 96 logs in the river near a saw-mill, 
 and 7 on the river bank. How many logs were there 
 in all? 
 
 88. A lady bought 9 yards of hall carpeting, and 37 
 yards of parlor carpeting. How many yards of car- 
 peting did she buy ? 
 
 89. One forenoon I traveled 69 miles by railroad, and 7 
 miles by stage. How far did I travel that forenoon ? 
 
 90. In the afternoon I walked 6 miles. How far did I 
 travel that day ? 
 
 01. A farmer has 98 acres of cleared land, and 8 acres 
 of woodland. How many acres are there in his farm ? 
 9$. 83 + 9 = how many ? 9 + 37 = how many ? 
 
 3. Addition by Decades, or Skips of Ten. 
 
 . /. 
 
 93. Add 1 to 10, 20, 30, 40, 50, 60, 70, 80, and 90. 
 
 (See Manual, page 171.) 
 
 94. What is the sum of 11 and 1? 21 and 1? 31 and 1? 
 41 and 1 ? 51 and 1 ? 61 and 1 ? 71 and 1 ? 81 and 1 ? 
 
 91 and 1 ? 
 
 95. What is the sum of 12 and 1 ? 22 and 1 ? 82 and 1 ? 42 
 and 1 ? 52 and 1 if 62 and 1 ? 72 and 1 ? 82 and 1 ? 
 
 92 and 1 ? 
 
 96. How many are 13 and 1 ? 23 and 1 ? 33 and 1 ? 43 
 and 1 ? 53 and 1 ? 63 and 1 ? 73 and 1 ? 83 and 1 ? 
 
 93 and 1 ? 
 
 97. How many arc 14 and 1 ? 24 and 1 ? 34 and 1 ? 44 
 and 1 ? 54 and 1 ? 64 and 1 ? 74 and 1 ? 84 and 1 ? 
 
 94 and 1 ? 
 
 98. How many are 15 and 1 ? 25 and 1 ? 35 and 1 ? 45 
 and 1 ? 55 and 1 ? 65 and 1 ? 75 and 1 ? 85 and 1 ? 
 
 95 and 1 ? 
 
 90. Add 1 to 16, 26, 36, 46, 56, 66, 76, 86, and 96. 
 
 2 
 
18 FIBST COURSE IX INTI.uKRS. 
 
 100. Add 1 to 17, 27, :J7, 47. ;, 87, and 
 
 101. Add 1 to 18, 28, 38, 48, 58, 68, 78, 88, and 98. 
 
 1 .. What is the sura of 19 and 1 ? 29 and 1 ? 39 and 1 ? 
 49 and 1 ? 59 and 1 ? 69 and 1 ? 79 and 1 ? 81- 
 
 1 ? 99 and 1? 
 
 o 
 
 v . 
 
 103. Add 2 to 10, 20, 30, 40, 50, 60, 70, 80, and 00. 
 
 Add 2 to every tenth number from 11 to 91 inclu 
 
 105. Add 2 to 12, 22, 82, and so on to 92 inclusive. 
 
 106. How many are 13 and 2 ? 23 and 2 ? 33 and 2 ? 43 
 and 2? 53 and 2? 63 and 2 ? 73 and 2 ? 83 an 
 
 ;id 2? 
 
 How many are 14 and 2? 24 and 2? 34 and 2 ? 44 
 and 2? 54 and 2? 64 and : 74 and 2 ? *4 an- 
 
 10S. How many are 15 and 2 ? 25 and 2? 85 
 
 I ? 65 and 2 ? 75 and 2 ? 85 an 
 
 100. Add 2 to 16, 26, 36, 46, 56, 66, 76, 86, and 9. 
 110. Add 2 to 17, 27, 37, 47, 57, 67, 77, 87, and 97. 
 ///. Add 2 to 18, 28, 38, 48, 58, 68, 78, 88, and 98. 
 lit. What is the sum of 19 and 2 ? 29 and 2 ? 89 and 2 ? 
 49 and 2 ? 59 and 2 ? 69 and 2 f 79 and 2 ? 80 
 
 J-. 
 
 113. Add 3 to every tenth number from 10 to 90 i 
 ll'f. Add 3 to every tenth numluT from 11 to 91 D 
 
 Add 3 to .'. and so on to 92 inclusi . 
 
 //<:. A. Id 3 to \:\. ::',. :',:!. 4:J, 58, 63, 73, 83, and 98. 
 \dd 3 t.) 14. M, :u. n. M, M, M, s4, and 94. 
 IW. Add 3 to 15, 25, 35, 45, 55, 65, 75, 85, and 95. 
 
 1 96. 
 
 \ Id :] to 17. 27. 37. 47. r.T 7. and 97. 
 
 121. Add 8 to 18, 28, 88, 48, 58, 68, 78, 88, and 98. 
 199. Add 3 to 1" M, 7 ' W. H 
 
ADDITION. 19 
 
 123. Add 4 to every tenth number from 10 to 90 inclusive. 
 
 124. Add 4 to every tenth number from 11 to 91 inclusive. 
 
 125. Add 4 to 12, 22, 32, and BO on to 92 inclusive. 
 
 126. Add 4 to 13, 23, 33, 43, 53, 63, 73, 83, and 93. 
 
 127. Add 4 to 14, 24, 34, 44, 54, 64, 74, 84, and 94. 
 
 128. Add 4 to 15, 25, 35, 45, 55, 65, 75, 85, and 95. 
 
 129. Add 4 to 16, 26, 36, and so on to 96 inclusive. 
 
 130. Add 4 to every tenth number from 17 to 97 inclusive. 
 
 131. What is the sum of 18 and 4 ? 28 and 4 ? 38 and 4 ? 
 48 and 4 ? 58 and 4 ? 68 and 4 ? 78 and 4 ? 88 and 
 4 ? 98 and 4 ? 
 
 132. Add 4 to 19, 29, 39, 49, 59, 69, 79, 89, and 99. 
 
 5. 
 
 133. Add 5 to every tenth number from 10 to 90 inclusive. 
 
 134. Add 5 to 11, 21, 31, 41, 51, 61, 71, 81, and 91. 
 
 135. Add 5 to every tenth number from 12 to 92 inclusive. 
 
 136. Add 5 to every tenth number from 13 to 93 inclusive. 
 
 137. Add 5 to 14, 24, 34, and so on to 94 inclusive. 
 
 138. Add 5 to 15, 25 35, and so on to 95 inclusive. 
 
 139. Add 5 to 16, 26, 36, and so on to 96 inclusive. 
 
 140. Add 5 to every tenth number from 17 to 97 inclusive. 
 
 141. What is the sum of 18 and 5 ? 28 and 5 ? 38 and 5 ? 
 48 and 5 ? 58 and 5 ? 68 and 5 ? 78 and 5 ? 88 and 5 ? 
 98 and 5 ? 
 
 142. Add 5 to 19, 29, 39, and so on to 99 inclusive. 
 
 6. 
 
 143. Add 6 to 10, 20, 30, and so on to 90 inclusive. 
 
 144. Add 6 to 11, 21, 31, and so on to 91 inclusive. 
 
 145. Add 6 to every tenth number from 12 to 92 inclusive. 
 
 146. Add 6 to every tenth number from 13 to 93 inclusive. 
 
 147. Add 6 to 14, 24, 34, and so on to 94 inclusive. 
 
20 FIRST COUBSE IN INTEGERS. 
 
 148. Add 6 to 15, 25, 35, and so on to 95 inch; 
 
 149. Add 6 to 16, 20, 30, and so on to 90 inclusive. 
 
 150. Add C to cvcrj- tenth number from 17 to 97 inclusive. 
 l.'l. What i* the sum of 18 and ? 28 and 6 ? 88 and ? 
 
 48 and ? 58 and 6 ? 68 and 6 ? 78 and 6 ? 88 and 
 6 ? 98 and 6 ? 
 153. Add 6 to 19, 29, 89, and so on to 99 inclusive. 
 
 153. Add 7 to 10, 20, 30, and so on to 90 in 
 
 AM.l 7 to 11, 21, 81, and so on to 91 inclusi 
 
 155. Add 7 to 12, 22, 32, 42, 52, I and 92. 
 
 Add 7 to every tenth number from 13 to 93 inclusive. 
 \ld 7 to 14, 24, 84, and so on to 94 inclusive. 
 
 158. Add 7 to r.. K, :, and BO on to 95 inclusive. 
 
 159. Add 7 to 16, 26, 86, and so on to 90 inclusive. 
 1GO. Add 7 to 17. 27. 37, and so on to 97 inclusive. 
 
 161. Add 7 : h number from 18 to 98 inclusive. 
 
 162. How many are 19 and 7 ? 29 and 7? 89 and 7 ? 49 
 ad 71 59 and 7? 69 and 7 ? 79 and 7? 89 an 
 
 99 an.l 7 ' 
 
 8. 
 
 163. Commencing at 10, add 8 to every t nth number to 90 
 inclu 
 
 164. Commence at 11, and add 8 to every tenth number to 
 91 inclu.- 
 
 Add 8 to 12, 22, 32, i '. b2, and 92. 
 
 166. Add 8 to 13, 23, 83, and so on to 93 inclu -i . 
 
 Add 8 to every tenth number from 14 to 94 inclusive. 
 168. Add 8 to every tenth numlier from 15 to 95 inclusive. 
 
 ! low many are 1C and 8 ? 26 and 8 ? 36 and 8 ? 46 and 
 
 8 ? 56 and 8 ? 60 and 8 ? 76 and 8 ? 86 and 8 ? 96 
 
 and 8? 
 170. Add 8 to 17, 27, 87, and so on to 97 inclusive. 
 
ADDITION. 1 
 
 171. Add 8 to every tenth number from 18 to 98 inclusive. 
 
 172. How many are 19 and 8 ? 39 and 8 ? 39 and 8 ? 49 
 and 8? 59 and 8? 69 and 8? 79 and 8? 89 and 8? 
 99 and 8 ? 
 
 9. 
 
 173. Add 9 to every tenth number from 10 to 90 inclusive. 
 
 174. Add 9 to 11, 21, 31, 41, 51, 61, 71, 81, and 91. 
 
 175. Commence at 12, and add 9 to every tenth number to 
 92 inclusive. 
 
 176. Add 9 to 13, 23, 33, and so on to 93 inclusive. 
 
 177. Add 9 to every tenth number from 14 to 94 inclusive. 
 
 178. Add 9 to every tenth number from 15 to 95 inclusive. 
 
 179. How many arc 16 and 9 ? 26 and 9 ? 36 and 9 ? 46 and 
 
 9 ? 56 and 9 ? 66 and 9 ? 76 and 9 ? 86 and 9 ? 96 
 and 9? 
 
 ISO. Add 9 to 17, 27, 37, and so on to 97 inclusive. 
 
 18 1. Add 9 to every tenth number from 18 to 98 inclusive. 
 
 182. Add 9 to every tenth number from 19 to 99 inclusive. 
 
 w. 
 
 183. Add 10 to every tenth number from 10 to 90 inclusive. 
 
 184. Add 10 to 11, 21, 31, and so on to 91 inclusive. 
 
 185. Add 10 to 12, 22, 32, and so on to 92 inclusive. 
 
 186. Add 10 to 13, 23, 33, 43, 53, 63, 73, 83, and 93. 
 
 187. Add 10 to every tenth number from 14 to 94 inclusive. 
 
 188. Add 10 to every tenth number from 15 to 95 inclusive. 
 
 180. How many arc 16 and 10 ? 26 and 10 ? 36 and 10 ? 46 
 and 10? 56 and 10? 66 and 10? 76 and 10? 86 and 
 
 10 ? 96 and 10 ? 
 
 190. Add 10 to 17, 27, 37, and so on to 97 inclusive. 
 
 191. Add 10 to every tenth number from 18 to 98 inclusive. 
 
 192. Add 10 to every tenth number from 19 to 99 inclusive. 
 
 (Sec Manual, page 171.) 
 
FIRST COURSE IN INTEGERS. 
 
 SECTION III. 
 
 A US TEA C TJ OJV. 
 4. Prom 1 minus 1 to 20 minus 10. 
 
 WE can see 3 ,,f th< windows of this school-house; 
 1 of them is small, and the others are large. How 
 many large windows can we see ? Mfthod*, pgr /; /. 
 
 1 tree from 2 trees leaves how many trees I 
 
 OIK <>f til-* four girls in the yard is sitting < 
 and the others are at play. I low many art 
 
 2 hoys from 2 lioys leave how many boys? 
 
 In the street are 4 children at play, and <,f 
 boys. How many are girls ? Method*, poo. 
 2 marhlc* from .3 m.irhles leave how many marbles? 
 I hoop from 1 hoop leaves how many hoops? 
 Then- an* : school clays in 1 week If Julius is ab- 
 ? day-;, how many days is he in scL 
 
 Florence brought 7 roses to school, and 
 them to her teacher. How many had she i 
 
SUBTBACTIOtf. 23 
 
 10. In a pasture were 9 horses, but 1 of them jumped 
 out. How many remained in the pasture ? 
 
 11. Otis had 7 doves, hut 2 of them have died. How 
 many has he now ? Methods, page 174. 
 
 12. A girl bought some steel pens for 2 cents, and gave 
 in payment a 10-cent piece. How many cents in 
 change did she receive ? 
 
 U. Eliza is 11 years old, and Hannah is 2 years younger. 
 How old is Hannah ? 
 
 14. A silversmith made 12 butter knives, and sold all 
 but 2 of them. How many did he sell ? 
 
 !'). 4 boys were skating, but 3 of them went home. 
 How many then remained on the ice ? 
 
 16. A cabinet maker made 5 tables, and sold 3 of them. 
 How many had he left ? 
 
 11. On a pear tree were 8 pears, but Julia picked 3 of 
 them. How many were left on the tree ? 
 
 18. Seven carpenters commenced building a house, but 
 five of them left. How many remained ? 
 
 19. A man earns 10 dollars in a week, and his son earns 
 3 dollars. How much more does the father earn than 
 the son ? 
 
 20. If a dress-maker earns $12 in a week, and expends 
 $3, how much does she save ? 
 
 2L A farmer having 6 calves, sold 4 of them to a 
 butcher. How many had he left ? 
 
 22. Irene had 8 canary-birds, but 5 of them escaped. 
 How many had she then ? 
 
 23. A tinsmith made 13 pails, and sold 4 of them. How 
 many remained unsold ? 
 
.M ruisT co UK si: i :: INTEGERS. 
 
 24. One morning 
 
 re lying at a wharf, 
 but during the day 4 of 
 
 thrill sailed away. II<>w 
 many \ I the 
 
 wharf at night? 
 
 25. No vessels from four vessels 
 leave how many vessels? 
 
 26. A Mak. T made 9 baskets, 4 >f tlum of 
 si>]' 1 the others of willow. How m 
 
 Willow 1 lid lie 111;;' 
 
 .,. I paid a >\\\> r-mith $11 for a cak*.- basket, and $4 
 less for a set of tea-spoons. How much dil 
 spoons cost ni' ? 
 
 u'li of the preceding problems w 
 two numhers from another to timl the difference. 
 
 Xtib/rfirfitt/i -cess of taking one of two numbers 
 
 from tin- i 
 
 The 'tinndimlcr or />ijj'< / 
 sul fraction. 
 
 The .iffnurtHl is th:it one of two numbers from wh; 
 other is to be taken. 
 
 The XithfrttJu-tnl i> that one of two numbers which is to 
 be takt n from the other. 
 
 The Xi*/n <>f .s'// /, made thus, , is < 
 
 Minus; and when written between two numbers, it signifies 
 that the number arter it is to be suhtruete 1 from the number 
 before it. Thus, ir, - C is read, ' !" minus 6," and signifies 
 that is to be subtracted from 15. 
 
 low many are 10 sheep 8 sheep ? 
 89. 12 cows 5 cows = how many cows ? 
 
 AVh.it is the difTerei; \\ 11 horses and 4 horses? 
 
 The minuend is 9 and the subtrahend is 1. What is the 
 remainder ? 
 
SUBTRACTION. 25 
 
 32. A wood dealer sold 6 cords of wood, from a pile of 
 7 cords. How many cords were left in the pile ? 
 
 33. A boy sold a water-melon for 8 cents, and a bunch 
 of grapes for 6 cents. How much more did he get 
 for the melon than for the grapes ? 
 
 34' A man bought 9 pounds of butter, and his family 
 used 6 pounds of it in a week. How many pounds 
 were left ? 
 
 35. There are G passengers in a stage-coach, which has 
 seats for 15 passengers. IIov/ many vacant seats are 
 there in the coach ? 
 
 36. A soldier's monthly pay is 813. If he spends 86, 
 how much does he save-? 
 
 37. Of the 1C schools in a certain town, G are taught 
 by gentlemen. How many are taught by ladies ? 
 
 38. One Saturday 7 boys and 7 girls were skating. How 
 many more boys than girls were there ? 
 
 39. James has 9 rabbits ; 7 of them are gray, and the 
 others are white. How many white rabbits has 
 he? 
 
 40. In traveling 12 miles, I rode 7 miles, and walked 
 the remainder of the distance. How many miles did 
 I walk ? 
 
 41. The minuend is 14, and the subtrahend is 7. What is the 
 difference ? 
 
 4?,. A merchant has two clerks. To the older one he 
 
 pays 816 a month, and to the younger one 87 less. 
 
 How much are the monthly wages of the younger 
 
 clerk? 
 43. A farmer having 15 cows, sold 7 of them. How 
 
 many did he keep ? 
 
26 FIRST COURSE IX INTEGERS. 
 
 44. Of the 17 cars of a freight train, 7 are empty. 
 How many are loaded ? 
 
 45. Of the loaded cars 7 contain grain, and the- others 
 flour. llo\v many cars contain flour ? 
 
 46. 7 and how many arc 11 ? Methods, page 174. 
 
 47. Nelson is 12 years old. How old was h< 1 y. ars ago ? 
 
 48. Andrew has caught 8 trout, and Louis 8. Which 
 has caught the greater number ? 
 
 : . I Tow many more must Andrew catch to haw II ? 
 
 How many more to have 15 ? 
 50. Which is the greater, 13 8 or 14 9 ? 
 
 \ gun.-mith made 10 rifles, and sold 8 of them. 
 How many remained unsold ? 
 
 52. 8 and how many are 18 f 
 
 53. A gardener carried 17 bushels of green peas t<> the 
 city. II. sold 8 bushels on First Street, and 
 remainder on Second Street How man\ 
 
 did he sell on Second Street? 
 
 54* 8 and how many are 18 ? 10 and how many are 18 ? 
 How many arc 18 less 9 ? 17 less 10 ? 
 i ;xkc 18 minus 10 from 18 minus 8. 
 
 f tin- length of a barber's pole are above 
 the ground, and the pole is 15 feet long. How 
 
 much of the pole is in tin- ground ? 
 
 58. One day a newsboy sold 19 morninir id 10 
 evening papers. How many more morning than 
 evening papers did he sell ? 
 
 59. A blacksmith bought 10 tons of coal, and li 
 used 9 tons of it How much coal has lie 1 
 
SUBTRACTION. 27 
 
 60. Seven dollars have been paid on a note for nineteen 
 dollars. How much remains due ? 
 
 61. How old were you 5 years ago ? 
 
 62. A farmer paid $16 for a corn-planter, and after 
 using it two seasons, sold it for $9. How much did 
 the use of it cost him ? 
 
 63. 13 boys entered school afc the beginning of the win- 
 ter term, and 8 of them continued in school all the 
 term. How many left school before the term closed ? 
 
 64. A potter made 17 two-gallon jugs, and 9 one-gallon 
 jugs. Of which kind did he make the greater num- 
 ber, and how many ? 
 
 65. Subtract 1 from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11, in this 
 manner: 1 from 1 leaves 0, 1 from 2 leaves 1, 1 from 3 
 leaves 2, 1 from 4 leaves 3, and so on. (See Manual, page 172.) 
 
 66. Subtract 2 from 2, 3, 4, 5, C, 7, 8, 9, 10, 11, and 12. 
 
 67. Subtract 3 from 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13. 
 
 68. Subtract 4 from 4, 5, 6, 7, and so on to 14 inclusive. 
 
 69. Take 5 from 5, 6, 7, 8, and so on to 15 inclusive. 
 
 70. Take G from 6, 7, 8, 9, and so on to 16 inclusive. 
 
 71. How many are 7 minus 7 ? 8 minus 7 ? 9 minus 7 ? 
 
 10 minus 7 ? 11 minus 7 ? 12 minus 7 ? 13 minus 7 ? 
 
 14 minus 7 ? 15 minus 7 ? 16 minus 7 ? 17 minus 7 ? 
 
 72. How many are 8 minus 8 ? 9 minus 8 ? 10 minus 8 ? 
 
 11 minus 8 ? 12 minus 8 ? 13 minus 8 ? 14 minus 8 ? 
 
 15 minus 8 ? 16 minus 8 ? 17 minus 8 ? 18 minus 8 ? 
 
 73. What is the remainder, after taking 9 from 9 ? 9 from 10 ? 
 9 from 11 ? 9 from 12 ? 9 from 13 ? 9 from 14 ? 9 from 
 15 ? 9 from 16 ? 9 from 17 ? 9 from 18 ? 9 from 19 ? 
 
 74. How many are 10 10 ? 11 10 ? 12 10 ? 13 10 ? 
 14-10? 15-10? 16-10? 17-10? 18-10? 
 19-10? 20-10? 
 
28 FIRST COURSE IN INTEGERS. 
 
 5. Subtraction, from 20 minus 1 to 110 minus 10. 
 
 77. Homer having 2G rabbits, sold 5 of them. How 
 many had he lei 
 
 76. A farmer had 87 sheep, but 3 of them were killed 
 by dogs. How many sheep had he K ; 
 
 77. A man bought a watch for $59, and sold it for $9 
 less than cost How much did he get for it '; 
 
 78. From a farm of 89 acres, tin- owner s. 
 How many acres had he then ? 
 
 79. There were 20 roses on a bush, and Kmik \ 
 8 of them. How many were left on the bu 
 
 80. A market woman took 3G geese t d sold 
 
 all but 7 of them. How many did she .- 
 
 81. A stove dealer sold a stove for $23, and his pr.-iit 
 was $4. How much did the stove cost him !' 
 
 I gain $6 by selling a lumber wagon for $91, h\v 
 much did it cost m ? 
 
 race is 9 years old, and ht-r father is !.". What is 
 the diUcremv in their ages? 
 
 >ma pile containing '-M cords of wood, a tea; 
 drew 6 cords. How much wood was left in the 
 
 pil 
 
 cloth CO yards long, .-hrank ;! yard- in 
 fulling. What was its length tin -n ? 
 
 86. A man having $36, paid $8 for a silk hat. ll>w 
 much money had lu- : 
 
 rom a cask containing :>3 gallons <>f oil, gallons 
 were drawn. How much oil was left in the cask ? 
 
 88. Of 43 guests who dined at a hotel, 
 
 many w.-re g-ntl. in.-n ? 
 
SUBTRACTION. 29 
 
 89. I have 840. If I pay $5 that I owe, what sum shall 
 I have left? 
 
 90. What ia the difference between 31 and 8 ? 
 
 91. The minuend is 42, and the subtrahend is 7. What is 
 the difference ? 
 
 92. Which is the greater, 54 9 or 49 6 ? Methods, p. l?4. 
 
 OS. A cooper made 100 barrels, and 5 of them were 
 condemned as bad. How many were good ? 
 
 04. Of the good ones, 7 were pork barrels, and the 
 remainder were flour barrels. How many were 
 flour barrels ? 
 
 05. After selling 8 flour barrels, how many had he 
 left? 
 
 06. From a chest containing 82 pounds of tea, a grocer 
 sold 5 pounds. How much tea was left in the 
 chest? 
 
 07. From a coil of rope 76 feet long, a piece 9 feet long 
 was cut. What was the length of the remainder 
 of the coil ? 
 
 98. Which is the greater, 102 9 or 100 7 ? 
 
 00. The distance from A to B is 105 miles by canal, 
 and 8 miles less by railroad. What is the distance 
 by railroad ? 
 
 100. A crockery dealer, on opening a case containing 
 108 fruit cans, found 9 of them broken. How 
 many were whole ? 
 
 101. After selling 8 of the perfect cans, how many had 
 he left? 
 
 102. Harry having 78 cents, spent 9 cents for fire- 
 crackers. How much money had he then ? 
 
30 FIllST COUBSE IX INTEGERS. 
 
 6. Subtraction by Decades, or Skips of Ten. 
 /. 
 
 103. Subtract 1 from 10, 20, 80, 40, 50, 60, 70, 80, 90, and 100. 
 
 (See Manual, p*^ 
 
 104. What is the remainder, after taking 1 from 11 ? 1 from 
 21 ( 1 from 31 i 1 from 41 ? 1 from 51 ? 1 from 
 
 1 from 71 ? 1 from 81 ? 1 from 91 ? 
 
 105. What is the remainder, after taking 1 from 12 ? 1 from 
 
 '. 1 from 32 ? 1 from 42 ? 1 from 52 ? 1 from 62 ? 
 
 1 from 72 ? 1 from 82 ? 1 from 92 ? 
 
 106. Subtract 1 from 13. 23, 83, and so on to 98 inclu^ 
 
 107. Subtract 1 from 14, 24, 34, and so on to 94 i 
 
 108. Subtract from 15, 25, 85, and so on to ( .r, iiu lu 
 100. Subtract from 16, 26, 86, 46, 56, 66, 76, 86, and 96. 
 
 110. Subtract from 17, 27, 87, 47, 57, 67, 77, 87, and 97. 
 
 11 1. Subtract from 18, 28, 88, 48, 58, 68, 78, 88, and 98. 
 11*. Subtract from 19, 29, 89, and so on to 99 inclu.-! 
 
 2. 
 
 US. Subtract 2 from 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. 
 
 114. Subtract 2 from every tenth number from 11 : 
 inclusive. 
 
 115. Subtract 2 from 12, 22, 82, and so on to 92 inclu> 
 
 116. What is the remainder, after taking 2 from l: 
 
 23 ? 2 from 33 ? 2 from 43 ? 2 from 53 ? 2 from 63 ? 
 
 2 from 78 ? 2 from 83 ? 2 from 93 \ 
 
 117. Take 2 from 14, 24, 84, and so on to 94 inclusive. 
 
 118. Take 2 from 15, 25, 85, and so on to 95 inclusive. 
 m Subtract 2 from 16, 26, 86, 46, 56, 66, 76, 86, and 96. 
 ISO. Subtract 2 from 17. 7. 57, 67, 77, 87, and 
 
 121. Sul -tract 2 from 18, 28, 88, 48, 58, 68, 78, 88, and 98. 
 
 122. What is the remainder, after takin- 2 from 19? 2 from 
 29? 2 from 39? 2 from 49 ? 2 from 59 ? 2 from 69 ? 
 2 from 79 ? 2 from 89 ? 2 from 99 ? 
 
SUBTRACTION. 31 
 
 3. 
 
 123. Subtract 3 from every tenth number from 10 to 100 
 inclusive. 
 
 124. Subtract 3 from every tenth number from 11 to 101 
 inclusive. 
 
 125. Subtract 3 from 12, 22, 32, and so on to 102 inclusive. 
 
 126. Subtract 3 from 13, 23, 33, 43, 53, 63, 73, 83, and 93. 
 
 127. Subtract 3 from 14, 24, 34, 44, 54, 64, 74, 84, and 94. 
 
 128. Subtract 3 from 15, 25, 35, 45, 55, 65, 75, 85, and 95. 
 120. Subtract 3 from 16, 26, 36, 46, 56, 66, 76, 86, and 96. 
 ISO. Subtract 3 from 17, 27, 37, 47, 57, 67, 77, 87, and 97. 
 
 131. Subtract 3 from 18, 28, 38, 48, 58, 68, 78, 88, and 98. 
 
 132. Subtract 3 from 19, 29, 39, 49, 59, 69, 79, 89, and 99. 
 
 . 
 
 133. Subtract 4 from every tenth number from 10 to 100 
 inclusive. 
 
 134. Subtract 4 from every tenth number from 11 to 101 
 inclusive. 
 
 135. Subtract 4 from 12, 22, 32, and so on to 102 inclusive. 
 
 136. Subtract 4 from 13, 23, 33, 43, 53, 63, 73, 83, 93, and 103. 
 
 137. Subtract 4 from 14, 24, 34, 44, 54, 64, 74, 84, and 94. 
 
 138. Subtract 4 from 15, 25, 35, 45, 55, 65, 75, 85, and 95. 
 130. Subtract 4 from 16, 26, 36, and so on to 96 inclusive. 
 
 140. Subtract 4 from every tenth number from 17 to 67 
 inclusive. 
 
 141. What is the remainder, after taking 4 from 18 ? 4 from 
 28 ? 4 from 38 ? 4 from 48 ? 4 from 58 ? 4 from 68 ? 
 4 from 78 ? 4 from 88 ? 4 from 98 ? 
 
 142. Subtract 4 from 19, 29, 39, 49, 59, 69, 79, 89, and' 99. 
 
 5. 
 
 143. Subtract 5 from 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. 
 144- Subtract 5 from 11, 21, 31, 41, 51, 61, 71, 81, 91, and 101. 
 145. Subtract 5 from every tenth number from 12 to 102 
 
 inclusive. 
 
32 II KST COURSE IN 1NTEGEBS. 
 
 146. Subtract 5 from every tenth number from 13 to 103 
 inclu 
 
 147. Subtract 5 from 14, 24, 34, 44, 54, 64, 74, 84, 94, and 104. 
 
 148. Subtract 5 from 1",, 2.~>, 35, and so on to 95 inch; 
 
 149. Subtract 5 from 16, 26, 86, and so on to 96 inch: 
 
 150. Subtract 5 from every tenth number from 17 to 97 
 inclusive. 
 
 151. What is the remainder, after taking 5 from 18 ? 5 from 
 28 ? 5 from 88 ? 5 from 48 ? 5 from 58 ? 5 from 68 ? 
 
 -om78? 5 from 88? 5 from 98? 
 Subtract 5 from 19, 29, 89, and BO on to 99 inclusive. 
 
 (J. 
 153. Subtract 6 from 10, 20, 80, and so on to 100 inclu 
 
 Subtract 6 from 11, 21, 31,41, and so on to 101 inclu 
 . Subtract (i fnm every tenth number from 12 to H2 
 
 inclusive. 
 166. Subtract from c\-ry tenth numlxr from 13 to 103 
 
 inclusive. 
 
 Subtract 6 from 14, 24, 84, and so on to 104 inch. 
 158. Subtract 6 from 15, 25, 85, and so on i isive. 
 
 Subtract 6 from 16, 26, 86, and so on to 96 inch: 
 
 160. Subtract 6 from every tenth number from 17 to 97 
 inch: 
 
 161. What is the remainder, after taking 6 from 18? 6 from 
 28? 6 from 88? 6 from 48 ? 6 from 58 ? 6 from 68 ? 
 6 from 78? 6 from 88 ? 6 from 98 ? 
 
 162. Subtract 6 from 19, 29, 39, and so on to 99 inclusive. 
 
 7. 
 
 163. Subtract 7 from 10. 20, 30, and so on to 100 inch: 
 ,164. Subtract 7 from 1 1. 21. Ml, 41, and so on to 101 inclu 
 
 165. Subtract 7 from 1 . ',2. 52. 62, 72. 82. 92. and 
 
 166. Subtract 7 from every tenth number from 13 to 103 
 inclusive. 
 
SUBTRACTION". 
 
 33 
 
 167. Subtract 7 from 14, 24, 34, and so on to 104 inclusive. 
 108. Subtract 7 from 15, 25, 35, and so on to 105 inclusive. 
 
 169. Subtract 7 from 16, 26, 36, and so on to 106 inclusive. 
 
 170. Subtract 7 from 17, 27, 37, and so on to 97 inclusive. 
 
 171. Subtract 7 from every tenth number from 18 to 98 
 inclusive. 
 
 172. What is the remainder, after taking 7 from 19 ? 7 from 
 29 ? 7 from 39 ? 7 from 49 ? 7 from 59 ? 7 from 69 ? 
 
 7 from 79 ? 7 from 89 ? 7 from 99 ? 
 
 8. 
 
 173. Commencing at 10, subtract 8 from every tenth number 
 to 100 inclusive. 
 
 174. Commence at 11, and subtract 8 from every tenth num- 
 ber to 101 inclusive. 
 
 775. Subtract 8 from 12, 22, 32, 42, 52, 62, 72, 82, 92, and 102. 
 
 176. Subtract 8 from 13, 23, 33, and so on to 103 inclusive. 
 
 177. Subtract 8 from every tenth number from 14 to 104 
 inclusive. 
 
 178. Subtract 8 from every tenth number from 15 to 105 
 inclusive. 
 
 170. What is the remainder, after taking 8 from 16 ? 8 from 
 26 ? 8 from 36 ? 8 from 46 ? 8 from 56 ? 8 from 66 ? 
 
 8 from 76 ? 8 from 86 ? 8 from 96 ? 8 from 106 ? 
 
 180. Subtract 8 from 17, 27, 37, and so on to 107 inclusive. 
 
 181. Subtract 8 from every tenth number from 18 to 98 
 inclusive. 
 
 182. Take 8 from 19, 29, 39, 49, 59, 69, 79, 89, and 99. 
 
 0. 
 
 183. Subtract 9 from every tenth number from 10 to 100 
 inclusive. 
 
 184. Subtract 9 from 11, 21, 31, 41, 51, 61, 71, 81, 91, and 101. 
 
 185. Commence at 12, and subtract 9 from every tenth num- 
 ber to 102 inclusive. 
 
34 FIRST COURSE IN INTEGERS. 
 
 186. Subtract 9 from 13, 23, 33, and so on to 103 inclu 
 
 187. Subtract 9 from every tenth number from 14 to 104 
 inclusive. 
 
 188. Subtract 9 from every tenth number from 15 to 105 
 inclusive. 
 
 180. What is the remainder, after taking 9 from 16? 9 from 
 26? 9 from 36? 9 from 46 ? 9 from 56 ? 9 from 
 
 9 from 76 ? 9 from 86 ? 9 from 96 ? 9 from 106? 
 Mil, tract 9 from 17, 27, 37, and so on to 107 inch; 
 
 r.>l. Sul. trad U from every tenth number from 18 to 108 
 inchi 
 
 1ft?. Subtract 9 from every tenth number from U t ij 
 inclusive. 
 
 fO. 
 
 193. Subtract 10 from every tenth number from 10 to 100 
 incli; 
 
 194. Subtract 10 from 11, 21, 81, and BO on to 101 inclusive. 
 
 195. Subtract 10 from 12, 22, 82, and so on to 102 inclusive. 
 
 196. Subtract 10 from 18, 23, C3, 43, 53, 68, 73, 88, 93, and 103. 
 
 197. Subtract 10 from every tenth number from 14 to 104 
 inch; 
 
 198. Subtract 10 from every tenth number from 15 to 105 
 inch: 
 
 '-Vhat U the remain. 1- ikinir 10 from 16? 10 from 
 
 lofromiu;,' 10 from 46? 10 from 56? 10 from 66? 
 
 10 from 76? 10 from 86? 10 from 96? 10 from 106? 
 00. Sul >tract 10 from 17, 27, 37, and so on to 107 includTe. 
 201. Subtract 10 from every tenth number from 18 to 108 
 
 inclusive. 
 
 80$. Subtract 10 from every tenth number from 19 to 109 
 inclusive. 
 
REVIEW PROBLEMS. 35 
 
 SECTION IV. 
 
 1. EDWARD gave 5 cents for a pencil, 4 cents for a cake 
 of rubber, and 7 cents for drawing paper. How 
 many cents did he expend ? Methods, page 174. 
 
 2. A man husked 9 bushels of corn in the forenoon, 7 
 bushels in the afternoon, and 3 bushels in the even- 
 ing. How much corn did he husk in all ? 
 
 8. Albert has 6 apples, Frank has 8, and Edgar has 5. 
 How many apples have the three boys ? 
 
 4. In a certain school there are 5 pupils in the A class, 
 9 in the B class, 7 in the C class, and 8 in the D 
 class. How many pupils are in the 4 classes ? 
 
 5. A wood dealer has 26 cords of maple wood, 7 cords 
 of hickory, 9 cords of beech, and 5 cords of hemlock. 
 How much wood has he ? 
 
 6. 37 -f 8 + 9 = how many ? 
 
 7. What is the sum of 66, 5, 6, and 9 ? 
 
 8. How many are 48 + 3 + 6 -f 9 + 4 ? 
 
 9. Reuben having 9 peaches, gave 5 to Ada, and 4 to 
 Juliet How many has he left ? Methods, page 174. 
 
 10. If I have $17, and I spend $6 for pictures, and $8 
 for books, how much money shall I have left ? 
 
 11. From a bin that contained 64 bushels of wheat, 10 
 bushels were taken at one time, and 3 at another. 
 How much wheat remained in the bin ? 
 
 12. A high rock on the sea-shore stands 7 feet in the 
 water. If the tide rises 7 feet, and afterward falls 9 
 feet, how many feet of the rock will be under water ? 
 
 Methods, page 175. 
 
36 FIRST COURSE IN INTEGERS. 
 
 15. A laborer earned $11 one week, $6 the next, and 
 spent $8 in the t much money had 
 he 1 
 
 14. 89 + 8 5 = how many ? 
 
 r>. Kiijlit less than ri^hty-eight, plus nine, are how many? 
 
 16. 50 8 8 arc how many ? 
 
 17. If I \\a\\- 75 books, and give away 10 of thorn, and 
 
 ;-d 1'iiy 7 more, how many books shall I then 
 h;r. 
 
 /v. If I owe $54, $8, and $4, and I pay all but $10, how 
 
 much do 1 ] 
 
 I low many more than 7 is the sum of 91, 5, and 10 '- 
 SO. 84 - 9 - 6 - 7 = how many? 
 2 1. 87 + 8 + 8 9 5 are how many ? 
 
 ha\ini: i: doves, sold 6 to Walter, 5 to Alvan, 
 and 4 to Luther. How many doves had he ;!i n ? 
 
 ,?.;. Kalph had a 10-cent piec . and a 5-cent pure : but 
 he has paid 8 cents of his money for a top, and 7 
 cents for marbles. Uow many cents has he K 
 
 24. A silversmith melted together 25 ounces of I 
 and 6 of copp.T. II< u- -1 1 ounces of Lfafl mixture 
 t r tea-spoons, 8 ounces for table-spoons, ami 
 rest for forks. How much did he use for forks ? 
 
 25. How old were you 7 years ago ? How old wil' 
 be 7 years hei 
 
 26. In 5 years Ira will 1 n old. How old was he 
 6 years ago ? 
 
 27. Levi has 9 pears in his hat, 10 in his pockets, and 3 
 in his hand. If he gives 7 pears to his brother, and 
 5 to his sister, how many pears will he hav 
 
MULTIPLICATION. 
 
 SECTION V, 
 
 MUZ TI'PZICATIOJV. 
 / From 2 times 1 to 10 times 10. 
 
 1. Itf each of two wagons there is one barrel of flour. 
 How many barrels in both wagons ? 
 
 2. Two horses are called a span. How many horses 
 are there in two spans ? 
 
 3. There are 3 windows in one side of a mill, and 3 in 
 one end. How many windows are in the side and 
 end? 
 
 i. A wagon has 4 wheels. How many wheels have 2 
 
 wagons ? 
 o. Each railing of a bridge has 5 posts. How many 
 
 posts have the 2 railings? 
 
 6. A little girl bought 2 sticks of cream candy, 2 of 
 lemon, and 2 of peppermint. How many sticks of 
 candy did she buy ? 
 
38 FIBST COURSE IN I N T 11 <; i: BS. 
 
 7. There are 2 boys on one seat, 2 on another, 2 on 
 
 anoth.-r, and 2 on another. How many bo 
 the 4 scats? 
 
 8. If you siiily > hours on Monday, 2 hours on 
 
 day. -, l 1 lours on W dnesday, 2 hours on Thursday, 
 
 iiours on Friday, how many hours will 
 study in 
 
 .''. How many are 1 + 1, or 2 times 1 ? 
 J". I low many are 2 + 2. or 2 times 2 1 
 7 /. How many arc 3 + 3, or 2 times 8 f 
 If. How many are 4 + 4, or 2 times 4 ? 
 IS. How many are 5 + 5, or 2 times 5 ? 
 
 ::iany arc 2 + 2 + 2, or 8 times 2 ? 
 i low many are 2 -f 2 -f 2 -f 2, or 4 times 2 f 
 How much will 2 barrels of flour cost, at $8 a 
 
 barrel ? Mrthod*, page 17 S. 
 
 How many days i .s? 
 
 . A cooper can make 10 barrels in 1 day. How many 
 can IK- make in 2 days ? 
 
 /.''. I low much will 2 papers of ground ]> \ ]> r cost, at 9 
 Htfl a pa]> 
 
 .'". How much will 9 axes cost, at $2 apiece? 
 
 &?. Two oxen are called a yoke. How many oxen are 
 ;i yoke of oxen ? 
 
 .'.'. Hou many clu-rries are 
 
 thriv in ;> dusters of 3 
 
 clu-rries each? 
 -.'>. IIo\\ many cherries are 
 
 there in 4 such clusters? 
 
 !Iow many in 5 clus- 
 ters? 
 
MULTIPLICATION. 39 
 
 2o. How many roses are on 
 3 branches, there being 
 5 roses on each branch ? 
 
 26. How many buds are on 
 3 stems of a rose-bush, 
 if there are 4 buds on 
 each stem ? 
 
 27. How many leaves are on 
 
 3 branches, if there are 6 leaves on each branch ? 
 
 28. A miller sold 6 barrels of corn meal, at $3 a barrel. 
 How much did he receive for it ? 
 
 20. If a cow gives 7 quarts of milk a day, how much 
 will she give in 3 days ? 
 
 30. How many eggs are 3 times 8 eggs ? 8 times 3 eggs ? 
 SI. How many stars are 3 times 1 stars ? 10 times 3 stars ? 
 32. How many trees are 3 times 9 trees ? 9 times 3 trees ? 
 
 In each of the preceding problems we have found the sum 
 of as many times one of the two given numbers as there are 
 ones in the other given number. 
 
 .Iff/It/ plication is a short process for finding the sum of 
 as many times one of two numbers as there are ones in the other. 
 
 The 'Product is the result obtained by Multiplication. 
 The Factors are the numbers used to obtain the product. 
 
 The Multiplicand is that factor which is to be taken any 
 certain number of times. 
 
 The Multiplier is that factor which shows how many 
 times the multiplicand is to be taken. 
 
 The Sian of Multiplication^ made thus, x , when 
 placed between two numbers, signifies that they are to be 
 multiplied together. It is read " times," or " multiplied by." 
 Thus, 4 x 9 is read " 4 times 9," or " 4 multiplied by 9." 
 
40 FIRST COURSE IN INTEGERS. 
 
 S3. The factors are 4 and 9. What is the produ 
 
 nc multiplicand is 8, and the multiplier is o. What is 
 the prod . 
 85. What is the product of 5 x 7 peaches ? Of x $3 ? 
 
 \ hat is the product of 4 x ? 0x4? 
 87. 2x7 = how many ? 8x5 = how many ? 
 
 38. How much will 4 primers cost, at 4 cents api' 
 
 '.''. II<. u much will r pounds of rha! nts a 
 
 pound ? 
 40. 6 spoons, forks, or knives are t-all.-d a <rt. ll..\v 
 
 many forks are tin n- in 4 sets? 
 
 .J/. If 8 acres of grass can be cut with a nn>uin:- 
 machine in a day, how much can lx rut in 4 da; 
 
 42. How mucli will 4 l.uf ralo-robes cost, at *'. 
 
 43. If a forwarder loads 4 boats a day, how many will 
 
 : in 7 days? 
 
 44. If a laborer can dig 4 bushels of potatoes in an 
 hour, how many bushels can he dig in 10 hours ? 
 
 ; ',. Ii .re is 5 cents, how miu-h will 5 
 
 ridi-s r. 
 
 46. How many tea-spoons an tlim in G sets? 
 ID visit. <! S jiatiri-- 
 
 lluw many visits did he make? 
 
 48. Tin- milroad fan- from Cleveland to Cincinnati is 
 $7. What will tin- tickets for C passengers ( 
 
 49. On a freight -train are (\ brakmim, each of whom 
 rarns $9 a w t k. How much do all of tluin earn ? 
 
 measuring depths at sea, 6 feet are a fathom. 
 Hw many IVet are there in 10 fathom 
 How many days an- thm- in 7 weeks? 
 
MULTIPLICATION. 41 
 
 52. How many week-days are there in 9 weeks ? 
 
 JJ. A miller can pack 8 barrels of flour in an hour. 
 How many barrels can he pack in 7 hours ? 
 
 '~>' h What is the cost of a quarter of lamb that weighs 7 
 pounds, at 10 cents a pound ? 
 
 55. If a joiner can make 8 doors in a week, how many 
 doors can he make in 10 weeks ? 
 
 56. A blackberry girl sold 10 quarts of berries, at 9 cents 
 a quart How much did she get for them ? 
 
 57. She bought 9 pounds of sugar, at 9 cents a pound. 
 How much did it cost her ? 
 
 58. A music-teacher gives 8 lessons in a day. How 
 many lessons does she give in 8 days ? 
 
 59. Two men built a stone-wall in 10 days, building 10 
 rods each day. How many rods long was the wall ? 
 
 GO. At a certain sea-port are 9 pilots, each of whom 
 piloted 8 vessels into the harbor in one week. HoW 
 many vessels entered the harbor that week ? 
 
 61. Which is the greater, 7 x 9 or 8 x 8 ? (See Manual, page 172.) 
 
 fif, Multiply 2 successively by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. 
 
 63. Multiply 3 successively by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. 
 
 64. Multiply 4 successively by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. 
 
 65. How many are time 5 ? 1 time 5 ? 2 times 5 ? 3 times 5 ? 
 
 4 times 5 ? 5 times 5 ? G times 5 ? 7 times 5 ? 8 times 
 
 5 ? 9 times 5 ? 10 times 5 ? 
 
 66. How many are time 6 ? 1 time 6 ? 2 times 6 ? 3 times G ? 
 4 times 6? 5 times 6 ? 6 times 6 ? 7 times G ? 8 times 6? 
 9 times 6 ? 10 times 6 ? 
 
 67. Multiply 7 by 0, 1, 2, 3, 4, and so on to 10 inclusive. 
 
 68. Multiply 8 by 0, 1, 2, 3, 4, and so on to 10 inclusive. 
 GO. Multiply 9 by each number from to 10 inclusive. 
 70. Multiply 10 by each number from to 10 inclusive. 
 
42 r i R8T OOU us i: i x i - 
 
 SECTION VI 
 
 8. Prom 2 in 2 and ono half of 2, to 10 in 100 and one 
 tenth of 100. 
 
 /. If 3 hogsheads of sugar m for a dray, 
 
 how many loads will u hogsheads mak 
 .'. How many load^ will !) ho^ln-ads in; 
 
 S. A drayman has 12 hogsheads to draw from a fr 
 house. How many loads will tln-v inn!. 
 
 "(8** HMO*!, p^ 17*.) 
 
 4* At $3 apiece, how many summer coats can bo 
 bought for $3 ? 
 
 5. At 2 cents apiece, how many peaches can you l.uy 
 for 8 cents ? Method*, *>./< / . 
 
 '. How many double desks arc required to seat 10 
 
 pupils ? 
 
 7. A coppersmith gets three dollars apiece for m;; 
 stove boilers. How many boilers must he i 
 cam tw nt \ -one dollars? 
 
 8. C skates are- how many p: 
 
DIVISION. 43 
 
 9. A hatter received $14 for wool hats, at $2 apiece. 
 How many hats did he sell ? 
 
 10. 18 oxen are how many yoke ? 
 
 11. 16 gloves are how many pairs ? 
 
 12. How many cents must Asa have, to buy 20 marbles, 
 if he gets 2 for a cent ? 
 
 13. If one coat can be made from 3 yards of cloth, how 
 many coats can be made from 18 yards ? 
 
 lJ h How many 3-cent postage stamps can be bought for 
 24 cents? 
 
 15. A farmer sowed 30 bushels of plaster on a field of 
 clover, sowing 3 bushels to the acre. How many 
 acres of clover were there ? 
 
 1G. At $4 a ream, how many reams of letter-paper can I 
 buy for $8 ? 
 
 17. If a family use 4 pounds of butter in one week, how 
 many weeks will 20 pounds last them ? 
 
 IS. If 4 plums cost one cent, how many cents will 12 
 plums cost ? 
 
 19. How much will 24 pounds of coffee cost, at the rate 
 of 4 pounds for a dollar ? 
 
 20. A canvassing agent received &3G for books, at $4 
 apiece. How many books did he sell ? 
 
 21. How many horse shoes can a blacksmith set with 33 
 nails, using 8 nails for each shoe ? 
 
 ?. If you put 8 cows in 2 yards, putting the eame 
 number into each yard, how many cows will there 
 be in one yard ? Method*, page 17 s. 
 
 23. In 2 farm-yards are 4 horses, an equal number in 
 each yard. How many horses are in one yard ? 
 
44 
 
 FIRST COURSE IX INTEGERS. 
 
 When any number of thingn it separated or divided into two 
 equal portion* or part*, one of the parts it one half of the uhoU 
 
 One half Is written }. 
 
 f. How many are j of 4 horses ? A of 8 cows? 
 
 25. A farmer has 6 calves in 2 yards, J of them being 
 in each yard. How many calves has he in . 
 
 &6. $ of 2 colts are how many colts f 
 .. A farmer havini: 10 sheep, put of them into his 
 barn-yard. How many were in the barn-yard ? 
 
 28. A milkman sold 2 quarts of milk for K> cents. 
 What was the price of a quart ? 
 
 ."'. Tt \! loaves of bread cost 1C cents, how much will 
 one loaf cost ? 
 
 SO. If it tak<-> 1 I yards of car]--ting to cover 2 flights 
 of stairs, how many yards will it take to cover one 
 flight ? 
 
 31. A chwse-monger bought two cheeses for $18. How 
 much did he pay apiece for them? 
 
DIVISION. 45 
 
 32. How inucli is the fare from Detroit to Milwaukee, 
 if 2 tickets cost 820 ? 
 
 83. If I divide 6 pears equally among 3 girls, how 
 many pears will each girl have ? 
 
 34. If 4 boys together gather 8 quarts of chestnuts, how 
 many quarts arc there in each boy's share ? 
 
 When any number of tilings, ones, or units is divided into three 
 equal parts, one part is one third of the number divided; and 
 
 When any number of things, ones, or units is divided into four 
 equal parts, one part is one fourth of the number divided. 
 
 One third is written ^ ; and one fourth, . 
 
 So. A physician charged a patient 83 for 3 visits. How 
 much did he charge for one visit ? 
 
 3G. If I divide 18 Brazil-nuts equally among 3 children, 
 how many nuts shall I give to each child ? 
 
 37. If a steam-ship uses 27 tons of coal in 3 days, how 
 much docs she use in one day ? 
 
 38. A farmer plowed 12 acres of land in 4 days. How 
 many acres did he plow in one day ? 
 
 30. In an orchard, 24 trees stand in 4 equal rows. How 
 many trees are there in a row ? 
 
 40. A lady used 20 yards of lace in making curtains for 
 4 windows. How many yards did she use for each 
 window ? 
 
 41. How many hours must a man work each day, to do 
 30 hours' work in 3 days ? 
 
 42. If 4 quarts of blue-berries cost 28 cents, how much 
 will one quart cost ? 
 
 43. A furrier sold 4 buffalo-robes for 840. How much 
 did he receive for each robe? 
 
46 I I R S T C O U R S L IN INTEGERS. 
 
 44* If 3 tons of coal cost $24, how much will 1 ton cost ? 
 
 \ carman drew 36 barrels of lim ,nal loads. 
 
 How many barrels did he draw at one load 
 
 In solving each of the first twenty-one problems in this 
 Section, we found how many times one of two numl>crs of the 
 same kind is contained in the other; and in solving each of 
 the other problems, we separated one of two numbers into as 
 many equal parts as there arc ones in the other. 
 
 n is the process of finding how ninny times one of 
 two numbers is contained in the other ; or of finding one of the 
 equal parts into which a number may be divided. 
 The Quo fi cut is the result obtained by division, 
 The /><> -i dcnd is the number to be divided. 
 
 'Divisor is the number by which ; ^ to be 
 
 di\ile 1. 
 
 The Sign of Division, made thus, -*-, when placed be- 
 tween two numbers, signifies that the number before i 
 be divided by the number after it. It is read, "divided l>y. 
 Thus, 85 -i- 7 is read, " 85 divided by ; 
 
 28, and the divisor is 4. What 
 quotient ? 
 
 47. What is the quotient of $40 divided l.y 4 1 
 
 48. 27 -4- 8 = how many t 
 
 49. How many are 12 -j- 2 ? 
 60. 15 -f- 5 = what number ? 
 
 5L A man paid $25 for coal, at $5 a ton. How many 
 tons did he buy ? 
 
 .".'. How many .Vdollar bills must a butcher pay, fora 
 
 cow that costs him $40 ? 
 55. 85 miles are how many times 5 miles t 
 64. A grocer sells raisins, at 5 pounds for a dollar. How 
 
 many dollars will he r r 45 pounds ? 
 
DIVISION. 47 
 
 55. A lady taught school 50 days, teaching 5 days in a 
 week. How many weeks did she teach ? 
 
 56. A carpenter framed a barn in 12 days. How many 
 weeks did it take him ? 
 
 57. lie finished the barn in 24 days more. How many 
 weeks was he in finishing it ? 
 
 58. When shingle nails cost 6 cents a pound, how many 
 pounds can be bought for 36 cents ? 
 
 50. How many weeks arc there in 42 working days ? 
 
 60. 48 tea-spoons are how many sets ? 
 
 61. Celia paid 18 cents for thread, at G cents a spool. 
 How many spools did she buy ? 
 
 62. If a farm hand can hoe 5 acres of corn in 5 days, 
 how many acres can he hoe in one day ? 
 
 63. Bertha picked 18 quarts of berries in 6 hours. How 
 many quarts did she pick in one hour? 
 
 When any number of things, ones, or units is divided into five 
 equal parts, one part is one fifth of the number divided; and 
 
 When any number of things, ones, or units is divided into six 
 equal parts, one part is one sixth of the number divided. 
 
 One fifth is written ; and one sixth, $. 
 
 64. How many pens are ^ of 10 pens ? 
 
 65. How many pencils are | of 6 pencils ? 
 
 66. If 5 baskets of peaches cost $10, how much will one 
 basket cost ? 
 
 67. A piece of land containing 20 acres was fenced off 
 into 5 equal fields. How many acres were there in 
 each field ? 
 
 68. A carpenter gave 30 cents for 5 lead-pencils. How 
 much did he pay apiece for them? 
 
48 Finsx co u RSI: IN INTI:GERS. 
 
 69. One month a teamster fed 30 bushels of oats to 6 
 Imrses. How many oats did he feed to one horse ? 
 
 70. A laborer bought a cow for $3G, and paid for 1 
 
 jiial. monthly payments. llo\v much I 
 pay m- -in ? 
 
 71. If 42 pounds of bur from tin- milk 
 of 6 cows, in a week, how many pounds can be made 
 from tlu- milk of one cow, at the same r 
 
 72. A joiner cut a strip of molding, 25 inches long, into 
 
 s. How long was each piece ? 
 
 73. If one :n do a piece of work 
 how many days can 5 men do it ? 
 
 74- In a ganl -n are 48 strawberry plants, i: 
 
 rows. How many plants :. 
 75. How many days will it take a man to do 54 hours' 
 
 work, if h. works G hours each day? 
 
 70. One 4th of July, Jerome spent 28 cents for fnv- 
 crackers, at 7 cents a bunch. How many bunches 
 did he buy? 
 
 , :. How many bananas can be bought for 14 cents, at 
 7 cents apiece ? 
 
 78. 60 -T- 8 = how many ? 
 
 70. A and B are driving on the road, in the sanc- 
 tion, ainl A is 56 rods ahead of B. In how many 
 minutes will J5 overtake A, if he gains 7 rods in a 
 minute? 
 
 80. How many weeks will it take a girl to bra' 
 palm-leaf hats, if she braids 9 hats in a week ? 
 
 SI. Into how many lots, of 9 acres each, can 27 acres of 
 land be divided ? 
 
 82. How many papers of carpet tacks can be bought f<r 
 16 cent* at 8 cents a paper? 
 
DIVISION. 49 
 
 83. Nathan paid 9 cents for cocoa-nuts, at 9 cents 
 apiece. How many cocoa-nuts did he buy ? 
 
 SJf. At $8 a ton, how many tons of hay can be bought 
 for $32 ? How many tons for $64 ? 
 
 85. 30 soldiers were detailed for duty, in squads of 10. 
 Into how many squads were they divided ? 
 
 86. How many papers of needles can be bought for 48 
 cents, at 8 cents a paper ? 
 
 87. At 9 cents apiece, how many pine-apples can be 
 bought for 36 cents ? How many for 54 cents ? 
 
 88. How many sheets of drawing paper can I buy for 
 40 cents, at 10 cents a sheet ? 
 
 89. Ella paid 60 cents for strawberries, at 10 cents a 
 quart. How many quarts did she buy ? 
 
 99. Rosa bought some ribbon, at 8 cents a yard, and 
 paid 72 cents for it. How many yards did she buy ? 
 
 ft I. When filberts are 9 cents a pound, how many 
 pounds can be bought for 63 cents ? 
 
 a.'. At $8 a bushel, how many bushels of clover seed 
 can be bought for 880 ? 
 
 93. David received 81 cents for walnuts, at 9 cents a 
 quart. How many quarts did he sell ? 
 
 94. How many bushels of charcoal, at 9 cents a bushel, 
 can be bought for 90 cents ? 
 
 95. How many bushels, at 10 cents a bushel ? 
 
 96. A painter received $100 for painting wagons, at 
 $10 apiece. How many wagons did he paint ? 
 
 07. If 7 tons of coal cost $35, how much will one ton 
 
 cost? 
 98. A grocer sold 7 bushels of cranberries for $21. 
 
 How much did he get a bushel for them ? 
 
<> IIKST COURSE IX INTEGERS. 
 
 One of tetcn equal part* into whirh any number of things, one*, 
 or units in 'l, i# one seventh ' AT/ 
 
 One of eight equal part* in one eighth ; 
 
 One of nine equal partt it one ninth ; and 
 
 One of 'ten. equal parts i one tenth. 
 
 One seventh is written ) ; one eighth, \ ; one ninth, |; and 
 one tenth, T V 
 
 90. * of 14 days arc how many days ? 
 
 100. I of 8 reams of pa]> r aiv liow many reai; 
 
 101. A lan.i-T used 56 rails in making 7 lengths of 
 
 . many rails did he use for ^\\\ \ 
 
 ' >n<- man can do a certain piece of w 
 -. In how many days can 7 m-n d<> it ? 
 
 103. A gentleman paid $G3 for 7 weeks' board. II \\- 
 much was that p 
 
 104. Ira sold 7 bunches of grapes for 49 cents, 
 much did he get for one hunt 
 
 106. Edwin paid 70 cents for 7 pints of pea-nuts. II >v 
 iniu-h did they cost a pint ? 
 
 106. A boot maker received $16 for making 8 pairs of 
 coarse boots. How much did he receive for making 
 one pair? 
 
 107. In a game of base-ball there were 8 boys on 
 side. One side kept their innings until tln-y had 
 ha 1 -.' 1 knocks. How many knocks did each boy 
 hai 
 
 108. A gardener sold 9 quarts of currants for 45 cents. 
 II >w much did he get a quart for them ? 
 
 ! f I give 20 apples for 10 pears, how many apples 
 do I give for one pear ? 
 
 110. A carman received 40 cents for drawing 8 K. 
 of flour. How much was that per ban 
 
DIVISION. 51 
 
 111. A crockery dealer bought 10 China tea-sets for 
 $90. How much did one set cost him ? 
 
 112. A wood dealer sold 10 cords of wood for $50. 
 "\Vhat was the price per cord ? 
 
 113. A stove dealer bought 10 parlor stoves for $80. 
 What was the price of each ? 
 
 114. A boy sold 9 quarts of cherries for 72 cents. How 
 much did he get a quart for them ? 
 
 115. If 10 sets of silver-plated forks cost $GO, how much 
 will one set cost ? 
 
 11G. A farmer gathered 100 bushels of apples from 10 
 trees. How many bushels was that to each tree ? 
 
 111. A blacksmith paid 56 cents for 8 pounds of nail- 
 rod iron. How much was the iron per pound ? 
 
 118. A merchant paid 72 dollars for 8 pieces of dress 
 goods. How much did they cost per piece ? 
 
 110. How many times is 2 contained in 2 ? In 4 ? In C ? In 8 ? 
 In 10? In 12? In 14? In 16 ? In 18? In 20? 
 
 120. Divide by 3, from 3 in 3 to 8 in 30, thus : 3 in 3, once ; 
 
 3 in 6, 2 times ; 3 in 9, 3 times ; and so on. 
 
 121. Divide by 4, from 4 in 4 to 4 in 40 ; thus : 4 in 4, once ; 
 
 4 in 8, 2 times ; 4 in 12, 3 times ; and so on. 
 
 122. How much is of 2 ? ot'4? of6? of8? oflO? 
 of!2? of!4? of!6? of!8? |of20? 
 
 (See Manual, page 172.) 
 
 123. How much is of 3? ofG? of9? ofl2? of 15 2 
 of!8? | of 21? of24? of27? $ of 30 ? 
 
 124. How much is | of 4 ? of 8 ? of 12 ? of 16 ? of 20 ? 
 |of24? of28? of32? of 36 ? of40? 
 
 125. How many times is 5 contained in 5 ? In 10 ? In 15 ? 
 In 20 ? In 25 ? In 30 ? In 35 ? In 40 ? In 45 ? In 50 ? 
 
 126. Divide by 6, from C in 6 to 6 in 60 ; thus : 6 in G, once ; 
 6 in 12, 2 times ; 6 in 18, 3 times ; and so on. 
 
FIRST corn- 1: i \ i x r I 
 
 127. Divide by 7, from 7 in 7 to 7 in 70. 
 
 128. Find, successively, | of 5, 10, 15, 20, 25, 30. 
 and 50. 
 
 1W. Find, successively, \ of 6, 12, 18, 24, 30, 3C. 
 
 and 00. 
 ISO. Find, successively, | of 7, 14, 21, 28, 85, 42, 49, 
 
 and 70. 
 
 I'll. Divide by 8, from 8 in 8 to 8 in 80. 
 139. Divide by 9, from 9 in 9 to 9 in 90. 
 
 133. Divide by 10, from 10 in 10 to 10 in 100. 
 
 134. Find, successively, \ of 8, 18, 24, 82, 40, 48, 56, 64, 72, 
 and 80. 
 
 135. Find, successively. ; of 0, is, 27, 30, 45, 54 
 and 90. 
 
 136. Find, successively, -, 1 * of 10, 20, 80, 40, 50, 60, 70, 80, 90, 
 
 i 100. 
 
 SECTION VII. 
 
 1. KMMA bought M ncils, at 5 cents a] 
 
 a sheet of drawing paper for 8 cents. How much 
 money did she pay out ? 
 
 2. A man earns $9 a week, and his son $4. If the 
 fath.-r v, reks, and the son 1 wn-k. how much 
 do they earn ? Method*, page ITS. 
 
 3. A farmer gave 10 barrels of apples, worth $3 a bar- 
 ivl, and $5 in money, for a suit of clothes. What 
 was the cost of the cloth 
 
 4. How many days are 5 times 8 days, + 9 days t 
 
 . Mow many hours are 7 times 7 hours, -f 10 hours? 
 
 6. How many miles are 9 times 6 miles, + 7 miles ? 
 
 7. 8 times 7 feet, + 6 feet are how many feet ? 
 
 5. 6 timps 10 ynr.N. : :i y:irl- :m> ln>w many yards? 
 
RE VIEW PROBLEMS. 53 
 
 0. Aaron sold 4 melons, at 9 cents apiece, and ex- 
 pended all the money but 6 cents for a slate. How 
 much did the slate cost him ? Methods, page 175. 
 
 10. Julius gave 2 10-cent pieces to pay for a writing- 
 book, and received 5 cents in change. What was the 
 cost of the writing-book ? 
 
 11. How many bushels arc 4 times 7 bushels, 9 bushels ? 
 U. How many pecks arc 3 times 9 pecks, 5 pecks ? 
 
 18. 6x7 quarts, 4 quarts = how many quarts ? 
 
 14. 9x5 pints, 10 pints = how many pints ? 
 
 15. If C travels east 3 miles an hour, and B west 5 
 miles an hour, how far apart will they be in 6 hours ? 
 
 (Sec Manual, page 173.) 
 
 16. If they both travel in the same direction, how far 
 apart will they be in 8 hours ? 
 
 17. A grocer sold 7 pounds of starch to one customer, 
 and 3 pounds to another, at 9 cents a pound. How 
 much did he receive ? 
 
 18. If 7 pairs of cuffs can be made from 1 yard of linen, 
 how many pairs can be made from two pieces, one 
 containing 4 yards, and the other 5 yards ? 
 
 19. How many gallons are 6 x 3 gallons, + 4 gallons ? 
 
 20. How many half-pints are 10 times 2 half-pints, + C half- 
 pints ? 
 
 21. A grocer having 14 oranges, sold all but 5 of them, 
 at 3 cents apiece. How much did he get for those 
 he sold ? 
 
 2.1. How much will be the cost of 9 sheep, at $3 apiece ; 
 
 and 2, at $4 apiece ? 
 23. A confectioner sold 7 ounces of candy, at 6 cents an 
 
 ounce; and 2 ounces, at 5 cents an ounce. How 
 
 much did he receive ? 
 
54 FIRST COURSE IX INTEGERS. 
 
 24. Pauline practices on her piano 3 hours every I 
 day, and spends '2 hours with her drawings i 
 in a week. IIow many hours in a week does she 
 
 >te to drawing and music ? 
 .. ". <> times 7 -H 2 times 5 = how many? 
 
 :'. a how many ? 
 times 10 arc how many more than 4 times 21 
 
 28. 8 times 7, are how many ? 
 
 29. 4 times 9, 5 are how many ? 
 
 . ". I low many are 9 times 8, less 7 1 
 .;/. How nr.my :irv 7 timrs5,leSB 8 t 
 
 ..'.'. If :i i:. i ditch in 9 days, hw : 
 
 diiT it in GDC day? Method*, page 17-.. 
 
 .11 in 7 days, in how many 
 days can one man lay it ? 
 
 34* How many men will l>e n-qtiir the same 
 
 wall in one day ? 
 
 of hay will keep 9 sheep 1 nn.nt!.-. II ., 
 many months will it keep one she 
 
 . . How many months will it keep U sh- 
 
 .. If :; ootdl \' wood cost $18, how much will I 
 
 cost? How much will :> cords cost? 
 38. In how many d L 6 in n dig a cellar, that 3 
 
 i di:; in 10 d;: 
 
 . A mechanic ran htiild a sidewalk in ."> days, wcrk- 
 in-_T hours a day. In how many days can he build 
 it. working 10 hmirs a d:: 
 
 40. If G3 yards of bhi'- broadrloth will make T uniforms. 
 Imw many yards will makr -\ uniforms:' 
 
 41. 4 times 9 are how many times ? M> Mhwtef ;"?/' i7.~. 
 JS. 8 times 10 are how many times times 6 1 
 
HE VIEW PROBLEMS. 55 
 
 43. 6 times 4 are how many times 3 ? How many times 2 ? 
 How many times 8 ? How many times 12 ? 
 
 The factors of 12, in sets of two each, are 2 and 6, or 3 and 4. 
 
 44. What are the factors of 14, in sets of 2 each ? Of 15 ? 
 Of 16 ? Of 18 ? (See Manual, page 173.) 
 
 A number that can be separated into factors, is a Composite 
 Nwnber. 
 
 45. Name, in sets of two each, the factors of all the composite 
 numbers from 1 to 10. From 10 to 20. 
 
 46. Name, in sets of two, the factors of the composite num- 
 bers from 20 to 30, not using any factor greater than 10. 
 
 47. In the same manner, name, in sets of two each, the factors 
 of all the composite numbers from 30 to 40. From 40 to 
 50. From 50 to 60. 
 
 48. Name, in sets of two, the factors of the composite num- 
 bers from 60 to 100, not using any factor greater thao 10. 
 
 49. 54 is how many times 9 ? 
 
 50. 64 is how many times 8 ? 
 
 51. 36 is how many times 4 ? How many times 6 ? 
 
 52. 28 is 4 times what number ? 
 
 53. 45 is 9 times what number ? 
 
 54. 63 is 7 times what number ? 
 
 55. How much is \ of 2 times 10 ? Methods, parjc 173. 
 
 56. How much is of 6 times 6 ? 
 
 57. How much is ^ of 6 times 5 ? 
 
 58. How much is of 2 times 6 ? 
 
 59. If ton of hay costs $7, how much will a ton cost ? 
 GO. If | acre of land is worth $10, how much is 1 acre 
 
 worth ? 
 
 Gl. If a mechanic can earn 9 cents in t of an hour, 
 how much can he earn in an hour ? 
 
 o 1 .?. Of what number is 1 1 half? 1 third ? 1 fourth ? 1 fifth ? 
 ? 1 seventh ? 1 eighth ? 1 ninth ? 1 tenth ? 
 
56 FIBST COUBSI: IN iMi:.ii:us. 
 
 63. Of what number is 2 1 half? 1 third ? 1 fourth ? 1 fifth ? 
 1 sixth ? 1 seventh ? 1 :ith ? 
 
 64. Of what number is 3 1 half? 1 third ( 1 fourth ? 1 fifth ? 
 
 thl 1 seventh ? 1 eighth ? 1 ninth : 
 
 Of what number is 4 1 half? 1 third ? 1 fourth \ 1 fifth ? 
 
 1 sixth? 1 seventh ? 1 eighth ? 1 nit nth.' 
 
 66. Name, successively, the numbers of which 5 is $, |, f |, 
 
 l I, li f ^d lV (Se Manual, page 173.) 
 C7. Name, successively, the numbers of which G is J, $, J, |, 
 
 ififand^. 
 . Name, successively, the numbers of M ->ii| 
 
 fcttfcfcndA* 
 
 6P. Name, success numbers of which 8 b J, J, J, |, 
 
 Name, successively, the numbers of which 9 is 4, J, |, {, 
 |, f |, |, and ^. 
 
 A miller sold a barrel of fine flour for $7, a kinvl 
 of family Hour for $9, and a barrel of XX flou: 
 $11. What was the average price? Method*, P . / 
 
 Martin's standing in his arithmetic class on Mon- 
 day was 7; on Tuesday, 9 ; on Wednesda 
 
 Thursday, in ; and on Friday, s. What'wa.- 
 average standing for k ? 
 
 73. A butcher bought 2 calves, at $7 and ono 
 
 calf for $10. What was their average cost ? 
 
 I n 4 hours a hors .9 miles, 8 miles, 
 
 and 5 miles. What was his average rate of spe- 
 
 low much is 7 times \ of 
 Mow much is 9 times | of 
 
 i-w much is 6 times f of 63? 
 
 78. How much is 8 times of 28 ? 
 
 79. How much is 5 times -,V of 80 ? 
 
 80. How much is 10 times \ of 81 ? (See Manual, page 173.) 
 
CHAPTER II. 
 
 *K| __:OND COURSE IN INTEGERS. ]; 
 
 ^^-H^^ ^ a 
 
 "**<** 
 
 SECTION I, 
 
 9. From 10 and 10 to 100 and 100. 
 
 1. IF a cultivator costs $10, and a cart $30, what is the 
 cost of both ? 
 
 2. A traveler has come 40 miles, and he has 30 miles 
 yet to go. What is the length of his journey ? 
 
 8. At what price must an agent sell a sewing-machine, 
 that cost him 880, to gain $20? 
 
 4. A merchant bought a chest of Old Hyson tea, con- 
 taining 90 pounds, and a chest of Young Hyson, 
 containing GO pounds. How many pounds of tea 
 were there in both chests ? 
 
 5. A butcher killed two sheep, one of which weighed 
 GO pounds, and the other 70 pounds. How much 
 did both sheep weigh ? 
 
 6. A farmer sows 20 acres of land to oats, 30 to wheat, 
 and 10 to corn. How many acres does he sow ? 
 
 7. A farmer has 30 Saxony, 40 South-Down, and 50 
 merino sheep. How many sheep has he ? 
 
 5 
 
58 SECOND COURS 1. 
 
 8. I paid 30 cents for a pound of coffee, and 1-1 
 for a quart of molasses. How much did 1 JK 
 
 both ? M,t/,ods, page 175. 
 
 9. A boy gave GO cents for a knife*, un<l 
 
 box of water-colors. How many cents did h. 
 for both ? 
 
 10. A grazier has 70 bead of cattle in one pa 
 
 41 head in another. How many cattle has he in 
 both past u i 
 
 11. A cotton manufacturer sold 40 bales of shcr 
 and 38 bales of shirtings. How many bales of i 
 kinds of goods did lie sell? 
 
 / .'. I n one week a shoe dealer sold 70 cases of boot 
 56 cases of shoes. How many cases did lie s-.-ll ? 
 
 til dealer bought 30 pairs of gloves, 40 pairs 
 18 pairs of gauntlets. How many 
 pairs of all kinds did h- 1 
 
 14. One day a peddler sold a gold, hunter-case 
 
 f.T $100, an open-face, gold watch for $i!U, and a 
 silver watch for $25. How much did he r 
 
 the three watch 
 
 15. A railroad company bought 80 cords of wood at 
 one station. ;:> eonls at another, and 4 cords 
 third. How many cords of wood did they buy ? 
 
 16. In a village school are 24 girls, and 15 boys. How 
 many pupils are in that school? 
 
 :i cents for a pietuiv. and 18 cents for a 
 frame. How much did both cost him /;.-. 
 
 18. Harriet paid <',:', . and 31 cents for coffee. 
 How much did her purchases amount 
 
 19. A marble dealer paid $48 for a block of IP. 
 
 $12 for freight on i:. What 
 
SUBTRACTION. 59 
 
 20. Owen gave 45 cents for a -pair of skates, and 18 
 cents for straps. How much did they cost him ? 
 
 21. Helen's furs cost $28, and Lucy's cost $27. How 
 much did both sets cost ? ^\ 
 
 ?. Eva paid 38 cents for lace, and 25 cents for ribbon. 
 How much did she pay for both ? 
 
 23. In one week a hotel keeper received $37 from board- 
 ers, and $54 from travelers. What were his receipts 
 for the week ? \ 
 
 A farmer has 89 sheep, and 24 lambs. How many 
 sheep and lambs has he ? 
 
 26. Upon a steam-boat there are 92 gentlemen, and 57 
 ladies. How many passengers arc on the boat ? 
 
 26. How many men are 96 men -f 15 men? 
 
 27. How many horses are 41 horses and 98 horses ? 
 
 28. $34 + $27 + $45 = how many dollars ? ' , - 
 
 29. 56 sheep -f 18 sheep + 68 sheep = how many sheep ? 
 SO. What is the sum of 44, 37, 16, and 7 ? 
 
 SECTION II. 
 
 ft A. C T 
 10. From 20 minus 10 to 200 minus 100. 
 
 1. A MAN owing a debt of $30, paid all but $10. How 
 
 much did he pay ? Methods, page 175. 
 
 2. Jesse had 100 cents, but he paid 20 cents for admit- 
 tance to a concert. How many cents had he left ? 
 
 3. A fish-monger sold CO pounds of steak, from a hali- 
 but that weighed 80 pounds. How much remained 
 unsold ? 
 
50 SECOND COURSE IX INTEGERS. 
 
 4. From a hogshead of West India molasses which 
 contained 110 gallons, 70 gallons have been drawn 
 out. How many gallons are 1 
 
 .". Philip threw his ball against a barn 50 feet d. 
 and it rebounded 30 feet How far was it then 
 from him ? 
 
 6. A cutler having 90 knhvs, .--..Id -10 of them. Ib>\v 
 my had he left? 
 
 tinman having 70 sheets of tin, used 50 sheets for 
 pans, and the rest f ; IIow many f! 
 
 h.' make into pa!. 
 
 8. A lady went shopping with $C3, and had $20 when 
 she return d. How much ha-! :it ? 
 
 ' ~ t :> giufti irha I 
 
 rem _ r !it. How many left : 
 
 JO. A farm, r liaving 79 fleeces of wool, sold 30 11 
 How many had he left ? 
 
 11. A physician paid $87 for a horse, and $60 less for a 
 harness. How much did the harness cost h 
 
 -hipped 96 bottles of win- to a eu.-- 
 but only 80 rea< ; unbroken. 
 
 many were brokrii ? 
 
 book-binder bought 72 sheets of straw-board, and 
 d 60 of tin-ill. H<>w many had he 1- 
 J4* A builder bought (HI barrds nf water-lim.-. and nsed 
 81 barrels. How many barrels had lu : 
 
 irrain buy. r bought wheat at 90 cents a 1>; 
 and sold it at 108 cent-. How much did he gain a 
 bushel ? 
 
 16. Elvira is 16 years old, and Laura is 13 
 How old is Lai;. 
 
SUBTRACTION. 61 
 
 17. From a piece of sheeting containing 39 yards, a 
 merchant sold 15 yards. How many yards were left 
 
 in the piece ? Methods, page 176. 
 
 18. A shoe dealer bought 48 "boxes of blacking, and sold 
 25 boxes. How many boxes had he left ? 
 
 10. Luke and Ezra ran a race. Luke ran G9 rods, while 
 Ezra ran 58. How many rods did Luke beat Ezra ? 
 
 20. A manufacturer made 53 hay rakes in a week, and 
 sold 44 of them. How many had he left ? 
 
 21. A farmer earned 72 bundles of straw to the city, 
 and sold 56 bundles in the forenoon. How many 
 had he to sell in the afternoon ? 
 
 ;?. A coal dealer bought 83 tons of stove coal, and 57 
 tons of chestnut coal. How much more of the stove 
 than of the chestnut coal did he buy ? 
 
 ,?J. A grocer bought one cheese weighing 91 pounds, 
 and another weighing 26 pounds less. How much 
 did the second cheese weigh ? 
 
 24. Upon a note of 875, $47 have been paid. How 
 much is yet due ? 
 
 25. In my farm there are 84 acres, 19 acres of which 
 are woodland. How much cleared land have I ? 
 
 26. In the town of Essex there are 76 square miles, and 
 in Franklin 39 square miles less. How many square 
 miles are there in Franklin ? 
 
 27. 97 49 = how many ? 
 
 28. 103 pigeons 69 pigeons = how many pigeons ? 
 SO. Ill swallows are how many more than 28 swallows ? 
 SO. 108 robins 99 robins are how many robins ? 
 
 31. 50 cents are how many less than 100 cents ? 
 
62 SECOND COURSE IX IXTi:;i:RS 
 
 SECTION III, 
 
 11. From 10 times 10 to 10 times 100. 
 
 1. Ax $20 an acre, how much will 3 acres of land cost? 
 ..'. A m-rcliant s.dd 4 shawls, at $30 Bpieoe, How 
 
 much did he receive for them ? M 
 ?. How many yards in 5 pieces of brown linen 
 
 piece containing 40 yards? 
 
 4. A wagon maker sold 3 light wagons, at $90 a; 
 How much did he get for them? 
 
 5. How much will 50 pounds of sugar cost, at 10 
 a pound ? 
 
 ' II o\\- murh must I pay for 40 boxes of table salt. :it 
 
 9 cents a box ? 
 ;. I low many yard-: in '? pieces of carpel 
 
 containing 70 yards? 
 8. A man tra\. -1. -d 7 miles an hour for GO hour-. II . 
 
 far did lie tnr 
 0. How murh will 40 silk vesta cost, at $G ; 
 
 10. How many acres of land in 8 Government lots, of 
 80 acres each ? 
 
 11. How much will ;> pounds of l>utt-r cost, at 23 cents 
 
 a pound ? Method*, pag* 176. 
 
 J :. How many yards an- there in 4 pieces of oil-cloth, 
 each piece containing 42 yards ? 
 
 13. If a boy emu :>l c'-nts a day, how much can h- 
 earn in 5 days ? 
 
 14. A cooper made '. 1-anvls a day. f.ir " t \ days. H..-.V 
 many barrels did he mak 
 
 15. At $35 Bpieoe, how much will 3 cutters cost? 
 
MULTIPLICATION. G3 
 
 16. How much must be paid for 2 barrels of pork, at 
 $26 a barrel ? 
 
 17. How much must be paid for 4 bales of hops, at $44 
 
 a bale ? Methods, page 176. 
 
 18. A fruit dealer bought 28 cocoa-nuts, at 8 cents 
 apiece. How much did they cost him ? 
 
 19. How much must be paid for bottoming 6 cane-seat 
 chairs, at 45 cents a piece ? 
 
 20. In a barrel of K Y. State salt are 5 bushels, of 56 
 pounds each. How many pounds are in a barrel ? 
 
 21. How far will a railroad train run in 9 hours, run- 
 ning 28 miles an hour ? 
 
 22. A field of 10 acres of barley yielded 36 bushels to 
 the acre. What was the total yield ? 
 
 23. At 75 cents apiece, how much will 6 school readers 
 cost? 
 
 24. If I pay 6 cents for the use of 1 dollar for a year, 
 how much must I pay for the use of 37 dollars ? 
 
 2o. How much will 84 pairs of boots cost, at $5 a pair ? 
 
 26. How much will 69 yards of cassimere cost, at $2 a 
 yard? 
 
 27. What will be the railroad fare from A to B, 98 
 miles, at 3 cents a mile ? 
 
 28. A paper maker sold 93 reams of book paper, at $7 a 
 ream. How much did it come to ? 
 
 20. A freight-train of 10 cars is loaded with flour, each 
 car carrying 86 barrels. How many barrels are on 
 the train ? 
 
 30. How much will 4 cows cost, at $79 apiece ? 
 
 31. How much will 8 sewing-machines cost, at $56 each ? 
 
64 SECOND COURSE IX INTEGERS. 
 
 ; .'. I low much will 7 acres of land cost, at $65 an acre ? 
 S3. How much will 47 tons of hay cost, at $10 a ton ? 
 
 strain-boat plys between two places that 
 mik.s apart. How many miles does she make in 8 
 trips? 
 S5. 9 times 81 are how many ? 
 
 36. 4 times 67 are how many ? 
 
 37. 5 times 84 are how many I 
 
 38. 7 x 27 = how many ? 
 
 39. 6 x 83 = how many ? 
 
 40. 8 x 95 = how many ? 
 
 41. 88 x 8 = how many I 
 
 SECTION IV. 
 
 1 2. Prom 2 in 20 to 10 in 1000. 
 
 /. A i A KM hand received $60 for 3 months' ^ 
 How much were his monthly wages ? 
 
 .. A milliner sold 4 yards of ribbon for 80 > 
 What was tin- price per yard? Met hods, JMW /;* 
 
 3. A tea<-h< T paid 360 cents for 9 dozen lead p 
 How much did they cost him a do; 
 
 4. If a factory pirl can weave 180 yards of cloth in 
 days, how much can she weave in a day? 
 
 dairy-man sold '.' cheeses, the total weight of 
 which was 630 pounds. What was their average 
 weight ? 
 
 6. A milkman bought 8 cows for $320. TVha 
 tlvir average cost? 
 
 7. 5 persons earned $250 in a month. What were their 
 average monthly earning 
 
DIVISION. Go 
 
 S. A butcher killed 8 sheep, the aggregate weight of 
 which was 720 pounds. What was their average 
 weight ? 
 
 9. At what price per light will 8 lights of French 
 plate-glass cost $400 ? 
 
 10. How many barrels of lime can be bought for $153, 
 at $3 a barrel ? 
 
 11. A man threshed 48 bushels of beans in 3 days. How 
 many bushels did he average per day ? Methods, 170. 
 
 /?. If 6 boys pick up 96 bushels of apples in a day, 
 what is the average number of bushels to a boy ? 
 
 13. Olivia expended 75 'cents for grapes, at 5 cents a 
 bunch. How many bunches did she buy ? 
 
 14- How many suits of clothes can be made from 91 
 yards of cloth, allowing 7 yards to a suit ? 
 
 l~>. How many weeks will 108 loaves of bread last a 
 family, that use 9 loaves a week ? Methods, page 170. 
 
 16. A lady teacher received $175 for 7 months' services. 
 How much did she receive per month ? 
 
 17. A farm of 415 acres is to be divided equally among 
 5 heirs. How many acres will each heir receive ? 
 
 18. A crockery dealer sold 144 plates, in sets of G plates. 
 How many sets did he sell ? 
 
 19. A lawyer paid $110 for 5 months' board. How 
 much did he pay per month ? 
 
 20. A farmer received $301 for wood, at $7 a cord. 
 How many cords did he sell ? 
 
 21. In making a book of 224 pages, 7 sheets of paper are 
 us,ed. How many pages of the book does each sheet 
 of paper make ? 
 
 6 
 
nr> u.Ni) CO r i: B ;: i N 
 
 ..'.'. How many hours will it take a steam-boar t> run 
 280 miles, running 8 miles an hour? 
 
 ' C48 chestnuts be di\id< -d equally among 1' 
 how many will each hoy t 
 
 railroad train ran lls miles in G hours. AVhat 
 tnoe did it run per hour? 
 
 put up 238 gallons of cider in 7 casks. 
 How much did he put into each cask? 
 
 ni <T< 'hunt's store expenses are $10 a day. In how 
 many days will 1 .ses amount to $780? 
 
 27. During a heavy rain storm, that will hold 
 
 432 barn -Is of into, was iill.-d in s hours. How 
 much wat.-r ran into the ci>: 
 
 29. A a house and lot for $8-1 
 
 : ii in 7 r.jual payments. llw mu<-!. 
 each p.: 
 
 . I low many pairs of boots, at $G a pair, can be bought 
 
 SO. If 7 pounds of crushfil --ost 119 cents, how 
 
 much will 1 pound cost ? 
 
 \t $10 a barrel, how many barrels of fish can he 
 bought for $750? 
 
 .'. How many cist rn juimps, at $8 ; MI he 
 
 bought for $448 ? 
 S3. If 7 coal stoves cost $308, what is ih. price of 1 ? 
 
 34* At how much apiece will G lumber wagons cost 
 $588? 
 
 . At what price per acre will 10 acres of land cost 
 $910? 
 
REVIEW PROBLEMS. 
 
 67 
 
 1. OXE winter, a farmer fed 5 tons of hay to his horses, 
 G tons to his sheep, and 14 tons to his cows. How 
 much hay did it Jake to winter his live stock ? 
 
 2. How many feet have all the quadrupeds in this 
 picture ? 
 
 3. How many pounds of wool are there in 11 fleeces, 
 that average 5 pounds each ? 
 
 4* Anson bought 7 doves, paying 18 cents apiece for 
 them. How much did they cost him ? 
 
 5. How much would the teeth for a 24-tooth harrow 
 cost, at 9 cents each ? 
 
 G. A farmer milks 9 cows, and obtains 135 quarts of 
 milk daily. What is the average number of quarts 
 to a cow ? 
 
C8 B BOO N i> 00 r B8 i: i N i N r BG i: B 
 
 7. If 1 horse cats r.* quart- of oat.- in a day, how many 
 quarts will 2 horses cat in the month of April ? 
 
 8. How many per being 8 quarts in a p 
 
 ''. II.\v many bushels, there being i 
 
 10. A village school-luuis" ha- two rdoms, one of whic-h 
 contains seats for 50 pupils, and th. ,-tlu r, seats for 
 GO. How many pupils can be seated in Loth KM 
 
 .vsboy distributes 49 morning papers, n: 
 
 iiini: papers. H'-w manj i apcrs doc.- 
 tribute each day? 
 
 12. A draler I- 
 
 bushels of sour ones. nyappl- 
 
 ^rraph operator sent one dispatch of 84 v 
 
 and another f o; words. How many words ! 
 tlu n- in the two dispatches? 
 
 14. Mattlicw uti nd d Bobo 
 
 i 7<) days in th- winter. How many da;. 
 
 atu-ml srhonl in the \ 
 16. I j>aid a carpenter $72 for building a :d th<- 
 
 lumber cost me $35. What was the cost of th- 
 
 . V florist has GO varieties of roses, 30 varieties of 
 
 dahlias, and 17 Tl ;m-. 11. >w B 
 
 Htfi kinds of flowers 1 
 
 from the schnnl-lious.-. and walk east 90 
 rods, and th n wst 50 rods, how far will you be 
 from the school-house ? 
 
 18. At a found ns of iron :uary, 
 
 and 27 ton ruary. How many tons 
 
 Iran us.-d in 1-Vhruar 
 
REVIEW PROBLEMS. 69 
 
 10. Mark dug 62 bushels of potatoes in two days, dig- 
 ging 35 bushels the first day. How many bushels 
 more did he dig the first day than the second ? 
 
 20. At $90 a thousand, how much will 9 thousand hop- 
 poles cost ? 
 
 21. A surveyor received 8174 for his services, at $6 a day. 
 How many days was he employed ? 
 
 At 8 cents apiece, how much will 48 cocoa-nuts cost ? 
 
 2J. How many lengths, each 9 feet long, are there in a 
 post-and-rail fence 783 feet long ? 
 
 24. If A can build 8 rods of wall while B builds 5 rods, 
 how many rods can he build while B builds 35 rods? 
 
 2o. A person bought 3 books, giving for the first a 
 25-cent currency note, and receiving back 10 cents; 
 for the second he gave 20 cents more than the first 
 cost him, and received back 5 cents ; the third book 
 cost him as much as the other two, and he sold it 
 for 50 cents. How much did he gain on the third 
 book? 
 
 Philip lives 40 rods from the school-house, Edwin 
 50 rods further away, and Arthur 60 rods further 
 than Edwin. How far does each have to walk in 
 coming to school ? 
 
 In building a school-house, a mason worked 46 days, 
 a carpenter 64 days, and a painter 18 days. How 
 many days did they all work upon it ? 
 
 A steam-ship sailed from New York for Liverpool 
 with 72 first-class, 45 second-class, and 16 steerage 
 passengers. How many passengers did she carry ? 
 ?-9. A man owing $86, paid $49 one day, and $18 tho 
 next day. How much did he then owe ? 
 
70 SECOND COUB81 i .V i N T r. i, i: us. 
 
 30. A map agent took 53 subscriptions in Januu 
 
 in 1-Vbruary. 47 in March, and :)'. in April. . 
 many <>rd<T>. did In- take in the four months? 
 
 ->'/. A wood dealer sold to three persons, I'. 1 
 
 cords, and 36 cords of wood, and had 29 cords 
 IIn\v many cords had rst? 
 
 .... I'lMin a kiln of 100 thousand brick. 31 
 
 \\vn- sold to one build* r, ' thousand to an- 
 
 other. How many brick In? 
 
 105 cents, but he has 
 
 Edmnn .ts to John, 19 cents t . and 
 
 I' 1 . nti 1" M* 1\ in. II m many cent.- 
 
 haul has M yards of cl..ih in f;. 
 ii contains 29 yards, and an 
 B '.v many yards m ;hird 
 
 piece? 
 
 I>cr paid $98 for a hore< 
 
 $15 for hi.- 1I rivi\vd $3C for his use, 
 
 and sold him lor $80. Did h 
 mr. 
 
 . \ mannfactun r mad'- ',''> pain -f 
 
 weeks sold 54 pairs. How many pairs had IK 1 
 
 >r a sled, and 50 cents for a 
 
 knifv*. and gave thorn both f>r a pair of skates worth 
 100 cents. Did he gain or 
 
 88. I owe $120; $: $36 to B, $41 to C. and the 
 
 balance to D. Ho\v niu-.-: D? 
 
 39. Oscar had 40 cents, and (Ian nee 60. O^r 
 
 as many cents as Claivn< . and he then had 
 
 . II-.v.- many c^nls did ('!. 
 
REVIEW PROBLEMS. 71 
 
 40. A bought a watch for $65, and offered to sell it for 
 $20 more than cost, but finally sold it for $16 less 
 than his asking price. At what price did he sell it? 
 
 41. If I go east 57 miles, then west 24 miles, then east 
 17 miles, and then west 32 miles, will ; I be east or 
 west from the place of starting, and how far? 
 
 42. From a roll of carpeting containing 120 yards, three 
 carpets of 28 yards, 36 yards, and 44 yards were cut. 
 How many yards were left in the roll ? 
 
 43. If I deposit $64 and $70 in a bank, and draw out 
 $48, $36, and $25, how much will I have left in the 
 bank? 
 
 44- The railroad distance between Syracuse and Roch- 
 ester is 81 miles. If one man leaves Syracuse, and 
 travels toward Rochester 5 miles an hour, and an- 
 other leaves Rochester, and travels 4 miles an hour 
 toward Syracuse, how far will they be apart in 1 
 hour ? 
 
 4~>. How far will each have traveled in 5 hours ? 
 
 46. How far will they be apart in 7 hours ? 
 
 47. In how many hours will they meet ? 
 
 48. When they meet, how far will each have traveled ? 
 
 49. How far will the Rochester man go, while the Syra- 
 cuse man is going 45 miles ? 
 
 GO. Mabel bought 10 yards of calico, at 13 cents a yard, 
 
 and 8 yards of ribbon, at 20 cents a yard. How 
 
 much did her purchases amount to ? 
 51. A drover bought 25 sheep, at $2 apiece ; 34, at $3 
 
 apiece ; and 18, at $4 apiece. How many sheep did 
 
 he buy ? 
 5& How much did they cost him ? 
 
72 SET o.\ I) COURSE IN* INTEGERS. 
 
 53. What is the sum of 10 times 7, and 3 times 9 ? 
 
 54. What is the sum of x 8 and 5x7? 
 What is the sum of 4 x 7 and 8x9? 
 
 is the different i 9 x 6 and 7x7? 
 
 57. What is the difference between 10x6 and 0x8? 
 
 58. What is the different i 8 x 7 and 5x9? 
 
 1 Im.-hrl of wheat is worth 08 much a> 
 of corn, and 1 bushel of corn as much as v! l-u-ln-N 
 of oats, how many bushels of oats ; 
 much as 76 bushels of wh 
 GO. A merchant bought 5 pieces of cam' 
 
 containing 41 yards, at 10 cents a }urd. I low much 
 did it cost nim? 
 
 ' '. How nv.ny quiivs of j, ; . .jiiire, can 
 
 be bought i li of doth, at 30 cents a yar 
 
 \ boy exchanged 3 dozen of eggs, at 33 
 doz-n. for 4 pounds of raisins. What was the price 
 
 of tip- rai-'.is? 
 
 OS. In how many months will 8 horses eat as much as 
 10 hors'.s will . at in 12 months? 
 
 how man" days can 7 men earn as much as G 
 
 ' . How mud grass seed, at $4 a bushel, will pay for 
 invls of apples, at $3 a bar 
 
 . IIo\\ many noes, at 80 cents each, can be bought 
 
 for 10 brooms, a b each ? 
 
 1 ;. A man has a job of work that lie can do i: 
 
 days. If he employs 5 men to assist him, in how 
 many days will they do i 
 
 (>^\ If 8 men can lay a mile of railroad track in 1". 
 in how many days can 12 men lay 
 
REVIEW PROBLEMS. 73 
 
 60. If 5 yards of calico cost 80 cents, how much will 9 
 yards cost ? 
 
 70. If a workman earns $72 in 8 weeks, how much can 
 he earn in 24 weeks ? 
 
 71. If a ship sails 42 miles in 7 hours, how far will she 
 sail in 20 hours ? 
 
 ?~ 7 . How many peaches, at the rate of 4 for 8 cents, 
 can you buy for 22 cents ? 
 
 73. A boy sold 16 bunches of grapes, at the rate of 3 
 bunches for 15 cents. How much did he get for 
 them ? 
 
 74' A f armcr s ld 8 barrels of apples at $4 a barrel, and 
 enough more at $3 a barrel, to realize $101. How 
 many barrels did he sell at the second price ? 
 
 75. One Fourth of July, Orrin had 83 cents. He bought 
 4 bunches of fire-crackers, at 12 cents a bunch, and 
 spent the rest of his money for pea-nuts, at 7 cents 
 a cup. How many cups of pea-nuts did he buy ? 
 
 76. A fruit dealer bought 24 baskets of peaches, at $2 a 
 basket, and sold them all for $60. How much was 
 his gain ? 
 
 77. A furniture dealer bought 8 wash-stands for $40, 
 and sold thenrat $6 apiece. How much did he gain? 
 
 7S. A drover bought 75 sheep for $225, and sold them 
 at $4 apiece. How much did he gain ? 
 
 70. A mechanic worked for a grocer 17 days, at $3 a 
 day, and received in pay $19 in money, and the 
 balance in groceries. How many dollars' worth of 
 groceries did he get ? 
 
 80. If the wages of 3 men for 6 days arc $36, what are 
 the wages of 4 men for 8 days ? 
 
U SECOND COURSE IX INTEGERS. 
 
 81. If 4 men build 40 rods of wall in 5 days, how many 
 rods will 10 men build in G da; 
 
 82. 8 men, in days, made 1 11 pairs of shoes. At the 
 same rate, how many pairs will 9 men mak- 
 days? 
 
 in 1 da\ - 
 many vests can 1C girN make in 9 days? 
 
 84* A dairy -man who had 20 cows, made 900 pounds of 
 rliLvso iii 15 days. At th-- .sun -w many 
 
 pounds of cheese can be made in 11 days, from the 
 milk of 13 cows? 
 
 85. 10 times of 24 are bow many f 
 
 86. 4 ; :r> :ir< how many ? 
 
 i of 48 arc how many? 
 
 88. 7 times ^ of 60 arc how many f 
 
 89. 8 times J of 72 arc how many ? 
 
 90. G times } of 95 arc how many t 
 
 ues I of 108 arc how many? 
 OS. 3 times ^ of 1 76 arc how many ? 
 
 many arc 4 times J of 10 times 8 f 
 I low many arc 6 times J of 5 times 9? 
 1 low many are 5 times | of 6 times 12 ? 
 I low many iiro 8 times \ of 9 times 4 ? 
 
 in:iiiy arc- 7 times | of 6 times Ki ? 
 How many arc 9 times \ of 8 times 7 1 
 1) is | of what number? 
 100. 8 is \ of what mini! 
 I. 1 ) is^ of what mini 1 
 
 102. \ of 104 is | of what nun 
 
 103. \ of 215 is \ of what mm. 
 
 104. I ! of %\h:i; I 
 
y 
 
 CHAPTER III. 
 UNITED STATES MONEY, 
 
 SECTION I. 
 
 VC TZOJYS. 
 
 77nited States Money, or Fed- 
 eral Money, consists of dollars, 
 cents, and mills. 
 
 10 mills are 1 cent. 
 100 cents are 1 dollar. 
 
 1 dollar is 100 cents. 
 1 cent is 10 mills. 
 10 dollars are sometimes called an Eagle, 
 and 10 cents a Dime. 
 
 jm 
 
 K&& 
 
76 
 
 UNITED STATES M .\ 
 
 UNITED STATES COIN TABLE. 
 
 METALS. KAVXS OF COIXS. 
 
 TAI.CRS. VCTALS. 
 
 
 5n. dollar piece. 
 
 $50.00 | 
 
 
 Double eagle, 
 
 20.00 
 
 Gold, . 
 
 Btgte, 
 
 Half-eagle, 
 
 10.00 c 
 
 5.0u 
 
 
 8-dollar ]> 
 
 3.00 
 
 
 Quarter-eagle, 
 
 
 [Del 
 
 1.00 ( 
 
 ( 2-cent i 
 Copper, j ( 
 
 !<el. 
 
 .01 
 
 HAVES OF COIXS. VALtTSS. 
 
 f Dollar. $1.00 
 
 Half-dollar, .50 
 Quarter-dollar, .25 
 
 Dime, 
 Half-dime. 
 3-ecnt ; 
 
 piece, 
 
 .10 
 .03 
 
 .05 
 .03 
 .01 
 
 If v dollar into 10 equal parts, each of the parts 
 
 is 1 tentkof the dollar, and i- r ' ; 2 I' the part* are 
 
 x of a doi: met; 8 parts are 3 f*vtfof a dollar. 
 
 or 8 dimes, and so on. 
 
 Dividing each of the tenths of a dollar, or each din: 
 10 equal parts, v dolUrio times 10. ..r loo 
 
 f these parts is 1 hwdrcdth of a dollar, 
 
 l)i\idinu r each of the h of a dol'... 
 
 into 1" '. ' have in the whole dollar I'- 
 
 ll <>f these parts is 1 thoiuaiulth of a 
 dollar, and is called 1 / ./" 7 . Hence, 
 
 1 tenth of 1 dollar is 1 dime, which is written $.1 or $.10. 
 
 .th of 1 dime, or 1 hundredth of a dollar, 
 whieh is written $.01. 
 
 :,th of 1 cent, or 1 thousandth of a dollar, is 1 mill, 
 v.liir 1 . D s.nni. 
 
 When the dollar mark ($) is used in w riling any sum of 
 money, the D.\'i'm>il Pmnt which is a period or point (.) 
 mu-t always be i >re the cent-. Thus. $17.42 ; $.37. 
 
 From the preceding illustrations we see, that 1 tenth of a 1 
 is 1 tenth, and is written .1 ; 1 tenth of .1 i- 1 
 i-* written .01 ; and 1 tenth of .01 is 1 thousandth, and i 
 ten .001. That ia 
 
NOTATION AND REDUCTIONS. 77 
 
 The first place at the right of the decimal point is the place 
 of tenths, the second place is the place of hundredths, and 
 the third place is the place of thousandths. 
 
 The first two figures at the right of the decimal point ex- 
 press cents, and the third figure expresses mills. Thus, 
 
 $.03 expresses 3 cents. 
 
 $.87 " 87 cents. 
 
 $7.03 " 7 dollars 8 cents. 
 
 $3.54 " 3 dollars 54 cents. 
 
 $.007 " 7 mills. 
 
 $.092 "' 9 cents 2 mills. 
 
 $.625 " G2 cents 5 mills. 
 
 $14.706 " 14 dollars 70 cents 6 mills. 
 
 1. How many mills are there in 4 cents ? 
 
 2. How many mills in 10 cents? 
 
 3. How many mills are a half-cent ? 
 
 4. 5 dimes are hpw many cents ? 
 
 5. 3 half-dimes are how many cents ? 
 C. How many doflars are 6 eagles ? 
 
 7. 3 dollars are how many cents ? 
 
 8. 10 dollars are how many cents? 
 
 9. 5 half-dollars arc how many cents ? 
 
 10. Agnes has 3 dimes and a half-dime. How many 
 cents has she ? 
 
 11. Janet gave a half-dollar, 2 dimes, and, a half-dime 
 for a grammar. How many cents did it cost? 
 
 12. How many dollars arc 5 eagles and a half-eagle ? 
 
 13. How many dollars are a double eagle and 8 eagles? 
 
 14. A man was paid a 50-dollar piece for making cigars, 
 at a cent apiece. How many cigars did he make ? 
 
 15. How many cents are an eagle and a dollar worth ? 
 
 16. 30 mills are how many cents ? 
 
 17. 87 mills are how many cents and mills? Methods, p. no. 
 
 18. 100 mills are how many cents ? 
 
78 UNITED STATES M01JEY. 
 
 10. 45 mills are how many rents ? 
 
 20. 60 cents are how many dimes ? 
 
 x'7. How many dimes and cents are 36 cents ? 
 
 . How many eagles are 40 dollars f 
 
 J. How many eagles and dollars are 96 dollars ? 
 
 24. How many picture books, at a dime .in lo 
 
 bought for 50 cents? 
 ~ 7. If 1 ton of plaster costs a ha' ;ow main 
 
 can be bought for $70 ? 
 26. A merchant exchanged $120 for its value in gold 
 
 eagles. How in - did In- r 
 
 i a dime apiece, how many spools of thread can In- 
 bought for 80 cents? 
 tS. 500 cents are how many dollars ? 
 
 000 cents are how m many eagles ? 
 
 SO. How many pairs of slippers, at $1 a pair, can 1 Imy 
 
 for GOO cents ? 
 .//. I Iw man;. s, at $1 a -an !. 
 
 bought for 900 cents? 
 
 A?. How many cents are 5 dollars and 60 cents ? 
 S3. How many cents are 8 dollars and 34 cents f 
 Af. How many cents are 15 dollars and cei 
 SJ. A stationer received 7 dollars 58 cents for 
 
 cils, at 1 cent apii-cf. How many pencils did h< 
 36. A boy who prddK-d apples at 1 < >ok in 
 
 5 dollars 4 cents in one week. How many ni 
 
 did he soil? 
 . . How many sheets of paper, at 1 cent a she. t. can l.-j 
 
 bought for 10 dollars 7.~> oenta ? 
 S8. 225 cents arc how many dollars and cents ? 
 9. .". ,:iny dollars and cents? 
 
 40. How many pocket-knives can I Imy with \ 
 
 at $1 apiece, and how many cents will 1 ha- 
 
COMPUTATIONS. 79 
 
 SECTION II. 
 
 T&TA TIOJVS. 
 
 1. NEWTOX paid 1 dollar 25 cents for a pair of birds, 
 and 1 dollar 50 cents for a cage. How much did he 
 pay out ? 
 
 2. A gardener gave 1 dollar 50 cents for a spade ; 88 
 cents for a hoe, and 1 dollar 25 cents for a rake. 
 How much did he give for all ? Methods, page 176. 
 
 {/S. I paid $3.50 for a coat, $1.75 for a hat, and $5.50 for 
 a pair of shoes. How much did they all cost me ? 
 
 4. Rufus gave $.80 for a reader, $1.40 for an arith- 
 metic and slate, and $2.25 for a geography. How 
 much did his school books cost him ? 
 
 5. How much will be the cost of a pair of scissors at 45 
 cents, a penknife at 81 cents, a work basket at 94 
 cents, and a thimble at 50 cents ? 
 
 6. I paid 19 dollars 67 cents railroad fare, 7 dollars 11 
 cents hotel bills, and 3 dollars GO cents for horse 
 hire. How much did my journey cost me ? 
 
 7. Calvin having 5 dollars 84 cents, bought a ball and 
 bat for 1 dollar 56 cents. How much money had he 
 
 left ? Methods, page 176. 
 
 8. Edith took 1 dollar 25 cents, with which to buy 
 some silk for an apron ; but it cost only 95 cents. 
 How much money did she bring home ? 
 
 9. I owe 7 dollars 48 cents, and I have 5 dollars 75 
 cents. If I pay all the money I have, how much 
 will I then owe ? 
 
 10. Lilian gave a $5 hill in payment for a pair of shoes 
 that cost $3.75. How much change did she receive ? 
 
80 \ITED STATES MONEY. 
 
 11. If I have $6.30, how much more mon i him-, 
 
 to buy a watch worth $25 ? 
 
 .'.. A m. -reliant bought broadcloth at $3.~~ a yurd, and 
 sold it at $5.25. IIow much did he gain on a yard ? 
 
 13. How much will 1 pounds of crushed SUL: 
 17 cents a pound ? 
 
 14. At 22 cents a pound, how much will :> pounds of 
 * raisins cost ? 
 
 15. How much will a laborer earn in 6 days, at 1 
 
 HrthodM, pagr I ; ;. 
 
 /' . How much will 8 fruit-knives cost, are 25 
 
 ,. \Vhat will be the cost of 10 p:ij is, at $.88 
 
 api- 
 18. How much will 7 tons of coal cost, at $G.:> 
 
 : 8 pounds of dried plums cost 1 dollar 28 cents, 
 what is the cost of 1 pound ? 
 
 20. If 5 yards of delaine cost $1.85, how much will 1 
 
 1 COSt ? Method*, paffr 1 . ::. 
 
 uhat ] : ill 4 baskets of p- 
 
 l.rin.u *:;.: 
 
 \ gardener soM 7 bushels of sweet-potatoes for 9 
 
 dollars 80 cents. What is the price per bu^! 
 
 il - i !i must I earn each da\ 
 10 days? 
 
 ?.' f . If 8 reams of paper cost $34, what is the price per 
 ream ? 
 
 1 90 cents for needles, at 6 cents a \ 
 How many papers did she bi: 
 
 ,;>'>. How many pounds of rice, at 8 cents a pound, can 
 be bought for 2 dollars 24 cents ? Method*, page / 
 
COMPUTATIONS. 81 
 
 27. A laborer received 3 dollars, for threshing oats at 4 
 cents a bushel. How many bushels did he thresh ? 
 
 28. In one month a young man paid out $6.50 for 
 cigars, at 10 cents apiece. How many cigars did he 
 buy? 
 
 29. At 9 cents a box, how many boxes of blacking can 
 be bought for $4.95 ? 
 
 SO. Amelia had 1 dollar 42 cents, but she has paid out 
 56 cents for ribbon, and 37 cents for buttons. How 
 much money has she left ? 
 
 81. Hugh had 84 cents, his mother gave him 68 cents, 
 and he gave 96 cents for a hatchet How much 
 money had he then ? 
 
 82. A gentleman bought a pair of gloves for $.63, and 
 an umbrella for $1.75, and gave the shop-keeper a 
 half-eagle in payment. How much money did he 
 receive in return ? 
 
 33. Luella bought 8 yards of cambric, at 23 cents a 
 yard, and 30 cents' worth of machine twist. How 
 much did her purchases amount to ? 
 
 34. How much will be the cost of a jar of 10 pounds of 
 butter, at 28 cents a pound, and 56 cents for the 
 jar? 
 
 85. I bought a pound of tea for $1.62, and 7 pounds of 
 lard at 17 cents a pound. How much did my 
 purchases cost me ? 
 
 86. How much will you have to pay for 9 quires of 
 letter-paper at 38 cents a quire, and a quart bottle 
 of ink at 75 cents ? 
 
 37. Jason has $1.38, and he wishes to buy 6 pine-apples, 
 which cost $.25 apiece. How much more money 
 must he have, to make the purchase ? 
 
82 UNITED STATES MONEY. 
 
 38. A man bought 8 pounds of stove pipe, at 19 cei 
 
 i:il. an<l paid 95 cents. How much did lu then 
 owe upon it ? 
 
 How inm-ii money must be given, with a kt 
 oysters worth $1.25, in exchange for a turkey which 
 weighs 9 pounds, at $.26 a pound V 
 
 A lady had 27 quarts of currants, and 
 $2.48 for more at $.08 a quart How many <j 
 of currants had she then ? 
 
 . Clemen: s and Amos 69 cents, and th< -y 
 
 spent the whole of their money for 5 pounc 
 almonds. How much did the almonds 
 poa 
 
 A grocer paid 6 dollars 3 cents for 9 bu 
 tomatoes, and sold them at 85 cents a bushel How 
 
 much did lu- :ain mi a bushel? 
 
 43. Viola paid $.92 for pears, at $.04 apiece, A 
 
 inir i of them to Louise, how many had she lei 
 
 44. A man who had $12, gave all but $2.10 of 
 
 much w ce? 
 
 5 gallons of oil cost $3.39, how run 
 Ions cost? 
 Jt'l. If 10 bushels of corn cost $8.40, how much will C 
 
 ost? 
 
 of a cow for 7 weeks costs $' 
 how much will 1 rage cost for 9 wet 
 
 K A paid $28 for 8 sh 1> bought ."> a' 
 
 price. How much did 1? pay tor i 
 
 49. If 4 m< 
 
 nil n earn in 10 days? 
 
''"ill f^~' 
 
 j^S 
 
 -^^1 CHAPTER IY. 
 
 jtF 
 
 ^^-~v-' ^*^^**^ i ^ 
 
 8^4^- 
 
 COMPOUND NUMBERS. 
 #?*$&*** 
 
 SECTION I. 
 
 "We determine the quantity of all articles bought and sold, 
 by either measuring, weighing, or counting them. 
 
 ^Denomination is the name of the unit of a concrete num- 
 ber; as, gallon, foot, pound, hour, dollar. 
 
 A ^Denominate J\~umbcr is a number applied to a 
 denomination ; a*, 9 quarts, 4 feet, $7. 
 
 A Simple . 1 'umber is an abstract number, as, C, 43, 915; 
 or a concrete number of but one denomination, as, 78 men, 324 
 miles. 
 
 A Compound J\*umbcr is a number expressed in two or 
 more denominations ; as, 4 pounds 10 ounces, 15 gallons 3 
 quarts 1 pint. 
 
 If iff her Denomination* are those -which express the 
 greater amount or quantity. And 
 
 flower ^Denominations are those which express the less 
 amount or quantity. Thus, a peck is a higher denomination 
 than a quart, and a lower denomination than a bushel. 
 
 A ^Denominate Unit is one of any denomination; as, 1 
 pound, 1 foot, 1 quart, 1 dozen. 
 
 In computations in Compound Numbers, it is often neces- 
 sary to change units of higher denominations to those of 
 lower, as gallons to quarts or pints ; or units of lower denom- 
 inations to those of higher, as feet to rods or miles. 
 
84 COMPOUND NUMBERS. 
 
 JHrtioHS arc processes of changing numbers from one 
 denomination to another without changing values. They arc 
 of two kinds, Reduction Descending and Reduction Accn<i 
 
 ftcdnrfioti /><.;<!>!/ is the process of changing num- 
 bers from higher to lower denominations ; and 
 
 Reduction Ascendinff is the process of changing num- 
 bers from J _rher denominations. 
 
 SECTION II. 
 
 13. Liquid Measure. 
 
 In im-:isuri:iu r oil. molasses, 
 syrups, wines, milk, and 
 
 otln-r liquids, 
 
 ^- 
 
 *)arelpt (pint.) 
 2 pt. 1 qt (quart.) 
 
 4 qt. " 1 gal. (gallon.) 
 
 1 -rul. is 4 qt. 
 1 qt. " 2 pt. 
 
 1 pt. " 4 gi. 
 
 (See Manual, p*g 173.) 
 
 7. 10 gallons are how many quarts ? How many pints ? 
 jf. Change 7 quarts to gilla. M<thod, pagt /;;. 
 
 3. If a pastry-cook uses 1 gill of wine cv< h< w 
 many days will she use a gallon ? 
 
 4. In how many days would she use 4 gal. 1 qt. 1 pt. 
 3gi.? JTetfeNte, ii / /;; 
 
 5. How ninny ]>int bottles will bo required to h 
 
 1. 2 qt of tomato catsup ? 
 
 6. A milk-man sold 8 . <>f milk, at 8 cr 
 quart. How much did it amount to? 
 
 7. How many gallons arc 82 quarts? 
 
REDUCTION'S. 
 
 85 
 
 8. If you buy 1 pint of milk a day, how many quarts 
 will you buy in GO days ? How many gallons ? 
 
 0. A druggist put up 180 gill bottles of castor-oil. 
 How many gallons of oil did he use ? Methods, P . 177. 
 
 10. Change 103 pints to gallons. 
 
 11. Reduce 217 pints to gallons. 
 
 14. 
 
 Dry 
 
 measure- 
 
 In measuring 
 grain, seeds, 
 fruits, berries, 
 several kinds 
 of vegetables, 
 lime, charcoal, 
 and some oth- 
 er articles, 
 
 2 pt. are 1 qt. 
 
 8 qt. " 1 pk. (peck.) 
 
 4 pk. " 1 bu. (bushel.) 
 
 6 quarts dry measure are equal to nearly 7 quarts liquid 
 measure. 
 
 12. To how many persons will a grocer sell 8 bushels of 
 apples, if he sells 1 peck to each person ? 
 
 13. 3 pecks are how many pints ? 
 
 L' h How many quart boxes will 2 pk. 5 qt. of straw- 
 berries fill ? 
 7.>. How many pints are 2 bu. 1 pk. 3 qt. ? 
 
 1 bu. is 4 pk. 
 1 pk. " 8 qt. 
 1 qt. " 2 pt. 
 
86 COMPOUND NUMBERS. 
 
 16. A boy gathered 3 bushels 4 quarts of chestnuts. 
 How many times would they fill a pint m 
 ! low many half-peeks are 9 bushels 2 pecks ? 
 
 IS. If tomatoes sell at 3 cents a quart, how miu 
 Imsh.-l worth ? 
 
 c 320 pints to bushels. 
 
 50. A grocer sold 198 pecks of charcoal in one 
 I low many bushels did he sell ? 
 
 51. 642 pints are how many pecks ? How many bushels ? 
 80, If a boy sells ID quarts of jva-nuts a day, how many 
 
 bushels will he s.'ll in 
 23. Reduce 59 qua: >ns. 
 
 . man pirkrd .'JO.') pints of 
 in his garden. Hw mai,;. 
 
 15. Linear measure. 
 
 In measuring distances, and th? dimensions of things, as, 
 
 their length, wi.lt h. thirkn-ss. hright, and depth. 
 
 1-: in. .!:; 
 
 3 ft 1 > 1 (yard.) 
 
 5.5 or 5J yd. " 1 nl. (rod.) 
 
 320 nl. " " 1 mi. (mile.) 
 
 1 mi. is 320 r.l. 
 
 1 nl. " 5.5 or 5^ yd. 
 
 1 yd. " 8 ft. 
 
 1 ft. " 12 inches. 
 
 Ami, in measuring goods sold by the yard in 
 
 4.5 or 4} in. are 1 eighth. 
 
 rhths, or 9 in. " 1 qr. 
 4 qr. " 1 yd. 
 
 1 yd. is 4 qr. 
 1 qr. " 9 in. 
 1 eighth " 4.5 or 4$ in. 
 
 The first of these lines is 1 inch long, the second is 2 inches, 
 
 and the third is 3 inches. 
 
 25. In 9 feet are how many inches ? 
 
 26. How many rods are 3 miles ? 
 
REDUCTIONS 
 
 87 
 
 27. Change 6 yards to feet, and 4 yd. 2 ft. to inches. 
 
 28. In 43 inches are how many feet and inches ? 
 
 29. 136 inches are how many feet ? 
 SO. Change 92 inches to yards. 
 
 31. How many steps, each 2 ft. long, will James take in 
 
 walking 110 yarfls ? 
 J?. If a man travels 50 rods in 5 minutes, how long will 
 
 it take him to travel a mile ? 
 83. 35 quarters are how many yards ? 
 
 34. Change 3 yards 2 quarters to feet, and also to inches. 
 
 35. 205 inches are how many yards ? 
 
 16. Square Xfteasure. 
 
 An Angle is the difference of direc- 
 tion of two lines that meet in a point. c 
 
 Thus, ADC is an angle. 
 
 A 'Right- Angle is one formed by two lines perpendicular to 
 each other. Thus, the angles A D B and ADC are right angles. 
 
88 
 
 COMPOUND NCMBEB8. 
 
 A Surji/cc is a figure that has I< : 
 and breach h. 
 
 A Xectfinffle is a four-sided figure 
 having only right angles. Thus, the 
 surface A B C D is a rectangle. 
 
 A Square is a figure bounded by 
 four equal sicks, and having four right 
 
 1 ,l,rh ],,- 
 
 A Square Inch is a square 1 inch 
 
 long and 1 inch \\\ 
 
 A Square Foot is a square 1 foot 
 long ami 1 i'.M.t wide; 
 
 A 8f**n Rod is a square 1 red 
 long and 1 r. 1 wide; and 
 
 A SyiKirc . }file is a square 1 mile long and 1 mile v. 
 
 36. A blackboard is 4 feet wide and 10 feet long. 
 many square feet of surface has it ? Method*, / 
 
 -,. IIi.w many square rods are there iii : l rods 
 
 square ? 
 SS. How many panes of glass are th-iv in a window 
 
 that is 4 paiu-s in width, and G panes in h .-iirht '/ 
 39. What is the number of square inches on the surface 
 
 of a mirror 10 inches long and 8 incht 
 .}'>. How many square yards of carpeting will e<>vi r the 
 
 floor of a room 6 yards long and 5 yards wide ? 
 
 41. The title ( -)vcr of this book was engraved on a block 
 of box- wood 4 by 6 inches. How much did the wood 
 cost, at 5 cents per square inch ? 
 
 42. One side of a slate that is 10 inches long, mea 
 80 square inches. How wide is it ? Mftt,o<i*. 
 
 43. In drawing a map, Julia used a piece of drawing 
 paper ) inches loni:. and which contait. 
 
 TI"W ni.Miy inch.-s wid-- \\a- tl; 
 
KEDUCTIOtfS. 
 
 89 
 
 44. The floor of a bedroom 9 feet wide contains 108 
 square feet. What is the length of the room ? 
 
 45. A school yard of 120 square rods is 8 rods wide. 
 How long is it ? 
 
 46. A certain town is 7 miles long, and it contains 28 
 square miles. What is its Width ? 
 
 In computing the area of land, flooring, plastering, and 
 other surfaces, 
 
 144 sq. in. (square in.) are 1 sq. ft. 
 9 sq. ft. " 1 sq. yd. 
 
 30.25 or 30^ sq. yd. " 1 sq. rd. 
 160 sq. rd. " 1 A. (acre.) 
 
 640 A. " 1 sq. mi. 
 
 1 sq. mi. is 640 A. 
 1 A. " 160 sq. rd. 
 
 3 sq. yd. 
 
 1 sq. yd. " 9 sq. ft. 
 1 sq. ft. " 144 sq. in. 
 
 47. 3 square feet are how many square inches ? 
 4S. How many square feet of paving stone are there in 
 a flag-stone that measures 3 sq. yd. 4 sq. ft. ? 
 
 49. How many square rods are 1 A. 40 sq. rd. of land ? 
 
 50. How many acres are 640 square rods ? 
 
 51. 36 square feet are how many square yards ? 
 
 52. Reduce 121 sq. yd. to square feet. 
 
 63. I low many square inches are there in a board 15 
 
 feet long and 10 inches wide ? 
 54. How many square feet are there on a roof that is 40 
 
 feet long and 20 feet wide on each of the two sides ? 
 &>. A field 16 by 20 rods contains how many acres ? 
 
 E D 
 
 1 / Cubic Zffeasure* / 
 
 A Solid or jBody is a figure that 
 has length, breadth, and thickness. 
 
 A (Rectangular Solid is a body 
 that has six sides or surfacos, each 
 
00 
 
 COMPOUND) NUMBERS. 
 
 of which is a rectangle. Thus, 
 the solids ABCDEFG and 
 MNOPQR8 are rectangular 
 solids. 
 
 A f 'if>>< is a body that has six 
 t-ju;il sijiuiv >i'l( - <>r Mil-font 
 
 A CM fit*' ///(-A is any body or 
 u of space 1 inch long, 1 
 inch wide, and 1 iiu h thick. 
 
 A Cr >t has six equal 
 
 >ot square ; and 
 
 A CMf'ir }'(trd has six equal 
 surfaces each 1 yard square. 
 
 . II many cubic i; 
 arc tiu r in a block 1 
 long, 6 in. w idt . and 3 in. 
 thick? 117. 
 
 <:. \Viiat ii the solidity of a 
 
 Mock of marble 8 
 
 long, 7 feet wide, and 3 
 
 thick? 
 5S. How many blocks, rai-li containing 1 cul)ic fo< 
 
 be c-pial to a block 7 feet long, nd 4 
 
 59. A common brick is 2 by 4 by 8 inches. What are 
 its solid contents ? 
 
 60. How long must a box be, that : 
 
 t thick, to contain 72 cu. ft ? Method*. 
 
 : purity of a rectangular ci-t-rn fi ft. wide and 
 
 :> ft. diH-ji. is -r.n en, ft \\ 
 
 69. In dinging a cellar V nd 1"> y;ir.l< long, 
 
 1 culiic yards of earth wore removed. ll"'.v many 
 yards wide v;: '.!ar V 
 
REDUCTIONS. 91 
 
 In computing the solidity of timber, stone, portions of earth, 
 and many other articles, and in estimating the capacity of 
 bins, boxes, casks, etc., 
 
 1,728 cu. in. (cubic in.) are 1 cu. ft. 
 
 1 cu. yd. is 27 cu. ft. 
 
 1 perch ) I"-* or 
 ( lG.Vcu.ft. 
 
 16.5 or 16} cu. ft. " 1 perch. 
 
 27" cu. ft, " leu. yd. 
 
 ' leu. ft. "l,728cu.in. 
 
 63. In 5 cu. yd. are how many cubic feet ? 
 
 64. How many cubic yards in 81 cu. ft. ? 
 
 65. How many cubic inches in 1 cu. ft. 7 cu. in. ? 
 
 66. How many cubic feet in 2 cu. yd. 8 cu. ft, ? 
 
 67. What will be the cost of a piece of timber 1 foot 
 square and 20 feet long, if 4 cubic feet cosfr $1 ? 
 
 68. I low many cubic yards are 87 cubic feet ? 
 
 '>''. How many loads of earth of one cubic yard each, 
 must be removed, in digging a cellar 21 feet long, 
 18 feet wide, and 6 feet deep ? 
 
 70. How many cubic feet are there in a stick of timber 
 1C inches wide, 9 inches thick, and 13 feet long? 
 
 71. How many cubic blocks, measuring 2 inches on a 
 side, can be put into a box whose inside measure- 
 ments are 4, 8, and 10 inches ? 
 
 72. How thick is a block of stone that is 15 ft. long and 
 4 ft. wide, and whose contents are 180 cu. ft. ? 
 
 18. Wood Measure. 
 
 In measuring wood, and also rough stone when it is sold by 
 the cord, 
 
 16 cu. ft. are 1 cd. ft. (cord ft.) 
 
 cd.ft,or) u 
 8 cu. ft. J 
 
 , . < 128 cu. ft, 
 1CCL 19 |or8cd.ft. 
 1 cd. ft. " 16 cu. ft. 
 
 Surveyors of wood commonly call the cord foot A Foot of 
 

 COMPOUND K U M i; . 
 
 75. Htfxv many rtiMr feet are 5 cord fc 
 
 - of wood are how many cord f- 
 f.-ct arc 90 cubic feet? 
 
 76. In 47 cord feet are how many corda ? 
 
 . ;. A pOe of stone ' Mr, and 4 feet lii-l 
 
 1 cord. What is its length ? 
 ; . How v. any cords of wood are there in a pile 1 
 
 long, r j feet wide, and r, t\vt liigh ? 
 ; . What cost 5 cords of wood, if 4 cord feet cost 3 
 
 doll;. 
 80. How many cord feet of wood in 3 loads, each 8 feet 
 
 long, 3 fei-t wide, and 4 feet high? How many 
 
 cor. 
 
 v/. How many cords of wood are 1,280 cubic fe 
 ..A pil.' of tan bark (M- feet Ion-. ide. and G 
 
 i hiirli contains how many cor,; 
 
K E D U C T I 2T S . 
 
 93 
 
 19. Weight. 
 
 In weighing most kinds 
 of produce, provisions, . 
 groceries, metals, coal, and 
 many other articles, 
 
 16 oz. (ounces) are 1 Ib. (pound.) 1 T. is 20 cwt. 
 
 100 Ib. " 1 cwt. (hundred-weight.) 1 cwt. " 100 Ib. 
 
 20 cwt. " 1 T. (ton.) 1 Ib. " 16 oz. 
 
 A barrel of flour weighs 196 Ib., and a barrel of pork, beef, 
 or fish 200 Ib. 
 
 S3. How much will 1 pound of indigo cost, at 20 cents 
 an ounce ? How much will 7 pounds cost ? 
 
 84. At 10 cents an ounce, how much will 3 Ib. 8 oz. of 
 nutmegs cost? 
 
91 COMPOUND X I M I! r. 
 
 85. II v, many pounds of cloves can be bought for 3 
 dollars 8 ;s an oui. 
 
 86. 95 ounces an Imw many pounds? 
 
 87. 1 ' > pounds to In: ^ht 
 
 ii at will 7 pounds G ounces of meat cost, 
 cents a ; 
 
 89. II 'V, much will 50 pounds of flour c< lollars 
 
 : it? 
 
 90. What will -,' 1!). ii oa. of cheese cost, at ^.lOapound? 
 .''/. How miu-h will ;. 11 >. r> oz. of bi: . at $.32 a 
 
 :ul ? 
 
 $10at< 
 .' . Eow rnnch wfll a nek of flour n 'imds, 
 
 Co> in dollars a l'::rr. 1 ? 
 
 ' ;. \\ : Is for $32 a barr.-l. lm\ v mr 
 
 pmiiuls < 
 \Vhat will ^ T. 1 < v ;. ,,f hay cost, at $20 a to- 
 
 inn flour sells at G cents a pound, how much does 
 a b; 
 
 t $40 for 5 cwt. of iron castings, how much will 1 
 ton cc.- 
 
 20. Time. 
 
 In expressing port time or duration of different 
 
 tangti 
 CO sec. (seconds) are 1 min. (minute.) 
 
 60 min. are 1 h. (hour.) 
 
 21 h. Ida, (day.) 
 
 " 1 wk. 
 
 \ 1 common yr. 
 or 805 da. ( " / 
 
 or 366 da. 
 
 100 yr. " 1 century. 
 
 ' Unual, page 173.) 
 
 1 century is lOOyr. 
 
 , 
 
 loommonyr.-] , 
 
 i v,-k. " ; 
 
 1.1:1. " 2 Ml. 
 
 Hi. " 60 min. 
 
 1 iniu. u 60 sec. 
 
REDUCTIONS. 
 
 95 
 
 Every fourth 
 year from the 
 beginning of a 
 century is a leap- 
 year. 
 
 The year is 
 divided into 12 
 calendar months, 
 and these are ar- 
 ranged in 4 sea- 
 sons of 3 mouths 
 each, as shown in 
 the diagram on 
 the next page. 
 
 February has 
 28 days in a com- 
 mon year, and 29 
 in a leap-year. 
 
 In most busi- 
 ness transactions, 
 30 days are re- 
 garded as a 
 month. 
 
 98. In 3 hours are how many minutes ? 
 
 99. Change 5 minutes 20 seconds to seconds. 
 
 100. How many days are 72 hours ? 100 hours ? 
 
 101. How many weeks are 17 days ? 
 
 102. How many weeks are there in July, August, and 
 
 September ? 
 1 i-l. If a man walks \ mile in 10 minutes, how long 
 
 will it take him to walk 12 miles ? 
 I't.'i. How many days are there from the 7th of May to 
 
 the 4th of July ? 
 Jf>~>. If a man earns $2 in 6 hours, how much will he 
 
 earn in 12 clays of 10 working hours each ? 
 
96 
 
 COMPOUND NUMBERS. 
 
 106. When the sun sets at 4 h. 50 min. P. M., what is 
 
 th >f the day? 
 
 107. When the sun rises at 5 h. 15 min. A. M., what is 
 
 length of the night ? , s Manual. P.VC 173 -> 
 
 lOth 
 
 108. How many weeks in 1 year and 17 weeks ? How many 
 days? 
 
 '.!' a man earns $12 a wivk, and pays $12 a mnth 
 for his board, how many dollars will h. sn in 10 
 months, working four ach month ? 
 
 110. How many days in the winter season ? In the 
 spring? In summer? In autumn ? 
 
REDUCTIONS. 97 
 
 21. Faper and Counting-. 
 In the paper trade, 
 
 24 sheets are 1 quire. 
 20 quires " 1 ream. 
 
 1 ream is 20 quires. 
 1 quire " 24 sheets. 
 
 In counting several classes of articles for market purposes, 
 
 12 things are 1 doz. (dozen.) 
 12 doz. " 1 gro. (gross.) 
 
 1 gro. is 12 doz. 
 1 doz. " 12 things. 
 
 Two things of a kind are often called a Pair; six things, a 
 Set; and twenty things, a Score. 
 
 111. A market woman sold G7 cucumbers. How many 
 dozen did she sell ? 
 
 112. If a yoke of oxen sells for 180 dollars, how much is 
 one of them worth ? 
 
 113. How many are 3 score nud 10 years ? 
 
 114. What is the cost of 6 quires of paper, at $4 a ream ? 
 llo. A grocer, in one day, took in 8 doz. and 10 eggs. 
 
 How many eggs did he take in ? 
 
 116. What cost two gross of copy-books, at $.10 apiece ? 
 
 117. A silversmith sold 42 tea-spoons in one week. 
 How many sets did he sell ? 
 
 118. A shop-keeper sold, in one week, 2 gross and 6 
 fancy buttons, at ten cents a dozen. How much 
 did he receive for them ? 
 
 119. A stationer paid 2 dollars a ream for paper, and 
 sold it for 18 cents a quire. How much was his 
 gain on one ream ? 
 
 120. A grocer bought 3 pounds of nutmegs, at 128 cents 
 a pound, and sold them at 10 cents an ounce. 
 How much was his gain ? 
 
 121. A market woman who took 5 dozen of eggs to 
 market, broke 3 of them, and sold the others at 24 
 cents a dozen. How much did she receive ? 
 
 8 
 
98 COMPOIND Nl-MDERS. 
 
 SECTION III. 
 
 A :/; '/> / / IOJV. 
 
 1. Add 7 bushels 1 15 bushels 2 pecks. 
 
 f. What i> tin- sum B 5 quarts, and 1 peck 7 quarts? 
 
 3. How many sq. yd. in the sum of 4, 6, 7, 8, 5, ar. 
 
 4. A grocer sold, on Mond asses ; 
 on Tuesday, 3 gal. 1 jt. : and on Wednesd; 
 
 2 qt How much did he sell? Method*, pa fff 17*. 
 
 6. One week a druggist used 2 gal. 1 it. of al 
 and tli k 3 gaL 3 qt 1 pt How much did 
 
 he use in ti ks? 
 
 G. One month a tailor used 2 gross 5 dozen buttons. 
 and in another month 3 gross 8 dozen. Il"\v many 
 buttons did he use in the 2 months? 
 
 ;. Ho\v man;. n -.' li.-lds, one contain- 
 
 ing 9 A. 70 sq. rd., and tin- other T A. 90 sq. rd. ? 
 
 5. A farmer sowed 2 bu. 4 qt of clover seed, and 1 hu. 
 :> j.k. ; jt. of timothy >ord. How much seed did IK- 
 SOW of both kinds? 
 
 9. Tin- foiv (purlers of a lamb wished " t lb. o;:. each, 
 and the hind (juarters 8 lb. 11 oz. caeh. How much 
 did the lamb wei^h ^ 
 
 . h:it is the sum of 2 yd. 2 ft. 9 in., and 3 yd. 1 ft. 8 in. ? 
 : a laborer removes CO cti. yd. 13 cu. ft. in di_ 
 a cellar, and 11 cu. yd. 19 cu. ft. in digging the 
 drain, how much earth does In- remove? 
 /.'. If a fruit dealer sells 5 bu. 3 j.k. of peaches, 2 b. 1 
 pk. 6 qt of plums, and 3 bn. ;! pk. 2 qt of pears, 
 how much fruit does he sell of the three kit, 
 . A coal dealer delivered 13 T. 11 CWt to A. T. i:> 
 cwt. to B, and 7 T. 4 cwt. to ('. How nun -!i o.al did 
 he sell to the thr- 
 
SUBTRACT I OX. 99 
 
 SECTION IV. 
 s v% Tftd. c now. 
 
 1. From 9 bushels 3 pecks subtract 5 bushels 2 pecks. 
 
 2. A grocer bought 12 Ib. 6 oz. of Castile soap, and sold 
 5 Ib. 8 oz. How much had he left ? Methods, 173. 
 
 3. From \ bushel take peck. 
 
 4- From 6 feet 5 inches take 4 feet 7 inches. 
 
 5. On a lot 30 ft. 6 in. wide, stands a house 19 ft. 10 in. 
 wide. How much wider is the lot than the house ? 
 
 6. From a cask containing 1C gal. 2 qt. of vinegar, a 
 man drew 8 gal. 3 qt. How much vinegar remained 
 in the cask ? 
 
 7. A farmer sowed 20 bu. 2 pk. of wheat, and 11 bu. 3 
 pk. of buckwheat. How much more wheat than 
 buckwheat did he sow ? 
 
 8. A man removed 42 cu. yd. 10 cu. ft. of earth in dig- 
 ging a cellar, and 7 cu. yd. 19 cu. ft. in digging the 
 drain. How much more earth did he remove from 
 the cellar than from the drain ? 
 
 0. If it takes 9 h. to go from Albany to New York by 
 steam-boat, and 5 h. 15 min. by railroad, how much 
 longer does it take to go by boat than by cars ? 
 
 10. When the sun rises at 5 o'clock and 40 minutes, 
 what is the length of the forenoon ? 
 
 11. How much of my 9 weeks' vacation is to come, when 
 5 weeks 4 days of it have passed ? 
 
 12. From a piece of land containing 7 acres, I sold 3 
 acres 75 square rods. How much land had I left ? 
 
 13. I bought a crock of butter weighing 27 Ib. 9 oz., but 
 the crock alone weighed 7 Ib. 12 oz. How much did 
 the butter weigh ? 
 
100 COMPOUND NUMBERS. 
 
 SECTION V. 
 
 TITL ZCsi 
 
 1. Hew much tea will it take to fill :. pnitfent 
 
 ll'iMill^r VI 1!'. S cz. ? Method*, page /;*. 
 
 a horee eats 2 bu. 2 j.k. 4 qt. of oats in 1 week, 
 how much will ho eat in 4 weeks ? 
 
 5. A painter used 2 qt 1 pt of tu y day, 
 for 9 days. How much turpentine did he use ? 
 
 L 2 qr. of cassimerc to make on 
 of clothes, how miuh will it take to make 2 suits? 
 
 1 cow eat 1 ton r> hu ight of hay in the 
 
 winter, how inueh will 5 cows eat ? 
 
 6. How much paper will a lawyer use in a year, at the 
 rate of 3 quires 7 sheets per month ? 
 
 7. Oliver is 7 years 9 months old, and his moth- 
 times as old. How old is his moth 
 
 S. How much wheat will l>e required to seed 3 acres, 
 
 allowing 1 bu. 2 pk. 4 qt to the ai 
 
 a rail mad train runs 15 miles 80 rods in one 
 
 hour, how tar will it move in 4 hours? 
 1". William's fish line is 10 yards 2 feet long, and his 
 
 kite string is 10 times as long, llow long is his 
 
 kite string ? 
 11. How many ste< ill be used in a Commercial 
 
 College in 8 months, if 3 gross 7 dozen are 
 
 monthly ? 
 1 .'. If a farmer can plow 2 A. 40 sq. rd. of land in 1 day, 
 
 how much can he plow in G days ? 
 13. How much wood is there in 3 piles, each pil 
 
 taining 7 cords 12 cubic feet ? 
 
DIVISION. *** 101 
 
 14. If a family use 2 dozen 8 eggs in a v:eck, lioiv ni'aiiy ; 
 
 will they use in 4 weeks, at the same rate ? 
 .75. If 60 cu. yd. 15 cu. ft. of earth are removed from 
 
 each of two cellars, how much earth is removed 
 
 from botk ? 
 
 16. If a painter uses 2 gal. 2 qt. 1 pt. of linseed-oil in 
 painting 1 wagon, how much will he use in painting 
 5 wagons ? 
 
 17. What is the weight of 8 loads of hay, each weighing 
 1 T. 250 Ib. ? 
 
 SECTION VI. 
 
 DIVISION. 
 
 1. IF a steam-boat runs 22 mi. 40 rd. in 2 hours, how 
 far does she run in 1 hour ? 
 
 2. If it takes 13 bu. 3 pk. of oats to seed 5 acres, how 
 much does it take for 1 acre ? Methods, page 17 s. 
 
 3. If it takes 5 yards of cloth for one military suit, 
 how many suits can be made from a piece contain- 
 ing 32 yards, and what remnant will be left ? 
 
 4. If 7 men can mow 21 acres 35 square rods of grass 
 in a day, how much can 1 man mow ? 
 
 5. If a cooper can make 4 barrels in 5 hours, how long 
 will it take him to make 1 barrel ? 
 
 6. If 3 cheeses weigh 96 Ib. 12 oz., what is their average 
 weight ? 
 
 7. A grocer sold a barrel of flour to 4 persons, who 
 shared it equally. How many pounds did each per- 
 son have ? 
 
 8. If a man lays 25 rd. 15 ft. of stone-wall in 5 days, 
 how much does he lay in 1 day ? 
 
1 <! a fc-P U X D NUMBERS. 
 
 ttmefl'JobiWs.-age is 42 yr. 9 mo. -M ila. What 
 is his QL 
 
 10. A lady put s qt. 1 pt 1 gL of currant v. 3 bot- 
 
 L How much did she put into each bott 
 
 11. \ man kill.-d 7 sheep, and their united u 
 
 280 Ib. 14 oz. Wliat was their average weight ? 
 ; '.' pk. 4 <jt. of ch 
 
 tin-in equally. How much was each boy's sha; 
 13. If one apple liarrel holds 2 bu. 3 ]>k., how many bar- 
 
 Ifl will be required to hold 11 bu. of apples? 
 IJf. A housekeeper made 3 gaL 1 qt. 1 pt, 2 gi. of cur- 
 rant jelly, and put it up in 5 jars. How much did 
 
 jar contain ? 
 
 / '. II)\v many writin.ir-books can be made from 1 (juire 
 d' foolscap paper, allowing 3 sheets for each book? 
 1 1 w many can be made from 1 n am ? 
 16. If a railroad train runs 80 miles in 4 hours, in how 
 many minutes will it run 1 mile ? 
 
 man had a pile of wood containing 7 cords 4 cord 
 . and he drew it in 5 loads. How much d 
 draw at a load ? 
 
 A batch r kill d 4 hogs, whose united w 
 M cwt. 40 Ib. What was their average weight ? 
 . A -sold ->! gross 7 dozen writ in g-bo- ' 
 
 ; days. What wen' th'- average daily ga'. 
 
 20. A man cut 4 T. 10 cwt. of hay from 3 acres. What 
 was tin- average per acre ? 
 
 21. A tinsmith used 3 bu. 3 pk. of charcoal in 8 
 What wafl the av.-rage amount used per da 
 
REVIEW PROBLEMS. 103 
 
 SECTION VII, 
 
 1. How many pint bottles will be required to contain 
 
 3 gal. 3 qt. of strawberry wine ? 
 
 2. If 3 pints of blackberries cost 21 cents, how much 
 will a bushel cost ? 
 
 S. Reduce 33 yards to rods. 
 
 4- At 2 cents an inch, how much will 2 yards of silver 
 wire cost ? 
 
 5. A man paid 9GO dollars for land, at one dollar a 
 square rod. How many acres did he buy ? 
 
 6. A stone-mason laid up 4 perch of stone in one side 
 of a cellar wall. How many cubic feet did he use ? 
 
 7. If 4 cord feet, or 1 half-cord, of wood cost 2 dollars, 
 what is the cost of 3 cords ? 
 
 8. A grocer sold 5 quarts of cranberries to one person, 
 7 quarts to another, and 1 peck 4 quarts to a third. 
 How many pecks did he sell ? 
 
 9. A lawyer used 1 ream of legal-cap paper in 10 
 weeks. How many sheets did he use in a day, on 
 an average ? 
 
 10. If 3 eggs cost 5 cents, how much will 9 dozen eggs 
 cost? 
 
 11. Which contains the more land, a field 12 rods 
 square, or a field 9 by 1C rods ? 
 
 12. From a pile of wood containing 7 cords, a man sold 
 
 4 loads, each 12 feet long, 4 feet wide, and 4 feet 
 high. How much remained ? 
 
 13. If you can read 5 pages in 10 minutes, in how many 
 hours can you read a book of 150 paires ? 
 
104 COMPOUND NUMBEBS. 
 
 14. If a family use 5 Ib. 9 oz. of butter in 1 week, how 
 miu-h will they use ifl 6 week 
 
 A druggist has 13 gaL 3 qi of alcohol If h 
 
 on an average, 2 qt 1 pt a day, for 6 dins. h..\\- 
 
 iniic-h will 1: !'t ? 
 
 nson has a quart measure and a pin- 
 
 How many times can he fill each of them, sepan. 
 
 from 1 bushel of beans ? 
 17. When peas are worth ll.GO a bushel, what will 4 
 
 quarts cost ? 
 / . 1 1 ow much clover seed, at 1 pk. 5 qt per acr 
 
 be rr|uhvd to seed a field of 8 acres ? 
 19. How many rods long must a field be, that is 20 rods 
 
 wide, to contain 3 acres? 
 SO. The floor of a bedroom 8 feet wide is covered by 8 
 
 square yards of carpeting. How many feet long is 
 
 the room ? 
 21. How many blocks 2 in< -lit > square can be cut from 
 
 a piece of board 6 by 8 inci 
 ... II<>w many cords of wood are there in a pile 12 feet 
 
 long, 4 1* . and 8 foot high ? 
 
 1 1 MU mm -h will 10 Ib. 15 oz. of ham cost, at 32 cents 
 
 a pound ? 
 
 24. How many pounds of ground pepper will be re- 
 quired to fill 100 boxes, each box holding 4 oui. 
 v grocer sold, to 5 customers, 6 oz., 1 Ib. 8 oz., 12 
 
 oz., 8 oz., and 1 Ib. 4 oz. of allspice. How much did 
 
 he sell in all '! 
 26. How many barrels of flour are there in 8 
 
 ca^i containing 49 pounds ? 
 .:. If a family use 10 pounds of pork P..T week, how 
 
 many wvrk> will a barrel last them? 
 
REVIEW PROBLEMS. 105 
 
 28. A grocer bought a barrel of pork, and sold, to cus- 
 tomers, 5 lb., 8 lb., 9 lb., 4 lb., 6 lb., 13 lb., 44 lb., 
 and 10 lb. How many pounds were then left in the 
 barrel ? 
 
 29. At $60 a ton, how much will 14 hundred-weight of 
 railroad iron cost ? 
 
 30. A farmer bought 2 T. 12 cwt. of plaster. He sowed 
 1 T. 15 cwt. on his wheat field, and the balance on 
 his clover lot. How much did he sow on the clover ? 
 
 31. A stationer bought a gross of pens for 72 cents, and 
 sold them at 10 cents a dozen. How much did he 
 gain on 1 dozen ? How much on the gross ? 
 
 32. At $.04 a sheet, how many quires of gilt paper can 
 be bought for 81.44 ? 
 
 33. How long is a fence which incloses a piece of land 
 60 rods long and 40 rods wide ? 
 
 3. f f . In a year how many days are there in the months 
 that have 31 days each ? 
 
 35. A paper mill that runs 12 hours per day, turns out 
 72 reams of print paper daily. How many reams is 
 that per hour ? How many quires per minute ? 
 
 36. How many square inches are there on one side of a 
 common brick ? On both sides ? On both edges ? 
 On both ends ? 
 
 37. A grocer having 8 lb. of cinnamon, sold to custom- 
 ers 4 oz., 12 oz., 6 oz., and 8 oz. How much had he 
 left? 
 
 38. How many pint and quart bottles, of each an equal 
 number, can be filled from 19 gal. 3 qt. 1 pt. of cur- 
 rant wine ? 
 
&#*r>9#- 
 
 ^ 
 
 "^**. . 
 
 M CHAPTER Y. 
 
 IUM.'**^-^'^ s -**~< 
 
 FRACTIONS. 
 
 SECTION I. 
 
 1. How many apples arc one half of 60 a j >]>!..>? One 
 third of GO apples ? One fourth of CO apples? 
 
 2. How many dollars are one half of $60 ? One third 
 of $60 ? One fourth of $60 ? 
 
 3. How many bushels arc one half of 60 bushels ? One 
 t liird of 60 bushels ? One fourth of 60 bushels ? 
 
 .- do you find one half of any number of thing* f One 
 third f One fourth f One fifth f 
 
 When an dollar, a bushel, 
 
 or a one of any kind, is divided into 
 two equal parts, one of the parts is 
 one half (}) of the one divi 
 
 When a one of any kind is divided into three equal parts, 
 one of tin- parts is one third ($); 
 
 When a one is divided into four equal parts, one < 
 parts is one fourth (^) ; and so on. 
 
 When a one is divided into tlmv c<;uil parts, two of the 
 parts are tico third* () ; when into four equal parts, two of 
 the parts are two fourth* (), and three of the parts are three 
 fourths (J) ; when into five equal parts, one of the parts is 
 
DEFINITIONS. 107 
 
 one fifth (|), two of the parts are two fifths (), three of the 
 parts are three fifths (f ), and four of the parts are four fifths (|). 
 
 When a one is divided into six equal parts, the parts are 
 sixths; when into seven equal parts, they are sevenths; when 
 into eight equal parts, they are eightlis; when into nine equal 
 parts, they are ninths ; when into ten equal parts, they are 
 tenths; and so on. 
 
 Each of the numbers fa fa fa fa and so on, expresses one of 
 the equal parts of a one. 
 
 The number, f expresses, either that 2 is divided into 3 
 equal parts ; or that 1 is divided into 3 equal parts, and 2 of 
 those parts are taken. 
 
 5. What does the number |- express ? What the number ? 
 
 6. What does the number f express ? The number ? 
 
 7. What is expressed by the number $ ? By f ? By ^ ? 
 
 8. What is expressed by the fraction f of an apple ? 
 
 9. What do you understand by $f ? 
 
 10. Explain the meaning of 7 9 g lb., and ^ doz. 
 
 A Fractional Unit is one of the equal parts into which 
 a thing, or the unit 1, is divided : as, fa , fa fa and so on. And 
 
 A Fraction is a number consisting of one or more frac- 
 tional units : as, fa f , $, ^ lb. 
 
 11. What is the fractional unit of *} ? Of J ft. ? Of | lb. ? 
 7,?. What is the fractional unit of J yd.? Of {} bu.? 
 
 OfJfecwU 
 
 The Terms of a fraction are the two numbers used to ex- 
 press it. Thus, the terms of the fraction are 5 and 7. 
 
 The ^Denominator of a fraction is that term which ex- 
 presses the number of equal parts into which one is divided ; 
 it is written below the horizontal line. 
 
 The Numerator is that term which expresses the number 
 of equal parts indicated by the fraction ; it is written above 
 the line. Thus, in the fraction fa the 5 is the denominator, 
 
108 FRACTION 
 
 and expresses that 1 is divided into 5 equal parts ; a: 
 
 1 i- tii Hum* rator. and expresses that 4 of the equal 
 (fifths) are indicated by the fraction. 
 
 15. What are the terms of the fractions f , f , fa and ff t 
 
 L' f . Wh:it i-i tlu- denominator of each of the fractions},-,^, 
 ^ J, and ,'y, and what does it express t 
 
 uerator of each of the fractions |, -,V f, 
 and |f, and what does it express ? 
 
 16. Namo the terms, the denominator, the numerator, 
 the fractional unit, and the number of fractional 
 units in T 7 . In f mi. In } eq. yd. In ?. gaL 
 
 A Proper /-'/-action is a fraction whose value is less than 
 1 ; as |, T^, {, J f . Its nu: always less than its dc- 
 
 nonni: 
 
 An Jiniir<.;.>-r t&octio* ! i i i^n whose Talue equals 
 1 ; as f, fj, l H IJ- Ite numerator is never less 
 than its denomh 
 
 xii/u'ltir /*r(irt;<>Hs arc those that have a common frac- 
 tional unit ; as, \ and {; |, I, and |. 
 
 The dcnominutors of similar fractions are alike. Such frac- 
 tions are said to have a Common Denominator. 
 si itiil ft r /-'rncfinnt are those that lur. 
 tional units ; as, } and f ; f , f , and \. 
 
 17. If "> apjiK'S are di- 
 vided e<|uall\ 
 twreii *J elii'. 
 what part of 
 apples will each 
 child h:i 
 
 18. How many apples must be cut into equal par 
 
 19. If 5 apples are divided equally between cbi 
 how many apples will each child receive? 
 
 20. If I divide 8 pears equally amon.ir X girls, how many 
 whole pears can I izive to each pirl ? 
 
DEFINITIONS. 
 
 109 
 
 21. Into what equal parts must the other pears be cut ? 
 J.?. How many of these equal parts will there be ? 
 ,.'-A If I divide 8 pears equally among 3 girls, how many 
 pears will each girl receive ? 
 
 One lemon is what part 
 
 24. Of 2 lemons ? 
 
 25. Of 3 lemons ? 
 
 26. Of 5 lemons ? 
 
 27. Of 7 lemons ? 
 
 28. Of 10 lemons ? 
 9. Of -15 lemons? 
 
 What part of 
 
 SO. 1 doz. oranges is 1 orange ? 
 
 31. 1 ft. is 1 in. ? 
 
 32. 1 Ib. is 1 oz. ? 
 
 , 3|, 
 
 tfo 
 
 , A. 
 
 ?. 1 qt. is 1 pt. ? 
 . 1 gal is 1 pt. ? 
 85. 1 yd. is 1 in. ? 
 
 When a number is expressed by an integer and a fraction, 
 it is a Mixed Number; as, 8|, llf, 14|$. 
 
 56'. Which of the fractions in the margin are 
 proper fractions, and why ? 
 
 87. Which are improper fractions, and why ? 
 
 88. Which are mixed numbers, and why ? 
 
 39. Which are similar fractions, and why ? 
 
 40. Which are dissimilar fractions, and why ? 
 
 41. What do you understand by 1 half of any number or 
 thing ? By 1 third ? 1 fourth ? 1 fifth ? 1 eighth ? 
 
 42. What do you understand by 2 thirds of any number or 
 thing ? By 3 fifths ? By 7 eighths ? 
 
 43. What do you understand by 2 halves of any number or 
 thing? By f? By |? By f ? By ? By ? 
 
 *, 
 
110 FRACTIONS. 
 
 SECTION II. 
 
 22. Fractions to Lowest Terms. 
 
 1. IF a pie be cut into 10 equal parts, what will one of 
 
 th. parts be? 
 .. Into how many fifths can a pie be cut ? Into how 
 
 many halves? 
 
 . || are how many fifths ? How many halves f 
 .;. How many fifths of a pie are there in ^ ? In -,< ? 
 
 In ,".. 
 
 5. Reduce -& to halves. 
 
 6. f of a melon are how many halves ? 
 
 7. | of a melon are how many fourt 
 
 8. T 8 8 of a melon are how many eighths ? IIow many 
 fourths ? How many halves ? 
 
 9. Change |4 of a cubic yard to thirds. Method*, pay 
 
 10. % of a dollar are how many tenths ? How many 
 
 fifths? 
 
 / /. :l I of a dollar are how many fifths ? 
 12. Reduce VfcV to sixtieths. To thirtieth?. To fiftee* 
 IS. Dividing both term* af a fraction by the tame numfcr, hat 
 fffcct upon the value of the fraction f 
 
REDUCTIONS. Ill 
 
 When the terms of a fraction have no common factor, they 
 are 2>rime to JZach Ofhc>\ 
 
 A fraction is in its Z,owest Terms, when its terms are 
 prime to each other. 
 
 14. Reduce & to its lowest terms. Methods, page 17 8. 
 
 15. What are the lowest terms of the fraction &$ ? 
 
 16. Reduce the fractions fa and T T to their lowest terras. 
 
 17. Reduce fa and f to their lowest terms. 
 
 18. Reduce ff and f to their lowest terms. 
 
 19. James has g of an apple, and Charles has -f t . Which 
 has the greater fraction ? 
 
 20. Which is the greater sum of money, $ 3 fi or $| 8 ? 
 
 21. Andrew dug 5 rows of potatoes, which yielded re- 
 spectively bu., )-f bu., f bu., T 8 2 bu., and 4i bu. 
 Which row gave the greatest yield ? 
 
 22. Reduce ||, f, and f| to their lowest terms. 
 
 23. Fractions to Given Denominators. 
 
 23. If a pie is cut into 10 equal pieces, how many of 
 these pieces will there be in one half of the pie ? 
 How many of these equal pieces will there be in I 
 of the pie ? Jf ow many in of it ? In | ? In | ? 
 
 25. Reduce |, f , , and to tenths. 
 
 26. 1 half of an apple is how many quarters or fourths ? 
 1 third of a pear is how many sixths ? 
 
 28. How many eighths of a bushel is j bu. ? 
 20. Change J of an hour to fifteenths of an hour. 
 80. 2 thirds of a pear are how many sixths ? 
 
 31. How many eighths of a bushel are | bu. ? 
 
 32. Reduce jj Ib. to sixteenths. Methods, page 173. 
 
 . Reduce to eighths. To twelfths. To twentieths. 
 84. How many twenty-fourths are ? How many are f ? 
 Are ? ? ? ? 
 
11.' FRACTIONS. 
 
 S5. Multiplying loth term* of a fraction ly the same number hat 
 what effect upon the value of the fraction t 
 
 36. $ equals how many tenths ? 
 
 37. By what number will you multiply the terms of the frac- 
 tion 'I, to rediic- it t< t \\vntv-lifthst 
 
 38. Reduce 1 1 
 
 low may fourths be reduced to twentieths? Eighths to 
 
 fortieths ? 
 40. What is the least denominator, greater than :'. to which 
 
 thirds can be reduced ? Why ? 
 /,/. Xame the first three denominators, in order of size, to 
 
 which fifths can be redi: 
 43. Why can fifths be reduced to each of these denominators ? 
 
 43. jf any fraction it reduced to an equal fraction, h<i 
 greater denominator, what mutt that denominator le f 
 
 44. Reduce to i ft., and | It. ; J doz.,and 
 
 45. Reduce } A. an 1 A. i - i\\ mieths of an acre? 
 
 IttBgQ as many as possible of tli>- following fnic- 
 tijns to twenty-fourths: j da., f da., $ da., T 7 f da^ 
 T ^ da>, ft dm A **" ad A da, 
 
 47. What fraction* can T* reduced to a given denominator? 
 
 48. How may f be rolucr.1 to fortieths ? 
 
 49. How may ^ be reduced to one hundred forty-sevenths ? 
 60. Reduce $J, $], $J, $ r ' , l^and $^3 to hundredtha. 
 
 24. Dissimilar Fractions to Similar Fractions. 
 51. Reduce } and f to sixtlis. 
 5$. Change f and f to twelfths; and f and \ to thirty.fifthfi. 
 
 53. Reduce |, f, and | to ninetieths. 
 
 54. In the results in the three preceding problems, the com- 
 mon denominator of the sin ions is the pr< 
 
 of what terms .' 
 
 55. What is the common denominator of the similar fra 
 to which J, *, and f may be rediu 
 
REDUCTIONS. 113 
 
 56. In solving problem 55, by what numbers must the terms 
 of be multiplied ? The terms of ? Of f ? 
 
 57. Li reducing dissimilar fractions to similar fractions, by what 
 must the terms of each given fraction be multiplied f 
 
 58. Reduce f and f to similar fractions. 
 
 59. Reduce f and $ to similar fractions. Methods, page 178. 
 CO. What similar fractions are equal to T \- and | ? 
 
 61. Change ^, \, and ^ f to similar fractions. 
 
 62. Reduce and T 8 S to fractions of the same fractional unit. 
 
 63. Reduce , , $, and -J to similar fractions. 
 
 64. Reduce the same fractions to similar fractions having 72 
 for a common denominator. Reduce them to forty-eighths. 
 
 65. Reduce the same fractions to twenty-fourths. To twelfths. 
 
 66. What fractions can be reduced to twelfths ? Why ? 
 
 67. Which of the fractions $, {., f , f, and can be reduced to 
 eighteenths, and which can not ? Why ? 
 
 68. What fractions can be reduced to equal fractions Jiaving a 
 given denominator f 
 
 69. Wftat is the denominator of the least similar fractions to which 
 any two or more given fractions can be reduced? 
 
 70. What are the denominators of the fractions which can be 
 reduced to fifteenths ? To sixteenths ? To twentieths ? 
 
 71. What fractions can be reduced to thirty-ninths ? To 
 sixty-fourths ? To eighty-firsts ? To two hundredths ? 
 
 72. Reduce , , , and -J to least similar fractions. 
 
 73. Reduce ~ cu. yd., $ cu. yd., and J cu. yd. to least 
 similar fractions. 
 
 74. What is the common denominator of the least similar 
 fractions equal to the fractions , ^, and -*- ? What are 
 the new numerators ? 
 
 75. Reduce |, f , -/ s , and -& to least similar fractions. 
 
 76. What is the fractional unit of the least similar fractions 
 equal to ^, ^, ff, and ? 
 
 77. What are the least similar fractions ? 
 
1H PBACTIOXS. 
 
 78. Change ft, If f , ft, iV, <"<! A to least similar fractions. 
 What is the least common fractional unit ? 
 Iteduce |, f and | to least similar fractions. 
 
 25. Improper Tractions to Integers or Mixed Numbers. 
 
 SO. How many dollars arc 2 halves of a dollar ? 5 fifths 
 
 of a dollar? 8 eighths of a doll- 
 81. When i* the talue of a fraction a onef 11 
 
 . A boy has 4 half-dollars. How many dollars has he ? 
 83. A girl buys 12 fourths of a yard of ribbon. ! ! m 
 many yards does she 1 
 I < >w many feet are J of a foot ? Method*, p v . 
 
 85. How many dozen are 3 G of a do; 
 
 86. Reduce V gaL to gallons. 
 
 87. A barber receives 5 half-dollars for each day's work. 
 How much are his daily wages ? 
 
 88. One week a cook used J of a gallon of syrup. II 
 many gallons did she use ? 
 
 .v. A tailor used * g < yd. of beav in making an 
 
 overcoat How many yards did he use ? 
 
 90. One day a confectioner sold 63 quarter-pound pack- 
 ages of candy. How many pounds did he sell .' 
 
 01. Reduce J 5 7 min. to minutes. 
 
 92. Reduce -if* to a mixed number. 
 
 03. ff are how many ones ? 
 
 04. Change .41, ^ A|i, and |J to integers or mixed numbers. 
 
 26. Integers or Mixed Numbers to Fractions. 
 
 ' ". II"\v many Iialf-Kanvis can bo filled with 3 barrels 
 of flour ? 
 
 96. How many tenths of a dollar are 7 dollars ? 
 
 97. Reduce 9 yards to fourths. To eighths. 
 
REDUCTIONS. 115 
 
 98. Reduce 27 to fifths. To ninths. 
 
 99. Reduce 8| to ninths. Methods, page 179. 
 
 100. How many eighths of a cord of wood in 2| cords ? 
 
 101. How many quarter-dollars will it take to pay for a 
 fur cap that costs $6| ? 
 
 102. How many half-yards are one rod ? How many 
 half-feet ? 
 
 103. 5 1 tons of hay are how many fifths of a ton ? 
 
 104. How many sixteenths of a pound are 3 T 9 <j pounds 
 of butter ? 
 
 105. Reduce 27 T 3 <j A. to tenths of an acre. 
 
 106. Reduce 29 and 7-&V * improper fractions. 
 
 SECTION III. 
 
 ADDITION. 
 
 1. A MOTHER having a melon, gave 2 ninths of it to 
 her boys, and 5 ninths of it to her girls. How many 
 ninths of the melon did she give to her children ? 
 
 2. A teamster feeds his horses of a bushel of oats in the 
 morning, f at noon, and | at night. How many 
 eighths of a bushel does he feed his horses daily ? 
 
 3. A lady paid $ r 3 for eggs, and 8-,% for butter. How 
 much did the butter and eggs cost her ? 
 
 4. Cynthia paid $J for a pair of gloves, $f for a hand- 
 kerchief, $| for a neck ribbon, and $ for a collar. 
 How many dollars did she expend ? 
 
 5. How many hours are f h., I h., h., and f h. ? 
 
 6. What is the common fractional unit of -f , f , |, and % ? 
 
 7. How many fractional units does each of these fractions 
 express? 
 
110 FRACTIONS. 
 
 8. lie sum of these fractional units f 
 
 9. How are similar fraction* added t 
 
 10. What similar fractions are equal to $ and 
 
 11. What is the sum of these similar fractions? 
 
 1 $i for 
 
 bagc. How much did she pay for both ? 
 13. My door-yard contains { A., ami my pardon J A. 
 
 I Iw much land in my door-yard and gard 
 14* Roger worked T 7 h. to saw his wo<> h. to 
 
 split it. I low many hours did he work 't 
 .''. A !,i;ni i :; | of his meadow one day, : 
 
 1 1 day. How much of it did he cut in the 
 
 tWO days ? Jrr//io<**, page i 
 
 16. A .s I A. of tomatoes, and f A. of cu- 
 
 cumbers. How much land has he planted to l> 
 Vh:it U t he sum off and {? Of^Endf! 
 
 28. Add | and f; also | an.: 
 
 In adding diuimilarfactivnt, what it the first ricpt 
 
 SO. What it the second ttep? 
 
 21. During a campaign ^ of a regiment werv k i 
 
 wi-iv wounded, and \ were taken prisoners. What 
 ]>urt uf the ivLrinu-nt was lost to the sen 
 
 . .'. Id;i bought a box of figs, and gave of them t 
 father, | of tin-in to lu-r mother, and 7 ' of them to 
 her sister. What part of them did she giv. 
 . LevigavcfcJ f>r his skates, $^ for the > traps fur th- in, 
 and $5 f r n i s sled- How much did all cost him ? 
 
 ':-. I^arnct has mi. of rail fence on his fa- 
 mi. of board fence, and T 7 mi. of stone fence. How 
 much fence is there on his farm? 
 
 2J. A lawyer used T 7 of a quire of 1 paper on 
 
 Monday, of a quire on Tuesday, of a quire on 
 
ADDITION. 117 
 
 "Wednesday, of a quire on Thursday, and | of a 
 quire on Friday. How much paper did he use ? 
 26. What is the sum of $, T \, and ? 
 
 27. Add , |, and f 
 **. Add ^F, f and f 
 
 #9. Add |-, |, and f . 
 SO. Add |, , A, and f. 
 
 31. Hattie's age is 6} years, Jennie's age is 5J years, and 
 
 the age of their brother Harry is 3 ^ years. What 
 
 is the sum of their ages ? 
 82. A merchant sold 2 bu. of clover seed to one farmer, 
 
 I bu. to another, and | bu. to a third. How much 
 
 did he sell to all of them ? 
 33. A teamster drew J cd. of wood at one load, and 1 \ 
 
 cd. at another load. How much wood did he draw ? 
 84. A mechanic earned $H in the forenoon, and $1| in 
 
 the afternoon. How much did he earn in the day ? 
 35. Jonas gave 82.J for a sheep, and sold it for $ T 7 more 
 
 than it cost him. For how much did he sell it ? 
 86. What is the sum 3 of and G j ? 
 
 37. Add 15f and 8f ? 
 
 38. Add 4& and | ? 
 
 39. Add5and7 T V 
 
 40. Add 6, 2, and f 
 
 41. Add 18^4- and 7f. 
 4#. Add 5|, 7, and 4 
 
 ?. A man, in trying the speed of his horse, trotted him 
 one mile in 2 T 7 ^ min., a second mile in 2| min., and 
 a third mile in 2.J min. In how many minutes did 
 the horse trot the three miles ? 
 
 44* In a city are four street railroads, one 3 \ mi. long, an- 
 other 2 T 9 mi. long, another 4 J mi. long, and the fourth 
 If mi. long. What is the length of all of them ? 
 What is the sum 
 
 45. Of f 2f , and 17 ? \ 47. Of 2|, 4|, and 3f ? 
 
 4 Of I, , , and | ? I 48. Of 8*, 2fc 4f , and 6 ? 
 
118 FRACTIONS. 
 
 SECTION IV. 
 
 1. AMANDA cut f of a yard of silk from a pi. -re that 
 
 contained J of a \a: !. How many ei-hths of a \ard 
 
 of silk were left 111 the piece? 
 han gathered j, 1 . liu. of walnuts, and sold all hut 
 
 T 4 8 bu. of them. IIow many did he sell ? 
 8. From -^ subtract ^. 
 4' One forenoon a man sawed I cd. of wood, and his 
 
 son sawed j cd. How much more did the fat In -r 
 
 saw than the son ? 
 '/'if ard similar fraction* subtracted f 
 
 6. What similar fractions are equal to $| and $] ? 
 
 7. Find thf. difference between these similar fraci 
 
 8. Gerald having $f, gave $3 for a slate. H><\\ 
 money had he left? Method*, pagr r, >.>. 
 
 9. What is the difference between f and f ? 
 
 7fl. A dniggist poured ^ gaLof alcohol from a jr.. 
 
 contained gaL How much alcohol was left ? 
 11. It' I have a village lot of f 9 A., and I sell ^ F A^ how 
 
 large a lot shall I have left? 
 . A in- reliant hin < ui-l;i- . and sells it at $J J 
 
 a gallon. How muuh is his gain per gallon ? 
 IS. I -fa = what number I 
 
 14. |. |- =r what number ? 
 
 15. What is the <lit; J and ^? 
 
 16. In subtracting difiirni <s, icJiat u tltcjirst ttup? 
 
 17. What it the second step f 
 
 1^. Eli paid 4 of the cost of a sled, and Carlos paid the 
 rest How much of the cost did Carlo- ];-. 
 
SUBTRACTION. 119 
 
 19. Anna will be 13 years old in f of a year. How old 
 
 is She nOW ? Methods, page 179. 
 
 20. A housekeeper bought 2 bu. of potatoes, and used f 
 bu. the same day. How many had she left ? 
 
 21. If I buy a hammer for l/^, and I give in payment a 
 5-dollar bill, how much change shall I receive ? 
 
 S3. 30 is how much more than ? 
 
 23. A grain buyer paid $lf a bushel for wheat, but was 
 obliged to sell it at a loss of $J a bushel. At what 
 price did he sell it ? 
 
 24. A gardener raised 11 J bu. of beans, and sold T \ bu. 
 How many had he left ? Methods, page 170. 
 
 25. I owe $5A ; if I pay $J, how much shall I then owe ? 
 
 26. 4 T 5 ff is how much greater than ? 
 
 27. 64-j^ is how much greater than f ? 
 
 28. What is the difference between Cf and 4; . ; 
 
 20. If I have $5 J, and I pay $21 for a pair of fur gloves, 
 how much money shall I have left ? 
 
 30. A laborer who earns $8| a week, expends $G j. How 
 much does he save weekly ? 
 
 31. From a cask of vinegar containing 32* gal., a clerk 
 drew 5 -J gal. How much vinegar was left in the cask ? 
 
 32. A butcher sold 9 T 5 ff Ib. from a quarter of beef that 
 weighed 93 1 Ib. How many pounds had he left ? 
 
 33. A man traveled 161 mi. in the forenoon, and 31 f mi. 
 in the day. How far did he travel in the afternoon ? 
 
 34. From 17 T V subtract 4. 
 
 85. 25| is how much greater than 6 T 4 7 ? 
 
 36. 6 is how much greater than 4 ? 
 
 37. From a box containing 10 pounds of raisins, a 
 grocer sold 4| pounds. How many pounds of rai- 
 sins were left in the box ? 
 
130 FRACTIONS. 
 
 SECTION V. 
 
 Ml' f. 
 
 27. A Traction by an Integer. 
 
 1. 1 low many seven 1 1 1 : i mcs 1 se ' 
 of a week ? 
 
 2. IIow many fifths of a dollar arc G times 2 fifths of a 
 dolh r I II" \v many dollars ? 
 
 . How much will 6 bushels of apples cost, at $| per 
 
 bushel ? Method*, pagr 170. 
 
 .'. i low many acres of corn can G men hoe in a <!. 
 
 they average J of an acre each '' 
 
 Bow much will 12 11). wool cost, at $fj a pound ? 
 ' What effect it produced by multiplying the numerator of a 
 
 fraction by an integer J 
 
 7. Multiply 2 1 
 
 8. What is the product off} multiplied by 7? 
 
 9. How much is 28 times 5 sq. yd. of carp< t i 
 JO. What part of 5 bushels is 1 busln 1 ? 
 
 11. What part of 5 bushels are 2 bushels? Are 3 
 
 . . A L -.::,;. :. r bought ." (jt. of Early Kent peas. AVhat 
 
 part of a pock did he luy ? 
 
 / .. A fanner having a bushel (or 5G Ib.) of coarse salt, 
 used 28 Ib. of it in packing a barrel of beef. V 
 part of a bushel did he use to the barrel ': 
 What part of 
 
 14. C yd. arc 5 yd. ? 
 
 pailfuls arc 4 pailfuls ? 
 
 16. 25 bar. are 9 bar. f 
 
 17. 12 candles are 8 candles? 
 
 18. 1 gal. are 2 
 
 pk. arc 4 qt. ? 
 SO. 1 mi. are 240 rd. ? 
 21. 1 Ib. are 6 oz. ? 
 
 J.'. If : boy* share :5 bushels of butternuts equally, 
 what part of a bushel has each boy ': 
 
MULTIPLICATION. 121 
 
 28. A Mixed Number by an Integer. 
 9. How much milk will be required to fill 3 pails, each 
 
 of which holds 2J gallons ? 
 24. How much will 15 barrels of XX flour cost, at $7 T 7 a 
 
 per barrel ? Methods, page 179. 
 2-5. A sheriff, in pursuing a thief, drove ?g miles an 
 
 hour for 5 hours. How many miles did he drive ? 
 20. A grocer bought one dozen boxes of layer raisins, at 
 
 $1 T 7 5 per box. How much did he pay for them ? 
 27. 5 times 6 T S = how many ? 50 times 4'- how many? 
 
 29. An Integer by a Fraction. 
 ,>'. When G Ib. of crushed sugar sell for $1, how much 
 
 does 1 pound cost ? 
 29. When wood is $5 a cord, how much must I pay for 
 
 Of a COrd ? Methods, page 179. 
 
 How much is 
 
 30. 1 fourth of 3 yd. ? 
 81. 1 seventh of 5 da. ? 
 32. 1 twelfth of 7 A. ? 
 
 33. T V of 6 dimes ? 
 
 34. & of 24 bu. ? 
 
 35. of 24 h. ? 
 
 36. If a man lays 44 rods of stone-wall in 5 days, how 
 many rods does he lay in 1 day ? 
 
 37. A farmer raised 150 bushels of wheat on 7 acres. 
 What was the average yield per acre ? 
 
 38. At $363 for 9 chests of tea, how much will 1 chest 
 
 cost? 
 
 How much is 
 
 39. $ of 89 rods ? 
 
 40. | of 182 pounds ? 
 
 41. T V of 166 bu. ? 
 
 42. & of 630 gal. ? 
 
 43. \ of 365 da. ? 
 
 44. of 752 ? 
 
 45. How much is 1 seventh of $42 ? How much are 6 
 
 sevenths of $42 ? 
 40. A laborer who earns $42 a month, pays | of his 
 
 earnings for his board and washing. How much do 
 
 his board and washing cost him ? 
 10 
 
122 FRACTIONS. 
 
 47. The cleared land on a farm of 80 acres is T 7 of the 
 whole farm. How many acres are clear 
 
 48. Last year a dairy-man made 77 cheeses, and this 
 \ ar he has made jf as many. How many cheeses 
 IMS h made this year ': 
 
 ; '. I' ii school are 40 pupils, ? of whom study 
 
 grammar. How many study grammar ? 
 
 50. A lumber dralrr has ^:>0 thousand feet of lun, 
 of which is pine. How many feet of pine lu 
 bathe? 
 
 "/. In a shoe-store there are 12 doz. pairs of m 
 
 and J of them are ladies' sizes. How many pairs of 
 ladies' rubbers are there in the stoi 
 
 I ind f 9 of $100. 
 
 How much is 
 
 53. |of!26gnl. ? 55. $ off of 182? 
 
 5 4> A of I of 126 gal.? 66. f of} of 182? 
 
 <;. llo\\- iniu-h will I Ib. of cinnamon cost, at $.GO a 
 pound ' J . VtOMUt ,"../' 179. 
 
 68. A tinsmiih used $ of 3 sheets of tin, in making a 
 pail. How much tin did he use? 
 
 69. How much is j of 9 feet ? 
 
 010. When coal is $8 a ton, how much does | of a ton 
 cost? 
 
 IIow much is 
 
 S of 5 sq. yd. ? 
 62. | of 4 quires ? 
 
 63. -& of 63 gal. ? 
 
 64. A of 13:> 
 
 30. An Integer by a Mixed Number. 
 
 65. At $.10 a pound for sal soda, how much will 2 Ih 
 cost ? How much will A Ib. cost ? How much will 
 2J Ib. cost ? 
 
 66. In a pasture are 15 cows, and 4 1 tinii-s as many 
 sluvp. How many sheep are in tho pasture? 
 
MULTIPLICATION. 123 
 
 67. One family burned 12 thousand feet of gas in a 
 year, and another burned 3 times as much. How 
 many thousand feet did the second family burn ? 
 
 68. How many miles will a railroad train run in 2] h., 
 at the rate of 24 mi. an hour ? Methods, page 179. 
 
 69. How much will 3$ gross of wood screws cost, at $.64 
 per gross ? 
 
 70. One year I raised 18 bu. of turnips, and 4f times as 
 many potatoes. How many bushels of potatoes did 
 I raise ? 
 
 71. A family, in one year, use 20 Ib. of coffee, and S/^ 
 times as much sugar. How much sugar do they use ? 
 
 How much are 
 
 72. 3| times 5 yd. ? 
 
 73. 12 times 8 da. ? 
 
 74. 15 times 9 ? 
 
 75. 6f times 8 gal. ? 
 
 76. 6f times 5 mi. ? 
 
 77. 24| times 8 ? 
 
 3J A Fraction or a mixed Number by a Fraction or a 
 IVXixed Number. 
 
 78. Grace used 1 half of f of a roll of wall paper, in 
 papering a box. What fraction of a roll did she use ? 
 
 70. When a bushel of com is worth $|, how much will 
 1 fourth of a bushel cost ? How much will 3 fourths 
 of a bushel cost ? 
 
 80. How much will -J gal. of molasses cost, at $| per 
 
 gallon ? Methods, page 179. 
 
 81. If I feed my chickens f of f of a bushel of grain in 
 a week, what part of a bushel do I feed them ? 
 
 82. A man who owned i of a schooner, sold | of his 
 share. What part of the schooner did he sell ? 
 
 What fraction is equal to 
 
 83. f Of ft of ft rod I 
 
 84. | of -&V of a cargo of tea ? 
 
 85. f of |f ? 
 
 86. | of -f of f i ? 
 
U'i FRACTIONS. 
 
 . Lust year my trees bore 2^ bushels (or J bushels) of 
 plums, and I sold J of them. How numy bushels 
 
 aid i s-ii :- 
 
 88. At $1 1 a pound, how much will I Ib. of tea cost ? 
 0. How much is J of Is? 
 
 H'-w much is 
 
 00. i of 15f t ftf. ^ f of 6f ? 
 
 ;of4*tt PA ^ of 0^? 
 
 t& is how many tw in . thsof ft dollar? How i 
 is \ of $^ ? Then, how much is } of $J ? 
 !Io\\- niudi is | of $J ? How much is J of * 
 
 96. How much is J of | yd. ? 
 
 '',. How much is ? Of J yd. ? Method*, page I 
 
 ^5. How much will J Ib. of shot cost, at $, 3 a pound ? 
 ' '. If a boy saws | of a cord of wood in a day, how 
 much can ho saw in J of a day ? 
 
 100. A family burns 3 of a gallon of kerosene in a week. 
 How much do thy burn in f of a week ? 
 
 101. In the last problem, how may the numerator of the 
 result be obtained ? How may the denominator 'J i 
 obtained? 
 
 102. When the factors are fraction*, June may their product "be 
 obtained f 
 
 How much is 
 10S. of * mi. i 
 
 104. -,V of f da. ? 
 
 What is the product of 
 
 107. ^timef of a ton t 
 
 108. | multiplied by ^ ? 
 
 105. | of $| ? 
 10G. if of } T. ? 
 
 111. At $ j a yard, how much must I pay for 2J yards 
 (or V yards) of linen ? 
 
 V farmer, in seeding 8| acres of land, usc-d I of a 
 bushel of clover sei-d to the acre. How much 
 clover seed did he use ? 
 
DIVISION. 125 
 
 113. The sulphur and saltpeter in a pound of gun- 
 powder weigh -f s of a pound, and the charcoal 
 weighs 3 J times as much. What is the weight of 
 the charcoal ? 
 
 114- A young man bought 2] yd. of broadcloth for a 
 coat, at $5i a yard. How much did the coat pat- 
 tern cost ? 
 
 115. How much will 8J cd. of wood cost, at $6| per cord ? 
 
 116. A boy husked 7J bu. of com in a day, and his 
 father husked 3] times as much. How many 
 bushels did the father husk ? 
 
 117. A merchant having 10.] yd. of serge, sold ? of it, at 
 $1 T ' a yard. How much did he receive for it ? 
 
 What is the result in each of the next eight problems ? 
 
 118. * of $2f ? 
 
 119. | x 64|? 
 
 120. f of 7| bar. ? 
 
 121. 13}doz. x 
 
 122. \ mi. x 4f ? 
 
 123. 2% x f yd. ? 
 
 124. $x fVof Gf lb. 
 J25. 2 x Cf x 8| ? 
 
 SECTION VI. 
 
 3) lYIS ION. 
 32. A Fraction by an Znteger. 
 
 1. IF I divide | of a melon equally between two girls, 
 what part of the of a melon will each girl have ? 
 
 2. How much is 1 half of of a melon ? 
 
 3. What is the quotient of f divided by 2 ? 
 
 4. Multiplying by obtains the same result as dividing by 
 what number ? Multiplying by \ : ? By ? 
 
 <. If 3 oranges are worth T 9 of a pine-apple, what part 
 
 of a pine-apple is 1 orange worth ? 
 6. If 8 yd. of shirting cost $|i, how much will 1 yd. cost ? 
 
12G FRACTIONS. 
 
 much i.i What i< the quotient of 
 
 "ne half off ? 11. $ 
 
 8. One ninth of ff ? 12. ff divid.-d by 9? 
 
 9. One sixth of f \ ? IS. $ff divided by $6 ? 
 10. One fifth of ff ? 14. ff Ib. di\ i lb. f 
 
 What effect it produced by dividing the numerator of a frac- 
 tion by an integer f Why f 
 Divide ff by 9. Divide the same fraction by 6. 
 77* iff are uow many times 4 ? How many times 8 ? 
 
 18. A boy sold 6 quarts of beechnuts for $Jf. How 
 much did he rec quart for them ? 
 
 10. If J5 of a barrel of flour will last 12 persons 1 week, 
 how much Hour will last 1 person the sam< 
 
 20. I cut \ of a melon into 2 equal pieces. AYh; 
 
 of the melon was each 
 .'/. H.w iniu-li is 1 half of ^ of a melon? 
 
 .'.'. If I pay $| (or $fj) for 4 pounds of sugar, how 
 much is the sugar per pound ? 
 
 .A : feeds 2 horses 5 of a bushel of oats daily. 
 
 1 1 < >w many oats does he feed each horse ? 
 
 IIow many times are 
 24. I contained in f ? 
 
 in f ? 
 
 26. 8 contained in ? 
 
 How much is 
 
 27. One third of |? 
 
 28. One fifth off? 
 
 29. One eighth of | 
 
 50. What tffect it produced by multiplying the denominator of a 
 fraction by an integer f Why f 
 
 51. A fruit-dealer sold 10 muskmelons for $J. How 
 much did IK apiece for them? 
 
 >hanna picked J of a bushel of strawK-rru-s in 4 
 hours. IIow many berries did she pick in an hour? 
 S3. Find the quotient of f divided by 0. Of | divided by 5. 
 $4. |$f is 12 times what number ? 
 
DIVISION. 127 
 
 33. A Mixed Number by an Integer. 
 
 85. If li apples are divided equally between 2 boys, how 
 many thirds of an apple will each boy receive ? 
 
 36. If 7 bushels of oats cost $2|, what is the price per 
 bushel ? 
 
 87. A man mowed 41- acres of grass in 3 days. How 
 much did he mow in 1 day ? 
 
 88. When photographs cost $2 } 2 per dozen, how much 
 are they apiece ? 
 
 80. When eggs are $.37 per doz., what is 1 egg worth ? 
 
 40. A butter buyer paid $84? for 9 tubs of butter. How 
 much did he pay for 1 tub ? 
 
 How many times are 
 
 41. $6 contained in $41$ ? 
 
 42. 8 h. contained in 16f h. ? 46. | of 16 h. ? 
 
 How much is 
 
 45. 
 
 47. $ of 23 yd. ? 
 
 48. of 54 bu. 
 
 43. 5 yd. contained in 28 yd. ? 
 
 44. 45 bu. contained in 54bu.? 
 
 40. How many weeks will 35| pounds of butter last a 
 family that use 4 pounds per week ? 
 
 50. If 3 ,'j bar. of flour last 49 persons 1 month, what 
 part of a barrel will last 1 person the same time ? 
 
 34. An Integer by a Fraction. 
 
 51. If each person at dinner receives J of a pie, and a 
 whole pie is eaten, how many persons dine ? 
 
 62. Among how many children can a melon be divided, 
 if each child receive -^ of a melon ? 
 
 53. At $\ apiece, how many market-baskets can be 
 bought for $2 ? How many for $3 ? For $5 ? 
 
 54. How many bushels of lime can be bought for $4, at 
 $| a bushel ? 
 
 55. How many bushels can be bought for $4, at $| a 
 
 bushel ? Methods, page ISO. 
 
128 FRACTIONS. 
 
 56. Into how many pieces, each yd. long, can yd. of 
 
 wire 1" cut ? O 
 .<;. How many days will i Imshcls of oats last a horse, 
 
 if he eats j of a bushel daily ? 
 
 68. A merchant paid $30 for a piece of linen, at $ T 8 per 
 How many yards were there in i 
 
 I low many tinu-s a: 
 59. f gal. contained in 7 
 CO. | yd. contained in 16 yd.yf 
 67. wk.contaiiu-d in 1:2 wkf? 
 
 What is the- quotk-nt of 
 
 . ;:i!. divided |,y *? ' 
 
 63. 16yd. divi.h .1 by I?' 
 
 .' wk. dividrdbyf? 
 
 35. An Integer by a Mixed Number. 
 
 . How many neck-ties, each 1 J yd. (or J 
 be made from a piece of ribbon containing 1 (> } 
 
 66. A iiKTrhunt tailor made 30 yd. of cussimere i 
 suits of clothes, using 7J yd. of cloth for 
 llow many suits did he mak< 
 
 67. A grocer paid $18 for mackerel, at $1 j a kit How 
 many kits did lu- I my ? f /) 
 
 68. At $2| a bushel, how many bushels of grass seed 
 can be bought for $20 ? 
 
 69. How many yards of cloth can be mu<l< fr-mi <l^ Ib. 
 of wool, allowing lj 11 . to the yard? $7 fa ~ 
 
 70. A bricklayer received $72 for lal.>r. at $2^ j>cr day, 
 How many days did he work ?^ > 
 
 71. How many times arc 2| contained in 13 ? 
 
 78 . 80 -~ 2f = how many ? | 73. 625 -s- 6J = how many ? 
 
 36. Fractional Part or Parts given, to find tho Whole. 
 
 1 1* \ bar. of flour costs $2, how much will 1 bar. c 
 
 It' '. of a Imshel of potatoes will last a family 5 days* 
 
 how many days will a bushel last tl. 
 76. If i quire of paper costs $.12J, how much will a 
 
 quire cost ? 
 
DIVISION. 129 
 
 77. If a farmer can hoe -1 of an acre of corn in 8 hours, 
 how many hours will it take him to hoe an acre ? 
 
 78. If i of a ton of old iron is worth $4J, hew much is 
 a ton worth ? 
 
 79. I of my kite string is 7j yd. long. What is the 
 length of my kite string ? 
 
 80. Reuben gave $vv 3 for bananas, spending -] of all his 
 money. How much money had he ? 
 
 81. One day a hunter used -J Ib. of shot, which was 4 of ^ 
 all he had. How many pounds of shot had he ? 
 
 82. 12 is | of how many ? i 86. & is \- of what number ? 
 
 83. 36 is | of how many ?// '\ 87. 3^ is % of what number ? / ' 
 8J>. T ^ is \ of what numluT ? ' s',s'. 17j- is ?. of what number ? 
 85. \% is | of what number V f 59. 9 is | of what number ? 
 
 . 
 
 P0. If | of a cord of wood costs $6, how much does 
 
 of a cord cost ? 
 91. If i of a pound of raisins cost $.16, how much will 
 
 J of a pound cost ? How much will a pound cost ? 
 
 03. If a man can cut ~ of a cord of wood in 4 hours, 
 how many hours will it take him to cut 1 cord ? 
 
 93. When -5 bar. of flour are worth $6, what is the price 
 per barrel ? 
 
 94. A mechanic worked f of a week, and received $10. 
 How much were his weekly wages ? 
 
 95. A fruit-grower, after selling 9 bushels of plums, 
 found he had \ of his plums left. How many 
 plums did he raise ? 
 
 96. 8 is f of what number ? 
 
 97. 6 is | of what number ? 
 
 98. 10 is f of what number ? /* 
 
 99. 12 is of what number ? 
 
 100. 22 is | of what number ? 
 
 101. 35 is f of what number ? j 
 
 102. 125 is |f of what number? 
 
 103. 150 is T L of what number ? 
 
130 FRACTIONS. 
 
 37. A Fraction or a Wlixcd Number by a Traction* 
 
 A blacksmith received J of a dollar for s 
 horse-shoes, at J of a dollar each. How many 
 shoes did he set ? 
 
 105. If I of a yard of velvet ribbon will cover In 
 book, how many needle-books will .* of a yard co 
 1 low many books will lj yards (or V jd)> Tt 
 
 106. Some soldiers who messed toj: ed 6| 
 pounds of meat daily. How many soldiers v. 
 there, there being J of a pound of in. at in a 
 
 107. A ship's crew have 9J barrels of biscuit How 
 many weeks will it last them, if they use f of a 
 barrel weekly ? 
 
 108. When dividend and dicuor an nmilar fraction*, how u the 
 ditition performed t 
 
 What is the quotient of 
 100. | yd. divided by f ? I 113. 5f divided by f ? 
 
 110. ffc mi, divided by ^? llf. 6f Ib. divided by f Ib. ? 
 
 111. Wf divided by ^ ? 115. 5f Ib. divi.kd by \ II). ? 
 11*. 16| divi.K-.l by | ? | 116. 4| wk. ,livick-.l by f wk. ? 
 
 ^ome men bought J of a steam-boat, each man 
 huyini: ^ of her. How many men wcr 
 118. How much kerosene can be bought for tfa at $] 
 
 Ballon ? Method*, page ISO. 
 
 \ i'armer sold some corn at $J a busli.-l. and re- 
 
 ifed ^7| for it How many bushels did he 
 . How many days will 6J pounds of butter last a 
 
 family, that use J of a pound a day ? 
 121. Halbert skated 1CJ miles, at the rate of 7 5 8 of a 
 mile in a minute. How many minutes did it take 
 him! 
 
 How many times are 
 12*. | contained in J ? 
 
 123. -fy contained in 4$ 1 
 
 124. \ contained in J ? 
 
 Divide 
 
 1S5. A T. by | T. 
 126. 5Vy Ib. by | Ib. 
 le^ft. by {ft. 
 
DIVISION. 131 
 
 128. How many quires of note paper can I buy for f of 
 a dollar, at i of a dollar per quire ? 
 
 129. If a family use J of a barrel of potatoes in a week, 
 how many weeks will of a barrel last them ? 
 
 130. At $ j a pound, how many pounds of coffee can be 
 bought for $ T 9 ? 
 
 How many times is 
 
 131. | contained in | ? 
 
 132. \ contained in ^ ? 
 
 133. contained in ? 
 
 What is the quotient of 
 134. 2f- wk. divided by wk. ? 
 J35. 5| mi. divided by T V mi. ? 
 156. 3 mi. divided by $ mi. ? 
 
 137. How many pounds of citron can be bought for $|, 
 at $| per pound ? 
 
 138. Nellie paid out $ for candies, at $?- a pound. 
 How many pounds of candies did she buy ? 
 
 130. If a farm hand can plant 4 3 of a field in one clay, 
 how many days will it take him to plant f of it ? 
 
 140. A grocer exchanged cheese for honey, at the rate 
 of 1 Ib. of cheese for f of honey. How many 
 pounds of cheese did he give for 4J Ib. of honey ? 
 
 141. If dividend and divisor are dissimilar fractions, wTiat step 
 is necessary, preparatory to performing the division ? 
 
 142. Then, when can a mixed number or a fraction le divided ty 
 a fraction? 
 
 143. When dividend and divisor are dissimilar fractions, how is 
 the division performed f 
 
 144- How many milk-cans can be made from 12 f boxes 
 of tin, if it takes | of a box for one can ? 
 
 145. is how many times f ? 
 
 146. \^ are how many times f ? 
 
 147. %\ are how many times -fa ? 
 
 148. Divide 2 by f 
 
 149. Divide 7-J- by f 
 
 150. Divide 4 by f . 
 
 151. My garden, which con tans | of an acre, is | of my 
 whole village lot. What is the size of my lot ? 
 
FB ACTIONS. 
 
 I-''. In January I used t \ of a ton of coal, which was 
 T 2 5 of my year's supply. How much was my 
 supply ? 
 
 Jasper is 18} years old. and his age is equal 
 of his father's age. How old is his fat! 
 V man's family expenses, which are $12} a 
 are J of what he earns. What are his earnings ? 
 I gave J as much for my wagon as for my horse, 
 and my wagon cost me $96}. How much did my 
 horse cost me ? 
 
 \ is | of what number ? 
 } J is | of what number ? 
 
 158. ft is J of what number ? 
 
 159. -fj'is-fyof what numltcr ? 
 
 160. ~fa is j | of what number ? 
 
 161. 3} is 4 of what number? 
 
 162. 5f is | of what nut: 
 
 163. 4f is f of what nun. 
 
 164. 7| is Vft of what number! 
 1 8} is | of what number ? 
 
 38. A Fraction or a lYIixod Number by a Zttixod Number. 
 
 . I low many days will 11 j lb. of meat last a family 
 that EUKfl Ij lb. daily? Jf*t*w, |> / t*t, 
 
 I Iw many j. ws-liarj-s can be bought for $.18J, at 
 $.06 j apiece? 
 
 168. At $61 a pair, how many pairs of boots can be 
 bought for *! 
 
 169. A boy can nil res of hay in a day. How 
 long will it take him to rake J of an a< 
 
 170. How much clover seed can be bought for $|, at 
 $3| a bushel ? 
 
 11 1. When cranberries are $9J a barrel, what part of a 
 barrel can be bought for * 
 
 What is the quotient of 
 17S. I divided by 2J ? 
 175. f divided by 3} ? 
 6| divided by lOf? 
 
 How many timc^ are 
 
 175. \\ contained in 5f ? 
 
 176. 3J contained in 
 : contained in 
 
DIVISION. 133 
 
 178. A carman drew 13 4 3 T. of freight, taking 1| T. at a 
 load. How many loads did he draw ? 
 
 179. A wood sawyer sawed and split 12 \ cd. of wood in 
 6 J days. How many cords did he average per day ? 
 
 180. If 3 J bu. of wheat cost $4?, how much will 1 bu. 
 cost? 
 
 181. How many hours will it take a canal-boat to run 
 21 1 miles, at the average rate of 2^ miles an hour ? 
 
 182. What part of a barrel of sweet-potatoes can be 
 bought for $3J, at $6| a barrel ? 
 
 How many times arc 
 
 183. 2f contained in 5$ ? 
 
 184. If contained in 4/ ff 
 
 185. S 1 contained in 8 
 
 What part 
 186. Of $8 are 
 157. Of 10 ft. are 2^ ft. ? 
 188. Of 4 T V h. are If h. ? 
 
 159. TFfon the divisor is a mixed number, what step is necessary, 
 'before performing the division f 
 
 190. Then, how is a mixed number or a fraction divided ty a 
 mixed number f 
 
 191. A farmer cut 7J T. of hay from a meadow, that 
 yielded 1 T. to the acre. How many acres were 
 there in the meadow ? 
 
 A hop grower picked 6| T. of hops, from a yard 
 which averaged 1 T. to the acre. How many 
 acres were there in the hop-yard ? 
 103. What part of a basket of peaches can be bought for 
 $11, at $31 per basket? 
 
 How many times are 
 104. $1| contained in 
 195. 2 J yd. contained in 5f yd.? 
 
 What is the quotient of 
 
 196. $1| divided by $12 ? 
 
 197. 2 yd. divided by 5f yd.? 
 
134 I'll ACTIONS. 
 
 SECTION VII 
 
 1. Reduce ff, 4f J, and fff to their lowest terms. 
 
 2. Reduce {, f , and j to similar fractions. 
 
 S. What is tin- ronunoM .It-nominator of the least similar 
 fractions to which fifths, eighths, and tenths can be re- 
 luced? 
 
 4. A grocer has T * 2 bar. of A sugar, ] J bar. of B sugar, 
 and T Vo bar. of yellow sugar. Of what kind of ^ugar 
 lias he the most ? 
 
 5. How many yards of Marseilles goods will be required 
 for 3 doz. Tests, allowing } yd. to a Test? 
 
 G. Kate bought 10 yards of Scotch gingham, at * 
 
 y:ml. How much did it cost her ? 
 . In a certain Tillage th-n.- are 497 dwelling houses, 
 ami i of them aiv <>f 1-rick. How many 1 trick 
 houses arc there in the Tillage ? 
 
 8. How many days are f of a common year ? 
 
 9. How much arc the daily wages of a factory girl, who 
 
 ek ? 
 
 JO. A young lady paid $5 for 1 doz. handkor. 
 
 What part of a dollar did each handkerchief cost? 
 11. At $4 for 5 ducks, how much will 1 duck cost ? 
 
 / .'. 1 low many hours must a boy work to earn $.; 
 $.10 an hour ? 
 
 How much is 
 
 13. \ of 92 dozen ? 16. | of ! 
 
 14. H of $32 ? 17. Jh of 925 ? 
 1 '- iV of H of a box of soap ? 18. & of ft ? 
 
 19. One week a factory operative made only -fa of full 
 time. How many days did he work ? 
 
REVIEW PROBLEMS. 135 
 
 20. A lady having -}5 of a pound of worsted, used f of 
 it in making a lamp mat. What part of a pound 
 did she use ? 
 
 21. I bought % of a piece of carpeting which contained 
 61 : j yards, for a carpet. How many yards were 
 there in the carpet ? 
 
 22. A hardware dealer sold a keg of nails for $5 3 7 , and 
 his gain was $~. How much did the nails cost him? 
 
 23. If I have $7n 9 , how much must I earn to have $10 ? 
 
 24. If a farm hand earns $9 in of a month, what are 
 his monthly wages? 
 
 25. If 4 yards of silicia costs $!J, how much will 3 yards 
 cost? 
 
 26. 10 is | of some number ; how much is | of the number ? 
 
 27. 12 is of some number ; how much is f of the number ? 
 
 28. 20 is | of some number ; how much is ^ of the number ? 
 
 29. How much is -^ of the number of which 120 is |f ? 
 
 30. How much is -^ of the number of which 144 is T 9 7 ? 
 
 31. If 5 bushels of wheat cost f of $10, what will be the 
 cost of 6 bushels ? 
 
 32. If a barrel of flour is worth 12 times as much as a 
 bushel of oats, and flour is $8| a barrel, how much 
 are oats a bushel ? 
 
 33. A driver paid $287^ for two yoke of oxen. How 
 much did he pay for 1 ox ? 
 
 34. If a man's wages are $9 a week, in how many weeks 
 will he earn $33| ? 
 
 35. If two boxes of lemons cost $5J, how many boxes 
 can be bought for $16 ? 
 
 36. A drover, by selling a lot of sheep for $25 above 
 cost, gained \ of their cost. For how much did he 
 sell the sheep ? 
 
FBACTIONS. 
 
 /;. My harness cost $31 j. which was * as much I 
 
 cost of mj cutter. What was the cost of both ? 
 
 38. A mason used 12 J bu. of sand in making a bat 
 mortar, using Ijj bu. of sand to 1 bu. of lime. How, 
 many bushels of lime did he use! 
 
 39. } of 12 are how many times 3 ? 
 
 40. f of 27 are what part of 54? 
 
 41. f of 27 are 3 times what number? 
 
 42. | of 27 arc ) of what number ? 
 
 43. } of 27 are f of what number ? 
 
 44. 48 arc | of what number ? 
 
 45. A man paid $3} for a satin vest pan ing at 
 the rate of $8j a yard. What was the length of the 
 Test pattern ? 
 
 10 pound out | gal. of win- from a gallon 
 jug that was j full How much wine was tin -n left 
 in the jug? 
 
 47. I bought 3 T. of coal, and used j T. one month and 
 T 9 T. the next month. How much coal had I 1 
 
 48. A, B, and C together own a woolen factory. A owns 
 of it, and B J of it What part of it does C own ? 
 
 49. A man travrlrd 14 J mi. by railroad, 64 mi. by 
 steamboat, and far enough by stage to mak 
 whole journey 108 F 9 3 mi. How far did he travel by 
 stage? 
 
 <". What number must be added to the sum of $ and 
 
 6J to make 103? 
 
 51. From the sum of |, f , |, and $, subtract If. 
 
 52. From 16} subtract the sum off, |, and lOf. 
 
 53. 1 + 5 are how much less than 10 + 4| ? 
 
 54. What is the difference between J + i and | + |l 
 
 55. 12 times fj are J of what number? 
 
 56. | of 10 times |f are -^ of what number? 
 
KEVIEW PROBLEMS. 137 
 
 57. How many yards of silk will a tailor use in facing 9 
 
 coats if he uses A? of a yard for each ? 
 55. | of 12 are $ of what number? 
 
 59. \ of 15 are $ of what number ? 
 
 60. f of 24 are f of what number ? 
 
 61. of 48 are ^ of what number ? 
 
 62. | of 30 are of what number ? 
 
 63. How many hours must a boy work to earn $J if he 
 earns $ 5 3 an hour? 
 
 64. At $12 a ton, how much will f T. of hay cost ? 
 
 65. If the materials for 7 gal. of wine cost $4, how much 
 will they cost for 4 gal. ? 
 
 66. If a man can saw and split 6 cd. of wood in 4 da., 
 how long will it take him to saw and split 9 cd. ? 
 
 67. How much will 8| Ib. of candy cost at $f a pound ? 
 
 68. What will be the cost of 12f yd. of carpeting, at 
 $1 1 a yard? 
 
 69. James hoed a piece of corn in 5 da., hoeing f A. 
 each day. How many acres were there in the piece ? 
 
 70. Farmer F. has 25 cows, and his neighbor G. has 5 
 less than f as many. How many cows have both ? 
 
 71. If a boy can pump 4 gal. of water in 1 minute, 
 how many minutes will it take him to fill a tank 
 which holds 155 gal.? 
 
 72. At $lf a basket, how many baskets of tomatoes can 
 
 be bought for $9 ^ ? 
 
 73. 48 is $ of how many times 10 ? 
 
 74. | of 64 are | of how many times 12 ? 
 
 75. | of 64 are | of how many times of 24 ? 
 
 76. | of 64 are 4 times what part of 50 ? 
 
 11 
 

 >,/*- 
 
 **-"% 
 
 CHAPTER YI. & 
 
 ~~~~~~i** 
 
 CONVERSE OPERATIONS. 
 
 SWBTXACTJ 
 
 1. THE parts of a farm arc 35 acres of tilled land, 1 7 
 acres of meadow, 25 acres of pastun \ and '^ acres 
 of woodland. IIow many acres are tin-re in tin- 
 farm ? 
 
 A kin / K per in Chicago has 35 carriages, 
 
 Hi of which an- douMe rama^s. How in;:. 
 carriages has h- 't 
 
 3. Two pieces of cloth nu 'usniv :>", yd. 1 jr., and one 
 of them is 8 yd. 3 qr. long. What is the l-n^h of 
 the otli 
 
 .. A woman wrht to a t-;i store with $'-2.1'>. Sh- paid 
 $.75 for 6 pounds of sugar, $.40 for 2 pounds of 
 coffee, and the balance of her money for a poun 
 tea. IIow much was the t-a a pound ? 
 
 5. A miller had 269 bushels of wheat, but aft* r grind- 
 ing a part of it into flour. In- liiuls he has 87 bushels 
 remaining. How many buslu-ls has he ground ? 
 
 <?. A Vermont farm- r. liter Belling 806 sheep, hju 
 n-maining. How many ifliirp liad he at lir 
 
MULTIPLICATION AND DIVISION. 139 
 
 7. Joel is 5 ft. 2 in. high, and Jasper is 3 ft. 11 in. high. 
 What is the difference in their heights ? 
 
 8. What is the sum of 2A da., 5f da., 9^ da., and | da. ? 
 
 Addition is putting parts together to form a whole, and sub- 
 traction is taking away a part or parts from the whole. Hence, 
 addition is the reverse of subtraction. 
 
 Conrcrsc Operations are those arithmetical processes 
 which are the reverse of each other. 
 
 9. The parts of a number are 15, 92, and 43. What is the 
 number ? 
 
 10. The sum of two numbers is 18 gal. 2 qt., and one of them 
 is 4 gal. 3 qt. 1 pt. What is the other ? 
 
 11. The sum of three numbers is 37 ; one of them is 18|, and 
 another is 12. What is the other number ? 
 
 12. The minuend is 94, and the subtrahend is 48. What is 
 the difference ? 
 
 13. The minuend is 3$, and the remainder is 2f. What is the 
 subtrahend ? 
 
 U t . The subtrahend is 10 11). 4 oz., and the remainder is 5 Ib. 
 C oz. What is the minuend ? 
 
 15. What is the difference between i| wk., and -J-fJ. wk. ? 
 
 16. The greater of two numbers is $3.15, and the less is $1.27. 
 What is their difference ? 
 
 17. The greater of two numbers is $3/ ff , and their difference 
 is $1|. What is the less number ? 
 
 IS. The less of two numbers is $1.27, and their difference is 
 $1.87. What is the greater number ? (Sec Manual, P a g o 173.) 
 
 SECTION II. 
 
 MVZ.TITZICd.TIOJV dLJV DITISIOJV. 
 
 1. How many square rods arc there in a field 35^ rd. 
 long and 9 rd. wide ? 
 
 2. In finding the cost of 30 barrels of apples, at $2.12A 
 per barrel, which number is the multiplicand, which 
 is the multiplier, and which is the product ? 
 
140 CONViiKSi; OP1EJLTI01 
 
 3. A grocer bought 10 banvis of i>otatoes containing 
 2 bu. 3 }'k. t adi. and ivtail.-d tli-m at $.60 a bi: 
 How much diil lie receive lor them? 
 
 4. This y.-ar I ITU!, r-d 7 times as many apples as pears 
 from my garden, and I gathered 40 bu. 1 pk. of ap- 
 ples. How many pears did I gath 
 
 6. A shoe deaK-r paid *300 for 1 alf boots, at $5 
 a pair. How many cases, of 12 pairs rach. did IK 
 
 '.'. My L r anl<-n contains ;) A., and my door-yard J$ A. 
 My garden is how many times as large as my door- 
 rd? 
 
 7. Ii % I of apinr-apple are divided among 5 childivn. 
 what part of a pin.'-appl- will rat-h child h:r 
 
 5. A woman put 4 gal. 1 (\\. 1 pt. of catsup into pint 
 and quart bottles, using 2 times as many of the 1 
 
 as of 1 1 . How many bottles of cacl , 
 
 she use ? 
 
 0. A dressmaker used 11} yd. of poplin, in makii. 
 >kirt> Q| x' \\alkinLr-dre8ses, using 1.1 yd. 
 1-nadth. How many breadths were there in 
 .-kirt l- 
 
 JO. A farmer finds that, if he divides his farm equally 
 among his 6 children, eaeh of them will hav 
 acres of land. What is the size of his farm ? 
 
 Multiplication is rqnMtcd addition of the same part or num- 
 ber, and division is repeated subtraction of the same part or 
 number. Hence, multiplication is the reverse of division. 
 11. What is the product of 9 and 23 ? Of 9 times $2.30 ? 
 ;.'. Tin* multiplicand is '2 gal. 1 qt., and the multiplier is 9. 
 
 What is the product ? 
 
 13. Find the product of the factors 6, 5, and 8}. 
 1$. The product is 7f, and one factor is 5. Find the other 
 (factor 
 
CONVERSE REDUCTIONS. 141 
 
 15. . The product of three factors is 8|, and two of the factors 
 are and 14. What is the other factor ? 
 
 16. The product is 6|, and the multiplier is f . What is the 
 multiplicand ? 
 
 17. The multiplicand is 2 bu. 1 pk., and the product is 24 bu. 
 3 pk. What is the multiplier ? 
 
 18. The divisor is 6, and the dividend is 29. What is the 
 quotient ? 
 
 19. The dividend is 29, and the quotient is 4f. What is the 
 divisor ? 
 
 SO. The divisor is 6, and the quotient is 4. What is the 
 dividend ? 
 
 SECTION III. 
 
 39. Denominate Tractions to Compound Numbers. 
 
 1. A MERCHANT bought two pieces of linen, paying $J 
 a yard for one, and $ T 9 C a yard for the other. How 
 many cents a yard did each piece cost him ? 
 
 (See Manual, page 173.) 
 
 2. Reduce gal. to quarts and pints. Methods, pagciso. 
 8. What compound number is equal to 3| bu. ? 
 
 4. How many inches is | yd. ? Is T ^ yd. ? Are j- yd. + ^ 
 yd.? 
 
 5. The rows of vines in a grapery are J rd. apart, and 
 the vines in the rows are } rd. apart. What is the 
 distance in feet and inches between the rows ? 
 
 G. What is the distance between the vines ? 
 
 7. The fence which incloses my orchard is -?-% mi. in 
 
 length. What compound number expresses the 
 
 length of the fence ? 
 
142 CONVERSE OPERATION . 
 
 tf. II >w many square feet and square inches are 
 
 on the surface of a mirror, that is 1 J yd. long a: 
 
 \<1. wide? 
 9. H"W many cubic feet of bricks ar 
 
 of brick wall, if ,1 f the wall is mortar ? 
 70. How many ounce bullets can be made from 
 
 of lead r 
 77. I feed my cow -f 9 cwt of hay daily. H..W many 
 
 pounds do I f >1 h r ': 
 /.'. If a loenni'.tive burns ig T. of coal in runn! 
 
 mi., liow many pounds does it burn ? 
 IS. A haker used $ bar. of flour in making 100 loaves 
 
 of bread. How many pounds of flour did he use ? 
 1<> hours of work a day an- full time, how much 
 
 time will the hands work daily, in a fu-tnry that is 
 
 running on 5 tin. 
 
 .' : . When the time of sunrise is } of th<- time from mid- 
 night to midday or noon, at what hour and minute 
 
 does the sun rise ? 
 
 ioner sold T 7 , of a gross of steel pens. II -u 
 
 many dozen pens did he sell r 
 77. A mot! ! , 8 5 of a roam of manilla 
 
 supplying her customers with putt- in.-. llu\v many 
 
 quires and sheets did she use ? 
 
 40i Compound Numbers to Denominate Fractions* 
 
 18. The value of the old New England shilling was 
 $.10 j. What fraction of a dollar was it? 
 
 /"'. What fraction of a dollar were 7 New York shillings, 
 .-: 
 
 20. One day a hotel cook used 1 pt. 3 gi. of molass 
 making fruit -c;ike. What jiart of a quart did 
 . What part of a gallon? 
 
CONVERSE REDUCTIONS. 143 
 
 21. 1 pk. 5 qt. of beans are what fraction of a bushel ? 
 
 Aletliods, page ISO. 
 
 22. Express 4 bu. 3 qt. 1 pt. by a mixed number. 
 
 23. 7 in. are what part of a foot ? 
 
 24. What mixed number is equal to 72 rd. 4 yd. 1 ft. ? 
 
 25. 2 sq. ft. 72 sq. in. are what fraction of a square yard 
 
 26. What fraction of an acre is a village lot, which is 4 
 rd. front and 9 rd. deep ? 
 
 27. If 4 shingles, each 4 in. wide, are laid 6 in. to the 
 weather, what part of a square foot do they cover ? 
 
 28. A block of marble 2 by 2| by 1J feet, is what part 
 of a cubic yard ? 
 
 20. 60 Ib. of wheat arc a bushel. What part of a bushel 
 are481b.? 
 
 30. How much must I pay for 7 Ib. 10 oz. of butter, at 
 $.36 a pound ? 
 
 31. One month a dairy-man made 43 Ib. 12 oz. of cheese, 
 from the milk of 1 cow. What part of a hundred- 
 weight of cheese did he make ? 
 
 32. If school is in session 5 days of the week, what part 
 of the school week has passed, at noon, Thursday ? 
 
 33. In 45 N. latitude, on the shortest days of the year, 
 the sun is above the horizon 8 h. 40 min. What 
 part of the 24 h. is day, and what part is night ? 
 
 34. One season Hudson River was closed by ice for 4 mo. 
 12 da. What fraction of a year was the river closed ? 
 What part of a year was it open ? 
 
 35. A grocer having 1 gro. of boxes of matches, sold 6 
 doz. and 9 boxes of them. What part of the whole 
 gross did he sell ? 
 
 86. A printer used 13 quires 8 sheets of paper, in print- 
 ing handbills. What part of a ream did he use ? 
 
CHAPTER YII. 
 % f ,.f&u*3fL*+3f^' ^-^^^^^j^-^^sr 
 
 | HW***. 
 
 PERCENTAGE. 
 
 SECTION I. 
 41. />/// v. r/ //". r.v .^.r# ^vr^ // 
 
 THE term /Vr On* in business transactions signifies hun- 
 dredths of any thing or number. Thus, 1 JUT rent is one hun- 
 dredth, or 1 of every hundred ; 6 i< B hundredths, or 
 
 6 of every hundred ; 16f per cent is 16| hundredths, < 
 
 /. How many hun.lredths of a number is 1 per cent of it ? 
 
 I I>\v many liundrcdths are t of it ? 
 
 tl r|u-r(vnt? 7 per cent? 8 per cent? 10 per cent? 
 . Wliat fr:u tion in its lowest terms expresses 15 \ 
 
 15 hundredths f 
 
 5. 25 ]) r .nt of a number is what part of it ? 50 per 
 75 per cent ? (See Maniui, pap? ITU 
 
 4, 6| per cent of a numl>cr is what part of it? 8J p< i 
 i> what part ? 12^ per cent is what part ? 
 What part of a number is 10| per cent of it ? What part 
 is 66 \ per cent of 
 
 6. What part of a number is 100 per cent of it ? Is 1 1 
 cent of it ? 
 
 7. What fraction expresses 150 per cent of a number : 11'^ 
 per cent ? 140 per cent ? 112$ per cent .' 133J per . 
 
 s> . N\ hat part of a number is 4 per cent of it ? Is } per cent ? 
 | per cent ? -^ per cent ? ^ per cent ? ^ per cent ? 
 
GENERAL CASES OF PERCENTAGE. 145 
 
 9. What part of any number is per cent of it ? Is per 
 
 cent ? ^ per cent ? | per cent ? f per cent ? 
 3frz/e?, or ftate 2>er Cent, is the number which expresses 
 the per cent, or number of hundredths. 
 
 The term Percentage has two significations : 
 1st. It is the process of finding any per cent of a number ; 
 2d. It is the name of the result of the computation. 
 The 2?ase is the number on which the percentage is com- 
 puted. 
 
 The Amount is the base plus the percentage. 
 The ^Difference is the base minus the percentage. 
 The Commercial Sign, fa signifies per cent. 
 EXAMPLE. 24$ of 50 cords of wood is .24, or -$&, of 50 
 cords, or 12 cords. In this example, 24$ is the rate; 50 cords, 
 the base; 12 cords, the percentage; 62 cords (= 50 + 12), the 
 amount, and 38 cords (= 50 12), the difference. 
 
 Per cent may be applied to any number, great or small, con- 
 crete or abstract. Thus, 
 
 40 per cent of 1 bushel = .40 bu. = -^ bu. = bu. ; 
 88 " " 27 miles = .88 = -flfr = ff of 27 mi. ; 
 14 " " 395 days = .14 = & of 395 da. ; 
 7 " " $85.42 = .07 = T^ of $85.42 ; 
 65 " = .65 = fa = H of 93 *- 
 
 SECTION II, 
 THE FIYE GEJV&'Rd.L CASES OF 
 
 42. Base and Rate given, to find Percentage. 
 
 1. How much is 6$ of $100 ? 
 
 2. A man bought a horse for $125, and paid 20$ of it 
 down. How much money did he pay down ? 
 
 8. A farmer raised 500 bu. of corn, and sold 25% of it. 
 How many bushels did he sell ? Methods, page iso. 
 12 
 
M' ; PERCENT \ 
 
 -}. \ty% of an army of 90,000 men \\viv killed and 
 wounded in an engagement How many weiv killed 
 and wounded ? 
 
 I rom a yard containing 150 cattle, 66|< were sold 
 he first market day. How many were sold '-. 
 
 fruit grower sent 75 baskets of peaches to ni; 
 but In fore they were sold, 8# of them were sj. 
 How many baskets did he lose ? 
 much ia 
 
 7. -V of HOrd. of WOOd? 
 
 8. 8# of 250 yd. of sheetings? 
 
 9. 3 of 50 thousand shingles? 
 
 10. 12J* of $75 ? 
 
 11. 80 of 190 mi. ? 
 IS. 554 of 230 bu, ? 
 
 43. Base and Percentage given, to find Rate. 
 
 13. A sewing-machine winch cost $100, was sold fur 
 $80. What % of the cost did it sell f 
 
 14. A sheep grower having 450 sheep, sold 150 of tlu-m. 
 What % of his flock did he sell ? Method*, page iso. 
 
 '. A boy having 15 apples, ;_ 
 
 What % of his apples did he give away? 
 
 1>>. A man having $50, paid out $10 of it for provi 
 What ^ of his money did nd ? 
 
 17. A landlord rents a honse worth $1,250, for 
 \var. What ^ on its value does the house rent 
 
 18. A farmer pays $3 per acre, for the use of land vulu -d 
 at $50 per acre. What ^ on the valui.- of the land, 
 does he pay for the use of it ? 
 
 10. V/ha: of oOO bu. an- 50 bu. ? 
 
 X.W. What ', of 7.") melons an- l."i intU.ns .' 
 
 SI. $119 are what % of $340 ? 
 
 SS. 1 bu. 3 pk. are what % of 6 bu. 1 pk. ? 
 
 S3. f of an hour niv what ^ of f of an hour ? 
 
GENERAL CASES OF PERCENTAGE. 147 
 44. Rato and Percentage given, to find Ease. 
 
 24. From a certain regiment, 100 men are detailed on 
 picket duty, and the number detailed is 12 % of 
 the whole number who are fit for duty. How many 
 men of that regiment are fit for duty ? 
 
 2-j. A gentleman sold his house and lot for 25% above 
 cost, and made $500. How much did the property 
 
 COSt ? Methods, page 180. 
 
 26. From 1 day's sales a merchant received $133, which 
 was 1% of his weekly sales. How much were his 
 receipts for the week ? 
 
 27. A farmer carried to mill 10 bushels of wheat, which 
 was \% of his whole crop. How many bushels did 
 he raise ? 
 
 25. This year a hop grower sold his hops at 24 cents a 
 pound, which was 80$ of the price he received last 
 year. At what price did he sell his crop last year ? 
 
 29. A certain school closed its winter term with 115 
 pupils, which was 92$ of the number with which 
 the term commenced. With how many pupils did 
 it commence ? 
 
 SO. $600 arc 6$ of what sum of money ? 
 
 31. 800 is 10$ of what number ? 
 
 82. 1,500 is 33 of what number ? 
 
 45 Base and Rate given, to find either Amount or 
 Difference. 
 
 33. If maple wood is worth 20$ more than oak, and 
 oak sells at $7.50 per cord, how much is a cord of 
 
 maple WOrth ? Methods, page ISO. 
 
 34. A gentleman having $600, paid 20$ of it for a gold 
 watch. How much had he remaining ? 
 
148 I'KKr KNTAGE. 
 
 . ^ntl'-man liavinir x;;,o dcjio-iK'.l in a bank, 
 chtrkrd out 33 *# of it How much r> in 
 deposit ? 
 
 36. A merchant bought Memmac prints at 20 cents a 
 yard, but the next y as obliged to pay 
 
 more for the same class of goods. How much did 
 he pay per yard ? 
 
 87. A merchant started in bu.-'. 
 
 $2,400, and added to it 33J# in two years. A\ 
 was his capital at the < \ pirat ion of the second y 
 
 38. The base is 35, and the rate is 25. What is the amount \ 
 What is the difference ? 
 
 i-l the amount, and also the diffcrcnc ie base 
 
 is | and the rate is 8J 
 
 46. Amount or Difference) and Rate given, to find Base. 
 
 40. A speculator bought cheese at two factories, buying 
 9,000 Ib. at one, which was 50$ more than he bought 
 at UK oth,-r. How much did he buy at the second 
 
 factory ? Method., page 18O. 
 
 41. A man on a journey travel <>f tlu wlml- 
 
 ' by stage, and the remainder, which was 140 
 mile*, by railroad. How many miles did h 
 
 .; .. A widow expended 25j of her income for hi r 
 port, and saved $60 a month. What wa.s lu-r in- 
 come? 
 
 43. A physician's practice is worth :><>; m.>r 
 
 than it was last, and this year it is worth $2 
 How much was his practice worth last year ? 
 
 44' 87 cows are 116 of how many cows I 
 
 45. 1 Ib. 11 oz. are 112# of what number? 
 
 46. $44 are 22^ of how many dollars T 
 
 47. 57 ft. are 95< of how many feet ? 
 
APPLICATIONS OF GENERAL CASES. 149 
 
 SECTION III. 
 
 SPECIAL APPLICATIONS Of 1 THE FIYE 
 GEJYEKAZ, CASES. 
 
 47. Insurance* 
 
 Insurance is a security against loss or damage within a 
 given time, guarantied to one party by another, for a specified 
 consideration. 
 
 7 '(dualion is the sum for which property, life, or health is 
 insured. 
 
 Premium is the sum paid for the insurance. 
 
 The Policy is the contract between the insurer and the 
 insured. 
 
 In computations in insurance, valuation is the base, premium 
 is the percentage, and rate % is the rate. 
 
 1. At \% premium, how much must be paid for an 
 insurance of $600 on a quantity of grain ? 
 
 2. A gentleman effected an insurance of $1,500 on his 
 house, at 2% premium. How much did he pay for 
 his policy ? 
 
 3. A cabinet maker paid k% for an insurance of $3,000 
 on his stock and shop. How much did the insur- 
 ance cost him ? 
 
 4. What must be paid for an insurance of $5,000 on a 
 stock of goods, at \\% ? 
 
 5. A produce dealer paid $25 for an insurance of 
 $5,000, on a cargo of produce. What % premium 
 did he pay ? 
 
 6. A hardware merchant paid an insurance agent $50 
 premium, for a policy of $2,500, on a stock of stoves. 
 What % did he pay? 
 
 7. What % premium does that man pay, who pays $9 
 for a policy of $1,200, on his house and furniture ? 
 
150 i'i:i: i: XT AGE. 
 
 8. If a lawyer pays $15 for an insurance on his clothing 
 and library, at f $, what amount does he get insu 
 
 9. A fanner paid an agent $8 for insuring his barn 
 and its contents, at \%. What amount did he get 
 insured ? 
 
 48. Commission. 
 
 hajiffcitf. CbmmtutOM .)/'/<//,/,//. / ;/, -A//% or ^Bro- 
 ker is a person who, by . buys and sells goods, or 
 
 transacts other financial business for another. 
 
 / is the person or party for whom an agent 
 transacts business. 
 
 is the sum paid an agent or commission -mer- 
 chant tor transacting business, 
 
 hi (Deputations in commission, the sum expended : 
 lected by the agent, for tlic principal, is the base; commission 
 is tin- percentage ; rate is the rate; and the sum on which 
 commission is computed, plus the commission, is the amount 
 
 10. A person collects accounts amounting to $50< 
 
 ives 10$ on the money collected for his sen 
 How much does he receive ? 
 
 i air- in in New York buys goods to the amount 
 of $3,000, and receives 5$ commission. Huw much 
 does he r 
 
 12. A planter sends 40,000 Ib. of cotton to his corres- 
 pondent in New York, who sells it at 15 cents a 
 pound, and retains 8} commission. How much 
 
 I tlu- plunUT : 
 
 13. A collector's fees are \% on all sums paid to him 
 within 30 days after receiving his warrun:. 
 
 on all amounts collected th<: 
 his town are $15,000, $5,000 of which 
 within the 30 days, and the balance there;: 
 What ai\- his ices for collecting? 
 
APPLICATIONS OF GENERAL CASES. 151 
 
 14. A druggist sent his broker $630 with which to buy 
 goods, after deducting his commission of 5$. How 
 much did the broker expend for goods ? 
 
 1-1. A manufacturer sends to a wool broker $2,600 with 
 which to purchase wool, allowing him 2% brokerage 
 on the money paid out. How much money will the 
 broker expend for wool ? 
 
 1G. A book buyer in New York receives $800 to expend 
 for books for a library, after deducting his commis- 
 sion of 12|^. How much will he expend ? 
 
 17. A brewer allows 4$ for buying hops, and sends his 
 broker $5,200. How many pounds of hops, at 25 
 cents a pound, will he receive ? 
 
 18. A collector received $40 for collecting bills, at 5% 
 commission. How much money did he collect ? 
 
 10. A horse dealer received $15 for selling a horse, which 
 was 10$ of his value. For how much was he sold ? 
 
 49. Profit and Loss. 
 
 'Profit t in business, is the sum above cost for which goods 
 are sold. 
 
 Ztoss is the sum below cost for which goods are sold. 
 
 In computations in profit and loss, the cost is the base ; the 
 profit or loss is the percentage ; the rate % is the rate, and the 
 selling price is the amount or difference. 
 
 20. Last year a farmer had 450 sheep, and his flock has 
 increased 30% in the year. How many more sheep 
 has he than lie had last year ? 
 
 21. A hen hatched a brood of 15 chickens, but lost 40$ 
 of them. How many chickens did she lose ? 
 
 22. A grocer sold white-fish that cost $16 a barrel, at 
 50$ profit. How much did he gain on a pound ? 
 
1 .''.' PERCENTAGE. 
 
 .'''. The bread made from a barrel of flour weighs 40$ 
 more than the flour. How many pounds more does 
 it weigh ? 
 
 24. A man sold a city lot which cost him $160, at an 
 advance of 212^$. How much did IK- pi: 
 
 . '. A. card of green beech wood weighs 6,000 Ib., and it 
 loses 27$ of its weight in seasoning. How much 
 liirhh-r is a cord of dry beech than a cord of green ? 
 
 26. A merchant sold broadcloth that cost him $5} a 
 yard, at a loss of 33J$. How much did he lose on 
 a yard ? 
 
 \ i-iiys sugar at $.10 a pound, and sells it at 
 
 a profit of 30$. For how much does he sell it ? 
 
 28. I bought 6 cords of wood for $10. At what 
 per cord must I sell it, to make 20# ? 
 
 29. A grocer sold t a that cost him $.78 a poun> 
 loss of 15%. What did he get a pound for it ? 
 
 . \ -]n c ulator bought butter at $.35 a pound, but was 
 
 obliged to sell it at a loss of 12J$. For how much 
 
 did he sell it? 
 81. A gentleman bought a house and lot for $1,600, paid 
 
 10$ for repairs and painting, and sold it for 15# 
 
 profit How much did he get for it ? 
 .. A manufacturer finds that it costs him $1.20 a yard 
 
 to manufacture his cloth, and he wishes to sell it at 
 
 a profit of 25$. How much will he make a yard, 
 
 and how much a yard will he sell it for ? 
 S3. A gentleman sold a horse and harness for $180, 
 
 which was 10^ less than cost. How much did they 
 
 cost him ? 
 84. A manufacturer sold damaged cloth at cost, or $1.50 
 
 a yard, which was 33]$ below the marked price. 
 
 What was the marked price ? 
 
APPLICATIONS OF GENERAL CASES. 153 
 
 So. A silversmith sold tea-spoons at $1.65 each, and 
 made 25^. How much did they cost him ? 
 
 36. A jeweler sold a watch for $69, which was 15$ ad- 
 vance on the cost. How much was the cost ? 
 
 37. A grocer bought sugar at $.08 a pound, and sold it 
 at $.10. What % did he make ? 
 
 38. A book-seller sold a book for $1.00, that cost him 
 $.75. How much % did he make ? 
 
 39. A carman sold a truck for $87A, which cost him 
 $100. At what % less than cost did he sell it ? 
 
 40. A flour dealer bought flour for $6 a barrel, and sold 
 it for $7. What % did he make ? 
 
 41. What % does a grocer make, by selling eggs at \ of 
 their cost ? 
 
 J t 2. If kerosene is bought at f of the market price, and 
 sold at 10% below the market price, what % is lost ? 
 
 50. Stocks. 
 
 A Corporation is a company established by law, having 
 power to transact business as an individual. 
 
 Stock is the property invested in the business of a corpora- 
 tion. 
 
 A Share is one of the equal parts into which the stock of a 
 corporation is divided. It is usually $100. 
 
 The 'Par Value of stock is the sum stated in the certifi- 
 cate ; and 
 
 The Market Value is the sum for which it will sell. 
 
 Stock is jit jPar when the market value is the par value, 
 or 100#. 
 
 Stock is Above 3?ar when the market value is above the 
 par value, or more than 100$ ; and 
 
 Stock is Selow *Par when the market value is below the 
 par value, or less than 100$. 
 
154 PERCENTAGE. 
 
 is the excess over 100^ in the value of stock 
 that is above par; . 
 
 Discount is the deficiency under 100# in the value of 
 stock that is below par. 
 
 A .N'A"-X- ///'/- / ot Stock ./-,'>'< r is a person who deals 
 in stocks. 
 
 -//' is the commission paid to stock brokers for 
 luiying and selling stocks for ot 
 
 In rnmput:itions in stocks, the par value U the La 
 premium or the discount is the percentage, the rate $ \< the 
 rate, and the market value is the amount or differ 
 
 43. A stock jobber bought $3,000 w. I J. R. stock, 
 and sold it at a loss of 10<. How much did he lose ? 
 
 44. For how much did he sell it ? 
 
 silver is at a premium of 15& how much currency 
 will a man have to pay for $50 in silv 
 
 46. A broker jaid $2,900 in bills for gold, when gold wa.s 
 at a premium of 45$. How much gold did he buy ? 
 
 47. He sold his gold at a premium of 5(#. How much 
 did he make in the tu.. transactions? 
 
 . \VlKitistheiiKirketvalucofashareofmining8tock, 
 
 that sells at 32 j below par? 
 40. A brok ved $1,750 for 15 shares of insurance 
 
 stock. What was the market value of a sh;; 
 50. A man paid $262.1 for stock in a toll-bridge, at 12 # 
 
 discount How many shares did he buy? 
 
 51. Taxes. 
 
 7'ff.rcs arc sums of money assessed upon persons and prop- 
 erty, to meet public expenses, 
 
 Property is of two kinds: '/' -/ /;VA//V. or houses and 
 Ian. Is ; and 
 
 fersonal ^Property, or movable property. 
 
INTEREST. 155 
 
 In computations in taxes, the valuation of property is the 
 base ; the rate % is the rate ; and the tax is the percentage. 
 
 51. A tax of $250 was levied on a village, in which the 
 real estate was assessed at $19,000, and the personal 
 property at $6,000. What was the rate % of tax ? 
 
 52. The taxable property in a certain school district is 
 valued t $20,000, and a tax of $50 is voted to repair 
 the school-house. What is the rate % of the tax ? 
 
 53. A's property is assessed at $2,500. How much is 
 his tax ? 
 
 54. B is assessed for $3,000. How much is his tax ? 
 
 55. C is assessed for 84,500. What is his tax ? 
 
 56. How much is D's tax, his property being assessed at 
 $1,500 ? 
 
 57. E is assessed for $8,500. How much must he pay ? 
 
 58. A machine costing $150, is put into a planing-mill 
 owned by 8 men, whose shares of the capital arc, 
 respectively, $600, 8400, $1,200, $500, $1,500, $800, 
 $300, and 82,200. How much of the cost of the 
 machine must each partner pay ? 
 
 SECTION IV. 
 
 Interest is the sum paid for the use of money. 
 
 ^Principal is the sum for the use of which interest is paid. 
 
 Amount is the sum of principal and interest. 
 
 (Rate per Cent per Annum is the interest on $1 for 1 
 year. 
 
 In computations in interest, principal is the base ; the prod- 
 uct of rate % per annum and time expressed in years, is the 
 rate ; and interest is the percentage. Interest is the product 
 of the three factors, principal, rate, and time. 
 
PERc i:\TAGE. 
 
 52. Interest for Tears, or Months, or Days. 
 
 /. What is tli..- int.-r.-st of $75 for 2 years, at - 
 
 .'. What is ilit- interest of $500 for 3 years, at 7#? 
 
 3. A gentleman has a mortgage for $1,000, diu- in 4 
 years, at 1%. How much interest will he receive ? 
 
 4- A man purchased a city house and lot for $4,500, 
 paying $1,500 in cash, and giving a mortgag< 
 tin- balance due in 5 years, at 8$, interest payable 
 annually. How much interest did he pay yearly? 
 
 5. How much money, principal and interest, did lie 
 pay for the property ? 
 
 6. What part of a year is 1 month? Arc 2 months! 6 
 months ? 8 months ? 
 
 7. 9 months are what part of a year ? 4 months ? 7 months ? 
 
 8. The interest of any sum of money for 10 months will l>o 
 what part of the interest of the same sum for 1 year? 
 
 0. The interest for 5 months will be what part of 1 year's 
 
 interest? 
 
 /". What is the interest of $450 for 4 months, at G 
 11. At 7 . what is the interest of $50 for 3 months ? 
 /.'. What part of the principal will cijnal the in 
 for 9 months, at 6 
 
 13. How much intn, st must be paid for the use of $120 
 for 10 months, at 
 
 14. What part of a month, or 30 days, is 1 day ? Are 8 days ? 
 8 days? 10 days? 20 days? 
 
 15. 14 days are what part of a month ? 15 days ? 24 days ? 
 
 16. The interest of any sum of money for 25 days will be what 
 part of the interest of the same sum for 1 month ? 
 
 /:. What part of the intenst f.-r 1 month is the interest for 
 
 18 days ? Is the interest for 12 days ? For 28 days ? 
 7,v. What is the interest on a note for $75, due in 15 
 days, at 
 
APPLICATIONS OF GENERAL CASES. 157 
 
 19. I borrowed 6150 for 3 weeks, at 10^. How much 
 interest did I pay ? 
 
 20. At 24^b per annum, what is the rate % per month ? 
 Per day ? 
 
 21. A broker loaned $750 for 18 days, at 2$ per month. 
 How much interest did he receive ? 
 
 53. Interest for any Given Time. 
 
 22. What part of a year are 7 mo. 15 da. ? 4 mo. 24 da. ? 
 
 23. The interest of any sum of money for 6 mo. 18 da. will be 
 what part of the interest of the same sum for 1 year ? 
 
 2J^ How much interest has accrued on an account of 
 $45, which lias been due 2 yr. G mo., at % ? 
 
 2.j. At 7$, how much must I pay for the use of $150 
 for 1 yr. 4 mo. ? 
 
 J'>. What is the interest of $750 for 3 mo. G da., at 6$? 
 
 27. A mechanic while building a house, borrowed $380 
 for 7 mo. 15 da., at 8$. How much interest did he 
 pay? 
 
 28. How much will $30 gain in 2 yr. 2 mo. 20 da., at 
 6$ ? To how much will it amount ? 
 
 29. At \% a month, how much will a banker receive 
 for the use of $100, for 2 yr. 5 mo. 10 da. ? 
 
 80. Find the interest of $150 for 1 yr. 6 mo. 12 da., at 
 
 31. How much interest has accrued on a mortgage for 
 $300, which has been running 4 yr. 4 mo. 15 da., at 
 7#? 
 
 32. A man paid 6^ interest on a note for $450, which 
 had been due 2 yr. 10 da. How much interest did 
 he pay ? 
 
158 i- 1: it i: .> T A 
 
 54. Converse Operations in Interest* 
 
 will $50 gain $15 int. : mo.? 
 
 34. At what per cent will $30 gain $4/. ) o interest in 1 yr 
 
 9 mo. ? (See Manual, page 178.) 
 
 55, If 1 pay *:. 1 i T the use of $200 for :J yr. -1 mo. 15 
 da., wh.. :it do I pay? 
 
 \t what \ will $50 amount to $G0.50 in 3 years? 
 
 the amount of $250 for 4 years is $310, what is 
 the rate of interest ? 
 
 I loan $500, and at the end of 2 yr. C mo. receive 
 $587.50, what rate of interest d I 
 
 i ho interest on $25 for 20 years is $25, what 
 rate#? 
 40. At what per cent will $73 gain $75 interest in 1 
 
 .: what per cent will any given principal donhle 
 itself in 10 years ? In 12} years ? 
 At Gf/, what principal will gain $24 in 8 years ? 
 What principal will <;ain $28 in 8 years, at 7#? 
 ; ;. What sum will earn $35 interest in 4 years, at 
 ; . At 1J$ a month, what principal will gain $300 in- 
 n-rest in 5 yr. G mo. 20 da. ? 
 
 . . What principal will amount to $171 in 2 yr., at7#? 
 .;;. What sum of money put at inter -HI at \\ foe 
 6 mo., will amount to $52 ? 
 
 48. At 5, what principal will amount to $480 in 4 
 
 49. The time is ID yr. 8 mo., the rate is 6$, and the 
 amount is $82. What is the principal? 
 
 50. In what time will $90 gain $10.80, at 6#? 
 
 51. In what time will $125 gain $25, at I 
 
 . Kor how long a time must $75 be at inu : 
 to gain $16 ? 
 
DISCOUNT. 159 
 
 53. In what time will any sum of money double itself, 
 at 5$ ? At 6$ ? At *t% ? At 8%, ? At 10$ ? 
 
 &. For how long a time must $250 be at interest, at 
 G, to amount to $300 ? 
 
 JJ. In what time will $64, at 7#, amount to $76.20 ? 
 
 SECTION V. 
 
 DISCO UJYT. 
 55. Commercial Discount 7 or Per Cent Off. 
 
 The Face of an obligation is the sum to be paid when the 
 obligation is due. 
 
 Commercial %)iscotent, or (Per Cent Ojf, is a deduc- 
 tion from the face of the obligation, of some $ agreed upon, 
 without regard to time. 
 
 In computations in commercial discount, invoice price, or 
 the face of the obligation, is the base ; rate % off is the rate ; 
 and the commercial discount is the percentage. 
 
 1. I bought articles that I retailed at $1.00, at \ off 
 What % did I make ? 
 
 2. A book-seller buys books that retail at $.80, at j off. 
 What % does he make ? 
 
 3. A merchant bought linen which retailed at $.50 a 
 yard, at 50$ off. What % did he make, by selling 
 it at the regular price ? 
 
 4. The proprietor of a variety store buys toys that re- 
 tail at $.12, at J off. What % does he make ? 
 
 ~>. A stationer buys ink that retails at $.10 a bottle, at 
 
 20$ off. What % does he make ? 
 G. A merchant bought $4,000 worth of goods, on a 
 
 credit of 6 months, but got a discount of 5$ off for 
 h. What was the cash cost of his goods ? 
 
160 PEK< i: N T \ 
 
 f goods are sold at 1UO less than cost, how much 
 do they bring ? 
 
 8. If slates are sold at wholesale, at 40# off from retail 
 or list prices, and a further discount of 5# off is 
 made for cash, what is the total % off from 
 vs, for cash ? 
 
 . to buy goods at 30 off and 5% 
 off for cash, or to buy at 5 off and 30^ off for cash ? 
 
 56. True Discount. 
 
 Discount is a sura deducted for the payment, before it 
 becomes due, of a note or otli drawing interest 
 
 present )*'<>////. <>r 7'/-<ccds, is the face of an obliga- 
 tion less the discount. 
 
 In computations in a discount, present worth or proceeds is 
 the base ; the product of the rate per cent per annum and the 
 \pressed in years, is the rate ; the face of the obligation 
 is the amount ; and the discount is the percentage. 
 
 10. How much must be discounted for the present pay- 
 ment of a note for $84, il; are, money being 
 worth 6 
 
 / /. I bought a note for $207, due in G months, at 1% 
 discount How much did I pay for it ? 
 
 /.'. A man sold property for *!.>..:>. taking notes cltir in 
 3 months, and tlu-n sold the notes at 10$ discount 
 for cash. How much discount did he give ? How 
 much cash did ho roe 
 
 13. A broker bought a note for $412, due in 2 months, 
 at a discount of \\% a month. How much did he 
 pay for it ? 
 
 14. I owe $530, due in 4 mo. 15 da., and I find ] 
 
 hn y the debt at 1G^ discount for cash. How much 
 cash will pay the debt? 
 
REVIEW PROBLEMS. 161 
 
 SECTION VI. 
 
 1. Only J of a certain regiment are fit for duty. What 
 
 % are on the sick list ? 
 ,'. A teacher, whose salary is $800 a year, expends $700 
 
 in support of his family. What % of his salary docs 
 
 he save ? 
 
 3. A father gave to each of 2 sons 25$ of a farm con- 
 taining 500 acres. How much land was given away, 
 and how much had he remaining? 
 
 4. A farmer bought a cow for $GO, and sold her so as to 
 gain 20$. How much did he gain ? 
 
 5. The interest received on $1,000 for 10 years was T 7 5 
 of the principal. What was the rate % of interest 
 received ? 
 
 G. Two regiments went into battle with 800 men each. 
 After the battle, one mustered G25 men, which was 
 25$ more than the other mustered. How many men 
 did the second regiment muster ? 
 
 7. A produce dealer sends to his factor in Boston 
 25,000 Ib. of butter, which he sells at $.20 a pound, 
 and charges 7$ commission and guaranty. How 
 much does the dealer receive for his butter? 
 
 8. A grape-grower refused $.15 a pound for his grapes, 
 but afterward sold them at 1G*$ less. How much 
 did he get a pound for them ? 
 
 0. A book-seller sold goods to the amount of 8900 in 
 one month, at an average profit of 25$. What was 
 the cost of his goods ? 
 
 10. At what $ will $75 amount to $87 in 4 years ? 
 
 13 
 
162 PERCENTAGE. 
 
 11. \ steam-boat is owned by 5 men, A owni: 
 
 shares, B 100 shares, C 150 shores, D 200 shares, 
 
 1 275 shares. An assessment of $4,000 is made 
 
 for repairs. How much must each stockholder pay ? 
 
 2 '. What principal will gain $76 in 6 yr. 4 mo., a 
 
 13. If I receive $2,736 for 24 shares of bank li 
 is the value of 1 share ? 
 
 \ t 8^, in how long a time will the interest on $30 
 amount to $12 ? 
 
 r, in how long a time will *i 
 $14'.'. 
 
 16. A grocer buys molasses, which retails at $.80 a gal- 
 lon, for 20^ off. What % does he mak 
 
 17. 14 f per cent is what fraction of a number ? 
 
 18. A policy of $150,000 was obtained on a Teasel and 
 cargo, for the voyage, at g. IIow much was paid 
 for the insurance ? 
 
 19. A country merchant has | of his capital invested in 
 dry goods, 7 3 of it in groceries, in hardware, and 
 the balance in crockery. What % of his capital is 
 invested in each of these classes of goo< 
 
 SO. In the year 1863, a merchant sold cotton goods at 
 33 \% above cost, and received $.36 a yard for them. 
 How much did they cost him JKT yard ? 
 
 21. If I burn 4 T. of coal during the summer months, 
 and what I burn in the summer is 75 of as much 
 as I burn in the winter, how much coal do I burn 
 in a year ? 
 
 28. A fruit dealer sold 10 baskets of peaches, that cost 
 $1.25 per basket, at 12J below cost How much 
 did he lose on them ? 
 
REVIEW PROBLEMS. 163 
 
 23. A merchant bought cassimerc, at auction, at 28;}$ 
 below the manufacturer's price, paying $1.25 a yard 
 for it. He retailed it at 32$ above manufacturer's 
 price. What was his retail price ? 
 
 24. A stationer sold paper that cost him $.75 a ream, for 
 $1.50. What % profit did he make ? 
 
 25. A boy bought apples at the rate of 3 for 5 cents, and 
 sold them at the rate of 2 for 3 cents. What % did 
 he make ? 
 
 26. A dairy-man contracted his cheese at $.15 a pound, 
 but at the time of delivery this price was 25$ below 
 the market price. What was the market price ? 
 
 27. An importer in Philadelphia, who pays 16-$ for 
 buying and insurance, remits to his agent in London 
 $5,684. How many dollars' worth of goods ought 
 he to receive ? 
 
 28. If gold is at a premium of 174& how much cur- 
 rency will a man receive for $80 in gold ? 
 
 29. How much are 5 shares of bank-stock worth, at 
 18 \i advance? 
 
 30. A Louisiana planter paid a New Orleans merchant 
 an account of $450, which had been due 3 yr. 7 mo. 
 C da. What was the interest on the account, at 5$ ? 
 
 31. If I receive $63 interest for the use of $250 for 4 yr. 
 2 mo. 12 da., what per cent do I receive ? 
 
 31. At what per cent will any given principal double 
 itself in 14f years ? In 16| years ? In 8J years ? 
 
 33. The time is 5 yr. 3 mo., the rate is 8$, and the in- 
 terest is $84. What is the principal ? 
 
 84. A man loaned $150 for a certain time, at 7$, and 
 received $42 for the use of the loan. For how long 
 a time was it at interest ? 
 
CHAPTER Y: 
 
 MISCELLANEOUS PROBLEMS. 
 
 -,. ^ ** 
 
 fc 
 
 \ 
 
 7. A MAN bought a wagon for $43, and after paying $0 for 
 having it painted, he sold it at a gain of $6. 1 : 
 did he get for 
 
 j?. The parts are 70, 9, 8, 8, and 6. What is the sum ? 
 
 3. A grocer who had 100 sacks of flour on hand in the morn- 
 ing, sold 9 sacks in the forenoon, and G in the after: 
 I I"\v many sacks had he left at night ? 
 
 }. Kunice was 7 years old 9 years ago. Marion is C 
 mire, and 8 years older than Ruth, 
 old is Ruth ? 
 
 5. A cotton broker sold to one merchant 56 bales of eotton, 
 to another (57 bales, and to another 19 bales less than to 
 th. tins!. How many bales did he sell in all ? 
 
 ' A drover bought 37 head of eattle on Monday, 20 head 
 more on Tuesday than on Monday, and 18 head more on 
 
 Inesday than on Tuesday. How many 
 buy? 
 
 7. Silas lives 81 rods nearer school than Ernest. If the 
 from home at the same time, Silos walking 9 rods an<! 
 nest 12 rods a minute, they will reach the school-house 
 together. How far does each live from school ? 
 
 8. If 3 men can chop 12 cords of wood i. much 
 con 1 man chop in 1 day ? 
 
MISCELLANEOUS PROBLEMS. 165 
 
 9. If a man can earn $75 in 3 months, how many months -will 
 it take him to earn $200 ? 
 
 10. I have two farms, that, together, contain 134 acres, and 
 one contains 14 acres more than the other. How many 
 acres would there be in the two farms, if each was of the 
 size of the smaller ? How many acres are there in the 
 smaller farm ? How many acres in the larger ? 
 
 11. A grocer has 75 pounds of tea in two chests, one of which 
 contains 15 pounds more than the other. How many 
 pounds are there in each chest ? 
 
 12. Two men earn $60 in a week, and one of them cams $10 
 more than the other. How many dollars does each man 
 earn? 
 
 13. Upon a vessel are 105 persons, and the number of passen- 
 gers is 13 more than the number in the crew. How many 
 passengers are there aboard the vessel ? 
 
 14. Ida's grandmother is 65 years older than she, and the sum 
 of their ages is 87 years. How old is each ? 
 
 15. The sum of two numbers is 98, and their difference is 44. 
 What are the numbers ? 
 
 16. The sum of two numbers is 133, and their difference is 97. 
 What are the numbers ? 
 
 17. I have 49 cents. If I give to each of 5 boys as many cents 
 as I can, how many cents will I have left? 
 
 18. Into how many 10- acre lots can a farm of 87 acres be di- 
 vided? 
 
 10. How many plows, at $7 apiece, can be bought for $60 ? 
 %Q. At $9 apiece, how many bureaus can be bought for $100 3 
 
 21. A farmer having 98 gallons of cider, filled as many 10-gal- 
 lon kegs as he could, and sold the rest at 26 cents a gallon. 
 How many kegs of cider had he, and how much did he re- 
 ceive for what he sold ? 
 
 22. How many weeks and days are 100 days ? Are 150 days ? 
 
 23. What is the width of a room which requires 8 breadths of 
 Brussels carpeting to cover the floor, each breadth being 2 
 ft. 3 in. wide ? 
 
16G MISCELLANEOUS PROBLEMS. 
 
 a horse eats 6 qt. of oats in a day, how man 
 will 7 bo. 4 qt last him? 
 25. A gardener sold 5 bo. 3 pk. of tomatoes, at $.60 a 
 
 Uow much did he sell tl. 
 
 J sl. nl. of lami \i M 3 bu. of potatoes, how many 
 bushels will 1 A. 50 sq. rd. produce? 
 
 w much will 2 Ib. 11 oz. of 1. utter cost, at $.48 per 
 pound? 
 
 28. A tailor bought 1 1 gross 8 dozen of buttons, and used 7 
 gross 9 dozen of them. How many buttons had he 1. 
 
 20. Nancy covered a box which was 10 inches long, inc-hcs 
 :<, and 8 inches deep, with gilt paper. How many 
 square inches of pajx-r <li.l >lu use? 
 
 50. The front wall of a brick house is 25 feet long, 20 feet high, 
 and 1 foot th'u-k. How many cubic feet does it contain, 
 allowing 7 cubic yards for the openings for doors 
 wind 
 
 . '/. I low much will 1 ream of paper cost, if 10 sheets arc 
 worth 7 cents? 
 
 51. If mackerel arc worth 13 cents a pound, how much will a 
 barrel sell for ? 
 
 . If J sq. r.l. of land yield 8 bu. of potatoes, how many 
 bushels will 1 A. 50 sq. rd. produce ? 
 
 ;i farmer sows 14 pounds of clover seed to the acre, how 
 many acres can he sow with 2 bushels 20 pounds, allowing 
 60 pounds to the bushel ? 
 
 you can count 90 eggs in one minute, how many dozen 
 can you count in an hour ? 
 
 36. A tinsmith made a 8-gallon rectangular can, which was 7 
 by 9 inches on the bottom. How many inches deep was 
 it. there l".inu r '-Ml cubic inches in a liquid gallon? 
 
 37. If a wheel is 5 yards in circumference, how many 
 will it revolve in going a mile ? 
 
 38. How much will be the expense of plastering n ceiling 27 
 feet long, and 24 feet wide, at $1 for every 3 square yards ? 
 
MISCELLANEOUS PKOBLEHS. 167 
 
 59. What is the cost of 2 A. 80 sq_. rd. of land, at $50 an acre ? 
 
 40. How many cubic feet are there in a stick of timber 16 
 inches wide, 9 inches thick, and 13 feet long ? 
 
 41. A publisher uses 6 sheets of book paper for one copy of a 
 book that contains 288 pages. How many copies can he 
 make from 10 reams? 
 
 4S. How many days are there in the first 3 months of a com- 
 mon year ? Of a leap-year ? 
 
 43. How many days from Apr. 1 to Aug. 1 in any year ? 
 
 44. A merchant buys a bill of goods, Jan. 1, on 60 days' credit. 
 When is the payment due ? 
 
 45. On the 20th day of Sept. a man sold a village lot, which 
 was to be paid for in 4 months 15 days. On what day was 
 the payment due ? 
 
 46. |45 are of the cost of 9 yd. of velvet. At what price 
 per yard must it be sold, to gain 20$. 
 
 47. When potatoes sell at $1|- per barrel of 2 bu. 3 pk., how 
 much is a bushel worth ? 
 
 48. A farmer having 77 bu. of greenings, kept \ of them, and 
 sold the remainder at $3.12 per barrel. How much did 
 he receive for them ? 
 
 49. f of 3 times are f of what number ? 
 
 60. -| of 6 times -^ are -/ f of what number ? 
 
 51. A boy gave 2 cents more than of his money for peaches, 
 1 cent more than of the remainder for marbles, and had 
 4 cents left. How much money had he at first ? 
 
 52. If a boarding-house keeper uses on an average 10 Ib. of 
 flour a day, how many barrels will he use in 14 weeks ? 
 
 53. If a farmer's family use 8 Ib. of pork a week, how many 
 barrels will they use in 50 weeks ? 
 
 64. A farmer drew 4 loads of hay, which weighed respec- 
 tively 18 cwt., 1 T. 3 cwt., 1 T. 2 cwt, and 17 cwt. How 
 much hay did he draw ? 
 
 55. A market gardener sowed a field of 4 A. to peas, beets, 
 and onions. He had 3| A. of peas, and {$ A. of beets. 
 How many acres of onions had he ? 
 
1G8 MISCELLANEOUS PROBLEMS. 
 
 56. 6f, 5}, and bow many are 16) ? 
 : . 11 100 gal. flow from a spring in 9 h., what part of 100 gal. 
 
 will flow from the same spring in 5} h. f 
 68. In repairing a culvert, a pile of stone 3$ ft. Ion- 
 
 and 3 ft. high was used. What part of a cord of ston 
 
 used? 
 59. At $f for f of a pound of English breakfast tea, how 
 
 much will } of a pound cost? 
 
 GO. The pier of a bridge is 24 feet hiirh, and of this height 
 is twice the height What part 
 
 of the pier is above water? 
 
 01. At $7 a barrel, how many barrels of flour must be given 
 for f of a hogshead of W. I. molasses, at $72 a hogshead ? 
 
 63. Two men purchased a load of potatoes, one paying $4, the 
 
 : *:j. What part of the load ought each to have ? 
 
 C5. Three men pay $20 for the use of a piece of land, from 
 whi( h t!u v li:u-\.-t 800 bushels of wheat A pays $6, B 
 $0, and C $5. How many bushels of wheat ought e:. 
 have? 
 
 64. Two men joined in a business transaction, A fun 
 twice as much money as B. and they made $600. 
 much wa ich ? 
 
 65. B put |200 into n certain l>n>inoss, and nfler 1 year A put 
 $400 into the business with him. At the end of two years 
 their whole profits were $600. How much was 
 
 ner's share ? 
 
 6. Three men hire a pasture together, paying $40. A put in 
 a horse, B 4 cows, and (' 40 ; lu-ep. the men agreeing that 
 ws should be considered cq.ial to one horse, and 4 
 sheep to 1 cow. What ought each to pay ? 
 
 67. A and B agreed to harvest a field of wheat for $1 1 
 sent 4 men for 5 days, and B 5 men for G d;. :,uch 
 ought each to ha\ 
 
 68. A, B, and C enter upon a speculation, A investing $* 
 
 B $70. They train $120, of which TVs share is $48. What 
 should A and i eivc, and what docs C in 
 
MISCELLANEOUS PROBLEMS. 169 
 
 69. A, B, and C commence trade together, A investing twice as 
 much, and C three times as much as B. They gain $720. 
 How much ought each to receive ? 
 
 70. A merchant tailor's sales amount to $12,000 a year ; his 
 average profits are 20$ of his sales, and his store expenses 
 are 25$ of his profits. How much is his net gain ? 
 
 71. A man sold a horse, which cost him $150, for $10 more 
 than $ of cost. "What $ did he make ? 
 
 72. An agent, whose commission is 8$, receives $5,427 from his 
 principal. How much of this sum will he retain for his 
 commission, and how much will he expend for his prin- 
 cipal ? 
 
 73. 16f $ of a certain farm is woodland, 10$ of it is under til- 
 lage, and the remainder, which is 110 acres, is in meadow 
 and pasturage. Of how many acres does the farm consist ? 
 
 74. A grocer sold eggs at $.20 a doz., which was 16f $ less than 
 cost. For what should he have sold them, to make 16$ ? 
 
 75. A sleigh maker sold a cutter, which cost him $25, at 144$ 
 advance, and another for $45, which was 25$ less than cost. 
 How much was his total gain or loss in the two transac- 
 tions ? 
 
 76. A person found a knife, and no one claiming it, he sold it 
 for $.25. What $ did he make ? 
 
 77. A tax of $10 is levied on persons assessed for the following 
 amounts of property : $50, $25, $75, $40, $60, $25, $125, 
 $150, and $250. What is each one's share of the tax ? 
 
 78. What is the amount of $500 for 4 yr. 7 mo. 15 da., at 8$ ? 
 
 79. In 7 yr., at 8$, what principal will amount to $117 ? 
 
 80. For how long a time must $84 be at interest, at 10$, to 
 amount to $112? 
 
 81. A druggist buys perfumery at off. What $ does he make 
 by selling it at the regular price ? 
 
 82. A gentleman wishing to buy a coat, agrees to pay the mer- 
 chant any price he may ask for the cloth, less 100$. What 
 
 wilHbe cloth cost? 
 
170 MISCELLANEOUS PROBLEMS. 
 
 83. Wool that crvt $.-12 per pound, shrunk 44 ; i 
 
 and after being cleansed, was sold at 88|# above cost At 
 what price per pound was it sold ? 
 
 84. When the sum of two parts, and one of the parts are 
 given, how is the other part found ? 
 
 85. When the sum of any number of parts, and a: 
 lut one are given, how is that part fou: 
 
 86. When thr difference and minuend are given, 
 subtrahend found ? 
 
 87. When tin- sulttruhend and remainder are givm. IK >v. 
 minuend found ? 
 
 88. When the greater of two numbers, or iflerence are 
 given, how is the less number found ? 
 
 89. ^~hen the less of two number- iterance are 
 given, how is the greater number found i 
 
 90. To what, in , does the minuend in subtr 
 correspond? To what do subtrahend and remui 
 correspo: 
 
 01. How is the product of any numlx-r of factors found \ 
 
 9S. When tho product and one of two factors arc given, how 
 
 is the other factor found ? 
 03. When the product of several factors, and all 
 
 but one are given, how is that factor for. 
 
 94. When the product and multiplier are given, how is the 
 multiplicand found ? 
 
 95. When the product and multiplicand are given, how is tho 
 multiplier found ? 
 
 96. When the dividend and quotient arc given, how 
 divisor found? 
 
 .'O. When the divisor and quotient are given, ho-.v is the divi- 
 dend found ? 
 
 ..*. What terms in multiplication and division correspond to 
 each other ? 
 
 99. What processes in multiplication and division are converse 
 operations ? 
 
.A. 1ST U 
 
 or 
 
 METHODS AND SUGGESTIONS. 
 
 TO TEACHERS. This Manual contains hints and suggestions intended 
 to aid you in the successful use of the book. Many suggestions valuable in 
 mental work will be found in the Manuals of the other books of this Series, 
 which, to avoid repetition, have been omitted from this work. 
 
 The Methods given in this Manual as models of solution are brief, strictly 
 logical r and in accordance with the true philosophy of development; but ex- 
 perience teaches that it is not best to require pupils to adhere rigidly to any 
 one method. Encourage them to solve problems in various ways : an original 
 solution, if correct, is better them any memorized formula. 
 
 J '<!</<> 9. Give exercises in writing and reading numbers in the following 
 order : 
 
 1st. Numbers expressing hundreds only ; 
 
 2rf. Numbers expressing hundreds and tens ; 
 
 3d. Numbers expressing hundreds and ones ; 
 
 4th. Numbers expressing hundreds, tens, and ones. 
 
 Require pupils to master thoroughly each of these classes of numbers, in 
 order, before passing to the next. 
 
 I'nt/c. 11. Pupils who have been through the First Lessons in Numbers, 
 in this Series, or any similar work, may omit Sections II., III., IV., V., and 
 VI., and commence at Review Problems, page 52. 
 
 rntff /.>. Problem 59. These ten exercises are intended as a substitute 
 for the Addition Table. First require the class in concert, and then each pupil, 
 to recite a set of combinations repeatedly, till all can recite them correctly and 
 rapidly. The combinations mny be mastered in three steps, as follows : 
 
 First Step.l and 1 are 2, 2 and 1 are 3, 3 and 1 are 4, 4 and 1 are 5, and so 
 on, to 10 and 1 are 11 ; then reversing the order, 10 and 1 are 11, 9 and 1 arc 10, 
 8 and 1 are 9, and so on, to 1 and 1 arc 2. 
 
 Second Step.l and 1 are 2, 1 and 2 arc 3, 1 and 3 are 4, 1 and 10 are 
 
 11, 1 and 9 are 10, 1 and 8 are 9 
 
 Third Step.l and 1 are 2, 2 and 1 or 1 and 2 are 3, 3 and 1 or 1 and 3 are 4, 
 
 4 and 1 or 1 and 4 are 5 10 and 1 or 1 and 10 are 11, 9 and 1 or 1 and 9 are 
 
 10, 8 and 1 or 1 and 8 are 9 
 
 /'"r/'' 17. Problem 93. The suggestions under the last reference may be 
 applied to drills upon this and the next four pages. 
 
 J>ftr/t: 21. Problem 192. Pupils will acquire familiarity with the com- 
 bination of any two figure*, by being questioned in the following manner: 
 When 1 is added to any number whose right-hand figure is 0, what is the 
 right-hand figure of the sum ? What is it, when the right-hand figure is 1 ? 
 
ITS MANUAL. 
 
 
 
 What, when I tU 2? When it in 3 r 4? etc. What i* the right-hand-figure of 
 the ram, when 9 is added to any nmnbor whose right-hand figure Is 0? 1? 8? 
 8? etc. Ask similar questions for 3, 4, 5. 
 
 -7. Problem 65. These ten exercises arc intended a* a eu 
 for the Subtraction Table. A method of drill should be adopted f. 
 combination*, similar to the method for those in addition given on j.:. 
 
 IVoblem lOO.-Snggcstlons nnder the last reference may bo 
 applied to drills upon the combinations given in the exercises on t 
 five pages. 
 
 /-< / /. Problem 61. Tho next nine problems are Intended as a sub- 
 stitute for the Multiplication Table. These drills should be graded in three 
 
 Ftrtt 5fcp.-0nce S 1s t, 9 times S are four, 8 times 2 are 6, 4 times I are 
 10 times 2 are X): then reversing the order, 10 times 9 are SO, times 
 2 are 18, 8 times 2 are 10, ..... once I Is S. 
 
 Bteond Stop. 3 times 1 are 2, 2 times 9 are 4, 2 times 8 are , 9 times 4 are 8, 
 and so on: 2 times 10 are 20, times 9 are 18, 2 times 8 are 16, and so on. 
 
 Third Sffp.-Oncc 2 or 2 times 1 are 2, 2 times 2 are 4, 8 times 2 or 2 times 8 
 are 6, 4 times 2 or 2 times 4 are 8, and so on : 10 times 2 or 2 times 10 are 90, 9 
 times 2 or 2 times 9 are 18, 8 times 2 or 2 times 8 arc 1C, and so on. 
 
 49. Problem S.-Lead the pupil to deduce the process of division 
 from subtract i in this problem, 1 load of a hogsheads taken from 13 
 
 hogsheads tares 9 hogsheads, 1 load more taken leaves 6 hogsheads, and so 
 on. Then he has taken 1 load, and 1 toad, and 1 load, and 1 load, or 4 loads. 
 
 ra ff r St. Problem 124. -The remaining exercises In this Section, com- 
 mendng with 119, are* a substitute fur both forms of the Division Table. 
 These drills may be graded in three stepe, as follows : 
 
 Ftrtt Step. Require the pupil to go through with each exercise separately, 
 until he makes no mistakes ; thus, Exercise H9,-2 in 2 once, 9 in 4 2 times, t 
 in 6 8 times, 2 in 8 4 times, and so on ; then, reversing the order, 2 in 20 10 
 
 <-, 2 in 10 8 times, and so on. 
 
 >e 122.-* of 2 Is 1, v of 4 is 2, , of 6 Is 8, i of 8 is 4, and so on ; and i of 
 20 is 10, ft of 18 is 9, t of 16 Is 8, and so on. 
 
 Second Sttp. Rcqnirc the pupil to change divisor and quotient with each 
 
 vi-,- no. -2 In 2 once, 2 in 4 2 times, 2 In 8 times and 8 
 
 In 6 2 times, S In 8 4 times and 4 in 8 2 times, and so on ; 2 in 20 10 times and 
 
 10 in 20 2 times, 2 in 18 9 times and 9 in 18 2 times, 2 in 16 8 times and 8 in 
 
 16 2 times, and so on. 
 
 Exercise 122, i of 2 Is 1, * of 4 is 2, ft of 6 is 8 and } of 6 Is 1 ft of 8 is 
 4 and J of 8 is 2, * of 10 is 5 and J of 10 is 2. and so on ; | of 80 is 10 and ,', of 
 20 is 2, i of 18 is 9 and I of 18 is 2, ft of 16 is 8, and } of 16 is 2, and so on. 
 
 Third Step. Combine the exercises that contain the same results, as Exer- 
 cises 119 and 122. 120 and 123, and so on.-and recite them as fellows-taking 
 Exercises 120 and 123 for exampl : ce. \ of 3 is 1 ; 3 in 6 2 times and 
 
 2 in 6 3 times, i of 6 is 2 and i of 6 is 3; 3 in 9 3 times, J of 9 i - 
 times and 1 in ' of IS is 4 and i of 12 is 8 ; 3 in 15 5 times and 5 in 
 
 i:> 3 times ' of 15 i 5 and J of 15 is 8; and so on ; then in reverse order. 8 in 
 30 10 times and 10 in 80 3 times, \ of 30 is 10 and A of 30 is 3; 3 in 27 9 times 
 and 9 in 27 3 times, i of 27 is 9 and J of 27 is 8: and so on. 
 
MANUAL. 173 
 
 Par/f- S3. Problems 15, 16. It is good practice fo require pupils to draw 
 diagrams for use,'iu solving problems like these two; also, to require them to 
 solve problems in as many different ways as possible. 
 
 Pnf/f .7.7. Problem 44. Require pupils to recite the factors of all the 
 composite numbers in order, to 100 inclusive. See Factor Table, First 
 Lessons in Numbers, page 107. 
 
 I'itf/c ,7<';. Problem CO. The drill upon each of these 5 sets of exercises 
 should be in two steps. 
 
 /\'/vtf Step. Lei the pupilo recite each exercise, thus 5 is of 2 times 5 or 
 10, 5 is i of 3 times 5 or 13, 5 is J of 4 times 5 or 20, and so on ; then reversing 
 the order, 5 in ^ of 10 times 5 or 50, 5 is J of 9 times 5 or 45, 5 is J of 8 times 
 5 or 40, and so on. 
 
 Second Step. 5 is J of 10, 5 Is % of 15, 5 is J of 20, and so on ; and then, 5 is 
 ^ of 50, 5 is J of 45, 5 id of 40, and so on. 
 
 Pago 56. Problem 80. Pupils should complete this book to this place, 
 before commencing the study of the Common School Arithmetic. From this 
 place the same subjects in the two books should bo studied in connection. 
 
 Pttfjr f>.">. Problem 18. Give pupils considerable practice in separating 
 given dividends into parts which are exact multiples of the given divisors. 
 Thus 81 -*- 7, 84 = 70 + 14 ; 56 + 4, 5C = 40 + 10 ; 90 -*- G, 96 = CO + 30. 
 
 Pntjo 84. Liquid Measure. Every school-house should be supplied with 
 the following weights and measures, to be used by the pupils while learning 
 the tables of Compound Numbers : a liquid pint, a quart, and a gallon measure 
 of tin ; a dry quart, i peck, peck, and i bushel measure of wood, and a bushel 
 br.sket ; a foot-rule divided into inches, a yard-stick, and a tape measure or 
 string at least 1 rod long; a cubic inch, and a cubic-foot, of wood or paste- 
 board ; a balance or a pair of pastry scales with 1 oz., 2 oz., 4 oz., 8 oz., 1 lb., 
 2 lb., and 4 lb. weights (or if the scales and weights can not be had, sacks of 
 eand or shot of these several weights distinctly marked). 
 
 J'ftr/c 94. Time. Children have an imperfect appreciation of the three 
 smallest denominations of time. It will be found a good exercise to require 
 them, first in concert, then singly, to beat and audibly count seconds, first 10 
 seconds, then 20, then 30 or i minute. After thin, require them to count 
 silently I minute, then a minute, and to raise hands when they are through, 
 the exact time being noted by the time-piece. Again, all the school may be 
 required to eit still 1 minute, then 2, 3, 4, and 5 minutes successively. 
 
 Page 96. Problems 100, 107. Give several problems like these two, show- 
 ing that the length of the day, i. <?., from sunrise to sunset, is equal to double 
 the time of the sun's setting; and the length of the night, f.c., from sunset 
 to sunrise, is equal to double the time of the sun's rising. 
 
 Page 139 Problems 16, 17, 18 illustrate the manner in which the conditions 
 of a problem may be eo varied as to form several problems. Each of the prob- 
 lems In Sections I. and II. should be varied in a similar manner by the class. 
 
 J'df/c. 14 1. Problem 1. These problems in Reductions maybe made to af- 
 ford double practice, by requiring pupils to form and solve the converse of each. 
 
 Page 144. Problem 3. In Percentage, require pupils to give the per cent, 
 first in hundredths, and then in a common fraction reduced to its lowest terms. 
 
 Pfigc 158. Problem 3-1. Require pupila to form and eolvc the converse 
 of each of these problems. 
 
/'</'/'' 11. 1- (1.) There are 5 boys in the group ; because 8 
 boys and 2 boys are 5 boys. Or, 
 
 There are in the group 8 boys and 2 boys, which are 5 boys. 
 2. 1 tree and 2 trees are 3 trees. 
 
 Page 12. 82. (1.) He shot 12 birds; because pigeons and 
 quails are birds, and 10 birds and 2 birds, are 12 birds. or. 
 (2.) Since pigeons and quails are birds, he shot 10 birds and 2 
 
 which are 12 birds. 
 
 !'"</<* 22. 1. We can see two largo windows; because 1 
 window from 3 windows leaves 2 windows. 
 
 5. (1.) 2 are girls ; because 2 children, the boys, from 
 rhil.lrm h-iivo 2 children, the girls. 
 (2.) 4 children leas 2 children, the boys, are 2 child r 
 
 Page 23. 1L (1.) He has 5 doves ; because 2 doves from 7 
 doves leave 5 doves. Or, 
 
 (2.) He has 7 doves less 2 doves, which are 5 doves. 
 
 I'iff/e 26. 46. 7 and 4 more arc 11 ; because 7 from 11 leaves 4 
 
 Pd(/< :> !>. r. 54-9 is the greater ; because 54-9=45, and 
 49-6=43, and 45 is greater than 43. 
 
 Page 35. 1. (1.) He expended 16 cents; because 5 cents, 4 
 cents, and 7 cents are 16 cents. Or, 
 
 lie expended 5 cents, 4 cents, and 7 cents, which are 16 
 cents. Or, 
 
 (8.) He expended the sum of 5 cents, 4 cents, and 7 cents, 
 which is 16 rents. 
 
 1 .) He has given away 5 peaches and 4 peaches, which are 
 9 peaches ; and he has left 9 peaches less 9 peaches, which are 
 peaches. Or, 
 
 (2.) From the 9 peaches, he gave 5 to Adah, which loft him 4 
 peaches, Then from the 4 peaches, he gave 4 to Juliet, which 
 leaves him peache*. 
 
METHODS. 175 
 
 Page 35. 12. When the tide rises 7 feet, the rock will be 7 
 feet and 7 feet; or 14 feet, under water ; and afterward, when it 
 falls 9 feet, the rock will be 14 feet less 9 feet, or 5 feet, under water. 
 
 Page 38. 16. (1.) They will cost $16 ; because 2 times $8 
 are $16. Or, 
 
 (2.) They will cost 2 times $8, which are $16. 
 
 Page 42. 5. (1.) You can buy. 4 peaches ; because 2 cents 
 are contained in 8 cents 4 times. Or, 
 
 (2.) Since the number of times 2 cents are contained in 8 cents 
 equals the number of peaches, and 2 cents are contained in 8 
 cents 4 times, you can buy 4 peaches. 
 
 Page 43. 22. (1.) There will be 4 cows ; because \ of 8 
 cows is 4 cows. Or, 
 
 (2.) In each pasture there will be \ of 8 cows, which is 4 cows. 
 
 Page 52. 2. In 4 weeks the father earns 4 times $9, or 
 $36 ; in 1 week the son earns $4 ; and both earn in all $36 and 
 $4, which are $40. 
 
 Page 53. 9. He sold the 4 melons for 4 times 9 cents, or 36 
 cents ; and the slate cost him 36 cents less 6 cents, which are 30 
 cents. 
 
 Page 54. 32. It will take 9 times as many men to dig the 
 ditch in 1 day as to dig it in 9 days, and 9 times 3 men are 27 
 men. 
 
 41. 4 times 9 are 36, and 36 is 6 times 6. 
 
 Page 55. 55. 2 times 10 are 20, and of 20 is 4. 
 
 Page 50. 71. The three barrels cost the sum of $7, $9, and 
 $11, which is $27 ; and the average price is ^ of $27, which is $9. 
 
 Page 57. 1. The cost of both is the sum of $10 and $30, 
 which' is $40. 
 
 Page 58. S. I paid for both the sum of 30 cents and 14 
 cents. 14 cents are 10 cents + 4 cents. 30 cents and 10 cents 
 are 40 cents, and 40 cents and 4 cents are 44 cents. Hence, I paid 
 44 cents for both. 
 
 17. Both cost him the sum of 21 cents and 18 cents. 21 cents 
 and 10 cents are 31 cents, and 31 cents and 8 cents are SO cents. 
 Hence, both cost him 39 cents. 
 
 rage 59. L He paid the difference between $30 and $10, 
 which ia $20. 
 
I',') METHOD . 
 
 (51. 77. There was left the difference 1 
 yards and 15 yards. 10 yards from 39 yards leave 29 yards, and 
 5 yards from 29 yards leave 24 yards. Hence, 24 yards wi 
 in the j 
 
 I '<!!/< <'> 9. . 4 shawls will cost 4 times as much as 1 I 
 and 4 times $30 are $120. 
 
 : pounds will cost 3 times as much as 1 pound 3 times 20 
 cents are 60 cents, 8 times 8 cents are 9 cents, and GO cents + 9 
 cents are 09 cents. Hence, 8 pounds will cost 69 cents. 
 
 yv/f/r *;:;. r.ir 4 bales of imjr* 1 \\\\\^ . ist be 
 
 paid as for 1 bale. 4 times $40 are $160, 4 times $4 arc *1G, and 
 $160 + $16 are $176. Hence, $176 must be paid for 4 bales. 
 /'</'/' />' /. l ; -ml will cost i as much as 4 yards, m 
 80 cents is 20 cents. 
 
 yv/r/r f>'.7. //. The daily average was ^ of the nun 
 , thrrsh.nl in :J days, that is, i of 48 bushels. 48 1. 
 are 30 bushels + 18 bushels. } of 30 bushels is 10 bushels, \ of 
 18 bushels is 6 bushels, and 10 bushels + 6 bushels an 
 
 . tli,- daily :iv.-rage was 16 bushels. 
 
 15. The number of times 9 loaves are contained in 108 loaves 
 equals the number of weeks. 9 loaves are contained in 90 loaves 
 
 -3, in 18 loaves 2 times, and 10 times and 2 t 
 times. Hence, 108 loaves will last them 12 weeks. 
 
 /X'/' rr. 
 
 10 mills arc contained in S? mills equals the 11111; ;its, and 
 
 tin- remainder equals the number of mills. 87 mills are 80 mills 
 
 M-atest part that will contain 10 mills) and 7 mills 
 maimler). 10 mills are contained in 80 mills 8 times. 
 mills are 8 cents 7 mills. 
 
 yv/r/r ;.<>. li pave the. sum of $1.50, $.88, and $1.25. 
 $1.50 and $.88 are $2.88 ; $2.88 and $1 are $8.88, and $3.88 and 
 $.25 are $3.63. Hence, he gave $3.63 for all. 
 
 ile had left the difl $5.84 and $1.56. $1 
 
 from $5.84 leaves $184, and $.50 from $4.84 leave $4.28. ' 
 he had $4.2S Irft. 
 
 I'ttf/e SO. 1~>. In 6 days he will earn 6 times as :.. 
 1 day! timrs 
 $4.50; and $6 + $i.50 arc $10.50. Hence, he will earn $10.50. 
 
METHODS. 177 
 
 Page 80, 20. 1 yard will cost as much as 5 yards. $1.85 
 are $1.50 + $.35. i of $1.50 is $.30, of $.35 is $.07, and $.30 + 
 $.07 are $.37. Hence, 1 yard will cost $.37. 
 
 The number of times $.08 are contained in $2.24 equals the 
 number of pounds. $2.24 are $1.60 + $.64. $.08 are contained 
 in $1.60, 20 times, in $.64, 8 times, and 20 times + 8 times are 28 
 times. Hence, 23 pounds can be bought. 
 
 Page 84. 2. 7 qt. are 7 times as many pints as 1 qt., and 7 
 times 2 pt. are 14 pt. 14 pt. are 14 times as many gills as Ipt., 
 and 14 times 4 gi. are 56 gi. Hence, 7 qt. are 56 gi. 
 
 4. In as many days as there are gills in 4 gal. 1 qt. 1 pt. 3 gi. 
 4 gal. are 4 times 4 qt,, or 16 qt., and 16 qt. + 1 qt. are 17 qt. 17 
 qt. are 17 times 2 pt., or 34 pt., and 34 pt. + 1 pt. are 35 pt. 35 pt. 
 are 35 times 4 gi., or 140 gi., and 140 gi. + 3 gi. are 143 gi. Hence, 
 she would use 4 gal. 1 qt. 1 pt. 3 gi. in 143 days. 
 
 Page 85. 0. He used as many gallons as are equal to 180 
 gills. Since every 4 gi. are 1 pt., and 4 gi. are contained in 180 
 gi. 45 times, 180 gi. are 45 pt. Since every 2 pt. are 1 qt., and 2 
 pt. are contained in 45 pt. 22 times, with a remainder of 1 pt., 45 
 pt. arc 22 qt. 1 pt. Since every 4 qt. are 1 gal., and 4 qt. are con- 
 tained in 22 qt. 5 times, with a remainder of 2 qt., 22 qt. are 5 
 gal. 2 qt., and 22 qt. 1 pt. are 5 gal. 2 qt. 1 pt Hence, he used 5 
 gal. 2 qt. 1 pt. 
 
 l*(tge 88. 30. A surface 4 ft. wide contains 4 times as many 
 square feet as a surface of the same length 1 ft. wide. A surface 
 10 ft. long and 1 ft. wide contains 10 sq. ft., and 4 times 10 sq. ft. 
 are 40 sq. ft. Hence, the black-board has 40 sq. ft. of surface. 
 
 ^?. Since every inch in width of the surface measures 10 sq. in., 
 the number of tunes 10 sq. in. are contained in 80 sq. in. equals 
 the number of inches in the width of the slate. 10 sq. in. are 
 contained in 80 sq. in. 8 times. Hence, the slate is 8 in. wide. 
 
 I*age, f)O. 5G. A block 6 in. wide contains 6 times as many 
 cubic inches as a block 1 in. wide ; a block 3 in. thick contains 3 
 times as many cubic inches as a block 1 in. thick ; and a block 
 12 in. long, 1 in. wide, and 1 in. thick, contains 12 cu. in. 6 times 
 12 cu. in. are 72 cu. in., and 3 times 72 cu. in. are 216 cu. in. 
 Hence, the block contains 216 cu. in. 
 
 <'><>. Since every foot in length, of a body 2 ft. wide and 3 ft. 
 thick, contains 6 cu. ft., the number of times 6 cu. ft. are contained 
 
 14 
 
178 METHODS. 
 
 in 72 cu. ft. equals the number of feet in the length of the box. 
 cu. ft. are contained in 72 cu. ft 12 times. I: box is 
 
 long. 
 
 !'<(</< </,S. .;. 1 1- sold the sum of 5 gal. 2 qt, 3gal. 1 qt ..ami 
 4 gal. 2 qt. 5 gal. 2 qt. + 3 gal. are 8 gal. 2 qt., 8 gal. 2 qt. + 1 qt. 
 arc 8 gal 3 qt., 8 gal. 3 qt. + 4 gaL are 12 gal. 3 qt., and 
 8 qt. + 2 qt. are 12 gal. 5 qt., or 13 gaL 1 qt. Hence, he sold 18 gal. 1 qt. 
 
 /'</</' .'/.'>. 2. He had left the difference between 12 Ib. 6 oz. 
 and 5 Ib. 8 ox. 12 Ib. 6 oz. less 5 Ib. are 7 Ib. 6 oz., an 
 6 oz. less 8 oz. are Ib. 14 oz. Hence, he hadO ll>. 1 
 
 l'<rt/c 1OO. 1. To fill 5 canisters, it will take 5 times as 
 much a.* to fill 1 canister, or 5 times 2 Ib. 8 oz. 5 times 2 Ib. arc 
 10 Ib., 5 times 8 oz. are 40 oz., or i! Ib. 8 oz.. and 10 Ib. + 2 Ib. 8 oz. 
 Ib. 8 oz. Hence, it will take 12 Ib. 8 oz. to fill 5 canisters. 
 
 l'f/r 1O1. 2. To seed 1 acre, it will take i as many oats as 
 to seed 5 acres, or fc of 13 bu. 3 pk. i of 10 bu. h 2 l.u., 3 bu. 
 8 pk. are 15 pk., } of 15 pk. are 8 pk., and 2 bu. + 3 pk. are 2 bu. 
 3 pk. Hence, it will take 2 bu. 8 pk. to seed 1 acre, 
 
 / '<{>/< / 1O. 9. 1 cu. yd. is H cu. yd., i cu. yd. Is /r c 
 and the number of times /? cu. yd. are contained in i? cu yd. 
 equals the number of thirds. -, y : cu. yd. arc contained in $ f cu. yd. 
 2 times. Hence H cu. yd. are cu. yd. 
 
 I '<i'!> 111. 14, Since the value of a fraction is not changed 
 by dividing both of its terms by the same number, we divide 
 both by the common factor 4. and obtain ? ; and since 2 and 7 are 
 prime to each other, the fraction f is in its lowest terms. 
 
 32. 1 Ib. is \\ Ib., i Ib. is i as many sixteenths as 1 Ib., and 
 $ Ib. are 5 times as many sixteenths as i Ib. i of 1 Ib. is 
 and 5 times ft Ib. are } Ib. Hence, $ Ib. are jg Ib. 
 
 I'<Kt< ll.i. ~>9. (1) Since each denominator must be a fac- 
 tor of the common denominator, sevenths and ninths can be re- 
 duced to sixty-thirds. Multiplying both terms of $ by 9 
 |$, and both terms of $ by 7 gives , v Hence, 5 and equal the 
 similar fractions, * J , an 
 
 Since (}'} \* the product of 7 and 9, sevenths and ninths can 
 be reduced to sixty-thirds. Multiplying both terms of $ bv 
 
 r<tt/< 1 14. V.'t. i ft. are 1 ft., and the numlx-r of times J ft. 
 are contained in 5 ft. equals the number of " \ ft. are 
 
 contained in f ft. 2 times, with a remainder of \ ft. Hence, J ft 
 eqnnls ^ ft. 
 
METHODS. 179 
 
 Page 115. 09. 8 is 8 times as many ninths as 1. 1 is jf, 8 
 times | are ^, and V + 1 are z^. Hence, 8 J are V- 
 
 Page 116. 15. In the two days he cut the sum of and of 
 it. f=ff.f=H> and H +*$=*! Hence, he cut fj of the meadow 
 ia the two days. 
 
 Page 118. 8. Ho had left the difference between $ and 
 $i. !*=$& $I=$A-, and $*{}-$&=$&. Hence, he had $& 
 left. 
 
 Paflre 119. 10. (1.) She is now 13 yr. less f yr. old. 13 yr. 
 =12yr. + yr, yr.-g- yr.=f yr, and 12 yr. + f yr.=12 yr. 
 Hence, she is now 12 J yr. old. Or, 
 
 (2.) She is now 13 yr. less f yr. old. 13 yr.= fi ^yr. f and fi 5 yr. 
 | yr.=V- yr., or 12J yr. Hence, etc. 
 
 He had left the difference between 1H bu. and -fa bu. 11J- 
 bu.=10 bu. + H bu. or bu. or \$ bu. |f bu. -fa bu.=W bu., or 
 bu., ard 10 bu. + $ bu.=10} bu. Hence, he had 10} bu. left. 
 
 Page 12O. 3. 6 bu. will cost G times as much as 1 bu, or 
 G times $*. 6 times $J are $ 1 6 2 -, or $2f. Hence, G bu. will cost 
 $2*. 
 
 Page 121. 24- 15 bar. will cost 15 times as much as 1 bar., 
 or 15 times $7-,V 15 times $7 are $105 ; 15 times $ -fa are $*/\f , or 
 $10i; and $105 + $10^ are $115$. Hence, 15 bar. will cost $115^. 
 
 29. \ cd. will cost { as much as 1 cd, or ^ of $5. i of $5 is 5 
 times as much as of $1. i of $1 is $K and 5 times $Jr are $|. 
 Hence, i cd. wiU cost $|. 
 
 P(7C J^^. 57. f lb. will cost 3 times i of the cost of 1 lb., 
 or 3 times $ of 60 cents, i of 60 cents is 7i cents, and 3 times 
 7J cents are 22$ cents. Hence, f lb. will cost 22^ cents. 
 
 Page 123. GS. In 2J h. a train will run 2J times as far as 
 in 1 h, or 2J times 24 mi. 2 times 24 mi. are 48 mi, J times 24 
 mi. are 18 mi., and 48 mi. + 18 mi. are 66 mi. Hence, the train 
 will run 66 mi. 
 
 80. gal. will cost 3 times as much as i gal. or 3 times 
 of $. i of $} is $i, and 3 times $ are $2-. Hence, f gal. will 
 cost $J. 
 
 Paf/e .1^4. 57. f of { yd. are 3 times as much as i of I yd. 
 * yd.=2& yd, i of ^ yd. is -fa yd, and 3 times fa yd. aro Ji yd. 
 Hence, ^ of $ yd. are Jfc yd. 
 
180 M KT II DS. 
 
 ) The number of times $| are oonta: 
 -$ V, and $| are con 
 in $ .-a Hence, 10} bushels can be bought < 
 
 timber of times $} are contained in $4 equals the 
 i usliela $} are contained in $4 i as many 
 as $1. $i is contained in $1 8 times, in $i 4 times h 
 
 s are V times, Of 
 
 I'tit/r !.;<>. (I.) The number of times $1 is cor 
 
 in $,** equals the numlx-r of gallons. $i=$ A, and 4 twelfths of 
 
 contained in 7 twelfths of a dolL 
 Hence, 1J gallons can bo bought. Or, 
 
 number of times $i ia contained inffr equ: 
 number of gallons. $1 is contained in .7 1 :: times, in $,4 i 1 * of 3 
 
 '. times. 
 and 7 tim s ; time ur.- 1 ; times. Hence, 
 
 />/'/< / " ''. The number of times 1 Ib. are con 
 
 11>. equals the number of days, llflb.r , 11> . 1 
 and .*> thirds of a pound are contained in :r tliinls 
 /- ///. ,' 5 jral. = 5 of 4qt. are Vqt-, <>r -Jj qt. : i qt.= 
 r 1 pt.; n: 1 j.t. Hence, f gal.= 
 
 ) qt. 1 i>t. 
 
 r<r<,< 1 /.;. 1 is ipk., 5 qt. are 5 pk., and 1 pk.+ 
 
 i pk.=lj pk., or V pk. 1 i i , and V P^. are J , 
 
 i bu .. or \l bu. Hence, 1 pk. 5 qt. = ^| bu. 
 rtn/f It',. .?. Since 2W are flfo ^e >ld -ftft or i of 500 
 
 . bushehi. 
 
 /V/r/r //^'. /4- 150 sheep arc iJo. or i of 450 sheep. Since 430 
 sheep are 100 , 150 sheep are i of 100*, or 83i*. 
 
 rnf/r in. "ce he gained $500 by selling I 
 
 above cost, $500 ia 252 or } of the cost, and the whole cost is 4 
 times $500, or $2,000. Or, 
 
 net, 100, the whole cost, is 100 
 I A of $->00, which is $2.000. 
 
 33. Since th<> inapl wood is worth 'JO- more than the oak, it is 
 worth $7.50 + 20?, or i of $7.50. i of $7.50 is $1 .50, and s 
 si "''i are $9. Henc--, th.> maple wood is worth $9 a cord. 
 
 1 00* + 50*. or 150 of the number 
 .iids he bought at tin- first iVtory ; and 
 9,000 Ib. are ? of 2 times ; of 9,000 Ib., which arc 6,000 Ib. ! 
 ho bought 6,000 Ib. at the first factory. 
 
TA 
 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 
Franklin Si: 
 
 i. FRENCH'S ARITHMET: 
 
 
 II. HARPER'S WRITING BOOKS. 
 
 III. HARPER'S SCHOOL AND FAMILY SLATE, 
 
 lozen.