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 AN INTRODUCTORY 
 
 ARITHMETIC 
 
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 mTRODUCTORY ARITHMETIC 
 
 BY 
 DAYID M. SE^N^SEKIG, M.S. 
 
 KOBEET F. ANDERSOJS^, A.M. 
 
 INSTRUCTORS IN MATHEMATICS, STATE NORMAL SCHOOL, 
 WEST CHESTER, PENNSYLVANIA 
 
 SILVER, BURDETT AKD COMPAlSrY 
 
 NEW YORK BOSTON CHICAGO 
 
aAio3 
 
 S4- 
 
 Ete Srngenifi'^ntiergon Series of arithmetics 
 
 By DAVID M. SENSENIG, M.S., and ROBERT F. 
 ANDERSON, A.M., Instructors in Mathematics, 
 State Normal School, "West Chester, Pennsylvania. 
 
 AN INTRODUCTORY ARITHMETIC. A first 
 book in arithmetic, inductive in method and carefully 
 graded, developing the subjects by natural steps. It 
 gives the pupil an intelligent understanding of processes 
 and abundant practice in operations. 262 pp. 
 
 ESSENTIALS OF ARITHMETIC. A compre- 
 hensive and practical book for grammar grades, giving 
 thorough instruction and drill in fundamental processes 
 and much information that is useful in business transac- 
 tions. The treatment of mensuration leads up to algebra 
 and geometry. 343 pp. 60 cents. 
 
 THE NEW COMPLETE ARITHMETIC for 
 
 High Schools, Academies, and Normal Schools. A prac- 
 tical text-book in which, besides the usual topics, special 
 attention is given to business papers, with photographic 
 reproductions of business forms, to property and life 
 assurance, and mensuration. 437 pp. 90 cents. 
 
 SILVER, BURDETT AND COMPANY 
 
 New York Boston Chicago 
 
 eOUCATION DCTf I 
 
 Copyrighi, 1903, 
 By Silver, Burdett and Company 
 
<UL 
 
 PREFACE 
 
 Iij this volume the authors assume that the pupil can 
 read easy sentences and that he has had at least one year 
 of number work. 
 
 The aim of Chapter I. is to develop easily and naturally 
 the idea of number without making use of elaborate pic- 
 tures; to provide numerous exercises, both oral and writ- 
 ten, by means of which the pupil may become proficient in 
 forming, writing, and reading numbers, and in the funda- 
 mental operations; to furnish him with such suggestions 
 and solutions as will make each step in his progress in- 
 telligible to him. 
 
 Other important features of the book are: 
 
 1. The inductive methods employed in leading the pupil 
 by logical questions to the fundamental conceptions of 
 every subject. 
 
 2. The use of simple diagrams, easily constructed by the 
 pupil himself, for purposes of illustration. 
 
 3. Carefully graded concrete problems, involving only 
 such terms as the pupil is supposed to be familiar with. 
 lu other words, the authors have endeavored to keep within 
 the field of the pupil's experience. 
 
 54 J 543 
 
iv PREFACE. 
 
 4. The separation of the process of finding one of the 
 equal parts of a number. Division, and of finding how 
 many times one number contains another as a unit of 
 measure, Mensuration. Division as usually treated in- 
 volves two cases so obviously different in their nature that 
 they ought to be considered separate processes under ap- 
 propriate names. The process of separating a number into 
 a number of equal parts to determine one of these parts is 
 properly named Division. The process of determining 
 how many times one number contains another as a unit of 
 measure, which is generally called division, is primarily 
 finding the relation which one number bears to another 
 taken as a unit of measure; this is simply measuring one 
 number by another, and is properly named Mensuration. 
 
 5. A simple treatment of Percentage, Interest, and Busi- 
 ness Forms, introduced to meet the demands of such pupils 
 as are compelled to leave school at an early age. 
 
 David M. Sensenig. 
 RoBEKT F. Anderson. 
 
CONTENTS. 
 
 CHAPTER I. 
 
 Page 
 Whole Numbers and Fractional Parts of Whole Num- 
 bers 1-143 
 
 Forming, Writing, and Reading Numbers to 10 ; Addition 
 
 and Subtraction 1 
 
 Forming, Writing, and Reading Numbers from 10 to 20 ; 
 
 Addition and Subtraction 13 
 
 Forming, Writing, and Reading Numbers from 20 to 100 ; 
 
 Addition and Subtraction 28 
 
 Forming, Writing, and Reading Numbers from 100 to 
 
 1000 ; Addition and Subtraction 36 
 
 Multiplication, Division and Mensuration 47 
 
 Forming, Writing, and Reading Numbers from 1000 to 10000 78 
 
 Roman Notation 79 
 
 United States Money 81 
 
 Making Change 83 
 
 Addition and Subtraction 84 
 
 Multiplication, Division and Mensuration 89 
 
 Forming, Writing and Reading Numbers above 10000 ; 
 
 Fundamental Operations 132 
 
 Factors 141 
 
 Divisors 143 
 
 CHAPTER II. 
 
 Fractions 144-176 
 
 Introductory Problems and Definitions 144 
 
 Reduction 147 
 
 Multiplication and Division 151 
 
 V 
 
vi CONTENTS. 
 
 Fractions — continued. Paob 
 
 Reduction 154 
 
 Addition and Subtraction 156 
 
 Multiplication 161 
 
 Division and Mensuration 168 
 
 Complex Fractions 176 
 
 CHAPTER III. 
 
 Decimals 177-201 
 
 Introductory Problems and Definitions 177 
 
 Reading and Writing Decimals 178 
 
 Reduction 182 
 
 Addition and Subtraction 185 
 
 Multiplication, Division and Mensuration 186 
 
 CHAPTER IV 
 
 Denominate Amounts . 202-240 
 
 United States Money 202 
 
 Bills and Accounts 206 
 
 Measures of Time 209 
 
 Measures of Capacity 211 
 
 Measures of Weight 213 
 
 Measures of Length 216 
 
 Measures of Surface 221 
 
 Cubic Measure 227 
 
 Rectangles 230 
 
 Carpeting 232 
 
 Lumber Measure 233 
 
 Rectangular Solids 235 
 
 Compound Denominate Amounts 237 
 
 CHAPTER V. 
 
 Percentage 241-252 
 
 Interest 247 
 
 Business Papers 249 
 
 Miscellaneous Problems 252 
 
An Introductory Arithmetic. 
 
 ^ 
 
 CHAPTER I. 
 
 WHOLE NUMBERS AND FRACTIONAL PARTS 
 OF WHOLE NUMBERS. 
 
 Forming, Writing, and Reading Numbers to 10; 
 Addition and Subtraction. 
 
 1. Oral Exercise. 
 
 How many dots are there in this square ? * I 
 
 The figure i stands for one. 
 
 How many are 1 and 1 ? ** 
 
 The figure 2 stands for two. 
 
 How many are 2 and 1 ? 1 and 2 ? 
 The figure 3 stands for three. 
 
 How many are 3 and 1 ? 1 and 3 ? 
 How many are 2 and 2 ? 
 The figure 4 stands for four. 
 
 
 • •• 
 
 
.a*. : WH;fc>i'5J.NtJ>ifiEHa and fractional parts. 
 
 IIow many are 4 and 1 ? 1 and 4 ? 
 How many are 3 and 2 ? 2 and 3 ? 
 The figure 5 stands for five. 
 
 How many are 5 and 1 ? 1 and 5 ? 
 How many are 4 and 2 ? 2 and 4 ? 
 How many are 3 and 3 ? 
 The figure 6 stands for six. 
 
 How many are 6 and 1 ? 1 and G ? 
 
 How many are 5 and 2 ? 2 and 5 ? 
 
 How many are 4 and 3 ? 3 and 4 ? 
 
 The figure 7 stands for seven. 
 
 How many are 7 and 1 ? 1 and 7 ? 
 How many are 6 and 2 ? 2 and 6 ? 
 How many are 5 and 3 ? 3 and 5 ? 
 How many are 4 and 4 ? 
 The figure 8 stands for eight. 
 
 
 • 
 • ••• 
 
 
 
 
 • • 
 • • • 
 
 
 
 
 • 
 
 
 
 
 • • 
 • ••• 
 
 
 
 
 1 ••• 
 
 
 
 
 • 
 
 
 
 •• 
 
 
 
 ••• 
 •••• 
 
 
 
 • 
 
 
 • • 
 
 
 
 • • • 
 
 
 • • • 4 
 
 • • • • 
 
NUMBERS T0^>0: 
 
 How many are 8 and 1 ? 1 and 8 ? 
 How many are 7 and 2? 2 and 7 ? 
 How many are 6 and 3 ? 3 and 6 ? 
 How many are 5 and 4 ? 4 and 5 ? 
 The figure g stands for nine. 
 
 2 pins and 2 pins are how many pins ? 
 
 • 
 
 
 • • 
 
 
 
 • • • 
 
 
 • • • 
 • • • • 
 
 • 
 • 
 
 nil 
 
 How many marbles are 3 marbles and 2 marbles ? 
 
 2 pears and 3 pears are how many pears ? 9^9 9^ 
 
 4 rings and 2 rings are how many rings ? 
 
 How many pies are 2 pies and 4 pies ? OOOO OO 
 
 How many cards are 3 cards and 3 cards ? nnri ["100 
 
 5 balls and 2 balls are how many balls ? 
 2 oranges and 5 oranges are how 
 many oranges ? 
 
 How many pencils are 4 pencils and 3 pencils ? 
 3 girls and 4 girls are how many girls ? 
 
 6 crosses and 2 crosses are how many crosses ? 
 2 poles and 6 poles are how many 
 
 poles 
 
 XXXXXX XX 
 
'4'*.:'i^Hi)Li:''i^im.i5?itS.AND fractional parts. 
 
 5 books and 3 books are how many books ? 
 
 How many letters are 3 letters and rirnririri nnn 
 o letters i 
 
 //// //// 
 
 How many fingers are 4 fingers and 4 
 fingers ? 
 
 7 stamps and 2 stamps are how many stamps ? 
 
 How many beans are 2 beans and 7 /^^^y^^^^ ^^ 
 beans? 0000000 00 
 
 6 apples and 3 apples are how many 
 
 apples P \\\\\\\\\ 
 
 How many tops are 3 tops and 6 tops ? 
 How many logs are 5 logs and 4 logs ? 
 How many beads are 4 beads and 5 beads ? |nJ I 
 
 2. The sign + stands for the word and. 
 The sign = stands for are or is. 
 
 Thus, 2 and 1 are 3 may be written 2 -\- 1 = S. 
 
 3. Oral Exercise. 
 
 Read : 
 
 1+1=2 3+1=4 4+1=5 
 1+2=3 1+3=4 1+4+5 
 2+2=4 3+2=5 5+1=6 
 
 4. Exercise. 
 
 Copy, writing the proper figures in place of the dots: 
 
ADDITION AND SUBTRACTION. 
 
 1 + 1 = • 
 
 4 + 2= . 
 
 2 + 6= . 
 
 2 + 1= • 
 
 2 + 4= « 
 
 5 + 3 = . 
 
 
 1 + 2 = 
 
 3 + 3 = 
 
 3 + 5 = 
 
 
 3 + 1= . 
 
 6 + 1 = 
 
 4 + 4 = 
 
 
 1 + 3=: 
 
 1 + 6 = 
 
 8 + 1= . 
 
 
 2 + 2 = 
 
 5 + 2 = • 
 
 1 + 8 = 
 
 
 4 + 1 = . 
 
 2 + 5 = . 
 
 7 + 2= . 
 
 
 1 + 4== 
 
 4 + 3 = . 
 
 2 + 7= « 
 
 
 3 + 2 = 
 
 3 + 4 = 
 
 6 + 3 = 
 
 
 2 + 3 = . 
 
 7 + 1= . 
 
 3 + 6 = 
 
 
 5 + 1 = 
 
 1 + 7 = 
 
 5 +4= . 
 
 
 1 + 5 = 
 
 6 + 2= . 
 
 4 + 5 = . 
 
 
 5. Oral Exercise. 
 
 Eead Exercise 4, supplying the missing numbers. 
 
 6. Exercise. 
 
 Copy, writing in each case the proper figure in place of 
 the dash : 
 
 2 men -\ men = 4 men. 
 
 3 women H women = 5 women. 
 
 2 boys H boys = 5 boys. 
 
 4 girls H girls = 6 girls. 
 
 2 horses -{ horses = 6 horses. 
 
 3 cows H cows = 6 cows. 
 
 5 mules -\ mules = 7 mules. 
 
 2 goats -\ goats = 7 goats. 
 
 4 kittens H kittens = 7 kittens. 
 
 ooooo 
 
 ^Ei^^ ^b ^^ ht^ ^b 
 
6 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 '> hens H hens = 7 hens. 
 
 6 ducks -] ducks = 8 ducks. 
 
 2 geese -\ geese = 8 geese. 
 
 5 turkeys -I turkeys = 8 turkeys. ####### 
 
 3 crows + — crows = 8 crows. 
 
 4 wrens H wrens = 8 wrens. 
 
 7 robins H — - robins = 9 robins. 
 
 2 doves H doves = 9 doves, 
 
 6 jays + — jays = 9 jays. #1 
 
 3 sparrows -I sparrows = 9 sparrows. 
 
 5 parrots H parrots = 9 parrots. 
 
 4 larks H larks = 9 larks. 
 
 7. Exercise. 
 
 Copy, writing the proper figure in place of the dots 
 
 1 + • 
 
 = 2 
 
 4 + 
 
 . = G 
 
 2 + 
 
 . =8 
 
 2+ • 
 
 = 3 
 
 2 + • 
 
 = 6 
 
 5 + 
 
 = 8 
 
 1 + • 
 
 = 3 
 
 3 + . 
 
 = G 
 
 3 + 
 
 . =8 
 
 3 + . 
 
 = 4 
 
 c + . 
 
 = 7 
 
 4 + . 
 
 = 8 
 
 1 + • 
 
 = 4 
 
 1 + • 
 
 = 7 
 
 8 + 
 
 ' = 9 
 
 2+ . 
 
 = 4 
 
 5 + . 
 
 = 7 
 
 1 + 
 
 = 9 
 
 4 + . 
 
 =^5 
 
 2 + 
 
 • = 7 
 
 7 + 
 
 . =9 
 
 1 + ' 
 
 = 5 
 
 4 + 
 
 • = 7 
 
 2 + 
 
 . =9 
 
 3 + 
 
 . =5 
 
 3 + 
 
 . = 7 
 
 G + 
 
 . =9 
 
 2 + 
 
 . =5 
 
 7 + 
 
 . =8 
 
 3 + 
 
 . =9 
 
 5 + 
 
 . =G 
 
 1 + 
 
 . =8 
 
 5 + 
 
 . =9 
 
 1 + 
 
 ► = 6 
 
 C + 
 
 . =8 
 
 4 + 
 
 . =9 
 
ADDITION AND SUBTRACTION. 
 
 8. Oral Exercise. 
 
 I Read Exercise 7, supplying the missing numbers. 
 
 9. Exercise. 
 
 Copy, writing in each case the proper figure in place of 
 the dash : 
 
 — birds + 2 birds = 4 birds. 
 
 — mice + 2 mice = 5 mice. 
 
 — rats + 3 rats = 5 rats. 
 
 — bugs + 2 bugs — 6 bugs. 
 
 — flies + 4 flies = 6 flies. 
 
 — fishes + 3 fishes = 6 fishes. 
 
 — lambs + 2 lambs = 7 lambs. 
 
 — trees + 5 trees = 7 trees. 
 
 — shrubs + 3 shrubs = 7 shrubs. 
 
 — pinks + 4 pinks = 7 pinks. 
 
 — daisies + 2 daisies = 8 daisies. 
 
 — buds 4- 6 buds = 8 buds. 
 
 — leaves + 3 leaves = 8 leaves. 
 
 — roses 4- 5 roses = 8 roses. 
 
 — violets + 4 violets = 8 violets. 
 
 — cars + 2 cars = 9 cars. 
 
 — carts + 7 carts — 9 carts. 
 
 — ships + 3 ships = 9 ships. ( 
 
 — boats + G boats = 9 boats. 
 
 — bricks 4- 4 bricks = 9 bricks. 
 
 — stones + 5 stones = 9 stones. 
 
 ooooo 
 
 iXi aSU ^b Ai wT^ i^r^ 
 
 ^r \r ^r tc t? <p 
 
 /////// 
 
8 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 10. Exercise. 
 
 Copy, writing the proper figures in place of the dots 
 
 . + 1 = 2 
 
 . + 2 = 6 
 
 . +6 = 8 
 
 . + 1 = 3 
 
 . +4 = 6 
 
 . + 3 = 8 
 
 • +2 = 3 
 
 .+3 = 6 
 
 .+5 = 8 
 
 . +1 = 4 
 
 . + 1 = 7 
 
 . +4 = 8 
 
 . +3 = 4 
 
 . + 6 = 7 
 
 .+1 = 
 
 . + 2 = 4 
 
 ► + 2 = 7 
 
 . + 8 = 9 
 
 . + 1 = 5 
 
 ► +5 = 7 
 
 .+2 = 9 
 
 . + 4 = 5 
 
 ► +3 = 7 
 
 .+7 = 9 
 
 . + 2 = 5 
 
 . +4 = 7 
 
 -r 3 = 9 
 
 . + 3 = 5 
 
 . + 1 = 8 
 
 + 6 = 9 
 
 .+1 = 6 
 
 + 7 = 8 
 
 + 4 = 9 
 
 .+5 = 6 
 
 + 2 = 8 
 
 + 5 = 9 
 
 11. Oral Exercise. 
 
 Bead Exercise 10, supplying the missing numbers. 
 
 12. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 4 nails less 2 nails are — nails. I I I I 
 
 5 grains of corn less 2 grains of corn are — grains of corn. 
 
 5 pods less 3 pods are — pods. T T T T T 
 
 6 spoons less 2 spoons are — spoons. 
 
 6 forks less 4 forks are — forks. OOOOOO 
 
 6 cups less 3 cups are — cups. 
 
 7 knives less 2 knives are — knives. 
 
 7 spoons less 5 spoons are — spoons. ^A A A A A A 
 7 fishes less 3 fishes are — fishes. 
 
ADDITION AND SUBTRACTION. 
 
 9 
 
 7 eels less 4 eels are — eels. 
 
 8 cents less 2 cents are — cents. 
 
 8 dollars less 6 dollars are — dollars. 
 
 8 cars less 3 cars are — cars. XXXXXXXX 
 
 8 carts less 5 carts are — carts. 
 
 9 cards less 2 cards are — cards. 
 
 9 spools less 7 spools are — spools. #•####### 
 9 matches less 3 matches are — matches. 
 9 brooms less 6 brooms are — brooms. 
 9 turkeys less 4 turkeys are — turkeys. 
 9 chairs less 5 chairs are — chairs. 
 
 13. The sign — stands for the word less. 
 Tims, 6 less 4 are 2 may be written 6 — Ji. = 2. 
 
 14. Oral Exercise. 
 Eead : 
 
 2-1 = 1 4-1:^3 5-1 = 4 
 
 3-1 = 2 4-2 = 2 5-2 = 3 
 
 3-2 = 1 4-3 = 1 5-3 = 2 
 
 15. Exercise. 
 
 Copy, writing the proper figures in place of the dots : 
 
 2-1 = 
 3 - 1 = 
 3-2 = 
 4-1 = 
 4-3 = 
 4-2 = 
 5 - 1 = 
 
 5-4 = 
 
 5-2 = 
 
 5 - 3 = 
 
 6 - 1 = 
 6 - 5 = 
 G - 2 = 
 6-4 = 
 
 G - 3 = 
 7-1 = 
 
 7-6 = 
 
 7-2 = 
 7 - 5 = 
 7-3 = 
 7-4 = 
 
10 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 8- 1 = . 
 
 8-5 = 
 
 9-7= . 
 
 8-7= o 
 
 8 -4= . 
 
 9-3 = . 
 
 8-2= o 
 
 9 - 1 = . 
 
 9- 6= . 
 
 8- G = . 
 
 9- 8 = 
 
 9 -4= . 
 
 8-3= • 
 
 9-2= . 
 
 9-5= . 
 
 16. Oral Exercise. 
 
 Read Exercise 15, supplying the missing numbers. 
 
 17. Oral Exercise. 
 
 How many stars are 2 stars and 2 stars ? 
 
 How many more than 2 dots are 4 dots ? 
 
 How many rings are 3 rings and 2 rings ? 
 
 How many squares must be put with 3 squares to make 5 
 
 squares ? 
 How many more than 2 blocks are 5 blocks ? 
 
 How many strokes are here ? ////// 
 
 If you take away 4 strokes, how many will be left ? 
 How many more than 2 strokes are here .^ 
 How many more than 3 strokes are here ? 
 
 Head, supplying the missing numbers : 
 
 4+-=6 G-4 = . 6-. =4 
 
 2+.=6 6-2 = . 6-. =2 
 
 3+.=6 6-3 = . r, -.=3 
 
 How many squares are here ? [__] | j LJ Lj L_ J LJ LJ 
 
 How many more than 5 squares are 7 s(]uares ? 
 How many squares must you put with two squares to 
 make 7 squares ? 
 
ADDITION AND SUBTRACTION. 1 1 
 
 If you take away 4 squares, how many will be left ? 
 How many more than 3 squares are 7 squares ? 
 Read, supplying the missing numbers : 
 
 5+-=7 7-5=. 7-. =5 
 
 2 + . =7 7-2 = . 7_ . =2 
 
 4+ . =7 7-4= . 7- . =4 
 
 3+. =7 7-3=. 7-. =3 
 
 How many rings are here ? OOOOOOOO 
 
 How many more than 6 rings are 8 rings ? 
 
 How many rings must you put with 2 rings to make 8 
 
 rings ? 
 If you take 3 rings from 8 rings, how many will be left ? 
 How many more than 3 rings are 8 rings ? 
 How many rings must you put with 4 rings to make 8 
 
 rings ? 
 
 Read, supplying the missing numbers : 
 
 6+.=8 4+.=8 8-3 = . 
 
 2+.=S 8-6=. 8-4=. 
 
 5+.=8 8-2 = . 8-. =5 
 
 3+.=8 8-5=. 8 — .=3 
 
 How many crosses are here ? XXXXXXXXX 
 
 How many more than 7 crosses are here ? 
 
 How many crosses must you put with 2 crosses to make 9 
 
 crosses ? 
 If you take 6 crosses from 9 crosses, how many will be 
 
 left? 
 How many more than 3 crosses are 9 crosses ? 
 
12 WHOLE NUMBERS AND FRACTIONAL PARTS 
 
 How many more than 5 crosses are 9 crosses ? 
 
 If 5 crosses are taken from 9 crosses, how many are left ? 
 
 Read, supplying the missing numbers : 
 
 7 + . =9 
 
 9-7 = 
 
 9- . 
 
 . =7 
 
 2+ . =9 
 
 9-2 = 
 
 9 - 
 
 . =2 
 
 6 + . =9 
 
 9-6 = 
 
 9- 
 
 . = 6 
 
 3 4- • = 9 
 
 9-3 = 
 
 9- 
 
 . =3 
 
 5 + . = 9 
 
 9-5 = 
 
 9- 
 
 . = 5 
 
 4+ . =9 
 
 9-4= . 
 
 9 - . 
 
 = 4 
 
 Forming, Writing, and Reading Numbers from 10 
 to 20; Addition and Subtraction. 
 
 18. Oral Exercise. 
 
 How many are 9 and 1 ? 
 Ten ones make a ten. 
 Ten is written 10. 
 
 How many are 10 and 1 ? 
 Eleven is written 11. 
 
 How many are 10 and 2 ? 
 Twelve is written 12. 
 
 How many are 10 and 3 ? 
 Thirteen is written 13. 
 
 How 111 any are 10 and 4 ? 
 Fourteen is written 14. 
 
NUMBERS FROM 10 TO 20. 
 
 13 
 
 How many are 10 and 5 ? 
 Fifteen is written 15. 
 
 How many are 10 and 6 ? 
 Sixteen is written 16. 
 
 How many are 10 and 7 ? 
 Seventeen is written 17. 
 
 How many are 10 and 8 ? 
 Eighteen is written 18. 
 
 How many are 10 and 9 ? 
 Nineteen is written 19. 
 
 19. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 2 beans and 8 beans are — beans. 
 
 4 pears and 6 pears are — pears. 
 
 3 cherries and 8 cherries are — cherries. 
 
 5 berries and 5 berries are — berries. 
 
 4 lemons and 7 lemons are — lemons. 
 
 5 figs and 6 figs are — figs. 
 
 3 pies and 7 pies are — pies. 
 
 2 apples and 9 apples are — apples. 
 5 grapes and 7 grapes are — grapes. 
 
 4 plums and 8 plums are — plums. 
 
 5 rings and 8 rings are — rings. 
 
 6 pens and 6 pens are — pens. 
 
14 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 3 cakes and 9 cakes are — cakes. 
 
 6 rolls and 8 rolls are — rolls. 
 
 5 hawks and 9 hawks are — hawks. 
 
 7 crabs and 8 crabs are — crabs. 
 
 4 rails and 9 rails are — rails. 
 
 6 posts and 7 posts are — posts. 
 
 8 boards and 9 boards are — boards. 
 
 6 screws and 9 screws are — screws. 
 
 7 saws and 7 saws are — saws. 
 
 8 houses and 8 houses are — houses. 
 7 cans and 9 cans are — cans. 
 
 9 strings and 9 strings are — strings. 
 9 caps and 10 caps are — caps. 
 
 20. Exercise. 
 
 Copy, writing the proper figures in place of the dots 
 
 9 + 1 = 
 
 6 + 4 = 
 
 8 + 3 = 
 
 9 + 3 = 
 
 6 + 6 = 
 
 7 + = 
 7 + 7 = 
 9 + 7 = 
 9 + 9 = 
 
 8 + 2 = 
 5 + 5 = 
 
 7 + 4 = 
 
 8 + 4 = 
 
 9 + 4 = 
 9 + 5 = 
 9 + 6 = 
 8 + 8 = 
 
 10 + 8 = 
 
 7 + 3 = 
 9 + 2 = 
 
 6 + 5 = 
 
 7 + 5 = 
 
 8 + 5 = 
 8 + 6 = 
 
 8 + 7 = 
 
 9 + 8 = 
 10 + 9 = 
 
 21. Oral Exercise. 
 
 Read Exercise 20, supplying the missing numbers. 
 
ADDITION AND SUBTRACTION. 
 
 15 
 
 22. Oral Exercise. 
 
 1 star and how many stars are 10 stars ? 
 
 5 buttons and how many buttons are 10 
 buttons ? 
 
 2 mugs and how many mugs are 10 mugs ? 
 4 boxes and how many boxes are 10 boxes ? 
 
 3 dimes and how many dimes are 10 dimes ? 
 
 10 
 
 2 bricks and how many bricks are 11 
 bricks ? n 
 
 5 ribbons and how many ribbons are 11 ribbons ? 
 
 3 tacks and how many tacks are 11 tacks ? 
 
 4 tubs and how many tubs are 11 tubs ? 
 
 3 ropes and how many ropes are 12 
 ropes ? 
 
 6 caps and how many caps are 12 caps ? 
 
 4 rugs and how many rugs are 12 rugs ? 
 
 5 lamps and how many lamps are 12 lamps ? 
 
 • •••• 
 
 • • 
 
 12 
 
 4 globes and how many globes are 13 , •©••• 
 
 globes ? ' — 
 
 • •« 
 
 6 maps and how many maps are 13 maps ? 
 5 slates and how many slates are 13 slates ? 
 
 13 
 
 • •••• 
 
 • •••• 
 
 14 
 
 5 pencils and how many pencils are 
 14 pencils ? 
 
 7 crayons and how many crayons are 14 crayons ? 
 
 6 chains and how many chains are 14 chains ? 
 
 • ••• 
 
16 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 6 blocks and how many blocks 
 are 15 blocks ? 
 
 7 buttons and how many buttons 
 are 15 buttons ? 
 
 15 
 
 • •••• 
 
 • •••• 
 
 16 
 
 7 hooks and how many hooks are 
 
 16 hooks ? 
 
 8 papers and liow many papers are 16 papers ? 
 
 8 plants and how many plants are ••••• •• 
 
 17 plants ? 
 
 ••••• 
 
 17 
 
 9 acorns and how many acorns are 
 18 acorns ? 
 
 10 chestnuts and how many chest- 
 nuts are 18 chestnuts ? 
 
 10 walnuts and how many walnuts 
 are 19 walnuts ? 
 
 • •••• 
 
 • •••• 
 
 • •• 
 
 • •••• 
 
 18 
 
 • •••• 
 
 • •••• 
 
 • ••• 
 
 19 
 
 23. Exercise. 
 
 Copy, writing the proper figures in place of dots 
 
 9 4- 
 
 • = 10 
 
 9 + • 
 
 = 12 
 
 8 + . = 14 
 
 5 + . 
 
 ► = 10 
 
 G + . 
 
 = 12 
 
 9 + • = 15 
 
 8+ . 
 
 . = 10 
 
 8 + . 
 
 = 12 
 
 8 + • = 15 
 
 6 + « 
 
 . =10 
 
 7 -f • 
 
 = 12 
 
 9 + . = 16 
 
 7 + 
 
 . = 10 
 
 + . 
 
 = 13 
 
 8 + • = 16 
 
 9 + 
 
 . = 11 
 
 7 + . 
 
 = 13 
 
 9 + . = 17 
 
 6 + 
 
 . = 11 
 
 8 + . 
 
 = 13 
 
 9 + . = 18 
 
 8 + 
 
 ► = 11 
 
 9 + • 
 
 = 14 
 
 8 + • = 18 
 
 7 + • 
 
 ► = 11 
 
 7+ . 
 
 = 14 
 
 9 + . = 19 
 
ADDITION. 17 
 
 24. Oral Exercise. 
 
 Read Exercise 23, supplying the missing numbers. 
 
 25. Oral Exercise. 
 
 flow many melons and 5 melons are , 
 
 10 melons ? ^0 
 
 How many lemons and 2 lemons are 10 lemons ? 
 How many shrubs and 4 shrubs are 10 shrubs ? 
 How many baskets and 3 baskets are 10 baskets ? 
 
 How many dots and 2 dots are 11 dots ? [»#»»»»#♦»» 
 How many trees and 5 trees are 11 11 
 
 trees ? 
 How many ducks and 4 ducks are 11 ducks? 
 How many geese and 3 geese are 11 geese ? 
 
 How many bears and 3 bears are 12 #• 
 
 bears ? • 
 
 12 
 
 How many camels and G camels are 12 camels ? 
 
 How many monkeys and 4 monkeys are 12 monkeys ? 
 How many lions and 5 lions are 12 lions ? 
 
 • •0 
 
 How many deer and 4 deer are 13 
 
 deer? | ••••••••*>1 
 
 How many goats and 6 goats are 13 goats ? 
 How many rabbits and 5 rabbits are 13 rabbits ? 
 
 How many owls and 7 owls are 14 i ##^#####«0 i 
 
 owls ? 14 
 
 llow many bats and 5 bats are 14 bats ? 
 How many minks and G minks are 14 minks ? 
 
18 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 How many flags and 6 flags are 15 
 flags ? 
 
 15 
 
 IIow many hoops and 8 hoops are 15 hoops ? 
 
 How many wheels and 8 wheels arc 
 10 wheels ? 
 
 16 
 
 How many spokes and 7 spokes are IG spokes ? 
 
 How many trout and 8 trout are 17 | — 
 
 trout ? 
 How many frogs and 7 frogs are 17 frogs 
 
 17 
 
 How many shingles and 8 shingles r— - 
 
 are 18 shingles ? 
 How many nails and 9 nails are 18 nails ? 
 
 How many wheels and 9 wheels are i 
 
 18 
 
 19 wheels ? 
 
 19 
 
 26. Exercise. 
 
 Copy, writing the proper figures in place of dots : 
 
 . + 9 = 10 
 
 ► + 9 = 12 
 
 . + 8 = 14 
 
 . + 5 = 10 
 
 . + 6 = 12 
 
 . + 9 = 15 
 
 . + 8 = 10 
 
 + 8=12 
 
 . + 8 = 15 
 
 . + 6 = 10 
 
 + 7 = 12 
 
 + 9 = 16 
 
 . + 7 = 10 
 
 + 9 = 13 
 
 + 8= 16 
 
 . + 9 = 11 
 
 + 7 = 13 
 
 • + 9 = 17 
 
 . + 6 = 11 
 
 + 8 = 13 
 
 + 9 = 18 
 
 . +8 = 11 
 
 . + 9 = 14 
 
 + 10 = 18 
 
 . + 7 = 11 
 
 + 7 = 14 
 
 + 9 = 19 
 
SUBTRACTION. 
 
 19 
 
 27. Oral Exercise. 
 
 Bead Exercise 26, supplying tlie missing numbers. 
 
 28. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 10 horses less 1 horse are — horses. 
 10 cows less 6 cows are — cows. 
 10 calves less 8 calves are — calves. 
 10 mules less 2 mules are — mules. 
 10 sheep less 7 sheep are — sheep. 
 10 goats less 4 goats are — goats. 
 10 pigs less 9 pigs are — pigs. 
 10 birds less 5 birds are — birds. 
 
 10 geese less 3 geese are — geese. 
 
 11 ducks less 2 ducks are — ducks. 
 11 carts less 5 carts are — carts. 
 11 coats less 8 coats are — coats. 
 11 vests less 3 vests are — vests. 
 11 hats less 6 hats are — hats. 
 11 caps less 4 caps are — caps. 
 11 collars less 7 collars are — collars. 
 
 11 buttons less 9 buttons are — buttons, 
 
 12 pins less 3 pins are — pins. 
 12 needles less 6 needles are — needles. 
 12 skates less 8 skates are — skates. 
 12 plows less 5 plows are — plows. 
 12 wheels less 4 wheels are — wheels. 
 12 rings less 7 rings are — rings. 
 12 cuffs less 9 cuffs are — cuffs. 
 
 • •••• 
 
 • •••• 
 
 • • 
 
20 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 13 matches less 4 matches are — matches. 
 13 lamps less 6 lamps are — lamps. 
 13 cars less 8 cars are — cars. 
 13 boys less 5 boys are — boys. 
 13 girls less 7 girls are — girls. 
 
 13 women less 9 women are — women 
 
 14 dogs less 5 dogs are — dogs. 
 14 cats less 8 cats are — cats. 
 14 mice less 6 mice are — mice. 
 14 birds less 9 birds are — birds. 
 
 14 flowers less 7 flowers are — flowers, 
 
 15 houses less 6 houses are — houses. 
 
 15 boards less 8 boards are — boards. 
 
 15 shingles less 9 shingles are — shingles. 
 
 15 bricks less 7 bricks are — bricks. 
 
 16 slates less 7 slates are — slates. 
 16 pencils less 9 pencils are — pencils. 
 
 16 buds less 8 buds are — buds. 
 
 17 twigs less 8 twigs are — twigs. 
 
 17 trees less 9 trees are — trees. 
 
 18 shrubs less 9 shrubs are — shrubs. 
 
 • •••• 
 
 • •••• 
 
 • •• 
 
 • •••• 
 
 • •••• 
 
 • •••• 
 
 • •••• 
 
 • •••• 
 
 • •••• 
 
 • •• 
 
 ••• 
 
 • •••• 
 
 • •••• 
 
 • •• 
 
 • ••• 
 
 29. Exercise. 
 
 Copy, writing the proper figures in place of dots : 
 
 10 - 1 = . 10 - 7 = • 11 - 9 = 
 
 10-9=- 10-4=. 11-3 = 
 
 10-2=. 10-6=. 11-8 = 
 
 10-8=. 10-5=. 11-4 = 
 
 10-3=. 11-2=. 11-7 = 
 

 ADDITION 
 
 
 21 
 
 11-5 = 
 
 13 - 9 = 
 
 15 - 6 = • 
 
 
 11 - 6 = < 
 
 13 - 5 = 
 
 15 - 9 = « 
 
 
 12-3= ^ 
 
 13 - 8 = < 
 
 15 - 7 = . 
 
 
 12 - 9 = . 
 
 13 - 6 = . 
 
 15 - 8 = ' 
 
 
 12-4= . 
 
 13 - 7 = 
 
 16 — 7= . 
 
 
 12 - 8 = . 
 
 14 - 5 = . 
 
 16 - 9 = « 
 
 
 12 - 5 = . 
 
 14 - 9 = 
 
 16 - 8 = . 
 
 
 12-7= . 
 
 14 - 6 = . 
 
 17-8= . 
 
 
 12-6 = 
 
 14 - 8 = « 
 
 17-9= . 
 
 
 13 - 4 = . 
 
 14 - 7 = • 
 
 18 - 9 = . 
 
 
 30. Oral Exercise. 
 
 Eead Exercise 29, supplying the missing numbers. 
 
 31. If we count 3 to 4, we have 7. 
 Counting 3 to 4 is called adding 3 to 4. 
 
 32. Oral Exercise. 
 
 2 4 13 
 
 9 
 
 To each of the numbers above the line: 
 
 /. Add 1. Thus, 2 and 1 are 3, 4 and 1 are 5, and so on. 
 
 2. Add 2. 4. Add 4. 6. Add 6. 8. Add 8. 
 
 3. Add 3. 5. Add 5. 7. Add 7. 9. Add 9. 
 
 33. Oral Exercise. 
 
 To the teacher. — Teach Roman notation to XIX. Teach United 
 States coin to one dollar. 
 
 /. Charles had 2 goldfish and his uncle gave him 3 
 more ; how many had he then ? 
 
22 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 2. Sara found 3 eggs in one nest and 4 in another ; how 
 many did she find in all ? 
 
 3. Mr. Rice has 2 sons and 4 daughters ; how many 
 children has he ? 
 
 4. A farmer had 4 sheep and bought 5 more ; how 
 many had he then ? 
 
 5. James is 2 years older than Mary ; if Mary is 6 
 years old, how old is James ? 
 
 6. How many lambs had a farmer at first, if he had 5 
 left after selling 6 ? 
 
 7. Jane spelled 6 words correctly and missed 4 ; how 
 many was she given to spell ? 
 
 8. How many horses has a man, if he keeps 3 to drive 
 and 6 to work ? 
 
 9. Harry has walked 4 miles toward home and has 7 
 miles yet to go ; how far from home was he when he 
 started ? 
 
 10. How many animals did a blacksmith shoe to-day, if 
 he shod 7 horses and 5 mules ? 
 
 //. How many boys were there at first in a class, if 7 re- 
 mained after 3 were promoted ? 
 
 12. How many policemen must be on duty so that when 
 4 go home 8 remain ? 
 
 10 cents make 1 dime. 
 
 13. 1 cent and how many cents make a dime ? 
 
 14. A dime is how much more than a 5-cent piece ? 
 
 15. A dime and a cent make how much ? 
 
 16. A dime and a 5-cent piece make how much ? 
 
ADDITION AND SUBTRACTION. 23 
 
 17. A dime, a cent, and a 5-cent piece make how 
 much ? 
 
 18. A dime is worth how many 5-cent pieces ? 
 
 19. A cent and a 5-cent piece are together worth how 
 much less than a dime ? 
 
 34. Exercise. 
 
 To the teacher. — Let the pupil solve problems in Exercises orally 
 when possible. 
 
 /. There are 3 persons in a boat that will carry 8 per- 
 sons ; how many more may get in ? 
 
 2. I found 6 eggs ; how many more must I get to have 
 
 12 ? 
 
 7 days mahe 1 week. 
 
 3. Name the days of the week. 
 
 4. Name the first day of the week ; the third ; the 
 second ; the fourth ; the sixth ; the fifth ; the seventh. 
 
 5. Last week father worked 4 days ; how many days 
 was he idle ? 
 
 6. A man owns 6 horses ; how many more must he buy 
 to have 14 ? 
 
 7. Samuel has spent 2 days with his cousin ; how long 
 has he yet to stay, if his visit is to last a week ? 
 
 8. Mother put up 17 cans of fruit to-day ; 8 of them 
 were pears and the others peaches ; how many were 
 peaches ? 
 
 9. I had to write 16 words ; I have written 7 of them ; 
 how many have I yet to write ? 
 
24 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 10. My uncle wishes to have 12 cows ; he now has 5 ; 
 how many more must he get ? 
 
 11. K boy paid 10 cents for a loaf of bread and a pound 
 of sugar. If the sugar cost 6 cents, what did the loaf of 
 bread cost ? 
 
 12. How many days of the week are left after Wednes- 
 day has passed ? 
 
 35. If we take 3 from 7, we have 4. 
 
 Taking 3 from 7 is called subtracting 3 from 7. 
 
 36. Oral Exercise. 
 
 Subtract : 
 /. 2 from 
 
 2 4 3 O 9 5 8 10 7 11 
 
 Thus, 2 from 2 leaves 0, 2 from 4 leaves 2, and so on, 
 
 2. 3 from 
 
 3 6 4 9 5 8 12 lO 7 11 
 
 3. 4 from 
 
 7 5 6 4 12 8 11 9 13 10 
 
 4. 5 from 
 
 8 5 O 12 14 11 9 13 lO 7 
 
 6. 6 from 
 
 8 10 6 9 12 7 14 11 13 15 
 
 6. 7 from 
 
 8 lO 9 7 12 14 11 16 13 15 
 
 7. 8 from 
 
 10 12 14 16 8 9 11 13 16 17 
 
 8. 9 from 
 
 11 13 9 12 16 10 14 17 15 18 
 
ADDITION AND SUBTRACTION. 25 
 
 37. Oral Exercise. 
 
 /. Mary saw 8 stars, but a cloud now covers 3 of them ; 
 how many can she still see ? 
 
 2. There were 7 houses in a row, but a fire burned 3 of 
 them ; how many were then left ? 
 
 3. A gardener planted 9 trees, but 4 of them died ; how 
 many lived ? 
 
 4. A farmer had 11 colts, but sold 5 of them ; how 
 many had he left ? 
 
 5. 9 boys were examined ; if 5 of them failed, how 
 many passed ? 
 
 6. Amos had 10 problems to solve ; if he has solved 3, 
 how many has he yet to solve ? 
 
 7. There were 12 women in a parlor, but 4 of them 
 went away ; how many remained ? 
 
 8. A woman bought 12 eggs, and cooked 6 of them for 
 supper ; how many had she left ? 
 
 12 is called a dozen (doz.). 
 
 9. A man bought a dozen oranges and ate 3 of them ; 
 how many had he left ? 
 
 10. A lady bought a dozen ears of corn and cooked 8 of 
 them for dinner ; how many had she left ? 
 
 //. James planted 15 ferns, but only 9 of them lived ; 
 how many died ? 
 
 12. A boy had 10 firecrackers and shot off 6 of them ; 
 how many had he then left ? 
 
26 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 33. Oral Exercise. 
 
 /. A farmer had 9 lambs ; if he sold all but 2, how 
 many did he sell ? 
 
 2. A newsboy bought 15 morning papers and sold all 
 but 6 ; how many did he sell ? 
 
 3. Jessie bought a pound of sugar and gave the store- 
 keeper 10 cents. He gave her 4 cents change ; how much 
 did he charge for the sugar ? 
 
 4. There are 4 collars left in a box that had contained 
 a dozen ; how many were taken out ? 
 
 5. 14 persons came into the dining room for dinner ; 
 there is room for only 9 ; how many must wait ? 
 
 6. Frank has 6 cents left out of 14 cents that his father 
 gave him ; he spent the rest for a tablet ; how much did 
 it cost ? 
 
 7. Chester had 13 marbles, but he lost all but 4 ; how 
 many did he lose ^ 
 
 8. How many shad did a man sell, if he had a dozen 
 and sold all but 3 ? 
 
 9. Last spring I planted 12 shade trees ; they all died 
 but 4 ; how many died ? 
 
 10. K boy had 11 pigeons and sold all but 4 ; how many 
 did he sell ? 
 
 //. Frank had a dozen plums ; he kept 4 for his sister 
 and ate the others ; how many did lie eat ? 
 
 12. I have 5 cents yet to get in order to have 14 cents ; 
 how much money have I ? 
 
ADDITION AND SUBTRACTION. 27 
 
 39. Oral Exercise. 
 
 /. 6 pupils are absent from a class and 9 are present ; 
 how many belong to this class ? 
 
 2. A man was sent to prison 5 years ago and he has yet 
 7, years to serve ; how many years must he serve in all ? 
 
 3. There were 12 knives on a table, but only 9 forks ; 
 how many more knives than forks were there ? 
 
 4. A farmer had 8 sheep left after selling 7 ; how many 
 had he at first ? 
 
 5. There were 16 tramps in a workhouse, but 7 of them 
 were set free ; how many were held ? 
 
 6. How many girls were in a class at first, if 7 remained 
 after 6 were promoted ? 
 
 7. How many cents must I put in my money bank to 
 have 14 cents in it, if it already contains 9 cents ? 
 
 8. I have put 4 cans of corn into a box that will hold 
 a dozen cans ; how many more will it hold ? 
 
 9. There are 14 sheep and lambs in a field ; how many 
 of them are lambs, if there are 6 sheep ? 
 
 10. How many men must my father hire to have 14, if 
 he already has 7 ? 
 
 //. After a fire had burned 8 stores in a block, there 
 were 9 left ; how many were there before the fire ? 
 
 12. A girl bought a pound of sugar for 6 cents and re- 
 ceived 4 cents change ; how much money did she give the 
 grocer ? 
 
28 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 Forming, Writing, and Reading Numbers from 20 
 to lOO; Addition and Subtraction. 
 
 40. Two tens make twenty , written 20. 
 
 Twenty 
 
 Two tens and one make twenty-one, written 21. 
 
 Twenty-one 
 
 Two tens and two make tiventy-two, written 22. 
 
 Twenty-two 
 
 Two tens and three make twenty-three, writ- 
 ten 23. 
 
 ij 
 
 Twenty-three 
 
 1!" 
 
 Twenty and four make twenty-four, written 24. 
 
 Twenty-four 
 
 Twenty and five make twenty -five, written 25. 
 
 Twenty-five 
 
 Twenty and six make twenty-six, written 26/ 
 
 Twenty and seven make tiventy-seven, 
 written 27. 
 
 Twenty-six 
 
 TTll 
 
 Twenty-seven 
 
NUMBERS FROM 20 TO 100. 
 
 29 
 
 Twenty and eight make twenty -eight, 
 
 written 28. ^ ^ 
 
 Twenty-eight 
 
 Twenty and nine make twenty -nine, ffll ffl 1 1 1 1 j 1 1 
 
 written 29. li 11 1 I I 1 1 1 J 
 
 Twenty-nine 
 
 41. Oral Exercise. 
 
 Beginning at 1, count to 29. 
 
 Read these numbers : 20, 21, 22, 23, 24, 25, 26, 27, 28, 29. 
 
 Tell the number of tens and ones in each of the above 
 
 numbers. 
 How many ones are there in 2 tens and 4 ? 2 tens and 6 ? 
 
 Three Tens 
 
 42. Three tens make thirty, written 30. 
 
 Three tens and one make thirty-one, writ- 
 ten 31. 
 
 43. Oral Exercise. 
 
 Three tens and two make what number ? 
 Three tens and three make what number ? 
 Three tens and four make what number ? 
 Three tens and five make what number ? 
 Three tens and six make what number ? 
 Three tens and seven make what number ? 
 Three tens and eight make what number ? 
 Three tens and nine make what number ? 
 
 Thirty-one 
 
30 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 Beginning at 30, count to 30. 
 
 Read these numbers : 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. 
 
 Tell the number of tens and ones in each of the above 
 
 numbers. 
 How many ones are there in 3 tens and 1 ? 3 tens and 6 ? 
 
 Four Teng 
 1?^ 
 
 44. Four tens imxkQ forty, written 40. 
 
 -1 
 i 
 
 Forty 
 
 45. Oral Exercise. 
 
 Four tens and one make what number ? 
 
 Beginning at forty, name the numbers that are formed 
 by forty and one ; forty and two ; forty and three ; forty 
 and four ; forty and five ; forty and six ; forty and seven; 
 forty and eight ; forty and nine. 
 
 Read : 40, 41, 42, 43, 44, 45, 46, 47, 48, 49. 
 
 Beginning at forty, count to forty-nine. 
 46. Five tens make Jifii/, written 50. 
 
 Six tens make sixty, written 60. 
 
 Seven tens make seventy, written 70. 
 
 Eight tens make eighty, writ- 
 ten 80. 
 
 Five Tens 
 
 itj 
 
 ui 
 
 Fifty 
 Six Tena 
 
 Eighty 
 
NUMBERS FROM 20 TO 100. 
 
 31 
 
 Nine Tens 
 
 Nine tens make ninety, written 
 90. 
 
 Ninety 
 
 Ten Tens 
 
 Ten tens combined make one hundred, 
 written 100. 
 
 One Hundred 
 
 47. Oral Exercise. 
 
 /. Name the numbers from fifty to sixty. 
 
 2. Name the numbers from sixty to seventy. 
 
 3. Name the numbers from seventy to eighty. 
 
 4. Name the numbers from eighty to ninety. 
 
 5. Name the numbers from ninety to one hundred. 
 
 6. Pvead : 50, 51, 52, 53, 54, 55, 56, 57, 58, 59. 
 
 7. Read : 60, 61, 62, 63, 64, 65, 66, 67, 68, 69. 
 
 8. Read : 70, 71, 72, 73, 74, 75, 76, 77, 78, 79. 
 
 9. Real! : 80, 81, 82, 83, 84, 85, 86, 87, 88, 89. 
 10. Read : 90, 91, 92, 93, 94, 95, 96, 97, 98, 99. 
 
 48. Exercise. 
 
 Write in fiofures the numbers : 
 
 /. From one to ten. 
 
 2. From ten to twenty. 
 
 3. From twenty to thirty. 
 
 4. From thirty to forty. 
 
 5. From forty to fifty. 
 
 6. From fifty to sixty. 
 
 7. From sixty to seventy. 
 
 8. From seventy to eighty. 
 
 9. From eighty to ninety. 
 10. From ninety to one hun- 
 dred. 
 
5. 
 
 32 
 
 9. 
 
 51 
 
 13. 
 
 44 
 
 17. 
 
 72 
 
 21. 91 
 
 6. 
 
 34 
 
 10. 
 
 57 
 
 14. 
 
 46 
 
 18. 
 
 70 
 
 22. 19 
 
 7. 
 
 36 
 
 11. 
 
 20 
 
 15. 
 
 64 
 
 19. 
 
 15 
 
 23. 92 
 
 8. 
 
 39 
 
 12. 
 
 33 
 
 16. 
 
 69 
 
 20. 
 
 88 
 
 24. 87 
 
 32 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 49. Oral Exercise. 
 
 Read : 
 /. 22 
 2. 25 
 5. 28 
 4. 30 
 
 50. Oral Exercise. 
 
 /. Count from 10 to 20. 
 
 2. Count backwards from 20 to 10. 
 
 3. Count from 20 to 30. 
 
 4. Count backwards from 30 to 20. 
 
 5. Count from 30 to. 40. 
 
 6. Count backwards from 50 to 40. 
 
 7. Count from 50 to 60. 
 
 8. Count backwards from 70 to 60. 
 
 9. Count from 70 to 80. 
 
 10. Count backwards from 90 to 80. 
 
 51. In numbers of two figures, the right-hand 
 figure is called the Units' figure, and the left-hand 
 figure the Tens' figure. 
 
 52. Oral Exercise. 
 
 /. In 87 name the tens' figure ; the units' figure. 
 
 2. In 63 how many tens are there, and how many 
 units ? 
 
 3. In 90 how many tens are there, and how many units ? 
 
 4. How many figures are needed to write a number 
 mailc uj) of 3 tens and 2 units ? 
 
ADDITION AND SUBTRACTION. 33 
 
 5. Name the number made up of 6 tens and 2 units. 
 
 6. What is the largest number that can be written with 
 one figure ? With two figures ? 
 
 7. What two numbers can be written with the figures 
 8 and 9 ? 
 
 To the teacher. Teach Roman notation to C. See p. 79. 
 
 53. Oral Exercise. 
 
 /. Add each of the numbers 2, 5, 3, 6, 4, 7, 9, 8, 10 to 
 
 10 20 30 40 50 60 70 80 90 
 
 Name results only. Thus, 12, 15, 13, and so on ; then 22, 25, 
 23, and so on ; etc. 
 
 2. Add each of the numbers 2, 5, 3, 6, 4, 8, 7 to 
 
 11 21 31 41 51 61 71 81 91 
 
 3. Add each of the numbers 2, 5, 3, 6, 4, 7 to 
 
 12 22 32 42 52 62 72 82 92 
 
 4. Add each of the numbers 2, 5, 3, G, 4 to 
 
 13 23 33 43 53 63 73 83 93 
 
 5. Add each of the numbers 2, 5, 4, 3 to 
 
 14 24 34 44 54 64 74 84 V\ 
 
 6. Add each of the numbers 2, 4, 3 to 
 
 15 25 35 45 5^ 65 75 85 95 
 
 7. Add each of the numbers 3 and 2 to 
 
 16 26 36 46 56 66 76 86 96 
 
 8. Add 2 to 
 
 17 27 37 47 57 67 77 87 97 
 
 8 
 
34 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 64. Oral Exercise. 
 
 Note. The sign ? denotes how many? 
 
 /. 74.3_|_4_5=? Answer thus : 7, 10, 14, 0. 
 
 2. 3+4 + 2=? 7. 5 + 4 + G + 3=? 
 
 3. 7+5 + 6=? 8. 7 + 4 + 3-5=? 
 
 4. 2 + 5-1 = ? 9. 9-4 + 6-7=? 
 
 5. 14 - 9 + 7 = ? /(?. 14 - 9 + 8 - 6 = ? 
 ff. 18 - 9 - 4 = ? //. 18 - 9 - 3 - 4 = ? 
 
 55. Exercise. 
 
 /. I bought a tablet for 4 cents, a pencil for 5 cents, 
 and a sponge for 6 cents ; how much did I pay for all ? 
 
 2. There are 4 chairs at each side of a table and 1 at 
 each end ; how many are there in all ? 
 
 3. A bicycle, a cart, and a wagon have, in all, how 
 many wheels ? 
 
 4. From a box of 1 dozen collars I sold 6 to one man 
 and 3 to another ; how many remain ? 
 
 5. A man owed 12 dollars. lie paid 4 dollars at one 
 time and 3 dollars at another ; how much does he still owe ? 
 
 6. A boy added three numbers, and the answer was 10. 
 If two of the numbers were 3 and 5, what was the third ? 
 
 7. 2 sheep, 4 cows, 2 horses, and 2 mules make how 
 many head of stock ? 
 
 8. A laborer had 5 dollars left of his month's wages 
 after paying 4 dollars house rent and 9 dollars store bill ; 
 what were his wages ? 
 
 9. Out of a dozen eggs mother used 2 for breakfast, 4 
 for dinner, and 4 for supper ; liow many were left ? 
 
ADDITION AND SUBTRACTION. 35 
 
 10. 6 women, 5 girls, 3 men, and 2 boys are how many 
 persons ? 
 
 //.I have 4 brothers and 3 sisters ; how many children 
 are there in our family ? 
 
 12. Mother sent me to the store for a 5-cent spool of 
 thread, a 4-cent loaf of bread, and a 2-cent box of matches. 
 How much change should I bring back to her out of a 
 dime and a 5-cent piece ? 
 
 66. Oral Exercise. 
 
 /. Add each of the numbers 2, 5, 3, 6, 4, 8, 7, 9 to 
 19 29 39 49 59 69 79 89 
 
 Name results only. Thus, 31, 24, 23, and so on ; then 31, 34, 
 33, and so on ; etc. 
 
 2. Add each of the numbers 2, 5, 3, 0, 4, 8, 7, 9 to 
 18 38 58 28 48 68 88 78 
 
 3. Add each of the numbers 5, 3, 6, 4, 8, 7, 9 to 
 17 37 57 27 47 67 87 77 
 
 4. Add each of the numbers 5, 8, 6, 9, 7, 4 to 
 
 16 36 56 26 46 . 66 86 76 
 
 5. Add each of the numbers 5, 8, G, 7, 9 to 
 
 15 35 55 25 45 65 85 75 
 
 6. Add each of the numbers G, 8, 7, 9 to 
 
 14 34 54 24 44 64 84 74 
 
 7. Add each of the numbers 8, 7, 9 to 
 
 13 33 53 23 43 63 83 73 
 
 8. Add each of the numbers 8 and 9 to 
 
 12 32 52 22 42 62 82 72 
 
 9. Add 9 to 
 
 11 31 51 21 41 61 81 71 
 
36 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 Forming, Writing, and Reading Numbers from 1 GO 
 to lOOO; Addition and Subtraction. 
 
 57. Two hundred is written 200 ; three hundred, 
 300 ; nine hundred, 900. 
 
 58. One hundred and one make one hundred one, 
 written 101. 
 
 One hundred and two make one hundred two, 
 
 written 102. 
 One hundred and ten make one hundred ten, 
 
 written 110. 
 Two hundred and forty make two hundred forty, 
 
 written 240. 
 Six hundred and seventy-two make six hundred 
 
 seventy-two, written 672. 
 Nine hundred and ninety-nine make nine hundred 
 
 ninety-nine, written 999. 
 
 59. In numbers of three figures the first from the 
 right is called the Units' figure, the second the Tens* 
 figure, and the third the Hundreds* figure. 
 
 60. Exercise. 
 Write in figures : 
 
 /. Four hundred ; seven hundred. 
 2. Five liundred ; eight hundred. 
 5. Six hundred ; nine hundred. 
 
 4. One hundred three ; one liundred eleven. 
 
 5. Two liundred twenty ; three hundred ninety-nine. 
 
 6. Four hundred four ; five hundred sixty-eight. 
 
NUMBERS FROM 100 TO 1000. 
 
 37 
 
 7. Six hundred sixteen ; seven hundred seventy-seven. 
 
 8. Nine hundred ninety-nine ; four hundred forty-four. 
 
 61. Oral Exercise. 
 
 
 
 
 
 
 
 Read : 
 
 
 
 
 
 
 
 
 /. 103. 
 
 8. 213. 
 
 15. 
 
 900. 
 
 22. 
 
 527. 
 
 29. 
 
 149. 
 
 2. 112. 
 
 9. 400. 
 
 16. 
 
 901. 
 
 23. 
 
 752. 
 
 30. 
 
 222. 
 
 3. 126. 
 
 10. 407. 
 
 17. 
 
 910. 
 
 24. 
 
 257. 
 
 31. 
 
 806. 
 
 4. 129. 
 
 //. 510. 
 
 18. 
 
 888. 
 
 25. 
 
 600. 
 
 32. 
 
 419. 
 
 5. 131. 
 
 12. 111. 
 
 19. 
 
 808. 
 
 26. 
 
 999. 
 
 33. 
 
 344. 
 
 6. 209. 
 
 13. 222. 
 
 20. 
 
 919. 
 
 27. 
 
 909. 
 
 34. 
 
 707. 
 
 7. 211. 
 
 /4. 876. 
 
 21. 
 
 764. 
 
 28. 
 
 526. 
 
 35. 
 
 818. 
 
 62. Oral Exercise. 
 
 /. Count from 100 to 110. 
 
 2. Count from 330 to 340. 
 
 3. Count from 489 to 500. 
 
 4. Count from 789 to 911. 
 
 63. Oral Exercise. 
 
 /. In 765 how many units ? 
 hundreds ? 
 
 2. In 860 how many units ? 
 
 hundreds ? 
 
 3. In 409 how many units ? 
 
 hundreds ? 
 
 5. Count backwards from 
 
 210 to 200. 
 
 6. Count backwards from 
 
 370 to 360. 
 
 7. Count backwards from 
 
 910 to 890. 
 
 8. Count backwards from 
 
 701 to 689. 
 
 how many tens ? how many 
 how many tens ? how many 
 how many tens ? how many 
 
38 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 4. llow iiijuiy figuroK iiiu; ii(3(3dod to write u number made 
 
 14) of 3 hundreds, 2 tens, and 5 units ? 
 
 5. How many figures are needed to write a number made 
 
 up of 4 hundreds and 2 tens ? 
 
 6. How many figures are needed to write a number made 
 
 up of 2 hundreds and 3 units ? 
 
 7. Name tlie number made up of 2 hundreds and 2 tens. 
 
 8. What is the largest number that can be written with 
 
 three figures ? What is the smallest ? 
 To the teacher. — Teach Roman notation to M. See p. 79. 
 
 64. The process of taking two or more numbers 
 together is Addition. 
 
 65. The answer in addition is called the Sum. 
 
 66. Add 427 and 532. 
 
 2 units and 7 units are 9 units. 
 
 427 
 
 3 tens and 2 tens are 5 tens. 
 
 - — 5 hundreds and 4 hundreds are 9 hundreds. 
 Sum 959 „ 
 
 The sum is 9o9. 
 
 Tn practice^ say 2 and 7 are 9 ; S and 2 are 5 ; 5 and ^ are 9. 
 
 67. Exercise. 
 Copy and add : 
 
 /. 28 3. 43 5. 50 7. 25 
 
 JU 36^ 32 43 
 
 21 
 
 2. 52 4. 05 6. 43 8. 10 
 
 ^ 34 j^ 52 
 
 31 
 
ADDITION AND SUBTRACTION. 39 
 
 9. 80 
 
 13. 235 
 
 17. 222 
 
 21. 222 
 
 11 
 
 723 
 
 333 
 
 333 
 
 7 
 
 
 
 444 
 
 10. 53 
 
 14. 327 
 
 18. 423 
 
 22. 708 
 
 23 
 
 652 
 
 322 
 
 260 
 
 13 
 
 
 
 31 
 
 //. 42 
 
 15. 326 
 
 /5. 321 
 
 23. 421 
 
 35 
 
 362 
 
 432 
 
 243 
 
 22 
 
 
 146 
 
 324 
 
 12. 14 
 
 /ff. 342 
 
 20. 321 
 
 24. 423 
 
 32 
 
 635 
 
 372 
 
 332 
 
 23 
 
 
 305 
 
 143 
 
 68. The process of taking one number from another 
 is Subtraction. 
 
 69. The answer in subtraction is called the Differ- 
 ence. 
 
 70. Subtract 252 from 594. 
 
 2 units from 4 units leaves 2 units. 
 Minuend 594 5 tens from 9 tens leaves 4 tens. 
 Subtrahend 252 2 hundreds from 5 hundreds leaves 3 hun- 
 
 Difference 342 ^reds. 
 
 The difference is 342. 
 
 In practice, say 2 from 4 haves 2 ; 5 from 9 leaves J^ ; 2 from 5 
 leaves 3. 
 
40 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 71. Exercise. 
 
 
 
 
 Copy and subtract : 
 
 
 
 /. 57 
 
 7. 38 
 
 13. 456 
 
 19. 704 
 
 23 
 
 17 
 
 234 
 
 203 
 
 2. 8G 
 
 8. 26 
 
 U. 397 
 
 20. 420 
 
 52 
 
 4 
 
 175 
 
 310 
 
 3. 65 
 
 9. 48 
 
 /5. 658 
 
 21. 517 
 
 32 
 
 33 
 
 423 
 
 306 
 
 4. 79 
 
 10. 99 
 
 16. 965 
 
 22. 427 
 
 _45 
 
 66 
 
 532 
 
 120 
 
 5. 59 
 
 //. 87 
 
 n. 878 
 
 25. 575 
 
 16 
 
 75 
 
 532 
 
 475 
 
 6. 97 
 
 12. 74 
 
 /S. 757 
 
 24. 379 
 
 6 
 
 33 
 
 243 
 
 375 
 
 72. Add 76 and 38. 
 
 8 units and 6 units are 14 units, or 1 ten and 4 units. 
 76 Write 4 in units* place and add 1 to the tens. 1 ten, 
 38 3 tens, and 7 tens are 11 tens, or 1 hundred and 1 
 
 114 ten. Write 1 in tens' place and 1 in hundreds' place. 
 
 The sum is 114. 
 In 'practice, say 8 and 6 are 14; 1, 3 and 7 are 11. 
 
 73 Exercise. 
 
 
 
 
 Copy and add : 
 
 
 
 
 /. 43 
 
 2. 53 
 
 3. 78 
 
 4. 73 
 
 48 
 
 27 
 
 51 
 
 36 
 
ADDITION AND SUBTRACTION. 41 
 
 5. 48 
 
 /3. 89 
 
 2/. 82 
 
 29. 93 
 
 85 
 
 97 
 
 20 
 
 27 
 
 
 
 19 
 
 34 
 
 
 
 
 55 
 
 6. 79 
 
 14. 98 
 
 22. 58 
 
 30. 75 
 
 66 
 
 43 
 
 67 
 
 89 
 
 
 
 38 
 
 32 
 
 
 
 
 56 
 
 7. 37 
 
 /5. 39 
 
 23. 27 
 
 31. 185 
 
 87 
 
 93 
 
 96 
 
 237 
 
 
 
 14 
 
 
 8. 54 
 
 16. 37 
 
 24. 89 
 
 52. 476 
 
 98 
 
 99 
 
 9 
 
 238 
 
 
 
 17 
 
 
 9. 76 
 
 17. 54 
 
 25. 37 
 
 35. 567 
 
 59 
 
 77 
 
 29 
 
 196 
 
 
 
 41 
 23 
 
 
 10. 27 
 
 /5. 87 
 
 26. 17 
 
 34. 438 
 
 98 
 
 16 
 
 29 
 
 299 
 
 
 
 51 
 93 
 
 
 //. 89 
 
 19. 48 
 
 27. 99 
 
 35. 347 
 
 7 
 
 37 
 
 9 
 
 468 
 
 
 55 
 
 83 
 
 
 
 
 20 
 
 
 f2. 58 
 
 20. 98 
 
 28. 54 
 
 36. 298 
 
 ^ 
 
 32 
 
 35 
 
 386 
 
 
 29 
 
 27 
 
 
 
 
 58 
 
 
42 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 37. 275 
 
 40. 74 
 
 43. 127 
 
 46. 175 
 
 378 
 
 186 
 
 346 
 428 
 
 319 
 416 
 
 38. G54 
 
 41. 237 
 
 44. 486 
 
 47. 209 
 
 196 
 
 179 
 
 201 
 
 127 
 
 
 
 302 
 
 348 
 
 39. 289 
 
 42. 37 
 
 45. 174 
 
 45. 498 
 
 69 
 
 864 
 
 297 
 
 126 
 
 
 
 488 
 
 299 
 
 74. Subtract 37 from 65. 
 
 7 units cannot be taken from 5 units. Take 1 ten 
 
 from the G tens, leaving 5 tens. Add this 1 ten, 
 Mm. 65 . , . . ^ . ^ . 
 
 o 1. oi*y or 10 units, to 5 units, making 15 units. 7 units 
 
 ^.^ — from 15 units leaves 8 units. 8 tens from 5 tens 
 Diff. 28 
 
 leaves 2 tens. 
 
 The difference is 28. 
 In practice, say 7 from 15 leaves 8; 3 from 5 leaves 2. 
 
 76. Exercise. 
 
 Copy and subtract : 
 
 
 
 /. 37 
 
 5. 56 
 
 9. 70 
 
 13. 27 
 
 19 
 
 89 
 
 18 
 
 18 
 
 2. 42 
 
 6. 74 
 
 10. 62 
 
 14. 43 
 
 29 
 
 36 
 
 9 
 
 19 
 
 3. 45 
 
 7. 40 
 
 //. 53 
 
 n. 67 
 
 26 
 
 29 
 
 18 
 
 19 
 
 4. 81 
 
 8. 91 
 
 12. 61 
 
 16. 46 
 
 38 
 
 82 
 
 14 
 
 4 
 
ADDITION AND SUBTRACTION. 43 
 
 17. 52 
 
 23. 34 
 
 29. 
 
 70 
 
 35. 436 
 
 28 
 
 15 
 
 
 27 
 
 187 
 
 18. 70 
 
 24. 90 
 
 30. 
 
 52 
 
 36. 491 
 
 36 
 
 44 
 
 
 36 
 
 238 
 
 19. 32 
 
 25. 21 
 
 31. 
 
 186 
 
 37. 572 
 
 27 
 
 9 
 
 
 28 
 
 387 
 
 20. 50 
 
 2^. 41 
 
 32. 
 
 192 
 
 38. 500 
 
 41 
 
 29 
 
 
 49 
 
 283 
 
 21. 93 
 
 27. 56 
 
 33. 
 
 228 
 
 39. 406 
 
 84 
 
 17 
 
 
 182 
 
 308 
 
 22. 77 
 
 28. 92 
 
 34. 
 
 374 
 
 40. 702 
 
 58 
 
 13 
 
 
 182 
 
 184 
 
 76. Exercise. 
 
 Find the missing numbers : 
 
 /. 8+9+6:rro 3. 2 + 3+ 4 = 
 
 16 + 32 4- 27 = o 20 + 30 4- 40 = 
 24 + 41 + 44 = . 200 + 300 + 400 = 
 
 + • = 
 
 2 4- 3 4- 4 
 
 4. Add down ; subtract across. 
 
 2. 11 4- 27 + 38 = . . 186 - 27 = • 
 
 9 4- 18 4- 60 = . 220 - 185 = . 
 
 36 4- 7 4- 8 =^ 407 - 200 =^ 
 
 • 4~ •4" • -— • • — • — — • 
 
44 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 77. Exercise. 
 
 /. There are 30 days in June, 31 days in July, and 31 
 days in August. How many days are there in these 3 
 months ? 
 
 30 is the number of days in June. 
 
 31 " " *' " " " July. 
 31 '* " ** " '' '' August. 
 
 T " '' ** *' " " the 3 months. 
 
 2. A drover sold in one day 36 cows, 42 hogs, and 21 
 sheep ; how many head of stock did he sell ? 
 
 5. A woman sold a dealer 28 pounds of poultry, 16 
 pounds of butter, and 36 pounds of lard ; how many 
 pounds of produce did she sell ? 
 
 4. A laborer worked 26 days in January, 23 days in 
 February, and 25 days in March ; how many days did he 
 work during these months ? 
 
 5. I spent at a grocer's to-day 36 cents for coffee, 24 cents 
 for sugar, and 78 cents for meat ; how much did I spend 
 in all ? 
 
 Note. Ct. stands for cent or cents. 
 
 36 ct. was the amount spent for coffee. 
 24 ct. " '* '* " " sugar. 
 
 78 ct. " '' " " " meat. 
 
 ? '' '' '' " " all. 
 
 e. A clerk had $25 of liis month's salary left nftor pay- 
 ing a $20 store bill and $16 for house rent ; wliul was liis 
 month's salary ? 
 
ADDITION AND SUBTRACTION. 45 
 
 7. After 28 yards were sold from a piece of bunting, 
 there remained 32 yards ; how many yards were there in 
 the piece at first ? 
 
 8. A farmer had 36 bushels of wheat and used 19 
 bushels of it for seed ; how many bushels had he left ? 
 
 36 is the number of bushels the fanner had. 
 19 " *' " " " he used for seed. 
 T '' " " " '' " had left. 
 
 9. A girl invited 40 of her friends to a picnic, but 12 
 of them failed to come ; how many came ? 
 
 10. There are 88 houses on a certain street ; if 28 of 
 them are on one side of the street, how many are on the 
 other side ? 
 
 If. A huckster had 80 shad ; if he sold all of them but 
 18, how many did he sell ? 
 
 12. A field of 68 acres was divided into two parts ; if 
 the first part has in it 49 acres, what is the size of the 
 second part ? 
 
 68 acres is the size of tlie field divided, 
 
 49 " " " " " " first part. 
 ? " '' " " " " second part. 
 
 13. How much older is my father than I am, if his age 
 is 70 years and mine 24 years ? 
 
 14. I sold 32 yards from a piece of cheese cloth contain- 
 ing 60 yards ; how much remained ? 
 
 15. A dealer bought 3 pieces of printed lawn containing 
 50 yards, 15 yards, and 36 yards ; how much did he buy 
 in all ? 
 
46 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 16. K flagpole 86 feet long had 37 feet broken from the 
 top ; how long was the piece that was left standing ? 
 
 17. A. contractor has employed 2G Italians, 14 Hun- 
 garians, and 22 Polanders ; how many laborers has he 
 employed ? 
 
 18. A boy had 18 papers left after selling 24 morning 
 papers and 21 evening papers ; how many had he to 
 begin with ? 
 
 19. 52 girls were given a problem ; if 19 of them had 
 the wrong answer, how* many solved the problem cor- 
 rectly ? 
 
 20. A drover sold a horse for 95 dollars ; after he had 
 paid a debt of 27 dollars out of this sum, how much had 
 he left ? I 
 
 21. K boy weighed 101 pounds and has since gained 19 
 pounds ; how much does he now weigh ? 
 
 22. There were 28 men, 7G women, 62 boys and 78 
 girls at a Sunday-school picnic ; how many persons were 
 there ? 
 
 23. There are 68 apple trees in an orchard and 18 more 
 pear trees than apple trees ; how many trees are there 
 of both kinds ? 
 
 24. A man's wages are 42 dollars a month and his son's 
 18 dollars less ; how mucli do both earn in a month ? 
 
 25. A drover had 264 sheep and bought 187 more ; how 
 many had he then ? 
 
 26. Find the sum of three hundred fifty, two hundred ' 
 twenty-five, and one hundred eighty. 
 
MULTIPLICATION, DIVISION, MENSURATION. 47 
 
 27. A has 275 dollars and B 189 dollars ; how much 
 would each have if A were to give B 186 dollars ? 
 
 28. I owed 278 dollars, but paid him 129 dollars ; 
 how much do I still owe him ? 
 
 29. A miller had 736 bushels of wheat but sold 478 
 bushels of it, and later bought 127 bushels ; how many 
 bushels had he then ? 
 
 30. Add six hundred eighty-nine and two hundred six- 
 teen, and take four hundred four from the sum. 
 
 Multiplication, Division, and Mensuration. 
 
 78. Oral ExercisCo 
 
 Count by 2's : 
 
 /. From 2 to 20 ; from 20 to 2. 
 Thus, 2, 4, 6, etc. ; then 20, 18, 16, etc. 
 2. From 1 to 21 ; from 21 to 1. 
 
 Count by 3's : 
 
 5. From 3 to 30 ; from 30 to 3. 
 
 4. From 1 to 31 ; from 31 to 1. 
 
 5. From 2 to 32 ; from 32 to 2. 
 
 79. Oral Exercise. 
 
 How many are 1 and 1 ? 
 
 1 and 1 are how many times 1? #+• = •• 
 
 How many are 2 times 1 ? 
 
 What are the two parts of 2 ? 
 
48 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 What are the two parts of 3? •# + • = ••• 
 
 llow many are 2 and 2 ? 
 
 2 and 2 are how many times 2? ••-{-•# = ###• 
 
 JIow many are 2 times 2 ? 
 
 What are the two parts of 4 here shown ? 
 
 Are these parts alike ? 
 
 When the parts of a number are alike they are said to 
 he equal. 
 
 Wliat is one of the two equal parts of 2? •• = #-4-# 
 
 How many ones are there in 2 ? 
 
 What is one of the two equal •••• = ##-f-## 
 
 parts of 4 ? 
 How many twos (2's) are there in 4 ? 
 How many are 2 times 3 ? 
 
 • • • 
 What is one of the two equal parts of 6 ? • • • 
 
 Each of the ttvo equal parts of a 7iumber is called one 
 half of it. 
 
 One half is written •}. 
 
 What is one half of 6 ? 
 
 llow many 3's are there in 6 ? 
 
 llow many are 2 times 4 ? • • • • 
 
 AVhat is one half of 8 ?• • • • # 
 
 How many 4's are there in 8 ? 
 
 How many are 2 times 5 ? • • • • • 
 
 What is i of 10 ? • # • • • 
 
 How many 5's are there in 10 ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 49 
 
 ;Io\v many are 2 times 6? •••••• 
 
 What is i of 12 ? •••••• 
 
 g_ How many 6^s are there in 12 ? 
 
 How many are 2 times 7? ••••••• 
 
 What is ^ of 14 ? ••••••• 
 
 How many 7's are there in 14 ? 
 
 How many are 2 times 8? •••••••• 
 
 What is i of 16? •••••••• 
 
 How many 8's are there is 10 ? 
 
 How many are 2 times 9? ••••••••• 
 
 What is i of 18? ••••••••• 
 
 , How many 9's are there in 18 ? 
 
 80. Oral Exercise. 
 
 How many are 3 times 1 .'' 
 i What is one of the tliree equal parts of 3 ? 
 
 Bach of the three equal parts of a fiumber is called 
 I one third of it. 
 
 One third is written ■^. 
 
 [ What is i of 3 ? 
 
 How many I's are there in 3 ? 
 
 How many are 3 times 2 ? • • 
 
 What is i of 6 ? J J 
 
 How many 2's are there in 6 ? 
 4 
 
60 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 IIow many are 3 times 3 ? • • • 
 
 What is i of ? • • • 
 
 How many 3's are there in 9 ? 
 
 How many are 3 times 4 ? • • • • 
 
 What is i of 12 ? * • • • • 
 
 # • • • 
 How many 4's are there in 12 ? 
 
 How many are 3 times 5 ? 
 
 What is i of 15 ? 
 
 How many 5's are there in 15 ? 
 
 How many are 3 times G ? 
 
 What is i of 18 ? 
 
 How many G's are there in 18 ? 
 
 How many are 3 times 7 ? 
 
 What is ^ of 21 ? 
 
 How many 7's are tliere in 21 ? 
 
 How many are 3 times 8 ? 
 
 What is i of 24 ? 
 
 How many 8's are there in 24 ? 
 
 How many are 3 times 9 ? 
 
 What is 4 of 27 ? 
 
 How many 9'8 are there in 27 ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 51 
 
 81. The sign x is read times. 
 
 82. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 1 + 1 = 
 2x1 = 
 
 2 + 2 = 
 2x2 = 
 
 3 + 3 = 
 2x3 = 
 
 4 + 4 = 
 2x4 = 
 
 5 + 5 = 
 2x5 = 
 G + G - 
 2 x G = 
 
 7 + 7 
 2x7 
 
 8 + 8 
 2x8 
 
 9 + 9 
 2x9 
 
 83. Exercise. 
 
 Copy, supplying the missing numbers, and learn 
 
 2x1 = 
 2x2 = 
 2x3 = 
 
 TABLE. 
 
 2x4 = 
 2x5 = 
 2 X G = 
 
 2x7 = 
 2x8 = 
 2x9 = 
 
 84. Exercise. 
 
 Copy, supplying the missing numbers 
 
 2x1+1= 
 
 2x4 + 4 = 
 
 2x7 + 7= . 
 
 3x1 = 
 
 3x4=. 
 
 3x7=. 
 
 2x2+2= 
 
 2x5 + 5= « 
 
 2x8 + 8= . 
 
 3x2 = 
 
 3x5 = 
 
 3x8=. 
 
 2x3 + 3= . 
 
 2 X G + 6 = . 
 
 2x9+9=. 
 
 3x3=. 
 
 3x6=. 
 
 3x9=. 
 
62 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 85. Exercise. 
 
 Copy, supplying the missing numbers, and learn : 
 
 TABLE. 
 
 3x1=. 3x4=. 3x7=. 
 
 3x2=. 3x5=. 3x8=. 
 
 3x3=. 3x6=. 3x9=. 
 
 86. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 /. 
 
 2 
 
 X 
 
 2= . 
 
 19. 
 
 . X 
 
 1 = 2 
 
 37. 
 
 3 
 
 X 
 
 . =9 
 
 2. 
 
 3 
 
 X 
 
 8= . 
 
 20. 
 
 2 X 
 
 .= 10 
 
 38. 
 
 3 
 
 X 
 
 . =27 
 
 3. 
 
 2 
 
 X 
 
 7= . 
 
 21. 
 
 3 X 
 
 7= . 
 
 39. 
 
 • 
 
 X 
 
 4= 12 
 
 4. 
 
 3 
 
 X 
 
 3= . 
 
 22. 
 
 . X 
 
 1 = 3 
 
 40. 
 
 • 
 
 X 
 
 2=4 
 
 6. 
 
 2 
 
 X 
 
 .= 6 
 
 23. 
 
 2 X 
 
 1 = . 
 
 41. 
 
 3 
 
 X 
 
 . =3 
 
 6. 
 
 2 
 
 X 
 
 . = 4 
 
 24. 
 
 3 X 
 
 .= 21 
 
 42. 
 
 • 
 
 X 
 
 6= 18 
 
 7. 
 
 . 
 
 X 
 
 9 = 27 
 
 25. 
 
 2 X 
 
 4= . 
 
 43. 
 
 2 
 
 X 
 
 . = IG 
 
 8. 
 
 3 
 
 X 
 
 5 = . 
 
 26. 
 
 . X 
 
 9 = 18 
 
 44. 
 
 • 
 
 X 
 
 3 = 9 
 
 9. 
 
 • 
 
 X 
 
 8 = 24 
 
 27. 
 
 2 X 
 
 3= . 
 
 45. 
 
 3 
 
 X 
 
 . = 15 
 
 10. 
 
 • 
 
 X 
 
 2 = 4 
 
 28. 
 
 2 X 
 
 6 = . 
 
 46. 
 
 . 
 
 X 
 
 7 = 21 
 
 11. 
 
 3 
 
 X 
 
 6 = . 
 
 29. 
 
 • X 
 
 5 = 10 
 
 47. 
 
 • 
 
 X 
 
 5 = 15 
 
 12. 
 
 2 
 
 X 
 
 .= 8 
 
 30. 
 
 2 X 
 
 .= 14 
 
 48. 
 
 3 
 
 X 
 
 2= . 
 
 13. 
 
 2 
 
 X 
 
 5 = . 
 
 31. 
 
 3 X 
 
 .= 24 
 
 49. 
 
 2 
 
 X 
 
 9= . 
 
 14. 
 
 2 
 
 X 
 
 .= 2 
 
 32. 
 
 2 X 
 
 8= . 
 
 50. 
 
 3 
 
 X 
 
 • = 12 
 
 15. 
 
 2 
 
 X 
 
 .= 18 
 
 33. 
 
 3 X 
 
 9= . 
 
 51. 
 
 • 
 
 X 
 
 7 = 14 
 
 16. 
 
 2 
 
 X 
 
 .= 12 
 
 34. 
 
 . X 
 
 1 = 2 
 
 62. 
 
 3 
 
 X 
 
 1 = . 
 
 17. 
 
 3 
 
 X 
 
 .= 6 
 
 35. 
 
 . X 
 
 G = 12 
 
 53. 
 
 3 
 
 X 
 
 . = 18 
 
 18. 
 
 3 
 
 X 
 
 4= . 
 
 36. 
 
 • X 
 
 2 = 6 
 
 64. 
 
 • 
 
 X 
 
 8 = 16 
 
MULTIPLICATION, DIVISION, MENSURATION. 63 
 
 87. Oral Exercise. 
 
 /. What do 2 ])osUil cards cost ? 
 
 2. What do 2 two-cent stamps cost ? 
 
 1 pint. 
 
 1 quart. 
 
 There are tivo pints (pt.) m a quart (qt.). 
 
 3. How many pints are there in 2 qnarts ? 
 
 4. How many pints are there in 3 quarts ? 
 
 5. What do 3 one-cent stamps cost ? 
 
 6. How many feet have 2 horses ? 
 
 7. How many horses are needed to make 2 six-horse 
 teams ? 
 
 8r How many horseshoes will it take to shoe 3 horses 
 all around ? 
 
 Measure a yard-stick with a foot-rule to find that : 
 
 There are three feet (ft.) in a yard {yd.). 
 
 9. How many feet are there in 2 yards ? 
 70. How much fare will two persons pay, if each pays 
 5 cents ? 
 
 //. How many days are there in two weeks ? 
 
 12. How many feet are there in 3 yards ? 
 
 13. How many days are there in 3 weeks ? 
 
54 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 1 quart. 
 
 1 gallon. 
 
 There are four quarts in a gallon {gal.), 
 
 14. How many quarts are there in 2 gallons ? 
 
 15. How many trees are there in two rows, each con- 
 taining 8 trees ? 
 
 16. How many quarts are there in 3 gallons ? 
 
 17. Three persons each pay 5 cents car fare ; how much 
 do they all pay together ? 
 
 18. How many panes of glass are needed for 3 windows, 
 if 8 panes are needed for each window ? 
 
 19. I can hold out 9 pounds in each hand ; what weight 
 can I hold out with both hands ? 
 
 20. How many persons are there at 3 tables, if 6 per- 
 sons are at each table ? 
 
 21. A grass-plot is enclosed by 3 rows of hedge, each 9 
 yards long ; how many yards of hedge are there in all ? 
 
 Find the cost of : 
 
 22. 2 tablets at 6 cents each. 
 
 23. 3 lemons at 3 cents each. 
 
MULTIPLICATION, DIVISION, MENSURATION. 55 
 
 24. 3 pounds of sugar at 6 cents a pound. 
 
 25. 2 sheep at 4 dollars apiece. 
 
 88. Exercise. 
 
 Copy, writing in each case the proper figure in place 
 of X : 
 
 /. i of 2 = X 
 
 7. 1 of 14 = X 
 
 13. 
 
 1 of 12 = X 
 
 2. i of 4: = X 
 
 8. ^ of 16 = X 
 
 14. 
 
 1 of 15 =3 X 
 
 5. i of 6 = X 
 
 9. i of 18 == X 
 
 15. 
 
 i of 18 =: X 
 
 4. ^ of 8 = X 
 
 10. ^ot 3 = X 
 
 16. 
 
 i of 21 = X 
 
 5. 1 of 10 = X 
 
 11. ^ of 6 = X 
 
 17. 
 
 J of 24 = X 
 
 6. i of 12 = X 
 
 /2. 1 of 9 = X 
 
 18. 
 
 i of 27 = X 
 
 89. Oral Exercise. 
 
 Read Exercise 88, supplying the missing numbers. 
 
 90. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 13. 15 = — fives. 
 
 14. 27 = — nines. 
 
 15. 14 = — sevens. 
 
 16. 18 = — sixes. 
 
 17. 16 = — eights. 
 
 18. 24:=:— eights. 
 
 91. Oral Exercise. 
 
 Read Exercise 90, supplying the missing numbers. 
 
 92. Exercise. 
 
 /. i of 8 pints are — pints, or — quarts. 
 
 2. J of a dozen are how many ? 
 
 3. Divide 6 cents equally between 2 boys. What part 
 
 /. 
 
 2 = — ones. 
 
 7. 
 
 9 = — threes. 
 
 2. 
 
 4 = — twos. 
 
 8. 
 
 12 — — fours. 
 
 3. 
 
 3 = — ones. 
 
 9. 
 
 12 =: — sixes. 
 
 4. 
 
 6 = — threes. 
 
 10. 
 
 8 = — fours. 
 
 6. 
 
 6 = — twos. 
 
 11. 
 
 21 = — sevens. 
 
 6. 
 
 10 = — fives. 
 
 12. 
 
 18 = — nines. 
 
66 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 of the money does each receive ? How much does each 
 receive ? 
 
 4. If 2 quarts of syrup cost 12 cents, 1 quart will cost ^ 
 of — cents, or — cents. 
 
 5. How much oil does a stove burn in 1 hour, if it 
 burns 4 quarts iu 2 hours ? 
 
 6. If I buy 3 pints of ice cream for 3 persons, how mucli 
 will that allow for each person ? 
 
 7. When 6 quarts of milk fill 3 cans of the same size, 
 how much does each can hold ? 
 
 8. 18 pails were tied in 2 bundles of the same size ; how 
 many were put in a bundle ? 
 
 9. I wish to have 18 pounds of sugar put up in 3 pack- 
 ages of the same weight ; how much must be put in each 
 package ? 
 
 10. 24 children are formed into 3 classes of the same 
 size ; how many are there in a class ? 
 
 //. Make and answer a question about J of 18 cents. 
 
 12. Mary spent 15 cents for 3 pounds of sugar. Ask a 
 question about this, and give the answer. 
 
 13. A boy had 12 cents. He spent ^ of it for fire- 
 crackers and J of it for ice cream ; how much did he 
 spend for both ? 
 
 14. A girl who earns 9 dollars and spends \ of it for 
 board has how much left ? 
 
 93. Exercise. 
 
 /. If one lemon costs 3 cents, for G cents — lemons can 
 be bought. 
 
MULTIPLICATION, DIVISION, MENSURATION. 57 
 
 2. How many 3-foot ropes can be cut from a rope 9 feet 
 long ? 
 
 3. How many times can a gallon measure be filled from 
 12 quarts of milk ? 
 
 4. How many 4-horse teams can be formed from 8 horses ? 
 
 5. How many 8-foot ropes can be cut from a rope 16 
 feet long ? 
 
 6. How many packages of oatmeal, each containing 4 
 pounds, must I buy to have 12 pounds ? 
 
 7. 2 quarts of raspberries at 8 cents a quart, with 5 
 cents, will pay for — sacks of salt at 3 cents a sack. 
 
 8. Last week I worked 3 days and was paid 6 dollars ; 
 how much was that a day ? 
 
 9. In 12 pints there are — quarts. 
 
 10. 15 cents will pay for — car rides at 5 cents each. 
 //. How many tables must be set for 24 persons, if 8 
 
 persons can be seated at a table ? 
 
 12. How many are there in half a dozen ? 
 
 13. How many are there in one third of a dozen ? 
 
 14. 2 pecks of potatoes at 8 cents a peck are worth — 
 pounds of flour at 4 cents a pound. 
 
 15. If I paid 10 cents for pencils at 5 cents apiece, 
 how many did I buy ? 
 
 94. Oral Exercise. 
 
 Count by 4's : 
 
 /. From 4 to 40. 4. From 2 to 42. 
 
 2. From 40 to 4. 5. From 3 to 43. 
 
 3. From 1 to 41. 6. From 43 to 3. 
 
58 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 Count by 5's : 
 
 7. From 5 to 50. 
 
 8. From 50 to 5. 
 
 9. From 1 to 51. 
 
 10. From 2 to 52. 
 //. From 3 to 53. 
 12. From 4 to 54. 
 
 95. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 3x1 + 1.= 
 
 3x4+4= 
 
 3x7 + 7= . 
 
 4x1=. 
 
 4x4 = 
 
 4x7=. 
 
 3x2 + 2=. . 
 
 3x5+5= 
 
 3x8 + 8= . 
 
 4x2=. 
 
 4x5 = 
 
 4x8=. 
 
 3x3 + 3= . 
 
 3x6 + 6= . 
 
 3x9 + 0= . 
 
 4x3=. 
 
 4x6 = 
 
 4x9=. 
 
 96. Exercise. 
 
 Copy, supplying the missing numbers and learn : 
 
 TABLE. 
 
 4x1=. 4x4=. 4x7 
 
 4x2=. 4x5=. 4x8 
 
 4x3=. 4x6=. 4x9 
 
 97. Exercise. 
 
 Copy, supplying the missing num^bers : 
 
 4x1+1=. 4x4+4=. 4x7+7 
 
 5x1=. 5x4=. 5x7 
 
 4x2+2=. 4x5+5=. 4x8+8 
 
 5x2=. 6x5=. 5x8 
 
 4x3+3=. 4x6+6=. 4x9+9 
 
 5x3=. 5x6=. 5x9 
 
MULTIPLICATION, DIVISION, MENSURATION. 59 
 
 98. Exercise. 
 
 Copy^ supplying the missing numbers and learn : 
 
 TABLE. ^ 
 
 5xl=» 5x4=» 5x7=» 
 
 5x2=- 5x5=» 5x8=- 
 
 5x3=- 5x6=« 6x9=- 
 
 99. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 /. 
 
 4 X 
 
 1 = . 
 
 19. 
 
 5 X . = 15 
 
 37. 
 
 4 
 
 X 
 
 .= 8 
 
 2. 
 
 4 X 
 
 . = 12 
 
 20. 
 
 . X 5 = 25 
 
 38. 
 
 . 
 
 X 
 
 4= 16 
 
 3. 
 
 4 X 
 
 6= . 
 
 21. 
 
 4x2=. 
 
 39. 
 
 5 
 
 X 
 
 4= . 
 
 4. 
 
 4 X 
 
 .= 32 
 
 22. 
 
 . X 6 = 24 
 
 40. 
 
 5 
 
 X 
 
 5 = . 
 
 5. 
 
 5 X 
 
 '= 20 
 
 23. 
 
 4 X 5 = • 
 
 41. 
 
 . 
 
 X 
 
 2 = 8 
 
 6. 
 
 4 X 
 
 4= . 
 
 24. 
 
 . X 1 =5 
 
 42. 
 
 5 
 
 X 
 
 .= 25 
 
 7. 
 
 5 X 
 
 . = 35 
 
 25. 
 
 . X 7 = 28 
 
 43. 
 
 • 
 
 X 
 
 5 = 20 
 
 8. 
 
 5 X 
 
 7 = . 
 
 26. 
 
 5 X . = 30 
 
 44. 
 
 4 
 
 X 
 
 7= . 
 
 9. 
 
 • X 
 
 2 = 10 
 
 27. 
 
 4 X . = 20 
 
 45. 
 
 4 
 
 X 
 
 .= 36 
 
 10. 
 
 5 X 
 
 3= . 
 
 28. 
 
 . X 6 = 30 
 
 46. 
 
 4 
 
 X 
 
 9 = . 
 
 11. 
 
 4 X 
 
 . = 4 
 
 29. 
 
 5x0=. 
 
 47. 
 
 • 
 
 X 
 
 9 = 45 
 
 12. 
 
 • X 
 
 9 = 36 
 
 30. 
 
 . X 3 = 15 
 
 48. 
 
 5 
 
 X 
 
 .= 45 
 
 13. 
 
 • X 
 
 8 = 40 
 
 31. 
 
 4x3=. 
 
 49. 
 
 5 
 
 X 
 
 6= . 
 
 14. 
 
 4 X 
 
 . =28 
 
 32. 
 
 5 X . = 10 
 
 50. 
 
 4 
 
 X 
 
 .= 16 
 
 15. 
 
 • X 
 
 7 = 35 
 
 33. 
 
 . X 1 = 4 
 
 51. 
 
 • 
 
 X 
 
 4 = 20 
 
 16. 
 
 4 X 
 
 8= . 
 
 34. 
 
 5 X . = 5 
 
 52. 
 
 4 
 
 X 
 
 . = 24 
 
 17. 
 
 5 X 
 
 . = 40 
 
 35. 
 
 5x8=. 
 
 53. 
 
 5 
 
 X 
 
 2= . 
 
 18. 
 
 5 X 
 
 1= . 
 
 36. 
 
 . X 3 = 12 
 
 54. 
 
 • 
 
 X 
 
 8 = 32 
 
60 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 iOO. Exercise. 
 
 /. In one week there are — days, and in 4 weeks there 
 are 4 times — days, or — days. 
 
 2. ^n one yard there are — feet, and in 5 yards there 
 are 5 times — feet, or — feet. 
 
 5. In one gallon there are — quarts, and in 4 gallons 
 there are 4 times — quarts, or — quarts. 
 
 4. In one quart there are — pints, and in 5 quarts there 
 are 5 times — pints, or — pints. 
 
 Q 
 
 1 quart. 1 peck. 1 bushel. 
 
 There are 8 quarts (qt.) in a peck (pk.). 
 There are Jf. jjecks in a hnshel [by.). 
 
 5. How many quarts are there in 4 pecks ? in 3 pecks ? 
 
 6. How many quarts are there in 2 pk. ? in 6 pk. ? 
 
 7. How many pecks are there in 4 bushels ? in 5 bushels? 
 
 8. How many pecks are there in 2 bu. ? in 3 bu. ? 
 5. 4 X 2 and how many make a dozen ? 
 
 10. A dime and how many cents will pay for 3 pounds 
 of sugar at 6 cents a pound ? 
 
 //. How much change should a lady receive who 
 bought 3 pounds of soap at 4 cents a pound and gave the 
 clerk a dime and a 5-cent piece ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 61 
 
 Find the cost of : 
 
 12. 2 pencils at 5 cents each. 
 
 13. 4 pounds of sugar at 5 cents each. 
 
 14. 5 oranges at 2 cents each. 
 
 15. 4 eye shades at 8 cents each. 
 
 16. 4: yards of ribbon at 6 cents a yard. 
 
 17. 6 packs of firecrackers at 5 cents a pack. 
 
 18. 5 loaves of bread at 6 cents a loaf. 
 
 19. 4 quarts of milk at 7 cents a quart. 
 
 20. 5 papers of pins at 5 cents a paper. 
 
 101. Each of the four equal jmrts of a number is 
 called one fourth (i) of it. 
 
 102. Each of the five equal parts of a number is 
 called one fifth (^) of it. 
 
 103. Exercise. 
 
 Copy, writing in each case the proper figure in place 
 of X : 
 
 /. i of 4 = X 7. i of 28 = X /3. J of 20 -- X 
 
 2. J of 8 = X S. i of 32 = X /4. ^ of 25 =r X 
 
 5. i of 12 = X 5. i of 36 = X 15. ^ of 30 = x 
 
 4. i of 16 = X /O. i of 5 = X 16. i of 35 = X 
 
 5. \ of 20 = X //. i of 10 == X 17. ^ of 40 = X 
 
 6. i of 24 = X 12. ^ of 15 == X 18. ^ of 45 = x 
 
 104. Oral Exercise. 
 
 Bead Exercise 103, supplying the missing numbers. 
 
62 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 105. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 1. 4 — — ones. 7. 24 = — sixes. 13. 30 = — sixes. 
 
 2. 10 = — twos. 8. 30 = — nines. 14. 6 = — ones. 
 
 3. 8 = — twos. 5. 20 == — fives. /5. 45 1= — nines. 
 
 4. 15 - —fives. 10. 12 = —threes. 16. 32 = —eights. 
 
 5. 16 = — fours. //. 25= — fives. 17. 35 = — sevens. 
 
 6. 20 = — fours. 12. 28 = — sevens. 18. 40 = — eights. 
 
 106. Oral Exercise. 
 
 Head Exercise 105,supplying the missing numbers. 
 
 107. Exercise. 
 
 /. If I pay 20 dollars for 4 weeks' board, how much is 
 that a week ? 
 
 2. I wish to cut 40 yards of carpet into 6 equal strips ; 
 how long must I make each strip ? 
 
 3. 10 pigeons will make — pair of pigeons. 
 
 4. How many quart bottles can be filled from 8 pints ? 
 
 5. How many 5-cent boxes of indigo can be bought for 
 20 cents ? 
 
 6. A school of 24 boys was divided into 4 equal classes ; 
 how many boys does each class contain ? 
 
 7. How many are 24 less 8 divided by 4 ? 
 
 8. How many times must I reach into a box containing 
 eggs to count out 2 dozen, if I take out 6 each time ? 
 
 9. In 10 quarts there are — pocks. 
 
 10. How many pieces, each 3 feet long, can I cut from 
 15 feet of twine ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 63 
 
 11. K painter received 18 dollars for painting a barn ; 
 if he worked 6 days, how much did he earn each day ? 
 
 12. IIow many 5-cent combs can be bought for 40 cents ? 
 
 13. How many gallon jugs can be filled with 20 quarts 
 of vinegar ? 
 
 14. Allowing a pound of meat for 2 persons, how much 
 meat should be bought for a dinner at which 10 persons 
 are to be served ? 
 
 15. How many pounds of sugar at 4 cents a pound can be 
 bought in exchange for 3 pounds of lard at 8 cents a pound ? 
 
 20 is called a score. 
 
 16. How many are there in i of a dozen ? In i of a 
 score ? 
 
 108. One of the two 
 equal parts of 1 is i ; or 
 ioflisi 
 
 One of the three equal 
 parts of 1 is i ; or ^ of 1 
 is i. 
 
 J of 2 is i plus -J, or f, 
 read two thirds. 
 
 109. Find J of 5. 
 
 Answer thus : | of 5 is 2 and 1 over ; i of 1 is |. 
 The answer is two and one half ; written 2|. 
 
 110. Oral Exercise. 
 
 Find: 
 /. J of 3. 3. J of 9. 5. I of 11. 7. i of 17. 
 
 2. J of 7. 4. i of 13. 6. ^ of 15. 8. J of 19. 
 
64 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 111. Find i of 17. 
 
 Answer thus : i of 17 is 5, and 2 over ; J of 2 is |. 
 Tlie answer is 5J. 
 
 112. Oral Exercise. 
 Find : 
 
 /. i of 5. 5. 4 of 4. 9. J of 10. 13. i of 13. 
 
 2. J of 8. 6. I of 7. 10. i of 22. 14. J of 25. 
 
 3. \ of 11. 7. i of IG. //. i of 23. 15. J of 26. 
 
 4. J of 14. 8. i of 19. /2. i of 28. /ff. J of 29. 
 
 113. Exercise. 
 
 /. J of 3 pints is — pints. 
 
 2. Find J of 7 feet. 
 
 5. Divide 8 yards of ribbon equally among 3 girls. 
 
 4. If a man earned 3 dollars in 2 days, in 1 day he 
 earned J of — dollars, or — dollars. 
 
 5. A lady bought 3 quarts of plums for 25 cents ; how 
 much were they a quart ? 
 
 6. At 7 cents a quart, what will a pint of milk cost ? 
 
 7. An iron rod 9 feet long was divided into 2 equal 
 parts ; find the length of each part. 
 
 8. When 3 loaves of bread cost 10 cents, how much 
 does one loaf cost ? 
 
 9. A family that uses a pound of tea in 3 weeks, uses 
 how much per week ? 
 
 10. When 3 quarts of oysters fill 2 cans of equal size, 
 how much does each can hold ? 
 
 //. How many days are there in lialf a week ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 65 
 114. How many 2's in 7 ? 
 
 3^ twos 
 
 (2) (2) (2) (lof2) 
 
 How many 3's in 11 ? 
 
 33-threes 
 
 11 = 3f threes. 
 
 (3) (3) (3) (|-of3) 
 
 116. Exercise. 
 
 Supply the missing numbers, using lines to illustrate : 
 /. 5 = — twos. 4. 7 = — threes. 7. 11 = — twos. 
 
 2. 4: = — threes. 5. 3 = — twos. 8. 10 = — threes. 
 5. 9 = — twos. 6. 8 — — threes. 9. 14 = — threes. 
 
 116. How many 2's in 7 ? 
 
 Answer thus: There are 3 twos in 7 and 1 over. 
 This 1 over is ^ of another 2. 
 Therefore, the number of 2's in 7 is 3i, read 
 three and one half. 
 
 117. Oral Exercise. 
 How many : 
 
 /. 2's in 3 ? 3. 2's in 13 ? 5. 2's in 17 ? 7. 2's in 19 ? 
 2. 3's in 5 ? 4. 3's in 20 ? 6. 3's in 16 ? 8. 3's in 25 ? 
 5 
 
66 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 118. Exercise. 
 
 /. In 7 pints there are — quarts — pint. 
 
 2. In 11 feet there are — yards — feet. 
 
 3. How many 2-cent stamps can be bought for 15 cents, 
 and what change will there be ? 
 
 4. 17 ducks will make how many pair, and leave how 
 many over ? 
 
 5. A liveryman hired out 21 horses, 9 of them for 
 driving singly and the others for double teams ; how 
 many double teams were there ? 
 
 6. How many sheets of drawing paper at 3 cents each 
 can be bought for 10 cents, and how much change will 
 there be ? 
 
 7. If one yard of braid costs 2 cents, for 9 cents as many 
 yards can be bought as — cents is contained times in — 
 cents, or 4^. 
 
 8. At 2 cents a pound, how many pounds of putty can 
 be bought for 7 cents ? 
 
 9. A man who earns 2 dollars a day must work how 
 many days to earn 11 dollars ? 
 
 10. How many bags of grain has a farmer, if he has 28 
 bushels in 3-bushel bags ? 
 
 119. Exercise. 
 
 /. What is each of the two equal parts of 
 1 called ? 
 
 2. How many halves are there in 1 ? 
 
 3. Read : ^ ; |. 
 
MULTIPLICATION, DIVISION, MENSURATION. 67 
 
 4. What is each of the four equal parts of 
 1 called ? 
 
 5. What are two of the four equal parts of 
 1 called ? 
 
 6. Read: i;f; };*. 
 
 i of 2 := J + J, or f , or J. 
 7. Show that J of 3 = }. 
 
 120. Find \ of 14. 
 
 Answer thus : i of 14 is 3 and 2 over ; i of 2 is |, or \, 
 The answer is 3i. 
 
 121. Oral Exercise. 
 
 Find : 
 
 /. \ of 5. 4. \ of 9. 7. \ of 25. 
 
 2. \ of 7. 5. \ of 11. 8. \ of 27. 
 
 5. J of 6. ff. J of 10. 9. J of 22. 
 
 10. \ of 31. 
 //. }of 33. 
 12. iof34. 
 
 122. How many 4's are there in 14 ? 
 
 **** **** **** ^** 14 = 3^ fours. 
 
 4 4 4 iof4 
 
 123. Exercise. 
 
 Supply the missing numbers, making drawings to illus- 
 trate : 
 
 /. 9 = — fours. 
 ^. 7 = — fours. 
 5. 6 = — fours. 
 
 4. 10 = — fours. 
 
 5. 13 = — fours. 
 
 6. 22 = — fours. 
 
 7. 15 = — fours. 
 
 8. 23 = — fours. 
 
 9. 25 = — fours. 
 
68 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 124. Exercise. 
 
 /. At 4 cents a yard, how many yards of lace can I 
 buy for a dime, and what change will there be ? 
 
 2. In 19 quarts there are — gallons — quarts. 
 
 3. At 7 dollars a bushel, what is a peck of clover seed 
 worth ? 
 
 4. When a gallon of oil costs 9 cents, how much is it a 
 quart ? 
 
 5. What is each of the five equal parts of 1 called ? 
 
 6. Read: i; |;|; t;|. 
 
 7. Find ^ of each number in the outer ring : 
 
 Suggestion, Solve as in S 120. 
 
 8. Show that there are 2| fives in 12. 
 
 9. 2 pounds of lard at 9 cents a pound will buy how 
 many yards of lining at 4 cents a yard ? 
 
 10. A boy had 22 cents in 5-cent and one-cent pieces. 
 He had 7 one-cent pieces ; how many 5-cent pieces had he? 
 
 //. How many 5-ccnt packages of fire-crackers can a 
 boy get for a pair of pigeons worth 28 cents ? How much 
 money will he have left? 
 
 12. A vessel that holds 9 quarts has in it 1 quart of 
 
MULTIPLICATION, DIVISION, MENSURATION. 69 
 
 water ; liow iiuiiiy gallons of water can still be ])oured 
 into it ? 
 
 13. I have four pieces of money, together worth 12 cents. 
 Two of them are one -cent pieces ; what are the other 
 two ? 
 
 125. 3 X 23 = 23 + 23 + 23 = G9. The answer may 
 be found by a shorter method by making use of the Table 
 on p. 120, thus : 
 
 ^3 3 X 23 = 3 X (3 units + 2 tens). 
 
 _£. 3x3 units = 9 units, which we write in units' place. 
 
 69 3x2 tens = 6 tens, which we write in tens' place. 
 
 The answer is 69. 
 
 In practice, say 3 times S are 9 ; 3 times 2 are 6. 
 
 126. The process of taking a number as many 
 times as there are units in anotlier number is called 
 Multiplication. The answer in multiplication is called 
 the Product. 
 
 127. Multiply 21 by 2. 
 Multiplicand 21 
 Multiplier 2 
 Product 42 
 
 128. Exercise. 
 
 Copy and multiply, and state which number is the mul- 
 tiplicand, which the multiplier, and which the product : 
 
70 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 /. 42 
 
 7. 
 
 30 
 
 13. 
 
 41 
 
 19. 
 
 201 
 
 25. 
 
 203 
 
 2 
 
 
 3 
 
 
 5 
 
 
 4 
 
 
 3 
 
 2. 33 
 
 8. 
 
 21 
 
 14. 
 
 120 
 
 20. 
 
 212 
 
 2ff. 
 
 121 
 
 3 
 
 
 3 
 
 
 2 
 
 
 4 
 
 
 4 
 
 3. 20 
 
 9. 
 
 21 
 
 15. 
 
 203 
 
 21. 
 
 200 
 
 27. 
 
 101 
 
 2 
 
 
 4 
 
 
 2 
 
 
 4 
 
 
 5 
 
 4. 40 
 
 10. 
 
 32 
 
 16. 
 
 101 
 
 22. 
 
 112 
 
 28. 
 
 323 
 
 2 
 
 
 4 
 
 
 3 
 
 
 4 
 
 
 3 
 
 5. 13 
 
 11. 
 
 40 
 
 17. 
 
 132 
 
 23. 
 
 102 
 
 29. 
 
 213 
 
 3 
 
 
 4 
 
 
 3 
 
 
 4 
 
 
 3 
 
 6. 32 
 
 12. 
 
 31 
 
 18. 
 
 332 
 
 24. 
 
 111 
 
 30. 
 
 222 
 
 3 
 
 
 5 
 
 
 3 
 
 
 5 
 
 
 4 
 
 129. One of the 3 equal parts of 39 may be found thus : 
 
 i of 39 = i of (3 tens + 9 units). 
 
 i of 3 tens = 1 ten, which we write in tens' place. 
 
 ■^*^ 3 of 9 units = 3 units, which we write in units' place. 
 The answer is 13. 
 In practice, my ^ of d is 1 ; ^ of d is S. 
 
 130. Finding one of the equal parts of a numbei 
 is called Division. The answer in division is called 
 the Quotient. 
 
 131. The sign of division is -^, read divided by. 
 
 Thus, 24 -s- 3 is read ^4 divided by 3. 
 Note. 24-1-3 may also be expressed 3)24. 
 
MULTIPLICATION, DIVISION, MENSURATION. 71 
 
 132. Divide 28 by 2. 
 Divisor 2)28 Dividend 
 Quotient 14 
 
 133. Exercise. 
 
 Copy and divide, and state which number is the divi- 
 dend, which the divisor, and which the quotient: 
 
 /. 2)42 7. 3)60 13. 4)80 19. 2)406 25. 4)444 
 
 2. 2)64 8. 3)33 14. 4)40 20. 3)333 26. 4 )480 
 
 5. 2)86 5. 3)69 /5. 5)^ 21. 3)369 27. 4 )408 
 
 4. 2)40 /O. 4)^ /^. 5)55 22. 3)960 25. 5 )555 
 
 5. 3)36 //. 4)44 /7. 2)222 23. 3)609 25. 5)505 
 5. 3)96 /2. 4)_48 /5 2 )264 24. 3)^06 50. 5)550 
 
 134. Multiply 45 by 4. 
 
 45 4 X 45 = 4 X (5 units + 4 tens). 
 4 4x5 units = 20 units, or 3 tens. 
 180 Write in units' place, and add 2 tens to the next 
 product. 
 
 4x4 tens = 16 tens, which added to the 2 tens makes 18 tens, 
 or 1 hundred and 8 tens. 
 
 Write 8 in tens' phxce and 1 in hundreds' place. 
 
 The product is 180. 
 
 In practice^ say If, times 5 are 20 ; Jf, times Jf, are 16, and 2 are 18. 
 
72 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 135. 
 
 Exercise. 
 
 
 
 
 
 
 Copy and multiply : 
 
 
 
 
 
 
 /. 37 
 
 7. 34 
 
 13. 
 
 66 
 
 19. 46 
 
 25. 
 
 192 
 
 2 
 
 3 
 
 
 4 
 
 5 
 
 
 5 
 
 2. 39 
 
 5. 87 
 
 14. 
 
 89 
 
 20. 55 
 
 26. 
 
 287 
 
 2 
 
 3 
 
 
 4 
 
 5 
 
 
 3 
 
 3. 48 
 
 9. 64 
 
 15. 
 
 94 
 
 2/. 136 
 
 27. 
 
 498 
 
 2 
 
 3 
 
 
 4 
 
 2 
 
 
 2 
 
 4. 56 
 
 10. 95 
 
 16. 
 
 19 
 
 22. 176 
 
 28. 
 
 185 
 
 2 
 
 3 
 
 
 5 
 
 3 
 
 
 5 
 
 5. 75 
 
 //. 23 
 
 17. 
 
 28 
 
 23. 135 
 
 29. 
 
 225 
 
 2 
 
 4 
 
 
 _5 
 
 3 
 
 
 4 
 
 ^. 29 
 
 12. 57 
 
 18. 
 
 37 
 
 24. 186 
 
 30. 
 
 199 
 
 _3 
 
 4 
 
 
 5 
 
 4 
 
 
 4 
 
 136. 
 
 Exercise. 
 
 
 
 
 
 
 /. How many pails are there in 4 bundles, if each 
 bundle contains 52 pails ? 
 
 52 is the number of pails in 1 bundle. 
 4 
 
 ? is the number of pails in 4 bundles. 
 2. Mow many are there in 4 score ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 73 
 
 3. How many oranges are there in 3 boxes each con- 
 taining 36 oranges ? 
 
 4. A bushel of oats weighs 32 pounds ; find the weight 
 of 3 bushels of oats. 
 
 82 pounds is the weight of 1 bushel of oats. 
 3 
 ? pounds is the weight of 3 bushels of oats. 
 
 5. A bushel of wheat weighs 60 pounds ; find the weight 
 of 5 bushels of wheat. 
 
 6. How much will a clerk save in 4 months, if he saves 
 $26 a month ? 
 
 There are 24 Jiours {hr.) in one day {da.). 
 
 7. How many hours are there in 4 days ? 
 
 8. A barrel of flour weighs 196 pounds; find the weight 
 of 4 barrels of flour. 
 
 9. Find the cost of 3 pounds of butter at 23 cents a 
 pound. 
 
 10. Find the cost of 4 pounds of ham at 16 cents a 
 pound. 
 
 //. K there are 24 sheets of paper in a box, how many 
 sheets are there in 4 boxes of the same size ? 
 
 12. Find the cost of 3 hundred shad at $25 per hundred. 
 
 137. Divide 312 by 4. 
 
 4 ) 312 i of 812 = i of (31 tens + 2 units). 
 78 i of 31 tens = 7 tens, and 8 tens over. 
 3 tens + 2 units = 32 units. 
 \ of 32 units = 8 units. The quotient is 78. 
 In practice, say i ^ 31 isl and 8 over ; i ^ 82 is 8. 
 
74 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 138. Exercise 
 
 
 
 
 
 
 Copy and divide : 
 
 
 
 
 
 /. 2)34 
 
 /2. 
 
 4)64 
 
 23. 
 
 7)91 
 
 34. 3)252 
 
 2. 2)76 
 
 13. 
 
 4)72 
 
 24. 
 
 8)96 
 
 35. 3)405 
 
 3. 2)92 
 
 14. 
 
 4)76 
 
 25. 
 
 7)98 
 
 36. 4)164 
 
 4. 2)58 
 
 15. 
 
 4)92 
 
 26. 
 
 2)124 
 
 37. 4)876 
 
 5. 2)98 
 
 16. 
 
 5)65 
 
 27. 
 
 2)136 
 
 38. 4)172 
 
 6. 3)42 
 
 17. 
 
 5)75 
 
 28. 
 
 2)154 
 
 39. 4)952 
 
 7. 3)48 
 
 18. 
 
 5)85 
 
 29. 
 
 2)306 
 
 40. 4)708 
 
 8. 3)54 
 
 19. 
 
 5)95 
 
 30. 
 
 2)178 
 
 41. 5)515 
 
 9. 3)72 
 
 20. 
 
 6)72 
 
 31. 
 
 3)153 
 
 42. 5)585 
 
 10. 3)84 
 
 21. 
 
 6)84 
 
 32. 
 
 3)657 
 
 43. 5)195 
 
 //. 4)56 
 
 22. 
 
 6)90 
 
 33. 
 
 3)174 
 
 44. 5)705 
 
 139. Exercise. 
 
 /. A dealer bought 4 dozen eggs for 84 cents ; how 
 much was that a dozen ? 
 
 84 cents was the cost of 4 dozen. 
 4) 84 cents 
 
 ? cents was the cost of 1 dozen. 
 
 2. IIow much was paid a week to a workman who 
 received $75 for 5 weeks' work ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 75 
 
 3. A piece of carpet measuring 72 yards was cut into 
 4 strips of equal lengtli ; find the length of each strip. 
 
 4. 56 chairs are to be arranged in 4 rows with the same 
 number in each row ; how many must be put in a row ? 
 
 56 is the number to be put in 4 rows. 
 4)56 
 
 ? is the number that must be put in a row. 
 
 5. 144 handkerchiefs were put up in 3 boxes, the same 
 number being in each box ; how many were put in a box ? 
 
 6. 5 bushels of feed weighed 225 pounds ; what did each 
 bushel weigh ? 
 
 7. A farmer sold 2 cows, the first for 35 dollars and the 
 second for 43 dollars ; what was the average selling price ? 
 
 35 dollars was the selling price of the first. 
 43 " " " " '' second. 
 
 ~78 "■ " " " " both. 
 
 2778 "• 
 
 ? was the average selling price. 
 
 8. A merchant bought 2 hams ; the first weighed 23 
 pounds and the second 25 pounds ; what was their average 
 weight ? 
 
 140. Finding hov7 many times 3 feet is contained 
 in 12 feet is measuring 12 feet by 3 feet. 
 
 141. The process of measuring one number by 
 another is Mensuration. 
 
 142. The sign of mensuration is :, read measured 
 hy. 
 
 Thus, 12 : 3 is read 12 measured by 3, 
 
76 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 143. The number of 4'8 in 12 is 3 ; that is, 12:4 = 3. 
 But 12^4 = 3. 
 
 Therefore, 12:4 = 12^4. Therefore, 
 To measure one number hy another^ divide the 
 first hy the second, 
 
 144. Oral Exercise. 
 Measure : 
 
 /. 12 by 4. Answer thus : 12 : 4 = 12 -i- 4, or 3. 
 
 2. 14 by 2. 6. 32 by 4. 10. 28 by 4. /4. 24 by 4. 
 
 5. 24 by 8. 7. 30 by 5. //. 40 by 5. 15. 35 by 5. 
 
 4. 18 by 2. 8. Ti by 3. 12. 32 by 4. 16. 18 by 3. 
 
 5. 27 by 3. 9. 36 by 4. 13. 21 by 3. 17. 25 by 5. 
 
 145. 2 feet is contained in 14 feet as many times 
 as 2 is contained in 14 ; that is, 
 
 14 feet : 2 feet = 14 : 2, or 14 -^ 2. Therefore, 
 
 To measure one amount hy another^ divide the 
 number of units in the first by the number of units 
 in the second, 
 
 146. Oral Exercise. 
 
 Measure : 
 
 /. 14 feet by 2 feet. 
 
 Answer tlms : 14 feet : 2 feet = 14 -*- 2 = 7. 
 
 2. 16 cents by 2 cents. 7. 45 dollars by 5 dollars. 
 
 3. 24 yards by 3 yards. 8. 28 men by 4 men. 
 
 4. 20 quarts by 4 quarts. 9. 30 feet by 5 foot. 
 
 5. 25 days by 5 days. 10. 20 pounds by 4 pounds. 
 B. 36 quarts by 4 quarts. //. 32 gallons by 4 gallons. 
 
MULTIPLICATION, DIVISION, MENSURATION. 77 
 
 147. Exercise. 
 
 /. A man bought 144 colored crayons in boxes contain- 
 ing four pieces each ; how many boxes did he buy ? 
 
 144 was the number of pieces bought. 
 4 was the number of pieces in each oox. 
 4) -144 
 
 ? was the number of boxes bought. 
 
 2. How many 2-cent stamps can be bought for 60 
 cents ? 
 
 3. How many gallon jugs can be filled with 64 quarts 
 of vinegar ? 
 
 A. How many 3-bushel bags are needed to hold 168 
 bushels of grain ? 
 
 5. How many horses can be shod all around with 264 
 horseshoes ? 
 
 6. How many bushels are there in 72 pecks ? 
 
 7. How many 5-cent pieces will make 75 cents ? 
 
 8. 144 dozen eggs are to be packed in crates, each hold- 
 ing 4 dozen ; how many crates are needed ? 
 
 9. At 5 cents a pound, how many pounds of sugar can 
 be bought for 90 cents ? 
 
 10. How many yards long is a rope that is 426 feet 
 long ? 
 
 //. If a family use 2 quarts of milk a day, in how many 
 days will they have used 5 gallons of milk ? 
 
 12. In how many days will a boy save 60 cents, if he 
 saves 5 cents a day ? 
 
78 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 Forming, Writing, and Reading Numbers from 
 lOOO to lOOOO. 
 
 148. Ten hundred make one thousand^ written 
 1000. 
 
 Two thousand is written 2000 ; three thousand, 
 3000. 
 
 One thousand one is written 1001. 
 
 One thousand ten is written 1010. 
 
 Five thousand two hundred is written 5200. 
 
 Four thousand seven hundred twenty is written 
 4720. 
 
 Nine thousand nine hundred ninety-nine is 
 written 9999. 
 
 149. Exercise. 
 
 Write in figures: 
 /. Three thousand. 7. Seven thousand. 
 
 2. Four thousand. 8. Eight thousand. 
 
 3. Five thousand. 9. Nine thousand. 
 
 4. Six thousand. 10. One thousand two. 
 
 5. Two thousand twenty. //. Six thousand five hundred. 
 
 6. Four thousand forty. 12. Nine thousand fifteen. 
 
 13. Seven thousand six hundred eighty-four. 
 
 14. Nine thousand four hundred forty. 
 
 15. Eight thousand six hundred four. 
 
 16. Seven thousand eight hundred sixty-six. 
 
 17. Nine thousaiid eiglit hundred twenty. 
 
 18. Four tliousand nine hundred ninety-nine. 
 
 19. One thousand one hundred one. 
 
ROMAN NOTATION. 79 
 
 160. Exei 
 
 else. 
 
 
 
 
 
 Read, 
 
 and write in words : 
 
 
 
 
 
 /. 400C. 
 
 
 5. 1200. 
 
 9. 
 
 1009. 
 
 13. 
 
 8777. 
 
 2. 7000. 
 
 
 6. 5021. 
 
 10. 
 
 9090. 
 
 14. 
 
 G666. 
 
 3. 7002. 
 
 
 7. 9888. 
 
 11. 
 
 5007. 
 
 15. 
 
 2754. 
 
 4. 1011. 
 
 
 8. 7232. 
 
 12. 
 
 8201. 
 
 16. 
 
 3215. 
 
 Roman Notation. 
 
 151. Capital letters are often used instead of 
 figures in numbering chapters and sections of books, 
 pages of prefaces and introductions, divisions on 
 clock dials, etc. 
 
 This method of writing numbers is called the 
 Roman System. 
 
 I=:l Y = 5 X = 10 L = 50 C = 100 
 
 D = 500 M = 1000. 
 
 Note. The number for which a letter stands \b called the 
 value of the letter. 
 
 152. If a letter is repeated its lvalue is repeated. 
 
 Thus, II = 2 ; III = 3 ; xx = 20 ; cc = 200 ; mmm = 3000. 
 
 153. If a letter is written before one of greater 
 7)alue^ the difference of tlielr values is expressed. 
 
 Thus, IV = 4 ; ix = 9 ; xl = 40 ; xc = 90. 
 
 154. If a letter or a combination of letters is 
 written after a letter of greater value, the sum of 
 the values is expressed. 
 
 Thus, VI =r 6 ; xiii = 13 ; lv = 55 ; lix = 59. 
 
80 WHOLE NUMBERS AND FitACTIONAL PARTS. 
 
 155. A dash placed over a letter or a combina- 
 tion of letters multiplies its value by 1000. 
 
 Thus, V = 5000 ; vli = 7000 ; Tx = 9000. 
 
 156. Units, tens, hundreds, and thousands only 
 are written according to the principles given above. 
 
 
 
 
 TABLE. 
 
 
 
 
 Units. 
 
 Tens. 
 
 
 Hundreds. 
 
 Thousands. 
 
 I = 1 
 
 X 
 
 = 
 
 10 
 
 C 
 
 = 100 
 
 M 
 
 = 1000 
 
 II =2 
 
 XX 
 
 = 
 
 20 
 
 CC 
 
 = 200 
 
 MM 
 
 = 3000 
 
 III = 3 
 
 XXX 
 
 = 
 
 80 
 
 CCC 
 
 = 300 
 
 MMM 
 
 = 3000 
 
 IV = 4 
 
 XL 
 
 = 
 
 40 
 
 CD 
 
 = 400 
 
 IV 
 
 = 4000 
 
 V =5 
 
 L 
 
 = 
 
 50 
 
 D 
 
 = 500 
 
 V 
 
 = 5000 
 
 yi = 6 
 
 LX 
 
 = 
 
 60 
 
 DC 
 
 = 600 
 
 vT 
 
 = COOO 
 
 VII = 7 
 
 LXX 
 
 = 
 
 70 
 
 DCC 
 
 = 700 
 
 vli 
 
 = 7000 
 
 VIII = 8 
 
 LXXX 
 
 = 
 
 80 
 
 DCCC 
 
 = 800 
 
 VIII 
 
 = 8000 
 
 IX =9 
 
 xc 
 
 = 
 
 90 
 
 CM 
 
 = 900 
 
 ix 
 
 - 9000 
 
 157. In writing numbers between those in the 
 above table, hundreds are written after thousands, 
 tens after hundreds, and units after tens. 
 
 Thus, 15G7 is written mdlxvii ; 2053, mmliii : 4508, fvDViii ; 
 
 3600, MMMDC. 
 
 Note, hit = 4 ; xxxx = 40 ; cccc = 400, are also iu use. 
 
 158. Exercise. 
 
 Write by the Roman method : 
 /. The nine simple numbers. 3. The nine hundreds. 
 2. The nine tens. 4. The first nine thousands. 
 
 The numbers between 
 
 5. 10 and 20. 8. 40 ami 50. //. 70 and 80. 
 
 6. 20 and 30. 9. 50 and 60. 12. 80 and 90. 
 
 7. 30 and 40. 10. 60 and 70. 13. 1)0 and 100. 
 
UNITED STATES MONEY. 
 
 81 
 
 The following numbers : 
 
 
 
 
 
 U. 101. 17. UO. 
 
 20. 
 
 400. 
 
 '23. 
 
 1899. 
 
 15. 120. 18. 149. 
 
 21. 
 
 6G6. 
 
 24. 
 
 1 90G. 
 
 16. 150. 19. 194. 
 
 22. 
 
 924. 
 
 25. 
 
 1910. 
 
 Write in figures the following : 
 
 26. IX. 
 
 27. XIV. 
 
 28. XIX. 
 
 29. XXXIV. 
 
 30. XXXVIII. 
 
 31. XLIX. 
 
 32. LXIV. 
 
 33. XCIX. 
 
 34. CLX. 
 55. CLXII. 
 55. CCCLXV. 
 37. CDIX. 
 55. CDLXIV. 
 39. DCCCV. 
 
 40. MCM. 
 
 4/. MCMV. 
 
 42. MCMIX. 
 
 43. MCMXIX. 
 
 44. MDCCCXCIX. 
 
 45. VII. 
 
 46. VCCIV. 
 
 United States Money. 
 
 159. In the money of the United States, 
 
 10 cents = 1 dime. 
 10 dimes = 1 dollar. 
 100 cents = 1 dollar. 
 
 160. The dollar sign is $. It is placed before the 
 number of dollars to be expressed. 
 
 Thus, 5 dollars is expressed $5. 
 
 161. If a sum of money consists of dollars and 
 cents, a point called the Decimal Point is written 
 between the number of dollars and the number of 
 cents. If the number of cents is less than ten, a 
 
 6 
 
82 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 cipher is written between the decimal point and the 
 number of cents. 
 
 Thus, S dollars 25 cents is expressed $3.25, and Jf. dollars 8 
 cents is expressed $1^.08. 
 
 162. The abbreviation for the word cent or cents 
 is ct. or ^. 
 
 Thus, 25 cents may be expressed 25 ct. or 25i^. 
 
 163. A sum of money less than a dollar, such as 
 36 cents, may also be expressed $0.36. 
 
 164. Oral Exercise. 
 
 
 
 Eead: 
 
 
 
 /. $2. 3. $15.25. 
 
 5. $0.62. 
 
 7. $88.66. 
 
 2. $3.05. 4. $37.50. 
 
 6. $0.07. 
 
 8. $ 0.12^. 
 
 165. Exercise. 
 
 Write, using the dollar sign : 
 
 /. 6 dollars. 4. 7 dollars 5 cents. 
 
 2. 75 dollars 25 cents. 5. 87 cents. 
 
 3. 11 dollars 15 cents. 6. 9 cents. 
 
 166. Exercise. 
 
 /. How many cents are there in $3 ? $5 ? $12 ? 
 2. Change $4.36 to cents. 
 
 $4.36 = 436 ct. 
 5. How many cents are there in $2.25 ? $4.36 ? $14.36 ? 
 
MAKING CHANGE. 83 
 
 4. Change to cents : 
 
 $6.84; $9.32; $15.36; $28.45. 
 
 5. Change 600 ct. to dollars. 
 
 600 ct. = $6.00, or $6. 
 
 6. Change to dollars : 
 
 500 ct. ; 900 ct.; 1500 ct. ; 2800 ct. 
 
 7. Change 324 ct. to dollars and cents. 
 
 324 ct. =$3.24. 
 
 8. Change to dollars and cents : 
 
 539 ct.; 608 ct.; 3125 ct.; 6175 ct. 
 
 Making Change. 
 
 167. A man bought a fork for 03^/ and gave the store- 
 keeper a dollar bill ; how will the storekeeper make the 
 change, using as few pieces of money as possible ? 
 
 The storekeeper will give the man 2 cents, a dime, and 
 a quarter-dollar. He may count out the change, saying, 
 63 ct., 65 ct., 75 ct., 1 dollar. 
 
 168. Oral Exercise. 
 
 Make the change in the following examples, using as 
 few pieces of money in each case as possible ; and state 
 how the change may be counted out : 
 
 Sales. Money Paid. 
 
 /. 17^'. Quarter-dollar. 
 
 2. 32^. Half-dollar. 
 
 3. 63r/. Dollar. 
 
84 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 4. 62^'. Half-dollar and quarter-dollar. 
 
 5. 12^'. A dime and a 5-cent piece. 
 
 6. 33^'. A quarter dollar and a dime. 
 
 7. $1.15 ^2-bill. 
 
 8. $2.12 $2-bill and a $l-bill. 
 
 9. $3.28 $5-bill. 
 10. 9^. $2-bill. 
 
 //. $28.37. $20-bill and a $10-bill. 
 
 Addition and Subtraction. 
 
 169. Add: 
 
 3745 In practice we ma}' say : 
 
 2G34 3, 7, 13. Write 2 in units' place and add 1 to the 
 
 1853 tens. 
 
 8232 Then 1, 6, 9, 13. Write 3 in tens' place and add 
 
 1 to the huncl reels. 
 
 Then 1, 9, 15, 23. Write 2 in the hundreds' place and add 2 to 
 the tliousands. 
 
 Then 2, 3, 5, 8. Write 8 in the thousands' place. 
 
 The sum is 8233. 
 
 170. Exercise. 
 
 
 
 
 Copy and add : 
 
 
 
 
 /. 345 3. 378 
 
 5. 765 
 
 7. 5482 
 
 9. 3482 
 
 870 745 
 
 080 
 
 2708 
 
 2351 
 
 2. 421 4. 987 6. 2768 8. 5832 10. 7683 
 899 876 1289 3168 2297 
 
ADDITION AND SUBTRACTION. 
 
 85 
 
 r/. 3275 
 
 13. 
 
 2845 
 
 15. 3754 
 
 17. 329 
 
 19. 
 
 328 
 
 876 
 
 
 738 
 
 2832 
 
 896 
 
 
 798 
 
 49 
 
 
 897 
 
 1709 
 
 539 
 
 854 
 
 
 654 
 29 
 
 r2. 832 
 
 14. 
 
 2597 
 
 16. 763 
 
 18. 327 
 
 20. 
 
 377 
 
 2375 
 
 
 3685 
 
 854 
 
 83 
 
 
 479 
 
 1783 
 
 
 1763 
 
 963 
 
 785 
 
 901 
 
 78 
 
 
 637 
 
 507 
 
 Find the missing numbers by adding down and across 
 
 21. 234 + 567 + 728 = 
 
 109 + 106 + 34 = 
 
 48 + 729 4- 138 = 
 
 •+• + • = 
 
 22. 728 + 925 + 324 = 
 
 75 + 109 + 7 = 
 768 + 325 + 785 =: 
 
 + 
 
 23. 308 + 78 + 230 = 
 
 106 + 7 + 98 = 
 
 99 + 126 4- 3 = 
 
 + 
 
 + • = 
 
 24. 1024 + 276 + 325 
 
 106 +72+78 
 48 + 9 + 3 
 
 + . = 
 
 Find the missing numbers by multiplying across and 
 adding down ; 
 
 25. 3 X 228 = . 26. A: X 164 = . 27. 5 x 75 = 
 
 3 X 456 = . 4 X 108 = . 5 x 110 =^ 
 
 3 X 325 = . 4 X 378 = . 5 x 306 = 
 
 3x184=. 4x76=. 5x 9 = 
 
 3 X 
 
 4 X . = 
 
 5 X 
 
86 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 171. Subtract : 
 
 111 ])iactice be^in at units and subtract thus : 
 8214 
 
 8 from 14 leaves 6. 
 1 7«3o 
 3 from 10 leaves 7. 
 
 7 from 11 leaves 4. 
 1 from 7 leaves 6. The difference is 6476. 
 
 172. Exercise. 
 
 Copy and subtract : 
 
 /. 832 6. 1000 //. 7001 16. 7200 2f. 3020 
 574 _389 2098 _99 1982 
 
 2. 722 7. 1070 12. 3010 17. 3G72 22. 7008 
 448 179 2111 908 1999 
 
 3. 320 8. 2080 13. 5002 18. 7202 23. G320 
 107 1979 4983 5193 2198 
 
 4. 250 9. 3420 14. 5000 /5. 8201 24. 3507 
 148 2837 3092 7192 2198 
 
 6. 700 10. 9000 /5. 8030 :?0. 3380 25. 4320 
 188 1807 1929 1099 1738 
 
 173. Find the sum of 113.25, 110.48, and 10.70. 
 
 113.25 Write the sums, placing dollars under dollars and 
 
 10.48 cents under cents. Add as in ordinary numbers, 
 
 Q' «6 and place the decimal point before the last two 
 
 $24.49 figures to separate dollars from cents. 
 
ADDITION AND SUBTRACTION. S7 
 
 174. Exercise. 
 
 
 
 
 Find the 
 
 sum : 
 
 
 
 
 1. 
 
 
 2. 
 
 3. 
 
 4. 
 
 % 3.25 
 
 
 $ 8.48 
 
 $12.38 
 
 $24.06 
 
 5.63 
 
 
 7.35 
 
 15.09 
 
 33.45 
 
 7.42 
 
 
 0.67 
 
 32.26 
 
 8.37 
 
 12.56 
 
 
 26.89 
 
 31.56 
 
 15.00 
 
 5. $7.25 4- $6.48 + $15.23 + $28.16. 
 
 6. $9.32 + $17 + $ 0.64 + $36.99. 
 
 7. $0.56 + $1.38 + $10.49 + $ 0.18 + $14.38. 
 
 176. From $27 take $14.27. 
 
 Write dollars under dollars and cents under 
 $27 00 
 
 cents. Subtract as in ordinary numbers, and place 
 
 the decimal point before the last two fissures to 
 
 separate dollars from cents. 
 
 176. Exercise. 
 
 Find the difference : 
 
 /. $4.26 2. $15.42 5. $146.38 4. $96.45 
 3.83 9.83 27.94 0.87 
 
 5. $34.10 - $19.46 7. $82.56 - 37.49 9. $10 - $ 6.48 
 
 6. $ 1.48 - $ 0.79 5. $ 5 - 3.69 10. $50 - $42.65 
 
 177. Exercise. 
 
 /. A man bought a lot of land for $350 and built on it 
 a house that cost $1875 ; how much did both cost him ? 
 
88 WHOLE NUMBERS AND FRACTIONAL PARTS- 
 
 2. James had $2.75 and earned $3.75 more ; liow much 
 had he then ? 
 
 5. In a certain town there are 35 78 males and 4423 
 females ; how many people has the town ? 
 
 4. Take 11.25 from 15.00. 
 
 5. I had a 1000-mile ticket, but have used 695 miles 
 of it ; how many miles may I yet ride on it ? 
 
 6. A farmer^s crop for a certain year was 268 bushels of 
 wheat, 308 bushels of oats, 564 bushels of corn, and 78 
 bushels of rye ; how much grain did he raise that year ? 
 
 7. Frank and John together have $4.85. If Frank has 
 $2.90, how much has John ? 
 
 8. A wagon loaded with coal weighed 5268 pounds. If 
 the wagon weighed 1825 pounds, what was the weight of 
 the coal ? 
 
 9. A farmer bought a plow for $8.75 and gave in pay- 
 ment a $20-bill ; how much change should he receive ? 
 
 10. A farmer was paid $175.20 for his wheat and $106.30 
 for his potatoes ; how much was he paid for both ? 
 
 //. The number of ladies at a normal school duriiiij a 
 certain year was 539 and the number of men 221 ; how 
 many were there of both ? By how many did the former 
 exceed the latter ? 
 
 12. My brother earned $1.75 on Monday, $1.60 on 
 Tuesday, $1.85 on Wednesday, $1.35 on Thursday, and 
 $1.75 on Friday ; how much did he earn in tlio 5 days ? 
 
 13. I owed B $100 and gave him a cow worth $45.50 
 and the balance in cash ; how much cash did I give 
 him ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 89 
 
 14. Find the sum of one thousand four hundred eight, 
 three thousand forty-eight, and six hundred seventy-six. 
 
 15. Find the sum of all numbers that are greater than 
 1298 and less than 1304. 
 
 16. The following table gives the number of bushels 
 of grain bought by a dealer in one week ; fdl in the 
 totals : 
 
 Grain. 
 
 Mon. 
 
 Taes. 
 
 Wed. 
 
 Thurs. 
 
 Fri. 
 
 Sat. 
 
 Total. 
 
 Wheat 
 
 235 
 431 
 500 
 
 27 
 
 300 
 
 307 
 
 480 
 
 45 
 
 201 
 
 408 
 
 578 
 
 38 
 
 406 
 
 560 
 
 401 
 
 46 
 
 327 
 
 456 
 
 492 
 
 62 
 
 195 
 
 231 
 
 324 
 
 14 
 
 
 Corn 
 
 Oats 
 
 Rye 
 
 
 Total 
 
 
 
 
 
 
 
 
 Multiplication, Division, and Mensuration. 
 
 178. Oral Exercise. 
 
 Count by 6's : 
 
 /. From 6 to 60. 
 
 2. From 60 to 6. 
 
 3. From 1 to 61. 
 
 4. From 2 to 62. 
 
 5. From 3 to 63. 
 
 6. From 4 to 64. 
 
 7. From 5 to 65. 
 
 8. From 65 to 5. 
 
 Count by 7's : 
 
 9. From 7 to 70. 
 10. From 70 to 7. 
 //. From 1 to 71. 
 12. From 2 to 72. 
 
 13. From 3 to 73. 
 
 14. From 4 to 74. 
 
 15. From 5 to 75. 
 
 16. From 6 to 76. 
 
90 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 179. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 5x1 + 1= . 
 
 5x4+4= 
 
 5x7 + 7= . 
 
 G X 1 = . - 
 
 6x4 = 
 
 6x7=. 
 
 5x2 + 2= . 
 
 5x5+5= 
 
 5x8 + 8= . 
 
 6x2=. 
 
 6 X 5= « 
 
 6x8=. 
 
 5x3+3=- 
 
 5x6+6= 
 
 5x9 + 9= . 
 
 6x3=. 
 
 6x6=, 
 
 6x9=. 
 
 180. Exercise. 
 
 
 
 Copy, supplying 
 
 the missing numbers and learn : 
 
 
 TABLE. 
 
 
 6x1=. 
 
 6x4=. 
 
 6x7=. 
 
 6x2=. 
 
 6x5=. 
 
 6x8=- 
 
 6x3=. 
 
 6x6=. 
 
 6x9=. 
 
 181. Exercise. 
 
 Copy, supplying the missing numbers 
 
 6x1+1=. 
 
 6x4+4= 
 
 6x7+7=. 
 
 7x1=. 
 
 7x4 = 
 
 7x7=. 
 
 6x2 + 2= . 
 
 6x5+5= 
 
 6x8 + 8= . 
 
 7x2=. 
 
 7x5=. 
 
 7x8=. 
 
 G X 3 + 3 = . 
 
 6x6+6= 
 
 6x9 + 9= - 
 
 7x3=. 
 
 7x6=. 
 
 7x9=. 
 
 182. Exercise. 
 
 Copy, supplying the missing numbers and learn : 
 7x1=. 7x4=. 7x7 = 
 
 7x2=. 7x5=. 7x8= 
 
 7x3=. 7x6=.. 7x9= 
 
MULTIPLICATION, DIVISION, MENSURATION. 91 
 
 183. Oral Exercise. 
 
 
 
 
 
 
 Eead, supplying 
 
 the missing numbers : 
 
 
 
 
 /. 6 X 3 = . 
 
 19. 
 
 • 
 
 X 6 = 42 
 
 37. 
 
 • X 
 
 1 = 6 
 
 2. 7 X 7 = . 
 
 20. 
 
 6 
 
 X 2= . 
 
 38. 
 
 6 X 
 
 4= . 
 
 5. 7 X . = 49 
 
 21. 
 
 • 
 
 X 4 = 24 
 
 39. 
 
 7 X 
 
 . =42 
 
 4. 7 X 9 = . 
 
 22. 
 
 7 
 
 X . =21 
 
 40. 
 
 7 X 
 
 . =63 
 
 5. 7x4=. 
 
 23. 
 
 6 
 
 X 5= . 
 
 41. 
 
 6 X 
 
 . = 12 
 
 ff. 6 X 8 = . 
 
 24. 
 
 • 
 
 X 2 = 14 
 
 42. 
 
 • X 
 
 7 = 42 
 
 7. 7 x . = 28 
 
 25. 
 
 . 
 
 X 6 = 36 
 
 43. 
 
 6 X 
 
 6 = . 
 
 8. . X 7 = 49 
 
 26. 
 
 . 
 
 X 8 = 56 
 
 44. 
 
 6 X 
 
 . =24 
 
 5. 6 X 7 = . 
 
 27. 
 
 6 
 
 X 1 = . 
 
 45. 
 
 7 X 
 
 7= . 
 
 10. . X 2 = 12 
 
 28. 
 
 6 
 
 X . =42 
 
 46. 
 
 6 X 
 
 . =30 
 
 //. 6 X . = 36 
 
 29. 
 
 6 
 
 X 9= . 
 
 47. 
 
 6 X 
 
 . =6 
 
 /2. 7 X 5 = . 
 
 30. 
 
 6 
 
 X . = 54 
 
 48. 
 
 7 X 
 
 • = 35 
 
 /5. 7 X 6 = . 
 
 31. 
 
 . 
 
 X 9 = 54 
 
 49. 
 
 • X 
 
 3 = 18 
 
 14. . X 8 = 48 
 
 32. 
 
 • 
 
 X 9 = 63 
 
 50. 
 
 • X 
 
 5 = 35 
 
 15. . X 4 = 28 
 
 33. 
 
 . 
 
 X 1 = 7 
 
 51. 
 
 7 X 
 
 2 = . 
 
 /e. 7 X 2 = . 
 
 34. 
 
 6 
 
 X . = 18 
 
 52. 
 
 • X 
 
 3 = 21 
 
 17. . X 5 = 30 
 
 35. 
 
 7 
 
 X 1 = . 
 
 53. 
 
 6 X 
 
 . =48 
 
 /5. 7 X . = 56 
 
 36. 
 
 7 
 
 X 8= . 
 
 54. 
 
 7 X 
 
 3= . 
 
 184. Exercise. ' 
 
 1. Find the cost of these groceries together : 
 
 6 pounds of sugar at 5 cents a pound. 
 2 pounds of crackers at 5 cents a pound. 
 2 quarts of vinegar at 4 cents a quart. 
 
 2. In a room there are 7 rows of desks and in each row 
 8 desks ; how many desks are there in all ? 
 
 5. A man who sleeps 9 hours a day sleeps how long each 
 week? 
 
92 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 4. A farmer bought 6 lambs at 4 dollars apiece and sold 
 them at 5 dollars apiece ; how much did he make on each 
 lamb ? How much on the 6 lambs ? 
 
 5. In 6 bushels there are — pecks. 
 
 6. In 7 pecks there are — quarts. 
 
 7. Mr. Brown gave 3 boxes of strawberries at 8 cents a 
 box for syrup at 6 cents a quart ; how many quarts did he 
 receive ? 
 
 8. A lady spends 6 cents a day for milk ; how much is 
 that a week ? 
 
 9. Show by dots that 6 x 3 — 18. 
 
 10. \ dozen pigeons will make how many pair ? 
 
 //. How many bushels will 7 two-bushel bags hold ? 
 12. How many pencils are there in 7 boxes, if each box 
 contains 6 pencils ? 
 
 185. Each of the six equal parts of a number is 
 called one sixth {\) of it. 
 
 188. Each of the seven equal parts of a number is 
 called one seventh (|) of it. 
 
 187. Exercise. 
 
 
 
 
 Copy, writing the 
 
 proper figures in 
 
 place of x^: 
 
 
 /. ^of 6 = x 
 
 7. J of 42 = X 
 
 13. \ of 28 = 
 
 X 
 
 2. i of 12 := x 
 
 8. \ of 48 = X 
 
 U. ^ of 35 = 
 
 X 
 
 5. \ of 18 = X 
 
 9. i of 54 = X 
 
 15. ^ of 42 = 
 
 X 
 
 4. J of 24 = X 
 
 10. \oi 7 = X 
 
 16. 1 of 49 = 
 
 X 
 
 5. \ of 30 = X 
 
 //. |of 14 = X 
 
 n. \ of 50 = 
 
 X 
 
 6. i of 36 = X 
 
 12. |of 21 =x 
 
 18. \ of 63 = 
 
 X 
 
MULTIPLICATION, DIVISION, MENSURATION. 93 
 
 188. Oral Exercise. 
 
 Read Exercise 187, supplying the missing numbers. 
 
 189. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 /. 12 = — twos. 7. 30 = — fives. 13. 63 = — nines. 
 
 2. 7 = — ones. 8. 24 = — fours. 14. 4'^ = — sevens. 
 
 3. 14 = — twos. 9. 48 = — eights. 15. 35 = — fives. 
 
 4. 18 = — threes. 10. 42 — — sixes. 16. 36 = — sixes. 
 
 5. 6 = — ones. //. 28 = — fours. /7. 4C = — sevens. 
 
 6. 21 = — threes. 12. 54 = — nines. 18. 56 — — eights. 
 
 190. Oral Exercise. 
 
 Read Exercise 189, supplying the missing numbers. 
 
 191. Exercise. 
 
 /. Divide 12 cards equally among 6 boys. What part 
 of them will each boy receive ? How many will each boy 
 receive ? 
 
 2. How many yards of carpet are there in a piece 21 
 feet long ? 
 
 3. 48 girls are marching 6 in a row ; how many rows 
 are there ? 
 
 4. How many 5-cent pieces should I get in exchange 
 for 30 cents ? 
 
 5. 3 gallons of syrup will fill how many 2-quart jars ? 
 
 6. How long will 3 pecks of oats last a horse that eats 
 4 quarts a day ? 
 
94 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 7. In 28 days there are — weeks. 
 
 8. At 4 for a cent, how much must I pay for 28 
 rivets ? 
 
 9. How many yards of muslin at 8 cents a yard can be 
 bought for 8 quarts of plums at G cents a quart ? 
 
 10. A boy earned 54 dollars in six months ; how much 
 was he paid a month ? 
 
 11. A dozen will make how many pair ? 
 
 12. How many working days are there in a week ? 
 
 13. A man who earns 3 dollars each working day earns 
 how much in a week ? 
 
 14. 6 pounds of lard at 8 cents a pound, and how many 
 cents, will pay for a 50-cent bucket ? 
 
 192. Oral Exercise. 
 
 Count by 8's : 
 
 /. From 8 to 80. 
 
 2. From 80 to 8. 
 
 3. From 1 to 81. 
 
 4. From 2 to 82. 
 
 5. From 3 to 83. 
 
 6. From 4 to 84. 
 
 7. From 5 to 85. 
 
 8. From 6 to 86. 
 
 9. From 7 to 87. 
 10. From 8 to 88. 
 
 Count by 9's : 
 
 //. From 9 to 90. 
 
 12. From 90 to 9. 
 
 13. From 1 to 91. 
 
 14. From 2 to 92. 
 
 15. From 3 to 93. 
 
 re. From 4 to 94. 
 
 17. From 5 to 95. 
 
 18. From 6 to 96. 
 
 19. From 7 to 97. 
 
 20. From 8 to 98. 
 
MULTIPLICATION, DIVISION, MENSURATION. 95 
 
 193. Exercise. 
 
 
 
 Copy, supplying 
 
 the missing numbers 
 
 
 7x1 + 1=. 
 
 7x4+4=. 
 
 7x7+7=. 
 
 8 X 1 r= . 
 
 8x4=. 
 
 8x7= • 
 
 7x2 + 2= . 
 
 7x5 + 5= . 
 
 ■7x8 + 8= . 
 
 8x2=. 
 
 8x5=. 
 
 8x8=. 
 
 7x3 + 3= . 
 
 7x6 + 6= . 
 
 7x9 + 9= . 
 
 8x3=. 
 
 -8x6=. 
 
 8x9=. 
 
 194. Exercise. 
 
 
 
 Copy, supplying 
 
 the missing numbers, 
 
 TABLE. 
 
 and learn : 
 
 8x1=. 
 
 8x4=. 
 
 8x7=. 
 
 8x2=. 
 
 8x5=. 
 
 8x8=. 
 
 8x3=. 
 
 8x6=. 
 
 8x9=. 
 
 195. Exercise. 
 
 
 
 Copy, supplying 
 
 the missing numbers 
 
 
 8x1 + 1= . 
 
 8x4 + 4= . 
 
 8x7 + 7= . 
 
 9x1=. 
 
 9x4=. 
 
 9x7=. 
 
 8x2 + 2= . 
 
 8x5 + 5= . 
 
 8x8 + 8= . 
 
 9x2=. 
 
 9x5=. 
 
 9x8=. 
 
 8x3 + 3= . 
 
 8x6 + 6= . 
 
 8x9 + 9= . 
 
 9x3=. 
 
 9x6=. 
 
 9x9=. 
 
 196. Exercise. 
 
 
 
 Copy, supplying 
 
 the missing numbers, 
 
 TABLE. 
 
 and learn : 
 
 9x1=. 
 
 9x4=. 
 
 9x7=. 
 
 9x2=. 
 
 9x5=. 
 
 9x8=. 
 
 9x3=. 
 
 9x6=. 
 
 9x9=. 
 
96 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 197. Oral Exercise. 
 
 Head, supplying the missing numbers : 
 
 /. 
 
 8 
 
 X 
 
 2= . 
 
 19. 
 
 9 
 
 X 
 
 .= 63 
 
 37. 
 
 . 
 
 X 
 
 1 = 8 
 
 2. 
 
 . 
 
 X 
 
 7 = G3 
 
 20. 
 
 • 
 
 X 
 
 9 = 81 
 
 38. 
 
 . 
 
 X 
 
 5 = 45 
 
 3. 
 
 • 
 
 X 
 
 1 = 9 
 
 21. 
 
 9 
 
 X 
 
 .= 36 
 
 39. 
 
 9 
 
 X 
 
 .= 72 
 
 4. 
 
 8 
 
 X 
 
 8= . 
 
 22. 
 
 9 
 
 X 
 
 5 = . 
 
 40. 
 
 8 
 
 X 
 
 7= . 
 
 5. 
 
 9 
 
 X 
 
 7= . 
 
 23. 
 
 8 
 
 X 
 
 . = 56 
 
 41. 
 
 9 
 
 X 
 
 9= . 
 
 6. 
 
 . 
 
 X 
 
 9 = 72 
 
 24. 
 
 9 
 
 X 
 
 3= . 
 
 42. 
 
 • 
 
 X 
 
 6 = 54 
 
 7. 
 
 • 
 
 X 
 
 8 = 72 
 
 25. 
 
 • 
 
 X 
 
 2 = 18 
 
 43. 
 
 . 
 
 X 
 
 4 = 36 
 
 8. 
 
 8 
 
 X 
 
 6= . 
 
 26. 
 
 9 
 
 X 
 
 .= 9 
 
 44. 
 
 9 
 
 X 
 
 .= 27 
 
 9. 
 
 9 
 
 X 
 
 8= . 
 
 27. 
 
 9 
 
 X 
 
 1 = . 
 
 45. 
 
 9 
 
 X 
 
 G = . 
 
 10. 
 
 8 
 
 X 
 
 .= 72 
 
 28. 
 
 • 
 
 X 
 
 2 = 16 
 
 46. 
 
 • 
 
 X 
 
 6 = 48 
 
 11. 
 
 8 
 
 X 
 
 . = 32 
 
 29. 
 
 8 
 
 X 
 
 .= 40 
 
 47. 
 
 9 
 
 X 
 
 .= 18 
 
 12. 
 
 8 
 
 X 
 
 .= IG 
 
 30. 
 
 8 
 
 X 
 
 . = 24 
 
 48. 
 
 8 
 
 X 
 
 .= 8 
 
 13. 
 
 8 
 
 X 
 
 5= . 
 
 31. 
 
 8 
 
 X 
 
 1 = • 
 
 49. 
 
 9 
 
 X 
 
 .= 54 
 
 14. 
 
 • 
 
 X 
 
 8 = G4 
 
 32. 
 
 . 
 
 X 
 
 4 = 36 
 
 50. 
 
 • 
 
 X 
 
 7 = 56 
 
 15. 
 
 9 
 
 X 
 
 4= . 
 
 33. 
 
 8 
 
 X 
 
 4 . 
 
 51. 
 
 9 
 
 X 
 
 . = 81 
 
 16. 
 
 8 
 
 X 
 
 9= . 
 
 34. 
 
 8 
 
 X 
 
 3= . 
 
 52. 
 
 • 
 
 X 
 
 3 = 27 
 
 17. 
 
 . 
 
 X 
 
 5 = 40 
 
 35. 
 
 9 
 
 X 
 
 .= 45 
 
 53. 
 
 • 
 
 X 
 
 3 = 24 
 
 18. 
 
 8 
 
 X 
 
 .= 64 
 
 36. 
 
 9 
 
 X 
 
 2= . 
 
 54. 
 
 8 
 
 X 
 
 . = 48 
 
 198. Exercise. 
 
 /. In 8 gallons there are — quarts. 
 
 2. In 8 weeks there are — days. 
 
 3. In 8 pecks there are — quarts. 
 
 4. 8 X 2 + . = 9 X 2. 
 
 5. 9 three-bushel bags will hold how much wheat ? 
 
 6. 8 two-cent stamps will cost how much ? 
 
 7. At 4 dollars a hundred, what will 9 hundred cabbage 
 plants cost ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 97 
 
 8. What should be paid for 9 dozen herrings at 8 cents 
 a dozen ? 
 
 9. What should be paid for 8 hundred rails at 6 dollars 
 a hundred ? 
 
 10. How many feet long is a fishing line 8 yards long ? 
 
 / /. How many persons are seated in a dining-room at 
 6 tables, if there are 8 persons at each table ? 
 
 12. A drover sold 8 pair of mules and one more ; how 
 many did he sell ? 
 
 13. After a farmer sold 8 bags of wheat each holding 3 
 bushels, he had 5 bushels left ; how many had he at first ? 
 
 14. In 1 bushel there are — pecks, and in 1 peck there 
 are — quarts ; then in 1 bushel there are — times — 
 quarts, or — quarts. 
 
 15. Show that there are 8 pints in a gallon. 
 
 199. Each of the 8 equal parts of a number is one 
 eighth (|) of it. 
 
 200. Each of the 9 equal parts of a number is one 
 ninth (i) of it. 
 
 201. Exercise. 
 
 Copy, writing the proper figures in place of x : 
 
 /. i of 8 = X 
 
 7. ^ of 56 = X 
 
 13. i of 36 = X 
 
 2. J of IG = X 
 
 8. '\ of 64 = X 
 
 14. ^ of 45 = X 
 
 3. 1 of 24 = X 
 
 9. \ of 72 = X 
 
 15. ^ of 54 = X 
 
 4. 4 of 32 = X 
 
 10. \Qi 9 = X 
 
 16. ^ of 63 = X 
 
 5. i of 40 = X 
 
 //. -iof 18 = X 
 
 n. ^ of 72 = X 
 
 6. -^ of 48 == X 
 7 
 
 12. i of 27 = X 
 
 18. i of 81 = X 
 
98 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 202. Oral Exercise. 
 
 Read Exercise 201, supplying the missing numbers. 
 
 203. Exercise. 
 
 Copy, supplying the missing numbers : 
 
 /. 8 = — ones. 7. 27 — — threes. 13. 72 = — nines. 
 
 2. 18 = — twos. 8. 56 = — sevens. 14. 04 = — oights. 
 
 3. 24 = — threes. 9. 45 = — fives. 15. 40 = — fives. 
 
 4. 32 = —fours. 10. 36 = —fours. 16. 63 = —sevens. 
 
 5. 9 = — ones. //. 48 = — sixes. 17. 72 = — eights, 
 ff. 16 = — twos. 12. 54 = — sixes. 18. 81 = — nines. 
 
 204. Oral Exercise. 
 
 Read Exercise 203, supplying the missing numbers. 
 
 205. Exercise. 
 
 /. 18 cents will buy — 2-cent stamps. 
 
 2. How many 8-foot logs can be cut from a log 40 feet 
 long ? 
 
 3. Make and solve a problem about ^ of 16 boys. 
 
 4. 800 posts cost 56 dollars ; how much was that for 
 each hundred posts. 
 
 5. My brother and I bought 9 dozen tomato plants for 
 72 cents ; how much was that a dozen ? How much 
 should he pay if he took 6 dozen ? 
 
 6. A log 42 feet long will make a 10-foot log and how 
 many 4-foot logs ? 
 
 7. A grocer put 40 pounds of sugar in 8 sacks of the 
 same size ; how much did he put in each sack ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 99 
 
 8. A farmer had 20 pigs. lie kept 4 of them and sold 
 the rest ; how many pair did he sell ? 
 
 9. How many 5-dollar bills should I get for 45 silver 
 dollars ? 
 
 10. A farmer needs 24 pounds of twine to bind his 
 wheat ; how many 3-pound balls must he buy ? 
 
 11. A woman sold a dealer chickens at 8 cents a pound ; 
 he paid her 72 cents for them ; how many pounds did she 
 sell him ? 
 
 12. I wish to plant 64 trees in 8 rows ; how many must 
 I put in a row ? 
 
 2 .r « 
 
 206. Find f of 9. 
 
 T0f9 
 
 Find f of 15. 
 
 i of 15 is 5, and f of 15 is 2 times 5 or 10. 
 
 207. Oral Exercise. 
 Find: 
 
 /. f of 6. 5. f of 12. P. ^ f of 28. 13. f of 20. 
 
 2. f of 3. 6. f of 21. 10. J of 32. 14. f of 30. 
 
 5. I of 9. 7. J of 12.* //. jof24. /5. I of 45. 
 
 4. f of 15. S. I of 16. 12. f of 10. 16. I of 25. 
 
 208. Exercise. 
 
 /. J of 27 ct. is — ct. ; and | of 27 ct. is 2 times — ct., 
 or — ct. 
 
 2. What is I of 6 pounds ? 
 
100 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 3. What is I of 12 quarts ? 
 
 4. J of 16 bushels is — bushels, and } of 16 bushels is 
 3 times — bushels, or — bushels. 
 
 5. Find J of 12 oranges. 
 
 6. Find f of 10 cents. 
 
 7. If 18 cents was the cost of 3 pounds of sugar, J of 
 18 cents, or — cents, was the cost of 1 pound, and 2 times 
 — cents, or — cents, was the cost of 2 pounds. 
 
 8. How much should be paid for 2 pencils, if 3 pencils 
 cost 15 cents ? 
 
 9. A baker charged me 12 cents for 3 loaves of bread ; 
 what should he charge me for 2 loaves ? 
 
 10. If 3 horses are fed 24 quarts of oats a day, how 
 much does that allow for 2 horses ? 
 
 11.1 owed a 16-dollar store bill and paid J of it ; how 
 much did I pay ? 
 
 12. Martha is 20 years old and May is J as old ; how 
 old is May ? 
 
 13. A boy paid 10 cents for a tablet, and J as much for 
 a ruler ; how much did he pay for both ? 
 
 14. If 5 loaves of bread cost 30 cents, 1 loaf costs J of 
 30 cents, or — cents ; and 4 loaves cost 4 times — cents, 
 or — cents. 
 
 15. Wliat should I be paid for 3 days' work, if I was 
 paid 15 dollars for 5 days' work ? 
 
 16. A boy was given 25 words to spell ; he missed | of 
 them ; how many did he spell correctly ? 
 
 17. There are 21 dots in three rows, each containing 
 the same number ; how many dots are there in 2 rows ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 101 
 
 18. A grocer charged me 9 cents for 3 lemons, bat one 
 of them was bad ; how much should he have charged me 
 for the good lemons ? 
 
 19. I just paid $30 for 3 months' rent ; I now wish to 
 pay 2 months' rent in advance ; how much should I pay ? 
 
 20. If 4 persons use 8 pounds of meat a week, how much 
 should 5 persons use ? 
 
 209. Exercise. 
 
 Copy and multiply : 
 /. 27 6. 19 //. 18 16. 13 21. 128 26. 123 
 
 6 7 8 9 8 8 
 
 2. 39 7. 28 12. 26 17. 24 22. 109 27. 109 
 
 _6 _7 _8 _9 7 8 
 
 3. 58 8. 36 13. 74 18. 37 23. 138 28. 108 
 
 _6 ^ _8 _9 7 9 
 
 4. 66 9. 54 14. 93 19. 55 24. 145 29. 117 
 
 _6 _7 _8 __9 6 8 
 
 5. 79 10. 70 15. 50 20. 86 25. 139 30. 122 
 
 6 7 8 9 6 8 
 
 210. Multiply $2.38 by 6. 
 $2.38 Multiply as in ordinary numbers, and place the 
 Q decimal point before the last two figures of the 
 $14 28 pro^^uct to separate dollars from cents. 
 
'io'S WHOL^' NUMBERS AND FRACTIONAL PARTS. 
 
 211. Exercise. 
 
 Multiply : 
 
 /. $4.28 3. $0.56 
 
 4 9 
 
 5. $48.07 
 8 
 
 7. $27.08 
 8 
 
 2. $8.72 4. $138.40 
 7 6 
 
 6. $94.18 
 9 
 
 8. $125.15 
 5 
 
 9. $3.25 by 5. //. $21.38 by 8. /5. $38.90 by 7. 
 10. $19.20 by G. 12. $75.03 by 9. 14. $1025.03 by 8. 
 
 212. Exercise. 
 
 Copy and fill in the missing amounts in the following: 
 
 /. The cost of : 
 
 6 plum trees at $1.25 each = $, 
 
 8 peach trees at $0. 80 each = 
 
 7 pear trees at $1.10 each = 
 
 9 apple trees at $0.75 each = 
 
 Total =i 
 
 The cost of : 
 
 4 kegs of nails at $2.75 each = $. . . 
 
 6 bushels of clover seed at 
 
 $5.75 each = ... 
 
 7 tons of bran at $18. (;0 each = ... 
 
 8 tons of coal at $5.75 each = . . . 
 
 Total =$... 
 
MULTIPLICATION, DIVISION, MENSURATION. 103 
 
 3. The cost of : 
 
 9 sheep at 16.75 each = 
 
 5 horses at $125 per head. — 
 8 cows at $40.50 per head. = 
 8 hogs at $8.75 per head. . = 
 
 Total = 
 
 213. Exercise. 
 
 /. Find the cost of 6 yards of cloth at 15 cents a yard. 
 
 2. A car that makes 24 trips a day makes how many 
 trips a week ? 
 
 3. How many hours are there in a week ? 
 
 4. A gardener planted 8 rows of trees ; he planted 16 
 trees in each row ; how many trees did he plant in all ? 
 
 5. A farmer sold 8 loads of wheat ; there were 25 bushels 
 in each load ; how many busiiels were there in all ? 
 
 6. A bushel of potatoes weighs 60 pounds ; find the 
 weight of 8 bushels of potatoes. 
 
 7. A bushel of corn weighs 56 pounds ; find the weight 
 of 6 bags of corn, each holding 3 bushels. 
 
 8. How many eggs will 9 crates hold, if each crate holds 
 6 dozen ? 
 
 9. How many persons can be seated in 8 rows of chairs, 
 if there are 38 chairs in each row ? 
 
 10. How many persons can be seated in 6 cars, if there 
 are 36 seats in each car and 2 persons can sit on each seat? 
 
 //. A dealer sold to each of 8 men 125 barrels of flour 
 and has 50 barrels left ; how many barrels had he at first ? 
 
104 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 12. My lot cost $125, and my house 6 times as much ; 
 how much did they both cost ? 
 
 214. Oral Exercise. 
 
 20 30 40 50 60 70 80 90 
 Multiply each of the numbers above the line 
 
 /. By 2. 
 Thus, 3 times 20 are 40 ; 2 times 30 are GO ; etc. 
 
 2. By 3. 
 
 4. 
 
 By 5. 6. 
 
 By 
 
 7. 
 
 8. By 9. 
 
 3. By 4. 
 
 5. 
 
 By 6. 7. 
 
 By 
 
 8. 
 
 
 215. Oral Exercise. 
 
 
 
 
 Multiply : 
 
 
 
 
 
 
 /. 25 by 3. 
 
 
 
 
 
 
 Thus, 3 times 20 
 
 are 
 
 60 and 3 times 5 are 15 ; 
 
 60 and 15 are 75. 
 
 2. 32 by 2. 
 
 
 9. 43 by 5. 
 
 
 16. 
 
 02 by 7. 
 
 3. 48 by 2. 
 
 
 10. 38 by 5. 
 
 
 17. 
 
 84 by 8. 
 
 4. 34 by 3. 
 
 
 //. QQ by 5. 
 
 
 18. 
 
 15 by 8. 
 
 5. 25 by 3. 
 
 
 12. 72 by 6. 
 
 
 19. 
 
 30 by 8. 
 
 6. 43 by 4. 
 
 
 13. 43 by 0. 
 
 
 20. 
 
 02 by 9. 
 
 7. 50 by 4. 
 
 
 14. 25 by 6. 
 
 
 21. 
 
 2b by 8. 
 
 8. QQ by 4. 
 
 
 15. 75 by 6. 
 
 
 22. 
 
 30 by 8. 
 
 216. Exercise. 
 
 /. AVhat is the cost of 2 handkerchiefs at 18 cents each ? 
 
 2. What is the cost of 3 hatchets at 30 cents each ? 
 
 3. How many boxes of rivets are there in 6 packages, 
 each package containing a dozen boxes ? 
 
 4. How many yards of picture cord are there in 4 coils, 
 each containing 25 yards ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 105 
 
 5. A lady bought 2 yards of gingham at 18 cents a 
 yard; how much change should she receive from 50 
 cents ? 
 
 There are 16 oimces {oz.) in a pound {lb.) avoirdupois. 
 
 6. How many ounces are there in 5 pounds avoirdupois ? 
 
 7. How many ounces are there in 3 pounds 2 ounces ? 
 
 8. 4 strips of carpet, each 8 yards long, are needed to 
 carpet a certain floor ; how many yards are required ? 
 
 9. Find the cost of 3 yards of muslin at 12 cents a yard, 
 and 3 yards of flannel at 20 cents a yard. 
 
 10. How much should a trader pay for 2 dozen eggs at 
 15 cents a dozen and 3 pounds of butter at 20 cents a 
 pound ? 
 
 //. How many are 4 score and 10 ? 
 
 12. How many are a half dozen dozen ? 
 
 13. How much should a bushel of potatoes cost at 15 
 cents a peck ? 
 
 14. How much is received for a gallon of cream at 16 
 cents a quart ? 
 
 15. If a peck of clover seed weighs 15 pounds, what 
 does a bushel weigh ? 
 
 16. The distance between two towns is 12 miles ; how far 
 docs a motorman ride each day, if he makes 4 round trips 
 on a trolley line connecting these towns ? 
 
 217. 3 rows of 4 dots each contain #^00 
 as many dots as 4 columns of 3 dots # • # ^ 
 each, which shows that 3x4 = 4x3. #••• 
 
106 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 218. Oral Exercise. 
 
 Multiply : 
 
 /. 2 by 20. Thus, 20 times 2 equals 2 times 20, or 40. 
 
 2. 2 by 25. 6. 3 by 60. 10. 4 by 60. 14. 6 by 48. 
 
 3. 2 by 40. 7. 3 by 25. //. 5 by 25. 15. 7 by 14. 
 
 4. 2 by 26. 8. 3 by 42. 12. 5 by 50. 16. 8 by 24. 
 
 5. 2 by 54. 9. 3 by 18. 13. by 36. 17. 9 by 31. 
 
 219. Exercise. 
 
 /. A boy sold 24 newspapers at 2 cents each ; how much 
 
 did he receive for them ? 
 
 Since he sold one newspaper for 2 cents, he sold 24 for 24 times 
 2 cents, which equals 2 times 24 cents, or — cents. 
 
 2. Find the cost of 20 two-cent postage stamps. 
 
 3. A trolley car conductor collected on one trip 5 cents 
 from each of 18 persons ; how much did he collect ? 
 
 4. How many persons are seated at 16 tables, if there 
 are 4 persons at each table ? 
 
 5. How many days are there in 21 weeks ? 
 
 6. How much does it cost to ride 28 miles on a railroad, 
 if the fare is 3 cents a mile ? 
 
 7. If school is in session 6 hours a day for 20 days of a 
 month, how many hours is it in session in a month ? 
 
 8. Find the gain on a dozen tablets bought for 50 cents 
 and sold at 6 cents each. 
 
 220. Find the cost of 126 yards of cloth at 5^ a yard. 
 $1.26 126 X 5^ =the cost. 
 
 5 But 126 X 5^ = 5 X 126^, or 5 x |1.26. 
 
 rrri Therefore, 5 x $1.26, or $6.30 = the cost. 
 
 In practice, multiply by the smaller mtn^>er. 
 
MULTIPLICATION, DIVISION, MENSURATION. 107 
 
 221. Exercise. 
 
 Find the cost of : 
 
 /. 126 bushels of seed at 15 per bushel. 
 
 2. 228 pounds of soap at 5^ per pound. 
 
 3. 476 pounds of sugar at 6^ per pound. 
 
 4. 208 quarts of milk at 6^* per quart. 
 
 5. 165 barrels of apples at $4 per barrel. 
 
 6. 125 yards of carpet at $2 per yard. 
 
 7. 288 fruit trees at $1 each. 
 
 8. 385 gallons of oil at 90 per gallon. 
 
 9. A bushel of chestnuts at 8^ a quart. 
 
 10. 75 cans of corn at 8^ each. 
 
 222. Exercise. 
 
 
 
 Copy and divide : 
 
 
 
 /. Q)Q^ 
 
 10. 7)84 
 
 19. 6)954 
 
 25. 8)624 
 
 2. 6)60 
 
 //. 8)96 
 
 20. 6)750 
 
 29. 8)920 
 
 3. 7)77 
 
 ' 12. 7)98 
 
 21. 7)147 
 
 50. 8)704 
 
 4. 7)70 
 
 13. 6)102 
 
 22. 7)791 
 
 31. 9)819 
 
 5. 8)88 
 
 14. 9)108 
 
 23. 7)812 
 
 52. 9)765 
 
 6. 6)84 
 
 15. 8)104 
 
 24. 7)903 
 
 55. 9)648 
 
 7. 6)90 
 
 16. 6)366 
 
 25. 7)814 
 
 34. 9)531 
 
 8. 6)96 
 
 17. 6)672 
 
 26. 8)248 
 
 55. 9)396 
 
 9. 7)91 
 
 18. 6)804 
 
 27. 8)896 
 
 36. 9)612 
 
 223. Divide $18.75 by 5. 
 5 "i 118 75 Divide as in ordinary numbers, and place 
 
 "T IT the decimal before the last two figures to sepa- 
 
 rate dollars from cents. 
 
108 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 224. Exercise. 
 
 Divide : 
 
 /. 2 )118.72 5. y )$35.14 9. $178.50 by 5 
 
 2. 3 )$31.05 6. 9 )1193.05 10. $374.24 by 4 
 
 3. 6 )115.48 7. 5 )1100.10 //. $127.00 by 5 
 
 4. 8 )133.60 8. 6 )$127.08 12. $38.07 by 9 
 
 225. Exercise. 
 
 Find the cost of 1 pound of each, if : 
 /. 6 lb. of coffee cost $2.10. 
 2. 8 lb. of dried beef cost $2.00. 
 5. 5 lb. of ham cost $0.80. 
 
 4. 4 lb. of tea cost $2.80. 
 
 5. 7 lb. of butter cost $1.96. 
 
 6. 9 lb. of cheese cost $1.44. 
 
 7. 3 lb. of yarn cost $1.05. 
 
 8. 8 lb. of prunes cost $1.20. 
 
 226. Exercise. 
 
 /. A lady bought 6 yards of cloth for 96 cents ; how 
 much was it a yard ? 
 
 2. A dealer sold 6 horses for $900 ; he received the 
 same sum for each ; how much did he receive for each ? 
 
 3. 7 men caught 819 shad and shared them equally ; 
 how many did each receive ? 
 
 4. A man earned $84 in 6 weeks and his son earned $66 ; 
 liow much did both earn ? How much did both earn in 
 a week ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 109 
 
 5. A man rode 644 miles on Tuesday and \ as far on 
 Wednesday ; how far did he ride in the two days ? 
 
 6. In 9 class-rooms there are 405 desks ; if each room 
 contains the same number of desks, how many are there 
 in each room ? 
 
 7. A dealer had 500 dressed chickens ; he sold 68 of 
 them and shipped the others in 6 barrels of equal size ; 
 how many did he put in each barrel ? 
 
 8. Divide 818 - 106 by 8. 
 
 9. I owed $718, and paid $32; I wish to pay the 
 rest in 6 equal parts ; how much must I pay in each 
 part ? * 
 
 10. Make and solve a problem about 672 trees that were 
 sold during 6 days. 
 
 //. Divide 386 + 428 - 128 by 7. 
 
 12. Divide $648 among 3 persons, giving the first 
 person ^ of the money, the second ^ of it, and the third 
 the remainder. 
 
 227. Exercise. 
 Measure : 
 
 /. 96 by 6. 5. 402 by 6. 9. 801 by 9. 
 
 2. 108 by 9. 6. 833 by 7. 10. 726 by 6. 
 
 3. 272 by 8. 7. 504 by 9. //. 749 by 7. 
 
 4. 896 by 7. 8. 376 by 8. 12. 816 by 8. 
 
 228. Measure $12.05 by $0.05. 
 
 $13.05 : $0.05 = 12050 : 5^ = 1205 -- 5, or 241. 
 
110 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 229. Exercise. 
 Measure : 
 
 /. $4.24 by $0.04. 7. $12.72 by 6^. 
 
 2. $5 by 5^'. 8. $0.96 by 4^. 
 
 3. $18.36 by $0.09. 9. $12.50 by 5^. 
 
 4. $12.32 by $0.08. /O. $12.25 by 5^. 
 
 5. $50 by $0.05. //. $81 by 9^. 
 
 6. $27.99 by $0.09. 12, $120 by 80. 
 
 230. Exercise. 
 
 Find how many can be bought : 
 /. 2-cent postage stamps for $1.72. 
 
 2. 5-cent tablets for $11.65. 
 
 3. 3-cent pencils for $0.84. 
 
 4. 5-ceut loaves of bread for $2.40. 
 
 5. 4-cent boxes of matches for $0.60. 
 
 6. 8-cent spools of thread for $1.12. 
 
 7. 8-cent note books for $3.44. 
 
 8. 5-cent spools of thread for $1. 
 
 231. Exercise. 
 
 /. llow many pecks are there in 216 quarts ? 
 
 2. How many weeks are there in 364 days ? 
 
 3. How many trains of 9 cars each can be made up 
 from 189 cars ? 
 
 4. How many weeks will it take to get $344 by saving 
 $8 a week ? 
 
 5. Find the cost of 108 marbles, if 9 are bought for a 
 cent. 
 
MULTIPLICATION, DIVISION, MENSURATION. 1 1 1 
 
 6. How many 8-cent stamps can you buy for 96 cents ? 
 
 7. How long will it take a boat to sail 224 miles, if it 
 sails 8 miles an hour ? 
 
 8. If coal costs $6 a ton, how many tons can be bought 
 for $216 ? 
 
 9. How many groups of 6 marbles each can be made 
 with 150 marbles ? 
 
 10. A dealer bought 8 dozen hats in boxes of 6 hats 
 each ; how many boxes were there ? 
 
 //. A dealer bought 750 cigars, and after selling 324 of 
 them, put the rest in packages of 6 each ; how many 
 packages had he ? 
 
 12. If the distance around a wheel is 6 feet, how many 
 times will it turn in going 882 feet ? 
 
 13. 144 trees can be planted in rows of 6 trees each, 8 
 trees each, or 9 trees each ; how many rows of each kind 
 would they make ? 
 
 232. Exercise. 
 
 /. What is each of the three equal parts 
 of 1 called ? 
 
 2. How many thirds are there in 1 ? 
 r 3. Read : i ; f ; |. 
 
 4. What is each of the six equal parts of 
 1 called ? 
 
 5. What are 2 of the six equal parts of 1 
 called ? 
 
112 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 6. Kead : J ; ^ ; f ; S ; I ; f 
 
 7. In J there are how many sixths ? 
 
 8. In f there are how many sixtlis ? 
 
 9. In J there are how many sixths ? 
 
 10. Show that ^ of 2 is |, or f 
 //. Show that ^ of 3 is J, or J. 
 12. Show that ^ of 4 is ^, or f. 
 /3. Show that J of 5 is |, 
 
 233. Find ^ of 26. 
 
 Answer thus : ^ of 26 is 4, and 3 over ; ^ of 2 is |, or §. 
 The answer is 2^. 
 
 234. Oral Exercise. 
 
 Find : 
 
 /. J of 7. 4. I of 13. 7. J of 28. 10. \ of 34. 
 
 2. ^ of 8. 5. ^ of 16. S. J of 25. //. J of 45. 
 
 5. I of 9. 6. ^ of 20. 9. J of 40. 12. J of 50. 
 
 235. How many 6's are there in 16 ? 16 = 2| sixes. 
 
 Supply the missing numbers, using drawings to illus- 
 trate : 
 /. 8 = — sixes. 4. 15 = — sixes. 7. 28 = — sixes. 
 2. 9 = — sixes. 5. 17 = — sixes. 8. 33 = — sixes. 
 5. 14 = — sixes. 6. 20 = — sixes. 9. 16 = — sixes. 
 
MULTIPLICATION, DIVISION, MENSURATION. 113 
 
 237. Exercise. 
 
 /. If G pounds of soap cost 25 cents, how much is the 
 soap a pound ? 
 
 2. A dealer has 50 handkerchiefs which he wishes to 
 put up in boxes of half a dozen each ; how many boxes 
 will there be, and how many handkerchiefs over ? 
 
 3. What is each of the seven equal parts of 1 called ? 
 
 4. Show that i of 2 is f . 
 
 5. Read : f ; f ; 4 : f ; f ; -I- 
 
 6. Show that there are 2f sevens in 16. 
 
 7. Find \ of each number in the outer ring of the left- 
 hand design. 
 
 8. Find how many 7's there are in each number in the 
 outer ring of the right-hand design. 
 
 9. 25 days are — weeks — days. 
 
 10. K man who earns 15 dollars in the G working days 
 of a week earns how much a day ? 
 
 //. January has 31 days ; this is how many weeks and 
 days ? 
 
 12. April has 30 days ; this is how many weeks and days? 
 8 
 
114 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 13. When board costs 10 dollars a week, how much is it 
 per day ? 
 
 14. How many pounds of sugar at 6 cents a pound can 
 be bought for 8 pounds of duck at 7 cents a pound ? 
 
 238. Oral Exercise. 
 
 \ 
 
 1. What is each of the 8 
 equal parts of 1 called ? 
 
 2. How many eighths are 
 there in 1 ? 
 
 3. How many eighths are 
 there in J ? in J ? 
 
 4. How many eighths are there in J ? 
 
 5. Eead : I ; f ; I ; I ; S ; |. 
 
 6. How many fourths are there in f ? in ^ ? in | ? 
 
 7. How many halves are there in ^ ? in f ? 
 
 8. What is each of the 9 equal parts 
 of 1 called ? 
 
 9. How many ninths are there in 1 ? 
 
 10. How many ninths are there in \ ? 
 inf ? 
 
 //. Read: | ; 4 ; | ; | ; 3 ; 4 ; i ; i 
 12. How many thirds are there in ^ ? ^ ? 
 
 1 
 ..............1 
 
 1 
 
 9 
 
 J ! 
 
 1 f 
 j I 
 
 239. Exercise. 
 
 /. Show that i of 2 is |, or J. 
 
 2. Show that i of 4 is |, or J. 
 
 3. Show that ^ of 6 is |, or J. 
 
 4. Show that -^ of 3 is ^, or J. 
 
 5. Show that i of G is i or |. 
 
MULTIPLICATION, DIVISION, MENSURATION. 115 
 
 240. Oral Exercise. 
 
 What is : 
 
 /. iof 5? 5. ^ of 30? //. iof 25 ? 
 
 2. ^ of 25 ? 7. ^ of 35 ? 12. 1 of 30 ? 
 
 5. i of 20 ? 8. \ of 42 ? /5. ^ of 38 ? 
 
 4. ^ of 22 ? 5. ^ of 50 ? /4. ^ of 40 ? 
 
 5. ^ of 18 ? 10. I of 12 ? 15. ^ of 53 ? 
 
 241. Exercise. 
 
 /. Show that there are 2 J eights in 20. 
 
 2. In 15 quarts there are — pecks — quarts. 
 
 3. In 25 quarts there are — pecks — quarts. 
 
 4. Show that there are 2f nines in 20. 
 
 5. Show that there are 2^ nines in 21. 
 
 6. If a peck of plums sold for 50 cents, how much were 
 they a quart ? 
 
 7. 25 cents will pay for how many pounds of rice at 8 
 cents a pound, and how many cents will be left over ? 
 
 8. 38 dots will make how many lines of 9 dots each, 
 and how many dots will be over? 
 
 242. Exercise. 
 
 /. How many days are there in G weeks ? 
 2. 30 quarts are — pecks — quarts. 
 5. 2 sets of casters, 4 in a set, cost 20 cents ; how much 
 did each caster cost ? 
 
 4. Find the gain on 40 papers bought at 1 ct. each and 
 sold at 2 ct. each. 
 
 5. Since 16 ounces make a pound, how many pounds 
 will 2 cakes of soap weigh, if each cake weighs 8 ounces ? 
 
116 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 6. How old is a man who was 40 years old 16 years ago ? 
 
 7. A trolley car that makes 2 round trips an hour over 
 a road 3 miles long, runs how far each hour ? 
 
 8. Supply the missing numbers : 
 
 1 — t — t = t = t = ff = f — ¥ = t" 
 
 9. Since — pints make a quart, and — quarts make a 
 gallon, there are — times — pints, or — pints, in a gallon. 
 
 10. At 8 cents a pint, what is the selling price of a gal- 
 lon of cream ? 
 
 11. A. dime, a 5-cent piece, and a one-cent piece are 
 together worth how much less than 2 dimes ? 
 
 12. How many crates does a market man require to pack 
 54 dozen eggs, if he puts 6 dozen in a crate ? 
 
 13. — pints make a gallon; how many gallons are 
 there in 64 pints ? 
 
 243. Oral Exercise. 
 Find : 
 
 /. f of 12. 6. f of 35. //. 4 of 70. 16. | of 48. 
 
 2. I of 18. 7. f of 28. 12. | of 16. 17. I of 80. 
 
 3. I of 30. 8. 4 of 21. 13. I of 32. 18. f of 27. 
 
 4. I of 24. 9. 4 of 42. 14. | of 40. 19. ^ of 36. 
 
 5. f of 14. 10. f of 49. 15. I of 24. 20. \ of 18. 
 
 244. Exercise. 
 
 /. If times a number is 30, the number is what part 
 of 30 ? What is the number ? 
 
 2. If times a number is 24, the number is — of 24, or 
 — ; and 5 times the number is — times — , or — . 
 
MULTIPLICATION, DIVISION, MENSURATION. 117 
 
 3. If 7 times a number is 56, what is 6 times the number? 
 
 4. ^^ of a score are how many ? 
 
 5. A farmer had 63 sheep and sold ^ of them ; how many 
 had he left ? 
 
 6. I of a week is f of — days, or — days. 
 
 7. A turkey weighing 13 pounds, live weight, weighed 
 only I as much when dressed ; how much did it lose in the 
 dressing ? 
 
 8. 7 cans of lard of equal size weighed 70 pounds ; how 
 much did 2 of them weigh ? 
 
 9. If 6 dozen bananas cost 60 cents, what should 3 dozen 
 cost? 
 
 10. If 6 hundred rails sold for 48 dollars, 2 hundred 
 should sell for — dollars. 
 
 //. I have 42 tablets in 7 packages of equal size ; how 
 many tablets are there in 3 of these packages ? 
 
 12. A miner earned $30 a month and his son ^V ^^ 
 much ; how much did both earn a month ? 
 
 13. If a turkey weighing 9 pounds sold for 90 cents, 
 what should one weighing 8 pounds sell for ? 
 
 14. In taking 8 steps a man walked 24 feet ; how far 
 had he walked when he had taken 6 steps ? 
 
 15. A father gave each of his 3 sons ^ of a farm of 56 
 acres ; how many acres had he left ? 
 
 16. If 8 times a number is 32, what is 7 times the 
 number ? 
 
 17. A of 90 cents is — cents, or — dimes. 
 
 18. A carpenter bought 18 hinges for 9 doors ; how many 
 will he use to hang 4 doors ? 
 
1 1 8 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 246. Exercise — Miscellaneous Problems. 
 
 /. Write the letters used in the Roman system of nota- 
 tion and the number for which each stands. 
 
 2. Express by the Roman system : 
 
 19; 44; 406; 1909. 
 
 3. Express in figures : 
 
 XCIV; MCD; MCMVI; CMI ; VIV. 
 
 4. In $7486, the 7 expresses how many dollars ? the 
 4 ? the 8 ? 
 
 5. 87 + 168 + 326 + 308 = ? 
 
 6. 327 + 109 + 426 + ? = 1000. 
 
 7. 1487 - 896 = ? 
 
 8. 2939 - ? = 1000 ? 
 
 9. ? - 526 = 879 ? 
 
 10. K dealer bought seventeen hundred forty bushels 
 of wheat and sold eleven hundred ninety bushels of it ; 
 how much had he left ? 
 
 //• What number is 101 greater than 999 ? 
 
 12. A. man bought a house costing $7250 and paid 
 $4750 on it ; how much does he yet owe ? 
 
 13. A man bought a vest for $2.75 and a pair of shoes 
 for $3.50 ; how much change should he receive from a 
 $10-bill ? 
 
 14. From twenty, dollars and seventy-five cents take the 
 sum of four dollars and twenty cents and six dollars and 
 eighty-five cents. 
 
 15. A farmer bought a horse for $160 and sold him so 
 
MISCELLANEOUS PROBLEMS. 119 
 
 as to gain ^ of this sum ; find the selling price of the 
 horse. 
 
 16. There were 1685 soldiers in a camp, but f of them 
 were sent away ; how many remained ? 
 
 17. Which is nearer 1000 and by how much, 899 or 
 1101? 
 
 18. From 4275 take 36 hundred. 
 
 19. How old was my father 25 years ago, if he is 74 
 years old now ? 
 
 20. If the first problem on a page is the 128th and the 
 last the 153d, how many problems are there on the page ? 
 
 21. Add down ; add across : 
 
 448 + 327 + 1320 = 
 
 79 + 108+ 768 = 
 
 175 + 927 + 7856 = 
 
 8 + 128 + 96 = 
 
 . + . + . = 
 22. Find the missing amounts by adding down and 
 subtracting across. See that the answer to (7) is the sum 
 of the amounts found for column (c). 
 
 
 (a) 
 
 (b) 
 
 (c) 
 
 (1) 
 
 $6750.30 - 
 
 $1007.50 = 
 
 p 
 
 (2) 
 
 35.35 - 
 
 20.95 = 
 
 ? 
 
 (3) 
 
 180.00 - 
 
 178.25 = 
 
 ? 
 
 (4) 
 
 3738.00 - 
 
 987.95 = 
 
 p 
 
 (5) 
 
 3753.60 - 
 
 8.85 = 
 
 p 
 
 (6) 
 
 37.85 - 
 
 5 
 
 13.70 = 
 
 ? 
 
 (7) 
 
 ? 
 
 ? 
 
120 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 246. The following table, called the Multiplica- 
 tion Table, shows the results obtained by taking 
 each of the numbers from 1 to 12, inclusive, from 1 
 to 12 times. 
 
 multiplication table. 
 
 1 X 
 
 1= 1 
 
 2x1=2 
 
 3x1=3 
 
 4x1=4 
 
 1 X 
 
 2= 2 
 
 2x2=4 
 
 3x2=6 
 
 4x2=8 
 
 1 X 
 
 3=3 
 
 2x3=6 
 
 3x3=9 
 
 4 X 3 = 12 
 
 1 X 
 
 4= 4 
 
 2x4=8 
 
 3 X 4 = 12 
 
 4 X 4 = 16 
 
 1 X 
 
 5= 5 
 
 2 X 5 = 10 
 
 3 X 5 = 15 
 
 4 X 5 = 20 
 
 1 X 
 
 6= 6 
 
 2 X 6 = 12 
 
 3 X 6 = 18 
 
 4 X 6 = 24 
 
 1 X 
 
 7= 7 
 
 2 X 7 = 14 
 
 3 X 7 = 21 
 
 4 X 7 = 28 
 
 1 X 
 
 8= 8 
 
 2 X 8 = 16 
 
 3 X 8 = 24 
 
 4 X 8 = 32 
 
 1 X 
 
 9= 9 
 
 2 X 9 = 18 
 
 3 X 9 = 27 
 
 4 X 9 = 36 
 
 1 X 
 
 10 = 10 
 
 2 X 10 = 20 
 
 3 X 10 = 30 
 
 4 X 10 = 40 
 
 1 X 
 
 11 = 11 
 
 2 X 11 = 22 
 
 3 X 11 = 33 
 
 4 X 11 = 44 
 
 1 X 
 
 12 = 12 
 
 2 X 12 = 24 
 
 3 X 12 = 36 
 
 4 X 12 = 48 
 
 5 X 
 
 1 = 5 
 
 0x1=6 
 
 7x1=7 
 
 8x1=8 
 
 5 X 
 
 2 = 10 
 
 6 X 2 = 12 
 
 7 X 2 = 14 
 
 8 X 2 = 16 
 
 5 X 
 
 3 = 15 
 
 6 X 3 = 18 
 
 7 X 3 = 21 
 
 8 X 3 = 24 
 
 5 X 
 
 4 = 20 
 
 6 X 4 = 24 
 
 7 X 4 = 28 
 
 8 X 4 = 32 
 
 5 X 
 
 5 = 25 
 
 6 X 5 = 30 
 
 7 X 5 = 35 
 
 8 X 5 = 40 
 
 5 X 
 
 6=30 
 
 6 X 6 = 36 
 
 7 X 6 = 42 
 
 8 X 6 = 48 
 
 5 X 
 
 7 = 35 
 
 6 X 7 = 42 
 
 7 X 7 = 49 
 
 8x 7 = 56 
 
 5 X 
 
 8 = 40 
 
 6 X 8 = 48 
 
 7 X 8 = 56 
 
 8 X 8 = 64 
 
 5 X 
 
 9 = 45 
 
 6 X 9 = 54 
 
 7 X 9 = 63 
 
 8 X 9 = 72 
 
 5 X 
 
 10 = 50 
 
 6 X 10 = 60 
 
 7 X 10 = 70 
 
 8 X 10 = 80 
 
 5 X 
 
 11 = 55 
 
 6 X 11 = 66 
 
 7 X 11 = 77 
 
 8 X 11 = 88 
 
 5 X 
 
 12 = 60 
 
 6 X 12 = 72 
 
 7 X 12 = 84 
 
 8 X 12 = 96 
 
 9 y 
 
 1= 9 
 
 10 X 1 = 10 
 
 11 X 1 = 11 
 
 12 X 1 = 12 
 
 9 X 
 
 2= 18 
 
 10 X 2 = 20 
 
 11 X 2 = 22 
 
 12 X 2= 24 
 
 9 X 
 
 3= 27 
 
 10 X 3 = 30 
 
 11 X 3= 83 
 
 12 X 3 = 36 
 
 9 X 
 
 4= 36 
 
 10 X 4 = 40 
 
 11 X 4= 44 
 
 12 X 4 = 48 
 
 9 X 
 
 5= 45 
 
 10 X 5= 50 
 
 11 X 5= 55 
 
 12 X 5 = 60 
 
 9 X 
 
 6= 54 
 
 10 X 6 = 60 
 
 11 X 6= 66 
 
 12 X 6= 72 
 
 9 X 
 
 7= 63 
 
 10 X 7 = 70 
 
 1 1 X 7 = 77 
 
 12 X 7 = 84 
 
 9 X 
 
 8= 72 
 
 10 X 8 = to 
 
 11 X 8= 88 
 
 12 X 8 = 96 
 
 9 X 
 
 9= 81 
 
 10 X 9 - 90 
 
 1 1 X 9 ^ 99 
 
 12 X 9 = 108 
 
 9 X 
 
 10= 90 
 
 10 X 10= 100 
 
 11 X 10= 110 
 
 12 X 10 = 120 
 
 9 X 
 
 U = 99 
 
 10 X 11 ■--- 110 
 
 11 X 11 = 121 
 
 12 X 11 = 132 
 
 9 X 
 
 12 = 108 
 
 10 X 13 = 120 
 
 11 X 12 = 132 
 
 12 X 12 = 144 
 
MULTIPLICATION, DIVISION, MENSURATION. 121 
 
 247. 10 X 5 = 50. From this we see that 
 
 Annexing a cipher to a number multiplies it 
 by 10. 
 
 248. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 /. 10 X 7 = 
 2. 10 X 9 = 
 5. 10 X 13 = 
 
 4. 10 X 17 = 
 
 5. 10 X 27 = 
 
 6. 10 X 35 = 
 
 7. 10 X 42 = 
 
 8. 10 X 54 = 
 
 9. 10 X 61 = 
 10. 10 X 75 = 
 //. 10 X 29 = 
 12. 10 X 80 =: 
 
 13. 10 X 225 = 
 
 14. 10 X 201 = 
 
 15. 10 X 278 = 
 
 16. 10 X 370 = 
 
 17. 10 X 300 = 
 
 18. 10 X 990 = 
 
 249. 100 X 5 = 5 X 100 = 500. From this we see 
 I that 
 
 Annexing two cipJiers to a number multiplies it 
 by 100. 
 
 250. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 /. 100 X 7 = 
 
 2. 100 X 9 = 
 
 3. 100 X 2 = 
 
 4. 100 X 6 = 
 
 5. 100 X 21 = 
 
 6. 100 X 15 = 
 
 7. 100 X 35 = 
 
 8. 100 X 20 = 
 
 9. 100 X 48 = 
 10. 100 X 99 = 
 
 //. 100 X 70 = 
 
 12. 100 X 10 = 
 
 13. 100 X 25 = 
 
 14. 100 X 72 = 
 
 15. 100 X 69 = 
 
 251. 1000 X ^ = ry X 1000 = 5000. From this we 
 see that 
 
 A nnexing three ciphers to a number multiplies it 
 by 1000. 
 
122 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 262. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 /. 1000 X 2 = . 4. 1000 X 1 = . 7. 1000 x 8 = • 
 2. 1000 X 4 == . 5. 1000 x = . 8. 1000 x 3 = . 
 5. 1000 X 7 = • 6. 1000 X 5 = . 9. 1000 x 6 = • 
 
 253. Exercise. 
 
 /. 100 dimes are worth — cents. 
 
 2. At 15 cents a quart, how much should be received 
 for 10 quarts of chestnuts ? 
 
 3. Find the weight of 10 shad, if they average 8 
 pounds a pair. 
 
 4. What must be paid for 100 postal cards ? 
 
 5. A drover bought 100 head of steers at an average of 
 $35 a head ; how much did he pay for them ? 
 
 6. Find the weight of 1000 two-pound sacks of salt. 
 
 7. Find the cost of a 100-acre farm at $20 an acre. 
 
 8. How many ounces are there in 100 pounds avoirdu- 
 
 pois ? 
 
 There are 12 months (mo.) in a year (yr.). 
 
 9. 100 years is called a century ; how many months 
 are there in a century ? 
 
 10. K keg of nails weighs 100 pounds ; find the weight 
 of 15 kegs of nails. 
 
 SUG. 15 X 100 lb. = 100 X 151b. 
 
 //. There are 100 cents in a dollar ; liow many cents are 
 there in 5 dollars ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 123 
 
 254. Multiply 27 by 300. 
 
 27 
 
 Since 300 = 100 x 3, 
 
 300 X 27 = 100 X 3 X 27 = 100 x 81 = 8100. 
 
 8100 
 
 255. Exercise. 
 
 Find the product of : 
 
 /. 20 X 15. 5. 50 X 33. 9. 200 x 35. 
 
 2. 30 X 45. 6. 60 X 75. fO. 200 x 47. 
 
 3. 40 X 62. 7. 70 X 38. //. 200 x 35. 
 
 4. 40 X 60. 8. 70 X 80. 12. 300 x 28. 
 
 266. Exercise. 
 
 /. Find the cost of 40 sewing machines at $28 each. 
 2. Find the tuition paid by 45 students, if each pays 
 1200. 
 
 SuG. 45 X $200 = 200 x $45. 
 
 5. How many feet of boards does a man buy, if he buys 
 500 boards each 18 feet long ? 
 
 4. How much fertilizer must be bought for a 12-acre 
 field, if 200 pounds are required for an acre ? 
 
 6. A barrel of beef weighs 200 pounds ; find the weight 
 of a shipment of 17 barrels of beef. 
 
 6. How many yards are there in 12 pieces of bunting, 
 each containing 50 yards ? 
 
 7. There are 24 sheets in a quire, and 20 quires in 
 a ream ; how many sheets are there in a ream of paper ? 
 
 8. How much house rent does a man pay in 3 years, 
 if he pays $20 a month ? 
 
124 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 267. Multiply 374 by 24. 
 
 374 
 
 24 
 
 We first multiply 374 by 4, obtaining 1496 for the prod- 
 uct. We next multiply 374 by 2, obtaining 748 for the 
 1496 product ; and since the 2 is 3 tens, we write 748 so that 
 748 the 8 stands in tens' place. The sum of these products, 
 QQ7fi o^ the entire product, is 8976. 
 
 268. Exercise. 
 Copy and multiply : 
 
 /. 43 8. 72 15. 59 22. 342 29. 198 
 
 13 87 57 13 39 
 
 64 
 
 9. 79 
 
 f6. 86 
 
 23. 452 
 
 30. 276 
 
 26 
 
 77 
 
 76 
 
 14 
 
 42 
 
 3. 94 
 
 10. 81 
 
 17. 38 
 
 24. 209 
 
 31. 378 
 
 28 
 
 98 
 
 57 
 
 16 
 
 28 
 
 4. 85 
 
 11. 45 
 
 18. 92 
 
 25. 390 
 
 32. 309 
 
 52 
 
 56 
 
 21 
 
 21 
 
 27 
 
 95 
 
 12. 99 
 
 19. 47 
 
 26. 409 
 
 33. 290 
 
 36 
 
 91 
 
 19 
 
 21 
 
 39 
 
 6. 96 
 
 13. 65 
 
 20. 51 
 
 27. 580 
 
 34. 409 
 
 49 
 
 37 
 
 99 
 
 22 
 
 26 
 
 7. 57 
 
 14. 48 
 
 21. 427 
 
 28. 214 
 
 55. 275 
 
 66 
 
 23 
 
 12 
 
 24 
 
 27 
 
MULTIPLICATION, DIVISION, MENSURATION. 125 
 
 259. Exercise. 
 
 /. Find the weight of 25 bushels of oats, if they weigh 
 32 pounds to the bushel. 
 
 2. How many hours are there in May, which has 31 
 days ? 
 
 3. How far will a steamboat run in a day, if it runs 16 
 miles an hour ? 
 
 4. A barrel of flour weighs 196 pounds ; find the weight 
 of barrels of flour. 
 
 5. Find the cost of 25 thousand feet of boards at $32 
 per thousand feet. 
 
 6. Find the cost of 16 hundred fence posts at $18 per 
 hundred. 
 
 7. A man left $8975 to his wife and 4 children, the 
 children receiving $1250 each ; how much did the wife 
 receive ? 
 
 8. A dealer bought 28 grain drills at $62 each and sold 
 them at 1100 each ; find his gain. 
 
 SuG. $100 - $62, or $38 = the gain on each. 
 
 9. A farmer bought 15 steers at $35 a head, and after 
 feeding them for 6 months at a cost of $40 a montli, 
 sold them at an average of $58 a head ; find his 
 gain. 
 
 10. If a clerk's wages are $30 a month, find his wages 
 for a year. 
 
 / /. 52 weeks and 1 day make a common year ; how many 
 days make a common year ? 
 
 12. A. farmer put 25 loads of lime on his lan^, each 
 
126 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 load averaging 75 bushels ; how much lime did he put on 
 his land ? 
 
 13. How many dozen eggs will 24 crates hold, if each 
 crate holds 72 dozen ? 
 
 260. Divide 435 by 4. 
 
 i of 435 = i of (4 hundred + 3 tens + 5 units). 
 4 ) 435 i of 4 hundred = 1 hundred. 
 
 108f i of 3 tens = tens, and 3 tens over. 
 
 3 tens + 5 units = 35 units. 
 I of 35 units = 8 units, and 3 units over, 
 i of 3 units = f of a unit. The quotient is 108f, 
 
 261. Exercise. 
 
 
 
 Copy and divide : 
 
 
 
 /. 2)37 
 
 10. 5)72 
 
 19. 7)93 
 
 25. 8)500 
 
 2. 2)51 
 
 //. 5)83 
 
 20. 7)99 
 
 29. 8)362 
 
 3. 3)40 
 
 12. 5)99 
 
 21. 7)130 
 
 50. 8)815 
 
 4. 3)47 
 
 13. 5)93 
 
 22. 7)152 
 
 5/. 8)854 
 
 5. 4)57 
 
 14. 6)79 
 
 23. 7)230 
 
 32. 8)963 
 
 6. 4)74 
 
 15. 6)87 
 
 24. 7)136 
 
 55. 9)200 
 
 7. 4)59 
 
 16. 6)92 
 
 25. 8)257 
 
 34. 9)309 
 
 8. 4)94 
 
 17. 6)89 
 
 26. 8)45^ 
 
 55. 9)401 
 
 9. 5)67 
 
 18. 6)94 
 
 27. 8)005 
 
 5tf. 9)118 
 
MULTIPLICATION, DIVISION, MENSURATION. 127 
 
 262. Exercise. 
 
 /. When handkerchiefs are sold at 2 for 25 cents, how 
 much are they apiece ? 
 
 2. If a turkey weighing 6 pounds sold for 75 cents, how 
 much was that a pound ? 
 
 3. In 2 rods there are 33 feet ; how many feet are there 
 in 1 rod ? 
 
 4. How much must be paid for a pint of varnish at 65 
 cents a quart ? 
 
 5. If 2 dressed hogs weigh 625 pounds, what is their 
 average weight ? 
 
 6. What was the price paid per acre, if a lot of 7 acres 
 cost $825 ? 
 
 7. What was the average weight of 2 steers, if one 
 weighed 875 pounds and the other 964 pounds ? 
 
 8. What is the average age of the five members of a 
 graduating class, if their ages are 17 years, 16 years, 18 
 years, 15 years, and 15 years, respectively ? 
 
 9. A farmer paid a boy $110 for 9 months' work ; what 
 were the monthly wages paid ? 
 
 10. A lady paid 50 cents for 4 yards of velvet trimming ; 
 how much was it a yard ? 
 
 //. Two cans of lard weighed 50 pounds apiece and a 
 third can weighed 48 pounds ; what was their average 
 weight ? 
 
 263. Divide 48 by 16. 
 
 ^48 ^^^ ^^ ^^ "^ ^' ^"^^^ 16 X 3, or 3 X 16 r= 48. 
 
128 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 264. Exercise. 
 
 Divide : 
 
 /. 22 by 11. 18. G5 by 13. 35. 051 by 93. 
 
 2. 3G by 12. 19. 54 by 18. 36. 406 by 58. 
 
 5. 28 by 14. 20. 95 by 19. 37. 384 by 48. 
 
 4. 45 by 15. 21. 100 by 50. 38. 423 by 47. 
 
 5. GO by 15. 22. 12G by G8. 39. 308 by 44. 
 
 6. GG by 22. 23. 108 by 3G. 40. 558 by 62. 
 
 7. 60 by 20. 24. 129 by 43. 4/. 305 by 61. 
 
 8. 72 by 24. 25. 124 by 31. 42. 134 by 67. 
 
 9. 81 by 27. 26. 288 by 72. 43. 102 by 34. 
 /O. 64 by 16. 27. 324 by 81. 44. 126 by 42. 
 //. 72 by 18. 28. 260 by 52: 45. 171 by 57. 
 
 12. 84 by 21. 29. 470 by 94. 46. 192 by 64. 
 
 13. 92 by 23. 50. 174 by 87. 47. 207 by 69. 
 
 14. 78 by 13. 31. 184 by 92. 48. 176 by 88. 
 /5. 90 by 18. 32. 228 by 76. 49. 300 by 75. 
 
 16. 96 by 16. 33. 318 by 53. 50. 440 by 55. 
 
 17. 91 by 13. 34. 576 by 96. 51. 140 by 28. 
 
 266. Divide 795 by 15. 
 
 iV of 79 is 5, the first figure of the quotient, 
 15 ) 795 ( 53 Taking 15 x 5, or 75, from 79, wo have 4 re- 
 -45 maining. 
 
 45 Annexing 5, the next figure of the dividend, to 
 
 the remainder, we have 45. 
 ^^0 of 45 ia 3,the second figure of the quotient. 
 Taking 15 x 3, or 45, from 45, we have notliing remaining. 
 The quotient is 53. 
 
MULTIPLICATION, DIVISION, MENSURATION. 129 
 
 266. Exercise. 
 
 Divide : 
 
 /. 143 by 11. 10. 656 by 41. 19. 3770 by 65. 
 
 2. 276 by 12. //. 867 by 51. 20. 4420 by 85. 
 
 3. 429 by 13. 12. 528 by 22. 21. 1804 by 82. 
 
 4. 602 by 14. 13. 1664 by 26. 22. 1932 by 21. 
 
 5. 795 by 15. U. 2088 by 72. 23. 1098 by 18. 
 
 6. 294 by 21. 15. 1092 by 42. 24. 1736 by 28. 
 
 7. 465 by 31. 16. 1056 by 24. 25. 3752 by 56. 
 
 8. 782 by 23. 17. 2024 by 44. 26. 2538 by 54. 
 
 9. 800 by 32. 18. 2520 by 56. 27. 1961 by 53. 
 
 Measure : 
 
 28. 252 by 12. 30. 684 by 38. 32. 4000 by 32. 
 
 29. 286 by 22. 31. 1215 by 45. 33. 3591 by 24. 
 
 267. Exercise. 
 
 /. A man was paid a debt of $125 in 25 bills of equal 
 value ; what was the value of each bill ? 
 
 2. The population of Railway, N. J., was 7105 in 1890 
 and 7935 in 1900 ; what was the average gain per year for 
 the ten years ? 
 
 3. A teacher was employed at $810 for 9 months, but 
 he resigned at the end of 7 months ; how much had he 
 earned ? 
 
 4. If a farm of 84 acres is valued at $2100, what value 
 is placed on each acre ? 
 
 5. What is the average number of miles that a train 
 
 9 
 
130 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 must run per hour to reach a city 990 miles distant in 18 
 hours ? 
 
 6. A man's lot of 25 acres and 2 cows are valued at $685 ; 
 if the cows are valued at $30 apiece, what value is placed 
 on the land per acre ? 
 
 7. A man bought property valued at $1872; how much 
 must he pay a year, if he is given 12 years to pay for it 
 and is to pay the same amount each year ? 
 
 8. If 12 acres of wheat yielded 336 bushels, how much 
 should 25 acres yield at the same average ? 
 
 9. I bought 14 thousand feet of white pine boards for 
 $448 ; what did I pay per thousand feet ? 
 
 10. A drover bought 25 sheep for $100 and sold them 
 for $150 ; what was the average gain per head ? 
 
 263. Exercise. 
 
 /. How many trips did a farmer make to haul away 900 
 bushels of wheat, if he hauled 75 bushels at a load ? 
 900 bushels was the amount hauled. 
 . ^ 75 bushels was the amount hauled at one load. 
 
 ^ 900 bu. : 75 bu. = 900 -f- 75, or • = the number of trips. 
 
 2. A clerk pays $25 a month rent for a house valued at 
 $3750 ; in how many months will the rent amount to the 
 value of the house ? 
 
 3. A dealer shipped 702 dozen eggs in crates holding 72 
 dozen each ; how many crates did he ship ? 
 
 4. llow many feet are there in 1728 inches ? 
 
 5. There are 32 quarts in a bushel ; how many bushels 
 are there in 608 quarts ? 
 
MULTIPLICATION, DIVISION, MENSURATION. 131 
 
 6. How many cows at 125 a head can be bought for 
 $320, and what amount will be over ? 
 
 25 ) 320 ( 12 1320 is the amount to be spent. 
 
 25 
 
 $25 is the price paid for each cow. 
 
 f-Q 1320 : $25 = 320 -f- 25, or 12, is the number that 
 
 "2() can be bought, with $20 over. 
 
 7. Corn weighs 56 pounds to the bushel. A farmer's 
 crop when sold weighed 7125 pounds ; how many bushels 
 had he, and how many pounds over ? 
 
 8. At 15 cents a yard, how many yards of flannel can be 
 bought in exchange for 9 pounds of chickens at 10 cents 
 a pound ? 
 
 9. If the distance around a wheel is 12 feet, how many 
 times will the wheel turn in going 5280 feet, or 1 mile? 
 
 269. Since 10 x 4 = 40, 40 -^ 10 = 4, or 4|0. 
 Since 100 x 4 = 400, 400 ^ 100 = 4, or 4|00. 
 Since 1000 x 4 = 4000, 4000 -^ 1000 = 4, or 4|000. 
 Therefore, 
 
 Cutting one cipher from the right of a nwnriber 
 divides the number by 10, cutting two ciphers di- 
 vides it by 100, three ciphers by 1000^ and so on. 
 
 270. Oral Exercise. 
 
 Read, supplying the missing numbers: 
 /. 30-^10=« 6. 400 -^ 100= .//. 7000 -^ 1000 = 
 2. 60 -^• 10 = . 7. 200 -^ 100 = . 12. 8000 -^ 1000 = 
 5. 90 -^ 10 = o 5. 500 -^ 100 = . 13. 9000 ^ lOOO = 
 4. 500 -^ 10 = . 9. 4000 -^ 100 = • 14. 5000 -^ 1000 = 
 
 5. 320 -f- 10 = . 10. 3200 
 
 100 =: . /5. 8000' -^ 1000 
 
132 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 271. 1200 ^ 20 = 60. 
 
 Also, 120|0 -r 6|0, or 120 -^ 2 = 60. 
 Therefore, 
 
 Qutting off tl\,e same number of ciphers from the 
 right of two numbers does not change tfteir quotient. 
 
 272. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 /. 40-^20=:. 5.150^30 = - 5. 3600 -^ 400 =• 
 2. 80 ^ 20 = • 6. 300 -r- 50 = • 10. 7200 -^ 600 = • 
 5. 90-^30=. 7.350^70=. //. 8000 -^ 4000 = • 
 4. 100 -T- 20 = . 5. 630 -^ 90 = . 12. 9000 ^ 3000 = • 
 
 Forming, Reading, and Writing Numbers Above 
 lOOOO; Fundamental Operations. 
 
 To the teacher. The study of numbers above 10000 may be de- 
 ferred, if desirable, and taken up at the close of Chap. II or 
 Chap. IIL 
 
 273. Thousands are counted up to 999 thousand. 
 
 274. A thousand thousand is called a million. 
 Millions are counted up to 999 million. 
 
 275. A thousand million is called a billion. 
 Billions are counted up to 999 billion. 
 
 276. When more than three figures are used to 
 write a whole number, they are separated by com- 
 mas into groups, or Periods, of three figures each. 
 
NUMBERS ABOVE 10000. 133 
 
 277. Counting I'roni the right, 
 
 In the lirst j)eriod any number of units from 1 to 
 999 is found. 
 
 In the second period any number of thousands 
 from 1 to 999 is found. 
 
 In the third period any number of millions from 
 1 to 999 is found. 
 
 In tlie fourth period any number of billions from 
 1 to 999 is found. 
 
 
 278. 
 
 TABLE. 
 
 
 
 m 
 
 (D 
 
 
 
 
 
 
 1 
 
 g 
 
 m 
 
 
 
 
 
 3 
 
 
 
 
 ^ 
 
 B m 
 
 O 
 
 a 
 
 
 
 ■■? § 
 
 a § 
 
 5 
 
 5J OQ 
 
 OD 
 
 
 '^ -a ^ 
 
 -S S £ 
 
 i 
 
 o g 
 
 'S 
 
 
 mdr 
 n-bi 
 lion 
 
 indr 
 Q-m: 
 llior 
 
 
 
 s 
 
 T3 
 
 
 
 § i 
 
 = « •« 
 
 = <u :r 
 
 3 
 
 5 .G 
 
 S 
 
 S 13 
 
 W Eh pq 
 
 W H ^ 
 
 w 
 
 H H 
 
 W 
 
 H t) 
 
 4 2 7 
 
 3 2 
 
 4 
 
 7 
 
 
 
 6 3 
 
 Billions. 
 
 Millions. 
 
 Thousands. 
 
 "" 
 
 Units. 
 
 4th period. 
 
 3d period. 
 
 2d period. 
 
 1st period. 
 
 279. 427,320,407,063 is read four hundred twenty - 
 seven billion three hundred twenty million four 
 hundred seven thousand sixty-three. 
 
 280. To read a number, 
 
 /. Beginning at the right, separate the number 
 into periods of three figures each. 
 
 2. Beginning at the left, read the number in 
 each period and give it the name of the period, 
 except in units, where the name of the period is 
 omitted. 
 
134 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 281. Oral Exercise. 
 Kead : 
 
 /. 
 
 10,000. 
 
 9. 
 
 300,000. 
 
 17. 
 
 2,725,248. 
 
 2. 
 
 20,000. 
 
 10. 
 
 401,000. 
 
 18. 
 
 46,701,000. 
 
 3. 
 
 25,000. 
 
 11. 
 
 520,000. 
 
 19. 
 
 530,800,500. 
 
 4. 
 
 38,000. 
 
 12. 
 
 725,001. 
 
 20. 
 
 2,486,430,002. 
 
 5. 
 
 47,001. 
 
 13. 
 
 706,020. 
 
 21. 
 
 8,000,700,049. 
 
 6. 
 
 48,026. 
 
 14. 
 
 . 804,802. 
 
 22. 
 
 3,007,428,304. 
 
 7. 
 
 74,800. 
 
 15. 
 
 900,027. 
 
 23. 
 
 48,006,928,040. 
 
 8. 
 
 59,704. 
 
 16. 
 
 450,006. 
 
 24. 
 
 867,049,302,742, 
 
 282. Exercise. 
 
 Write in words : 
 
 /. 60,000. 6. 2,425,070. //. 200,000,000. 
 
 2. 22,700. 7. 5,000,607. 12. 607,007,009. 
 
 3. 48,001. 8. 16,742,003. 13. 4,863,002,140. 
 
 4. 760,040. 9. 24,683,214. 14. 25,600,750,689. 
 
 5. 400,797. 10. 10,020,040. 15. 440,700,632,156. 
 
 283. Oral Exercise. 
 
 What number is : 
 
 /. 1 greater than 9,999 ? 1 less than 10,000 ? 
 
 2. 1 greater than 59,999 ? 1 less tlian 40,000 ? 
 
 3. 1 greater than 599,999 ? 1 less than 200,000 ? 
 
 4. 1 greater than 999,999 ? 1 less than 4,000,000 ? 
 
 5. In 427,635 there are how many thousands ? how 
 many units ? 
 
 6. In 50,700,040 there are how many millions ? how 
 many thousands ? how many units ? 
 
 7. What is the largest number that can be written with 
 six fijjures? the smallest ? 
 
NUMBERS ABOVE 10000. 135 
 
 284. Exercise. 
 
 Write in figures : 
 /. Ten thousand one hundred. 
 
 2. Fourteen thousand two hundred six. 
 
 3. Twenty thousand seven hundred twenty. 
 
 4. Fifty thousand forty-four. 
 
 5. Ninety-six thousand four hundred forty-four. 
 
 6. One hundred thousand one. 
 
 7. One hundred thousand one hundred. 
 
 8. Two hundred thousand forty-eight. 
 
 9. Four hundred eight thousand eighty. 
 
 10. Five hundred thousand six hundred thirty-four. 
 //. Nine million seventy thousand six hundred fifty. 
 
 12. Twenty-six million eight hundred thousand fifty-six. 
 
 13. Five hundred twenty million seventy-five thousand 
 fourteen. 
 
 14. Eight hundred million nine thousand five hundred six. 
 
 15. Two hundred twenty million six hundred twenty- 
 five thousand. 
 
 16. One billion one hundred million. 
 
 17. Six billion six million six hundred thousand four. 
 
 18. Seventy billion sixty-five thousand nineteen. 
 
 19. Nineteen hundred five. 
 
 20. Eighteen hundred sixty-five. 
 
 21. Fourteen hundred ninety-two. 
 
 22. Seventeen hundred seventy-six. 
 
 23. One hundred seventy-five billion three hundred forty- 
 eight million three hundred fourteen thousand two hun- 
 dred seventy-seven. 
 
136 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 285. Oral Exercise. 
 
 /. What is the largest number that can be written with 
 nine figures ? the smallest ? 
 
 2. In 7,777,777 what does each 7 represent? 
 
 3. Head 2,400 as hundreds ; as tens. 
 
 4. Head 1,200,000 as thousands ; as hundreds; as tens. 
 
 5. Give the name of the fourth period ; the first ; the 
 third ; the second. 
 
 6. Give the number of the period in which ten-millions 
 are found ; hundred-thousands ; hundreds. 
 
 7. How many ciphers are required to write one thou- 
 sand ? one million ? one hundred tliousand ? one billion ? 
 ten thousand ? ten million ? 
 
 286. Exercise. 
 
 
 Add: 
 
 
 2,991 
 
 2. 1,376 
 
 1,208 
 
 3,259 
 
 3,927 
 
 13,185 
 
 5,954 
 
 2,584 
 
 2,104 
 
 891 
 
 1,014 
 
 5,115 
 
 2,742 
 
 11,606 
 
 1,631 
 
 1,773 
 
 2,880 
 
 2,585 
 
 6,646 
 
 2,403 
 
 3. 37,718 
 38,316 
 39,385 
 36,425 
 32,033 
 34,871 
 28,646 
 35,637 
 35,393 
 33,220 
 
FUNDAMENTAL OPERATIONS. 137 
 
 4. $8.92 
 
 7. 12 
 
 10. $89,220,558.49 
 
 8.70 
 
 196,952 
 
 24,322,375.00 
 
 7.62 
 
 323,485 
 
 4,271,562.00 
 
 7.81 
 
 178,733 
 
 568,664.00 
 
 7.89 
 
 1,227 
 
 2,615,202.88 
 
 9.31 
 
 306,428 
 
 3,041,934.00 
 
 8.65 
 
 291,445 
 
 47,722.00 
 
 8.35 
 
 45,759 
 
 13,468,852.32 
 
 7.54 
 
 135,104 
 
 6,909,608.31 
 
 7.32 
 
 425,102 
 8. 424,228 
 
 195.41 
 
 5. $18.56 
 
 //. $ 402,515.47 
 
 18.19 
 
 15,474,447 
 
 154,093.73 
 
 13.76 
 
 4,799,742 
 
 3,785,926.74 
 
 19.72 
 
 6,891,601 
 
 975,429.33 
 
 17.70 
 
 50,711 
 
 3,062,808.61 
 
 15.75 
 
 5,015,965 
 
 611,534.09 
 
 13.53 
 
 1,599,374 
 
 601,806.54 
 
 14.31 
 
 3,617,497 
 
 70,235.22 
 
 11.38 
 
 547,641 
 
 64,029,115.36 
 
 11.72 
 
 1,478,018 
 
 25,178,552.61 
 
 6. $916.67 
 
 9. 584,120 
 
 12. $ 792,657.23 
 
 625.00 
 
 15,122,948 
 
 2,859,789.02 
 
 458.33 
 
 457,106,995 
 
 964,528.68 
 
 291.67 
 
 263,457,239 
 
 8,035,946.35 
 
 250.00 
 
 26,493,855 
 
 76,730.18 
 
 208.33 
 
 535,872,240 
 
 38,694,831.27 
 
 166.67 
 
 244,909,123 
 
 6,618,659.50 
 
 150.00 
 
 159,311,527 
 
 157,927.87 
 
 150.00 
 
 39,251,413 
 
 22,073,559.51 
 
 150.00 
 
 99,586,188 
 
 1,092,016.89 
 
138 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 13. From 62,727 16. 1,209,090 19. 29,387.00 
 take 24,536 1,150,777 4,097.65 
 
 14. From 13,000 17. 162,685.27 20. 6,415,000.00 
 take 12,880 64,059.85 6,075.35 
 
 15. From 4,221,085 18. 2,032,088.69 21. 1,222,117.55 
 take 488,086 9,879.79 1,071,828.75 
 
 287. Exercisco 
 
 Multiply ; 
 
 /. 170 6. 5,714 //. 43,982.58 16. 719,258 
 
 18 8,601 .94 1,328 
 
 2. 4,018 7. 71,015 12. 25,053.86 17. $150.78 
 
 1,541 55,602 800 550 
 
 3. 1,742 8. 807,017 13. 409,297 18. $47.23 
 121 6,951 4,513 7,230 
 
 4. $L56 9. $50.41 14. $131.25 19. $409.46 
 30 750 25 62 
 
 5. 8,781 10. 2,301 15. 1,020,248 20. 0,046,045 
 8,107 74,000 7,564 28,031 
 
FUNDAMENTAL OPERATIONS. 139 
 
 288. Exercise. 
 
 Divide : Measure : 
 
 /. 5405 by 23. 17. 15,260 by 35. 
 
 2. $29.76 by 8. 18. $80.64 by 13.36. 
 
 3. $15.12 by 42. 19. 304,992 by 72. 
 
 4. 42,804 by 123. 20. $1,638.00 by $3.25. 
 
 5. $1,045.80 by 84. 21. 165,816 by 329. 
 
 6. $599.36 by 32. 22. $224.20 by $5.90. 
 
 7. 135,564 by 316. 23. $2,058.75 by $3.05. 
 
 8. $9,869.04 by 54, 24. $180.72 by $15.06. 
 
 9. 18,972 by 204. 25. $800.80 by $20.02. 
 10. 62,628 by 307. 26. $145.44 by $16.16. 
 //. 01,306 by 302. 27. $4,152 by $10.38. 
 
 12. $0,789.00 by 325. 28. $6,586.24 by $20.08. 
 
 13. $6,542.82 by 326. 29. $26,274.78 by $324.38. , 
 
 14. $65,700.50 by 202. 30. $28,809 by $800.25. 
 
 15. 2,428,040 by 808. 31. $28,317.63 by $325.49. 
 
 16. 1,522,756 by 1,234. 32. $180,443.76 by $678.36. 
 
 289. Exercise. 
 
 /. A laborer had $125.75 in a savings bank and drew 
 out $9.75 each week for 12 weeks ; how much had he left 
 in this bank ? 
 
 2. In the LVIIIth Congress there were 208 Republicans 
 in the House of Representatives and 178 Democrats ; how 
 many were there of both ? IIow many more Republicans 
 than Democrats ? 
 
 3. At the beginning of a trip a trolley car register 
 showed that 6107 fares had been collected, and at the end 
 
140 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 of the trip that 6298 had been collected ; how many fares 
 were collected during the trip ? 
 
 4. A farmer bought a stove for $25.75. He gave in pay- 
 ment his old stove weighing 286 pounds, for which he was 
 paid $0.01 a pound, and the balance in cash ; how mucli 
 cash did he pay ? 
 
 5. The following table shows the amount and the cost 
 of coffee imported to the United States for 11 months of 
 a certain year. Read the table and find the totals : 
 
 Imported From 
 
 Pounds. 
 
 Cost. 
 
 Central America 
 
 43,286,988 
 
 29,298,733 
 
 19,348,490 
 
 57,255,375 
 
 695,972,331 
 
 3,746,170 
 
 18.710,738 
 
 4,489.184 
 
 383,428 
 
 14,587,409 
 
 2,665,725 
 
 1,356,436 
 
 4.132,132 
 
 43,439,470 
 
 441.224 
 
 2,081,120 
 
 556,199 
 
 52,897 
 
 Mexico 
 
 West Indies 
 
 South America 
 
 Brazil 
 
 Europe 
 
 East Indies 
 
 Asia and Islands 
 
 Africa, etc 
 
 Totals 
 
 
 
 6. The distance from New York to Sun Francisco is 
 3250 miles and the distance from San Francisco to Ma- 
 nila is 6789 miles; what is the distance from New York 
 to Manila by way of San Francisco ? 
 
 7. How many $100-bills would make a million dollars ? 
 
 8. A farmer's tobacco crop consists of 1426 pounds of 
 wrappers and 720 pounds of fillers. He has two offers for 
 it : the first, 12 cents a pound for wrappers and 2 cents a 
 pound for fillers ; the second, 9 cents a pound for all. 
 Which is the better offer, and by how much ? 
 
FACTORS. 
 
 141 
 
 9. Find the sum of all numbers greater than 9996 and 
 less than 10005. 
 
 10. How many times is a million contained in a billion ? 
 //. What must a man^s income be per year in order that 
 
 his income in 40 years shall amount to a million dollars ? 
 
 12. If a boy saves 5 cents a day from the age of 10 years 
 to the age of 21 years, how much does he save in all, 
 counting 365 days to a year ? 
 
 13. Find the increase in population from 1890 to 1900 
 for each of the ten largest cities in the United States, as 
 follows : 
 
 Cities. 
 
 Population. 
 
 Increase. 
 
 . 1900. 
 
 1890. 
 
 New York, N. Y 
 
 ChicafiTO III 
 
 3,437,202 
 1,698,575 
 1,293,697 
 
 575,238 
 560,892 
 508,957 
 381,768 
 352,387 
 342,782 
 325,902 
 
 2,492,591 
 1,099,850 
 1,046.964 
 451,770 
 448,477 
 434,439 
 261,353 
 255,664 
 298,997 
 296,908 
 
 
 Philadelphia, Penn 
 
 St. Louis, Mo 
 
 Boston, Mass 
 
 Baltimore Md 
 
 Cleveland, Ohio 
 
 Buffalo, N. Y 
 
 San Francisco, Cal 
 
 Cincinnati, Ohio 
 
 Factors, 
 290. Exercise. 
 
 /. What two numbers multiplied together will produce 
 4? 6 ? 5 ? 9 ? 10? 15? 
 
 2. What three numbers multiplied together will produce 
 8 ? 12 ? 28 ? 30 ? 42 ? 
 
142 WHOLE NUMBERS AND FRACTIONAL PARTS. 
 
 The numbers which, when multiplied together, 
 will i)roduce a given number are the Factors of the 
 number. 
 
 3. Name two factors that will produce 14 ; 22 ; 33 ; 35; 
 
 C4 ; 72 ; 28 ; 84 ; 06. 
 
 4. What three factors will produce 45 ? 
 
 45 = 5x9 = 5x3x3. Therefore, the three factors of 45 arc 
 5, 3, and 3. 
 
 5. What three factors will produce 18 ? 24 ? 28 ? 30 ? 
 36 ? 40 ? 
 
 6. What are the two factors of 5 ? 7 ? 11 ? 13 ? 
 
 A number that has no other factors than itself smd 
 one is a Prime Number. 
 
 7. Tell which of the following numbers are prime : 
 
 2 5 8 11 14 17 21 
 
 3 6 9 12 15 18 23 
 
 4 7 10 13 16 20 25 
 
 When all the factors of a number are prime num- 
 bers, they are called the Prime Factors of the number. 
 
 8. Find the prime factors of 36. 
 
 36 = 4x9 = 2x2x3x3. Therefore, the prime factors of 
 36 are 2, 2, 3, and 3. 
 
 Find the prime factors of : 
 9. 15. 13. 60. 17. 24. 
 
 10. 30. 14. 72. 18. 35. 
 
 //. 36. 15. 96. 19. 25. 
 
 12. 4S. 16. 27. 20. 32. 
 
 21. 
 
 40. 
 
 25. 
 
 16. 
 
 22. 
 
 56. 
 
 26. 
 
 28. 
 
 23. 
 
 64. 
 
 27. 
 
 45. 
 
 24. 
 
 84. 
 
 28. 
 
 63. 
 
DIVISORS. 143 
 
 Divisors. 
 291. Exercise. 
 
 /. Name a number that will divide 4 without a re- 
 mainder. Name a number that will divide 9 without a 
 remainder. 
 
 A number that will divide a given number without 
 a 1 emainder is called an Exact Divisor of the number. 
 
 2. Name two exact divisors of 6 ; 8 ; 10 ; 14 ; 15 ; 21 
 27 ; 35. 
 
 3. Name three exact divisors of 12 ; 16 ; 18 ; 20 ; 24 
 30 ; 32 ; 36. 
 
 4. Name an exact divisor of both 6 and 9 ; 8 and 12 
 10 and 15. 
 
 An exact divisor of each of two or more numbers 
 is called a Common Divisor of these numbers. 
 
 5. Name a common divisor of 6 and 8 ; 10 and 15 ; 14 
 and 21. 
 
 6. Name two common divisors of 8 and 12 ; 9 and 18 ; 
 16 and 20. 
 
 7. Name three common divisors of 12 and 18 ; 30 and 
 42. 
 
 Name the greatest common divisor of : 
 
 8. 20 and 30. //. 36 and 48. 14. 18 and 24. 
 
 9. 24 and 36. 12. 21 and 28. 15. 16 and 24. 
 10. 30 and 45. 13. 36 and 45. 16. 24 and 32. 
 
CHAPTER II. 
 
 FRACTIONS. 
 
 Introductory Problems and Definitions. 
 
 292. Oral Exercise. 
 
 /. Line AB is divided into 
 
 A — 
 how many equal parts ? 
 
 2. What is each part called ? 
 
 3. How many halves are there in 1 ? 
 
 4. CD is divided into how . , 
 
 C f- 
 
 many equal parts ? ' I ' 
 
 5. What is each part called ? 
 
 6. What are 2 parts called ? 
 
 7. What are 3 parts called ? 4 parts ? 
 
 8. How many fourths are there in 1 ? 
 
 9. EF is divided into how i i i 
 many equal parts ? 
 
 10. What is each part called ? 
 
 //. What are 2 parts called ? 3 parts? 4 parts ? 6 
 parts ? 
 
 12. How many eighths are there in 1 ? 
 
 13. How many halves are there in 2 ? How many 
 fourths ? 
 
 14. How many fourths are there in J ? How many 
 eighths ? 
 
 I ' I ' I 
 
PROBLEMS AND DEFINITIONS. 
 
 145 
 
 15. How many halves are there in 1 J ? How many 
 fourths ? 
 
 16. What is J of J ? J of i ? 
 
 17. How many eighths are there in ^ ? in J ? in | ? 
 
 Read, supplying the missing numbers : 
 
 18. 1 = ^ 
 
 24. 
 
 I =S 
 
 30. 
 
 2 =4 
 
 36. f = :, 
 
 19. 1 = i 
 
 25. 
 
 \ =t 
 
 31. 
 
 H = i 
 
 37. 1 = J 
 
 20. I = ; 
 
 26. 
 
 3 =i 
 
 32. 
 
 1 =4 
 
 38. 1 = i- 
 
 2'- l = t 
 
 27. 
 
 li = t 
 
 33. 
 
 f =4 
 
 39. i of 1 = 
 
 22. i = J 
 
 28. 
 
 l} = t 
 
 34. 
 
 1 =.; 
 
 40. }of^ = 
 
 23. i = J 
 
 29. 
 
 ii = i 
 
 35. 
 
 i =i 
 
 ->/. Jof 1 = 
 
 293. Oral Exercise. 
 
 /. Line MN is divided I 
 
 M \- 
 
 into how many equal parts ? I 
 
 2. What is each part called ? 
 
 5. What are 2 parts called ? 3 parts ? 
 
 4. How many thirds are there in 1 ? 
 
 5. PQ is divided into 
 how many equal parts ? 
 
 6. What is each part called ? 
 
 7. What are 2 parts called ? 3 parts ? 6 parts ? 
 
 5. How many sixths are there in 1 ? 
 
 9. RS is divided into , , , 
 
 R ' I I M I I 
 
 I h 
 
 how many equal parts ? 
 
 10. What is each part called? What are 2 parts called? 
 12 parts ? 3 parts ? 
 
 / /. How many thirds are there in 2 ? How many sixths ? 
 10 
 
146 
 
 FRACTIONS. 
 
 12. What is J of J ? i of J ? 
 
 13. How many sixths are there in J ? How many 
 twelfths ? 
 
 14. How many sixths are there in f ? How many 
 twelfths ? 
 
 /5, How many sixths are there in J ? How many 
 twelfths ? 
 
 16. How many thirds are there in IJ ? How many 
 sixths ? 
 
 n. How many thirds are there in If ? How many 
 sixths ? 
 
 18. How many twelfths are there in |^ ? in J ? 
 
 Read, supplying the missing numbers : 
 
 19. 
 
 1= ^ 
 
 27. 
 
 n= i 
 
 35. 
 
 3 =* 
 
 43. 
 
 H= * 
 
 20. 
 
 1= t 
 
 28. 
 
 n= i 
 
 3e. 
 
 H=i 
 
 44. 
 
 iS=i 
 
 21. 
 
 1 = tV 
 
 29. 
 
 H = ij 
 
 37. 
 
 H = i 
 
 45. 
 
 V= i 
 
 22. 
 
 i = -6 
 
 30. 
 
 If = TV 
 
 38. 
 
 3 =i 
 
 46. 
 
   = 4 
 
 23. 
 
 1= -c 
 
 31. 
 
 ■ft" — 
 
 39. 
 
 3 =j 
 
 47. 
 
 J = * 
 
 24. 
 
 i = TV 
 
 32. 
 
 1 = i 
 
 40. 
 
 i ofi= . 
 
 48. 
 
 i =rt 
 
 25. 
 
 t = TV 
 
 33. 
 
 A= 4 
 
 41. 
 
 Jofi= . 
 
 49. 
 
   =i 
 
 26. 
 
 t = TV 
 
 34. 
 
 H= 5 
 
 42. 
 
 n = i 
 
 SO. 
 
 « = * 
 
 294. One of the equal parts into which a unit is 
 divided is a Fractional Unit. 
 
 Thus, \, ^, ^, ^, -jij are fractional units. 
 
 295. A number made up of like fractional units is 
 a Fraction. 
 
 Thus, I, g, 5, 6 7 V *ire fractions. 
 
REDUCTION. 147 
 
 296. When a fraction is written in figures, the 
 number below the line is called the Denominator and 
 the number above the line the Numerator. The 
 numerator and denominator together are called the 
 Terms of the fraction. 
 
 Thus, in the fraction f, 5 is the denominator, 4 the numerator, 
 and 4 and 5 togetlier are the terms. 
 
 297. A Proper Fraction is a fraction whose numera- 
 tor is less than its denominator ; as, |. 
 
 298. An Improper Fraction is a fraction whose nu- 
 merator is equal to or greater than its denominator ; 
 as, J and J. 
 
 299. An Integer is a whole number ; as, 7. 
 
 300. A Mixed Number is a number made up of an 
 integer and a fraction ; as, 2|. 
 
 Reduction. 
 
 301. - 
 
 I _L I J- I X I J- I ±1 X | -v--|--7--' 
 
 88^888 8T 
 
 Here we see that 
 
 Therefore, 
 
 Multiplying or dividing both terms of a fraction 
 by the same number does not change its value. 
 
148 
 
 FRACTIONS. 
 
 
 303. Oral Exercise. 
 
 
 , 
 
 
 Bead, siipp 
 
 lying the missing 
 
 numbers : 
 
 
 '■i = i 
 
 7. f = 5V 
 
 
 13. ^ = i 
 
 '»• n = i 
 
 ^- i = i 
 
 «• J = tV 
 
 
 u. I = t 
 
 '0- U = i 
 
 3. i = i 
 
 9- t = rt 
 
 
 ^5- J = i 
 
 2'- « = i 
 
 ^■i = i 
 
 '0- 1 - TT 
 
 
 ^6- U = i 
 
 22- H = i 
 
 «■ * = IS 
 
 "• l = 5S 
 
 
 ^7. H = t 
 
 '3. H = i 
 
 e- 1 = 51 
 
 '2- A = bV 
 
 
 /5. il = ^ 
 
 2^- M = * 
 
 303. Exercise. , 
 
 
 1 1 
 
 1 1 
 
 Show tliat : 
 
 1 
 mi 1 
 
 
 ' 1 
 , 1 
 
 1 1 
 1 1 
 
 /. 2J = |. 
 
 Thus, ' 
 1 
 
 
 1 1 
 
 1 
 
 1 ___J 
 
 
 
 
 
 
 2. 2 = |. 
 
 4. 2J = f . 
 
 6. 
 
 n = Y- 
 
 8. 3f = V^. 
 
 5. 3=.|. 
 
 5. 2i = i. 
 
 7. 
 
 n = V- 
 
 9- H = V- 
 
 304. Changing the form of a number without 
 changing its value is called Reduction. 
 
 305. Reduce 21 to thirds. 
 
 Since 1 equals 3 thirds, 2 equals 2 times 3 thirds, or 6 thirds, 
 and 2J equals 6 thirds plus 2 thirds, or 8 thirds. 
 
 306. Reducing 2 to J, or 2| to } is reducing a whole 
 or a mixed number to an improper fraction. 
 
 307. Oral Exercise. 
 Reduce : 
 
 /. 2 to halves. 5. 4 to halves. 
 2. 4 to thirds. 4. 3 to halves. 
 
 Reduce to improper fractions : 
 
 7. 2J. 10. 8f. 13. 7J. 
 
 8. SJ. //. 3i. 14. 6}. 
 
 9. 2f. 12. 3f. 15. 4J. 
 
 5. 
 
 2 to fifths. 
 
 6. 
 
 5 to thirds. 
 
 
 16. 
 
 4J. 
 
 
 17. 
 
 12J. 
 
 
 18. 
 
 131. 
 
REDUCTION. 
 
 149 
 
 308. Reduce 12| to fifths. 
 
 1 s 
 
 
 
 
 
 12 = 
 
 12f = 
 
 5' 
 
 13 X f , or ^/ . 
 ¥ + f , or %^. 
 
 
 
 
 
 309. Exercise. 
 
 
 
 
 
 Reduce to 
 /. 131. 
 
 2. 18|. 
 
 3. 161. 
 
 improper fractions : 
 
 8. GG§. /5. 
 
 5. 42f 16. 
 
 10. 20|. /7. 
 
 18|. 
 55|. 
 361. 
 
 22. 
 23. 
 24. 
 
 112^. 
 118f. 
 300f. 
 
 4. 14|. 
 
 //. 44f. 
 
 /5. 
 
 165. 
 
 25. 
 
 299|. 
 
 5. 37|. 
 
 6. ^2\. 
 
 7. 87J. 
 
 12. 30J. 
 /5. 48|. 
 14. 2G|. 
 
 19. 
 20. 
 21. 
 
 331. 
 14J. ' 
 67J. 
 
 26. 
 27. 
 28. 
 
 187}. 
 575f 
 
 627J. 
 
 310. Exercise. 
 
 
 
 
 
 Show that : i - i 
 /. \ = %\. Thus, r-^^ ^— 
 
 1 
 
 1 
 
 ~3 
 
 1. 
 T 
 
 i i 
 
 2. 1 = 3. 
 
 3. J = 3J. 
 
 ^- J -If. 
 5. V = 2}. 
 
 6. ^ = 3i, 
 
 7. ^^=^. 
 
 1 
 
 8. 
 9. 
 
 9? = i|. 
 
 311. Changing | to 2, or | to 3J, is reducing an 
 improper fraction to a loliole or mixed number. 
 
 iof 2 
 
 312. 
 
 Here we see that f = J of 2, or 2 h- 3. Hence, 
 A fraction may he considered to denote that the 
 numerator is to he divided hy the denominator. 
 
150 FRACTIONS. 
 
 313. Oral Exercise. 
 
 Reduce to a whole or mixed number : 
 /. J. Thus, I equals ^ of 7, or 2^. 
 
 2. f. 4. |. 6. ^. 8. Y- 10. V. 12- V- 
 
 5. |. 5. Y- 7. y. P. J^. //. J^. 13. Y. 
 
 314. A fraction is in its lowest terms when its 
 numerator and denominator have no common di- 
 visor. 
 
 Thus, f is in its lowest terms, since 3 and 4 have no common 
 divisor. 
 
 316. Reduce |^ to lowest terms : 
 
 Therefore, to reduce a fraction to its lowest 
 terms, 
 
 Divide out of both terms all common dimsors of 
 them; or^ 
 
 Divide hotli terms by their greatest common 
 divisor. 
 
 316. Oral Exercise. 
 
 
 
 
 
 
 
 Reduce to lowest terms : 
 
 
 
 
 
 
 '• A- 
 
 5. f,. 
 
 9. 
 
 fS- 
 
 13. 
 
 if- 
 
 17. 
 
 *i- 
 
 2. «. 
 
 «■ U- 
 
 10. 
 
 «• 
 
 14. 
 
 fJ- 
 
 18. 
 
 «• 
 
 3- !i 
 
 7- e- 
 
 11. 
 
 If- 
 
 15. 
 
 fl- 
 
 19. 
 
 n- 
 
 4. if. 
 
 «■ !«• 
 
 12. 
 
 if- 
 
 16. 
 
 if 
 
 20. 
 
 tW- 
 
MULTIPLICATION AND DIVISION. 
 
 151 
 
 317. 
 
 Multiplication and Division. 
 
 4 
 
 ' ^ 1 I I -I--,— 
 
 T—r 
 
 Here we see that 
 
 Therefore, 
 
 To multiply a fraction hy a whole number^ mul- 
 tiply the numerator or divide the denominator by 
 the whole nuuiber. 
 
 Note. Divide the denominator when possible. 
 
 318. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 /. 2 X 1 = < 
 
 13. 
 
 4 
 
 X 
 
 tV= • 
 
 2. 2 X i = . 
 
 14. 
 
 3 
 
 X 
 
 1 = • 
 
 5. 3 X f = 
 
 15. 
 
 3 
 
 X 
 
 1 = • 
 
 4. 2 X 21 = 
 
 16. 
 
 4 
 
 X 
 
 24 = . 
 
 5. 2 X 4i = . 
 
 17. 
 
 5 
 
 X 
 
 5A= • 
 
 tf. 3 X 9^ = 
 
 18. 
 
 5 
 
 X 
 
 3tV = • 
 
 7. 2 X 1 = . 
 
 19. 
 
 6 
 
 X 
 
 i - • 
 
 5. 3 X f = 
 
 20. 
 
 3 
 
 X 
 
 4 = • 
 
 i?. 5 X A - 
 
 21. 
 
 2 
 
 X 
 
 i = • 
 
 10. 2 x5t%= < 
 
 22. 
 
 G 
 
 X 
 
 ItV - • 
 
 //. 3 x3^ =: 
 
 23. 
 
 4 
 
 X 
 
 3f = . 
 
 12. 4 X 5y%=: 
 
 24. 
 
 4 
 
 X 
 
 n = • 
 
152 
 
 FRACTIONS. 
 
 319. 
 
 "j— I r 
 
 I 8 ^ ^ 
 
 
 Here we see that 
 
 I - 2 = J - Jl^; or, J - 2 = I - ,-f^. 
 
 Therefore, 
 
 To divide a fraction hy a whole number, divide 
 the numerator or multiply the denominator hy the 
 whole number. 
 
 Note. Divide tlie numerator when possible. 
 
 320. Oral Exercise. 
 
 Kead, supplying the missing numbers : 
 
 /. 
 
 1 
 
 -^ 2 = . 
 
 2. 
 
 1 
 
 -^ 3 = . 
 
 3. 
 
 f 
 
 -f- 3 = . 
 
 4. 
 
 i 
 
 -^ 4 = . 
 
 5. 
 
 4| 
 
 -^ 2 = . 
 
 6. 
 
 6| 
 
 -^ 3 = . 
 
 7. 
 
 1 
 
 -f- 3 = . 
 
 8. 
 
 A 
 
 -^ 5 = o 
 
 Note. 
 
 9- -h - 
 
 -10 =z . 
 
 17. ^ of 5i 
 
 = . 
 
 10. jt - 
 
 - 5 = . 
 
 /5. \ of IGJ 
 
 = • 
 
 //. 101 - 
 
 - 5 = . 
 
 ' /5. 1 of 1 
 
 = . 
 
 12. laij - 
 
 - 3 = . 
 
 20. J of § 
 
 r= . 
 
 13. A ot f = . 
 
 2/. 1 of 5 
 
 = . 
 
 14. ^ of 1 = . 
 
 22. i of J 
 
 — • 
 
 /5. i of J = 
 
 . 23. \ of ISi 
 
 = . 
 
 /fi. i of H = 
 
 • 24. i of 10 jV 
 
 — • 
 
 i of * hav 
 
 e the sail 
 
 le meaning. 
 
 
 321. Oral Exercise — Miscellaneous Problems. 
 /. Name at sight the whole or mixed number equivalent 
 to each of the following : 
 
MISCELLANEOUS PROBLEMS. 163 
 
 2. What part of a quart is a pint ? 
 
 3. A half peck is how many quarts ? 
 
 4. How many quarter pecks are there in a half peck ? 
 
 5. How many quarts are there in 3 pints ? 
 
 6. f of a foot is how many inches ? 
 
 7. How many half inches are there in a foot ? 
 
 8. How many half feet are there in a yard ? 
 
 9. What part of a dime is 1 cent ? 
 
 10. K woman used half a gallon of milk for breakfast 
 and one fourth of a gallon for dinner ; how many quarts 
 did she use for both meals ? 
 
 //. What will f of a pound of dried beef cost at 32 
 ct. per pound ? 
 
 12. If 4 pounds of coffee cost If, what part of a dollar 
 did 1 pound cost ? How many cents ? 
 
 13. If 3 pen trays cost $lf, what part of a dollar did 
 one cost ? How many cents ? 
 
 14. How many yards of ribbon are needed to make 5 
 bows, each | of a yard long ? 
 
 15. A. boy has four 2J-dollar gold pieces ; how much 
 money has he ? 
 
 16. If a $5-bill is exchanged for half dollars, how many 
 should be received ? 
 
 17. K rod contains 5|- yards ; how many yards are there 
 in 2 rods ? 
 
 18. How many yards are there in 3 rods ? 
 
154 FRACTIONS. 
 
 Reduction. 
 
 322. Reduce f, |, and i to 12ths. 
 
 12 = 4 X 3, 3 X 4, or 2 X G. 
 
 I = ii^ = A- 
 i = Tx-l = ->^- 
 
 b 2x6 ' ^ 
 
 323. Fractions that have the same number for a 
 denominator are said to have a Common Denominator. 
 
 324. Reducing f, |, and | tv) 12ths is reducing 
 fractions to a common denominator. 
 
 325. Fractions that have a common denominator 
 are called Similar Fractions. 
 
 Thus, A, i^if, JAiid [•}, haviug a common denominator, are similar 
 fractions. 
 
 326. Exercise. 
 
 Reduce : 
 
 /. I and f to 15ths. 7. f, |, and \ to 12ths. 
 
 2. I and f to 20ths. 8. |, J, and ^ to 30ths. 
 
 3. \ and | to 8ths. 5. J, f , and \ to 20ths. 
 
 4. -I and | to 18ths. 10. |, i, and f to 24ths. 
 
 5. 3% and ^ to lOOths. //. i, |, and ^ to 60ths. 
 
 6. f and ^ to 3Gths. 12. |, ^, and f to 72d8. 
 
 327. The Least Common Denominator (1. c. d.) of 
 two or mor(^ fractions in theii* lowest terms is the 
 least number tliat their denominators will divide: 
 
 Thus, the least common denominator of J, 5, and \ is 12, for 12 
 is the least number that 3, 4, and 6 will divide. 
 
REDUCTION. 156 
 
 328. Reduce J, f, and } to similar fractions having 
 their least common denominator. 
 
 The 1. c. d. of i, f, and f is readily seen to be 12. 
 Now, 12 = 6 X 2, 4 X 3, or 3 X 4. 
 
 1 _ 6^ _ 6 
 ■2 — 6x2 ~ ^''^' 
 
 1 = 3"^ = 1%. 
 
 329. Exercise. 
 
 Reduce to similar fractions having their least common 
 denominator : 
 
 /, f and f. 4. i and |. 7. J, i, and i. 
 
 2. J and f. 5. } and |. S. f, f, and |. 
 
 5. I and |. 6. f and Vo- 9. i, |, and |. 
 
 330. Reduce j\, f, and /^ to similar fractions having 
 their least common denominator. 
 
 When the 1. c. d. cannot readily be seen, as in the above 
 problem, it may be found thus : 
 
 12 = 2 X 2 X 3. The 1. c. d. must have in it the prime 
 
 g _ 2 X 2 X 2 factors 2, 2, and 3 in order that 12 may 
 
 divide it ; it must have in it the addi- 
 tional prime factor 2, in order tliat 8 
 may divide it, and the additional prime 
 2 X 3 X 5, or 120. factor 5 in order that 20 may divide it. 
 
 20 = 2 X 2 X 5. 
 1. c. d. = 2 X 2 X 
 
 Now, 120 -*- 13 = 10 ; 120 -^ 8 = 15 ; 120 -i- 20 = 6. 
 
 120 = 10 X 12, 15 X 8, or 6 X 20. 
 
 - 10x7 _ la 
 '12 ~ioVn- ■»2o- 
 
 K 15 X 5 7 5 
 
 16x8 
 
 — "120- 
 
 "s% — rIT^ — '^0' 
 
166 FRACTIONS. 
 
 331. Exercise. 
 
 Keduce to similar fractions having their least common 
 denominator : 
 
 1' i\, nh and ^j.. 5. A, ^, and Jf- 9. |J, \l and iJ. 
 
 2. -I, -i^, and }|. ff. A, f §, and A- ^^- i I'ff. and .^ 
 
 •?• ^S^ T% and f§. 7. ^\, jK, and ^'V- ^^- iz^ ^V and ^g^. 
 
 ^- 2\> ih and iJ. 5. ^\, A, and g^^. /2. ^^, ^^g, and H. 
 
 Addition and Subtraction. 
 
 332. Find the sum of f, |, and f 
 
 1. c. d. = 40. 
 
 _ 6J<J _ J 5 
 "8—6x8 — ^-^ 
 8 _ 10 X 3 _ ao 
 * — 10 X 4 "~ to* 
 
 4 _ 8x4 _ a« 
 ^ — 8 X 5 ~ *<> • 
 
 Sura = ^S = li§. 
 
 333. Exercise. 
 
 Find the sum of : 
 /. J, f , and f 5. I ^, and ^. 9. |, }ji, and |. 
 
 2. }, J, and ^. ff. }, I, and A- ^^- tV, H. and H 
 
 3. I -,% and H. 7. |, A, and i^. 11. ^\. j\, and h\. 
 
 4. I, /«, and ^V a. T^, ^V, and ^. 12. ^, iJ, and f f . 
 
 334. Find the sum of 12J, 16J, and 18^. 
 
 12i = 12ft. 
 16J = 16A. 
 18f = 18ft. 
 Sum = 46H = 47H. 
 
ADDITION AND SUBTRACTION. 157 
 
 335. Exercise. 
 
 Find the sum of : 
 
 /. 6J, 2J, and 3^. 6. 14f , 13J, and 10^^. 
 
 2. 7t, 8i and 6J. 7. 17i, 28^^, and ^^\, 
 
 3. 9f, 7J-, and 8f 5. 28^1^, 38/o, and 75. 
 
 4. S\, ^, and 9f. 9. 40f, 7f, and 125f . 
 
 5. 7|, 9^, and 4}^. /O. 84^, 75^^ and 96^V 
 
 336. Find the difference of ~-^ and ■^. 
 
 1. c. d. = 60. 
 
 -a. _ *iiL _ jji 
 
 15 ~ 4X15 — 6 0- 
 
 3 _ ^^3 _ la 
 JljL~ 6 X 10 ~ 6"- 
 
 Difference = i^ = 3V 
 
 337. Exercise. 
 
 Find the difference of : 
 
 /. f andf. 6. f and f. //. | and f. 
 
 2. I and |. 7. i| and |. 12. | and |. 
 
 5. i and f 5. ^ and Jf • ^5. Ji- and yV 
 
 4. ^V and |. 9. ^\ and ^g. /^. ^ and -^. 
 
 5. f and f. /(?. A and A- ^5. |f and i|. 
 
 338. Find the difference of 18| and 9f . 
 
 18f = ISif = 17|i Sua. i^ cannot be taken from 
 9f = 9i§ = 9if. i^ ; hence, reduce 1 of the 
 
 Difference = H\t 18 to |8 and add |g to H. 
 
158 FRACTIONS. 
 
 339. Exercise. 
 
 Find the difference of : 
 
 /. 25 and 6i. 6. 100 and 44f . //. lllj and 55J. 
 
 2. 100 and 37}. 7. 70f and 25^%. 12. 111^ and 77f 
 
 3. 87} and 62}. 8. 42f and 14f . 13. 333} and 107^^. 
 
 4. 66f and 33}. 9. 75} and 28/j. 14. 270} and 112J. 
 
 5. 87J and 18|. 10. 90| and 25|. /5. ■'20} and '76f. 
 
 340. Exercise — Miscellaneous Problems. 
 
 /. A market woman received $1J for butter, $2J for 
 eggs, $4} for vegetables, and $3 J for fruit; how much did 
 her produce amount to ? 
 
 2. 37} yards of bunting were sold from a piece contain- 
 ing 50 yards ; how much remained ? 
 
 5. To make a mixed tea a merchant used 12} pounds of 
 green tea and 18J pounds of black tea ; how many pounds 
 were there in the mixture ? 
 
 4. The sum of two numbers is 100 ; if one of them is 
 18}, what is their difference ? 
 
 5. How much change should a customer receive from a 
 $10-bill, if he buys groceries to the amount of I5J and dry 
 goods to the amount of $3| ? 
 
 6. A telegraph pole 40 feet long was set 4| feet in the 
 ground ; how many feet of it were above ground ? 
 
 7. A farmer owns 124^^ acres of land ; if 25} acres of 
 this is woodland and the rest farm land, how much farm 
 land has he ? 
 
 8. A girl received a mark of 80} in arithmetic and S6J 
 in geography ; what was her average in the two studies ? 
 
MISCELLANEOUS PROBLEMS. 159 
 
 9. Supply the missing number : 18| + 37| 4- ? = 100. 
 
 fO. 3 turkeys together weigh 20^^ pounds ; if one of 
 them weighs 6f pounds and another 8^ pounds, what does 
 the third weigh ? 
 
 341. Exercise — Miscellaneous Problems. 
 
 /. j\ of a dollar is equal to how many dimes ? How 
 many cents ? 
 
 2. One-half of a dollar plus one-fifth of a dollar is how 
 many tenths of a dollar ? How many cents ? 
 
 3. 25 quarter-dollars are equal to how many dollars ? 
 
 4. A man gave ^ of his property to each of his 4 sons 
 and the rest of it to his wife ; what part of the property 
 did she receive ? 
 
 5. If half a yard of silk costs $f , how much does a yard cost ? 
 
 6. ^ of a gallon plus J of a gallon is how many eighths 
 of a gallon ? How many pints ? 
 
 7. A lady who charged $1J a day for board should 
 charge how much for 6 days' board ? 
 
 8. J of a gallon of oil was taken from a can containing 
 I^ gallons ; what part of a gallon remained ? 
 
 9. What does a boy gain on 10 Sunday newspapers, if 
 he buys them at 2j- cents each and sells them for 5 cents ? 
 
 10. I exchanged 30 half-dollars for dollar bills ; how 
 many bills did I receive ? 
 
 //. At J of a cent a pound, what is the value of 8 
 pounds of old iron ? 
 
 12. A teacher had 20 pounds of candy put up in half- 
 pound boxes ; how many boxes were there ? 
 
160 FRACTIONS. 
 
 13. How far will a hoop go in turning 4 times, if the 
 distance around it is 1 J feet ? 
 
 14. A rod contains 5J yards ; how many yards are there 
 in J of a rod ? 
 
 15. Reduce 2f to an improper fraction. 
 
 16. At 18 cents a dozen, what will 'Z^ dozen eggs cost ? 
 /7. men hire a car for $18 J ; how much should each 
 
 man pay ? 
 
 18. J of a gallon of maple syrup will fdl how many 
 bottles, each holding J of a gallon ? 
 
 19. A farmer bought a plow for $10 and gave in pay- 
 ment wheat worth $7J, and the balance in cash ; how 
 much cash did he pay ? 
 
 20. Find the cost of all : 
 
 1 pair of shoes, $2J. 
 1 pair of gloves, $J. 
 1 handkerchief, %\. 
 
 21. 2J yards of ribbon were cut into pieces \ of a yard 
 long ; how many pieces were made ? 
 
 22. If ;[ of a pound of tea costs $g, how much does a 
 pound cost ? 
 
 23. A lady put J of a pound of green tea into a can con- 
 taining ^ of a pound of black tea ; how much tea was 
 there then in the can ? 
 
 24. A man bought a pair of 'shoes for I2|- and gave in 
 payment a $5-bill ; how much change should he receive ? 
 
 25. A farmer put up 10| pounds of butter in half-pound 
 prints ; how many prints had he ? 
 
MULTIPLICATION. 161 
 
 26. Reduce \^ to a mixed number. 
 
 27. If 5 rakes cost $f , what part of a dollar did each 
 cost ? 
 
 Multiplication. 
 
 342. J- 
 
 i \ ' 
 
 
 1 
 
 J_, 4. 
 
 ^ of 4 is I, or 1^. 
 
 343. Oral Exercise. 
 
 What is : 
 
 /. J of 3 ? 4. i of 5 ? 7. J of 2 ? /O. J of C ? 
 
 2. J of 5 ? 5. ^ of 7 ? S. J of :) ? //. } of 7 ? 
 
 5. J of 7 ? 5. i of 8 ? P. J of 5 ? /2. } of 11 ? 
 
 344. What is f of 4 ? 
 
 i of 4 is J, and § of 4 is 2 times ^, or |, or 2|. 
 Note, f of 4 and § x 4 have tiie same meaning. 
 
 345. Oral Exercise. 
 
 What is : 
 
 /. I of 5 ?. ff. f of 7 ? /a f of 6 ? 15. f of 3 ? 
 
 2. f of 7 ? 7. I of G ? //. I of 3 ? 16. f of 8 ? 
 
 5. I of 2 ? 5. A of 3 ? 12. I of 9 ? /7. | of 4 ? 
 
 4. 2J X 4, or f of 4 ? 13. 3J x 3 ? 18. 2f x 2? 
 
 5. 2| X 2 ? 5. 3^ X 3 ? /4. IJ X 5 ? /5. IJ x 2? 
 
 11 
 
102 
 
 FRACTIONS. 
 
 346. Here we see that § of f = t«6 = |A*. 
 
 +-H--f-h-- 
 
 ioH 
 
 2 t 1 
 
 TofT |ofi 
 
 Therefore, 
 
 7%6 product of two fractions equals the product 
 of their numerators divided by the product of their 
 denominators. 
 
 Note. ^ oi t and § x f have the same meaning. 
 347. Multiply f by |. 
 
 |xf=|4| = ,V. 
 
 
 348. Exercise. 
 
 
 Multiply : 
 
 
 /. i X f 5. i X ^. 
 
 5. A X f . 13. 1 X f 
 
 2. 1 X }. ff. f X 4. 
 
 10. 1,2 X i. /4. A X |. 
 
 5. t X J. 7. f X i 
 
 //. 1 X A. 15. H X |. 
 
 4. f X i S. f X |. 
 
 /2. J X |. /5. IJ X 4. 
 
 349. Multiply \i by f. 
 
 
 
 To reduce the product to its 
 
 8 15 ^ X ;^ 1x5 5 
 9^16~?'x;^-3x3~6* 
 
 lowest terms, we divide 8 and 
 16 by 8, and 15 and 9 by 3, and 
 
 8 2 
 
 cancel, that is, ei'ossout^ the num- 
 
 
 bers divided. 
 
 In practice the work may be done thus : 
 
 1 
 
 9 
 
 s 
 
 5 
 
 ;? 5 
 
 2 
 
MULTIPLICATION. 
 
 163 
 
 350. 2f by 3J. 
 
 
 
 
 
 
 3 
 
 3i X 2i = -^ X -5 
 
 ~ 5 - ''^• 
 
 
 
 
 
 361. Exercise 
 
 
 
 
 
 
 Find the products : 
 
 
 
 
 • 
 
 1- f X V. 
 
 9. f 
 
 X 
 
 1^ 
 
 
 17. IJ X IJ. 
 
 2- i X |. 
 
 /O. t 
 
 X 
 
 2|. 
 
 
 18. ^ X 3|. 
 
 5. f X f . 
 
 //. f 
 
 X 
 
 ^' 
 
 
 19. 7J X 2J. 
 
 4. 1 X f . 
 
 /2. 1 
 
 X 
 
 li 
 
 
 20. 3?j X 3J. 
 
 5- f X |. 
 
 /5. 2J 
 
 X 
 
 |. 
 
 
 21. 4f X 51 
 
 e- H X if. 
 
 /4. 3f 
 
 X 
 
 i 
 
 
 22. 8| X 7 J. 
 
 7. If X H. 
 
 /5. 7J 
 
 X 
 
 f. 
 
 
 25. 4} X ^. 
 
 «• A X |^ 
 
 16. 4f 
 
 X 
 
 |. 
 
 
 24. 31 X 6f. 
 
 352. Multiply : 
 
 IGGf by 7. 
 
 
 
 Multiply 126 by 5J. 
 
 166§ 
 
 
 
 
 
 126 
 
 7 
 
 
 
 
 
 of 
 
 1163 = 7 
 
 X 16G. 
 
 
 
 
 630 = 5 X 126. 
 
 4! = 
 
 7xi 
 
 
 
 
 94i =1 of 126. 
 
 1166§ = 
 
 7 X 166f. 
 
 
 
 
 724i = 5| X 126. 
 
 353. Exercise. 
 
 
 
 
 
 
 Multiply : 
 
 
 
 
 
 
 /. 216^ 
 
 5. 350| 
 
 
 5. 
 
 415^ 
 
 1 13. 135 
 
 6 
 
 8 
 
 
 
 15 
 
 6i 
 
 2. 335J 
 
 6. llSf 
 
 
 10. 
 
 6001 
 
 \ 14. 150 
 
 5 
 
 6 
 
 
 
 22 
 
 6J 
 
 5. 206f 
 
 7. 216| 
 
 
 11. 
 
 406j 
 
 1 15. 420 
 
 9 
 
 25 
 
 
 
 14 
 
 12J 
 
 4. 418| 
 
 8. 306| 
 
 
 12. 
 
 324^^ 16. 128 
 
 7 
 
 10 
 
 
 
 50 
 
 8i 
 
164 
 
 t 
 
 FRACTIONS. 
 
 
 n. 235 
 
 19. 220 
 
 21. 422 
 
 23. 200 
 
 H 
 
 n 
 
 lU 
 
 25J 
 
 18. 160 
 
 20. 406 
 
 22. 270 
 
 24. 605 
 
 13J 
 
 18i 
 
 18t 
 
 122§ 
 
 354. Oral Exercise — Miscellaneous Problems. 
 
 
 WM 
 
 W//A 
 
 4 
 
 
 
 
 
 rt 
 
 
 
 
 '■^M 
 
 ^^pf»m'^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 Read, supplying the missing numbers 
 
 /. 
 
 i = t 
 
 18. 
 
 4 = 1 V 
 
 55. 
 
 i = 7V 
 
 2. 
 
 i = t 
 
 19. 
 
 i = iV 
 
 5ff. 
 
 i =jTr 
 
 3. 
 
 1=^ 
 
 20. 
 
 i = TV 
 
 37. 
 
 * = ^V 
 
 4. 
 
 i = i 
 
 21. 
 
 i = TV 
 
 38. 
 
 ?=ijV 
 
 5. 
 
 « = t 
 
 22. 
 
 4 + i = rV 
 
 39. 
 
 i = zV 
 
 6. 
 
 i+4=6 
 
 23. 
 
 4 - } = rV 
 
 40. 
 
 i + i = s-o- 
 
 7. 
 
 i-4 = t 
 
 24. 
 
 1 X } = tV 
 
 41. 
 
 i + 1 = jV 
 
 8. 
 
 4 + 1 = ^ 
 
 25. 
 
 I + 4 = tV 
 
 42. 
 
 * + f = fV 
 
 9. 
 
 f-4 = « 
 
 26. 
 
 1 + 1 = TV 
 
 43. 
 
 l-i = i 
 
 10. 
 
 § - 4 = t 
 
 27. 
 
 1 - J = rV 
 
 44. 
 
 } - i = sV 
 
 11. 
 
 i~i = i 
 
 28. 
 
 |-f = ^3 
 
 45. 
 
 f - i = sv 
 
 12. 
 
 i-i = t 
 
 29. 
 
 1 -A= f3 
 
 46. 
 
 « - i = bv 
 
 13. 
 
 i-| = i 
 
 30. 
 
 1-tV=tV 
 
 47. 
 
 i-f = jj 
 
 14. 
 
 1 - 1 = c 
 
 31. 
 
 1 -A= TV 
 
 48. 
 
 1 -/»= jV 
 
 15. 
 
 1 - i = 
 
 32. 
 
 l-+i=TV 
 
 49. 
 
 2 - i = jV 
 
 16. 
 
 Jofi= . 
 
 33. 
 
 4of}= . 
 
 50. 
 
 i of i = . 
 
 17. 
 
 iof J= . 
 
 34. 
 
 iof4= • 
 
 61. 
 
 iof}= . 
 
MISCELLANEOUS PROBLEMS. 165 
 
 355. Oral Exercise — Miscellaneous Problems. 
 
 /. When thread is selling at 3 spools for 10 cents, how 
 much is that a spool ? 
 
 2. 2 pounds of pepper were put up in 8 packages of 
 equal size ; what part of a pound did each contain ? 
 
 3. 4 bottles of equal size together hold a pint ; what 
 part of a pint does each hold ? What part of a pint do 
 2 of them hold ? 
 
 4. What should f of a yard of silk cost at llj a yard ? 
 
 5. A piece of cloth 1^ yards long shrunk | of a yard ; 
 how long was it then ? 
 
 6. A can of lard weighed 36J pounds; if the can 
 weighed 2J pounds, what was the weight of the lard ? 
 
 7. How much should a laborer be paid for 6 days' work 
 at Hi a day? 
 
 8. When matches are selling at 3 boxes for 5 cents, how 
 much is that per dozen boxes ? 
 
 9. If IJ bushels of grass seed are sowed on 6 acres, 
 what part of a bushel is sowed on 1 acre ? 
 
 10. Find the cost of ^ of a pound of tea at 40 cents a 
 pound, and | of a pound of dried beef at 32 cents a 
 pound. 
 
 11. A lady ordered 10 blocks of ice cream, each con- 
 taining J of a pint ; how much did it cost her, at 40 cents 
 a quart ? 
 
 12. A lot containing | of an acre was divided into 3 
 lots of equal size, and 2 of them were sold ; what part of 
 an acre was sold ? 
 
 13. Reduce ^ to an integer. 
 
166 FRACTIONS. 
 
 14. How many bushels of corn is | of a barrel, if one 
 barrel is 2 J bushels ? 
 
 15. A lady had IJ dozen eggs and used 9 of them ; 
 how many had she left ? 
 
 16. Name the fraction equal to || that has the smallest 
 numerator and denominator possible. 
 
 17. If poultry lose about I of their weight in dressing, 
 how much should a 9-pound turkey weigh when dressed 't 
 
 18. A milkman put J of a gallon of cream into pint 
 jars and sold each jar for 12 cents ; how much did he 
 receive ? 
 
 Find the cost of : 
 
 19. 2J pounds of ham at 18 cents a pound. 
 
 20. IJ pounds of butter at 24 cents a pound. 
 
 21. 3f yards of cloth at 12 cents a yard. 
 
 22. 2 J bushels of onions at $1.50 a bushel. 
 
 23. 4J dozen eggs at 16 cents a dozen. 
 
 24. 3 bushels of seed at $5J a bushel. 
 
 25. 5 pair of gloves at $1J a pair. 
 
 26. 10 pounds of twine at GJ cents a pound. 
 
 27. 2 hundredweight of flour at $lf a hundredweight. 
 
 28. pounds of beefsteak at 12J cents a pound. 
 
 366. Exercise— Miscellaneous Problems. 
 
 /. When eggs are selling at 24 cents a dozen, how 
 much should be paid for 10} dozen? 
 
 2. 66 feet make 4 rods ; how many feet make a rod? 
 
 3. Find the selling price of 10 sheep at an average price 
 of $5} a head. 
 
MISCELLANEOUS PROBLEMS. 167 
 
 4. Find the selling price of 65|^ bushels of wheat at 
 $0.80 per bushel. 
 
 5. Allowing each of 25 sailors 1} pounds of meat daily, 
 how much meat must be supplied for them for a cruise of 
 10 days? 
 
 6. A barrel holding 42J gallons is f full of syrup ; how 
 many gallons of syrup are there in the barrel ? 
 
 7. What should be paid for 12^ cords of chestnut wood 
 at %i^ a cord ? 
 
 8. A dealer bought 28 pigs at IGJ a pair, and after keep- 
 ing them 10 weeks at a cost of $2 J a week, sold them for 
 $10J a pair ; find his gain. 
 
 9. Find the weight of a bolt of dress flannel of 40 yards, 
 if each yard weighs -f^ of a pound. 
 
 10. If } of a number is 42, what is 2J times the num- 
 ber? 
 
 //. A farmer sold 332 pounds of leaf tobacco at $0.07| 
 a pound ; how much did he receive for it? 
 
 12. A dealer sold a plow for $6J ; if J of this sum was 
 gain, what was the cost? 
 
 13. A laborer worked lOJ hours a day for the 6 working 
 days of a week ; if his wages were I0.12J an hour, how 
 much did he earn ? 
 
 14. A farmer sows 2 J bushels of wheat to the acre ; how 
 much does he sow on a field containing 10 J acres? 
 
 15. What do 3 J dozen arithmetics cost, at $5.7G a dozen? 
 
 16. When hay is selling for |18f a ton, what should be 
 paid for | of a ton? 
 
 17. From a piece of cloth containing 40 yards there 
 
168 
 
 FRACTIONS. 
 
 were sold 2 J yards, 18f yards, and 6 yards, 
 value of the remainder at IG cents a yard. 
 
 Find the 
 
 Division and Mensuration. 
 357. 4 is I of what number ? 
 
 -?-of 
 
 [ T of the number 
 
 3 °^ , 
 
 a number 
 
 
 1 xo^ the number 
 
 
 
 
 I" -^of the number 
 
 If f of a number is 4, 
 ^ of the number is ^ of 
 
 number is 3 times — . 
 
 358. Oral Exercise. 
 
 /. If J of a number is 3, | of the number is 2 times — , 
 or — . 
 
 2. If I of a number is 2, what is the number ? 
 
 3. 9 is f of what number ? 
 
 4. 4 is 1^ of what number ? 
 
 5. 10 is I of what number ? 
 
 6. 16 is I of what number? 
 
 7. If I of the length of a line is 8 inches, \ of its length 
 is ;J of — inches, or — inches, and | of its length is — 
 times — inches, or — inches. 
 
 8. 5 of the weight of a bushel of wheat is 50 pounds; 
 what is the weight of a bushel of wheat ? 
 
 9. A boy spelled correctly 20 words, which was f of the 
 number he was given; how many was he given ? 
 
 10. K farmer sold a cow for 32 dollars, which was f of 
 her cost; what was her cost? 
 
DIVISION AND MENSURATION. 
 
 169 
 
 359. 
 
 (1) If 3 X a number = 12, the number == 12 -^ 3. 
 
 (2) If 3 X a number = I, the number = f -=- 3. 
 
 (3) If I X a number = |, the number = f -^ |. 
 
 Now, if I of a number = f , 
 
 i of the number = J of J. 
 And I of tbe number = 3 x J of I, or | of 5. 
 
 That is, the number = f x J. 
 But the number = f ^- 1. [See (3).] 
 Therefore, f -r- 1 = | x |. 
 J is called the inverse of f . 
 
 Therefore, 
 
 To divide by a fraction, multiply by the inverse 
 of the fraction. 
 360. Divide f by f. 
 
 *-.* = |x- 
 
 = f = i-i. 
 
 
 
 
 Divide 4 by f . 
 
 
 
 
 4^f = § X 4 = 
 
 = Y = 6f . 
 
 
 
 361. Exercise. 
 
 
 
 
 Find the quotients : 
 
 
 
 1' t-|. 
 
 5. 2h 
 
 -|. 
 
 17. 
 
 IJ - H. 
 
 ^- f - f . 
 
 /O. 3 - 
 
 -f 
 
 18. 
 
 3i-lf. 
 
 5. 4 - |. 
 
 //. 7- 
 
 -f. 
 
 19. 
 
 ^^^. 
 
 4. ^-|. 
 
 /2. 5- 
 
 -f. 
 
 20. 
 
 H - n- 
 
 5- H - J- 
 
 /5. 4- 
 
 -14. 
 
 21. 
 
 If - 5J. 
 
 6. J-^tV 
 
 14. 9- 
 
 -3J. 
 
 22. 
 
 If -^ Gf . 
 
 7. A-H. 
 
 /5. 8- 
 
 ^31. 
 
 23. 
 
 12J-6}. 
 
 «■ i-M. 
 
 /5. 4 - 
 
 -7i. 
 
 24. 
 
 2f -^ 14f . 
 
170 FRACTIONS. 
 
 362. Divide 233^ by 12J. 
 
 
 12| 233^ 
 
 
 G 6 
 
 
 75) 1400 (18* Multiply 
 
 both dividend and divisor by 
 
 75 the 1. c. d. 
 
 of the fractions before divid- 
 
 em) ing. 
 
 
 600 
 
 
 M=« 
 
 
 363. Exercise. 
 
 
 Divide : 
 
 
 /. 100 by 14f. 
 
 6. 144f by 6f . 
 
 2. m\ by 62J. 
 
 7. 262J by 18J. 
 
 3. 133?5by66f. 
 
 8. 183J by 26f. 
 
 4. \n\ by Gi. 
 
 9. 237i by 33i. 
 
 5. 187J by 25. 
 
 10. 666| by 55|. 
 
 364. Oral Exercise. 
 
 /. If 9 cents is ^ of a sum of money, what is the sum ? 
 
 2. If J of a melon costs 10 cents, what will 2 melons 
 cost ? 
 
 3. If 3 pecks of potatoes cost 60 cents, 1 peck costs \ of 
 
 — cents, or — cents; and 4 pecks cost 4 x — cents, or — 
 cents. 
 
 4. If 3 pecks of apples cost -J of a dollar, 1 peck costs \ 
 of — of a dollar, or — of a dollar; and 4 pecks cost 4 times 
 
 — of a dollar, or — of a dollar. 
 
 5. If J of a bushel of apples costs § of a dollar, } of a 
 bushel costs J of — of a dollar, or — of a dollar; and J of 
 a bushel costs 4 times — of a dollar, or — of a dollar. 
 
DIVISION AND MENSURATION. 171 
 
 6. When I of a pound of tea cost 36 cents, how much 
 is that a pound ? 
 
 7. A farmer received $24 for f of his tobacco crop; 
 what should he receive for the whole crop at the same 
 rate? • 
 
 8. If ^ of a number is 1|, what is \ of the number ? 
 
 9. If f of an inch on a map represents a mile, what does 
 an inch on the map represent ? 
 
 10. 3| is f of what number? 
 
 11. K laborer saves $J a day, which is f of his daily- 
 wages ; what are his daily wages ? 
 
 12. 2 J is f of what number ? 
 
 13. If I of the length of a line is 2J- inches, what is J of 
 its length ? What is its length ? 
 
 14. In f of a week a laborer earned $4.50; what should 
 he earn in a week ? 
 
 /5. 2 dimes are f of how many cents? 
 
 365. Exercise. 
 
 /. If 2,000 pounds of fertilizer are put up in 12 bags of 
 equal size, how many pounds does each bag contain ? 
 
 2. A farmer sold a load of 50 bushels of oats which 
 weighed 1,575 pounds; what did each bushel weigh? 
 
 3. A drover bought 20 sheep for $130; what was the 
 average price paid per head ? 
 
 4. If an echo traveled 2, 191 J feet in 2 seconds, how far 
 did it travel per second ? 
 
 5. If it cost $136,000 to build ^ miles of a trolley line, 
 how much did it cost per mile on an average? 
 
172 FRACTIONS. 
 
 6. A train that ran 160 miles in 2^ hours, ran how far 
 each hour on an average ? 
 
 7. How much was paid per dozen for eggs, when $16J 
 was paid for 54 dozen ? 
 
 8. A can pay only | of what he owes B; if he can pay 
 B $1,004J^, how much does he owe B ? 
 
 9. A's farmer returned him $220J^ from a sale of corn; 
 if A received | of the selling price of the corn, how much 
 did the farmer receive ? What did the sale amount to ? 
 
 10. A bushel of corn weighs 5G pounds, which is \^ of 
 the weight of a bushel of clover seed ; what is the weight 
 of a bushel of clover seed ? 
 
 //. A woodchopper was paid $6J for chopping 12 J cords 
 of wood; how much was that a cord ? 
 
 12. A laborer earned $7 J in 4J days; how much did he 
 earn per day ? 
 
 366. How many times is f contained in J ? 
 
 -:^ or 1^ X ^ 
 
 Since | equals A and | equals \\, | is contained in f as many 
 times as 8 is contained in 9, or |, or H. 
 
 367. Oral Exercise. 
 
 (Reduce wliole or mixed numbers to improper fractions.) 
 How many times is : 
 
 /. f contained in | ? 5. J contained in 1 ? 
 
 2. J contained in J ? 4. f contained in 1 ? 
 
DIVISION AND MENSURATION. 
 
 173 
 
 5. 
 
 J contained 
 
 ill 
 
 f ? 
 
 /5. 
 
 1\ contained in 1} ? 
 
 6. 
 
 1 contained 
 
 in 
 
 2 ? 
 
 /4. 
 
 1 contained in | ? 
 
 7. 
 
 f contained 
 
 in 
 
 3 ^ 
 
 /5. 
 
 If contained in SJ ? 
 
 8. 
 
 J contained 
 
 in 
 
 4 ? 
 
 16. 
 
 3 contained in 1 1 ? 
 
 9. 
 
 1 contained 
 
 in 
 
 1 ? 
 
 17. 
 
 2| contained in IJ ? 
 
 10. 
 
 1 contained 
 
 in 
 
 5 ? 
 
 18. 
 
 IJ contained in 1 ? 
 
 11. 
 
 f contained 
 
 in 
 
 1 ? 
 
 19. 
 
 2J contained in 3| ? 
 
 12. 
 
 1 contained 
 
 in 
 
 i ? 
 
 20. 
 
 2 contained in If ? 
 
 368. To measure } by f is to find how many times 
 I is contained in |. 
 
 369. To measure one fraction by another^ reduce 
 them to a common denominator and divide the 
 
 numerator of the first by the numerator of the 
 second. 
 
 Thus, f : f = ,% -0% = 9 -5- 8 = I, or H. 
 
 370. Exercise. 
 
 
 
 
 
 ind the value of : 
 
 
 
 
 
 '• H : f 
 
 4. 7i 
 
 \h 
 
 7- A 
 
 7J. 
 
 2. -1 :tV 
 
 5- fl • 
 
 h 
 
 8. 25 
 
 :5J 
 
 3- |t:iV 
 
 6. 16J 
 
 If- 
 
 9. 6| 
 
 34 
 
 371. Oral Exercise. 
 
 /. If a boy has $2 in quarter-dollars and 13 in half- 
 dollars, how many pieces of money has he ? 
 2. What part of 2 quarts is 1 quart? 
 5. $1 is \ of 15, and 13 is 3 times \ of $5, or — of $5. 
 4. What part of 12 inches is 4 inches ? 
 
174 FRACTIONS. 
 
 5. When coal is selling, for $6 a ton, what part of a ton 
 
 can be bought for $2 ? 
 
 6. A lady spent $3 for cloth at $| a yard; how many 
 yards did she buy ? 
 
 Since $3 equal $\2^ the number of yards she bought at $\ a yard 
 was 12 divided by 3, or 4. 
 
 7. IIow many ropes, each § of a foot long, can be made 
 from a 6-foot rope ? 
 
 8. When apples are selling at $J a peck, how many pecks 
 can be bought for $f ? 
 
 9. If coal is selling at $6 a ton, what part of a ton can 
 be bought for SIJ ? 
 
 Since $1^ equal $| and $6 equal $V. the part of a ton that can 
 be bought is 3 divided by 12, or i^^, or I. 
 
 10. When potatoes are selling at %^ a bushel, how many 
 bushels can be bought for $5 ? 
 
 372. Exercise. 
 
 /. How many times is 1:2J contained in 200? 
 
 2. At 6J ct. a pound, how many pounds of sugar can 
 be bought for 75 ct. ? 
 
 3. If the distance around a wheel is 7J ft., how many 
 times will the wheel turn in going 2,640 ft. ? 
 
 4. A dealer bought cloth at 75 ct. a yard and sold it 
 at 87J ct. a yard; his gain was 75 ct. How many yards 
 of this cloth did he sell ? 
 
 5. If the cost of an article is 50 ct. and the selling 
 price 62 J^ ct., what part of the cost is gained in the 
 sale? 
 
DIVISION AND MENSURATION. 175 
 
 6. A barrel contains ol| gal. and a hogshead 63 gal. 
 How many barrels are there in a hogshead ? 
 
 7. If a house valued at $5,000 rents for I33J a month, 
 in how many months will the rent amount to the value of 
 the house ? 
 
 8. How many trees are there along a street for a distance 
 of 330 ft., if they are placed IGJ ft. apart? 
 
 373. Exercise — Miscellaneous Problems. 
 
 /. Supply the missing number: 
 
 9f + 37i + 50 + ? + 6} = 150. 
 
 2. A dealer bought a machine for $22J and sold it at a 
 gain of f of the cost; find the selling price. 
 
 3. How many bushels were there in my wheat crop, if, 
 after selling | of it, I had 353 bu. left? 
 
 4. 6G ft. make 4 rods; how many feet make 2J rods? 
 
 5. Which is the larger fraction and by how much, ^^ or ^? 
 
 6. A farmer raised 270 bu. of oats on 7J acres; what 
 was the yield per acre ? 
 
 7. If 8 men can do a piece of work in 10 days, how long 
 should it take 15 men to do it? 
 
 SuG. 1 man can do the work in 8 x 10 da., or 80 da. 
 15 men can do the work in ^V of 80 da. 
 
 8. If 6 men can do a piece of work in 7 J days, how 
 long should it take 5 men to do it ? 
 
 9. 1,000 - 12J = ? 
 
 10. I bought a house and 40 acres of land for $5,500. 
 If the house was valued at $250, what was the value of the 
 land per acre ? 
 
176 FRACTIONS. 
 
 Complex Fractions. 
 374. Such expressions as ~ ' -^^ -|-» and t^ 
 
 are called Complex Fractions. They denote that 
 the numerator is to be divided by the denominator. 
 
 f 
 
 Thus, —T~ denotes that f is to be divided b}^ 4. 
 
 376. Reduce • 
 
 -J to its simplest form. 
 
 
 
 
 1 
 4 
 
 = 4^1 = ^--* 
 
 • 
 
 376. Exercise, 
 
 
 
 
 Reduce to sim 
 
 iplest 
 
 form : 
 
 
 /. 
 
 ii. 
 
 4 
 
 
 '4- 
 
 100 
 
 03J- 
 
 2. 
 
 2 
 
 
 10. li. 
 5 
 
 100 
 
 3. 
 
 3 
 
 
 10 
 
 19. m. 
 
 50 
 
 4. 
 
 2 
 
 i 
 
 
 12. Ǥ. 
 30 
 
 20. _L. 
 * 
 
 5. 
 
 3 
 
 
 
 21. ±. 
 
 6. 
 
 5 
 f 
 
 
 14. 10 . 
 10§ 
 
 22. l+l 
 
 7. 
 
 6 
 V 
 
 
 
 23. 37i, 
 
 87i 
 
 8. 
 
 1 
 
 if 
 
 
 16 100 
 37J 
 
 ?4. >>n 
 
CHAPTER III. 
 DECIMALS. 
 Introductory Problems and Definitions. 
 377. Oral Exercise. 
 
 /. Into how many equal strips is this square divided ? 
 
 2. What part of the whole square is each strip ? 
 
 3. Into how many equal squares is the first strip divided ? 
 
 4. What part of a strip is a small square ? 
 
 12 
 
178 DECIMALS. 
 
 5. How many small squares would the large square 
 make? 
 
 6. What part of the large square is a small square ? 
 
 7. Into how many equal strips is one of the small 
 squares divided ? 
 
 8. How many small strips would a large strip make? 
 
 9. How many small strips would the large square make ? 
 10. A small strip is what part of the whole square? 
 
 //. How many tenths are there in one? 
 
 12. How many hundredths are there in one tenth ? 
 
 13. How many thousandths are there in one hundredth ? 
 
 14. \Y\mtk^ot-^? 
 
 15. Whatis^ij^of tJ^? 
 
 378. If anything is divided into 10, 100, 1000, etc., 
 equal parts, these parts are called Decimal Parts. 
 
 379. Any number of decimal parts of a unit is a 
 Decimal Fraction, or simply a Decimal. 
 
 Reading and Writing Decimals. 
 
 380. Decimal fractions may be written without a 
 denominator. A figure written in the first place to 
 the right of the decimal point expresses tenths; 
 in the second place, Jiundredtlis ; in the third place, 
 thousandths ; in the fourth place, ten -thousandths ; 
 in the fifth place, hundred-thousandths ; in the 
 sixth place, millionths. 
 
READING AND WRITING DECIMALS. 
 
 179 
 
 381. 
 
 
 
 
 
 TABLE. 
 
 
 
 
 
 
 GO 
 
 
 
 
 
 
 
 
 ^ 
 
 
 -O 
 
 
 
 
 
 
 
 
 ^ 
 
 
 a 
 
 
 
 
 
 
 
 
 GQ S 
 
 
 g 
 
 
 
 
 
 
 
 
 5 S 
 
 
 
 33 
 
 
 QQ 
 
 
 
 1 
 
 13 
 
 "2 o 
 
 i ^ s 
 
 C 
 
 1 
 
 J3 
 
 fl 
 g 
 
 1 
 
 
 CD 
 
 « 
 
 
 3 T3 -S 
 III 
 
 .2 
 
 'O 
 
 
 s 
 
 xs 
 
 CO S 
 
 •s 
 
 '2 
 
 3 
 
 
 S 
 
 
 g 
 
 o 
 .a 
 
 
 a ^ 
 
 
 g 
 
 O 
 ,£3 
 
 jL fl ^ 
 
 '^ 
 
 » 
 
 ^ 
 
 &H 
 
 w 
 
 H t3 
 
 H 
 
 w 
 
 H 
 
 H S !§ 
 
 5 
 
 3 
 
 8 
 
 7 
 
 4 
 
 2 3 . 
 
 2 
 
 3 
 
 5 
 
 G 4 8 
 
 
 Integral part 
 
 
 Decimal part 
 
 382. Oral Exercise. 
 
 /. Name the first place to the right of the decimal point; 
 the second; the fourth; the fifth; the third; the sixth. 
 
 2. Beginning at the decimal point, name the decimal 
 places in their order. 
 
 3. Counting from the decimal point, what is the num- 
 ber of the tenths' place ? the hundred-thousandths' ? the 
 thousandths' ? the millionths' ? the hundredths' ? the ten- 
 thousandths' ? 
 
 4. In the number written in the Table, how many tenths 
 are there? how many thousandths? how many hundred- 
 thousandths? how many tens? how many hundreds? how 
 many thousands? how many millionths? how many millions? 
 
 383. Oral Exercise. 
 Read : 
 
 /. .01; .0001; .1; .00001; .001; .000001. 
 
 2. .02.; .003; .0004; .5; .000007; .000009. 
 
 3. .006.; .7; .09; .0006; .000008; .000007. 
 
 4. .3.; .007; .08; .0005; .000002. 
 
180 
 
 DECIMALS. 
 
 384. Exercise. 
 Write in words: 
 
 /. .01, also .1. 
 
 2. .001, also .00001. 
 
 5. .0001, also .000001. 
 
 4. .2, also .002. 
 
 5. .0007, also .08. 
 
 6. .00009, also .006. 
 
 7. .02, also .0004. 
 
 8. .007, also .00005. 
 
 385. Exercise. 
 Write as decimals: 
 
 386. 
 
 *• TTJJ 1 > TOlT* 
 
 ^' TIHFOJ lOOOFffTTJ IIT* 
 
 .335 = ^ + tStt + T-u^o-TT = iVJl- + rh% + Tiftfn = t^o'I. = 325 tliou- 
 sandths. Hence, 
 
 Read the decimal as a whole number and give it 
 the name of the place occupied by the right-hand 
 figure. 
 
 Tluis, .0025 is read twenty-Jive ten-thottsandths, and 7.64 is read 
 seven and sixty-four hundredths. 
 
 387. Oral Exercise. 
 
 
 
 
 
 Read : 
 
 
 
 
 
 /. .25. 6. .201. 
 
 //. 
 
 .30014. 
 
 16. 
 
 .000204. 
 
 2. .37. 7. .0028. 
 
 /2. 
 
 .00154. 
 
 17. 
 
 12.5. 
 
 3. .752. 8. .0325. 
 
 13. 
 
 .00302. 
 
 18. 
 
 13.07. 
 
 4. .082. 9. .7248. 
 
 14. 
 
 .403. 
 
 19. 
 
 28.375. 
 
 5. .030. 10. .2004. 
 
 15. 
 
 7.24. 
 
 20. 
 
 36.004. 
 
READING AND WRITING DECIMALS. 181 
 
 388. .02} is read hvo and one four ill liundredths ; jiiid 
 3.12J is read three and twelve and one half hundredths. 
 
 389. Oral Exercise. 
 
 
 
 Read: 
 
 
 
 
 /. .06}. 
 
 4. .62 J. 
 
 7. .08 J. 
 
 /O. 6.66|. 
 
 2. .12 J. 
 
 5. .87 J. 
 
 8. .037 J. 
 
 //. 4.18|. 
 
 5. .37i. 
 
 6. .16f. 
 
 9. .334. 
 
 12. 5. 07 J. 
 
 390. Exercise. 
 
 "Write in decimal form: 
 ^- A- ^- tAo- 
 
 -^^ Too"* °- 100 000* 
 
 ^- TTrflTD"' ^' TOUOTTOir- 
 
 13. 18 hundredths. 
 
 /4. 15 ten-thousandths. 
 
 15. 25 thousandths. 
 
 16. 607 thousandths. 
 /7. 18 millionths. 
 
 18. 185 hundred-thousandths. 
 /5. 325 ten-thousandths. 
 
 20. Twenty-eight hundredths. 
 
 21. Six and twenty-one thousandths. 
 
 22. Two hundred four millionths. 
 
 23. Twenty and seven tenths. 
 
 24. Two hundred six thousandths. 
 
 25. Two hundred and six thousandths. 
 SuG. Two hundred is an integer. 
 
 7. 
 
 m- 
 
 10. 
 
 3A. 
 
 8. 
 
 1 b 0* 
 
 11. 
 
 ^T^o. 
 
 9. 
 
 1000- 
 
 12. 
 
 8toV 
 
182 DECIMALS. 
 
 26. Nine hundred and four thousandths. 
 
 27. Six hundred and five hundredths. 
 
 Reduction. 
 
 391. Oral Exercise. 
 
 /. When both terms of ^^ are multiplied by 10, what is 
 
 the result ? 
 
 2. Does A equal ^% ? Why ? [§ 301] . 
 
 3. When both terms of -^\ are multiplied by 100, what is 
 the result ? 
 
 4. Does ^ equal ^Wir ? Why? 
 
 5. When both terms of y^o ^^® multiplied by 1000, what 
 is the result ? 
 
 6. Does i8_ equal tWA? Why? 
 
 7. Does j\ equal A?o^A ? Why ? 
 
 8. By what must both terms of ^^ be divided in order 
 tliat the result may be ^ ? 
 
 9. Does dividing both terms of -^ by 10 change the 
 value of the fraction ? Why ? 
 
 10. Does f^4 equal 1^ ? Why? 
 //. Does 1%% equal A? Why? 
 12. Does .^oO^/A equal t\? Why? 
 
 392. ^ = m = ^A=^^<?A = WM' 
 Therefore, .8 = .80 = .800 = .8000 = .80000. 
 Hence, 
 
 Annexing ciphers to a decimal does not change 
 its value. 
 
REDUCTION. 
 
 183 
 
 Remomng ciphers from the right of a decimal 
 does not change its lvalue. 
 
 393. Exercise. 
 
 Reduce: 
 /. .3 to hundredths. 
 
 2. .64 to thousandths. 
 
 3. .255 to ten-thousandths. 9 
 
 4. .20 to tenths. 10 
 
 5. .240 to hundredths. //. 
 
 6. .5000 to tenths. 12. 
 
 7. .2 to thousandths. 
 
 8. .04 to thousandths. 
 .005 to millionths. 
 .200 to tenths. 
 .6000 to hundredths. 
 .25 to ten-thousandths. 
 
 394. Reduce .425 to a common fraction. 
 
 395. Exercise. 
 
 Reduce to common fractions or mixed numbers: 
 /. .6. 5. .075. 9. 7.5. 
 
 2. .08. 6. .225. 10. 1.08. 
 
 3. .25. 7. .450. //. 12.012. 
 
 4. .004. 8. .0025. 12. 6.775. 
 
 396. Reduce .16f to a common fraction. 
 
 1 fig — ^' — 3ji26i _ 6Q _ jL 
 
 397. Exercise. 
 
 
 
 
 Reduce to common 
 
 fractions : 
 
 
 
 /. .SJ. 
 
 5. .14f. 
 
 S. 
 
 .87f. 
 
 2. .6}. 
 
 6. .331. 
 
 10. 
 
 .SSJ. 
 
 3, .l^. 
 
 7. .66|. 
 
 11. 
 
 .28f 
 
 4. .16f. 
 
 8. .18J. 
 
 12. 
 
 .42f. 
 
184 DECIMALS. 
 
 398. Reduce J to a decimal. 
 
 i equals i of 3, which equals i of 30 tenths. 
 I of 30 tenths is 7 tenths, and 3 tenths remaining. 
 LLI — 2 tenths equals 20 hundredths. 
 ''^^ i of 20 hundredtlis is 5 hundredths. 
 Therefore, f equals .75. 
 
 Hence, to reduce a fraction to a decimal, 
 Annex ciphers to the numerator^ divide by the 
 denominator, and point off as many decimal places 
 in the quotient as there are ciphers annexed, 
 
 399. Another Method : | = ^-^ = ^Vo = -"^'^ 
 Multiply both terms of f by 25 to reduce the frac- 
 tion to hundredths. 
 
 400. Exercise. 
 
 Reduce to decimals : 
 
 /. J. 5. f. 9. /,. 13. A. 
 
 2. i. 6. i. 10. A. 1^- A- 
 
 3. |. 7. A. //. ^^. 15. ^. 
 
 4. f. 8. I. 12. ~f,. 16. ^V 
 
 401. Reduce | to hundredths ; | to thousandths. 
 
 6 )5.00 9 )8.00 
 
 ~~m\ .8881 
 
 402. Exercise. 
 
 Reduce : 
 /. J to tenths. 3. | to hundredths. 5. j*^ to thousandths. 
 2. I to tenths. 4. ^^ to hundredths. 6. f to thousandths. 
 
ADDITION AND SUBTRACTION. 185 
 
 Addition and Subtraction. 
 
 403. Find the sum of 2.7, 25.08, .075, and 27.25. 
 
 2.7 
 
 Write the numbers so that units of the same order 
 (vD.Uo 
 
 stand in the same column, and add as in addition of 
 .075 
 
 whole numbers. Place the decimal point between 
 
 27 25 
 
 — '- units and tenths in the sum. 
 
 55.105 
 
 404. Exercise. 
 
 Find the sum of : 
 
 /. 2. 3. 
 
 3.25 1.006 .3048 
 
 .0075 .25 2.96 
 
 18.2 24.07 .278 
 
 .2785 .8 18.075 
 
 4. .7, .045, and .62. 
 
 5. 3.18, 9.008, and 12.7. 
 
 6. .211, 2.55, .0175, and .004. 
 
 7. 20.02, 128.025, .07, and .7. 
 
 8. 9 tenths, 25 hundredths, and 17 thousandths. 
 
 9. 8 and 7 tenths, 12 thousandths, and 4 and 6 hun- 
 dredths. 
 
 10. 7 tenths, 87 hundredths, and 450 thousandths. 
 
 //. 16 and 25 ten-thousandths, 7 and 7 thousandths, and 
 25 hundredths. 
 
 12. 105 millionths, 1 and 70 hundred-thousandths, 44 
 and 125 thousandths, and 1 and 7 tenths. 
 
186 DECIMALS. 
 
 405. From 12.75 take 7.9. From 28.7 take 1.245. 
 12.75 28.700 
 
 7.9 1.245 
 
 4.65 27.455 
 
 Write the numbers so that units of the same order stand in 
 the same column, and subtract as in subtraction of whole num- 
 bers. Place the decimal point between units and tenths in the 
 difference. 
 
 406. Exercise. 
 
 
 
 
 /. 
 
 3. 
 
 5. 
 
 7. 
 
 From 8.362 
 
 2.000 
 
 9.2 
 
 4 
 
 take 2.41 
 
 1.875 
 
 1.075 
 
 2.375 
 
 2. 
 
 4. 
 
 6. 
 
 8. 
 
 From 3.50 
 
 3.2 
 
 25.6 
 
 29.01 
 
 take 1.27 
 
 .75 
 
 1.07 
 
 11.909 
 
 Find the difference between: 
 
 9. .8 and .3865. 12. 8.75 and .109. 
 
 10. 2 and .0375. 13. 1.09 and .009. 
 
 //. 4.010 and .099. U. 27.4 and .138. 
 
 15. 65 hundredths and 75 thousandths. 
 
 16. 1 and 9 tenths and 99 hundredths. 
 
 17. 109 ten-thousandths and 109 millionths. 
 
 18. 5 tenths and 499 thousandths. 
 
 Multiplication, Division, and Mensuration. 
 
 407. .3 X .4 = A X A = Anr = .1^. 
 
 408. Exercise. 
 
 /. Show that 3 X .4 = 1.2. 
 2. Show that .3x2 = .6. 
 
MULTIPLICATION, DIVISION, MENSURATION. 187 
 
 3. Show that .2 x .3 = .06. 
 
 4. Show that .3 x .04 = .012. 
 
 5. Show that .03 x .04 = .0012. 
 
 6. In problem 1, how many decimal places are there in 
 the multiplicand? How many in the multiplier? How 
 many in the product? 
 
 7. In problem 2, how many decimal places are there in 
 the multiplicand? In the multiplier? In the product? 
 
 8. In problem 3, how does the number of decimal places 
 in the multiplicand and multiplier together compare with 
 the number in the product ? 
 
 9. In each of problems 4, 5, and 6, compare the number 
 of decimal places in the product with the number in the 
 multiplicand and multiplier together. 
 
 10. Make a statement about the number of decimal places 
 in the product. 
 
 409. Multiply 6.5 by .25. 
 
 6.5 
 
 .25 
 
 325 .25 X 6.5 = t^o'o- X fB = i^oi = 1M% = 1.625. 
 
 130 
 1.625 
 
 From tMs illustration we see that to multiply 
 decimals, we 
 
 Multiply as in whole numbers, and point off as 
 many decimal places in the product as there are in 
 the multiplicands and multiplier together. 
 
188 
 
 DECIMALS. 
 
 
 410. Multiply 
 
 .075 by 45; .075 by 
 
 .45; .000075 by 420. 
 
 .075 
 
 .075 
 
 .000075 
 
 45 
 
 .45 
 
 4^0 
 
 375 
 
 375 
 
 1500 
 
 300 
 
 300 
 .03375 
 
 300 
 
 3.375 
 
 .O3150P 
 
 411. Exercise. 
 
 
 
 Multiply: /. 
 
 .25 by 7. 
 
 //. 54 by .06. 
 
 2. 
 
 3.25 by 5. 
 
 12. 4.8 by 7.8. 
 
 3. 
 
 .035 by 9. 
 
 13. .66 by .06. 
 
 4. 
 
 2.45 by 12. 
 
 14. .32 by 20. 
 
 5. 
 
 .095 by 15. 
 
 15. 1.75 by 240. 
 
 6. 
 
 .075 by 14. 
 
 16. .654 by 2500. 
 
 7. 
 
 8.36 by 40. 
 
 17. .375 by .0004. 
 
 8. 
 
 .375 by 30. 
 
 18. 100.5 by .25. 
 
 9. 
 
 .508 by 25. 
 
 19. 3.96 by .00256. 
 
 10. 
 
 .0086 by 54. 
 
 20. .879 by 7.56. 
 
 412. Show that : 10 x .0025 = .025. 
 
 SuG. 10 X .0035 = 10 X Tiftftfff 
 
 100 X .0025 = .25. 
 
 1000 X .0025 = 2.5. 
 
 From these illustrations we see that 
 
 Momng the decimal 'point one place rightward 
 multiplies hy 10, moving it two places rightward 
 multiplies hy 100, momng it three places rightward 
 multiplies hy 1000, etc. 
 
MULTIPLICATION, DIVISION, MENSURATION. 189 
 
 413. Oral Exercise. 
 
 
 
 
 
 Read, supplying the missing numbers : 
 
 
 /. 10 X .05 = 
 
 
 10. 
 
 1000 X 
 
 .075 = 
 
 
 2. 10 X .025 = 
 
 
 11. 
 
 1000 X 
 
 .758 = 
 
 
 3. 10 X .0075 = 
 
 
 12. 
 
 1000 X 
 
 .001 = 
 
 
 4. 100 X .0025 = * 
 
 
 13. 
 
 100 X 
 
 7.5 = 
 
 
 5. 100 X 2.85 = . 
 
 
 14. 
 
 100 X 
 
 .0075 = 
 
 
 6. 100 X .0001 = . 
 
 
 15. 
 
 1000 X 
 
 .07 = 
 
 
 7. 10 X 2.5 = . 
 
 
 16. 
 
 100 X 
 
 .5 = . 
 
 
 8. 10 X 2.56 = . 
 
 
 17. 
 
 1000 X 
 
 .7 = 
 
 
 9. 100 X .0075 = . 
 
 
 18. 
 
 10000 X 
 
 .00002 = . 
 
 
 414. Show that : 
 
 2.5 -f 
 
 10 = 
 
 .25. 
 
 
 
 Sdg. 2.5 ^ 10 = H -T- 10. 
 2.5 -^ 100 = .025. 
 2.5 ^ 1000 = .0025. 
 From these illustrations we see that 
 Moving the decimal point one place leftward 
 divides by 10^ moving it two places leftward divides 
 by 100, moving it three places leftward divides by 
 1000, etc. 
 
 415. Oral Exercise. 
 
 Read, supplying the missing numbers : 
 
 /. 
 
 .5- 
 
 -10 = . 
 
 8. 
 
 .9-^100 = . 
 
 15. 
 
 7 -^ 1000 = . 
 
 2. 
 
 .05- 
 
 -10 = . 
 
 9. 
 
 .27-^100 = . 
 
 16. 
 
 8.4 -^ 1000 = . 
 
 3. 
 
 2.5- 
 
 -10 = . 
 
 10. 
 
 .08 -^ 100=. 
 
 17. 
 
 75.6-^1000 =. 
 
 4. 
 
 .027- 
 
 -10 = . 
 
 11. 
 
 9.7 -i- 100=-. 
 
 18. 
 
 .01 -7- 1000=. 
 
 5. 
 
 8.5- 
 
 -10 = . 
 
 12. 
 
 68-^-100 = . 
 
 19. 
 
 25-^ 1000 = . 
 
 6. 
 
 .001 - 
 
 -10 = . 
 
 13. 
 
 37 -- 100 = . 
 
 20. 
 
 .7-^1000 = . 
 
 7. 
 
 5- 
 
 - 10 = . 
 
 14. 
 
 4 -J- 100 = . 
 
 21. 
 
 127.5^1000 = . 
 
190 DECIMALS. 
 
 416. Find the cost of 375 rails at $6.25 per hundred (C). 
 
 275 = 2.75 C 
 $6.25 = the cost per C 
 2.75 
 
 3125 
 4375 
 1250 
 
 117.1875, or $17.19 = the cost of 275. 
 Find the cost of 2400 shingles at $8.25 per thousand (M). 
 
 2400 = 
 
 = 2.m M 
 
 $8.25 = 
 
 = the cost per M 
 
 2.4 
 
 
 3300 
 
 
 1650 
 
 
 $19,800 = the cost of 2400. 
 
 417. Exercise. 
 
 Find the cost of; 
 
 /. 600 Havana cigars at $25 per M. 
 
 2. 275 chestnut posts at $6.50 per 0. 
 
 3. 385 shad at $22.50 per C. 
 
 4. 2500 cartridges at $6.50 per M. 
 
 5. 3250 gun wads at $0.45 per M. 
 
 6. 225 brass-head nails at $0.52 per M. 
 
 7. 2250 brass paper fasteners at $0.35 per C. 
 
 8. 375 paper bags at $1 .25 per M. 
 
 9. 250 envelopes at $2.25 per M. 
 
MULTIPLICATION, DIVISION, MENSURATION. 191 
 
 10. 1250 tags at $0.95 per M. 
 
 //. 3400 sheets of writing paper at $3.75 per M. 
 
 12. 10 boxes of loaded shells, each containing 25, at 
 $1.25 per C. 
 
 13. 40 packages of letter-heads, each containing 500, at 
 $1.36 per M. 
 
 14. 2275 plastering laths at $5.50 per M. 
 
 418. .04 - 2 = rfo - ^ = ifo = -03. 
 
 419. Exercise. 
 
 /. Show that .9-^3 = .3. 
 2. Show that .06 -^ 3 = .02. 
 5. Show that .12^4 = .03. 
 
 4. Show that .006 -^ 2 = .003. 
 
 5. Show that .015 -^ 3 = .005. 
 
 6. Show that .112 -f- 2 = .056. 
 
 7. In problem 1, how many decimal places are there in 
 the dividend ? How many in the quotient ? 
 
 8. In problems 2 and 3, how many decimal places are 
 there in the dividend ? How many in the quotient ? 
 
 9. In problems 4, 5, and 6, how many decimal places are 
 there in the dividend ? How many in the quotient ? 
 
 Notice that in each of the first 6 problems the divisor 
 is a whole number, 
 
 10. In the first 6 problems, how do the number of deci- 
 mal places in the dividend and in the quotient compare? 
 
192 
 
 DECIMALS. 
 
 420. From the illustration in Art. 419 we see that 
 ^Yhen the dlDtsor is a whole number, the number 
 of decimal places in the quotient equals the number 
 in the dividend. 
 
 421. Divide 7.75 by 25. 
 
 Divide .004 by 25. 
 
 35) 7.75 (.31 
 
 35). 00400 (.00016 
 
 75 
 25 
 25 
 
 35 
 
 150 
 
 150 
 
 422. Exercise. 
 
 
 Divide: /- .005 by 5. 
 
 //. .03 by 6. 
 
 2. .027 by 9. 
 
 12. .012 by 8. 
 
 3. .0425 by 5. 
 
 13. .015 by 25. 
 
 4. .375 by 15. 
 
 14. .004 by 8. 
 
 5. 8.75 by 25. 
 
 15. .006 by 8. 
 
 6. 4.00 by 25. 
 
 16. .00252 by 42. 
 
 7. 25.5 by 15. 
 
 17. .0125 by 25. 
 
 8. 6.4 by 16. 
 
 18. 191.52 by 42. 
 
 9. .0144 by 12. 
 
 19. .0375 by 625. 
 
 10. .039 by 13. 
 
 20. .025 by 16. 
 
 423. Divide .008 by .04. 
 
 
 •««^^-«^- 1000 -^100= 4 
 
 ^;w^-4^io--«-^- 
 
 lU 
 
 That is, .008 -*- .04 = .8 + 4. 
 
 From this illustration we see that 
 
 Moving the decimal point rightward or leftward 
 
MULTIPLICATION, DIVISION, MENSURATIjN. 193 
 
 the same number of places in hotli dividend and 
 divisor does not change the quotient. 
 
 424. Divide: 
 (1) .0625 by .25 ; (2) 6.25 by .0025 ; (3) 6.25 by 2500. 
 
 (1) .35). 0625 ( = 25)6.25 (25 
 
 50 
 
 125 
 
 125 
 
 (2) .0025 ) 6.25 ( = 25 ) 62500 ( 2500 
 
 50 
 125 
 125 
 00 
 
 (3) 2500 ) 6.25 ( = 25 ) .0625 ( .0025 
 50 
 125 
 125 
 
 From these illustrations we see that, in division 
 of decimals, we 
 
 Move the decimal point rightward or leftward in 
 both dividend and divisor such a number of places 
 as will make the divisor a whole number not ending 
 in ciphers ; then divide and point off in the quo- 
 tient as many decimal places as there are in the 
 dividend. 
 
 13 
 
1 94 DECIMALS. 
 
 425. Exercise. 
 
 Divide: /. .025 by .5. //. .02 by .002. 
 
 2. .075 by .15. 12. .5 by .0005. 
 
 3. .16 by .04. 13. .125 by .025. 
 
 4. .036 by .06. 14. 1 by .08. 
 
 5. 1.44 by .02. 15. 1.44 by .036. 
 ff. .048 by .12. 16. 86.4 by .24. 
 7. .144 by .012. 17. 256 by 200. 
 5. .0375 by .15. 18. 2.25 by 150. 
 9. .1728 by .036. 19. .9 by 360. 
 
 /O. 30.75 by .075. 20. 4840 by 16. 
 
 426. In practice tlie division is seldom carried be- 
 yond the fifth decimal place in the quotient, which 
 is usually expressed to the nearest ten-thousandth. 
 
 Thus, if the quotient is .76452 + , expressed to tlie nearest ten- 
 thousandth it is .7645. If the quotient is .76456 + , expressed to 
 tlie nearest ten-thousandth it is .7646. 
 
 Note. The sign + in the above illustration indicates that the 
 quotient expressed is not complete. 
 
 427. Exercise. 
 
 Express to the nearest ten-thousandth the value of : 
 /. 2.573 -^6. ff. 1 -^15. 
 
 2. 25.37 -T- 8. 7. .8-^ 11. 
 
 3. .075 -^6. 8. 325.5 -^ 16.5. 
 
 4. 37.52 -J- 9. 9. $375,875 -r 15. 
 
 5. .046 -J- .06. 10. $1000 ^ 12. 
 
MISCELLANEOUS PROBLEMS. 195 
 
 428. .25:5 = ^:^ = j% : M^ = 25 - 50 [§334] = 
 .25 -- 5. That is, .25 : .5 = .25 -- .5. Hence, 
 
 To measure one decimal hy another divide the 
 first hy the second. 
 
 429. Find the value of .455 : .35. 
 
 .455 :. 35 = .35). 455 ( = 35)45.5.(1.3 
 
 35 
 105 
 105 
 
 430. Exercise. 
 
 Find the value of : 
 
 /. .025 :5. 6. .0036 : 80. 
 
 2. .049 :.07. 7. .096 : 480. 
 
 3. 7.5 :.15. 8. 4.75 :2.5. 
 
 4. .27 :1.8. 9. 1 :.125. 
 
 5. 150 :.015. 10. 660 : 16.5. 
 
 431. Oral Exercise. — Miscellaneous Problems. 
 
 /. What is .01 of 15 ? 
 
 2. Read, supplying the missing numbers: 
 
 (a) 1 -T- .1 = . (c) 100 X .1 = o 
 
 (b) 1 -^ 100 = . (d) .1 X .1 = . 
 
 3. When $5 is gained on $100, what is gained on $1 ? 
 
 4. $12 is .01 ©f what sum ? 
 
 5. How long will it take a man to earn $12.50 at $1.25 
 a day? 
 
196 DECIMALS. 
 
 6. Read, supplying the missing numbers: 
 
 (a) 1 - .2 = . (c) .5 -^ 5 3= . 
 
 (b) 2 4- .08 = . (d) 10 X .5 = . 
 
 7. I bought 4 pounds of coffee at 35 ct. a pound ; how 
 much change should I receive from a $2- bill ? 
 
 8. If .1 inch in a drawing represents a yard, how many 
 inches will represent 10 yd.? 
 
 9. At 1.5 ct. per pound, how many pounds of old iron 
 did a boy sell, if he received 30 ct. for it ? 
 
 10. Read, supplying the missing numbers: 
 
 (a) 2.5 + .05 = . (c) 1 - .01 = . 
 
 (b) 50 ^ 100 = . (d) 5 4- .5 = . 
 
 11. K dealer paid $25.50 for 5 lambs; how much was 
 that apiece ? 
 
 12. Does.l = .10? Why? 
 
 13. Find the cost of a sheet of 200 two-cent stamps. 
 
 14. Does 10 X .1 = 1? Why? 
 
 15. A man who earns $2.25 a day and spends II a day 
 saves how much in a week (G da.) ? 
 
 16. Doesl -^ 10 =: .01? Why? 
 
 432. Exercise — Miscellaneous Problems. 
 
 /. A man's store bill for June was $28.75, for July 
 $30.68, and for August $28.75; what was his store bill for 
 the three months ? 
 
 2. The value of the English pound sterling in U. S. 
 money is $4.8GG5; how much less than $5 is this? 
 
 3. The German mark is worth $0.2385 in U. S. money; 
 how much less than a quarter-dollar is this ? 
 
( 
 
 MISCELLANEOUS PROBLEMS. 197 
 
 4. Find the amount of the following: 
 
 18 lb. Sugar @ 6 ct." per lb I 
 
 16 lb. Ham @ 18 ct. per lb 
 
 6 lb. Cheese @ 16 ct. per lb 
 
 18 yd. Muslin @ 12 ct. per yd 
 
 % 
 
 5. There are 5.5 yd. in a rod; how many yards are there 
 in a line 28 rods long ? 
 
 6. A cubic foot of water weighs 62.5 lb., and cork is .24 
 times as heavy as water; what is the weight of a cubic foot 
 of cork ? 
 
 7. A farmer sold 128 bu. of oats, which weighed 3904 
 lb. ; how much did these oats weigh to the bushel ? 
 
 8. What price per hundredweight did a farmer receive 
 for a dressed porker that weighed 3.75 hundredweight and 
 sold for $24.31 ? 
 
 9. When sugar is selling for $0.05375 per pound, how 
 many pounds can be bought for $32.25 ? 
 
 10. A merchant had on hand at the beginning of a day's 
 sales $60.18. During the day he took in $79.76, and paid 
 out for produce $26.10; how much money had he on hand 
 at the close of the day ? 
 
 433. Exercise — Miscellaneous Problems. 
 /. Wliat should be charged for 2200 lb. of coal at 
 $0.32 per 100 1b.? 
 
 2. Potatoes are .162 starch; how many pounds of starch 
 are there in a bushel (60 lb.) of potatoes? 
 
 3. .3 + .075 - .0075 = ? 
 
198 DECIMALS. 
 
 4. A yard is 36 inches, and a meter is 3.37 inches longer 
 than a yard; how long is a meter ? 
 
 5. From a thousand take a thousandth. 
 
 6. When $0.00 is charged for the loan of %\ for 1 year, 
 what should be charged for the loan of $225 for \\ years ? 
 
 7. A cubic foot of water weighs G2.5 lb., and. zinc is 
 7.19 times as heavy as water; what is the weight of a cubic 
 foot of zinc ? 
 
 8. 7865 plastering laths cost $31.46; how much was 
 that per M ? 
 
 SuG. 7865 = 7.865 M. 
 
 9. A dealer bought 7000 cigars at $4.75 per C, and 
 retailed them at 4 for 25 ct. ; how much did he gain ? 
 
 10. Divide 2002 hundred-thousandths by 2 thousandths, 
 and write the result in words. 
 
 //. If it costs $0.08f to ship 100 lb. of wheat, what will 
 it cost to ship 1,250 bu. of wheat, each weighing 60 lb.? 
 
 434. Exercise — Miscellaneous Problems. 
 
 /. If a laborer's wages are 20 cents an hour, and he 
 works 9 hours on Monday, 10 hours on Tuesday, 12 hours 
 on Wednesday, 11 hours on Thursday, 11 hours on Friday, 
 and 6 hours on Saturday, how much does he earn that 
 week ? 
 
 2. A man was employed as carrier in the rural free de- 
 livery service for a year, for which he was paid $600. Tie 
 bought two horses, one for $125 and the other for $110» 
 and paid $15 a month for their feed and other expenses; 
 he also bought a wagon for $75. Ilis board cost him $3.50 
 
MISCELLANEOUS PROBLEMS. 
 
 199 
 
 a week (52 weeks). How much had he clear at the end of 
 the year, if he sold the horses for $100 each and the wagon 
 for 125 ? 
 
 3. A father willed $1250 to each of his two daughters, 
 and twice as much to each of his three sons; to his wife he 
 willed as much as to a son and a daughter; how much did 
 he will to all ? 
 
 4. Fill in the totals in the following: 
 
 
 Christians. 
 
 Non-Christians. 
 
 Total. 
 
 Europe 
 
 340,320,000 
 
 124,740,000 
 
 3,800,000 
 
 7,240,000 
 
 12,480,000 
 170,000 
 
 
 America 
 
 Australia 
 
 Asia and Africa. . 
 Total 
 
 641,550,000 
 
 
 
 5. Which is nearer to a million dollars, and by how 
 much, $1,200,000, or $889,008 ? 
 
 6. I owed a man a debt of $220 and gave him 16 5-dollar 
 bills; how many 10-dollar bills must I give him to pay the 
 balance ? 
 
 7. A traveler has gone 1220 miles of a journey, which 
 is f of the distance he has yet to go; how long is his 
 journey ? 
 
 435. Exercise — Miscellaneous Problems. 
 
 /. A miller bought 46520 lb. of wheat at $0.80 per 
 bushel (60 lb.); find the cost. 
 
 2. A laborer worked for a merchant at $1.25 a day for 
 205 days. He bought from the merchant a suit of clothes 
 for $14.75, a pair of shoes for $2.75, and groceries to the 
 
BOO 
 
 DECIMALS. 
 
 amount of $38.05. The balance was paid in cash; how 
 much cash was paid ? 
 
 3. How many bushels of clover seed at $6.75 per bushel 
 can be bought for $1000? 
 
 4. A farmer bought 6 steers at $30 a head, and after 
 feeding them 4 months at a cost of $35 a month, sold them 
 for $410; find the average gain per head. 
 
 5. The sum of two numbers is 27000; if the larger of 
 the two numbers is 17538, what is their difference? 
 
 6. 324 + 4679 + ? + 389 4- 64 + 4642 = 16555. 
 
 7. Find the decrease in 20 years in each of the following 
 prices of farm implements : 
 
 Implements. 
 
 Mowers 
 
 Corn planters, hand 
 
 Plows, walking, steel 
 
 Plows, shovel 
 
 Pumps, wooden 
 
 Rakes, sulky 
 
 Seeders, 2-horse 
 
 Scythes 
 
 Shellers, corn 
 
 Sleighs 
 
 Stackers, hay 
 
 Wagons, farm 
 
 Hay carriers 
 
 Churns 
 
 Cultivators, walking, 2-horse. . 
 
 Potato diggers 
 
 Corn drills 
 
 Grain drills 
 
 Horse hay forks 
 
 Harrows 
 
 Potato hillers 
 
 Fanning mills 
 
 Harvesters, twine binders 
 
 Harvesters, combined 
 
 1900. 
 
 $65.00 
 
 $40.00 
 
 1.25 
 
 1.00 
 
 15.00 
 
 10.67 
 
 4.00 
 
 2.50 
 
 8.00 
 
 4.00 
 
 25.00 
 
 14.00 
 
 35.00 
 
 25.00 
 
 .80 
 
 .60 
 
 6.00 
 
 2.40 
 
 25.00 
 
 18.00 
 
 55. GO 
 
 40.00 
 
 90.00 
 
 57.00 
 
 10.00 
 
 3.50 
 
 7.30 
 
 5.33 
 
 20.00 
 
 13.00 
 
 20.00 
 
 10.00 
 
 12.00 
 
 8.00 
 
 50.00 
 
 30.00 
 
 :j.5o 
 
 1.00 
 
 15.00 
 
 10.00 
 
 12.00 
 
 8.00 
 
 35.00 
 
 20.00 
 
 325.00 
 
 120.00 
 
 110.00 
 
 65.00 
 
 Decrease. 
 
MISCELLANEOUS PROBLEMS. SOI 
 
 436. Exercise — Miscellaneous Problems. 
 
 /. A society rented a hall for $25 and paid $17.50 to 
 advertise a lecture. They sold 128 tickets at $1 each, 326 
 at 75 cents each, and 122 at 50 cents each. How much 
 did they clear, if they paid the lecturer $150 ? 
 
 2. From f of the sum of 1905 and 995 subtract twice 
 the difference between 701 and 599. 
 
 5. A congregation wishes to raise a fund of $10000. 4 
 men gave $1250 each, 2 men $250 each, and two collec- 
 tions amounted to $795 and $356 respectively; how much 
 must yet be raised ? 
 
 4. If a man pays 5 cents for the use of $1 for 1 year, 
 how much must he pay for the use of $500 for 3 years ? 
 
 5. If 5 cents is paid for the use of $1, how many dollars 
 should a man have the use of if he pays $20 ? 
 
 6. A dealer bought 6 cans of lard which weighed 261 
 pounds; the empty cans weighed 9 pounds. How many 
 pounds of lard were there in each can, if the cans were of 
 equal size ? 
 
CHAPTER IV. 
 DENOMINATE AMOUNTS. 
 
 437. Denominate Units are units established by cus- 
 tom or law to measure value, weight, time, length, 
 surface, solids, capacity, etc. 
 
 Thus, a dollar^ a pound, a day, a yard, etc., are denominate 
 units. 
 
 United States Money. 
 
 438. The standard unit of value in the United 
 States is the Dollar. 
 
 TABLE. 
 
 10 mills (m.) = 1 cent (ct.). 
 10 cents = 1 dime (d.). 
 
 10 dimes = 1 dollar ($). 
 
 10 dollars = 1 eagle (E.). 
 
 The coins of the United States, now authorized 
 by law, are : 
 
 Oold. Silver. Nickel. Bronze. 
 
 Double-Eagle, Dollar, Five Cents. One Cent. 
 
 Eagle, Half-Dollar, 
 
 Half-Eagle, Quarter-Dollar, 
 
 Quarter-Eagle. Dime. 
 Note 1. Any number of mills less than 10 may be expressed 
 
UNITED STATES MONEY. 203 
 
 by writing the figure iu the third place to the right of the decimal 
 point. 
 
 Thus, 5 mills may be expressed $0,005. 
 
 Note 2. In the settlement of business transactions, it is cus- 
 tomary to omit any number of mills less than 5, and to regard 5 
 mills or more as 1 cent. 
 
 Note 3. $4.8665 = 1 pound (£), the unit of value in English 
 money. 
 $0,193 = 1 franc, the unit of value in French money. 
 $0.2385 = 1 mark, the unit of value in German 
 money. 
 
 439. Oral Exercise. 
 
 /. How many mills are there in 3 ct.? 5ct.? Id.? $1 ? 
 
 2. How many mills are there in | ct? Jet.? Jet.? 
 li ct.? 
 
 3. How many cents are there in 3d.? 6d.? 8d.? 
 
 lOd.? 
 
 4. How many cents are there in $^ ? %\ ? IJ ? $| ? 
 
 5. How many cents are there in $^ ? $f? If? $|-? 
 
 6. How many dollars are there in 200 ct.? 500 ct.? 
 100 ct.? 300 ct.? 
 
 7. How many dimes should be given in exchange for a 
 half-dollar? 
 
 8. How many 5-cent pieces must be given for a quarter- 
 dollar ? 
 
 9. What decimal part of a dollar is 2d.? 7d.? 3ct.? 
 5d.? 
 
 10. K boy has a dollar in 5-cent pieces; how many coins 
 has he ? 
 
204 DENOMINATE AMOUNTS. 
 
 11. K mill is what part of a cent? 
 
 12. A cent is what part of a dollar ? 
 
 13. A mill is what part of a dollar? 
 
 14. How many $2^ gold pieces must be given in ex- 
 change for an eagle ? 
 
 15. The gold coins mentioned in § 438 have together 
 what value ? 
 
 16. The silver coins mentioned in § 438 have together 
 what value ? 
 
 17. IIow many pieces of money has a boy who has |3i in 
 quarter-dollars and 50 ct. in dimes ? 
 
 440. PAPER. 
 
 24 sheets = 1 quire. 
 20 quires = 1 ream. 
 
 2 reams = 1 bundle. 
 
 5 bundles = 1 bale. 
 
 441. COUNTING. 
 
 12 units = 1 dozen (doz.). 
 
 12 dozen = 1 gross (gro.). 
 
 12 gross = 1 great gross (G. gro.). 
 
 20 units — 1 score. 
 
 442. Oral Exercise. 
 
 /. How many units are there iu 6 doz.? J doz.? \^ 
 doz.? 2J doz.? 
 
 2. How many units are there in 3 score? 2 gro.? 
 
 3. How many sheets of paper are there in 2 quires? 
 J quire ? 
 
PAPER AND COUNTING. 205 
 
 4. A boy bought a gross of matches for 60 ct., and sold 
 them at 1 ct. a box; find his gain. 
 
 5. What should be paid for 8 eggs at 24 ct. per dozen ? 
 
 6. 6 eggs out of 4 dozen were broken; how many re- 
 mained ? 
 
 7. When lemons are selling at the rate of 3 for 10 ct., 
 how much is that a dozen ? 
 
 8. When eggs are selling at 24 ct. per dozen, how much 
 should be charged for a score ? 
 
 9. When matches are selling at 3 boxes for 5 ct., how 
 much should be paid for 1 dozen boxes ? 
 
 443. Exercise. 
 
 /. When matches are selling at 6 boxes for 25 ct., how 
 much are they per gross ? 
 
 SuG. A gross is how many times 6 ? 
 
 2. How many dozen crayons are there in 5 boxes, each 
 containing a gross? 
 
 3. 10 eggs weigh about 1 pound; find the weight of 20 
 doz. eggs. 
 
 Find the gain on : 
 
 4. 8 doz. note-books, bought at $1.60 per doz. and sold 
 at 15 ct. each. 
 
 5. 3 doz. rulers, bought at 50 ct. per doz. and sold at 
 5 ct. each. 
 
 6. 4 gro. erasers, bought at 13.20 per gro. and sold at 
 5 ct. each. 
 
 7. 2 gro. pencils, bought at $3.00 per gro. and sold at 
 2 for 5 ct. 
 
206 DENOMINATE AMOUNTS. 
 
 8. 2 reams water-color paper, bought at $20 per ream, 
 and sold at 5 ct. per sheet. 
 
 9. 5 reams drawing paper, bought at 35 ct. per ream 
 and sold at 3 sheets for 1 ct. 
 
 10. 1 quire blotters, bought at 60 ct. and sold at 3 ct. 
 each. 
 
 //. 2 M envelopes, bought at $1.30 per M and sold at 
 25 for 5 ct. 
 
 Bills and Accounts. 
 
 444. A Bill is a written statement of the names, 
 quantities, and prices of goods sold or services ren- 
 dered, together with the names of the parties and 
 the date of the transaction. 
 
 445. An Account is a record of business transac- 
 tions between two parties at a given date. 
 
 446. The Debtor (Dr.) is the party who buys the 
 goods or receives the service. 
 
 447. The Creditor (Cr.) is the party who sells the 
 goods or renders the service. 
 
 448. A Debit (Dr.) is an entry in a bill or an ac- 
 count against the debtor. 
 
 449. A Credit (Cr.) is an entry in a bill or an 
 account in favor of the debtor. 
 
 450. An Item is any separate debit or credit made 
 in a bill or an account. 
 
BILLS AND ACCOUNTS. 
 
 207 
 
 451. 
 
 jyruUb^ diAArnX±h/, 
 
 A EECEIPTED BILL. 
 
 West Chester, Pa., |xxm.. 20, 1903. 
 
 Bought of THOMAS HO AG. 
 
 ttv. Ocvffex 
 12 W-. sh\AXvaA/ 
 
 S5(^ 
 
 70(Ji 
 
 5(P 
 
 
 2 
 
 10 
 
 
 1 
 
 JfO 
 
 
 
 60 
 
 Jf 
 
 
 
 10 
 
 452. 
 
 AN ACCOUNT. 
 
 Falsington, Pa., iuyru/ l^y 1903. 
 In account loith C. D. BEANS «fe CO. 
 
 Dr. 
 
 10 'uxi. 11UA>^i/yv 
 
 15 U>, J^XAXUXh/   
 
 20 ^. CoA^la^ 
 
 Cr. 
 
 15 doa^. G<ixi/fi.' 
 IS Uv. Bu/tttA/ 
 
 ,80 
 
 $0.24 
 
 12 
 
 16 
 
 92 
 
 75 
 00 
 
 60 
 50 
 40 
 
 18 
 
 67 
 
 10 50 
 
 8 17 
 
208 
 
 DENOMINATE AMOUNTS. 
 
 463. Exercise. 
 
 /. Extend the items in the following bill and find the 
 total : 
 
 Cleveland, Ohio, A/ja>tt/vwU/V 15, 1903, 
 m/v. j3>a/vwtuX TlLaAyti/n/, 
 
 Bought of ROSS MILLER. 
 
 4 t-OcX^/ix \Zoii'bAyrUx^ $3.20 
 1 dxvo/. ca/rUi^ QxxVdo\raAXv QjciAA<iyoX^ 5.50 
 G 25-lL. lozou^ 'P\AA/nAJ^ .06^ 
 
 5 cAxi/tt/^ I^A^H^Y GAx:i/ni>-«AW/^ ^'50 
 
 2. Extend the items in the following account and find 
 the balance: 
 
 Baltimore, Md., OyjaA^t 1, 1904. 
 
 In account with STEINMAN & CO. 
 
 Dr. 
 
 1 (XcUi^oXt/TU/ J^tcVU^ 
 
 1 otoJiViMX/u a/Kbd j^tta/vn>Lv 
 
 2 PUyfHAAM/rui/ <!yUMAJ^ 
 
 Cr. 
 
 ^ (ma/. jhuL<L PcvtcUx>-tXix 
 
 .80 
 .75 
 
 00 
 
MEASURES OF TIME. 209 
 
 3. Sept. 1, 1903, Harry Watsoa presents to you the fol- 
 lowing bill for labor: 10 days carpentering, ^2.50 per day; 
 8 days painting, $3 per day; 4 days roofing, $2.75 per day; 
 3 days common labor, $1.25 per day. AVrite the bill and 
 find the amount due. 
 
 4. Oct. 1, 1903, James Wilson bought of Hiram Leonard, 
 Pittsburg, Pa., 40 bbl. AVinter Superfine Flour @ $2.80 
 per bbl.; 12 bbl. Winter Extra Flour @ $3 per bbl.; 14 
 bbl. Penna. Roller Flour @ $3.25 per bbl. At the same 
 time Mr. Leonard bought from James Wilson 80 bu. No. 2 
 Red Wheat @ 80 ct. per bu. ; GO bu. Corn @ 55 ct. per bn. ; 
 50 bu. Oats @ 43 ct. per bu. Make out the account and 
 find the balance due. 
 
 Measures of Time. 
 454. There are two principal units of time, the 
 Day and the Year. 
 
 TABLE. 
 
 60 seconds (sec.) = 1 minute (min.). 
 
 60 minutes — 1 hour (hr.). 
 
 24 hours = 1 day (da.). 
 
 7 days = 1 week (wk.). 
 
 52 weeks = 1 year (yr.), nearly. 
 
 365 days = 1 common year. 
 
 366 days = 1 leap year. 
 100 years = 1 century. 
 
 The week consists of 7 days of which the names 
 are as follows : Sunday^ Monday, Tuesday, Wednes- 
 day, TJiuTsday^ Friday , Saturday, 
 
910 
 
 DENOMINATE AMOUNTS. 
 
 The year is divided into 12 calendar months, as 
 follows : 
 
 Names. 
 
 Nam her 
 of Days. 
 
 Naniee. 
 
 Nambcr 
 of Days. 
 
 January 
 
 February 
 
 March 
 
 April 
 
 May 
 
 June 
 
 31 
 
 28 or 29 
 31 
 30 
 31 
 30 1 
 
 July 
 
 August 
 
 September 
 
 October 
 
 November 
 
 December 
 
 31 
 31 
 30 
 31 
 30 
 31 
 
 Note 1. A Centennial Year is one whose number is divisible hj 
 100. 
 
 Thus, 400, 1800, and 1900 were centennial years. 
 
 Note 2. Centennial years whose number is divisible by 400, and 
 other years whose number is divisible by 4, are Leap Years. 
 
 Thus, 1600, 1896, and 1904 were leap years. 
 
 Note 3. a.m. stands for forenoon; p.m. stands for afternoon; 
 7.45 P.M. means 45 minutes past 7 p.m. 
 
 465. Oral Exercise. 
 
 /. The winter months are December, January, and Feb- 
 ruary; how many days are there in the winter months? 
 
 2. A family that uses 2 qt. of milk a day spends how 
 much for milk during March, the cost of the milk being 
 5 ct. a quart ? 
 
 3. Name the 7th day of the week; the 5th; the 2d; the 
 1st; the 4th; the 3d; the Cth. 
 
 4. Name the months that have 30 days. 
 
 5. AVhen a pulse beats 18 times in 15 seconds, how many 
 times does it beat in a minute ? 
 
 6. A building was erected in MDCCCXC; how many 
 years ago was that ? 
 
MEASURES OF CAPACITY. 2 1 1 
 
 7. Name the months that have 31 days. 
 
 8. One coin is dated 1880, another 1903; how many 
 years are there between their dates ? 
 
 9. Name the 11th month; the 4th; the 7th; the 12th; 
 the 8th; the 3d; the 6th; the 1st; the 9th; the 2d; the 
 5th; the 10th. 
 
 10. Name the Roman letters that are used to write the 
 numbers of the present year. 
 
 11. At 20 ct. an hour, how much will a motorman earn 
 from 6 A.M. to 2 p.m.? 
 
 12. How much rent was paid in 1 yr. 6 mo. for a house 
 that rented for $20 a month ? 
 
 13. When a hotel is charging 50 ct. a meal and $1 for 
 lodging, how much is it charging per week at the same 
 rate? 
 
 Measures of Capacity. 
 
 DRY MEASURE. 
 
 466. The standard unit of dry measure is the 
 Bushel. 
 
 TABLE. 
 
 2 pints (pt.) = 1 quart (qt.). 
 
 2 quarts = 1 small measure. 
 
 8 quarts = 1 peck (pk.). 
 
 4 pecks = 1 bushel (bu.) stricken measure. 
 
 5 pecks = 1 heaped bushel, nearly. 
 
 LIQUID MEASURE. 
 
 467. The standard unit of liquid measure is the 
 Gallon. 
 
212 DENOMINATE AMOUNTS. 
 
 TABLE. 
 
 4 gills (gl)=^ 1 pint(pt.). 
 2 pints — 1 quart (qt.). 
 
 4 quarts = 1 gallon (gal.). 
 31 J gallons = 1 barrel (bbl.). 
 2 barrels = 1 hogshead (hhd.) = 03 gal. 
 
 458. Oral Exercise. 
 
 /. How many pints are there in 3 qt.? 
 
 2. How many pints are there in a gallon? 
 
 3. How many quarts are there in J gal.? 
 
 4. How many quarts are there in 3 pk.? 
 
 5. How many quarts are there in a bushel ? 
 
 6. How many quarts are there in J pk.? 
 
 7. When apples are selling at 10 ct. a half peck, how 
 much are they a bushel ? 
 
 8. A farmer bought a peck of grass seed for $0.60; how 
 much was it a bushel ? 
 
 9. What should be paid for 3 qt. of vinegar at IG ct. a 
 gallon ? 
 
 10. How many half -pint blocks can be made from a 
 gallon of ice cream ? 
 
 //. A family that uses 1 qt. of milk each week day and 
 2 qt. on Sunday, uses how many gallons a week ? 
 
 12. A trucker put 1 bu. of berries into 2-qt. boxes; how 
 many boxes were required ? 
 
 13. How many gill bottles are required to hold a quart 
 of alcohol ? 
 
 14. When potatoes are selling at 80 ct. per bushel, what 
 should be charged for J pk.? 
 
MEASURES OF WEIGHT. 
 
 213 
 
 Measures of Weight. 
 
 AVOIRDUPOIS WEIGHT. 
 
 459. Avoirdupois weight is used for weighing all 
 substances except those weighed by Troy weight, 
 medicines in prescription, diamonds, and pearls. 
 The standard unit is the Avoirdupois Pound. 
 
 TABLE. 
 
 16 ounces (oz.) = 1 pound (lb.). 
 25 pounds = 1 quarter (qr.). 
 
 4 quarters = 1 hundredweight (cwt.). 
 
 20 hundredweight = 1 Ton (T.). 
 Note 1. 1 lb. avoir. = 7000 Troy grains. 
 
 Note 2. The long hundredweight, 112 pounds, and the long 
 ton, 2240 pounds, are used in custom houses and in some wholesale 
 and retail transactions. 
 
 Thus, coal in Pennsylvania is bought and sold by the long ton. 
 
 460. The following table gives the weight of a bushel 
 of various grains, seeds and other produce : 
 
 TABLE. 
 
 
 Lb. 
 
 
 Lh. 
 
 
 LI. 
 
 Barley 
 
 48 
 
 Corn (shelled) 
 
 56 
 
 Potatoes 
 
 60 
 
 Beans 
 
 00 
 
 Corn (on cob) 
 
 70 
 
 Rye 
 
 56 
 
 Buckwheat 
 
 48 
 
 Clover seed 
 
 60 
 
 Timothy seed 
 
 45 
 
 Bran 
 
 20 
 
 Oats 
 
 32 
 
 Wheat 
 
 60 
 
 Note. 196 lb. is the weight of 1 barrel of flour. 
 
 200 lb. is the weiglit of 1 barrel of beef or pork. 
 100 lb. is the weight of 1 kec: of nails. 
 
214 DENOMINATE AMOUNTS. 
 
 TROY WEIGHT. 
 
 461. Troy weight is used in weighing gold, silver, 
 platinum, and jewels, except precious stones. The 
 standard unit is the Troy Pound. 
 
 TABLE. 
 
 24 grains (gr.) = 1 pennyweight (pwt.). 
 20 pennyweights = 1 ounce (oz.). 
 12 ounces = 1 pound (lb.). 
 
 Note 1. The unit of weight for precious stones is the Carat, 
 which equals 4 diamond grains, or about 3^ Troy grains. Pearls 
 are sold by the diamond grain. 
 
 Note 2. 412.5 gr. is the weight of a silver dollar. 
 
 462. Oral Exercise. 
 
 /. What should 4 oz. of cheese cost at IG ct. per pound ? 
 
 2. How many more pounds are there in a long ton than 
 in a short ton ? 
 
 3. What should 1000 lb. of hay cost at 118 per ton ? 
 
 4. How many 200-lb. sacks of fertilizer will make a ton ? 
 
 5. What part of a pennyweight is 8 gr.? 
 
 6. IIow much should \ bu. of wheat weigh ? 
 
 7. How much should a peck of potatoes weigh? 
 
 8. How many bales of hay, each weighing 4 hundred- 
 weight, will weigh a ton ? 
 
 9. What will J lb. of spices cost at 2 ct. an ounce ? 
 
MEASURES OF WEIGHT. 215 
 
 10. What will 1 lb. 12 oz. of dried beef cost at 24 ct. per 
 pound ? 
 
 //. 6 pieces of silverware, each weighing 4 oz., weigh 
 how many pounds ? 
 
 12. How many grains of gold are there in a piece of 
 jewelry weighing 2 pwt., if it is f pure gold ? 
 
 13. Find the weight of 2 bu. of oats. 
 
 463. Find the cost of 4500 lb. of hay at $18.75 per ton. 
 
 4500 lb. 
 
 = 4.500 M lb. = 
 
 : 2.25 T. 
 
 $18.75 = 
 
 : the cost per T. 
 
 
 2.25 
 
 
 
 9375 
 
 
 3750 
 
 
 
 3750 
 
 
 
 $42.1875, or $42.19 = the entire cost. 
 
 464. Exercise. 
 
 Find the cost of: 
 /. 1875 lb. of bran at $18 per ton. 
 
 2. 3880 lb. of straw at $0.25 per ton. 
 
 3. 4665 lb. of fertilizer at $14 per ton. 
 
 4. 1840 lb. of hay at $18.25 per ton. 
 
 5. 3250 lb. of mixed feed at $20.25 per ton. 
 
 6. 8560 lb. of phosphate at $18 per ton. 
 
 7. 10756 lb. of iron ore at $5.78 per ton. 
 
 8. 278 lb. of bran at $18.50 per ton. 
 
 9. 3425 lb. of old iron at $20 per ton. 
 10. 4596 lb. of coal at $5.75 per ton. 
 
216 
 
 
 DENOMINATE AMOUNTS. 
 
 
 
 Measures of Length. 
 465. Exercise. 
 
 
 
 1 1 
 
 3 
 
 1 1 
 
 1 1 
 2 
 
 1 1 
 
 1 i 
 1 
 
 ' 1 ' 
 
 
 /. How many inches long is this rule? 
 
 2. How many half inches are there in each inch? 
 
 3. How many half inches are there in 2 inches? in 3 
 inches? 
 
 4. How many quarter inches are there in each inch? 
 
 5. How many quarter inches are there in 2 inches? in 3 
 inches? 
 
 6. How many eighth inches are there in each inch? 
 
 7. How many eighth inches are there in 2 inches? in 3 
 inches? 
 
 8. How many half inches are there in IJ inches? in 2 J 
 inches? 
 
 9. How many quarter inches are there in IJ inches? in 
 1| inches? 
 
 10. Measure these lines and state how many inches long 
 each is. 
 
 //. Draw a line IJ inches long. 
 12. Draw a line 12 inches long. 
 
 12 inches make a foot* 
 
MEASURES OF LENGTH. 217 
 
 13. Draw a line 1 foot 6 inches long. How many inches 
 long is it? 
 
 14. How many inches are there in a half foot? In IJ ft.? 
 
 15. What part of a foot is 6 inches? 
 
 16. What part of a foot is 4 inches? 
 
 17. What part of a foot is 3 inches? 
 
 18. Measure this line. 
 
 , 1 
 
 How long is it? How long is each part of it? 
 
 19. Let each part represent a foot ; how many feet does 
 the whole line represent? 
 
 3 feet make a yard. 
 
 20. What does the line above represent? 
 
 21. How many feet are there in half a yard? 
 
 22. How many inches are there in a yard? 
 
 23. How many inches are there in half a yard? 
 
 24. How many inches are there in J yard? in | yard? 
 
 25. How many inches are there in | yard? in f yard? 
 
 26. What part of a yard is a foot? 
 
 27. What part of a yard is 2 feet? 
 
 28. What part of a yard is 6 inches? 
 
 29. What part of a yard is 4 inches? 
 
 466. The standard unit of length is the Yaed. 
 
 TABLE. 
 
 12 inches (in.) = 1 foot (ft.). 
 3 feet = 1 yard (yd.). 
 5 J yards = 1 rod (rd.). 
 320 rods = 1 statute mile (mi.). 
 
218 DENOMINATE NUMBERS. 
 
 467. Other Measures of Length. 
 
 A Fathom = 6 feet, used to measure the depth of the 
 sea. 
 
 A Hand = 4 inches, used in measuring a horse's 
 height. 
 
 A Geographic Mile, or Knot = G08G ft. 
 
 A League (England and U. S.) = 3 geographic 
 miles, used to measure distances at sea. 
 
 A Chain = 4 rd., used by surveyors in measuring land. 
 
 468. Oral Exercise. 
 
 /. How many inches long is a 2-foot rule? 
 
 2. How many 18-in. ropes can be made from a rope 6 
 ft. long? 
 
 3. How many yards are there in 3 rd. ? 
 
 4. How many inches are there in a J-ft. rule? 
 
 5. The ocean at a certain point is 20 fathoms deep; how 
 many feet is that? 
 
 6. A horse that is 14J hands high is how many inches 
 high? 
 
 7. How many feet are there in 3G inches? 
 
 8. 4 inches is what part of a foot? 
 
 9. What is the distance around a room 24 ft. long and 
 18 ft. wide? 
 
 10. A rule 1 k ft. long was marked off in inches; how 
 many inches were marked off? 
 
 11. K boy's hoop in turning 3 times passes over 10 ft.: 
 what is the distance around it? 
 
MISCELLANEOUS PROBLEMS. 219 
 
 12. How many feet are there in a rod? 
 
 13. How many feet high is a horse that is 15 hands high? 
 
 469. Oral Exercise — Miscellaneous Problems. 
 
 Read, supplying the missing numbers : 
 /. .5 of 18=. 
 
 2. 2480 -f- 8 = . 
 
 3. f of 100 = . 
 
 4. 8 = 1 of. 
 
 5. ^ + ^=» 
 
 6. %l - 87 ct. = — ct. 
 
 7. 35 ct. + • = II. 
 
 8. 4000 lb. = — tons. 
 
 9. 28 da. = — weeks. 
 
 10. IJ yd. of cloth at 18 ct. per yard cost — ct. 
 
 //. .25 of 244 = . 
 
 12. 200 shad at $20 per C cost — . 
 
 13. 3000 cigars at $30 per M cost — . 
 
 14. 3000 lb. of hay at $18 per T. cost — . 
 
 15. 1.5 ft. = — of a yard. 
 
 16. 2 -^ 100=. 
 
 17. $20 — 25 ct. =. 
 
 470. Exercise — Miscellaneous Problems. 
 
 /. If chestnuts are bought at $2.40 a bushel and sold at 
 5 ct. a pint, find the gain on a bushel. 
 
 2. How many seconds are there in an hour ? 
 
 3. When vinegar is retailed at 3 ct. per quart, how 
 much is received for a barrel containing 36 gal. ? 
 
220 DENOMINATE NUMBERS. 
 
 4. A dealer wishes to sell apples that cost him $1.20 per 
 bushel so as to double his money ; how much must he 
 cliarge per peck ? 
 
 5. How many hours are there in October ? 
 
 6. What should be paid per bushel for oats that weigh 
 only 28 lb. to the bushel, when oats are quoted at 36 ct. 
 per bushel (32 lb.) ? 
 
 7. In $7.50, how many dimes are there ? How many 
 cents ? 
 
 8. At 15 ct. per cwt., find the cost of shipping a ma- 
 chine weighing 3250 lb. 
 
 9. How many minute spaces does the minute hand of a 
 clock pass over in a day ? 
 
 10. How many bottles, each holding a gill, can be filled 
 from a gallon of ink ? 
 
 11. K clock that strikes the hours, strikes how many 
 times a day ? 
 
 12. A dealer put 3 pk. of peanuts into pint packages; 
 how many packages had he? 
 
 13. If J bu. of oats weighs 14^ lb., how much too light 
 are these oats per bushel ? 
 
 14. A ship was sunk in 80 fathoms of water ; how many 
 feet was that ? 
 
 15. Show that a mile contains 1760 yd. 
 
 16. Find the cost of the fertilizer needed for 6 acres of 
 land, if 400 lb. are sowed to the acre, and it costs $14 per 
 ton. 
 
 17. K miller bought 9540 lb. of corn at 60 ct. a bushel ; 
 how much did he pay for it ? 
 
MEASURES OF SURFACE. 221 
 
 18. When bran is selling for %'Z4: per ton, how many 
 pounds should be given for $15 ? 
 
 19. 4J bu. of wheat make a barrel of flour ; how many- 
 pounds of flour does 1 bu. of wheat make ? 
 
 20. How many 2-grain quinine pills can be made from a 
 pound (avoir.) of quinine ? 
 
 21. A farmer's wheat crop weighs 16515 lb.; how much 
 is it worth at 80 ct. a bushel ? 
 
 22. What should be charged for a sack of flour weighing 
 24^ lb., when flour is selling at $4.80 a barrel ? 
 
 23. Siiow that a mile contains 5280 ft. 
 
 24. What years since 1890 have been leap years ? 
 
 25. A surveyor's chain contains 100 links, each 7.92 in. 
 long ; how many feet long is the chain ? 
 
 26. How many days are there from June 1 to Sept. 15 ? 
 SuG. Count Sept. 15 but not June 1. 
 
 27. How many days are there from June 15 to Dec. 31 ? 
 
 28. What date is 00 da. after Apr. 20 ? 
 
 Measures of Surface. 
 471. The opening between two lines that meet is 
 called an Angle. 
 
 Acute Angle Right Angle Obtuse Angle 
 
 472. Anything that has length and breadth with- 
 out thickness is called a Surface. 
 
228 
 
 DENOMINATE AMOUNTS. 
 
 473. A Square is a surface that 
 has four equal sides and four 
 right angles. 
 
 474. Exercise. 
 /. "Which is larger, an acute angle or 
 
 A Square. a right angle ? A right angle or an 
 
 obtuse angle ? An acute angle or an obtuse angle ? 
 
 2. Draw an acute angle ; an obtuse angle ; a right angle. 
 
 3. Draw a square 2 inches long. 
 
 4. Draw a square 3 inches long. 
 
 5. Draw a square ^ inch long. *^ 
 
 476. Exercise. 
 
 /. Measure the length and the width of the square above. 
 
 How long is it ? How wide ? 
 
 A square one inch long and one inch wide is a Square 
 Inch {sq. in.). 
 
 2. Draw a square 
 inch. 
 
 5. H o w 1 ng is 
 square ABCD ? How 
 wide ? 
 
 4. What is the dis- 
 tance around it ? 
 
 5. Howmany square 
 
 inches does it con- 
 tain ? 
 
 6. How many sides 
 has a square ? 
 
 A 
 
MEASURES OF SURFACE. 
 
 223 
 
 7. How do the sides compare in length ? 
 
 8. Draw a square Ifoot long and 1 foot wide. 
 
 A square one foot long and one foot wide is a Square 
 Foot {sq. ft,). 
 
 Here is a drawing representing a square foot divided 
 into square inches. 
 
 9. How many square inches 
 are there in 1 row ? 
 
 10. How many rows of square 
 inches are there ? 
 
 //. How many square inches 
 are there in a square foot? 
 
 12. How many inches long 
 are the four sides of a square 
 foot? 
 
 13. How long is i of a square foot ? 
 
 14. How many inches is it around i of a square foot ? 
 
 15. How many square inches are there in ^ of a square 
 foot? 
 
 16. How many square inches are there in f of a square 
 foot ? 
 
 / 7. How many square inches are there in | of a square foot ? 
 
 18. How many square inches are there in -j'g- of a square 
 foot? 
 
 What part of a square foot is : 
 
 19. 12 sq. in. 22. 48 sq. in. 
 
 20. 24 sq. in. 23. GO sq. in. 
 
 21. 36 sq. in. 24. 72 sq. in. 
 
 25. 9G sq. in. 
 
 26. 108 sq. in. 
 
 27. 120 sq. in. 
 
224 
 
 DENOMINATE AMOUNTS. 
 
 476. Oral Exercise. 
 
 A square one yard long aiid one yard wide is a Square 
 Yard (sq. yd.). 
 
 1. How niuny feet long is a square one yard long ? 
 
 2. IIow many feet wide is a square one yard wide ? 
 
 This drawing represents a 
 
 square yard divided into square 
 feet. It is drawn on the scale 
 of half an inch to the foot. 
 
 5. What does each small 
 square represent ? 
 
 4. How many square feet 
 are there in each row ? 
 
 5. How manyrows are there? 
 
 6. How many square feet are there in a square yard ? 
 
 7. How many square feet are there in J of a square yard ? 
 
 8. How many square feet are tliere in f of a square yard ? 
 
 9. What part of a square yard is 1 sq. ft. ? 3 sq. ft. ? 
 G sq. ft.? 
 
 70. How many square feet are there in 2 square yards ? 
 
 477. TABLE. 
 
 144 square inches (sq. in.) = 1 square foot (sq. ft.). 
 
 9 square feet 
 30 J square yards 
 IGO square rods 
 
 10 square cliains 
 640 acres 
 
 = 1 square yard (sq. yd.). 
 = I square rod (sq. rd.). 
 
 = 1 acre (A.). 
 
 = 1 squan^ mile (sq. mi.). 
 
 Note. A square rod is also called a Perch. 
 
MEASURES OF SURFACE. 225 
 
 478. Exercise. 
 /. Draw a 2-incli square. 
 
 Note. By a 2-inch square is meant a square 2 in. long and 
 2 in. wide. 
 
 2. Divide the 2-in. square into square inches. How 
 many square inches are there in 1 row ? IIow many rows 
 are there ? How many square inches in the square ? 
 
 3. Draw a 3-in. square and find how many square inches 
 it contains. 
 
 4. Draw a square inch and divide it into 4 equal squares. 
 
 5. How long is each part ? How wide ? 
 
 6. A square half an inch long and half an inch wide is 
 what part of a square inch ? 
 
 7. Draw a square 4 inclies long and 4 inches wide. 
 
 8. How many square inches are there in a 4-in. sqnare ? 
 
 9. How many square feet are there in a square 5 ft. 
 long and 5 feet wide ? 
 
 10. How many square feet are there in a square 6 ft. 
 long and 6 feet wide? 
 
 //. How many square yards are there in a square 3 yd. 
 long and 2 yd. wide ? 
 
 12. Draw a square 5^ in. long and 5^ in. wide. Find 
 the number of sqnare inches in tliis sqnare. 
 
 13. If each inch of the square mentioned in problem 12 
 represents a yard, how long is the square ? How wide ? 
 How many square yards in it? 
 
 14. How many yards long is a square rod ? How many 
 yards wide ? 
 
 15 
 
226 
 
 DENOMINATE AMOUNTS. 
 
 15. How many square yards are there in a square rod ? 
 
 16. How many square yards are there in 4 sq. rd. ? 
 
 479. Exercise. 
 
 20 rd. 
 
 This drawing represents a square 
 20 rd. long and 20 rd. wide. 
 
 /. How many squares each 1 rd. long 
 could be placed along one side of this 
 square ? 
 
 2. How many rows of such squares 
 could be placed in the whole square ? 
 
 3. How many such squares would this square contain ? 
 
 4. What must be multiplied together to give the number 
 of square rods in this square ? 
 
 5. How many square rods are there in an acre ? 
 
 6. What part of an acre is represented by this square ? 
 
 7. How many square rods are there in a square 6 rd. 
 long and G rd. wide ? 
 
 8. How many acres are there in each of these squares ? 
 
 (c) 
 
 (d) 
 
 (b) 
 
 (a) 
 
 40 rd 
 
 60 rd. 
 
 80 rd.. 
 
 90 rd. 
 
CUBIC MEASURE. 
 
 227 
 
 Cubic Measure. 
 480. Anything that has length, breadth, and 
 thickness is a Solid. 
 
 481. A Cube is a solid bounded 
 by six equal squares. 
 
 482. Oral Exercise. 
 
 /. How many edges of this fig- 
 ure can you see ? How many faces ? 
 
 A Cube. 
 
 2. How many edges of this figure can you not see? How 
 many faces ? 
 
 3. How many edges has this figure? How many faces? 
 
 4. Measure the length of each edge that you can see. 
 Are the edges equal? 
 
 5. What is the name of this figure? 
 
 6. When a cube is an inch long, an inch wide, and an 
 inch high, what is it called ? 
 
 7. If each edge of this cube were a foot long, what would 
 the cube be called? 
 
 8. If each edge of this cube were a yard long, what 
 would the cube be called? 
 
 483. Oral Exercise. 
 
 This figure represents a cubic foot 
 with one layer of cubic inches in it. 
 
 /. How many cubic inches are there 
 in 1 row of this layer? 
 
 2. How many rows of cubic inches 
 are there in this layer? 
 
228 
 
 DENOMINATE AMOUNTS. 
 
 3. How many cubic inches are there in this layer? 
 
 4. ITow many iiiclies high is a cubic foot? 
 
 5. How many layers of cubic inches can be placed in a 
 cubic foot? 
 
 6. How many cubic inches are there in a cubic foot? 
 
 This figure represents a cubic 
 
 yard divided into cubic feet. 
 
 7. How many cubic feet are 
 there in one row of the upper 
 layer? 
 
 8. How many rows of cubic 
 feet are there in the upper 
 layer? 
 
 9. How many cubic feet are there in the upper layer? 
 
 10. How many layers of cubic feet are there in the 
 cube? 
 
 //. How many cubic feet are there in a cubic yard? 
 
 484. 
 
 TABLE. 
 
 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.). 
 27 cubic feet = 1 cubic yard (cu. yd.). 
 
 485. 
 
 Important Facts. 
 
 1 gallon = 231 cu. in. 
 1 bushel = 2150.42 cu. in. 
 1 bushel = '^i cu. ft. nearly. 
 62J lb. = the weight of 1 cu. ft. of water. 
 24 J cu. ft. = 1 perch of masonry. 
 
CUBIC MEASURE. 229 
 
 486. Oral Exercise. 
 
 /. How many cubic feet are there in 2 cu. yd. ? 
 
 2. How many cubic feet are there in | cu. yd.? 
 
 3. What part of a cubic yard is 9 cubic feet? 
 
 4. What part of a cubic yard is 18 cubic feet? 
 
 5. How many cubic feet are there in a bin that will hold 
 4bu.? [§485.] 
 
 6. How many cubic feet are there in a bin that will hold 
 10 bu.? 
 
 7. A bin containing 20 cu. ft. will hold how many 
 bushels? 
 
 487. Exercise. 
 
 This drawing represents a cube 5 in. 
 long, 5 in. wide, and 5 in. high. 
 
 /. How many cubic inches could be 
 placed in this cube along one edge? How 
 many rows would make one layer of cubic inches in the 
 cube? How many such layers could be placed in the cube? 
 How many cubic inches would this cube make? What did 
 you multiply together to get the number of cubic inches 
 the cube would make? 
 
 2. How many cubic inches are there in a cube 6 in. long? 
 
 3. Draw a cube 2 in. long and find the number of 
 cubic inches in it. 
 
 4. How many cubic feet are there in a cube 2 ft. long? 
 
 5. How many cubic yards are there in a cube 4 yd. 
 long ? 
 
 ^^\ 
 
 ^ 
 
 1 
 j 
 
 1 
 i 
 
 J 
 
 
 
 y^ 
 
230 
 
 DENOMINATE AMOUNTS. 
 
 6. Find the number of cubic feet in each of the cubes 
 represented by these drawings: 
 
 (c) 
 
 (a) 
 
 o 
 
 
 y^\ 
 
 "7 
 
 (b) 
 
 
 ! 
 
 5 
 
 1 
 
 i 
 1 
 
 } -- 
 
 /^i 
 
 y 
 
 
 i 
 1 
 
 
 
 / 
 
 
 / 
 
 3 ft. 
 
 5 ft. 
 
 8 ft. 
 
 Rectangle 
 
 Rectangles. 
 
 488. A Rectangle is a surface that 
 has four sides and four right an- 
 gles. 
 
 The opposite sides of a rectangle 
 are equal. 
 
 489. Exercise. 
 
 ABCD represents a rectangle 4 in. 
 long and 3 in. wide, divided into 
 square inches. 
 
 /. How many square inches are 
 there in one row of ABCD ? How many rows are there 
 in ABCD ? How many square inches ? 
 
 2. What numbers did you multiply together to get the 
 number of square inches in rectangle ABCD? 
 
 3. If each square in ABCD were a square foot, how 
 
RECTANGLES. 
 
 231 
 
 long would ABGD be? How wide? How many square 
 feet would it contain? 
 
 4. Draw a rectangle 5 in. long and 2 in. wide, divide it 
 into square inches, and find how many square inches there 
 are in it. 
 
 5. Draw a rectangle 4 in. long and ^ in. wide, and find 
 how many square inches it contains. 
 
 6. Find how many square feet there are in each of the 
 rectangles represented here : 
 
 8 ft. 10 ft. 12 ft. 
 
 490. Find the number of square inches in a window 
 pane 10 in. long, and 8 in. wide. 
 
 10 = the number of inches in the length of the pane. 
 8= " " " " " " width '' '' " 
 .'. 8x 10, or 80 = " " " square inches in the pane. 
 Note. The sign . •. is read therefore. 
 
 491. Exercise. 
 
 /. How many square feet of boards are there in a floor 
 12 ft. long and 9 ft. wide ? 
 
 2. How many square yards of bunting will it take to 
 make a flag 3J yd. long and If yd. wide ? 
 
 5. How many square rods are there in a lot 60^ rd. long 
 and 14 rd. wide ? 
 
 4. How many square miles are there in a rectangular 
 tract of land 5J mi. long and 3J mi. wide ? 
 
232 
 
 DENOMINATE AMOUNTS. 
 
 6. How many square yards of oil cloth will it take to 
 cover a floor 15 ft. long and 12 ft. wide ? 
 
 6. How many acres are there in a rectangular field 80 
 rd. long and 20 rd. wide ? 
 
 7. How many square yards of plastering are there in the 
 end wall of a room 12 ft. wide and 9 ft. high, if it contains 
 one door 7^ ft. long and 4 ft. wide ? 
 
 8. How many shingles are required to cover a roof 20 ft. 
 long and 16 ft. wide, if each shingle covers 20 sq. in. of 
 roof ? 
 
 15 a 
 
 Carpeting. 
 
 492. In determining the num- 
 ber of yards of carpet that must 
 be bought to carpet a floor, 
 the number of strips needed 
 should first be found ; a frac- 
 tional part of a strip should be 
 regarded as a full strip. 
 
 493. How many yards of car- 
 pet } yd. wide must be bought to 
 carpet a floor 24 ft. long and 15 
 ft. wide, the strips to be laid 
 lengthwise ? 
 
 15 ft., or 180 in. = the width of the floor. 
 
 i yd., or 37 in. = tlie width of a strip of carpet. 
 
 180 + 27, or 05 = the number of strips needed. 
 
 Then, 7 strips must be bought. 
 
 24 ft., or 8 yd. = the length of a strip. 
 
 Then, 7x8, or 56 = the number of yards required. 
 
LUMBER MEASURE. 233 
 
 494. Exercise. 
 
 /. How many strips of carpet 1 yd. wide must be bought 
 for a room 12 ft. wide, the strips to be laid lengthwise ? 
 
 2. How many strips of carpet J yd. wide must be 
 bought for a room 27 ft. long, the strips to be laid cross- 
 wise ? 
 
 3. How many strips of carpet J yd. wide must be bought 
 for a room 20 ft. long, 18 ft. wide : 
 
 1st, if the strips are to be laid lengthwise ? 
 2d, if the strips are to be laid crosswise ? 
 
 4. How many yards of carpet, 1 yd. wide, are needed to 
 cover a floor 12 ft. long and 9 ft. wide ? 
 
 5. How many yards of carpet, J yd. wide, are needed to 
 cover a floor 18 ft. long and 13J ft. wide ? 
 
 6. Find the cost of carpeting a floor 24 ft. long and 18 
 ft. wide with carpet | yd. wide, costing 10.90 per yard, 
 strips to be laid lengthwise. 
 
 7. Find the number of yards of carpet | yd. wide that 
 must be bought to carpet 40 rooms in a normal school, 
 each 16 ft. long and llj ft. wide, strips to be laid 
 lengthwise. 
 
 Lumber Measure. 
 
 495. Lumber, one or more inches thick, is meas- 
 ured by the board foot. 
 
 496. A Board Foot is a piece of lumber one foot 
 long, one foot wide, and one inch thick. 
 
 Note. A board one inch thick contains as many board feet as it 
 does square feet. 
 
234 DENOMINATE AMOUNTS. 
 
 497. Find the number of board feet in a board 16 
 feet long and 5 in. wide. 
 
 16 = the number of feet in the length. 
 
 A= " " " " " " width. 
 
 • *. 'h X 16, or '-^ = the number of board feet in the board. 
 
 Therefore, to fintl the number of board feet in a 
 board one inch thick : 
 
 Multiply the number of feet in the length by the 
 number of inches in the width and divide by 12, 
 
 498. Find the number of board feet in a plank 15 
 feet long, 7 inches wide, and 2 inches thick. 
 
 '^■~ = the number of board feet in the plank, if 1 inch thick. 
 . 2x7x15 ^ u u u u u .< .« u 2 inches thick. 
 
 • • 12 
 
 Therefore, to find the number of board feet in a 
 piece of lumber more than one inch thick : 
 
 Multiply together the number of feet in the 
 lengthy the number of inches in the widths and the 
 number of inches in the thickness, and divide by P2, 
 
 Note 1. Boards less than one inch thick are sold by the square foot. 
 Note 3. The number of board feet in a piece of lumber is spoken 
 of as the number of feet. 
 
 499. Exercise. 
 
 /. Find the number of feet in a board 16 ft. by 8 in. 
 
 2. Find the number of feet in a plank 15 ft. long, 9 in. 
 wide, and 2 in. thick. 
 
 3. Find the number of feet in a piece of scantling 14 ft. 
 long, 4 in. wide, and 3 in. thick. 
 
RECTANGULAR SOLIDS. 
 
 235 
 
 4. How many square feet are there in a board 12 ft. 
 long, 6 in. wide, and ^ of an inch thick ? 
 
 6. How many feet in the following bill of lumber ? 
 
 8 boards, 18 ft. by 8 in. 
 
 10 boards, 16 ft. by 8 in. 
 
 12 boards, 14 ft. by 9 in. 
 
 6. How many feet in a load of lumber containing the 
 following ? 
 
 3 joists, 16 ft. by 9 in. by 4 in. 
 
 4 scantlings, 14 ft. by 4 in. by 3 in. 
 2 planks, 12 ft. by 8 in. by 2J in. 
 
 8 boards, 18 ft. by 9 in. 
 
 7. Find the cost of : 
 
 6 boards, 16 ft. by 8 in., at $30 per M (1000 ft.). 
 8 pieces of scantling, 18 ft. by 4 in. by 3 in. , at $25 per M. 
 ' 4 planks, 12 ft. by 9 in. by 2 J in., at $28 per M. 
 
 Rectangular Solids. 
 
 600. A Rectangular Solid is a 
 solid all of whose faces are 
 rectangles. 
 
 A Rectangular Solid. 
 
 501. Exercise. 
 
 /. How many faces has solid 
 
 \( ? How many of them can 
 
 } u see ? What kind of figure 
 
 1 lach face ? What may the 
 
 solid be called ? 
 
 2. AC is divided into equal 
 
236 
 
 DENOMINATE AMOUNTS. 
 
 cubes. How many ©f these cubes are there in each row 
 of the upper layer ? How many rows are there in the 
 upper layer ? How many cubes are there in the upper 
 layer ? How many layers of cubes are there in AC ? 
 
 3. If each cube of AC were a cubic incli, how long 
 would the solid AC be ? How wide ? How high ? How 
 many cubic inches would it contain ? 
 
 4. What three numbers did you multiply together to 
 get the number of cubes in AC ? 
 
 5. If the rectangular solid were 4 feet long, 2 feet wide, 
 and 3 feet high, show that the number of cubic feet in it 
 would be 3 X 2 X. 4. 
 
 502. A pile of wood 
 or stone 8 ft. long, 4 ft. 
 wide, and 4 ft. high is 
 called a Cord. 
 
 603. Exercise. 
 
 /. How many cubic inches are there in a block 5 in. 
 long, 4 in. wide, and 3 in. high ? 
 
 5 = the number of inches in the lengtli of tlie block. 
 
 4 _. u (( u u u <4 width " " ** 
 
 3 _ w a a a u u ]]^,\crhl a «' « 
 
 ,-. 3 X 4 X 5, or GO — the number of cubic inches in the block. 
 
 2. How many oul)io feot of air are there in a room 12 ft. 
 long, 9 ft. wide, and 8 ft. Iiigh ? 
 
 3. How many cubic yards of earth must be removed in 
 ^liggi^ig a cellar 27 ft. long, 18 ft. wide, and 12 ft. deep ? 
 
COMPOUND DENOMINATE AMOUNTS. 237 
 
 4. Show that there are 128 cu. ft. in a cord. [See §502.] 
 
 5. Show that a wall 16^ ft. long, IJ ft. thick, and 1 ft. 
 high contains 24| cu. ft., or 1 perch. [See §485.] 
 
 6. Show that a tin vessel 11 in. long, 7 in. wide, and 
 3 in. deep, holds a gallon. [See §485.] 
 
 7. How many gallons of water will a cistern hold that is 
 28 ft. long, 22 ft. wide, and 12 ft. deep ? 
 
 8. If 1 bushel equals about IJ cu. ft., about how many 
 bushels will a granary hold that is 10 ft. long, 8 ft. wide, 
 and 6 ft deep ? 
 
 9. If a heaped bushel equals f| cu. ft., how many heaped 
 bushels will a corncrib hold that is 25 ft. long, 4 ft. wide, 
 and 10 ft. high ? 
 
 10. Potatoes are sold by the heaped bushel ; about how 
 many bushels of potatoes will a bin hold that is 10 ft. long, 
 8 ft. wide, and 5 ft. deep ? 
 
 //. How many cords of wood are there in a pile 256 ft. 
 long, 4 ft. wide, and 4 ft. high ? 
 
 Compound Denominate Amounts. 
 
 504. Find the sum of 4 bu. 3 pk. 2 qt., 3 bu. 1 pk. 
 5 qt., and 2 bu. 2 pk. 6 qt. 
 
 The sum of the quarts is 13 qt., or 1 pk. 
 
 bu. pk. qt. 5 qt. Write 5 under the quarts and add 1 pk. 
 
 4 3 2 to the pecks. The sum of the pecks is 7 pk., 
 
 '^ 1 ^ or 1 bu. 3 pk. Write 3 under the pecks and 
 
 '^ ^ ^ add 1 bu. to the bushels. The sum of the 
 
 10 3 5 bushels is 10 bu. 
 
 .*. The sum is 10 bu. 3 pk. 5 qt. 
 
238 DENOMINATE AMOUNTS. 
 
 yr. 
 
 mo. 
 
 da. 
 
 20 
 
 6 
 
 18 
 
 14 
 
 8 
 
 14 
 
 605. From 20 yr. G mo. 18 da. take 14 yr. 8 mo. 14 da. 
 14 da. from 18 da. leaves 4 da. Write 4 
 
 under the days. We cannot take 8 mo. from 
 6 mo., so we take 1 yr., or 12 mo., from 20 yr. 
 (leaving 19 yr.) and add it to 6 mo., making 
 18 mo. 8 mo. from IS mo. leaves 10 mo. Write 
 5 10 4 10 under the months. 14 yr. from 19 yr. leaves 
 5 yr. 
 
 .-. The difference is 5 yr. 10 mo. 4 da. 
 
 606. A man who was born Fob. 10, 1872 and died Aug. 
 17, 1903, lived to what age ? 
 
 He was born on the 10th day of the 2d 
 
 yr. mo. da. month of the year 1872, and died on tlie 17th 
 
 1903 8 17 (Jay of the 8th mo. of the year 1903. 
 
 •^^^^ ^ ^^ .-. 1903 yr. 8 mo. 17 da. -1872 yr. 2 mo. 
 
 31 7 10 da., or 31 yr. 6 mo. 7 da., was the age to 
 
 which he lived. 
 
 )7. Exercise. 
 
 
 
 
 
 
 Add: 
 
 1. 
 
 
 Add 
 
 : 
 
 5. 
 
 
 ft. 
 
 in. 
 
 
 
 T. 
 
 cwt. 
 
 lb. 
 
 3 
 
 8 
 
 
 
 2 
 
 13 
 
 48 
 
 6 
 
 9 
 
 
 
 1 
 
 7 
 
 82 
 
 9 
 
 10 
 
 
 
 2 
 
 8 
 
 10 
 
 Add: 
 
 2. 
 
 
 
 
 4. 
 
 
 lb. 
 
 oz. 
 
 pwt. 
 
 
 gal. 
 
 qt. 
 
 pt 
 
 3 
 
 !) 
 
 5 
 
 From 
 
 10 
 
 2 
 
 
 
 4 
 
 8 
 
 12 
 
 take 
 
 G 
 
 3 
 
 1 
 
 5 
 
 10 
 
 1() 
 
 
 
 
 
COMPOUND DENOMINATE AMOUNTS. 239 
 
 5. 
 
 
 
 6. 
 
 
 cu. yd. 
 
 cu. ft. 
 
 yd. 
 
 ft. 
 
 in. 
 
 From 25 
 
 10 
 
 From 16 
 
 2 
 
 3 
 
 take 14 
 
 24 
 
 take 8 
 
 2 
 
 9 
 
 7. In one bag there are 2 bu. 3 pk. of potatoes, and in 
 another 1 bu. 2 pk.; what is the amount of potatoes in 
 the two bags? 
 
 8. A keg contained 5 gal. 2 qt. of cider, but 2 gal. 3 
 qt. has been drawn off; how much remains? 
 
 9. A man was born Jan. 12, 1882, and had his life in- 
 sured on Feb. 9, 1902; how old was he when his life was 
 insured ? 
 
 10. George Washington was born Feb. 22, 1732, and 
 died Dec. 14, 1799; how old was he when he died? 
 
 //. Daniel Webster was born Jan. 18, 1782, and died 
 Oct. 24, 1852; how old was he when he died? 
 
 12. William Penn was born Oct. 14, 1644, and died July 
 30, 1718; how old was he when he died? 
 
 13. Henry Clay died June 29, 1852, at the age of 75 yr. 
 2 mo. 17 da.; when was he born? 
 
 508. Reduce 3 gal. 2 qt. 1 pt. to pints. 
 
 3 - 2 -• 1. 
 _4 1 gal. = 4 qt. 
 
 ■^n 3 gal. = 3 X 4 qt., or 12 qt. 
 
 14 3 gal. 3 qt. = 12 qt. + 2 qt., or 14 qt. 
 
 ^ 1 qt. = 3 pt. 
 
 28 
 2 14 qt. = 14 X 3 pt., or 38 pt. 
 
 29 ••• 3 gal. 2 qt. 1 pt. = 38 pt. + 1 pt., or 39 pt. 
 
240 DENOMINATE AMOUNTS. 
 
 509. Exercise. 
 
 /. Reduce 7 lb. 2 oz. (avoir.) to ounces. 
 
 2. Ueduce 4 T. 8 cwt. to hundredweight. 
 
 3. Reduce 4 du. 8 hr. to hours. 
 
 4. Reduce 4 A. 30 sq. rd. to square rods. 
 
 5. Reduce 12 pwt. 10 gr. to grains. 
 
 6. Reduce 2 mi. 18 rd. to rods. 
 
 7. Reduce 4 bu. 2 pk. G qt. to quarts. 
 
 8. Reduce 2 yd. 2 ft. 6 in. to inches. 
 
 610. Reduce 149 pt. to gallons, etc. 
 
 2 ) 149 i of the number of pt. = the number of (jt. 
 
 4)74-^ .-. 149 pt. = 74 qt. 1 pt. 
 
 18^ i of the number of qt. =r tlie number of gal. 
 
 .-. 74 qt. = 18 gal. 2 qt. 
 Hence, 149 pt. — 18 gal. 2 qt. 1 pt. 
 
 611. Exercise. 
 
 /. Reduce 3675 sec. to hours, etc. 
 
 2. Reduce 500 gi. to gallons, etc. 
 
 5. Reduce 150 qt. to bushels, etc. 
 
 4. Reduce 4875 lb. to tons, etc. 
 
 5. Reduce 275 pt. to gallons, etc. 
 
 6. Reduce 2000 yd. to miles, etc. 
 
CHAPTER y. 
 PERCENTAGE. 
 
 512. Instead of saying five Jiundredths of a mim- 
 ber, we may ^^ij five per cent of a number. 
 
 Per cent means hundredths. 
 
 Thus, 1 per cent of a number is j^tr, of it. 
 
 4 per cent of a number is i Jo, or -gV of it. 
 25 per cent of a number is -j^,^)-, or \, of it. 
 100 per cent of a number is \%% or once, tlie number. 
 200 per cent of a number is fHo, or twice, the number. 
 250 per cent of a number is fooi or 2^ times, tlie nmiiber. 
 12] per cent of a number is -J J*, or ^, of it. 
 
 513. The sign i stands tor per cent. 
 
 Thus, 5 per' cent of 60 may be expressed 5 % of 50. 
 
 514. Oral Exercise. 
 
 Wbat part of a number is : 
 
 /. 2^ of it? 5. 15 fo of it? 
 
 5. 
 
 30 ^ of it ? 
 
 2. 4^ of it? 6. 40 
 
 ^ of it ? 
 
 10. 
 
 80 ^ of it ? 
 
 3. 10 fc of it ? 7. 50 ^ of it ? 
 
 11. 
 
 00 ^ of it ? 
 
 4. 20 ^ of it ? 8. 75 
 
 fo of it ? 
 
 12. 
 
 45 ^ of it ? 
 
 515. Oral Exercise. 
 
 
 
 
 Express as a per cent : 
 
 
 
 
 /. }. 3. i. 5. |. 
 
 7- A. 
 
 9. 
 
 |. //. h 
 
 2. J. 4. |. 6. A 
 
 «• tV 
 
 10. 
 
 IJ. 12. i. 
 
 616. Find 5 ^ of 40. 
 
 
 
 
 5^ of 40 = j^, or -A-, of 40, 
 
 or 2. 
 
 
 
 10 
 
 
 
 
242 
 
 PERCENTAGE. 
 
 517. Oral Exercise. 
 
 Find: 
 /. 1 ^ of 200. 
 
 2. 50 i of 12. 
 
 3. 25 i of 8. 
 
 4. 20 i of 35. 
 
 5. 10 i of 70. 
 5. 5 ^ of 80. 
 7. 2 ^ of 150. 
 
 8. 4:fc of 100. 
 
 5. 40 fc of 15. 
 
 /O. 00 ^ of 50. 
 
 //. 30^ of 30. 
 
 12. 90 ^ of 90. 
 
 13. 75 ^ of 24. 
 /4. 8 ^ of 50. 
 
 /5. 25 ^ of $10. 
 
 /^. 12J ^ of $0.40. 
 /7. 4 ^ of $200. 
 
 18. 2^ of $1000. 
 
 19. 100 ^ of $2. 
 
 20. 200^ of $1.50. 
 
 21. 300 ^ of $3. 
 
 518. 2 is 25^ of what number ? 
 
 2 = i^tfo, or ^, of the required number. 
 
 .'. f of the required number = 4 x 2, or 8. 
 
 519. Oral Exercise. 
 
 Find the number of which : 
 
 /. is 50^. 6. 14 is 200^. 
 
 2. 8 is 25^. 7. 4 is 80j^. 
 
 3. 3 is 20^. 8. 20 is 400^^. 
 
 4. 2J is 10^. 9. 18 is 00^. 
 
 5. 5 is 1^. 10. 30 is 90^. 
 
 520. What per cent of 20 is 8 ? 
 
 8 = A, or I of 20. 
 
 . •. 8 = ^ of 100 ^ of 20, or 40 % of 20. 
 
 521. Oral Exercise. 
 
 What per cent of : 
 
 //. 10 is 12J^. 
 
 12. 15 is 75^. 
 
 13. 1.5 is 50^. 
 
 14. I is (>0^. 
 
 15. 8 is 33J^. 
 
 /. 4 is 2? 
 
 2. 5 is 3 ? 
 
 3. 10 is 1 ? 
 
 4. 75 is 25 ? 
 
 5. 50 is 2? 
 
 6. 100 is 5 ? 
 
 7. 30 is ? 
 5. 200 is 4? 
 9. 2 is 4 ? 
 
 10. 9 is 9 ? 
 
 //. 50 is 40? 
 
 12. 80 is GO ? 
 
 13. 1 is J ? 
 
 14. 5 is 2J ? 
 /5. i is J? 
 
PERCENTAGE. 243 
 
 622. Oral Exercise. 
 
 /. How much is 20^ of 120 ? 
 
 2. How much is H of 50 ct. ? 
 
 3. A farmer sold 50^ of 80 bu. of wheat ; how much 
 wheat did he sell ? 
 
 4. $18 is f of what sum ? 75^ ©f what sum ? 
 
 5. $20 is I of what sum ? 80^ of what sum ? 
 
 6. 2 yd. is 50 fo of what length ? 
 
 7. 2 lb. is bfo of what weight ? 
 
 8. 50 ct. is 2 times what sum ? 200^ of what sum ? 
 
 9. 6 ft. is 3 times what length ? 300^ of what length ? 
 10. 25 lb. is 200^ of what weight ? 
 
 11.1 qt. is what part of 4 qt. ? AVhat per cent of 4 qt.? 
 
 12. $2 is what part of $4 ? What per cent of 14 ? 
 
 13. 8 ct. is what part of 20 ct. ? What per cent of 
 20 ct. ? 
 
 14. 1 pk. is what part of 1 bu.? What per cent of 
 1 bu.? 
 
 15. 10 ct. is what part of $1 ? What per cent of 
 of $1? 
 
 16. G ct. is what part of $1 ? What per cent of II ? 
 
 623. Oral Exercise. 
 
 /. A boy was given 50 words to spell ; if he spelled 80^ 
 of them correctly, how many did he spell correctly ? 
 
 2. 75j^ of a class of 40 pupils were promoted ; how 
 many were promoted ? 
 
 5. A dealer bought a horse for $200 and sold him so as 
 to gain 20^ of tlie cost ; what did he receive for him ? 
 
344 PERCENTAGE. 
 
 4. A farmer's corn crop was 160 bu.; he used 37J,<^ of it 
 and sold tlie remainder ; how many bushels did he sell ? 
 
 6. A piece of silverware weighing 8 oz. is 02^^ pure 
 silver ; how many ounces of silver does it contain ? 
 
 6. A merchant asked $G for a coat, but sold it at 20j^ 
 below this price ; what ^lid he receive for it ? 
 
 7. A boy spelled correctly 20 words, which were 80^ 
 of the number given him ; how many were given him ? 
 
 8. A man earned $40 collecting bills that were overdue ; 
 how much did he collect, if he was paid 25^^ of the sum 
 collected ? 
 
 9. After a man sold 60^ of his land, he had left 20 A.; 
 how much had he at first ? 
 
 10. A laborer's wages were increased from $10 to $12 a 
 week ; find the per cent of increase. 
 
 //. What per cent should a girl receive who spells 
 correctly 20 words of the 25 given ? 
 
 12. A boy attended school 15 days out of 20 during a 
 certain month ; find the per cent of his attendance. 
 
 13. A merchant who buys oil at 8 ct. a gallon and sells 
 it at 10 ct. a gallon, gains what per cent of the cost ? 
 
 524. A dealer bought a horse for $175 and sold him at 
 a gain of 15^ of the cost ; find the gain. 
 
 $175 
 
 ll^ $175 = the cost. 
 
 875 15jf, or .15, of tlie cost = the gain. 
 
 175 .*. .15 X $176, or $26.25 = the gain. 
 
 $26.25 
 
PERCENTAGE. 245 
 
 525. Exercise. 
 
 /. A man had $250 in bank and withdrew 20^ of it; 
 how much did he withdraw ? 
 
 2. A dealer bought a cow for $42 and sold her at a gain 
 of 37J^ of the cost ; find the selling price. 
 
 Sdg. 37|^ of a number = .375 of it. 
 
 3. Milk yields butter to the extent of about 4;^ of its 
 weight ; how much butter will 175 lb. of milk yield ? 
 
 4. 10^ of all silver coin is copper ; find the weight of 
 the copper in a silver dollar, which weighs 412.5 gr. 
 
 5. A merchant agreed to settle some outstanding bills 
 amounting to 1385.25 for 75^ of their full amount; how 
 much did he lose ? 
 
 6. A merchant asked |>G.25 for a coat, but sold it for 00^ 
 of the price asked ; how much did he receive for it ? 
 
 7. A dealer bought a china dinner set for 137.50 and 
 asked for it 20^ more than the cost ; find the price asked. 
 
 8. A farmer had 672 bu. of oats, but sold 16|^ of it and 
 fed 25^ of the remainder ; how many bushels had he left ? 
 
 526. A dealer sold a horse at a gain of 130.00, which 
 was 15^ of its cost ; find the cost. 
 
 .15) $30.00 ($304 $30.60 = the gain. 
 
 30 15^, or .15, X cost = the gain. 
 60 .-. .15 X cost = $30.60. 
 
 60 Cost = $30.60-^.15, or $204. 
 
 527. Exercise. 
 
 /. A merchant failing in business paid 75^ of his debts; 
 if he paid $3757.80, what were his debts? 
 
246 PERCENTAGE. 
 
 2. A dealer sold a machine for $126, which was 90ji^ of 
 the cost ; find the cost. 
 
 5. A jeweler sold a clock for $15.50, which was 80j^ of 
 the price he asked for it ; what did he ask for it ? 
 
 4. An agent earned $275.50 by collecting rents, being 
 paid 2^ of the sum collected ; how much did he collect ? 
 
 5. A suit of clothes was sold for $2.25 more than it cost, 
 which was at a gain of 12^ of the cost ; find the cost. 
 
 6. A merchant sold a bureau for $24, which was 80ji^ of 
 the price he asked ; what was the price asked ? 
 
 7. If milk yields 4^ of its weight of butter, how many 
 pounds of milk will yield 150 lb. of butter ? 
 
 8. A farmer sold 437.5 bu. of wheat, which was 87J^ of 
 his wheat crop ; find his wheat crop. 
 
 Sua. 87^^ of his crop = .875 x his crop. 
 
 628. A clerk who earned $640 a year, paid $96 a year 
 for house rent; what per cent of his salary did he pay 
 for house rent ? 
 
 6.40)96.0(15 1640 = his salary. 
 
 ^^ .01 of $640, or $6.40 = the rent, if it were \% of the 
 
 320 salary. 
 
 320 •*• $96: $6. 40, or 15= the number of per cent required. 
 
 629. Exercise. 
 
 /. If in 300 lb. of corn there are 16.2 lb. of fat, what is 
 the per cent of fat in corn ? 
 
 2. A music dealer bought a second-hand piano for $275 
 and sold it at a gain of $49.50 ; what per cent of the cost 
 did he gain ? 
 
INTEREST. 247 
 
 5. A marketman sold for a merchant 178 worth of 
 poultry, charging $3.90 for making the sale; what per 
 cent of the selling price was charged ? ' 
 
 4. A lawyer collected a debt of $1200, charging $150 
 for making the collection ; what per cent of the debt did 
 he charge ? 
 
 5. I bought a bill of goods amounting to $112.50, but 
 the merchant deducted 14.50 from it for cash payment ; 
 what per cent of the bill did he deduct ? 
 
 6. A shoe dealer paid $3 for a pair of gum boots, and sold 
 them for $2.40 ; what per cent of the cost did he lose ? 
 
 7. A hardware dealer bought nails at $2.40 a keg and 
 sold them at $2.80 a keg; what per cent of the cost did 
 he gain ? 
 
 8. A butcher bought pork at $5.40 per cwt. and sold it 
 at $6.30 per cwt.; what per cent of the cost did he gain ? 
 
 Interest. 
 
 630. If a person borrows money he usually has to 
 pay a certain per cent of the sum borrowed for the 
 use of it each year. 
 
 Money paid for the use of money is called Interest. 
 
 The sum on which interest is paid is called the 
 Principal. 
 
 Thus, if a man borrows $100 for 3 years and has to pay 5% of 
 tliis sum for the use of it each year, lie must pay 2 times 5% of $100, 
 or $10, for the use of it for 2 years. Here $10 is the interest and 
 $100 the principal. 
 
S48 PERCENTAGE. 
 
 631. Oral Exercise. 
 
 What is the interest on: 
 
 /. $100 for 1 yr. at 6^? 6. $500 for ^ yr. at 6^? 
 
 2. $200 for 1 yr. at 5^? 7. $250 for ^ yr. at 4^? 
 
 5. $600 for 2 yr. at 4^? 8. $800 for 1^ yr. at 4^? 
 
 4. $300 for 3 yr. at G^? 5. $000 for 2| yr. at 3^? 
 
 5. $100 for 2^ yr. at 4^? /O. $000 for 1 mo. at 0^? 
 
 532. The time for which interest is paid is usually 
 reckoned in years and days, when it exceeds a year; 
 and in days only when it is less than a year^ the 
 exact number of days being counted. 
 
 Thus, if a sum of mouey is on interest from Jan. 2, 1901 to 
 March 1, 1903, the time is counted as follows: from Jan. 2, 1901 
 to Jan. 2, 1903 is 2 yr. ; and from Jan. 2, 1903 to Mar. 1, 1903 is 
 58 da., making in all 2 yr. 58 da. Again, if a sum of money is on 
 interest from Mar. 1, 1903 to Oct. 1, 1903, the time is 214 da. 
 
 533. Interest for time less than a year is usually 
 reckoned on the basis of 360 da. to the year. 
 
 Thus, in reckoning interest on a sum for 108 da., the time is 
 usually regarded as ^gg yr. 
 
 534. Find the interest on $175 from May 1, 1901 to 
 Sept. 1, 1903, at 4^. 
 
 $175 The time from May 1, 1901 to May 1, 1903 = 2 yr. 
 
 '0^ The time from May 1, 1903 to Sept. 1, 1903 = 
 
 ^^'^^ (30 + 30 + 31 + 31 + 1) da. = 123 da. 
 
 2 Vn- 
 
 ^^^ .'. The time the principal is on interest = 
 
 2.;j9j^ 2 yr. 123 da. = 2iV5 yr. 
 
 $lG.39i -^^ ^ $175, or $7 = tlie interest for 1 yr. 
 
 2,V.. > 
 interest. 
 
BUSINESS PAPERS. 
 
 249 
 
 635. Exercise. 
 
 Find the interest on: 
 
 /. $50 for 2 yr. at 6^. 
 
 2. $75 for 3 yr. at 4^. 
 
 3. $150 for 2 yr. at ^fo. 
 
 4. $350 for 90 da. at 3^. 
 
 5. $275.60 for 270 da. at 4^^. 
 
 6. $385.75 for 200 da. at 3^. 
 
 7. $75 for 2 yr. 210 da. at 4^. 
 
 8. $85.50 for 3 yr. 20 da. at 4^^. 
 
 9. $145 from Sept. 15, 1902 to Dec. 1, 1903, at 5^. 
 
 10. $850.60 from May 1, 1901 to Sept. 1, 1903, at m. 
 
 11. $205.25 from Jan. 2, 1902 to March 1, 1904, at 4^. 
 SuG. The time = 3 yr. 59 da. Why ? 
 
 12. $850.75 from May 1, 1903 to Dec. 31, 1903, at 5^. 
 
 BUSINESS PAPERS. 
 A PROMISSOKY NOTE. 
 
 
 r^ cyu"iJLi-.&,iL<\.r<' ) — > — 
 
 fiml?.) 
 
 
 536. A Promissory Note is a written promise to pay 
 a specified sum to a certain party at a certain time. 
 
250 PERCENTAGE. 
 
 637. The Maker of a promissory note is the party 
 who signs it and thereby promises to pay. The 
 Payee is the party whose name is written in the body 
 of the note and to whom the promise to pay is made. 
 The Face is the amount named in the note. 
 
 Thus, in the note on page 249 A. P. Reid is the maker , Geo. Morris 
 Philips the j>ayee, and forty-five r^ dollars thd/ace. 
 
 Note 1. A note may be written so as to include the payment of 
 interest. 
 
 Note 2. If a note is payable a certain number of days after 
 date, it is due at the expiration of that number of days after date, 
 not counting the date. 
 
 Thus, a note payable 60 da. after June 1 is due July 31. 
 
 Note 3. If a note is payable a certain number of months after 
 date, calendar months are to be counted. 
 
 Thus, a note payable 3 mo. after June 1 is due Aug. 1. 
 
 A CHECK. 
 
 No. / -1 5 Lancaster, Pa — £Luljjk_.aiv__190.a^ 
 
 First JknoNAL Bi^KoflAif caster 
 
 Pay lO the Orderof CjqrmJn ^ l[f->VmA^nnnrn 
 
 
 538. A Check is a written order by which a bank 
 is directed by a depositor to pay out money belong- 
 ing to him. 
 
 639. The holder of a check should have it cashed 
 
BUSINESS PAPERS. 251 
 
 on the day he receives it, or on the first business 
 day following. 
 
 640. Before the hold 
 
 ia/KVUiiy £^. ci^eyTixLeyVa 
 
 er of a check has it 
 
 cashed, he must write 
 
 his name across the back of it. This is called 
 
 indorsing the check. 
 
 A RECEIPT. 
 
 541. A Receipt is a written acknowledgment of 
 money or goods received, or of services rendered. 
 
 Note. When the money paid is only part of the debt owed, "on 
 account^'' should be written in the receipt instead of " in full of all 
 accounts to date.''' 
 
 542. Exercise. 
 
 /. When is the note on p. 249 due ? 
 
 2. When is a note due that is dated July 1, and payable 
 in 60 da. ? 
 
 3. When is a note due that is dated May 1, and payable 
 in 3 mo. ? 
 
252 MISCELLANEOUS PROBLEMS. 
 
 4. Who pays the note on p. 249, when due ? 
 
 5. Write a promissory note for $25 with yourself as 
 maker and L. M. Morris as payee, dating the note June 1, 
 1903, and making it payable in 90 da. 
 
 6. Suppose you buy a cow from F. P. Haws for $45.50, 
 payable in G mo. ; write the promissory note that you could 
 give him in payment. 
 
 7. Suppose you have money deposited in the Central 
 National Bank of Wilmington, Del. ; write the check with 
 which you could pay Joseph S. Walton $10. Show how 
 Joseph S. Walton would indorse the check before having 
 it cashed. 
 
 8. Write a receipt showing that C. V. Miller paid you 
 $75 to-day on account. 
 
 9. Write a receipt for $40 wages that were due you for 
 the month of June, 1903, from L. M. Haines, and paid 
 the last day of that month. 
 
 MISCELLANEOUS PROBLEMS. 
 
 543. Oral Exercise. 
 
 /. After a young man's salary had been increased ^ of 
 itself, it was $5.50 per week ; what was it before the 
 increase ? 
 
 2. How many times is J contained in 1 ? 
 
 3. $1,000,000 is how many times $100,000 ? 
 
 4. If an automobile runs 12 mi. per hour, in how many 
 minutes will it run a mile ? 
 
MISCELLANEOUS PROBLEMS. 263 
 
 5. What will it cost to send by mail a book weighing 
 19 oz., the rate of postage being 1 ct. for 2 oz. or fraction 
 thereof ? 
 
 6. If the cost of sending a telegram is 25 ct. for the first 
 10 words and 2 ct. for each additional word ; find the cost 
 of sending the following message : '^ Meet me at my office 
 to-morrow morning. Bring books. Important meeting. '* 
 
 7. What should 1 doz. loaves of bread cost when 3 loaves 
 cost 10 ct.? 
 
 8. Supply the missing numbers and read : 
 
 275 rails = hundred rails. 
 
 87.5 pounds = hundred pounds. 
 
 2735 shad = hundred shad. 
 
 7567 plants = thousand plants. 
 
 544. Exercise. 
 
 [From United States Civil Service Examinations.] 
 
 /. Divide 2,408,588 by 4,732. 
 
 2. Multiply 8,643 by 608, and then subtract 98,746. 
 
 3. A merchant who spent $225, bought 65 pounds of 
 butter at 30 cents per pound, 84 barrels of apples at 12.25 
 per barrel, and spent the remainder for coffee. How 
 much did he spend for coffee ? 
 
 4. During the month of August 450,000 bushels of wheat 
 were shipped from a certain port. During September 
 87,960 more bushels were shipped than during August. 
 What was the total number of bushels shipped in the two 
 months ? 
 
254 MISCELLANEOUS PROBLEMS. 
 
 6. Add the following, placing the total at the bottom : 
 
 742,155.74 
 
 429.39 
 
 6,873.68 
 
 397.49 
 
 1,956,374.20 
 
 6. If a railway mail clerk earns $800 in a year, how much 
 will he have left after paying his board at the rate of 
 $16 a month ? 
 
 7. If a railway mail clerk spends ten cents a day for 
 street-car fare, how much will he spend in six months of 
 30 days each ? 
 
 546.. Exercise. 
 
 /. If 4 men can do a piece of work in 8J- da., how long 
 should it take 1 man to do it ? 
 
 2. If I of a number is 12 J, what is f of the number ? 
 
 3. What date is 30 da. prior to Dec. 31 ? 
 
 4. A roll of wall paper is 8 yd. long and 18 in. wide ; 
 how many square feet does it contain ? 
 
 5. AVhat decimal taken 100 times will make .1 ? 
 
 6. How many 2-inch squares can be cut from a piece 
 of pasteboard 6 in. long and 5 in. wide ? How many 
 square inches of waste will there be ? 
 
 7. How many square feet of canvas is required to cover 
 a box 6 ft. 6 in. long, 4 ft. wide, and 3 ft. deep ? 
 
 8. What must be added to .001 to make .1 ? 
 
MISCELLANEOUS PROBLEMS. 255 
 
 9. A man who takes on an average 110 steps per 
 minute, each step 2J ft, long, is walking at the rate of 
 how many miles per hour ? 
 
 10. A rectangular piece of land containing 1 A. is 80 yd. 
 long ; find its width in yards. 
 
 //. A man bought a piece of oil cloth containing 20 sq. 
 yd. ; what is its length, if it is 1 J yd. wide ? 
 
 546. Exercise. 
 
 /. A man who was born 60 years ago has lived how 
 many hours, supposing that there have been 14 leap years 
 in the 60 years? 
 
 2. How many yards long is a tract of land containing an 
 acre, if it is 20 yards wide? 
 
 3. 2\ doz. hats cost $72; what should they sell for apiece 
 in order that the gain may be $1 on each hat? 
 
 4. How much waste will there be after cutting as many 
 2-inch cubes as possible out of a 5-inch cube? 
 
 5. A common brick is 8 in. long, 4 in. wide, and 2 in. 
 thick; how many square inches are there in its surface? 
 
 6. A mechanic was employed for 1 year at $60 a month; 
 if his expenses were $32 a month, how much did he save 
 during the year? 
 
 7. Find the total length of the edges of a box 6 in. long, 
 4 in. wide, and 3 in. high. 
 
 8. 12 bu. of wheat were raised on a piece of land 121 yd. 
 long and 10 yd. wide; at the same rate, what would be the 
 yield on an acre? 
 
 9. Show by an arrangement of dots that 3x2 = 2x3. 
 
256 MISCELLANEOUS PROBLEMS. 
 
 547. Exercise. 
 
 [From United States Civil Service Examinations.] 
 /. Multiply 7^ by 36.8, and divide the product by 1.92. 
 (Solve by decimals.) 
 
 2. A lot which was 53 feet wide and 150 ft. long sold 
 for $8347.50, which was one-fourth more than it cost. 
 What was the cost per square foot ? 
 
 3. Multiply 382.58 by f of 27,342, and divide the prod- 
 uct by J of 34.78. (Work by decimals.) 
 
 4. Divide 5f by ^, multiply the quotient by 3.5468, and 
 from the product subtract \^ of 13.70. 
 
 5. Multiply 37f by 400.3, and divide the product by 
 93.5. (Solve by decimals.) 
 
 6. A carrier can assort 43 letters or 37 papers in a 
 minute. At this rate, how many hours will it take him 
 to assort 3655 letters and 185 pounds of papers, averaging 
 7 papers to the pound ? 
 
 7. In a certain mail there are 294 pounds 14 ounces of 
 newspapers weighing at the rate of 3 papers to every 7 
 ounces. How many papers are there in the mail ? (16 
 ounces = 1 pound.) 
 
 8. If a cubic foot of coal weighs 63 pounds, find the 
 number of tons of coal in a bin 5 feet 6 inches wide, 6 feet 
 9 inches deep, and 19 feet 6 inches long. (1 ton = 2,240 
 pounds.) 
 
VB 35879 
 
 ^*i<^"f;.-;^ii'-«'' 
 
 5ll;H3 
 
 UNIVERSITY OF CALIFORNIA UBRARY