IN MEMORIAM 
 FLORIAN CAJORI 
 
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Digitized by the Internet Archive 
 
 in 2007 with funding from 
 
 IVIicrosoft Corporation 
 
 http://www.archive.org/details/elementaryarithmOOhamirich 
 
ELEMENTARY ARITHMETIC 
 
 FOR GRADED AND ITNGRADBD 
 SCHOOLS, V-Vr-M-X-- :. 
 
 BY 
 
 SAMUEL HAMILTON, Ph.D. 
 
 AUTHOR OF " THE RECITATION," AND SUPERINTENDENT 
 OF SCHOOLS, ALLEGHENY COUNTY, PA. 
 
 NEW YORK .:• CINCINNATI •:• CHICAGO 
 
 AMERICAN BOOK COMPANY 
 
Copyright, 190S, 1909, by 
 
 SAMUEL HAMILTON. 
 
 Entered at Stationers' Hall, London. 
 
 HAM. ELEM. AR. 
 
 w. p. 6 
 
 CAJORf 
 
 (y n 
 2 
 
 /Y^^ 
 
^^ 
 
 PREFACE 
 
 The "Elementary Arithmetic " is intended to cover the 
 work of the first five years. It is divided into four parts. 
 
 Part One includes the work ordinarily done during the 
 first and second years. 
 
 Part Two includes the work of the third year. It i& 
 devoted mainly to the presentation of the elementary facts- 
 and tables of arithmetic. 
 
 The text-book should be placed in the hands of the pupil 
 when he enters upon the work found in Part Two. 
 
 Part Three covers the work of the fourth year. Its pur- 
 pose is to give a mastery of the fundamental operations, and^ 
 through the study of problems, to develop the ability to use 
 these operations in a practical way. 
 
 Part Four includes the work of the fifth year. It gives 
 an elementary treatment of Fractions, Decimals, Percentage,. 
 Interest, Denominate Numbers, and Practical Measurements.. 
 
 The aim of this course is twofold : first, to give the child 
 mathematical skill ; second, to give him mathematical power. 
 
 To these ends attention is invited to the following : 
 
 1. The prominence given to drill intended to give skilly 
 and the frequency of systematic reviews. 
 
 2. The Study of Problems intended to give mathematical 
 power. 
 
 I 3. The plan which provides an easy treatment of eacli 
 subject before the complete treatment of it. 
 
 4. The easy steps in gradation. 
 
 5* The emphasis given to business arithmetic. 
 
iv PREFACE 
 
 6. The appeal made to observation as a stimulus to mathe- 
 matical thought. 
 
 7. The abundance of exercises for oral drill. 
 
 The importance of oral drill has led the author to lay 
 special emphasis on this kind of work. Pupils should be 
 drilled thoroughly on the oral development and exercises in 
 each subject, before taking up the written work. 
 
 In many schools the unit of classification is the half year. 
 With this in view, the subject-matter in the third, fourth, and 
 fifth years has been separated into two parts. The easy treat- 
 ment of topics covers the first half of the year, and the 
 more complete treatment the second half. 
 
 SAMUEL HAMILTON. 
 
CONTENTS 
 
 PART I — FIRST AND SECOND YEARS 
 
 Numbers to 12 
 
 Liquid Measures . . . . 
 Halves, Thirds, Fourths . . 
 
 Comparison 
 
 Dry Measures 
 
 Reading and Writing Num- 
 bers to 99 
 
 3-13 Roman Numbers to XX 
 
 6 Addition . . . . . 
 
 7 Subtraction . . . . 
 
 8 Multiplication by 2 . 
 11 Division by 2 . . . 
 
 Inch, Foot, and Yard 
 
 14, 16 Review 
 
 PAGES 
 
 16 
 
 17-20 
 
 21-23 
 
 24,25 
 
 26 
 
 27 
 
 28 
 
 PART II — THIRD YEAR 
 
 First Half Year 
 
 Reading and Writing Num- 
 
 
 bers to 9999 . . . 
 
 29,30 
 
 Addition 
 
 31-36 
 
 Subtraction 
 
 37-41 
 
 Addition and Subtraction 
 
 42 
 
 Multiplication by 3 and 4 
 
 43-47 
 
 Practical Problems . . 
 
 48 
 
 Division by 3 and 4 . , 
 
 49-53 
 
 Addition and Subtraction o1 
 
 I 
 
 United States Money . 
 
 54,55 
 
 Multiplication by 5 and 6 
 
 56-59 
 
 Division by 5 and 6 . . 
 
 60-62 
 
 Addition 
 
 63 
 
 Subtraction 
 
 64,65 
 
 Multiplication and Divisior 
 
 I 66 
 
 Dry Measures .... 
 
 67 
 
 Liquid Measures . . . 
 
 68 
 
 Measures of Weight . . 
 
 69 
 
 Measures of Length . . 
 
 70,71 
 
 Secoxd Half Year 
 
 Reading and Writing Num- 
 bers to 99,999 ; Roman 
 
 Notation 72 
 
 Addition and Subtraction, 
 
 including Fractions . . 73-77 
 
 Review 78 
 
 Multiplication by 7 and 8 . 79-81 
 
 Division by 7 and 8 . . . 82, 83 
 Multiplication by Mixed 
 
 Numbers 84 
 
 Multiplication by 9 . . . 85, 86 
 
 Division by 9 87 
 
 Division of U. S. Money . 88 
 
 Review 89,90 
 
 Addition and Subtraction . 91, 92 
 
 Review 93-96 
 
 Comparison 97 
 
 Time Measures 98, 99 
 
 Surface Measures .... 100, 101 
 
 Review 102-106 
 
CONTENTS 
 
 PART III — FOURTH YEAR 
 
 First Half Year 
 
 PAGES 
 
 Reading and Writing Num- 
 bers to 999,999,999 . . 107, 108 
 Addition and Subtraction . 109-111 
 Multiplication by 10, 11, 12 112-114 
 Division by 10, 11, and 12 . 115, 116 
 Review and Drills .... 117-120 
 Multiplication Table ... 121 
 
 Multipliers ending in . . 122, 123 
 Divisors ending in . . . 124, 125 
 Multiplication by 'i"\vo-figure 
 
 Numbers 126,127 
 
 Multiplication of Concrete 
 
 Numbers ..... 128,129 
 
 Comparison 130 
 
 Review of Short Division . 131 
 
 Long Division by Two-figure 
 
 Numbers 132-1.36 
 
 Division and Partition . . 137 
 
 Review 138-140 
 
 Measures of Time .... 141 
 
 Measures of Weight . . . 142 
 
 Measures of Length . . . 143, 144 
 Measures of Surface . . . 144-146 
 
 Second Half Year 
 
 Del 
 
 Reading and Writing Num 
 
 bers to Billions . . 
 Review and Drills . . . 
 Addition and Subtraction of 
 
 Mixed Numbers . . 
 Multiplication by Three 
 
 figure Numbers . . 
 Parts of Numbers ... 
 Multiplication by Mixed 
 
 Numbers . . . 
 Fractional Parts of a 
 
 lar 
 
 Long Division by Three 
 
 figure Numbers . . 
 Study of Problems of Two 
 
 Operations . . . 
 Review of Division 
 Combining Processes . 
 
 Analysis 
 
 Comparison .... 
 
 Bills 
 
 Review of Measures . 
 Review ..... 
 
 147 
 
 148-152 
 
 153-155 
 
 156- 
 
 -158 
 159 
 
 160 
 
 161 
 
 162 
 
 163- 
 
 170 
 171 
 172 
 173, 174 
 175, 176 
 177,178 
 179-181 
 182-185 
 
 PART IV — FIFTH YEAR 
 
 First Half Year 
 Fractions 186-235 
 
 Fractional Equivalents 
 
 Reduction 
 
 Addition 
 
 Subtraction .... 
 Multiplication . . . 
 Fractional Parts . . 
 
 Division 
 
 Comparison .... 
 Review Problems . . 
 
 186 
 195 
 197 
 201 
 207 
 208 
 221 
 230 
 232 
 
 Second Half Year 
 
 "* — ^ Decimals 236-253 
 
 Notation and Numeration 237 
 
 Comparison of Fractions 
 and Decimals .... 239 
 
 Addition 241 
 
 Subtraction 243 
 
 Multiplication .... 245 
 
 Division 248 
 
 Review I^roblems . . . 252 
 
 Percentage 254-259 
 
 Interest 258 
 
 Operations with United 
 
 States Money . . . 260,261 
 
 Bills 262-265 
 
 Denominate Numbers — 
 
 Tables 266-275 
 
 Practical Measurements . . 276-282 
 Lengths and Surfaces . . 276 
 
 Volume 278 
 
 Surfaces and Volumes . 280 
 
 General Review .... 283-288 
 
ELEMENTARY ARITHMETIC 
 
 PART I — FIRST AND SECOND YEARS 
 COUNTING NUMBERS TO TEN 
 
 Count these balls. How Q^ ^^ ^ (^ <^ 
 many are there ? ^ (^^ ^ ^ ^ 
 
 Count ten pupils. Count eight desks. Count nine 
 books. Count the days of the week. How many are 
 there ? 
 
 Numbers are used to tell how many. 
 
 You have named ten numbers and you can write 
 them either in words or in figures. 
 
 naught one two three four five six seven eight nine ten 
 
 
 
 1 2 
 
 6 
 
 8 9 10 
 
FIRST AND SECOND YEAR [Oral 
 
 THE NXlMBERS TWO AND THREE 
 
 2=^ Twol's 
 
 3 = 2 Three Vs 
 
 equals 3. 
 
 2. 1 1 
 
 2 
 
 + 2 +1 
 
 + 1 
 
 © and © are © 0. © © and © are © © ©. 
 
 1. 1 ball and 1 ball are how many balls? 
 
 1 ball + 1 ball = 2 balls. 
 
 When you unite 2 and 1, you add them and the an- 
 swer, 3, is called the sum. 
 
 The sign + is read and or plus. The sign = is 
 read equal or equals. 2 + 1 = 3 is read 2 plus 1 
 
 1 top 2 cups 1 car 
 
 + 2 tops + 1 cup + 2 cars 
 
 Sum 
 
 3. John had 3 cents and lost one of them. How 
 many cents had he left ? 
 
 3 cents — 1 cent = 2 cents. 
 
 4. How many more balls are 3 balls than 2 balls ? 
 3 balls less 2 balls = 1 ball. 
 
 You have subtracted 2 balls from 3 balls. The an- 
 swer, 1 ball, is the difference or remainder. 
 
 The sign — is read minus or less. 3 — 2 = 1 is read 
 3 minus 2 equals 1. 
 
 5. Subtract, beginning at the right: 
 3 3 3 2 1 
 
 13 2 11 
 
 Difference or remainder 
 
Oral] 
 
 NUMBERS TO TWELVE 
 
 THE NUMBERS FOUR AND FIVE 
 
 1 2 Four I's 
 3 2 Two 2»s 
 
 5 = ^ ^ FivePs 
 
 and 
 
 are 
 
 and ^^^ 
 
 are 
 
 ^. 
 
 1. Draw flags to show the following : 
 
 3 flags + 1 flag = ? 5 flags - 1 flag = ? 
 
 3 flags + 2 flags = ? 4 flags r- 3 flags = ? 
 
 2. Count the flags by 2's. Two 2's = ? 
 
 3. 2 flags taken two times are flags. 
 
 4. How many times must 1 flag be taken to have 
 
 4 flags ? 4 times 1 flag = flags. 
 
 5. 2 X 2 flags = flags. 
 
 The sign x is read time or times. 
 Give answers, reading across the page : 
 
 6. 
 
 1x1 
 
 5x1 
 
 1x2 
 
 2x2 
 
 3x1 
 
 7. 
 
 1x3 
 
 1x4 
 
 5x1 
 
 2 + 3 
 
 3 + 1 
 
 8. 
 
 1 + 4 
 
 4-1 
 
 5-2 
 
 4-3 
 
 1 + 4 
 
 9. 
 10. 
 
 2x2 rings = 
 
 1x3 balls - 
 
 3x1 box 
 2x2 boot 
 
 
 
 :s = 
 
 
 To THE Teacher. — Practice on similar work until pupils are 
 thoroughly familiar with the combinations up to twelve. 
 
FIRST AND SECOND YEAE, 
 
 [Oral 
 
 LIQUID MEASURES 
 
 For this exercise 
 a set of liquid meas- 
 ures should bemused. 
 
 1. Fill the pint 
 measure with water 
 and empty it into 
 the quart measure. 
 Do this a second 
 time. You have 
 shown that 2 pints equal a quart. 
 
 2. A quart is how many times a pint? A pint is 
 what part of a quart ? 
 
 3. Show by mea^ring with the quart measure that 
 4 quarts equal a gallon. 
 
 4. A gallon is how many times a quart ? A quart is 
 what part of a gallon ? 
 
 5. How many times can the teacher fill Mary's half- 
 pint milk bottle from the pint measure ? 
 
 6. Clare gets a pint of milk each morning and even- 
 ing. How many pints does he get in two days ? 
 
 7. Clare pays 2 cents for a pint of milk. How much 
 does he pay for 2 pints ? 
 
 8. Raymond delivers, each day, 4 quart bottles of 
 milk. How many gallons does he deliver? 
 
 9. Henry goes to the store for 2 quarts of molasses. 
 How many pints does he get ? 
 
Oral] 
 
 NUMBERS TO TWELVE 
 
 HALVES, THIRDS, AND FOURTHS 
 
 1. Cutan apple into 
 2 equal parts. What 
 is one part called ? 
 
 2. Into how many 
 halves can an apple be cut ? an orange ? a pie ? 
 
 One half of 1 is written |. 
 
 3. I of 2 oranges = — orange ; ^ of 4 oranges = 
 — oranges. 
 
 4. Cut an apple into 3 
 equal parts. What is 1 part 
 called? 
 
 One third of 1 is written I. 
 
 5. ^ of 3 pennies = ? i of 
 4 splints = ? 
 
 6. Cut an apple into 4 equal 
 parts. Each part is named one 
 fourth, or one quarter. 
 
 One fourth of 1 is written |. 
 
 7. How many fourths of an apple make a whole 
 apple ? 
 
 8. Write in figures : one half ; one third ; one fourth. 
 
 9. Find ^ of 4 cents ; ^ of 3 cents ; |^ of 2 cents. 
 
 10. Find 1 of 4 ; 1 of 3 ; i of 2 ; i of 1 ; i of 4. 
 
 11. Draw a circle showing halves; another showing 
 thirds ; one showing fourths. 
 
FIRST AND SECOND YEAR 
 
 [Oral 
 
 COMPARISON 
 1. Which line is the shortest ? the longest ? 
 
 2. Which lines are shorter than c ? 
 
 3. Which line is one half as long as 6 ? 
 
 4. Which line is one fourth 
 as long as 6^ ? 
 
 5. ^ is how many times as 
 large as (7? 
 
 6. How many times larger 
 than (7 is ^ ? 
 
 7. Are A, B, and C of the 
 
 A 
 
 
 
 B 
 
 
 
 
 C 
 
 
 
 Oblong 
 
 same width ? How many square 
 corners has each one ? 
 
 8. How many sides of A have 
 the same length ? 
 
 9. How many oblongs are there in ^ ? 
 
 10. How many equal sides has this 
 figure ? how many square corners ? 
 
 11. What is the name of the figure? 
 How long is each side ? 
 
 12. How many inches is it around 
 the square ? 
 
 13. One inch is what part of two inches ? 
 
 14. Two inches are what part of 4 inches ? 
 
 One 
 Square Inch 
 
 1 sq. in. 
 
Oral] NUMBERS TO TWELVE 
 
 THE NUMBERS SIX AND SEVEN 
 
 6 = 
 
 3 Six Ps 
 
 Three 2»s 
 3 Two 3»s 
 
 7 = 
 
 1 2 3 
 6 5 4 
 
 Seven l*s 
 
 1. With convenient objects show these combinations : 
 5 marbles + 1 marble = ? 7 marbles — 4 marbles = ? 
 
 4 marbles + 3 marbles = ? 6 marbles — 1 marble = ? 
 
 2 marbles 4- 4 marbles = ? 7 marbles — 3 marbles = ? 
 
 2. Add: 
 
 2 2 
 4 5 
 
 3. Fill in the blank spaces and add : 
 
 () ( ) () () ( ) ( ) () () () () 
 
 5243332161 
 
 6 5 
 
 7 
 
 6 
 
 5 
 
 4 
 
 7 
 
 6 
 
 6 
 
 5 
 
 4. Subtract: 
 
 
 
 
 
 
 
 
 
 7 6 
 6 5 
 
 6 
 3 
 
 6 
 1 
 
 7 
 5^ 
 
 7 
 2 
 
 7 
 4 
 
 6 
 2 
 
 6 
 
 4 
 
 7 
 3 
 
 5. Place six marbles in two equal groups ; in three 
 
 equal groups. 
 
 6. Give answers at sight : 
 3x2 2x3 
 
 1 of 6 i of 3 
 
 - 2 + 2 + 2 = ? 3 + 3 = ? 
 
 3 + 2 + 1 = ? linG,- 
 
 7x1 
 
 7-4 
 
 iof4 
 
 |of 6 
 
 
 1+3+2=? 
 
 times ? 
 
 3+2+2=? 
 
10 
 
 FIRST AND SECOND YEAR 
 
 [Oral 
 
 THE NUMBERS EIGHT AND NINE 
 
 , o Q 4 Eight I's 
 
 8 = ^ ^ ^ ^ Four 2>s 
 
 7 6 5 4 Two 4»s 
 
 9^1 2 3 4 Nine Vs 
 8 7 6 5 Three 3»s 
 
 1. With objects show the combinations that make 
 8 ; that make 9. 
 
 2. Count to 8 by 2's. ?x2 = 8? ?x4 = 8? 
 
 3. Count to 9 by 3's. ?x3 = 9? ?x2 = 6? 
 Add up, then down : 
 
 4. 432723456 
 456176543 
 
 5. 3422130234 
 2353302621 
 3113456144 
 
 6. From 9 take 8 ; take 7;6;5;3;2;4;1;9. 
 
 7. Subtract : 
 8868878888 
 3731654852 
 
 8. In 8 blocks, how many groups of 2's are there ? 
 In 9, how many groups of 3's are there ? 
 
 1 time 2 = ? 
 
 3 times 3 = ? 2 is contained in 4, times. 
 
 3 times 2 = ? 3 is contained in 6, times. 
 
 4x2 = ? 2 is contained in 8, times. 
 
 9.'4 + 4 = ? 5 + 4 = ? 8h-4 = ? iof8 = ? 
 
 10. iof6 = ? 
 
 Jof 6 = ? 
 
 iof9 = ? 
 
 Jof 8 = ? 
 
Oral] 
 
 NUMBERS TO TWELVE 
 
 11 
 
 DRY MEASURES 
 
 Pint Quart Peck Bushel 
 
 1. Name articles that you can purchase by the peck 
 or by the bushel. 
 
 2. Why are these measures called " dry measures " ? 
 
 3. The smallest dry measure shown in the picture 
 is called a pint. Fill a pint measure with sand and 
 empty it into the quart measure. Do this again. Is 
 the quart measure now full ? You have shown that 
 2 pints equal a quart. 
 
 4. What part of a quart is a pint ? 
 
 5. Show by measurement, as in example 3, that 
 8 quarts equal a peck. A quart is what part of a peck ? 
 
 6. Show as before that 4 pecks equal a bushel. A 
 peck is what part of a bushel ? 
 
 7. A bushel is how many times a peck ? A peck is 
 how many times a quart ? 
 
 8. Subtract: 
 
 8 qt. 7 qt. 8 pk. 6 pt. 8 bu. 
 
 4 qt. * 3 qt. 3 pk. 4 pt. 5 bu. 
 
12 
 
 FIRST AND SECOND YEAR 
 
 [Oral 
 
 THE NUMBERS TEN AND ELEVEN 
 
 10 = ^ -i d 4 D Pi 2's 
 9 8 7 6 5 !, 1 
 Two 5*s 
 
 11 
 
 12 3 4 5 
 10 9 8 7 6 
 
 Eleven 1' 
 
 Illustrate the combinations with convenient objects 
 or drawings. 
 
 1. Add up, then down : 
 
 
 
 
 
 
 10 2 1 
 
 1 
 
 4 
 
 3 
 
 2 
 
 4 
 
 2 4 3 3 9 
 
 6 
 
 5 
 
 1 
 
 5 
 
 7 
 
 8 6 5 7 1 
 
 4 
 
 2 
 
 6 
 
 2 
 
 
 
 2. From 10 take 3 ; take 5 ; 7 ; 8 ; 4 ; 2 ; 9. 
 
 3. .Give missing numbers : 
 
 2x 5, + ?=11 
 11-9 = ? 
 11-4 = ? 
 
 4 + 4 + ?= 11 3 + 3 + 3+? = 11 
 
 5 + 5 + ?= 11 5x2, + ?=11 
 
 6 + 3 + ?= 11 6x1, + ?= 11 
 
 4. Name the piece of mone}^ that has the same value 
 as ten pennies. 10 cents equal one dime. 
 
 5. How many nickels equal 1 dime ? 
 
 6. 5 dollars + 3 dollars + ? = 11 dollars. 
 
 The sign $ may be used for the word dollar or dollars, 
 and the sign ^ indicates cent or cents. $ 8 + $ 3 = ? 
 $5 + $6 = ? $9 + 82=? 4^ + 7^ = ? 10^+1^=? 
 
 7. In 11, there are 4's and over. 
 
 In 11, there are 5's and over. 
 
 In 11, there are 
 
 3's and 
 
 over. 
 
Oral] 
 
 
 NUMBERS TO TWELVE 
 
 THE NUMBER TWELVE 
 
 lb 
 
 1. Draw 12 lines. Erase J of 
 them. What is i of 12 ? 
 
 2. Count the eggs that you 
 see in the basket. 
 
 3. What name is sometimes 
 given to 12 eggs ? to 12 pins ? 
 to 12 lemons ? 
 12 things equal one dozen. 
 4. How many oranges equal ^ of a dozen ? 
 6. What number is doubled to make 12 ? 
 
 6. Make problems with : 
 4x3 cents 3x4 apples 
 
 6x2 horses 5x2 dollars 
 
 1 of 12 peaches 
 
 Subtract at sight : 
 
 1 of 12 cars 
 
 2x6 games 
 2x4 cakes 
 J of 12 apples 
 
 r 
 
 7. 12 
 
 12 
 
 12 
 
 12 
 
 12 
 
 12 
 
 12 
 
 12 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2 
 
 8. 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 tn 
 
 11 
 
 11 
 
 11 
 
 11 
 
 11 
 
 11 
 
 11 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 2 
 
 xo. Make problems with the above numbers. 
 
14 
 
 FIRST AND SECOND YEAR [Oral and Written 
 
 WRITING AND READING NUMBERS 
 
 1. Count thirteen, written 13. 
 
 2. Count fourteen, written 14. 
 
 3. Count fifteen, written 15. 
 
 4. Write sixteen, seventeen, eighteen, nineteen. 
 
 The figure is called naught, or zero. It stands for 
 nothing. When placed to the right of 1, the figures 
 stand for teii ; when placed to the right of 2, the figures 
 stand for tiventy. 
 
 5. Count twenty-one, written 21 ; twenty-two, writ- 
 ten 22 ; twenty-five, written 25. 
 
 6. Write twenty-six, twenty -seven. 
 
 7. Count thirty, written 30; forty, 40; fifty, 50; 
 sixty, 60 ; seventy, 70 ; eighty, 80 ; ninety, 90. 
 
 Count ninety-nine, written 99. 
 
 8. Make a number 
 
 board and write numbers 
 to 99 thus : 
 
 The first column is 
 made up of the ten 
 
 digits. 
 
 9. Write in figures : 
 Twenty-five, thirty-five, 
 forty-three, seventy- 
 three, sixty-four, eighty- 
 four, fifty-five, seventy-six. 
 
 Twenty-five cents. 
 
 Forty-five cents. 
 
 10 20 
 1121 
 
 12 2'j 
 
 13 23 
 14124 
 I5I25 
 1626 
 
 17 
 
 18 
 19 
 
 27 
 28 
 29 
 
 30 
 31 
 
 32 
 
 33 
 
 34 
 35 
 36 
 37 
 
 38 
 39 
 
 40 
 41 
 42 
 
 50 
 51 
 
 52162 
 
 435363 
 54:64 
 55J65 
 
 46156 66 
 
 44 
 45 
 
 57 
 
 58 
 59 
 
 67 
 68 
 69 
 
 70 
 71 
 
 72 
 
 80 
 81 
 
 82 
 
 83 
 
 90 
 91 
 
 92 
 
 93 
 
 76 
 
 77 
 
 8494 
 85|95 
 86 96 
 
 87 
 
 88 
 
 89 
 
 97 
 98 
 99 
 
 Sixty dollars. 
 Seventy-one dollars. 
 
Oral] 
 
 
 ADDITION 
 
 IIP 1. Head: 
 14 24 
 
 55 
 
 READING NUM] 
 
 48 51 
 
 15 34 
 
 56 
 
 49 56 
 
 16 44 
 
 57 
 
 ■ 50 59 
 
 15 
 
 64 
 
 70 
 
 91 
 
 40 
 
 60 
 
 80 
 
 90 
 
 55 
 
 76 
 
 89 
 
 99 
 
 73 
 
 The right-hand figure in a number is called ones' 
 figure ; the second figure is called tens' figure. 
 
 Point out the ones and the tens in each of the above 
 numbers; thus, 14 is 1 ten and 4 ones. 
 
 Table of Combinations in Addition 
 
 In addition there are 45 different combinations of 
 figures, taken two at a time, and 17 different sums or 
 amounts. Use these combinations for drill frequently : 
 
 1 
 
 
 2 
 
 
 2 3 3 
 
 4 
 
 
 
 3 
 
 4 
 
 5 
 
 1 
 
 
 1 
 
 
 2 1 2 
 
 1 
 
 
 
 3 
 
 2 
 
 1 
 
 4 
 
 5 
 
 6 
 
 
 4 5 6 7 
 
 
 
 5 
 
 6 
 
 7 
 
 8 
 
 3 
 
 2 
 
 1 
 
 
 i. 1 1 1 
 
 
 
 4 
 
 3 
 
 2 
 
 1 
 
 5 
 
 6 
 
 7 8 
 
 9 
 
 
 
 
 6 
 
 7 
 
 8 
 
 9 
 
 5 
 
 4 
 
 3 2 
 
 1 
 
 
 
 
 5 
 
 4 
 
 3 
 
 2 
 
 6 
 
 7 
 
 8 9 
 
 
 7 8 9 
 
 
 
 
 7 
 
 8 
 
 9 
 
 6 
 
 5 
 
 4 3 
 
 
 6 5^ 4 
 
 
 
 
 7 
 
 6 
 
 
 8 
 
 9 
 
 
 
 8 9 
 
 
 9 
 
 
 
 
 9 
 
 7 
 
 6 
 
 
 
 8 7 
 
 
 8 
 
 
 
 
 9 
 
16 
 
 FIRST AND SECOND YEAR 
 
 [Written 
 
 4 
 
 5 
 
 6 
 
 IV 
 
 V 
 
 VI 
 
 10 
 
 11 
 
 12 
 
 X 
 
 XI 
 
 XII 
 
 ROMAN NUMBERS TO TWENTY 
 
 1. The Romans wrote all numbers 
 up to 49 with the use of three let- 
 ters, I, Y, X. I stands f or 1 ; V 
 stands for 5; X stands for 10. 
 
 2. This is how the Romans wrote 
 their first twelve numbers : 
 
 1 2 3 
 
 I II III 
 
 7 8 9 
 
 VII VIII IX 
 
 3. Write the first twelve Roman numbers from 
 memory. 
 
 4. Read the Roman numbers on the clock face. 
 On clock faces IIII is used for IV. 
 
 5. Copy the following numbers : 
 . 13 14 15 16 17 
 XIII XIV XV XVI XVII 
 
 6. Write in Roman numbers, 9. 
 in the letters will make 11. 
 
 7. Write the Roman numbers from 1 to 20. 
 
 8. What time is it by the clock in the picture ? 
 
 The short hand is called the hour hand. The long 
 hand is called the minute hand. 
 
 9. Show the position of the hands at 30 minutes 
 after 9 ; at 30 minutes after 10 ; at 30 minutes after 11. 
 
 18 1^ 20 
 
 XVIII XIX XX 
 
 Show what change 
 
Oral and Written] ADDITION 17 
 
 t ADDITION 
 
 Sti 
 
 State sums at sight : 
 
 ah c d ^ f 9 7i i j 
 
 22 2 2222222 
 
 76 82 7462504153643072 
 
 2. Change the 2 above to 3 and add ; then to 4 : 
 
 3. 2222222222 
 85 65 75 55 45 63 73 93 43 83 
 
 4. 3333444444 
 
 59496979 4938 48 8878 5_8 
 
 5. 2324625252 
 42 3232435 
 3^43 1041^103 
 
 6. A boy spent 25 cents for a book and 12 cents 
 for a slate. How much did he spend for both? 
 
 Write ones under ones and tens under 
 25 cents tens. Add the right-hand column and 
 12 cents place the total, 7, underneath. Add the 
 37 cents second column and write the total un- 
 derneath. The answer is 37 cents. 
 
 IB 7. Find the sum of : 
 
 25 apples and 63 apples 24 boys and 15 boys 
 
 37 cakes and 42 cakes 32 chairs and 26 chairs 
 
 81 lemons and 17 lemons 47 books and 22 books 
 
 42 balls and 24 balls 36 bats and 52 bats 
 
18 FIRST AND SECOND YEAR [Written 
 
 Add: 
 
 
 
 
 
 
 
 a 
 
 h 
 
 c 
 
 d 
 
 e 
 
 / 
 
 9 
 
 1. 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 30 
 
 50 
 
 30 
 
 10 
 
 10 
 
 20 
 
 10 
 
 40 
 
 30 
 
 2. 
 
 3. 
 
 31 
 
 21 
 
 23 
 
 32 
 
 12 
 
 30 
 
 69 
 
 12 
 
 32 
 
 13 
 
 23 
 
 33 
 
 13 
 
 20 
 
 42 
 
 44 
 
 44 
 
 43 
 
 14 
 
 33 
 
 82 
 
 21 
 
 23 
 
 24 
 
 34 
 
 44 
 
 23 
 
 14 
 
 Add upward ; test by adding downward : 
 
 4. $45 $25 $35 • $34 $42 $55 $44 
 
 $14 $33 $54 $35 $45 $33 $22 
 
 5. 
 
 S16 
 
 $45 
 
 $67 
 
 $72 
 
 $81 
 
 $83 
 
 $59 
 
 S31 
 
 $54 
 
 $21 
 
 $25 
 
 $12 
 
 $15 
 
 $20 
 
 Only things having like names can be added. 
 
 a b c d e 
 
 6. 17 boys 36 caps 56 balls 35^ 46 ft. 
 
 12 boys 21 caps 32 balls 24^ 22 ft. 
 
 7. 
 
 a 
 12 girls 
 10 girls 
 23 girls 
 
 b 
 34 men 
 22. men 
 41 men 
 
 c 
 14 tops 
 13 tops 
 21 tops 
 
 d 
 15 books 
 20 books 
 31 books 
 
 14 cars 
 32 cars 
 22 cars 
 
 12 boxes 
 43 boxes 
 31 boxes 
 
 26 hats 
 42 hats 
 31 hats 
 
 16 days 
 22 days 
 41 days 
 
Written] 
 
 ADDITION 
 
 19 
 
 I 
 
 ADDITION 
 
 1. There are 54 houses on one street and 28 on an- 
 other. How many are there on both streets ? 
 ( Write ones under ones and tens under 
 
 54 houses tens. Add the ones' column. The sum 
 28 houses is 12 ones, or 1 ten and 2 ones. Write 
 82 houses the 2 under the ones' column and add 
 f the 1 ten to the tens' column. 1 ten + 2 
 
 ^ens + 5 tens = 8 tens. The answer is 82 houses. 
 
 I 
 
 Add and test : 
 a b 
 
 2. 36 47 
 25 24 
 
 c d 
 
 42 54 
 39 36 
 
 « 
 
 48 
 34 
 
 35 
 
 27 
 
 64 
 
 28 
 
 3. 46 
 
 19 
 
 29 
 
 18 
 
 38 
 
 17 
 
 39 
 
 36 
 
 24 
 
 10 
 
 36 
 
 17 
 
 46 
 
 45 
 
 4. 19 
 
 21 
 
 32 
 
 23 
 
 31 
 
 42 
 
 13 
 
 14 
 
 19 
 
 4 
 
 15 
 
 43 
 
 16 
 
 46 
 
 3 
 
 12 
 
 16 
 
 6 
 
 8 
 
 17 
 
 18 
 
 5. 11 
 
 16 
 
 19 
 
 41 
 
 39 
 
 42 
 
 15 
 
 31 
 
 10 
 
 20 
 
 23 
 
 20 
 
 18 
 
 41 
 
 29 
 
 49 
 
 17 
 
 18 
 
 18 
 
 20 
 
 38 
 
 6. 30 
 
 40 
 
 32 
 
 9 
 
 8 
 
 15 
 
 13 
 
 17 
 
 19 
 
 30 
 
 14 
 
 20 
 
 20 
 
 68 
 
 28 
 
 34 
 
 9 
 
 16 
 
 9 
 
 38 
 
 14 
 
 7. Count by 3's to 36 ; to 75. By 4's to 88. 
 
20 FIRST AND SECOND YEAR [Written 
 
 ADDITION 
 
 1. Thomas has $24 in the bank and $17 in his 
 pocket. How many dollars has he ? 
 
 2. A farmer sold 26 bushels of apples on Monday, 
 35 bushels on Tuesday, and 30 bushels on Wednesday. 
 How many bushels did he sell in the three days ? 
 
 3. On Tuesday a newsboy sold 28 morning papers 
 and 44 evening papers. How many papers did he sell ? 
 
 4. A girl had 42 cents left after spending 25 cents 
 for ribbon and 10 cents for pins. How much money 
 had she at first ? 
 
 5. Mrs. Jackson spent $24 for a suit, $31 for a coat, 
 and $12 for a hat. How much did all cost ? 
 
 6. Fred planted 29 potatoes in one row, 31 in an- 
 other, and 33 in a third row. How many potatoes did 
 he plant all together ? 
 
 7. Ned spent 35^ for a ball, 25^ for a bat, and 10/ 
 for car fare. How much did he spend ? 
 
 8. The girls spent at the park, 1 5 / for ice cream, 
 20/ on the roller coaster, 35/ in the picture gallery, 
 and 12/ for popcorn. How much did they spend for 
 all? 
 
 9. It took Mary 16 minutes to sweep and dust the 
 library, 12 minutes for the dining room, and 21 minutes 
 for the parlor. How long did it take for the three rooms ? 
 
 10. Edwin has 43 marbles, and Walter has 24 more 
 than Edwin. How many marbles has Walter ? 
 
Oral] SUBTRACTION 21 
 
 B SUBTRACTION 
 
 ^ 1. Mary has 9 cents. She spends 5 cents. How 
 many cents has she left ? 
 
 2. A farmer had 7 cows. After selling a number he 
 had 4 left. How many did he sell ? 
 
 IB ^' ^^^^ ^^^ 1^ towels to iron. When she had 
 ironed 9, how many were left to iron ? 
 
 IB 4. Liicy had 12 roses and gave Mary 5 roses. How 
 'many roses had Lucy left ? 
 
 Table of Combinations in Subtraction 
 
 In subtraction there are 45 different combinations of 
 figures, taken two at a time. Use these combinations 
 for drill frequently : 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 9 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 8 
 
 rr 
 i 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 1 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 6 
 
 6 
 
 6 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 1 
 
 2 
 
 3 
 
 G 
 
 6 
 
 6 
 
 5 
 
 5 
 
 5 
 
 5 
 
 5 
 
 4 
 
 4 
 
 5 
 
 6 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 1 
 
 4 
 
 4 
 
 4 
 
 3 
 
 3 
 
 3 
 
 2 
 
 2 
 
 1 
 
 1 "* 
 
 3 
 
 4 
 
 1 
 
 2 
 
 3 
 
 1 
 
 2 
 
 1 
 
 1 — 
 1 
 
 
 
 
 ~ 
 
 — 
 
 ~ 
 
 
 ~ 
 
22 
 
 FIRST AND SECOND YEAR 
 
 [Writtea 
 
 SUBTRACTION 
 
 1. James had 48 cents. He spent 25 cents. How 
 
 many cents had he then ? 
 48 cents Write ones under ones and tens under 
 
 25 cents tens, 8 ones — 5 ones = 3 ones. Write the 
 23 cents three ones in ones' place. 4 tens — 2 tens = 
 
 2 tens. The answer is 23 cents. 
 
 Test— 23 + 25 = 48. 
 Only like numbers can be subtracted. 
 Subtract and test : 
 
 a b c d e 
 
 2. 44 38 56 64 49 
 22 13 13 21 23 
 
 / 
 
 ff 
 
 65 
 
 45 
 
 32 
 
 23 
 
 3. 58 
 
 65 
 
 68 
 
 57 
 
 69 
 
 86 
 
 77 
 
 33 
 
 41 
 
 15 
 
 24 
 
 34 
 
 42 
 
 33 
 
 4. 77 
 
 88 
 
 75 
 
 96 
 
 87 
 
 94 
 
 52 
 
 44 
 
 55 
 
 25 
 
 46 
 
 53 
 
 41 
 
 40 
 
 5. 67 
 
 59 
 
 88 
 
 97 
 
 76 
 
 85 
 
 34 
 
 52 
 
 45 
 
 56 
 
 27 
 
 86 
 
 64 
 
 30 
 
 6. 99 
 
 96 
 
 87 
 
 79 
 
 98 
 
 77 
 
 59 
 
 38 
 
 74 
 
 64 
 
 38 
 
 84 
 
 63 
 
 50 
 
 7. 89 
 
 94 
 
 59 
 
 97 
 
 99 
 
 89 
 
 74 
 
 19 
 
 91 
 
 18 
 
 82 
 
 29 
 
 78 
 
 24 
 
 8. Make and solve 50 examples like the above. 
 
Written] PRACTICAL PROBLEMS 23 
 
 k 
 
 PRACTICAL PROBLEMS 
 
 1. David is 1 4 years old and Walter is 7 years younger. 
 How old is Walter ? 
 
 • 2. Edna spent 35 cents for butter. She gave the clerk 
 a half-dollar. How much change should she receive ? 
 
 3. A postal clerk sold 43 postal cards one week, 
 and 67 the next week. How many more did he sell in 
 the second week than in the first week ? 
 
 4. A man lives 68 miles from the city and has trav- 
 eled 24 miles toward the city. How many miles has he 
 yet to travel ? 
 
 5. Tom drove home 78 cows and Ned 56. How 
 many more cows were there in Tom's herd than in Ned's? 
 
 6. Edna had 78 pieces in her doll's dinner set, but 36 
 plates were broken. How many pieces remained ? 
 
 7. Mr. Wilson's farm contains 76 acres of land, which 
 is 14 acres more than his brother's farm contains. How 
 many acres are there in his brother's farm ? 
 
 8. William rode 27 miles on his bicycle on Thursday 
 and 14 miles on Friday. How much farther did he ride 
 the first day than the second ? 
 
 9. Make problems with : 
 
 pupils $ pictures lamps books 
 
 46-14 37-24 63-12 48-36 73-21 
 66-43 62-31 84-21 46-24 36-15 
 
 10. 34 children were invited to Kate's party. How 
 many of them were absent, if only 22 of them attended? 
 
24 
 
 FIRST AND SECOND YEAR 
 
 [Oral 
 
 He could 
 
 MULTIPLICATION 
 
 1. What is the cost of two 2-cent pencils? 2x2^=? 
 
 2. How much should you pay for three 2-cent apples ? 
 four 2-cent tops ? five 2-cent stamps ? six 2-cent papers ? 
 
 3. James counted 2^ seven times; thus, 2^ + 2^ + 2^-1- 
 2^ + 2^ + 2^ + 2^, and found that he had 14^. 
 have said seven 2's are 14, or 7 x 2 = 14. 
 
 4. Write in two other forms : 8x2 = 16; 
 nine 2's = 18; 10x2 = 20. 
 
 5. Build the table of 2's thus : 
 Write the sum of each column 2 
 
 beneath it. Look at each column. 2 2 
 
 See how many 2's it contains. Say, 
 
 1x2 = 2; 2x2 = 4; 3x2 = 6; 4x2 = 8; 5x2 = 10; 
 
 6x2 = 12; etc. 
 
 6. Find products : 
 
 5x2 caps 8x2 plums 9x2 birds 4x2 cups 
 6x2 dolls 3x2 hats 7x2 birds 2x2 hats 
 
 7. Memorize the table. 
 
 Table of 2»s 
 
 1x2= 2 
 
 6x2 = 12 
 
 2x2= 4 
 
 7x2 = 14 
 
 3x2= 6 
 
 8x2 = 16 
 
 4x2= 8 
 
 9x2-18 
 
 5x2 = 10 
 
 10x2 = 20 
 
 8. Multiply each number outside the circle by 2. 
 
I 
 
 Oral and Written] MULTIPLICATION 25 
 
 \ 1. How many are two 7's ? two lO's ? 
 
 2. Write these two problems in two other ways. 
 
 3. How many are two 34's ? This may be written : 
 
 34 + 34 = 68, or 34 
 
 4- 34 The sum of two 34's is 68. 
 
 68, sum. 
 t 4. A shorter process for finding two 34's is by multi- 
 plication ; written thus, 34 Write the multi- 
 
 ^ ^ plier 2 under the 
 
 68 right-hand figure 
 
 of the number to be multiplied, which is 34. Beginning 
 at the right, say 2x4 = 8. Write 8 in ones' place in 
 the answer. 2x3 = 6. Write 6 in tens' place in the 
 answer. The result is 68. Test by addition, 34 + 34 = 68. 
 
 Multiply, and test by addition : 
 
 a b c d e f 
 
 23 54 53 64 71 62 
 
 2 2 2 2 2 2 
 
 6. 40 81 94 70 63 53 
 _2 _^ _2 _2^ _2 _2 
 
 7. 93 72 62 53 82 91 
 
 2 2 2 2 2 2 
 
 44 
 
 32 
 
 83 
 
 24 
 
 84 
 
 74 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 11 
 
 73 
 
 22 
 
 33 
 
 92 
 
 44 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 _2 
 
26 FIRST AND SECOND YEAR [Oral and Written 
 
 DIVIDING BY 2 
 
 ^' II II II II II Count the splints by 2's. 
 How many times must two splints be taken to have 
 10 splints ? 10 splints contain 2 splints times. 
 
 2. 6 contains 2 times. 8 contains 2 
 
 times. 12 contains 2 times. 
 
 3. Into bow many groups of two each may 10 be 
 divided ? 10 divided by 2 equals 5, written 
 
 10 -^ 2 = 5, or 2)10. The sign -^ is read divided by. 
 5 
 
 Read, and give answers : 
 
 4. 4-2; 6-h2; 8-^2; 10^2. 
 
 5. 2)8; 2)10; 2}6 ; 2]1_2. 
 
 6. Divide 24 by 2. 
 
 2 is contained in 2 tens, 1 ten time; 
 2)24 write 1 in tens' place. 2 is contained in 
 12 4 ones, 2 times; wTite 2* in ones' place. 
 The answer is 12. 
 
 Find the answers : 
 
 a b c d e 
 
 7. 2)22 2)24 2)_26 2)_44 2)20 
 
 8. 2)28 2)40 2)48 2)42 2)_46 
 
 9. 2)_62 2)_66 2)60 2)64 2)_68 
 10. 2)80^ 2)_84 2)88 2)_86 2]82 
 
Oral] MEASURING LENGTH 27 
 
 MEASURING LENGTH 
 
 For this exercise the teacher should secure a foot rule and a yard 
 stick. 
 
 1. Examine a foot rule. Observe that it is divided 
 into 12 equal spaces. Each space is called one inch. 
 A foot rule is therefore 12 inches long. 
 
 2. The following represents a foot rule, although it 
 is only one fourth the real length. Count the number 
 of inch spaces. 
 
 -^+hH-H ' . l' M:^MIUI '|i j,| il WMi. |i | i ^ i|i .| i UcJl i y i |A | 
 
 3. Cut from cardboard a foot rule and mark the 
 inches on it. 
 
 4. With the rule draw a line 1 inch long ; 4 inches 
 long. 
 
 5. How many inches equal J of a foot ? J of a foot ? 
 1 of a foot ? 
 
 6. Draw an oblong 12 inches long and 8 inches 
 wide. How many inches is it around the oblong ? 
 
 7. Draw a 2-inch square. How many inches is it 
 around the square ? 
 
 8. Measure a yard stick with your foot rule. This 
 shows that there are 3 feet in a yard. 
 
 9. Mark off with the yard stick on the blackboard a 
 line 1 foot in length ; 2 feet in length ; 1 yard in 
 length. 
 
 10. How many feet equal 2 yards ? J of a yard ? 
 
28 FIRST AND SECOND YEAR [Written 
 
 REVIEW 
 
 1. A man paid $ 80 for 2 cows. How many dollars 
 did each cost ? 
 
 2. A family bought 48 pints of milk in a month. 
 How many quarts did they buy ? 
 
 3. How much will 2 lb. of tea cost at 40^ a pound ? 
 
 4. How many 2-cent stamps can be bought for 64 
 cents ? 
 
 5. Eva paid 86 cents for 2 yards of linen. What 
 was the cost of 1 yard ? 
 
 6. If Ruth takes 2 piano lessons every w^eek, how 
 many does she take in 44 weeks ? 
 
 7. A girl is 14 years old. Her brother is twice as 
 old. How old is her brother ? 
 
 8. How many pints are there in 44 quarts ? 
 
 9. If a clerk earns $ 44 a month, how much will he 
 earn in 2 months ? 
 
 10. Dick has 68 cents. He gives 35 cents to Kate. 
 How many cents has he left ? 
 
 11. If molasses costs 14 cents a pint, how much will 
 a quart cost ? 
 
 Find the cost of : 
 
 12. 2 pieces of soap at 10 cents a piece. 
 
 13. 2 pounds of butter at 24 cents a pound. 
 
 14. 2 dozen lemons at 12 cents a dozen. 
 
 15. 2 yards of muslin at 11 cents a yard. 
 
PART II — THIRD YEAR 
 READING AND WRITING NUMBERS 
 
 1. Count to one hundred. One hundred is written 100. 
 
 2. Count to one hundred one, written 101. 
 
 3. Write in figures : one hundred four ; one hundred 
 five ; one hundred seven. 
 
 4. Read, then write in words : 103, 105, 107, 109. 
 
 5. Add 100 to 100. The sum is two hundred, writ- 
 ten 200. Add 200 to 100. The sum is three hundred, 
 written 300. 
 
 6. Read, then write in words : 400, 500, 601, 700, 
 802, 900, 501, 404. 
 
 Read: 
 a 
 7. 109 
 
 6 
 309 
 
 e 
 
 506 
 
 d 
 
 836 
 
 e 
 
 707 
 
 8. 110 
 
 310 
 
 340 
 
 741 
 
 888 
 
 9. 112 
 
 311 
 
 765 
 
 952 
 
 999 
 
 The largest number that can be written with three 
 figures is 999. The next number is one thousand, 
 written 1000. 
 
 Write in figures : 
 
 10. Two thousand. 
 
 11. Five thousand. 
 
 12. Six thousand. 
 
 13. Seven thousand. 
 
 14. Eight thousand. 
 
 15. Nine thousand. 
 
 29 
 
30 THIRD YEAR [Oral and Written 
 
 16. Add 1 to 1000. The sum is one thousand one, 
 written 1001. 
 
 Write in figures : 
 
 17. One thousand two. 20. One thousand seven. 
 
 18. One thousand nine. 21. One thousand eight. 
 
 19. One thousand six. 22. One thousand three. 
 
 The first figure on the right is called the ones' figure ; 
 the next is called the tens' figure ; the next is called 
 the hundreds' figure ; the next is called the thousands' 
 figure. The tens are always read as so many ones. 
 Thus, 1625 is read, " 1 thousand, 6 hundred, 25." In 
 25, the 2 tens are read as 20. 
 
 ] 
 
 Read, then write : 
 
 
 
 
 23. 
 
 a 
 1025 
 
 6 
 2040 
 
 c 
 7028 
 
 d 
 1010 
 
 e 
 8099 
 
 24. 
 
 1125 
 
 2141 
 
 9208 
 
 1011 
 
 8999 
 
 25. 
 
 1139 
 
 3005 
 
 6721 
 
 2111 
 
 9999 
 
 26. 
 
 2014 
 
 4020 
 
 6099 
 
 7509 
 
 8001 
 
 Write as one number : 
 
 27. 6 hundreds, 4 tens, 8 ones. 
 
 28. 8 thousands, 5 hundreds, 3 tens, 3 ones. 
 
 29. 4 thousands, hundreds, 8 tens, 5 ones. 
 
 30. 5 thousands, hundreds, tens, 9 ones. 
 
 31. 9 thousands, 4 hundreds, tens, 5 ones. 
 
Oral and Written] 
 
 ADDITION 
 
 81 
 
 »K ADDITION 
 
 ^^ (Review pages 17 to 20) 
 
 1. Count from 2 to 100 by 2's. 
 2. Count from 1 to 101 by 2's. 
 1^ 3. Count from 3 to 102 by 3's. 
 
 4. Count from 4 to 100 by 4's. 
 
 5. Count from 1 to 101 by 4's. 
 
 6. Add the number in the cen- 
 ter to each number outside the circle. 
 
 7. Add 3 to each of the following numbers ; then 4 ; 
 then 5 : 
 
 m 
 
 24 
 
 34 
 
 
 44 
 
 
 55 
 
 65 
 
 75 
 
 36 
 
 46 
 
 
 66 
 
 
 66 
 
 76 
 
 86 
 
 47 
 
 67 
 
 
 27 
 
 
 38 
 
 58 
 
 78 
 
 Find sums. 
 
 Test 
 
 by adding 
 
 downwards : 
 
 
 a 
 
 
 6 
 
 
 C 
 
 
 d 
 
 e 
 
 8. 23 
 
 
 32 
 
 
 42 
 
 
 45 
 
 51 
 
 13 
 
 
 23 
 
 
 32 
 
 
 51 
 
 42 
 
 43 
 
 
 43 
 
 
 44 
 
 
 54 
 
 14 
 
 9. 44 
 
 
 21 
 
 
 53 
 
 
 32 
 
 31 
 
 55 
 
 
 32 
 
 
 32 
 
 
 24 
 
 24 
 
 33 
 
 
 12 
 
 
 43 
 
 
 32 
 
 32 
 
 The process of uniting two or more numbers to form 
 one number is called addition. 
 
 The numbers united are called addends. 
 
 The answer in addition is called the sum or amount. 
 
32 
 
 THIRD YEAR 
 
 [Written 
 
 ADDITION 
 
 1. Add 234, 359, and 266. 
 
 234 = 2 hundreds -f 3 tens + 4 ones 
 359 = 3 hundreds + 5 tens + 9 ones 
 266 = 2 hundreds + 6 tens 4- 6 ones 
 859 = 7 hundreds + 14 tens + 19 ones. 
 
 19 ones = 1 ten and 9 ones. Write the 9 in ones* 
 place and carry the 1 ten to tens' place. 14 tens + 1 
 ten =15 tens. Write the 5 in tens' place and carry 
 the 1 to hundreds' place. 7 hundreds + 1 hundred = 
 8 hundreds. 
 
 Write from dictation, then add and test : 
 
 
 a 
 
 6 
 
 c 
 
 d 
 
 e 
 
 / 
 
 2. 
 
 234 
 
 230 
 
 101 
 
 231 
 
 301 
 
 243 
 
 
 326 
 
 325 
 
 304 
 
 405 
 
 226 
 
 206 
 
 
 434 
 
 265 
 
 376 
 
 568 
 
 304 
 
 306 
 
 3. 
 
 405 
 
 304 
 
 604 
 
 400 
 
 291 
 
 905 
 
 
 304 
 
 349 
 
 787 
 
 697 
 
 743 
 
 634 
 
 
 296 
 
 200 
 
 842 
 
 345 
 
 456 
 
 393 
 
 4. 
 
 623 
 
 344 
 
 23 
 
 509 
 
 20 
 
 502 
 
 
 5 
 
 593 
 
 906 
 
 5 
 
 102 
 
 205 
 
 
 340 
 
 25 
 
 25 
 
 820 
 
 67 
 
 50 
 
 5. 
 
 708 
 
 931 
 
 68 
 
 7 
 
 423 
 
 791 
 
 
 55 
 
 67- 
 
 834 
 
 751 
 
 92 
 
 8 
 
 
 634 
 
 8 
 
 436 
 
 534 
 
 899 
 
 958 
 
Written] 
 
 I 
 
 ADDITION 
 ADDITION 
 
 33 
 
 Add rapidly : 
 
 abcdefgh 
 
 1. 54321987 
 98632052 
 01256267 
 18043616 
 83685638 
 76505981 
 25998273 
 69310437 
 
 j k I m n 
 
 6 6 8 
 
 7 3 7 
 9 3 
 
 8 3 9 
 3 4 
 9 6 
 9 3 
 5 
 
 3 2 
 
 5 3 
 
 7 3 
 
 8 
 
 6 5 
 8 6 
 
 8 9 5 
 
 9 4 3 
 
 300 
 
 5 
 794 
 896 
 
 25 
 
 29 
 330 
 
 57 
 
 8 
 
 901 
 
 6 
 306 
 
 27 
 
 407 
 
 92 
 
 602 
 74 
 
 909 
 40 
 29 
 
 90 
 67 
 80 
 395 
 74 
 
 Write from dictation, then add : 
 
 
 
 
 a 
 
 6 
 
 c 
 
 d 
 
 e 
 
 / 
 
 9 
 
 2. 305 
 
 542 
 
 740 
 
 8 
 
 70 
 
 79 
 
 500 
 
 79 
 
 67 
 
 90 
 
 48 
 
 84 
 
 342 
 
 7 
 
 6 
 
 500 
 
 708 
 
 600 
 
 395 
 
 9 
 
 48 
 
 394 
 
 9 
 
 502 
 
 540 
 
 4 
 
 805 
 
 6 
 
 3. 562 
 
 807 
 
 60 
 
 536 
 
 28 
 
 42 
 
 62 
 
 9 
 
 58 
 
 547 
 
 67 
 
 906 
 
 790 
 
 203 
 
 645 
 
 6 
 
 44 
 
 25 
 
 627 
 
 7 
 
 636 
 
 834 
 
 526 
 
 782 ■ 
 
 981 
 
 8 
 
 856 
 
 93 
 
 67 
 500 
 395 
 
 70 
 5 
 
34 THIRD YEAR [Written 
 
 ADDITION 
 
 1. Find the sum of 2430, 4307, and 68. 
 2430 = 2 thousands + 4 hundreds + 3 tens + ones 
 4307 = 4 thousands + 3 hundreds + tens -f- 7 ones 
 68 = thousands + hundreds + 6 tens 4- 8 ones 
 6805 = 6 thousands + 7 hundreds + 9 tens H- 15 ones. 
 
 15 ones = 1 ten + 5 ones. 1 ten + 9 tens = 10 tens 
 or 1 hundred. 1 hundred + 7 hundreds = 8 hundreds. 
 4 thousands + 2 thousands = 6 thousands. 
 
 Write from dictation, then add : 
 
 2. 
 
 a 
 
 b 
 
 C 
 
 d 
 
 e 
 
 23 
 
 378 
 
 298 
 
 1008 
 
 603 
 
 604 
 
 49 
 
 342 
 
 49 
 
 2798 
 
 3068 
 
 3067 
 
 6781 
 
 706 
 
 6987 
 
 1304 
 
 2004 
 
 4987 
 
 • 3740 
 
 6425 
 
 279 
 
 3050 
 
 . 9 
 
 609 
 
 4020 
 
 6000 
 
 50 
 
 807 
 
 4203 
 
 205 
 
 200 
 
 674 
 
 5002 
 
 6001 
 
 1347 
 
 6870 
 
 5475 
 
 64 
 
 21 
 
 3006 
 
 2 
 
 2681 
 
 370 
 
 2102 
 
 2904 
 
 3078 
 
 5004 
 
 4274 
 
 3478 
 
 799 
 
 2690 
 
 79 
 
 5007 
 
 9 
 
 6094 
 
 5. 2 + 3 + 7 + 9 + 6=? 7. 7 + 6 + 5 + 2 + 6 + 7=? 
 
 6. 6 + + 7 + 8 + 5=? 8. 5 + 4 + 3 + 8 + 6 + 9=? 
 
Written] ADDITION 35 
 
 I^^K ADDITION 
 
 l^^vi^rite from dictation, then add : 
 
 ■^ 1. Twenty-five ; two hundred twenty-five ; three 
 hundred fifty. 
 
 If 2. Four hundred two; seventy-three; nine; five 
 
 hundred sixty. 
 IB 3. Four thousand twenty; six hundred six; five. 
 
 4. Six hundred ninety; ten; three hundred; two 
 thousand four. 
 
 5. Two hundred eighty ; nineteen ; six ; one 
 thousand. 
 
 6. 230 + 65 -f- 100 + 405. 
 
 7. 300 + 9 + 25 -f 500. 
 
 8. 65^ + 10^+100^ + 1000^. 
 
 9. $ 42 + $ 504 + $ 105 + $ 3. 
 
 10. 24 pt. + 120 pt. + 7 pt. + 36 pt. 
 
 11. 1000 qt. + 14 qt. + 135 qt. + 10 qt. 
 
 12. 174 pk. + 130 pk. + 5 pk. + 800 pk. 
 
 13. 1200 in. + 10 in. + 100 in. + 20 in. 
 
 14. 60 dimes + 4000 dimes + 4 dimes + 300 dimes. 
 
 15. 16. 17. 18 
 
 2000 hours 1370 minutes 40 gallons 409 days 
 
 146 hours 234 minutes 209 gallons 3090 days 
 
 9 hours 30 minutes' 2900 gallons 9 days 
 
 3472 hours 605 minutes 4 gallons 374 days 
 
36 THIRD YEAR [Written 
 
 ADDITION 
 
 Read and solve : 
 
 1. 2465 + 3642 + 4612 + 5534 + 6342 = ? 
 
 2. 4756 + 3254 + 4321 + 4132 + 3536 = ? 
 
 3. 4234 + 3512 + 2435 + 1543 + 2453 = ? 
 
 4. 5243 + 2453 + 3215 + 4123 + 4231 = ? 
 
 5. 6314 + 1355 + 2652 + 1623 + 3245 = ? 
 
 6. 7664 + 2845 + 6246 + 3664 + 4554 = ? 
 
 7. 6050 + 4004 + 1804 + 4536 + 6143 = ? 
 
 8. 3652 + 4630 + 5672 + 3867 + 5468 = ? 
 
 9. 4876 + 6724 + 4116 + 3442 + 4162 = ? 
 
 10. 3640 + 4466 + 7201 + 404 + 162 = ? 
 
 11. A carpenter had 23 men and hired 13 more. 
 How many had he then ? 
 
 12. Mr. Jones deposited $ 123 in a bank on Monday; 
 $232 on Tuesday; and $321 on Wednesday. How 
 much did he deposit in the three days ? 
 
 13. A ship sailed 223 miles the first day, 320 miles 
 the second, and 231 miles the third. How many miles 
 did it sail ? 
 
 14. A farmer raised 230 bushels of wheat, 122 bush- 
 els of corn, 112 bushels of oats, and 323 bushels of rye. 
 How many bushels of grain did he raise ? 
 
 15. Mrs. Foster bought a bedroom set of furniture for 
 $ 125, a piano for $ 350, curtains for $ 52, pictures for 
 $ 128, and a rug for $ 23. How much did they all cost ? 
 
SUBTRACTION 
 
 SUBTRACTION 
 
 (Review pages 21 to S 
 
 Give differences: 
 
 1^ 
 
 Give answers quickly : 
 
 37 
 
 X 7 
 
 6 
 
 5 
 
 4 
 
 13 
 
 8 
 
 9 
 
 11 
 
 10 
 
 1 -4 
 
 -5 
 
 -2 
 
 -3 
 
 -8 
 
 -4 
 
 -5 
 
 -3 
 
 -3 
 
 2. 13 
 
 6 
 
 8 
 
 9 
 
 7 
 
 10 
 
 12 
 
 11 
 
 8 
 
 -6 
 
 -3 
 
 -3 
 
 -7 
 
 -2 
 
 -7 
 
 -4 
 
 -5 
 
 _ 
 
 3. 8 
 
 9 
 
 7 
 
 15 
 
 5 
 
 12 
 
 11 
 
 17 
 
 8 
 
 -6 
 
 -8 
 
 -5 
 
 -7 
 
 -4 
 
 -9 
 
 -7 
 
 -9 
 
 -7 
 
 4. 9 
 
 13 
 
 8 
 
 9 
 
 10 
 
 12 
 
 11 
 
 12 
 
 7 
 
 -6 
 
 -5 
 
 -5 
 
 -2 
 
 -8 
 
 -7 
 
 -4 
 
 -6 
 
 -6 
 
 5. 13 
 
 14 
 
 10 
 
 12 
 
 9 
 
 10 
 
 11 
 
 12 
 
 15 
 
 -9 
 
 -8 
 
 -9 
 
 -2 
 
 -3 
 
 -4 
 
 -8 
 
 -8 
 
 -8 
 
 6. 16 
 
 15 
 
 13 
 
 14 
 
 15 
 
 16 
 
 14 
 
 12 
 
 11 
 
 -8 
 
 -9 
 
 -7 
 
 -7 
 
 -6 
 
 -9 
 
 -9 
 
 -3 
 
 -6 
 
 7. 
 
 8-3, 
 
 18-3; 
 
 28-3, 
 
 48-3, 
 
 58-3; 
 
 8. 
 
 11-4, 
 
 21-4; 
 
 31-4, 
 
 41-4 
 
 51-4; 
 
 9. 
 
 9-5, 
 
 49-5; 
 
 59-5 
 
 89-5 
 
 69-5; 
 
 10. 
 
 7-6, 
 
 ,17-6; 
 
 27-6; 
 
 37-6, 
 
 47-6; 
 
 11. 
 
 13-7 
 
 , 23-7; 
 
 33-7, 
 
 43-7, 
 
 53-7; 
 
 12. 
 
 15-8, 
 
 25-8; 
 
 35-8 
 
 , 45-8 
 
 , 55-8; 
 
 13. 
 
 26-9 
 
 ; 36-9; 
 
 46-9 
 
 ; 56-9 
 
 ; 66-9; 
 
 88-3, 
 61-4. 
 79-5. 
 97-6. 
 83-7. 
 75-8. 
 96-9. 
 
38 THIRD YEAR - [Written 
 
 SUBTRACTION 
 
 1. From 83 subtract 35. 
 
 83 = 8 tens + 3 ones, or 7 tens + 13 ones 
 35 = 3 tens + 5 ones 
 
 48 = 4 tens + 8 ones. 
 
 Since 5 ones cannot be taken from 3 ones, take 1 ten 
 ( = 10 ones) from the 8 tens (leaving 7 tens) and add 
 it to the 3 ones, making 13 ones. 13 ones less 5 ones 
 equal 8 ones. 7 tens (remaining) less 3 tens equal 4 tens. 
 Before subtracting, the work may be expressed thus : 
 We think: "5 from 13 leaves 8j 3 from 7 ^ ^^ 
 leaves 4 ; 48." 8 3 
 
 Test — 48 + 35 = 83. 3_5 
 
 The process of finding the difference between two 
 numbers is called subtraction. 
 
 The number from which we subtract is called the 
 minuend; the number subtracted is called the subtra- 
 hend ; the result is called the difference or remainder. 
 
 Subtract, and test each result : 
 
 a b c d e f g 
 
 2. 63 92 84 57 84 34 91 
 27 69 39 38 49 17 54 
 
 3. 48 
 
 74 
 
 81 
 
 63 
 
 92 
 
 • 86 
 
 84 
 
 29 
 
 47 
 
 29 
 
 44 
 
 74 
 
 58 
 
 45 
 
 4. 55 
 
 80 
 
 31 
 
 61 
 
 21 
 
 34 
 
 47 
 
 19 
 
 27 
 
 18 
 
 57 
 
 13 
 
 16 
 
 38 
 
Written] 
 
 
 SUBTEAOTION 
 
 
 38 
 
 IB Subtract and test 
 
 : 
 
 
 
 
 1 ^ 
 
 H 1. 769 
 IB 374 
 
 6 
 
 819 
 568 
 
 c 
 
 346 
 
 94 
 
 d 
 665 
 374 
 
 e 
 749 
 
 298 
 
 / 
 
 864 
 539 
 
 n 2. 332 
 11 ^^^ 
 
 748 
 339 
 
 552 
 429 
 
 175 
 
 68 
 
 729 
 549 
 
 534 
 360 
 
 3. Make, solve, and test 200 problems like the above. 
 
 4. From 803 subtract 576. 
 
 7 9 13 
 
 803 = 7 hundreds + 9 tens + 13 ones 
 
 576 = 5 hundreds + 7 tens -f- 6 ones 
 
 2 2 7 == 2 hundreds -h 2 tens + 7 ones. 
 
 Take 1 hundred from 8 hundreds ; this leaves 7 hun- 
 dreds. 1 hundred equals 10 tens. Take 1 ten from 10 
 tens ; this leaves 9 tens. 1 ten and 3 ones are 13 ones. 
 803 then is equal to 7 hundreds, 9 tens, and 13 ones. 
 13 ones — 6 ones = 7 ones ; 9 tens — 7 tens = 2 tens; 7 
 hundreds— 2 hundreds =5 hundreds. Answer, 227. 
 
 Read, then subtract and test : 
 
 a b c d e 
 
 5. 8404 7604 5041 5202 7011 
 3625 4896 1979 1824 4583 
 
 6. 7024 8401 5401 8704 4087 
 3767 4574 2519 6247 1069 
 
 7. Subtract 187 from 9234; then take 187 from each 
 successive remainder, until the final remainder is 7364. 
 
40 THIRD YEAR [Written 
 
 SUBTRACTION 
 
 1. From 700 take 264. 
 
 6 9 10 
 
 700=6 hundreds + 9 tens + 10 ones 
 264 = 2 hundreds + 6 tens + 4 ones 
 436 = 4 hundreds H- 3 tens + 6 ones. 
 
 a bed 6 / 
 
 2. 500 600 900 400 800 700 
 
 154 247 678 197 372 309 
 
 3. 
 
 300 
 
 700 
 
 600 
 
 800 
 
 200 
 
 400 
 
 
 263 
 
 288 
 
 327 
 
 561 
 
 181 
 
 397 
 
 4. 
 
 604 
 
 809 
 
 701 
 
 902 
 
 606 
 
 705 
 
 
 160 
 
 341 
 
 202 
 
 720 
 
 408 
 
 496 
 
 5. 
 
 609 
 
 501 
 
 303 
 
 806 
 
 903 
 
 703 
 
 
 285 
 
 209 
 
 180 
 
 199- 
 
 287 
 
 587 
 
 6. 
 
 706 
 
 801 
 
 704 
 
 560 
 
 601 
 
 890 
 
 
 567 
 
 560 
 
 395 
 
 297 
 
 269 
 
 798 
 
 7. 
 
 2042 
 
 4106 
 
 5001 
 
 8012 ■ 
 
 7020 
 
 1407 
 
 
 1012 
 
 2014 
 
 3014 
 
 5707 
 
 2904 
 
 1289 
 
 8. 
 
 7018 
 
 5080 
 
 9001 
 
 8304 
 
 4400 
 
 1604 
 
 
 4009 
 
 3107 
 
 3082 
 
 5012 
 
 3870 
 
 1397 
 
I 
 
 ritten] 
 
 SUBTRACTION- 
 
 
 41 
 
 
 SUBTRACTION 
 
 
 
 Subtract : 
 
 
 
 
 
 a 
 
 b 
 
 c 
 
 d 
 
 e 
 
 1. 6432 
 
 7244 
 
 6475 
 
 7994 
 
 8641 
 
 4176 
 
 5371 
 
 3879 
 
 3877 
 
 1282 
 
 2. 4531 
 
 4351 
 
 4234 
 
 2432 
 
 2134 
 
 1522 
 
 1543 
 
 1235 ■ 
 
 1344 
 
 1545 
 
 3. 5423 
 
 4215 
 
 3254 
 
 3524 
 
 8231 
 
 2545 
 
 1567 
 
 1565 
 
 1566 
 
 4743 
 
 4. 4253 
 
 3231 
 
 5453 
 
 8121 
 
 6414 
 
 1464 
 
 1865 
 
 1974 
 
 3642 
 
 3892 
 
 M 
 
 5. 412 boys and 325 girls were enrolled in a school. 
 How many more boys than girls were enrolled ? 
 
 6. Harry has 42 chickens. After he has fed 15 of 
 them, how many chickens remain to be fed ? 
 
 7. John's home is 132 miles from New York, and 
 Mary's home is 341 miles from New York. How many 
 miles farther from New York does Mary live than John ? 
 
 8. The perimeter or distance around a dining table 
 is 28 feet and that of the library table is 21 feet. 
 
 ind the difference in the perimeters. 
 
 9. An automobile ran 312 miles one week and 145 
 miles the next week. How many more miles did the 
 automobile run the first week than the second week ? 
 
42 THIRD YEAR [Written 
 
 ADDITION AND SUBTRACTION 
 
 1. In the Central School, there are 398 pupils ; in 
 the Garfield School, 1045, and in the Holmes School, 
 2306. How many pupils are there in the three schools? 
 
 2. Mr. Adams's home cost $ 4370, and Mr. Boyd's cost 
 $3745. Find the difference in the cost of their homes. 
 
 3. John lives 5906 feet from his school, and Thomas 
 lives 2194 feet nearer the school than John. How far 
 does Thomas live from the school ? 
 
 4. Bertha counted the people in four parades. Tn the 
 first there were 208 ; in the second, 890 ; in the third, 
 1506 ; and in the fourth, 1781. How many were there 
 in all ? 
 
 5. In two city schools, boys parade as soldiers. In 
 the first school there are 1790 boys ; in the second 
 school 279 boys less than in the first. How many 
 boys are there in the second school ? 
 
 6. A merchant sold for the fourth of July, 3706 
 small flags, 1712 larger flags, and 19 flags for flag 
 poles. How many flags did he sell ? 
 
 7. In counting the steps to school, Joseph took 1370, 
 and Harvey took 940 less than Joseph. How many 
 steps did Harvey take ? 
 
 8. A street-car conductor collected 103 fares on the 
 first trip, 72 on the second, trip, 176 on the third trip, 
 and 39 on the fourth trip. How many fares did he 
 collect ? 
 
Oral] 
 
 MULTIPLICATION 
 
 43 
 
 MULTIPLYING BY 3 
 
 1. Count by 2's to 36 ; by 3's to 36. 
 
 2. How many are 3 + 3, or two 3's? 
 or three 3's ? 3 + 3 + 3 + 3, or four 3's ? 
 
 3. Three 3's are ; five 3's are — 
 
 six 3's are ; nine 3's are . 
 
 p 4. How many are 7x3? 5x3? 
 
 5. Build the table of 3's to 12 x 3 thus : 
 
 3 + 8 + 3, 
 
 3 
 
 3 3 
 
 333 
 
 8333 
 
 3 3 3 3 3 
 
 3 3 3338 
 
 Write the sum of each column beneath it. 3 3 3 3 3 3 3 
 Look at each column and say, 1x3 = 3 ; 
 2x3 = 6; 3x3 = 9; etc. 
 
 6. 3x8 = 8x? 3x5 = 5x? 9x8 = 3x? 
 
 Table of 3's 7. Memorize the table. 
 
 1x3= 3 
 
 7x3 = 21 
 
 2x3= 6 
 
 8x3 = 24 
 
 3x3= 9 
 
 9x3 = 27 
 
 4x3 = 12 
 
 10x3 = 30 
 
 5x3 = 15 
 
 11x3 = 33 
 
 6x3 = 18 
 
 12x3 = 36 
 
 Multiply at sight: 
 
 9. 4 2 5 
 
 3 3 3 
 
 7 
 3 
 
 9 
 3^ 
 
 8. 
 
 8 
 3 
 
 Give 
 
 6 
 
 3 
 
 products. 
 
 10 11 
 
 3 3 
 
 10. 12 20 40 
 3 3 3 
 
 30 
 3 
 
 50 
 3 
 
 70 
 3 
 
 60 
 _3 
 
 90 80 
 3 3 
 
44 
 
 THIRD YEAR 
 
 [Written 
 
 MULTIPLYING BY 3 
 
 1. Multiply 65 x 3. 
 3x5 ones = 15 ones, or 1 ten 
 
 and 5 ones. Write the 5 ones in 
 ones' place. 3x6 tens = 18 tens ; 
 18 tens + the 1 ten of the 15 ones 
 = 19 tens. The answer is 195. 
 We think : " 3 times 5 = 15; 3 times 
 
 18 ; 18 4- 1 = 19." Product 195. 
 
 The number multiplied is called the 
 
 multiplicand. The number showing how 
 
 .many times the multiplicand is taken is 
 
 called the multiplier. The result m multiplication is 
 
 called the product. 
 
 Multiply, and test each product by addition : 
 
 a he d e 
 
 2. 45 75 66 74 86 
 
 3 3 3 3 3 
 
 Multiplicand 
 
 65 
 
 Multiplier 
 
 3 
 
 Product 
 
 195 
 
 Test. 65 
 
 
 65 
 
 6 = 
 
 65 
 195 
 
 mi 
 
 3. 135 
 3 
 
 236 
 3 
 
 5. 209 
 3 
 
 6. 132 
 3 
 
 105 
 3 
 
 409 
 3 
 
 146 
 3 
 
 145 
 3 
 
 216 
 3 
 
 237 
 3 
 
 284 
 3 
 
 298 
 3 
 
 308 
 3 
 
 207 
 3 
 
 258 
 
 189 
 
 3 
 
 3 
 
 167- 
 
 248 
 
 3 
 
 3 
 
 276 
 
 287 
 
 3_ 
 
 3 
 
Written] 
 
 MULTIPLICATION 
 
 45 
 
 I 
 
 MULTIPLICATION OF CONCRETE NUMBERS 
 
 Numbers that name objects are concrete; as 6 apples, 
 3 boys, 5 yards. 
 
 Numbers that do not name objects are abstract ; as 
 7, 9, 3. 
 
 In multiplying concrete numbers, the multiplicand 
 and the product have the same name. 
 
 The multiplier is always an abstract number. 
 
 1. How many oranges are there in 3 dozen ? 
 
 12 oranges in 1 doz. 
 3 3 X 12 oranges = 36 oranges. 
 
 36 
 
 oranges in 
 
 3 doz. 
 
 
 
 Multiply : 
 
 a 
 2. 46jzf 
 
 3 
 
 h 
 
 24 cans 
 3 
 
 c 
 
 56 balls 
 3 
 
 d 
 
 28 qt. 
 3 
 
 3. 
 
 25 ft. 
 3 
 
 28 pt. 
 3 
 
 47 gal. 
 3 
 
 82 yd. 
 3 
 
 4. 
 
 96 da. 
 3 
 
 84 min. 
 3 
 
 75 poles 
 3 
 
 48 nfiles 
 3 
 
 5. 
 
 93 trees 
 3 
 
 88 dimes 
 3 
 
 52 eggs 
 3 
 
 93 birds 
 3 
 
 6. 
 
 86 wheels 
 3 
 
 48 cakes 
 3 
 
 72 pies 
 3 
 
 197 nuts 
 3 
 
46 
 
 THIRD YEAR 
 
 [Oral 
 
 MULTIPLYING BY 4 
 
 1. Count by 4's to 12 ; to 24 ; to 36 ; to 48 
 
 2. How many are 4 + 4, or two 4's ? 
 
 three 4's ? 4 + 4 + 4 + 4, or four 4's ? 
 
 3. Five 4's are ; six 4's are . 
 
 4. How many are 2x4? 4x4? 5x4? 
 
 5. Build the table of 4's to 12 x 4 thus : 
 
 Write the sum of each column beneath it. 
 Look at each column and say, 1x4 = 4; 
 2x4 = 8; 3x4 = 12; etc. 
 
 6. 4x8=?x4 9x4 = 4x? 6x4 = ?x6. 
 
 7. Memorize the table. Table of 4's 
 
 4 + 4 + 4, or 
 
 4 
 
 44 
 
 444 
 
 4444 
 
 44444 
 
 444444 
 
 8. Give products. 
 
 9. Give products at sight 
 5 7 9 11 
 4 4 4 4 
 
 1x4= 4 
 
 7x4 = 28 
 
 2x4= 8 
 
 8x4 = 32 
 
 3x4 = 12 
 
 9x4 = 36 
 
 4x4 = 16 
 
 10x4 = 40 
 
 5x4 = 20 
 
 11x4 = 44 
 
 6x4 = 24 
 
 12x4 = 48 
 
 12 
 4 
 
 10. 4x5 3x8 4x10 4x7 2x9 
 
 11. 3x6 4x12 3x2 3x10 4x4 
 
 12. 4 X 11 4x2 3 X 10 4x9 4x8 
 
Oral and Written] MULTIPLICATION 47 
 
 PRACTICAL PROBLEMS 
 
 1. Emma has 4 pieces of ribbon of 10 yards each. 
 How many yards has she in all ? 
 
 2. How many lemons are there in 4 dozen ? 
 
 3. How far can you ride in 4 hours in a carriage 
 that travels on an average of 4 miles an hour ? 
 
 4. How many pecks are there in 11 bushels ? 
 
 5. At 10^ a quart, how much will 1 gal. oil cost? 
 
 6. How many days are there in 4 weeks ? 
 
 Multiply, and test by addition : 
 
 a b c d e 
 
 7. 165 238 369 748 569 
 
 4: 4: 4: 4: 4 
 
 8. 
 
 293 
 4 
 
 687 
 4 
 
 574 
 4 
 
 862 
 4 
 
 738 
 4 
 
 9. 
 
 786 
 4 
 
 934 
 
 4 
 
 867 
 4 
 
 279 
 4 
 
 184 
 4 
 
 10. 
 
 915 
 4 
 
 846 
 4 
 
 739 
 4 
 
 862 
 4 
 
 475 
 4 
 
 11. 
 
 886 
 4 
 
 995 
 4 
 
 774 
 4 
 
 663 
 4 
 
 552 
 4 
 
 Give products at sight: 
 
 12. 4x20 4x50 4x80 4x25 4x17 
 
 13. 4x30 4x60 4x90 4x15 4x18 
 
48 THIKD YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. If a sail maker uses 18 yards of cloth in a main- 
 sail, how many yards would he require for 3 such sails ? 
 
 2. If it takes Helen 24 minutes to hemstitch a collar, 
 how many minutes will it take for 4 collars ? 
 
 3. A man bought 4 lots at $475 each. How much 
 did they cost ? 
 
 4. Mr. Home made 3 payments of $645 each for 
 his house. What was the cost of his house ? 
 
 5. If each pupil in a school of 658 has 4 books, how 
 many books have they all ? 
 
 6. A drover bought 3 horses at $235 each. How 
 much did he pay for all ? ^ 
 
 7. A farmer sold 276 sheep at $4 a head. How 
 much did he receive for all ? 
 
 8. If a train runs 476 miles in a day, how far can 
 I travel on it in 3 days ? 
 
 9. A ship sailed 364 miles each day. How far did 
 it sail in 4 days ? 
 
 10. A car carries 60 persons. How many persons 
 will 4 such cars carry ? 
 
 11. How many acres are there in 4 farms, if each 
 farm contains 175 acres ? 
 
 12. At $ 15 each, how much will 3 paintings cost ? 
 
 13. How many boys are playing soldier, if there are 
 4 rows and 16 boys in each row ? 
 
Oral and Written] 
 
 DIVISION 
 
 49 
 
 r 
 
 DIVIDING BY 3 
 
 1. Count by 3's to 9; to 18; to 30 ; to 36. 
 
 2. How many times does 6 contain 3? ||| 
 
 3. Show by separating into groups : 
 
 12 contains 3 
 18 contains 3 
 
 times 
 times 
 
 15 contains 3 — 
 21 contains 3 — 
 
 Give quotients at sight : 
 
 9 
 24 
 
 18^3 
 30^3 
 
 33^3 
 21 -f- 3 
 
 12^3 
 36-^3 
 
 - times 
 
 - times 
 
 27^3 
 15^3 
 
 5. Divide each number outside the 
 circle by 3. 
 
 6. Find: 
 I of 27 1 of 30 1 of 36 i of 15 
 1 of 12 J of 18 J of 21 1 of 33 
 
 7. Compare 6 and 2 ; thus : 6 is 3 
 times 2. 2 is i of 6. 
 
 The number divided is called the dividend. 
 
 The number by which we divide is called the divisor. 
 
 The answer in division is called the quotient. 
 
 Divide and test : 
 
 a b c d e 
 
 8. 3)24_ 3 )36 3 )27 3 )30 3 )21 
 
 9. 3 )393 
 10. 3)150 
 
 3 )363 
 3)900 
 
 3 )339 
 3 )660 
 
 3)933 
 3 )693 
 
 3 )303 
 3 )369 
 
50 THIKD YEAR [Oral and Written 
 
 1. The sign -^ is read divided by. 
 
 2. 24^-7-3^ means that we are to find how many 
 times 3P is contained in 24^; thus: 3^)24^ 
 
 8 times. 
 
 Find quotients : 
 
 3. 82 days -^ 2 days 9. 189 years ^3 years 
 
 4. 186 hours ^ 3 hours lo. 244 roses ^ 2 roses 
 
 5. 422 minutes -^ 2 minutes ii. 664 cents -^ 2 cents 
 
 6. 448 feet -^ 2 feet 12. 336 quarts ^3 quarts 
 
 7. 249 inches -H 3 inches 13. 144 gallons -^ 2 gallons 
 
 8. 622 dollars -^2 dollars 14. 428 pints -5- 2 pints 
 
 15. 24^^ 3 means that we are to find one third of 
 24 j^; thus: 1 of 24 j^ equals 8^, or 3 )24^. 
 
 8^ 
 
 Find quotients: 
 
 16. 224 days ^2 24. 844 gallons -f- 2 
 
 17. 333cents-^3 25. 646 quarts -^ 2 
 
 18. 216 dollars -^ 3 26. 969 pencils -^ 3 
 
 19. 622 birds -f- 2 27. 842 books -^ 2 
 
 20. 326 inches -^ 2 28. 936 hours ^3 
 
 21. 219 hours -^ 3 29. 288 pages -^ 2 
 
 22. 444 roses -^ 2 30. 428 pints ^ 2 
 
 23. 468 minutes ^ 2 31. 639 pens -^ 3 
 
Written] DIVISION 61 
 
 r 
 
 REMAINDER IN DIVISION 
 
 1. Divide 263 by 3. 
 
 Divisor 3)263 Dividend 26 tens -5-3 = 8 tens, and 2 tens 
 
 87 Quotient (20 ones) remaining. Write 
 
 Remainder 2 the 8 tens in the tens' place. 
 
 20 ones + 3 ones = 23 ones. 23 ones -^ 3 = 7 ones, and 
 
 2 ones remaining. Quotient 87 ; remainder 2. 
 
 We think : " 3 in 26, 8 times, and 2 remaining; 3 in 23, 
 7 times, and 2 remaining." Quotient 87 ; remainder 2. 
 
 Test. — If the answer is correct, then 3 x 87, or 261, 
 H- 2, the remainder, will equal 263, the dividend. 
 
 Divide and test by 2 ; by 3 : 
 
 a b c d e 
 
 2. 265 864 786 624 7368 
 
 3. 713 219 265 758 2457 
 
 4. Compare 12 ^ 2 and | of 12 ; 12 -^ 3 and J of 12. 
 
 To find ^ of any numher, divide the number hy 2. 
 To find -J- of any numher, divide the number by 3. 
 
 How many are : 
 
 a b c 
 
 5. 1 of 240 men ? J of 171 balls ? J of $ 7484 ? 
 
 6. 1 of 717 feet ? i of 216 mi. ? i of $ 3927 ? 
 
 7. 1 of 435 yd. ? ^ of 384 bu. ? i of $ 8064 ? 
 
 8. 1 of 759 gal. ? 1 of 902 in. ? i of $ 2160 ? 
 
 9. 1 of 285 pk. ? 1 of 405 f t. ? • J of $ 2754 ? 
 
[Oral and Written 
 
 52 THIRD YEAR 
 
 DIVIDING BY 4 
 
 1. How many are four 2's ? 4 in 8, - 
 
 2. How many are four 3's ? 4 in 12, 
 
 3. How many times does 16 contain 4? 
 
 4. 20 contains 4, times ; 24 contains 4, 
 
 times. 
 - times. 
 
 times ; 28 contains 4, 
 times. 
 
 times ; 32 contains 4, 
 
 5. 36^4 = ? 40-5-4 = ? 44-f-4 = ? 48-^4 = ? 
 
 36 
 
 20 
 
 /40 
 
 36 44 
 
 6. Give quotients. 7. Give parts. 
 
 Divide, and test by multiplication: 
 
 8. 4 )268 
 
 9. 4 )3604 
 
 10. 4 )4693 
 
 11. 4)5169 
 
 12. 4 )6981 
 
 13. 4)3204 
 
 h 
 
 4 )864 
 
 4)9216 
 
 4)5248 
 
 4 )2834 
 
 4 )1243 
 
 4)4126 
 
 c 
 
 4 )936 
 
 4)3704 
 4 )9270 
 
 4 )6573 
 4)6476 
 4)3958 
 
 4 )468 
 
 4)4008 
 
 4 )7354 
 
 4 )6291 
 4 )5034 
 
 4 )2976 
 
 4 )2240 
 4 )3246 
 
 4 )4687 
 4)8473 
 4 )2075 
 4)8169 
 
Written] DIVISION 63 
 
 DIVISION 
 
 1. Walter had 48 baskets of fruit. He sold an equal 
 number to 4 different buyers. How many baskets did 
 each buy ? 
 
 4 )48 Xo. of baskets. J of 48 baskets = 12 baskets. 
 
 12 No. of baskets to each. 
 
 2. Mary has 45 cents. How many 3 cent oranges 
 can she buy with her money ? 
 
 3^ = cost of 1 orange 3^) 45^ 
 
 15 times, or 15 oranges. 
 
 3. A man divided property valued at $ 369 equally 
 among his 3 children. How much did each receive ? 
 
 4. Mr. Bell earned $ 396 in 3 months. What were his 
 monthly wages ? 
 
 5. Find the cost of 1 bushel of wheat, if 4 bushels 
 cost 280 cents. 
 
 6. If a girl sews 4 buttons on each pair of gloves, 
 how many pairs has she finished when she has used 
 468 buttons? 
 
 7. A farmer having 96 hogs sold one third of them. 
 How many did he sell ? 
 
 8. In a car containing 639 baskets of peaches, one 
 third were spoiled. How many baskets were spoiled ? 
 
 9. How many pound boxes can be filled from 164 
 quarter pounds of candy ? 
 
 10. When molding costs 15^ a yard, how much will 
 1 foot of it cost ? 
 
 1 ft. = J of a yard j 1 ft. will cost i of 15^, or 5 cents. 
 
54 THIRD YEAR [Oral and Written 
 
 UNITED STATES MONEY 
 
 United States money is written in dollars and cents. 
 
 A period (.), named a ''decimal point/' is placed to 
 the right of dollars. After the point, cents are written 
 in two places. Thus, 5 dollars and 25 cents is 
 written $5.25. 
 
 1. Read: $8.40; $9.67; $3.14; $8.24; $7.05. 
 
 In addition and subtraction of United States money, 
 the point must be written under the point, dollars under 
 dollars, and cents under cents. 
 
 Read and add : 
 
 2. $3.45 $2.24 $3.14 $3.62 $2.43 
 
 2.61 3.36 1.35 2.45 3.25 
 
 Add across and in columns : 
 
 3. $ 2.24 + $ 3.25 + $ 6.42 + $ 2.56 4- $ 3.25 + $ 4.63 = 
 
 4. $ 3.14 + $ 2.35 + $ 3.11 + $ 6.14 + $ 2.65 + $ 6.15 = 
 
 5. $ 4.24 + $ 5.32 + $ 2.34 + $ 5.23 + $ 2.34 + $ 5.26 = 
 
 Read and find differences : 
 
 a h c d e 
 
 6. $3.46 $3.25 $3.41 $6.11 $5.13 
 
 1.25 2.74 2.56 2.65 2.65 
 
 7. $2 43 $3.25 $3.41 $6.11 $5.13 
 
 1.47 1.46 2.16 5.26 2.56 
 
 8. Add $4.25 and $2.64. lo. Add $ 2.54 and $ 1.36. 
 
 9. Add $ 3.62 and $ 2.16. ii. Add $ 3.26 and $ 1.56. 
 
UNITED STATES MONEY 55 
 
 UNITED STATES MONEY 
 
 Read and add : 
 
 abed 
 
 1. $246.25 $632.75 $327.56 $805.96 
 
 318.75 738.49 928.89 613.73 
 
 92.48 918.86 738.86 928.45 
 
 18.64 29.94 198.37 56.91 
 
 237.75 169.83 75.59 219.87' 
 
 2. 
 
 $178.84 $219.35 
 
 $165.27 
 
 $214.56 
 
 
 6.92 7.29 
 
 86.15 
 
 3.94 
 
 
 175.49 216.87 
 
 283.85 
 
 69.47 
 
 
 862.81 938.75 
 
 395.94 
 
 138.85 
 
 
 219.97 139.49 
 
 415.86 
 
 475.27 
 
 3. 
 
 $ 465.75 + $ 37.28 + $ 692.37 + $ 475.84 = 
 
 = ? 
 
 4. 
 
 $193.85+ $87.96+ $S 
 
 175.84 + $215.79 = 
 
 = ? 
 
 S. 
 
 $276.49 + $29.49 + $ 
 
 49.86 +$936.93: 
 
 = ? 
 
 6. 
 
 $ 475.98 + $ 18.07 + $ 126.92 + $ 214.85 ■■ 
 
 = ? 
 
 
 + + 
 
 + 
 
 = ? 
 
 Subtract and test : 
 
 
 
 
 a h 
 
 c 
 
 d 
 
 7. 
 
 $475.36 $435.24 
 
 $438.64 
 
 $821.42 
 
 
 196.28 178.95 
 
 195.73 
 
 195.38 
 
 8. 
 
 $317.61 $124.15 
 
 $326.47 
 
 $412.49 
 
 
 219.84 95.76 
 
 158.96 
 
 273.89 
 
 9. $246.37 -$174.75 lo. $235.55 -$169.73 
 
5Q 
 
 THIRD YEAR 
 
 [Oral 
 
 MULTIPLYING BY 5 
 
 1. Count by 5's to 10 ; to 30 ; to 45 ; to 60. 
 
 2. How much are two 5-cent pieces ? 2x5 = ? 
 
 3. How much are three 5-cent pieces ? 3x5=? 
 
 4. Tell the value of four 5-cent pieces; of 5 such 
 pieces ; of 6, 7, 8, 9, 10, 11, 12. 
 
 5. How many 5's are there in 10 ? in 20 ? in 30 ? 
 60? 25? 35? 45? 55? 40? 50? 15? ^ 
 
 6. Multiply each of the outside ^^ 
 iiumbers by 5. Change the number 
 within the circle to 4 and multiply; 
 then to 3 ; to 2. Build the table of 5's ^ 
 as you built the table of 4's 
 
 7. Memorize the table. 
 
 8. Supply the missing 
 numbers : 
 2x5 = ? 
 4x ?=20 
 5x5 = ? 
 ? x5 = 35 
 9x ? = 45 
 
 5 is ? of 10 
 ? is 1 of 20 
 25 is ? X 5 
 ? is ^■ of 35 
 
 Table of 5's 
 
 1x5= 5 
 
 7x5 = 35 
 
 2x5=10 
 
 8x5 = 40 
 
 3x5=15 
 
 9x5 = 45 
 
 4x5=20 
 
 10x5=50 
 
 5x5 = 25 
 
 11x5 = 55 
 
 6x5 = 30 
 
 12x5 = 60 
 
 I- of 45 is ? 
 
 9. Give products : 8 x 5 ; 
 9x5; 3x5; 5x5; 7x5; 6x5; 12x5. 
 
 10. What is the difference in value between : 
 3x$5and5x$3? 7x5 hats and 5 x 7 hats? 
 
 6x$5and5x$6? 2x4 books and 4 x 2 books? 
 
Written] 
 
 MULTIPLICATION 
 
 57 
 
 I 
 
 MULTIPLICATION OF DOLLARS AND CENTS 
 
 1. Multiply $3.65 by 3. 
 
 $3.65 
 
 3 
 
 $10.95 
 
 2. Multiply $ 0.65 by 4. 
 $0.65 
 
 I 
 
 $2.60 
 
 Multiply : 
 a 
 
 4. $3.50 
 2 
 
 5. $7.04 
 4 
 
 6. 22^ 
 
 3 
 
 In multiplying dollars and cents, place 
 the decimal point in the product directly 
 under the decimal point in the multipli- 
 cand. Write the dollar sign before the 
 number of dollars. 
 
 Multiply 70^ by 3. 
 70^ 
 3 
 210^= $2.10 (Why?) 
 
 3. 
 
 h 
 
 $3.05 
 4 
 
 $0.60 
 5 
 
 5 
 
 c 
 
 $6.05 
 3 
 
 $0.08 
 3 
 
 261^ 
 4 
 
 d 
 $9.40 
 5 
 
 74^2^ 
 _£ 
 
 5 
 
 7. How much will 3 pecks of peaches cost at 65^ a 
 peck? 
 
 8. A messenger boy delivers 4 messages at 45^ each. 
 How much does he earn for his company ? 
 
 9. May gets $ 3.75 per week in a department store. 
 Find her wages for 4 weeks. 
 
58 
 
 THIRD YEAR 
 
 [Written 
 
 PRACTICAL PROBLEMS 
 
 1. How many seats are there on 
 each side of the car ? 
 
 2. How many are two times 11 
 seats ? 
 
 3. The conductor collected 75 fares 
 on the first trip and 87 fares on the re- 
 turn trip. How many fares did he 
 collect ? 
 
 4. The fare is 5 cents. How much 
 money did he collect on both trips ? 
 
 5. A lady paid for herself and 5 
 children. She gave the conductor a 
 half dollar. How much change should 
 she receive ? 
 
 6. Each seat will accommodate two persons, 
 many persons can be seated in the car ? 
 
 7. The conductor earns $2.50 in a day. 
 much does he earn in 5 days ? 
 
 8. The motorman is paid $2.75 a day. How much 
 does he earn in 5 days ? How much more does he earn 
 in a day than the conductor ? 
 
 9. The line is 8 miles long. How far does a car run 
 in making 5 round trips ? 
 
 10. On one trip each seat was occupied, and 5 per- 
 sons had to stand. Ftud the amount of the fares for 
 the trip. 
 
 How 
 
 How 
 
Oral and Written] 
 
 DIVISION 
 
 69* 
 
 rp MULTIPLYING BY 6 
 
 1. Count by 6's to 12; to 24; to 48; to 60; to 72. 
 Build the table of 6's. 
 
 2. How many 6's are there in 12 ? in 18 ? 24 ? 36 ? 
 
 48? 54? 60? 66? 72? 
 
 
 
 Table of 6 
 
 's 
 
 
 1 
 
 x6 = 
 
 6 
 
 7 
 
 x6 = 
 
 42 
 
 2 
 
 x6 = 
 
 12 
 
 8 
 
 x6 = 
 
 48 
 
 3 
 
 x6 = 
 
 18 
 
 9 
 
 x6 = 
 
 54 
 
 4 
 
 x6 = 
 
 24 
 
 10 
 
 x6 = 
 
 60 
 
 5 
 
 x6 = 
 
 30 
 
 11 
 
 x6 = 
 
 66 
 
 6 
 
 x6 = 
 
 36 
 
 •12 
 
 X 6 = 
 
 72 
 
 5. Multiply each number outside 
 the circle first by 3, then by 4, then 
 by 5, then by 6. 
 
 3. Memorize the table. 
 
 4. Compare in two ways: 
 
 Thus 6 is 
 
 3 more than 
 
 3; 6 is 
 
 2x3. 
 
 6 and 3 
 
 12 and 3 
 
 6 and 4 
 
 12 and 4 
 
 6 and 5 
 
 12 and 5 
 
 4 and 2 
 
 16 and 4 
 
 outside 1 1 / 
 
 -^^-^ 
 
 3X 
 4X 
 5X 
 6X 
 
 Multiply by 6; by 5; by 4; by 3: 
 
 h c 
 
 567 149 
 
 295 293 
 
 8. 978 869 687 
 
 9. 207 890 903 
 
 a 
 
 6. 243 
 
 7. 679 
 
 10. Give products at sight : 
 6 X 40 5 X 20 6 X 80 
 
 6x70 5x35 5x32 
 
 6 X 90 
 
 x41 
 
 4x71 
 
 d 
 759 
 
 384 
 
 825 
 708 
 
 5x50 
 6x 25 
 4x92 
 
 e 
 894 
 
 679 
 
 856 
 
 605 
 
 6x61 
 6x42 
 6x81 
 
60 
 
 THIED YEAR [Oral and Written 
 
 DIVIDING BY 5 
 
 1. Count by 5's to 15 ; to 25 ; to 45 ; to 50 ; to 60. 
 
 2. ? X 5 = 15 ? X 5 = 20 ? X 5 = 40 
 
 3. Give answers : 
 5-^5 15^5 50-^5 45-^5 
 
 30-5 40-^5 35^5 10^5 
 55-^5 60-^-5 25 H- 5 20^5 
 
 25 ^0 
 
 Division may be indicated in three ivays: First, 8-^2; 
 second, 2]|8 ; third, f . Each is read 8 divided by 2. 
 
 4. Read and solve : 
 16 -f- 4 4}16 
 
 ¥ ¥- 
 
 5. ■ Divide by 5 and give remainders : 
 43 62 27 48 39 56 53 
 
 ¥ 
 
 ¥ 
 
 ¥ 
 
 ¥ 
 
 ¥ 
 
 125 
 
 324 
 
 340 
 
 2 84 
 
 S4£ 
 
 6. Find ^ of: 
 420 men 375 hr. 
 
 365 horses 180 da. 
 
 Divide and test : 
 
 7. 5 )4225 
 
 8. 5 )5693 
 
 9. 5)7024 
 
 b 
 
 5 )7086 
 
 5 )4287 
 5)9046 
 
 825 pt. 
 315 gal. 
 
 c 
 
 5 )9275 
 
 5 )1364 
 4:2753 
 
 $415 
 $630 
 
 d 
 
 5 )4376 
 
 5 )7006 
 5)4203 
 
 14 27 
 
 870 JJ' 
 560/^ 
 
 e 
 
 5 )8450 
 
 5 )7005 
 5)2004 
 
Oral and Written] DIVISION 61 
 
 DIVIDING BY 6 
 
 1. How many times is 6 contained in 12 ? in 18 ? 
 in 24? in 48? 60 ? 54 ? 36 ? 66 ? 42 ? 72? 
 
 2. (iive answers : 
 
 
 
 42-5-6 60 ^ 6 36 ^ 6 
 
 24^6 
 
 48^6 
 
 35 ^ 5 48 -:- 4 J of 35 
 
 lof 42 
 
 60^6 
 
 6|48 6^60 6)54 
 
 6)36 
 
 6)30 
 
 3. Divide each number by 6 : 
 
 
 
 480 600 624 
 
 540 
 
 366 
 
 720 618 246 
 
 726 
 
 612 
 
 4. Complete : 
 
 
 
 15-i-6= — and — over. 6x8,-f? = 
 
 = 50 6x9,-t-? = 59 
 
 45 -i- 6 = — and — over. ? x 6, -1- 2 = 
 
 = 56 6x? 
 
 ',-1-3 = 45 
 
 5. Divide by 5 and give remainders ; then by 6 : 
 843 864 631 7235 8697 
 675 293 845 4618 3256 
 931 787 569 8627 4367 
 
 6. Compare in two ways : $ 18 and $ 3 ; $ 36 and $ 6 ; 
 
 35 books and 5 books; 24 hats and 4 hats; 42 lemons 
 and 7 lemons; 45)^ and 5^. 
 
 7. Find the cost of : 
 
 6 oranges at 18^ a doz. 40 pears at 4^ each. 
 
 36 apples at 2^ each. 18 eggs at 10 j^ a doz. 
 
 8. At 3^ apiece, how many oranges can you buy for 
 18^? for 42^? for 36^? for 72)^? 
 
62 THIRD YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. Find the cost of 5 yards of cloth at $ .75 a yard. 
 
 2. Four boys deposited in the school bank as fol- 
 lows: $4.25, $6.93, $4.34, and $6.05. What was the 
 entire deposit ? 
 
 3. Julia went to the store with a twenty-dollar bill. 
 She paid 75 cents a yard for 6 yards of oilcloth, and 
 $ 9.50 for a rug. How much had she left ? 
 
 4. A box contains 360 oranges. If ^ of them are 
 bad, how many good ones are there in the box ? 
 
 5. At 36 cents a dozen, how much will 5 dozen 
 oranges cost ? 
 
 6. At 24 cents a dozen, how much will 6 dozen 
 oranges cost ? How much change should a lady receive 
 after paying for the oranges with a two-dollar bill ? 
 
 7. Make a problem with : $ 8.25, $ 6.32, $ 6.56, and 
 $5. 
 
 8. John paid a bill of $ 7.32 and had $ 6.54 remain- 
 ing. How much had he at first ? 
 
 9. If there are 28 lines on each page of a book, how 
 many lines are there on 9 pages ? 
 
 10. A furniture dealer paid $624 for tables at $6 
 each. How many did he buy ? 
 
 11. Jack has collected 250 post cards and pastes 5 on 
 each page of his album. How many pages do they fill ? 
 
 12. How many lamps, at $ 5 each, can be bought for 
 $ 83 ? How much money will remain ? 
 
Oral and Written] ADDITION 63 
 
 DRILLS IN ADDITION 
 
 Add rapidly, finding 3 answers in 1 minute. 
 
 a 
 
 b 
 
 C 
 
 d 
 
 e 
 
 1. 2345 
 
 3256 
 
 3556 
 
 4325 
 
 2546 
 
 3253 
 
 5433 
 
 5234 
 
 2534 
 
 3452 
 
 1432 
 
 2345 
 
 3245 
 
 3523 
 
 2543 
 
 2564 
 
 4356 
 
 5243 
 
 2456 
 
 3245 
 
 7316 
 
 5134 
 
 2356 
 
 5346 
 
 1236 
 
 2. 2434 
 
 3245 
 
 2546 
 
 6513 
 
 5342 
 
 3256 
 
 1452 
 
 4532 
 
 3245 
 
 4254 
 
 5145 
 
 5416 
 
 3251 
 
 5314 
 
 6143 
 
 4253 
 
 2533 
 
 5424 
 
 2425 
 
 3325 
 
 3242 
 
 3254 
 
 1243 
 
 5253 
 
 2543 
 
 3. 6325 
 
 6436 
 
 6323 
 
 6546 
 
 6546 
 
 4264 
 
 2462 
 
 2566 
 
 3562 
 
 4362 
 
 2633 
 
 6354 
 
 6344 
 
 6255 
 
 6543 
 
 • 1462 
 
 5633 
 
 2565 
 
 5364 
 
 2544 
 
 6326 
 
 3265 
 
 6355 
 
 4534 
 
 6355 
 
 4. Give sums at sight, 
 
 thus: 32 + 40=72; 72 + 5=77, 
 
 32 + 45 
 
 55 + 34 
 
 54 + 32 
 
 26 + 34 
 
 43 + 44 
 
 64 + 36 
 
 56 + 56 
 
 23 + 34 
 
 42 + 64 
 
 25 + 56 
 
 56 + 45 
 
 64 + 46 
 
 42 + 32 
 
 36 + 25 
 
 66 + 36 
 
 64 + 35 
 
 36 + 25 
 
 26 + 43 
 
 53 + 36 
 
 54 + 26 
 
 38 + 17 
 
 37 + 26 
 
 59+17 
 
 35 + 45 
 
 25 + 28:. 
 
 29 + 16 
 
 25 + 47 
 
 57 + 24 
 
 66 + 26 
 
 38 + 26 
 
 19 + 28 49 + 26 39 + 58 47 + 47 29 + 25. 
 
64 THIRD YEAR [Written 
 
 SUBTRACTION 
 
 From 804 take 365. 
 
 1. We cannot take 5 ones from 4 ones. 
 
 7 9 14 We cannot take 6 tens from tens. 
 ^ ^ ^ Take 1 hundred from 8 hundreds ; this 
 ^ ^ ^ leaves 7 hundreds. 1 hundred equals 10 
 ^ ^ 9 tens. Take 1 ten from 10 tens, leaving 
 9 tens. 1 ten and 4 ones are 14 ones. 
 804 therefore is equal to 7 hundreds, 9 tens, and 14 
 ones. Subtracting, the difference is 439. 
 
 Subtract : 
 a 
 
 2. 6304 
 3168 
 
 b 
 
 7065 
 1474 
 
 c 
 
 6401 
 3162 
 
 d 
 
 8014 
 6202 
 
 e 
 4706 
 2165 
 
 3. 4060 
 
 2976 
 
 8305 
 6012 
 
 8560 
 3574 
 
 6070 
 4304 
 
 4904 
 1060 
 
 4. 6105 
 2166 
 
 7805 
 4991 
 
 6099 
 4814 
 
 3940 
 
 2108 
 
 6303 
 1494 
 
 5. 8110 
 
 4884 
 
 4444 
 2666 
 
 6222 
 
 4879 
 
 8314 
 6070 
 
 8196 
 7246 
 
 6. 6162 
 3104 
 
 3110 
 2904 
 
 5641 
 3212 
 
 4132 
 1841 
 
 6112 
 
 3897 
 
 7. Find the difference between 8904 and 1996; 
 between 9630 and 2709. 
 
Written] SUBTEACTION 65 
 
 DRILLS IN SUBTRACTION 
 
 Subtract, finding 5 remainders in 1 minute: 
 
 a b c d e 
 
 1. 5434 3254 4203 6043 2015 
 3565 2435 1564 2564 1356 
 
 2. 4360 3204 3204 2010 3014 
 2654 1605 1316 1516 2546 
 
 3. 3105 4010 6302 3051 6031 
 1046 2505 2603 2103 5076 
 
 I 
 
 4. 6035 6501 1045 3060 4320 
 2456 2436 556 2065 1556 
 
 2601 
 
 3561 
 
 6306 
 
 1654 
 
 1456 
 
 2501 
 
 2041 
 
 6020 
 
 5031 
 
 1554 
 
 1615 
 
 1025 
 
 3014 
 
 2031 
 
 6072 
 
 2245 
 
 1505 
 
 4003 
 
 6203 
 
 4106 
 
 2435 
 
 5204 
 
 3502 
 
 1543 
 
 5. 1405 2601 3561 6306 5041 
 
 656 1654 1456 2501 1305 
 
 6. 6702 2041 6020 5031 6043 
 3026 1554 1615 1025 1245 
 
 7. 6103 3014 2031 6072 5102 
 2005 2245 1505 4003 3248 
 
 8. 5203 6203 4106 2435 5210 
 1546 5204 3502 1543 1435 
 
66 THIRD YEAR [Written 
 
 DRILLS IN MULTIPLICATION AND DIVISION 
 
 Multiply and divide each number by 2, 3, 4, and 5 : 
 
 a 
 
 b 
 
 c 
 
 a 
 
 e 
 
 / 
 
 1. 468 
 
 456 
 
 273 
 
 332 
 
 634 
 
 804 
 
 2. 684 
 
 654 
 
 372 
 
 233 
 
 436 
 
 972 
 
 3. 236 
 
 564 
 
 732 
 
 548 
 
 364 
 
 729 
 
 4. 632 
 
 542 
 
 412 
 
 485 
 
 184 
 
 908 
 
 5. 846 
 
 452 
 
 214 
 
 854 
 
 418 
 
 890 
 
 Multiply 
 
 and divide each number by 6, 
 
 5, 4, and 3 : 
 
 6. 426 
 
 848 
 
 408 
 
 798 
 
 249 
 
 284 
 
 7. 264 
 
 844 
 
 840 
 
 897 
 
 942 
 
 428 
 
 8. 624 
 
 853 
 
 480 
 
 789 
 
 429 
 
 842 
 
 9: 165 
 
 790 
 
 981 
 
 679 
 
 257 
 
 912 
 
 10. 561 
 
 970 
 
 189 
 
 796 
 
 725 
 
 192 
 
 Multiply 
 
 and divide each number by 2, 
 
 4,6,i 
 
 md 5: 
 
 11. 456 
 
 295 
 
 217 
 
 513 
 
 665 
 
 537 
 
 12. 654 
 
 925 
 
 172 
 
 135 
 
 656 
 
 357 
 
 13. 546 
 
 529 
 
 918 
 
 150 
 
 250 
 
 640 
 
 14. 237 
 
 592 
 
 189 
 
 510 
 
 520 
 
 460 
 
 15. 372 
 
 712 
 
 891 
 
 566 
 
 502 
 
 604 
 
 Multiply and divide each number by 3, 5, 6, and 4 : 
 
 16. 206 666 270 474 228 924 
 
 17. 620 246 720 276 282 492 
 
 18. 457 426 372 822 249 742 
 
 19. 475 642 723 726 846 952 
 
Oral] MEASURES 67 
 
 DRY MEASURES 
 
 1. Name some dry articles purchased by the pint ; by 
 the quart ; the peck ; the bushel. 
 
 2. Secure some sand or grain, and show by actual 
 measurements the number of pints in a quart ; the num- 
 ber of quarts in a peck ; the number of pecks in a 
 bushel. 
 
 3. Memorize this table : 
 
 2 pints = 1 quart ; written, 2 pt. = 1 qt. 
 8 quarts = 1 peck ; written, 8 qt. = 1 pk. 
 4 pecks = 1 bushel ; written, 4 pk. = 1 bu. 
 
 4. 1 bu. = pecks ; 1 pk. = — — quarts. 
 
 5. How many quarts equal 1 bushel ? 
 
 6. J pk. = quarts ; |^ pk. = quarts. 
 
 7. At 10^ per quart, find the cost of 8 quarts of 
 cherries. 
 
 8. At 6^ per quart, find the cost of 1 peck of hazel- 
 nuts. 
 
 9. A horse eats 12 quarts of oats a day. How 
 many quarts does it eat in 4 days ? 
 
 10. 21 pk. = quarts ; 16 qt. = pecks. 
 
 11. James bought 1^ bushels of tomatoes. How 
 many pecks did he buy ? 
 
 12. If I buy I peck of cherries, how many quarts, 
 should I get? 
 
68 ' THIED YEAE [Oral and Written 
 
 LIQUID MEASURES 
 
 1. Name some liquids sold by the pint ; by the quart ; 
 the gallon. 
 
 2. Memorize this table : 
 
 2 pints = 1 quart ; written, 2 pt. = 1 qt. 
 4 quarts = 1 gallon ; written, 4 qt. = 1 gal. 
 
 3. 2 gallons = how many quarts ? 
 
 4. From a gallon of milk how many quarts could be 
 sold ? how many pints ? 
 
 5. Mrs. Adams buys 2 quarts of milk per day. How 
 many quarts does she buy in 20 days ? how many 
 gallons ? 
 
 6. At 6^ per quart, how much does the milk cost 
 her per week ? 
 
 7. From a cask containing 3 gallons of vinegar, how 
 many quarts could be sold ? 
 
 8. How many pints are there in 12 quarts? how 
 many gallons ? 
 
 Copy these problems and insert the answers in the 
 blank spaces : 
 
 9. 1 qt. = pt. 14. 4 gal. = qt. 
 
 10. 8 qt. = gal. 15. 24 qt. = gal. 
 
 11. 16 pt. = qt. 16. 6 pt. = qt. 
 
 12. 8 gal. = pt. 17. 4 qt. = gal. 
 
 13. 8 pt. = qt. 18. 5 gal. = pt. 
 
Oral] 
 
 MEASURES 
 
 I 
 
 MEASURES OF WEIGHT 
 
 1. Tell how the following articles are sold : 
 Butter, eggs, milk, cheese, coal, oil. 
 
 2. Give the tables of 
 
 liquid measures and dry 
 measures. 
 
 The smallest weight 
 in the picture is called 
 an ounce weight. The 
 largest weight is a six- 
 teen-ounce weight, and 
 is called a pound weight. 
 
 Any article that the 
 pound weight balances 
 is said to weigh just one 
 pound. 
 
 16 ounces = 1 pound ; written, 16 oz. = 1 lb. 
 
 3. A lady's purchase at the store is balanced by the 
 8 oz. weight. What is the weight of her package ? 
 
 4. 6 oz. + 4 oz. 4- 6 oz. = lb. 
 
 5. 10 oz.-fl2 oz. + lO oz. = lb. 
 
 6. Jlb. = oz. ilb. = — oz. |-lb. = oz. 
 
70 THIRD YEAR [Oral 
 
 MEASURES OF LENGTH OR DISTANCE 
 
 1. Examine a foot rule. 
 
 2. Into how many parts do the long marks divide 
 the rule ? 
 
 3. The distance between any two of these marks is 
 called one inch. 
 
 4. Count the inches in a foot. 
 
 5. Place the rule on a paper or on the blackboard 
 and mark oft' a line 12 inches long. 
 
 6. A line 12 inches long is called one foot. 
 
 12 inches = 1 foot ; written, 12 in. = 1 ft. 
 
 7. Short distances are measured in inches ov feet, 
 
 8. 6 inches is what part of a foot ? 
 
 9. Draw a line J ft. in length. How many inches 
 long is the line ? 
 
 10. Draw a line J ft. in length. How many inches 
 long is this line ? 
 
 11. Without the aid of a rule, draw a line 12 inches 
 in length ; 6 inches in length ; 2 feet in length. 
 
 12. Place the rule on the lines in problem 11 and 
 observe how much too long or too short they were 
 drawn. 
 
 Pupils should practice this kind of work until they can esti- 
 mate length quite accurately. 
 
Oral and Written] MEASURES 73 
 
 MEASURES OF LENGTH OR DISTANCE 
 
 1. Measure the top of your desk in feet and inches. 
 
 2. J ft. = inches ; J ft. = inches. 
 
 3. Some articles are sold by a measure 3 times the 
 length of a foot rule. Name some of them. 
 
 4. Draw a line on the blackboard 3 feet in length. 
 
 5. The line you have drawn is one yard long. 
 
 3 feet = 1 yard ; written, 3 ft. = 1 yd. 
 
 6. A piece of cloth is 6 yards long. How many 
 
 feet is it in length ? 
 
 Copy and fill in the blanks : 
 
 7. 36in. = ft. 13. 4 ft. = in. 
 
 8. 3ft. = yd. 14. 21 ft. = in. 
 
 9. 2 ft. = in. 15. 31 yd. = ft. 
 
 10. 60in. = ft. 16. 15 ft. = yd. 
 
 11. 18ft. = yd. 17. 7 yd. = ft. 
 
 12. 3 ft. = in. 18. 6 ft. = in. 
 
 Change : 
 
 19. 2 ft. and 3 in. to inches. 25. 36 in. to yards. 
 
 20. 3 ft. and 4 in. to inches. 26. 12 ft. to yards. 
 
 21. 4 yd. and 1 ft. to feet. 27. 24 in. to feet. 
 
 22. 6 yd. and 2 ft. to feet. 28. 48 in. to feet. 
 
 23. 27 in. to feet and inches. 29. 36 yd. to feet. 
 
 24. 16 ft. to yards and feet. 30. 5^ yd. to feet. 
 
72 THIRD YEAR [Oral and Written 
 
 READING AND WRITING NUMBERS 
 
 In reading large numbers, separate them by commas 
 into groups of three figures each, beginning at the right. 
 
 Each group is called a period and has ones place, 
 tens^ place, and hundreds' place. The last period to the 
 left may contain only one or two figures ; as, 8,245 ; 
 28,375. 
 
 Beginning at the right, the places in 24,205 are called 
 ones^ tens, hundreds, thousands, tens of thousands. The 
 number is read, '' 24 thousand, 205." 
 
 Copy, point off into periods, and read : 
 
 abed 
 
 1. 45268 65283 25834 31849 
 
 2. 39371 94736 93687 40306 
 
 3. 20905 18110 60009 37000 
 
 ROMAN NUMERALS 
 
 1. Write the Roman numerals from 11 to 19. Place 
 X before each. This gives the numerals from 21 to 29. 
 
 2. XXX - 30. L = 50. XL = 40. 
 
 Write the numerals from 31 to 40 ; from 41 to 50. 
 
 3. LX = 60. LXX = 70. LXXX = 80. 
 Write the numerals from 50 to 70. 
 
 4. C = 100. CC = 200. XC = 90. XCIX = 99. 
 Write the numerals from 70 to 100. 
 
 Write 210, 290, 299, 300, 349, 235, 341. 
 Read XCIT, CIX, CCXL, CCXCIX 
 
Written] UNITED STATES MONEY 73 
 
 ADDITION AND SUBTRACTION OF U. S. MONEY 
 
 Eead and add : 
 
 a 
 
 6 
 
 e 
 
 d 
 
 $286.75 
 
 $364.92 
 
 $615.94 
 
 $961.37 
 
 931.49 
 
 19.39 
 
 293.29 
 
 149.95 
 
 86.72 
 
 187.46 
 
 89.67 
 
 98.69 
 
 73.87 
 
 29.84 
 
 173.28 
 
 83.75 
 
 68.45 
 
 382.73 
 
 8.75 
 
 278.87 
 
 $24.35 
 
 $15.46 
 
 $21.95 
 
 $43.74 
 
 13.64 
 
 33.71 
 
 15.84 
 
 17.27 
 
 71.25 
 
 16.15 
 
 22.65 
 
 33.75 
 
 45.32 
 
 32.43 
 
 16.34 
 
 45.45 
 
 3. $ 8692 + $ 193.75 + $ 475.86 + $ 286.37 + $ 90 
 
 4. $ 187.14 + % 275.61 + $ 630.18 + $ 5.25 + $ 0.18 
 
 5. $ 263.35 + $ 436.75+ $ 195.19 + $ 2.75 + $ 84 
 
 Subtract : 
 
 
 
 
 a 
 
 h 
 
 c 
 
 d e 
 
 6. $243.56 
 
 $315.46 
 
 $254.73 
 
 $269.46 $226.42 
 
 186.38 
 
 169.75 
 
 80.06 
 
 178.95 9.70 
 
 7. $486 35 $268.43 $124.39 $923.14 $275.86 
 
 129.76 174.85 86.41 189.67 185.86 
 
 Find the difference between : 
 
 8. $406.75 and $216.40 ii. $436.74 and $175.12 
 
 9. $325.43 and $ 74.65 12. $263.37 and $144.00 
 10. $468.36 and $196.09 13. $276.10 and $186.19 
 
74 THIED YEAR [Oral and Written 
 
 HALVES 
 
 1. Into how many parts has the circle 
 been divided ? What is the name of each 
 part ? Into how many halves can an ob- 
 ject be divided ? 
 
 2. 1 half apple + 1 half apple = ? $1 + $| = ? 
 
 3. 1 half dozen + 1 half dozen = ? ^ yd. + ^ yd. = ? 
 Find the sum of : 
 
 4. 11 gal. 
 3 gal. 
 
 5. 
 
 41 bu. 
 21 bu. 
 
 6. 51 
 
 yd. 7. 
 
 yd. 
 
 3Jqt- 
 *qt. 
 
 8. Add: 
 
 
 
 
 
 
 15^ i + i = l; 1 + | = 1|. 
 
 9J Write the fraction 
 
 6J numbers. 
 31J 
 
 • 
 J, and add 1 to the whole 
 
 9. 41 + 271 
 
 + H 
 
 
 11. 
 
 111 + 251 
 
 + 421 
 
 10. 91 + 181 
 
 + 27| 
 
 
 12. 
 
 9 +371 
 
 + 86^ 
 
 Insert the missing 
 
 13. ^ n 
 
 + + 
 
 number : 
 
 + 
 
 8* 
 + 
 
 9* 
 
 + 
 
 11 
 
 + 
 
 101 
 
 l^ 
 
 n 
 
 12* 
 
 18* 
 
 201 
 
 Subtract : 
 14. 81 
 
 -5 
 
 -3 
 
 12* 
 -10* 
 
 11* 
 
 - n 
 
 14* 
 
 - 7* 
 
 16* 
 
 - 8* 
 
 15. 241 
 
 - 71 - 
 
 17i 
 
 ^ 
 
 251 
 -18* 
 
 38* 
 
 -251 
 
 621 
 -37 
 
 49| 
 -261 
 
Oral and Written] 
 
 FRACTIONS 
 
 u 
 
 '/3 
 
 '/3 
 
 •/3 
 
 THIRDS 
 
 1. How many thirds are there in 
 the oblong? How many thirds are 
 there in one of anything ? in 1 yard ? 
 How many feet are there in 1 yard ? What part of a 
 yard is 1 foot ? What part of a yard is 12 inches ? 
 How many thirds are there in 2 oranges ? 
 
 Add: 
 
 2. i+i = i J + l + i=iorl |-|-| + | = |,or2 
 
 a h c d e 
 
 3. '" 
 
 5. 
 
 4* 
 
 61 
 
 5i 
 
 8J 
 
 9* 
 
 + 21 
 
 + li 
 
 + 4 
 
 + 5* 
 
 + 11 
 
 8J 
 
 7f 
 
 9* 
 
 7 
 
 12 
 
 10* 
 
 H 
 
 5 
 
 8| 
 
 8* 
 
 121 
 
 M 
 
 M 
 
 6i 
 
 9| 
 
 id the 
 
 missing number 
 
 : 
 
 
 
 ^ 
 
 % 
 
 7 
 
 15J 
 
 8f 
 
 + 
 
 + 
 
 + 
 
 + 
 
 + 
 
 111 
 
 14f 
 
 12| 
 
 18| 
 
 lit 
 
 7* 
 
 8§ 
 
 9f 
 
 18f 
 
 17| 
 
 -3 
 
 -5^ . 
 
 -4f 
 
 - 5| 
 
 -9| 
 
 7. I rubbed out 2| inches from a line 5f inches long. 
 How long was the part remaining ? 
 
76 
 
 THIRD YEAR [Oral and Written 
 
 FOURTHS 
 
 1. Into how many parts has the 
 square been divided? Give the name 
 of each part. What is the difference 
 between a quarter and a fourth of $ 1 ? 
 of 1 pie ? of 1 apple ? Into how many 
 fourths can any object be divided ? 
 
 4+i + 4=how many fourths ? f gal. -f J gal 
 
 Find the sum : 
 
 'U 
 
 'A 
 
 'A 
 
 y^ 
 
 2. $2i+$| 
 
 4. 
 
 6i 
 
 gal. + 1 gal. 6. 
 
 81 bu. + f bu. 
 
 3. 61+ i 
 
 5. 
 
 H 
 
 pk. +2|pk. 7 
 
 7|hr. + li hr. 
 
 Add: 
 
 
 
 
 
 a 
 
 h 
 
 
 c A 
 
 e / 
 
 8. 2i 
 
 6i 
 
 
 5i 3i 
 
 lOf 121 
 
 3f 
 
 11 
 
 
 6i 8i 
 
 7f 9 
 
 5i 
 
 8f 
 
 
 25i 9i 
 
 8| 8| 
 
 9. 11 
 
 18f 
 
 
 191 1 
 
 h\ 201 
 
 141 
 
 16f 
 
 
 8 1 
 
 6| 8 
 
 271 
 
 21| 
 
 
 62f 1 
 
 17 31| 
 
 Complete : 
 
 
 
 
 
 10. 41 + ?= 9f 
 
 12. 
 
 6i + ?=lli 
 
 14. ? + 8i = 15i 
 
 11. 6|+?=8| 
 
 
 13. 
 
 9i + ?=13f 
 
 15. ?+ 1= G| 
 
 Find the difference : 
 
 
 
 16. 81-7 
 
 
 19. 9|- SJ 
 
 22. 19|-7i 
 
 17. 16|-5i 
 
 
 20. 161- 71 
 
 23. 161-8 
 
 18. 23f-7f 
 
 
 21. 12|-11| 
 
 24. 141-7 
 
Written] PRACTICAL PROBLEMS 77 
 
 PRACTICAL PROBLEMS 
 
 1. A dealer sold 2^ tons of coal at one time and 3 J 
 tons at another time. How many tons did he sell ? 
 
 2. From a barrel containing 31J gallons, 25 gallons 
 were sold. How many gallons remained ? 
 
 3. A dairyman sold in one month 1875 J gallons of 
 milk. He sold 250 gallons less the next month. How 
 much did he sell the second month ? 
 
 4. A farmer picked potatoes as follows : 23 bu., 
 24ibu., and 111 bu. How many bushels did he pick? 
 
 5. After selling 56^ bu. of the potatoes, how many 
 bushels remained ? 
 
 6. 7f yards of silk were cut from a piece containing 
 18f yards. How many yards remained ? 
 
 7. A dressmaker used 5| yards of cloth for a skirt 
 and 2| yards for a waist. How many yards did she use 
 for both ? 
 
 8. Mr. Miller owned 301 acres of land. He kept 241 
 acres and sold the remainder at $48 an acre. How 
 much did he receive for the part sold ? 
 
 9. Find the weight of 4 baskets of butter contain- 
 ing 351 lb., 18 lb., 221 lb., and 16 lb., respectively. 
 
 10. Harry made 8 J gallons of lemonade and sold 7 
 gallons. How much was unsold ? 
 
 11. Find the distance around a room that is 18| ft. 
 long and 16 ft. wide. 
 
78 THIRD YEAR [Oral and Written 
 
 REVIEW 
 
 1. Count by 5's from to 100. 
 
 2. Count by 6's from to 120. 
 
 The sign @ followed by a price means " at " so much 
 a unit. ThuSj " 3 lb. steak @ 15 ^ " means " 3 lb. steak 
 at 15^ a pound;'' "6 doz. buttons @ 20^" means 
 "6 doz. buttons at 20^ a dozens 
 
 Find the amount of each of the following : 
 
 3. 3 lb. steak @ 15^'. 
 
 4. 6 bu. potatoes @ 48 ^. 
 
 5. 6 lb. sugar @ 4 ^. 
 
 6. 5 cans tomatoes @ 12^. 
 
 7. 6 doz. eggs @ 22^. 
 Find the cost of : 
 
 8. 5 sheep @ $ 4.75. i3. 6 hats @ $1.25. 
 
 9. 6 bureaus @ $7.75. 14. 5 books @ $ 1.75. 
 
 10. 6 cows @ $48. 15. 6 lamps® $1.33. 
 
 11. 6 rugs® $4.75. 16. 6 wagons ® $85. 
 
 12. 5 vases ® $2.65. i7. 5 horses ® $ 175. 
 
 18. Add 45 and 56, thus : 45 and 50 are 95 ; 95 and 
 6 are 101. 
 
 Add in the same way : 
 
 19. 35 and 48 23. 78 and 64 27. 19 and 96 
 
 20. 18 and 25 24. 84 and 76 28. 78 and 97 
 
 21. 20 and 46 25. 93 and 42 29. 87 and 46 
 
 22. 81 and 72 26. 48 and 75 30. 96 and 41 
 
Oral and Written] MULTIPLICATION 
 
 79 
 
 MULTIPLYING BY 7 
 
 1. Count by 7's to 21 ; to 42 ; to 63 ; to 84. 
 
 2. 2x7 = ? 3x7 = ? etc., to 12 x 7 = ? 
 
 3. Build the table of 7's. 3^-^ 
 
 4. Compare in value 5x7 and ^y ^^ 
 7x5; 3x7 and 7x3; 7x6 and J 7^. |5 
 6x7; 7 X 2 and 2 X 7; 4 x 7 and 7 x 4, 
 
 Table of 7's 
 
 8" ^ 
 
 1x7= 7 
 
 7x7 = 49 
 
 2x7 = 14 
 
 8x7 = 56 
 
 3x7 = 21 
 
 9x7 = 63 
 
 4x7 = 28 
 
 10x7 = 70 
 
 5 X 7 = 35 
 
 11x7 = 77 
 
 6x7 = 42 
 
 12x7 = 84 
 
 5. Memorize the table. 
 
 6. What multiplicand 
 and multiplier make: 
 
 49 12 36 28 24 
 
 35 30 14 18 14 
 
 25 42 20 27 21 
 
 63 84 77 72 54 
 
 a 
 2456 
 x7 
 
 7739 
 x7 
 
 h 
 3265 
 x7 
 
 8497 
 x7 
 
 C 
 
 4157 
 x7 
 
 6198 
 
 X 7 
 
 d 
 
 8963 
 x7 
 
 5424 
 x7 
 
 « 
 9045 
 x7 
 
 6339 
 
 X 7 
 
 Multiply by 7, testing answers : 
 9. 4693 7528 6934 8576 7935 
 
 10. 7208 5697 2469 3875- 8094 
 
80 
 
 THIRD YEAR [Oral and Written 
 
 MULTIPLYING BY 8 
 
 1. Count by 8's to 24 ; to 64 ; to 96. 
 
 2. How many are 2x8 balls ? 3 x 8 books ? 4x8 
 
 4 boys ? 5x8 pens ? 6x8 apples ? 
 
 ^"""^^ 3. Build the table of 8's. 
 12/ V 4. Give quickly: 
 
 '"^ / 6x 8 
 
 8x 6 7x8 5x 8 
 
 yii 8x 4 
 
 8x10 8x2 8x11 
 
 -^ 8x12 
 
 4x 8 6x8 8x 5 
 
 Table of 8's 
 
 5. Memorize the table. 
 
 1x8= 8 
 
 7x8 = 56 
 
 2x8 = 16 
 
 8x8 = 64 
 
 3x8 = 24 
 
 9x8=72 
 
 4x8 = 32 
 
 10x8 = 80 
 
 5x8 = 40 
 
 11x8 = 88 
 
 6x8 = 48 
 
 12x8 = 96 
 
 a 
 
 7. 6230 
 
 8. 2937 
 
 9. 9048 
 
 b 
 5178 
 8694 
 6937 
 
 6. Give answers: 
 
 ?x8 = 32 
 
 6x ? = 48 
 
 ?x8 = 72 
 lOx ? = 80 
 12x ? = 96 
 
 Multiply by 8 
 
 c d 
 
 8629 9310 
 
 9083 8697 
 
 2865 4705 
 
 7x ? = 56 
 ?x5 = 40 
 8x ?=64 
 ?x3 = 27 
 2x ?=18 
 
 e 
 
 7865 
 7289 
 8136 
 
 Give products at sight : 
 
 10. 8x50 8x70 8x91 8x12 8x31 
 
 11. 7x40 7x60 7x71 8x11 7x20 
 
 12. 8x90 7x81 8x30 7x21 8x61 
 
Written] 
 
 MULTIPLICATION 
 
 81 
 
 PRACTICAL PROBLEMS 
 
 1 
 
 
 
 I HBBBBB 
 
 BBBHBB 
 
 , BBBBBB J 
 • BBBBBB ' 
 
 BBBBBB 
 
 BBBBBB 
 BBBBBB 
 
 BBBBBB 
 ^—. fl 
 
 1. This schoolroom is 32 
 feet long and 28 feet wide'. 
 What is the distance around 
 it? 
 
 2. The glass in each win- 
 dow cost $2.50. How much 
 was paid for all the glass ? 
 
 3. Each desk cost $3.25. 
 Find the cost of the desks 
 in each long row. 
 
 4. Find the value of the desks in the 6 rows. 
 
 5. The attendance for the first 8 school days was as 
 follows: 36, 43, 42, 43, 37, 41, 43, 43, respectively. 
 What was the average attendance ? 
 
 Note. — To find the average add the eight numbers and divide 
 the sum by 8. 
 
 6. Eight tons of coal were used during the term. 
 How much w^as paid for the coal at $ 4.50 a ton ? 
 
 7. What is the amount of the teacher's salary for 8 
 months, at $ 50 a month ? 
 
 8. Find the entire cost of : 
 
 8 Advanced Geographies at $1.00 each. 
 8 Primary Geographies at $ .45 each. 
 8 Grammars at $ .50 each. 
 8 Language Lessons at $ .35 each. 
 8 Readers at $ .48 each. 
 
82 
 
 TPIIRD YEAR [Oral and Written 
 
 DIVIDING BY 7 
 
 1. How many times is 7 contained in 14? in 21? 
 42? 63? 28? 35? 49? 70? 77? 56? 
 
 2. Find! of 84; 63; 42; 35; 56; 70; 14; 21. 
 
 Divide : 
 
 a b c d e f 
 
 3. 7H2 7)63 7)56 7)49 7)84 7)35 
 
 4. 6)72 5)45 
 
 6)42 
 
 7)28 
 
 6)48 
 
 7)70 
 
 Divide by 7 : 
 
 
 
 
 
 5. 84 56 
 
 59 
 
 68 
 
 45 
 
 36 
 
 6. 217 364 
 
 427 
 
 637 
 
 273 
 
 696 
 
 Divide and test : 
 
 
 
 
 
 7. 7 )2436 6 )7391 7 )8693 6)7857 7 )4693 
 a 5)2609 7)8054 6)3079 7)2096 5)8097 
 
 9. 7 )7381 6)2867 7 )2536 5)3204 7 )6973 
 
 10. How many 7-pound boxes can be filled from 
 259 pounds of barley ? 
 
 11. How many weeks are there in 49 days ? 
 
 12. How many suits, each requiring 7 yards, can be 
 made from a piece of cloth containing 84 yards ? 
 
 13. How many 7^ packages of crackers can be bought 
 for $ 1, and how much money will be left ? 
 
Oral and Written] 
 
 DIVISION 
 
 83 
 
 1. 48-8-8-8 
 
 2. 2x8 = ? 16 
 
 3. 32^8 = ? 40 
 
 4. 64 contains 8, — 
 56 contains 8, — 
 96 contains 8, — 
 
 Give quotients : 
 a b 
 
 5. 8]64 8}32 
 
 6. 8U6 
 
 7. 7)_35 
 
 Find: 
 
 8. 1 of 72 
 
 9. 1 of 640 
 
 DIVIDING BY 8 
 
 8-8=? 48-^6 = ? 
 
 2 = ? 8x3 = ? 24-^8 = ? 8x4 = ? 
 
 5 = ? 56-^8 = ? 64^8 = ? 72-^8 = ? 
 
 times 
 times 
 times 
 
 72 contains 8, 
 48 contains 8, 
 88 contains 8, 
 
 7)_56_ 
 8)88 
 
 lof 64 
 1 of 720 
 
 c d 
 
 8}40 8)72 
 
 8 )24 7)63 
 
 7 )28 8)_96 
 
 1 of 32 1 of 56 1 of 48 
 1 of 400 i of 320 J of 800 
 
 times 
 times 
 times 
 
 e 
 
 8)56 
 
 8)48 
 
 8)80 
 
 Divide by 8: 
 
 10. 175 823 629 473 621 
 
 11. 8073 2096 3075 4083 6029 
 
 12. 2903 8107 2904 7908 8604 
 
 13. 6195 2936 8629 4175 2936 
 
 14. Hov^^ many tablets at 8^ each can be bought for 
 $ 1, and how^ many cents will be left ? 
 
 15. A furniture dealer paid $ 240 for ice chests at 
 $ 8 each. How many chests did he purchase ? 
 
84 
 
 THIRD YEAR 
 
 [Written 
 
 MULTIPLICATION BY MIXED NUMBERS 
 
 A mixed number is composed of an integer and a 
 fraction. 
 
 1. Multiply 16 by 2i. 
 
 16 
 
 2i 
 
 lofl6= 8 
 2 xl6 = 32 
 
 2 J times 16 means that 
 i of 16 is to be added to 
 
 21x16 = 40 
 
 Find products : 
 
 2. 
 
 -tt: 2 times 16. 
 
 3. 
 4. 
 5. 
 6. 
 7. 
 
 21x24 
 21x36 
 41 X 96 
 81x84 
 6| X 60 
 81x120 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 13. 
 
 71x336 
 81 X 124 
 91 X 276 
 71 X 324 
 51 X 288 
 7^x240 
 
 Shout Form 
 
 
 16 
 
 
 t 
 
 2i 
 8 
 
 
 3 
 
 32 
 40 
 
 
 14. 
 
 81 X 
 
 273 
 
 15. 
 
 61 X 
 
 258 
 
 16. 
 
 8ix 
 
 744 
 
 17. 
 
 91 X 
 
 275 
 
 18. 
 
 51 X 
 
 392 
 
 19. 
 
 9^x 
 
 413 
 
 Find the cost of: 
 
 20. 8|- gal. oil @ 12^. 27. 
 
 .21. 6|- bu. potatoes @ 80)^. 28. 
 
 22. 81 yd. silk @ $ 1.20. 29. 
 
 23. 7 1 gal. milk @ 16^. 30. 
 
 24. 6;^ doz. bananas @ 24^. 31. 
 
 25. 61 doz. buttons @ 54 j^. 32. 
 
 26. 7 J yd. ribbon @ 28^, 33. 
 
 71 doz. buttons @36^. 
 9-J- hours' work @ 18^. 
 8 J pounds butter @ 32 ^. 
 6^ pounds meat® 16^. 
 7^ pk. peaches @ 40^. 
 3|- yd. muslin @ 16^. 
 411b. candy @ 60^. 
 
Oral and Written] MULTIPLICATION 
 
 85 
 
 MULTIPLYING BY 9 
 
 1. Count by 9's to 27 ; to 54 ; to 72 ; to 108. 
 
 2. Build the table of 9's. 
 
 3. Compare 6x9 and 9x6; 8x9 and 9x8; 10 x 9 
 
 and 9 X 10. 
 
 4. Multiply at sight by 9 : 
 40 60 80 20 50 10 30 
 
 Table of p's 
 
 1x9= 9 
 
 7x9= 63 
 
 2x9 = 18 
 
 8x9= 72 
 
 3x9 = 27 
 
 9x9= 81 
 
 4x9 = 36 
 
 10x9= 90 
 
 5 X 9 = 45 
 
 11x9= 99 
 
 6 X 9 = 54 
 
 12x9 = 108 
 
 70 90 31 51 71 
 
 Memorize the table. 
 
 Give two numbers that form each of these products : 
 
 6. 21, 36, 44, 48, 50, 40, 54, 45, 33, 18, 27, 99. 
 
 7. 88, 90, 60, 77, 81, 63, 66, 72, 56, 108, 96, 80. 
 Multiply by 9 : 
 
 a b c d e 
 
 8. 4693 7286 4615 8738 6957 
 
 9. 4135 2874 6398 1869 7043 
 
 10. 8286 3697 4589 2893 9097 
 
 11. 9387 2945 9384 9387 2864 
 
 12. 6005 7894 5009 6090 7500 
 
 13. 5020 4080 3074 8005 9999 
 
86 
 
 THIED YEAR 
 
 [Oral and Writtea 
 
 
 MULTIPLYING BY 
 
 9 
 
 
 Multiply by 
 a 
 1. 4226 
 
 9: 
 
 b 
 8393 
 
 c 
 3786 
 
 a 
 
 2468 
 
 e 
 8321 
 
 2. 5483 
 
 6692 
 
 2294 
 
 8329 
 
 6245 
 
 3. 6396 
 
 2594 
 
 4968 
 
 5692 
 
 9374 
 
 4. 7278 
 
 7246 
 
 5328 
 
 7386 
 
 8928 
 
 Find the products: 
 5. 9 X 38 gal. 9 X 24 da. 9 x 16 min. 
 II 6. 9 X 17 bu. 9 X 25 mo. 9 x 25 horses 
 
 7. 9x12 ft. 9x18^ 9x35 cows 
 
 8. Find products by 7 ; by 8 ; by 6. 
 
 Table of Elementary Products 
 
 In multiplication, there are 45 different combinations 
 of figures taken two at a time, and 36 different prod- 
 ucts. Use these combinations for drill frequently : 
 
 1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 3 
 
 1 
 
 1 
 
 4 
 
 1 , 
 
 1 
 
 2 
 
 3 
 
 2 
 
 4 
 
 5 
 
 2 
 
 6 
 
 7 
 
 2 
 
 8 
 
 3 
 
 1 
 
 5 
 
 6 
 
 4 
 
 7 
 
 5 
 
 ,4 
 
 8 
 
 9 
 
 6 
 
 3 
 
 9 
 
 2 
 
 2 
 
 3 
 
 2 
 
 3 
 
 4 
 
 2 
 
 2 
 
 3 
 
 5 
 
 7 
 
 8 
 
 6 
 
 5 
 
 9 
 
 7 
 
 6 
 
 8 
 
 7 
 
 6 
 
 4 
 
 3 
 
 3 
 
 4 
 
 5 
 
 3 
 
 4 
 
 5 
 
 4 
 
 5 
 
 6 
 
 9 
 
 8 
 
 7 
 
 9 
 
 8 
 
 7 9 
 
 8 
 
 9 
 
 8 
 
 9 
 
 9 
 
 4 
 
 5 
 
 6 
 
 5 
 
 6 
 
 7 6 
 
 7 
 
 7 
 
 8 
 
 8 
 
 9 
 
Oral and Written] DIVISION 87 
 
 DIVIDING BY 9 
 
 1. How many tables, at $9 each, can be bought for 
 $18? for $27? for $36? for $45? for $63? 
 
 2. Give quotients at sight : 
 
 63 H- 9 
 
 81^9 
 
 45^5 
 
 36^4 
 
 108^9 
 
 72^8 
 
 54H-6 
 
 72-4-9 
 
 27^8 
 
 90^9 
 
 lof 36 
 
 ^of 63 
 
 lof 54 
 
 iof 56 
 
 ioi 72 
 
 J of 64 
 
 iof45 
 
 ^of45 
 
 lof 63 
 
 |of 56 
 
 3. Tell at sight which is greater and how much: 
 1 of 81 or 1 of 27 I of 40 or i of 45 
 
 1 of 64 or 1 of 16 1 of 63 or i of 81 
 
 Divide by 9 ; then by 8 : 
 
 a b c d e 
 
 4. 2637 1856 2934 7683 8174 
 
 5. 6385 2097 3084 6075 7238 
 
 6. 8462 3761 2985 2207 3604 
 
 7. 7581 6293 8697 2984 6093 
 
 8. Give quotients at sight : 
 
 180-^-9 360^9 900-^9 720-^9 729-^9 
 279^9 549^9 459^9 639^9 450^9 
 
 9. If a postman delivers 954 letters in 9 hours, how 
 many letters does he average in one hour ? 
 
 10. How many times can 9 inches be marked o£E 
 from a line 4J feet in length ? 
 
 11. At 3 melons for 15 cents, how many melons can 
 I buy for 45 cents ? 
 
88 . THIRD YEAR [Written 
 
 DIVISION OF DOLLARS AND CENTS 
 
 Find the products ; test and read answers : 
 
 a b c 
 
 1. 4 X $2.75 7 X $82.93 8 x $93.15 
 
 2. 5 X $3.86 8 X $46.25 9 x $73.86 
 
 3. 6 X $7.27 9 X $73.87 7 x $49.25 
 
 4. Divide $6.15 by 3. 
 
 Divide $ 6.15 by 3, placing a decimal 
 3)$ 6.15 point under tlie decimal point in the divi- 
 $2.05 dend. Write the dollar sign before the 
 number of dollars in the quotient. 
 
 Find the quotients , read and test answers : 
 
 a 
 
 5- $4.75-^2 
 
 b 
 
 $6.75 + 4 
 
 c 
 $29.34 + 9 
 
 6. 12.08 + 2 
 
 7. $9.27 + 3 
 Find: 
 
 $8.22 + 6 
 $9.05 + 5 
 
 $46.72 + 8 
 $71.05 + 7 
 
 a J of $27.15 i of $16.64 
 9. |of $18.24 ^of $26.70 
 10. iof $20.48 lof $38.40 
 Perform the operation indicated: 
 
 1 of $39.34 
 J of $97.68 
 lof $27.36 
 
 11. $273.84 + 6 
 
 $263.75 + 8 
 
 $375.42 + 6 
 
 12. $936.25x5 
 
 $423.96x9 
 
 $495.67 + 7 
 
 13. $475.83x6 
 
 $928.14 + 6 
 
 $321.21 + 9 
 
 14. $721.98 + 9 
 
 $743.68 + 7 
 
 $563.94x8 
 
 15. $435.72 + 8 
 
 $269.19 + 9 
 
 $732.75x6 
 
Written] MULTIPLICATION AND" DIVISION 
 
 89 
 
 PRACTICAL PROBLEMS 
 
 1. It requires 4 yd. of 
 material to make each 
 of these girls an apron. 
 How much will be re- 
 quired for the class of 7 
 girls ? 
 
 2. At 8^ a yd., how 
 much will 7 aprons cost ? 
 
 3. Out of 91 yd. of 
 cambric, how many caps, 
 requiring ^ yd. each, can 
 be made ? 
 
 4. How many pupils 
 can be supplied with 
 rolling pins and pie pans 
 
 out of $ 9, if each pin costs 20^, and each pan 10^? 
 
 5. At 18^ a yard, find the cost of lawn for sleeve 
 protectors for 7 girls, each sleeve requiring | yd. 
 
 6. Miss Blew, the teacher, purchases the following : 
 7 flour cans @ 40^, 7 cake pans @ 25^, 7 sugar shakers 
 @ 17^. Find the amount of her purchases. 
 
 7. Entertaining the directors, this class uses 7 spring 
 chickens @ 40^, 2 pecks of potatoes @ 15^, 1 head 
 cabbage @ 8^, 2 boxes tomatoes @ 10^, |- lb. butter @ 
 32^, 2 pt. cream @ 8^, and J gallon ice cream @ $ 1.50 
 per gallon. How much does the dinner cost them ? 
 
90 THIRD YEAR [Written 
 
 MULTIPLICATION AND DIVISION 
 
 Multiply and divide by 8 ; by 9 : 
 
 a b 
 
 c d e 
 
 1. 2465 2469 
 
 2816 6824 6178 
 
 2. 7381 8397 
 
 9375 4836 8293 
 
 Find: 
 
 
 3. \ of 4687 sbeep 5. 
 
 i of 7353 bu. 7. 1 of 3600 
 
 4. i of 9376 horses 6. 
 
 i of 4347 gal. a i of 7479 
 
 How much change shall I receive from $10 for 
 
 the following ? Name the' 
 
 coins in each purchase. 
 
 9. 21 yd. silk® 60^ 
 
 11. 24 lb. butter® $J 
 
 10. 7^ doz. eggs @ 30^ 
 
 12. 31 bu. plums @ $ 2.50 
 
 Market Report 
 
 Grapes, per crate, $2.75 
 
 Peaches, per basket, $1..S5 
 
 Blackberries, per crate, |3.50 
 
 Pears, per bbl., $3.75 
 
 Raspberries, per crate, $3.65 
 
 Apples, per bbl., $3.50 
 
 Elderberries, per crate, $1.75 
 
 Cantaloupes, per box, $4.50 
 
 From the above report find the cost of : 
 
 13. 4 crates of blackberries. 20. 9 baskets of peaches. 
 
 14. 5 baskets of peaches. 21. 6 crates of blackberries. 
 
 15. 3 crates of grapes. 22. 5 crates of elderberries. 
 
 16. 3 crates of elderberries. 23. 7 crates of raspberries. 
 
 17. 4 bbl. of pears. 24. 6 bbl. of pears. 
 
 18. 2 boxes of cantaloupes. 25. 8 boxes of cantaloupes. 
 
 19. 6 bbl. of apples. 26. 8 baskets of peaches. 
 Make other problems from this or another Market 
 
 Report. 
 
Written] ADDITION 91 
 
 UNITED STATES MONEY 
 
 (Notice the groups that make 10 or 15.) 
 
 Add: 
 
 KX, 
 
 6 
 
 C 
 
 d 
 
 e 
 
 515.73 
 
 $30:861 $ 
 
 6.93 
 
 % .48 
 
 $ .17 
 
 6.98 
 
 15.29)'' 
 
 32.63 
 
 2.75 
 
 .28 
 
 .371 
 
 8.88 
 
 4.30 
 
 .76 
 
 5.70 
 
 5.18 P" 
 
 •^^Il5 
 
 12.51 
 
 5.85 
 
 16.37 
 
 40.60 
 
 7.27 1 '' 
 
 8.78 
 
 40.20 
 
 4.70 
 
 5.891 
 
 ;■ 1ft 
 
 23.851 
 
 \ 1ft 
 
 .36 
 
 6.58 
 
 23.96 
 
 .31]'" 
 
 .25 f"* 
 
 .50 
 
 18.64 
 
 .85 
 
 2. Mr. Foster sold in 5 days as follows. Find each 
 day's sales, total sales, and receipts for each article. 
 
 
 MON. 
 
 Tubs. 
 
 Wed. 
 
 Thurs. 
 
 FBI. 
 
 
 a 
 
 6 
 
 C 
 
 d 
 
 e 
 
 Corn 
 
 $75.25 
 
 $68.75 
 
 $27.35 
 
 $87.45 
 
 $64.65 
 
 Oats 
 
 18.42 
 
 26.73 
 
 16.72 
 
 29.63 
 
 37.26 
 
 Bran 
 
 6.75 
 
 3.75 
 
 8.25 
 
 7.75 
 
 9.45 
 
 Chop 
 
 12.34 
 
 8.65 
 
 17.38 
 
 15.24 
 
 16.28 
 
 Meal 
 
 3.60 
 
 5.40 
 
 7.60 
 
 12.60 
 
 17.20 
 
 Flour 
 
 47.25 
 
 68.25 
 
 78.75 
 
 89.25 
 
 110.25 
 
 3. A man made 7 deposits as follows : % 145.75, 
 $123.34, $ 134.89, $ 645.75, $ 800.05, $ 900.25, $845.52. 
 How much money did he deposit ? 
 
 4. My expenses for 6 days were respectively, $ 1.42, 
 
 $2.05, $2.36, $2.12, $1.45, and $2.15. What were 
 my expenses for the week ? 
 
92 
 
 1 
 1 
 
 
 THIRD YEAR 
 
 
 [Writtea 
 
 
 
 SUBTRACTION 
 
 
 
 1. 
 
 From 5000 take 3456. 
 
 
 • 
 
 
 4 9 9 10 
 
 
 6 from 10 leaves 4 
 
 
 
 5000 
 
 
 5 from 9 lea^ 
 
 •es 4 
 
 
 
 3456 
 
 
 4 from 9 leaves 5 
 
 
 
 1544 
 
 
 3 from 4 leaves 1 
 
 
 
 a 
 
 6 
 
 c 
 
 d 
 
 e 
 
 2. 
 
 6734 
 
 8090 
 
 7004 
 
 6000 
 
 9000 
 
 
 4578 
 
 5694 
 
 5896 
 
 4187 
 
 3999 
 
 
 2156 
 
 2396 
 
 1108 
 
 1913 
 
 5001 
 
 Subtract : 
 
 
 
 
 
 
 a 
 
 h 
 
 c 
 
 d 
 
 e 
 
 3. 
 
 9084 
 
 7604 
 
 5003 
 
 8460 
 
 6080 
 
 
 6097 
 
 4909 
 
 3806 
 
 7469 
 
 5908 
 
 4. 
 
 9600 
 
 7039 
 
 6800 
 
 7001 
 
 4403 
 
 
 3097 
 
 6799 
 
 5009 
 
 1903 
 
 3040 
 
 5. 
 
 5004 
 
 8040 
 
 7409 
 
 6400 
 
 7003 
 
 
 3904 
 
 4409 
 
 3790 
 
 4986 
 
 6800 
 
 6. 
 
 8703 
 
 6009 
 
 8001 
 
 5904 
 
 9878 
 
 
 5008 
 
 4939 
 
 6809 
 
 3400 
 
 4980 
 
 7. 
 
 7003 
 
 5900 
 
 9204 
 
 7405 
 
 5900 
 
 
 4906 
 
 3098 
 
 8909 
 
 6097 
 
 4397 
 
Written] REVIEW 93 
 
 TEST EXERCISES 
 
 Multiply, practicing until nine products can be found 
 in 2 minutes. 
 
 1. 4987 by 7 4. 2475 by 8 7. 6894 by 9 
 
 2. 6879 by 8 5. 8689 by 9 a 9829 by 7 
 
 3. 9836 by 9 6. 3978 by 7 9. 6375 by 8 
 
 10. 8564 by 7 ^ 13. 8739 by 9 le. 8795 by 9 
 
 11. 9873 by 9 * i4. 6927 by 8 17. 6938 by 7 
 
 12. 8293 by 8 15. 8738 by 9 is. 9375 by 8 
 
 19. 9365 by 8 22. 7693 by 7 25. 8756 by 9 
 
 20. 8796 by 9 23. 8795 by 8 26. 7938 by 9 
 
 21. 2493 by 7 24. 9283 by 9 27. 4695 by 7 
 
 Add rapidly : 
 
 a b c d e 
 
 28. 2401 2409 8145 3629 8873 
 
 6375 3875 2693 9483 2345 
 
 5816 4693 7856 2637 5690 
 
 2487 9301 9037 3415 2295 
 
 1789 1432 5009 8007 7986 
 
 29. 
 
 7895 
 
 9982 
 
 7743 
 
 2239 
 
 4498 
 
 2398 
 
 1028 
 
 3838 
 
 4075 
 
 7659 
 
 2015 
 
 5690 
 
 9723 
 
 9320 
 
 3376 
 
 1920 
 
 5497 
 
 4587 
 
 8756 
 
 5072 
 
 6099 
 
 4705 
 
 8243 
 
 6008 
 
 3490 
 
94 
 
 THIKD YEAR 
 
 [Written 
 
 PRACTICAL PROBLEMS 
 
 1. The drafting room is 24 feet wide and 28 feet 
 long. What is the distance around the room ? 
 
 2. There are 7 stands in the room. Each one cost 
 $ 5.50. What was the cost of all ? 
 
 3. Each stand requires a " T " square, angles, scale, 
 erasers, thumb-tacks, etc. The instruments cost $ 28.35. 
 What was the average cost of each stand ? 
 
 4. The first class worked 40 minutes on Monday 
 and Friday of each school week. How many min- 
 utes were spent by the class during 4 school weeks ? 
 
 5. Each of 7 boys required a drafting board costing 
 50^, ink, paper, pencils, etc., costing 25)^. What was 
 the cost of these materials for the class ? 
 
 6. The boys made two chairs valued at $ 8.75 each, 
 ^3 tabourettes at $3.25 each, and 4 book racks at 
 $1.25 each. What was the value of all the articles? 
 
Written] EEVIEW 95 
 
 TEST EXERCISES 
 
 Divide, practicing until the quotients for 9 problems 
 can be found in 2 minutes: 
 
 V 2873 by 7 4. 8196 by 8 7. 2403 by 9 
 
 2. 9865 by 8 5. 7963 by 9 a 8173 by 8 
 
 3. 4793 by 9 6. 8910 by 7 9. 6294 by 9 
 
 10. 7386 by 8 13. 8197 by 8 16. 4003 by 8 
 
 11. 8794 by 9 i4. 6934 by 9 17. 6920 by 7 
 
 12. 9387 by 9 15. 7879 by 7 la 3784 by 9 
 
 19. 9234 by 7 22. 6010 by 9 25. 3215 by 7 
 
 20. 6875 by 8 23. 5362 by 7 26. 8629 by 9 
 
 21. 4132 by 9 24. 8104 by 8 27. 9273 by 8 
 
 Subtract rapidly : 
 
 2a 4284 - 2141 31. 8001 - 6448 34. 8004 - 2234 
 
 29. 8401-1762 32. 6001-4999 35. 7982-5460 
 
 30. 8109-4777 33. 9845-3677 36. 5698-3472 
 
 37. 6024-5107 40. 9045-4254 43. 3498-2004 
 
 3a 8460-6418 4i. 8700-4286 44. 6699-3342 
 
 39. 7200-4540 42. 8760-4197 45. 7583-5620 
 
 46. 8794-4587 49. 6001-2478 52. 5590-1056 
 
 47. 8476-7421 50. 6424-3150 53. 9930 - 7810 
 4a 8921-5879 51. 4030-3289 54. 9706-5897 
 
96 THIRD YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. A huckster's sales for the week were as follows : 
 $ 3.25, S 7.15, $ 2.45, $ 6.45, and $ 8.79. What was the 
 amount of bis sales ? 
 
 2. A boy's suit that was marked $ 6.98 was sold for 
 $ 1.25 less. What was the selling price of the suit ? 
 
 3. James had $ 5.94 ; he spent $ 2.85. How much 
 had he leit ? 
 
 4. What is the difference in the price of two hats 
 marked $ 4.50 and $ 3.60 ? 
 
 5. The following amounts were deposited in the 
 school savings bank: $2.15, $1.65, $7.09, $3.68, and 
 $9.15. What was the total of these deposits? 
 
 6. Mrs. Jones paid $2.75 for a turkey, $.30 for 
 cranberries, $ .15 for butter, and $ .48 for coffee. What 
 was the whole cost ? 
 
 7. How many school badges 4 in. long can be made 
 from 2 vd. of ribbon ? 
 
 8. A clock that strikes the half hours strikes how 
 many times in a day ? 
 
 9. How many square inches are there in an 8-inch 
 square ? 
 
 10. There are 639 oranges in 9 baskets, with the same 
 number in each. How many are there in each basket ? 
 
 11. If yoii receive $2.75, $6.96, and $8.15 and want 
 to change it into five-dollar bills, how many should you 
 get and how much money over? 
 
Oral and Written] MULTIPLICATION 97 
 
 COMPARISON 
 
 1. Compare 10 with 5; thus, 10 is two times 5. 
 
 2. Compare 5 with 10; thus, 5 is | of 10. 
 
 Note. — We might also compare 5 with 10 by saying 10 is 5 
 more than 5; but, unless otherwise stated, "compare" in this 
 book means "find the quotient of the first number divided by the 
 second." 
 
 3. Compare 30 with 10; 20 with 5; 24 with 6. 
 
 4. Compare 5 with 15; 8 with 24; 12 with 48. 
 
 5. Compare 40 with 10; with 8; with 5; with 4. 
 
 6. Compare 25 with 5; 5 with 25. 
 
 7. When 2 pencils cost 10^, how much will 8 cost? 
 
 8. When 6 hats cost $12, how much will 12 cost? 
 
 9. When 4 knives cost $6, how much will 8 cost? 
 
 10. At 6 pens for 10^, how much will 18 cost? 
 
 11. When 6 horses cost $900, how much will 24 cost? 
 
 24 horses are 4 times 6 horses. Hence, they will cost 4 x $900, 
 or $3600. 
 
 12. When 5 cows cost $160, how much will 30 cost? 
 
 13. When 3 barrels of apples cost $7.50, how much 
 will 12 cost? 
 
 14. If 5 tons of hard coal cost $32.50, how much will 
 
 30 tons cost? 
 
 15. At $45 for 60 bu. of wheat, how much will 12 
 bu. cost? 
 
 16. If 12 men earn $51 in one day, how much will 
 60 men earn in one day at the same rate? 
 
98 
 
 THIRD YEAR 
 
 [Oral 
 
 MEASURES OF TIME 
 
 1. Name the letters on the face 
 of the clock. Tell the time. 
 
 2. Observe the small spaces on 
 the outer edge of the face. These 
 are called minute spaces. 
 
 3. Over how many of these spaces 
 does the long or minute hand move 
 
 in passing around the face from XII to XII again ? 
 
 4. How long is the minute hand in passing from 
 XII to I? from V to VI? from X to XI ? 
 
 5. There are the same number of minute spaces 
 hetween any two hours. 
 
 6. While the minute hand passes from XII to XII 
 again, how far does the short or hour hand move ? 
 
 7. How many minutes are there in an hour? in 
 2 hr. ? in 4 hr. ? in i hr. ? 
 
 8. When the hour hand is at XII, what is the time 
 if the minute hand points to V ? to III ? to I ? 
 
 9. Count the hours on the clock face from 9 o'clock, 
 the opening of school, until 9 o'clock, the next morn- 
 ing. How many are there ? These 24 hours include 
 both day time and night time. 
 
 60 minutes = 1 hour ; written, 60 min. = 1 hr. 
 24 hours = 1 day; written, 24 hr. = 1 da. 
 
Oral] 
 
 MEASURES OF TIME 
 
 99 
 
 The day always begins at XII, midnight. The time 
 from midnight to noon is called forenoon. The time 
 from XII, noon, to midnight is called afternoon. 
 
 We write A.M. for forenoon and P.M. for after- 
 noon. 8 : 20 A.M. is read 20 minutes past eight in the 
 morning. 
 
 10. Read 6:10 a.m.; 4:25 a.m.; 6:30 p.m.; 6:45 
 P.M.; 10:00 A.M.; 5:05 P.M. 
 
 11. How many hours is it from 9 a.m. to 5 p.m.? 
 from 10 P.M. to 6 a.m. ? 
 
 12. How many days is it from 9 o'clock Monday 
 morning to 9 o'clock the next Monday morning? 
 
 7 days = 1 week ; written, 7 da. = 1 wk. 
 
 13. On what day did Feb. 1, 
 1907, fall ? Make a calendar for 
 February, 1907, similar to the one 
 for January. 
 
 14. Name the months of the 
 year, beginning with January. 
 
 •907jANUARy'907| 
 
 SUN 
 
 MON 
 
 TUE 
 
 WED 
 
 THU 
 
 FRI 
 
 SAT 
 
 .. 
 
 .. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 31 
 
 " 
 
 •• 
 
 12 months = 1 year ; written, 12 mo. = 1 yr. 
 
 15. How many months are there in 8 years ? 
 
 16. How many days are there in 6 weeks ? 
 
 17. How many hours are there in 9 days ? 
 
 18. How many minutes are there in 4 hours ? 
 
100 
 
 THIRD YEAR [Oral and Written 
 
 MEASURES OF SURFACE 
 
 1. Draw a square 1 inch long and 1 inch wide. 
 What shall we call it ? 
 
 2. Draw on the blackboard a square 1 foot long and 
 1 foot wide. Call it a square foot. 
 
 3. Draw on the blackboard a square 1 yard long 
 and 1 yard wide. Call it a square yard. 
 
 4. Separate by points, each 
 side of the square yard into 3 
 equal parts. Connect these 
 points by straight lines. What 
 is the size of each square ? How 
 many square feet are there in 
 a square yard ? 
 
 5. This picture shows a 
 square yard, smaller than it really is. How many 
 square feet does it show ? 
 
 On 
 
 e squ are 
 
 yard 
 
 9 square feet=l square yard; written, 9 sq. ft. = l sq. yd. 
 
 6in 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 6. This picture . shows an 
 oblong 6 inches by 4 inches. 
 Divide it into square inches. 
 How many square inches are 
 there in one row ? in 2 rows ? 
 in 3 rows ? in 4 rows ? 
 
 In 1 row there are 6 sq. in. 
 
 In 4 rows there are 4x6 sq. in. = 24 sq. in. 
 
Written] SURFACES 101 
 
 SURFACES 
 Draw figures and find the number of square inches in : 
 
 1. An oblong 1 in. wide and 4 in. long. 
 
 2. An oblong 2 in. wide and 6 in. long. 
 
 3. An envelope 2 in. wide and 6 in. long. 
 
 4. A blotter 3 in. v^ide and 6 in. long. 
 
 5. A page 4 in. wide and 6 in. long. ■ - '>;' 
 
 6. A square 3 in. on a side. , v _ : ,. . .'' v 
 
 7. A square 4 in. on a side. 
 
 8. The top of a box 5 in. on a side. 
 
 9. A picture 4 in. by 6 in. 
 
 With one inch representing a foot, draw figures and 
 find the number of square feet in: 
 
 10. A rug 3 ft. wide and 8 ft. long. 
 
 11. A hallway 4 ft. wide and 10 ft. long. 
 
 12. A table cover 7 ft. by 4 ft. 
 
 13. A window glass 4 ft. by 9 ft. 
 
 14. The glass for a picture 2 ft. by 3 ft. 
 
 With one inch representing a yard, draw figures and 
 find the number of square yards in : 
 
 15. A room 4 yards by 6 yards. 
 
 16. A porch floor 2 yards wide and 8 yards long. 
 
 17. A hallway 3 yards wide and 12 yards long. 
 
 18. A rug 3 yards wide and 5 yards long. 
 
 19. A porch rug 2 yards wide and 4 yards long. 
 
 20. A wall 3 yards in height and 6 yards long. 
 
 21. A blackboard 1 yard in height and 8 yards long. 
 
102 THIRD YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 Market Report 
 
 Apples. Best, $2.25; Eggs. 18<*perdoz. 
 
 Fair grades, $ 1.50 per bbl. Butter. Creamery, 28 f per lb. ; 
 Peaches. Good, $2.25; Dairy, 25 ^ per lb. 
 
 Fancy, $2.50 per bu. Cheese. Full cream, 12|^ per lb. 
 Pears. Best, $1.50 per bu. American, 15^ per lb. 
 
 Grapes. .Niagara, 25^ per 10-lb. Potatoes. 50^'perbu. 
 
 . bjiskst. ^ Sweet potatoes. Virginia, 80^ ; 
 
 Concords, 28 ^ per 10-lb. basket. Jersey, $ 1.25 per bu. 
 
 Frdni this market report find the cost of the following : 
 
 1. 8 bu. of fancy peaches. 
 
 2. 4^ lb. of butter, creamery. 
 
 3. 5| bu. of potatoes. 
 
 4. 8 10-lb. baskets of Concord grapes. 
 
 5. 7 bbl. of apples, best quality. 
 
 6. 9 cases of eggs, 30 dozen each. 
 
 7. 8 10-lb. baskets of Niagara grapes. 
 
 8. 8|- bu. of sweet potatoes, Virginia. 
 
 9. 7 bu. of peaches, good. 
 
 10. 9 full cream cheese, 15 lb. each. 
 
 11. 7 10-lb. baskets of Concord grapes. 
 
 12. 9J bu. of pears, best quality. 
 
 13. 8 bbl. of apples, fair grades. 
 
 14. 7 lb. of creamery butter and 32 lb. of dairy butter. 
 
 15. 8 bu. of fancy peaches, and 42 bu., good quality. 
 
 16. 8 10-lb. baskets of Concord grapes, and 6 
 10-lb. baskets of Niagara grapes. . 
 
Written] REVIEW OF THIRD YEAR 103 
 
 REVIEW OF THIRD YEAR 
 
 1. There are 8 pints in one gallon. How many 
 pints are there in 36 gallons ? 
 
 2. A train runs 26 miles in 1 hour. How far can 
 it run in 9 hours ? 
 
 3. How much will 8 J yards of cloth cost at 32 cents 
 per yard ? 
 
 4. At the rate of 9 pages an hour, how long will 
 it take to finish a story of 27 pages ? 
 
 5. Nine girls spent $4.95 at a picnic. What was 
 the average amount spent by each ? 
 
 6. At 6 cents a pound, how many pounds of sugar 
 can be bought for 138 cents ? 
 
 7. There are 168 cabbage plants in 8 rows. How 
 many are there in each row ? 
 
 8. James saves $ 7 a week from his wages. How 
 long will it take him to pay for a lot valued at 
 $238? 
 
 9. A drover paid $2040 for sheep at $6 a head. 
 How many did he buy ? 
 
 10. Eight lamps cost $17.28. Find the cost of one. 
 
 11. How many bushels equal 396 pecks ? 
 
 12. How many gallons equal 792 pints ? 
 
 13. How many tons of coal at $6 a ton can be 
 bought for $786? 
 
 14. How much milk at 8 cents a quart can be bought 
 for $2.56? ($2.56 = 256^.) 
 
104 THIRD YEAR [Written 
 
 15. I paid $12.54 for berries at 6 cents a box. How 
 many boxes did I buy ? 
 
 16. A man divided $875 among his 7 cbildren. 
 How much did each child receive ? 
 
 17. How many weeks are equal to 287 days ? 
 
 18. If 9 hours' work is counted as a day's work, for 
 how many days should a man be paid who has worked 
 342 hours ? 
 
 19. 6 melons cost 78 cents. How much is that 
 apiece ? 
 
 20. How many yards equal 54 feet ? 
 
 21. At 48 cents a gallon, what is the cost of a pint 
 of molasses ? 
 
 22. If 6 barrels of apples cost $13.50, what is the 
 cost of 1 barrel ? 
 
 Find the cost of : 
 
 23. 8 hats @ $3. 29. 7 pr. shoes @ $41 
 
 24. 7 beds @ $9. ^ 30. 12 melons @ 8^. 
 
 25. 7 qt. milk @ 8^. 3i. 6 bbl. flour @ $4i. 
 
 26. 8 books @ $2. 32. 71 lb. sugar @ 8^. 
 
 27. 4 gal. oil @ 25^. 33. 8 yd. of cloth @ 50^. 
 
 28. 6 chairs® $3^. 34. 8 spools tliread @ 10^. 
 
 35. Eight men paid $2.50 each to the Fresh Air 
 Fund. How much was given by all ? 
 
 36. Mr. Brown paid $400 for 8 acres of land. How 
 much were 24 acres worth ? 
 
Written] REVIEW OF THIRD YEAR 105 
 
 37. Seven o'clock a.m. is how many hours after mid- 
 night ? 
 
 38. 144 square inches make one square foot. How 
 many square inches equal 8 square feet ? 
 
 39. At $ 7.50 each, how much will 7 suits of clothing 
 cost ? 
 
 40. How much will 8|- pounds of pork cost at 12^ a 
 pound? 
 
 41. At $ 4.75 each, how much will 8 hats cost ? 
 
 42. Mrs. White paid $ 2.25 a yard for velvet. How 
 much would she pay for 7 yards at the same rate ? 
 
 43. Joseph Black employs 8 clerks at a salary of 
 $ 15.50 a week each. How much must he pay his 
 clerks at the eud of the week ? 
 
 44. At 3 palings to the foot, how many palings are 
 required for a fence 12 yards and 2 feet in length ? 
 
 45. How much will an 8J pound roast of veal cost at 
 16^ a pound? 
 
 46. 8 gallons of ice cream were sold at 15^ a pint. 
 How much was received for it ? 
 
 47. At 25^ a peck, for how much will 2 bu. of toma- 
 toes retail ? 
 
 48. A man sold a horse for $230 and lost $56. 
 How much did the horse cost him ? 
 
 49. Mr. Frank rented a house at $ 360 a year. How 
 much rent will he pay in 7| years? 
 
106 THIED YEAR [Written 
 
 50. A man hires a horse for 35^ an hour. How much 
 must he pay if he uses the horse from 10 a.m. until 
 5 p.m.? 
 
 51. A man bought a lot for $ 1275. He built a store- 
 room on it for $ 2450. He sold the property for $ 5000. 
 Find his gain. 
 
 52. What is the weight of 6 sacks of wheat, each 
 weighing 168 pounds? 
 
 53. How much will 8| tons of coal cost at $ 4.50 a 
 ton? 
 
 54. 9 tons of coal for a school cost $ 38.25. How 
 much was that a ton ? 
 
 55. A school has 2 floors, with 4 rooms on each floor. 
 How many pupils are there in the school, if there are 
 36 pupils in each room ? 
 
 56. A teacher in this school earns $ 65 per month, 
 and spends $ 35. How much does he save in 9 
 months ? 
 
 57. Find the cost of 8 J yards of dress goods at 48 
 cents per yard. 
 
 58. A pair of shoes costs $2|. How much will 7 
 pairs cost? 
 
 59. If I pay 96 cents for 3 yards of ribbon, how much 
 should I pay for 1 yard ? for 1^ yards ? 
 
 60. The distance from New York to Pittsburg is 444 
 miles. What is the fare for a round trip, at 2^ per 
 mile ? 
 
PART III — FOURTH YEAR 
 
 READING AND WRITING NUMBERS 
 
 Review pages 29, 30, and 72. 
 
 For convenience in reading large numbers, the figures 
 are generally separated by commas into groups of three 
 figures each, called periods. 
 
 The first period, counting from the right, is units ; 
 the second, thousands ; the third, millions. 
 
 The following table shows the arrangement of th^se 
 periods, and the three orders of figures in each period : 
 
 Millions' Period 
 
 Thousands' P 
 
 ERIOD 
 
 Units' 
 
 Period 
 
 is 
 
 § 3 
 
 n 
 
 CO 
 
 5 
 
 09 
 
 i 
 
 on 
 
 1 
 
 
 -o .2 
 MS 
 
 Teu- 
 millio 
 
 Millie 
 
 II 
 
 il 
 
 
 
 
 2 
 
 4, 
 
 6 
 
 4 
 
 L 
 
 3 
 
 7 6 
 
 The number in the table is read, " 204 million, 641 
 
 thousand, 376. 
 
 J) 
 
 
 
 Copy, point 
 a 
 1. 2000 
 
 off, and read : 
 b 
 20135 
 
 c 
 81125 
 
 d 
 125125 
 
 2. 20000 
 
 20648 
 
 48760 
 
 625840 
 
 3. 21000 
 
 56506 
 
 40084 
 
 1760894 
 
 4. 36000 
 
 94600 
 
 61006 
 
 8300404 
 
 107 
 
108 FOURTH YEAR [Oral and Written 
 
 READING AND WRITING NUMBERS 
 
 Express in figures : 
 
 1. Forty-two thousand. 
 
 2. Sixty-six thousand four. 
 
 3. Seventy-five thousand fifty. 
 
 4. Thirty-nine thousand one hundred twenty-two. 
 
 5. Two hundred ten thousand three hundred fifty. 
 
 6. Five hundred sixty-five thousand one hundred. 
 
 7. One million one hundred twenty-five thousand. 
 
 8. Three million six hundred thousand thirty-five. 
 
 9. Twenty-five million nine thousand twenty-six. 
 
 10. Eighty million twenty-six thousand sixty-four. 
 
 11. Nine hundred thousand nine. 
 
 12. Forty-six million four thousand sixteen. 
 
 13. One hundred ten million five hundred. 
 
 14. Three hundred thirty-six million one hundred four. 
 
 15. Five hundred seven million five thousand six. 
 
 16. Seventeen million three thousand seventy-five. 
 
 17. One million two thousand seven hundred four. 
 
 18. 1 million, 104 thousand, 185. 
 
 19. 21 million, 110 thousand, 109. 
 
 20. 604 million, 622 thousand, 468. 
 
 21. 101 million, 10 thousand, 10. 
 
Oral and Written] ADDITI0:N" AND SUBTKACTION 109 
 
 ADDITION AND SUBTRACTION 
 
 Review pages 32 to 43, 54, 55, 63, 64, 65, 73, 91, and 92. 
 
 1. Count by 4's from 2 to 100 ; from 3 to 99. 
 
 2. Count by G's from o to 99 ; from 5 to 101. 
 
 3. Count by 8's from 3 to 99 ; from 4 to 100. 
 Add the following, allowing five minutes for each : 
 
 abed 
 
 4. $32.45 -f $50.75 + $32.11 + $32165 = 
 61.79 + 1.24 + 2.84 + 94.76 = 
 
 8.15 + 6.19 + 16.31 + 8.92 = 
 
 23.42 + 83.72 + 5.49 + 143.74 = 
 94.76 + 9.85 + 26.32 + 25.81 = 
 
 $ +$ +$ +$ = 
 
 5. $35.18 + $85.24 + $21.89 + $ 86.42 = 
 
 92.76 + 8.93 + 39.65 + 93.84 = 
 
 9.84 + 16.82 + 84.21 + 2.69 = 
 
 26.37 + 73.25 + 16.93 + 39.87 = 
 
 81.74 + 4.68 + 12.85 + 71.44 = 
 
 $ +$• +$ +$ =$ 
 
 Subtract, allowing one half minute for each : 
 
 a b c d 
 
 6. $275.43 $536.75 $408.37 $674.26 
 167.35 308.28 286.58 210.75 
 
 7. $682.72 $826.45 $527.05 $763.72 
 79.80 60.76 89.98 140.80 
 
110 FOURTH YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. A man paid $2.50 for a hat and $15.50 for a 
 suit. How much did he pay for both ? 
 
 $ 2.50, cost of hat. 
 
 15.50, cost of suit. 
 
 $ 18.00, cost of both. 
 
 2. A merchant sold 425 bu. of potatoes, 232 bu. of 
 apples, aiid 189 bu. of onions. Find the total number 
 of bushels sold. 
 
 3. A lady paid $25 for a carpet, $71 for a rug, and 
 $ 7 for curtains. What was the amount of her bill ? 
 
 4. How many days are there in the last six months 
 of the year ? 
 
 5. A man left his estate to his wife, son, and daughter. 
 His wife received $9845, his son $3650, and his daugh- 
 ter $3500. What was the value of the whole estate? 
 
 6. I sold my house for $5675, thereby losing $897. 
 How much did the house cost ? 
 
 7. A lawn is 30 ft. long and 24 ft. wide. How many 
 feet is it around the lawn ? 
 
 8. New York is 327 miles east of Altoona by rail- 
 road and Pittsburg is 117 miles west. How far is it 
 from New York to Pittsburg ? 
 
 9. The pupils of a school deposited money in a sav- 
 ings bank as follows : January, $ 16.45 ; February, 
 $ 14.60 ; March, $ 18.35 ; and April, $ 17.51. Find the 
 total deposits. 
 
Written] SUBTEACTIOK 111 
 
 PRACTICAL PROBLEMS 
 
 1. A ranchman bought 468 cows and sold 239 of 
 them. How many had he left? 
 
 468, number of cows bought. 
 
 239, number of cows sold. 
 
 229, number of cows remaining. 
 
 2. Mr. Jones was born in 1851. How many years 
 old is he if now living ? 
 
 3. A man's property sells for $47892. He ow^es 
 $36987. How much has he left after paying all his- 
 debts ? 
 
 4. In a certain election A received 38714 votes and 
 B 29867 votes. How much did A's vote exceed B's? 
 
 5. I sold a farm for $5628, which w^as at a gain of 
 $1394. What was the cost of the farm ? 
 
 6. A merchant bought 26520 bu. of grain and sold 
 18296 bu. How many bushels had he left? 
 
 7. The population of a town is 8596. Ten years 
 ago it was 2397. What was the increase in ten years ?* 
 
 8. A man's salary is $2525 a year. His expenses 
 are $1786. How much can he save in a year? 
 
 9. A barrel of flour weighs 200 lb. The barrel itself 
 weighs 4 lb. How many pounds of flour are there in a 
 barrel ? 
 
 10. At an election the whole number of ballots cast 
 was 11342. Of this number A received 8673. How^ 
 many votes were cast for his opponent ? 
 
112 
 
 FOURTH YEAR 
 
 [Oral 
 
 MULTIPLYING BY lo 
 
 Review pages 56, 59, 66, 79, 80, 85, and 86. 
 
 1. Count by lO's to 100. Build the table of lO's. 
 
 2. How many are 9 X 10 ? 90 + ?= 100. 
 
 3. Place a naught to the right of 4. What number 
 have you ? 40 is how many times four ? Place a naught 
 to the right of 6; 3; 7; 9; 11; 12. See whether 
 each product has become ten times the minuend. 
 
 Annexing a naught to the right of a number multiplies 
 it hy 10. 
 
 4. Annex to each number. Notice the effect: 
 4 20 36 75 42 87 275 
 
 93 87 692 387 509 938 765 
 
 5. Memorize the table. 
 
 6. Compare : 
 
 10 X 5 with 5 X 10 
 8 X 10 with 10 X 8 
 
 11 X 10 with 10 X 11 
 40 and 80 100 and 10 
 
 120 and 12 110 and 11 
 
 Find the cost of : 
 
 7. 10 newspapers @ 5^. ii. 91 lb. lard @ 10^. 
 
 8. 8 ladies' hats @ $ 5. 12. 12^ doz. buttons @ 10^. 
 
 9. 10 oranges @ 2 for 5^. 13. 10 qt. milk @ 8^. 
 
 10. 101 yd. muslin @ 12 ^. i4. 101 bu. tomatoes @ 80^. 
 
 Table 
 
 of lO'S 
 
 1x10=10 
 
 7x10= 70 
 
 2x10 = 20 
 
 8x10= 80 
 
 3x10 = 30 
 
 9x10= 90 
 
 4x10 = 40 
 
 10x10=100 
 
 5 X 10 = 50 
 
 11x10=110 
 
 6x10=60 
 
 12x10 = 120 
 
ral] 
 
 MULTIPLICATIOK 
 
 113 
 
 I 
 
 WF MULTIPLYING BY ii 
 
 1. Count by ll's to 33; to 66; to 99. Build the 
 table of ll's. 
 
 2.9x11=? 99 + 11=? How many irs = 110? 
 
 3. 10 X 11 =? 10 times 11, plus 11 = ? How many 
 are 11x11? 
 
 4. To find 12 x 11 how many must 
 
 be added to 11 x 11 ? 
 
 12x11= ? 
 
 5. Give at sight : 
 
 
 
 10x11 12x11 
 
 
 5x11 
 
 3x11 4x11 
 
 
 8x11 
 
 6x11 11 X 9 
 
 
 llx 7 
 
 
 Table of 
 
 II'S 
 
 
 1x11 
 
 = 11 
 
 7 
 
 xll = 
 
 77 
 
 2x11 
 
 = 22 
 
 8 
 
 xll = 
 
 88 
 
 3x11 
 
 = 33 
 
 9 
 
 xll = 
 
 99 
 
 4x11 
 
 = 44 
 
 10 
 
 xll = 
 
 110 
 
 5x11 
 
 = 55 
 
 11 
 
 xll = 
 
 121 
 
 6x11 
 
 = 66 
 
 12 
 
 xll = 
 
 132 
 
 6. Memorize the table. 
 
 7. Compare : 
 
 11 X 7 with 7 X 11 
 9 X 11 with 11x9 
 
 11 X 4 with 4 X 11 
 
 12 X 11 with 11 X 12 
 6x11 with 11 X 6 
 
 8. Find the products : 
 
 11x60 11x80 11x40 11x100 
 
 11x90 11x50 11x20 llx 80 
 
 11x13 11x30 11x70 llx 15 
 
 Find: 
 
 9. j\ of 132 ; of 88 ; of 121 ; of 110. 
 
 11 X 30 
 11 X 25 
 11x18 
 
114 
 
 FOURTH YEAR [Oral and Written 
 
 MULTIPLYING BY 12 
 
 1. Count by 12's to 36 ; to 72 ; to 144. How many 
 are 12 times 12 ? Build the table of 12's. 
 
 Table of 12's 2. Memorize the table. 
 
 1x12 = 12 
 
 7x12= 84 
 
 2x12 = 24 
 
 8x12= 96 
 
 13x12 = 36 
 
 9x12 = 108 
 
 4 X 12 = 48 
 
 10x12 = 120 
 
 t5x 12 = 60 
 
 11x12 = 132 
 
 6x12 = 72 
 
 12x12 = 144 
 
 3. Multiply bj 
 
 - 12; by 11: 
 
 465 
 
 236 789 
 
 546 
 
 783 928 
 
 784 
 
 937 693 
 
 785 
 
 514 938 
 
 978 
 
 694 296 
 
 1 dozen =12 1 gross = 144 
 
 4. "What two numbers make the following products ? 
 25 27 28 30 32 35 36 40 42 45 48 
 49 56 60 63 64 66 72 80 84 88 96 
 
 MULTIPLICATION BY A MIXED NUMBER 
 
 1. Multiply 34 by 4^-. 4^ times 34 means that ^ of 
 34 34 is to be added to 4 x 34. 
 
 41 
 
 17 = i of 34 Find the products: 
 
 136 = 4 times 34 2. 8^ x 48 4. 8} x 120 
 
 5. 6ixl80 
 
 153 = 41 times 34 
 
 2. 81x48 
 
 3. 91x72 
 
 €. 71x84 
 
 7. 51x242 
 
 8. 121x224 
 
rral] DIVISIOiT 115 
 
 DIVIDING BY 10 
 
 1. Begin with and count by lO's to 100. Begin- 
 ning with 1 count by lO's to 101. 
 
 2. 50 is how many times 5 ? How does 60 compare 
 with 6 ? Remove zero from 80. What is the result ? 
 8 is what part of 80 ? 
 
 3. Remove naught from 30; from 90; from 70. How 
 does the result in each case compare with the number? 
 
 4. 3 is what part of 30 ? 4 is what part of 40? 
 J5of40 = ? 
 
 Removing a naught from the right of ariy number 
 divides it hi/ 10. 
 
 5. Divide by 10 : Complete in two minutes. 
 
 40 30 90 80 60 100 120 
 
 320 560 980 750 360 470 920 
 
 1450 1680 2450 1930 2210 9990 7400 
 
 6320 4040 3100 2010 8500 7280 6900 
 
 6. How many 10-cent balls can be bought for $1.00? 
 for $2.00? for $5.00? 
 
 7. At 10 cents a quart, how many quarts of milk can 
 be bought with $2.80 ? 
 
 8. How long will it take a motor car going 10 miles 
 an hour to travel 140 miles ? 
 
 9. If I pay 50^ for a telegram pf 10 words, how 
 much do I pay for each word ? 
 
116 FOURTH YEAR [Oral and Written 
 
 DIVIDING BY II AND i2 
 
 1. Subtract by ll's from 132 to 0. 
 
 2. State quotients at 3igbt : 
 
 33^11 66^11 88^11 132-^ll 
 
 44^11 77-^11 99H-11 121^11 
 
 3. Find ^3^ of : 88 ; 99 ; 22 ; 78 ; 33 ; 48 ; 44 ; 55 ; 
 69; 11; 66; 81; 77; 92; 88; 99; 110; 121; 83. 
 
 Divide by 11 : Test answers. 
 
 4. 2738 7. 6954 lo. 8923 13. 69753 
 
 5. 8294 8. 3986 11. 2158 i4. 73065 
 €. 2036 9. 3007 12. 8057 15. 90074 
 
 16. Subtract by 12's from 144 to 0. 
 
 17. State quotients at sight : 
 
 36-^12 
 
 60^12 
 
 84^-12 
 
 132^12 
 
 24^12 
 
 96^12 
 
 108^12 
 
 144^12 
 
 18. Find ^3^ of: 96; 84; 72; 36; 108; 24; 120; 
 132; 60; 48; 144. 
 
 Divide by 12 : Test answers. 
 
 19. 3678 24. 7817 29. 42192 34. 91875 
 
 20. 4135 25. 2936 so. 69378 35. 24726 
 
 21. 6973 26. 9238 31. 73945 36. 68359 
 
 22. 7128 27. 4697 32. 82659 37. 81763 
 
 23. 4693 28. 9384 33. 37296 38. 92364 
 
Oral] 
 
 MULTIPLICATION AND DIVISION 
 
 117 
 
 REVIEW 
 
 Find the cost of : 
 
 1. 9 rings @ $3 
 
 2. 12 cows @ $35 
 
 3. 10 hats @ $3.65 
 
 4. 10 rugs® $1.50 
 
 5. 3 wagons @ $85 
 
 6. 9 plates® $1.75 
 
 7. 10 knives® $.75 
 Find the cost of 1, when : 
 
 15. 12 lamps cost $51 
 
 16. 4 cases cost $32.48 
 
 17. 10 sleds cost $19.50 
 
 18. 10 sheep cost $45.00 
 
 19. 11 desks cost $35.75 
 
 20. 8 trunks cost $57.60 
 
 21. 10 clocks cost $48.50 
 
 22. 5 hats cost $15 
 
 23. 12 hats cost $27 
 
 24. 8 lb. rice cost 96^ 
 
 25. 3 clocks cost $9.75 
 
 26. 9 books cost $11.25 
 
 27. 5 chairs cost $15.45 
 
 28. 9 lb. nuts cost $2.25 
 
 29. 8 bu. coal cost $1.20 
 
 8. 10 vases @ $2.39 
 
 9. 10 horses ® $95 
 
 10. 11 books ® $2.25 
 
 11. 11 sheep ® $4.75 
 
 12. 10 chairs ® $5.25 
 
 13. 6 chickens ® 75^ 
 
 14. 12 pictures® $4.50 
 
 30. 10 satchels cost $35.50 
 
 31. 12 yd. lace cost 48 ^ 
 
 32. 11 lb. steak cost $1.98 
 
 33. 6 gal. vinegar cost 72^ 
 
 34. 12 bu. potatoes cost $9 
 
 35 . 1 2 . pk . t omatoes cost $ 3 
 
 36. 10 toy engines cost $35 
 
 37. 5 lb. steak cost $1.10 
 
 38. 8 qt. cream cost $1.60 
 
 39. 4 bu. cherries cost $15 
 
 40. 10 yd. silk cost $17.50 
 
 10 pt. cream cost $1.10 
 
 11 lb. butter cost $2.20 
 
 43. 3 pairs shoes cost $9.75 
 
 44. 12 collars cost $2.40 . 
 
 41. 
 42. 
 
118 FOURTH YEAR [Written 
 
 REVIEW 
 
 1. A train runs 378 miles in 7 hours. How 
 many miles is that in 1 hoar? 
 
 2. A ticket agent has $ 5.85 in his drawer. After 
 selling 2 tickets at 90^ each, 8 tickets at 70^ each, and 
 1 mileage book for $ 20, how much money should his 
 drawer contain ? 
 
 3. While the hour hand is going 8 times around 
 the dial how often does the minute hand go around ? 
 
 4. The treasury of a school district contains $ 2642. 
 After paying the salaries of six teachers for 8 months 
 at $45 per month, how much remains? 
 
 5. A farmer sold 4 jars of butter containing re- 
 spectively, 24 pounds, 27 pounds, 26 pounds, and 33 
 pounds. How many pounds did he sell ? 
 
 6. A newsboy earns 30 cents a day. How much 
 will he earn in 4 weeks of 6 days each ? 
 
 7. What is left from a $ 10 bill after paying for lOJ 
 lb. of tea at 60 cents a pound ? 
 
 8. The expenses for a family for a year are as follows : 
 food, $485; fuel and light, $86 ; car fare, $35; cloth- 
 ing, $ 285 ; church, $ 68 ; books and papers, $ 25 ; ser- 
 vant, $165; other expenses, $278. Find the entire 
 expenses. 
 
 9. In a school of 897 pupils, there are 487 girls. 
 How many boys are there? 
 
Written] EEVIEW 119 
 
 DRILL WORK 
 
 Write and add : 
 
 a b c 
 
 1. $2785.00 $5870.00 $475.00 
 
 597.55 29.60 6000.00 
 
 3000.00 587.25 459.06 
 
 987.46 45.03 250.00 
 
 6750.00 6540.20 4278.64 
 
 5340.02 8750.00 5782.98 
 
 9876.54 2346.59 8796.32 
 
 3201.89 4567.83 4123.56 
 
 2. $6004.50 $6550.00 $2987.35 
 
 500.83 
 
 6789.05 
 200.06 
 678.46 
 4586.23 
 2080.95 
 2345.10 
 
 3. $475.00 $1286.40 $7665.00 
 
 . 2050.50 
 
 2002:02 
 879.30 
 698.09 
 
 5000.10 
 898.45 
 
 4987.56 
 
 $6004.50 
 
 $6550.00 
 
 887.95 
 
 278.93 
 
 504.06 
 
 8.10 
 
 2874.59 
 
 200.02 
 
 850.00 
 
 7007.05 
 
 2250.05 
 
 520.84 
 
 275.83 
 
 4265.63 
 
 7817.89 
 
 6005.80 
 
 $475.00 
 
 $1286.40 
 
 6000.20 
 
 587.52 
 
 579.80 
 
 3873.20 
 
 1000.50 
 
 78.00 
 
 457.39 
 
 759.06 
 
 100.10 
 
 9300.00 
 
 4555.05 
 
 759.84 
 
 7016.89 
 
 5234.18 
 
120 FOURTH YEAR [Written 
 
 DRILL WORK 
 
 Subtract and test 5 problems in 1 minute. 
 
 a bed 
 
 1. $860.45 $874.61 $724.82 $870.62 
 
 178.62 126.42 109.87 188.94 
 
 2. $684.26 $962.41 $921.08 $700.64 
 
 397.84 802.96 120.09 188.96 
 
 3. $784.12 $908.07 $916.25 $864.30 
 
 479.63 194.72 721.24 497.86 
 
 4. $876.42 $900.40 $921.11 $422.33 
 
 91.76 87.80 888.66 188.88 
 
 5. $600.03 $744.44 $800.55 $111.21 
 
 187.69 299.99 288.85 108.89 
 
 6. $700.77 $644.41 $854.32 $765.43 
 
 188.99 387.64 123.45 112.34 
 
 7. $842.16 $964.21 $841.22 $742.24 
 
 199.97 188.74 108.62 604.28 
 
 8. $914.79 $30500 $965.06 $821.00 
 
 549.86 128.95 578 98 367.89 
 
Oral] 
 
 MULTIPLICATION 
 
 121 
 
 MULTIPLICATION TABLE 
 
 Review and memorize : 
 
 1x1= 1 
 
 Ix 2= 2 
 
 Ix 3= 3 
 
 Ix 4= 4 
 
 2x1= 2 
 
 2x 2= 4 
 
 2x 3= 6 
 
 2x 4= 8 
 
 3x1= 3 
 
 3x 2= 6 
 
 3x 3= 9 
 
 3x 4 = 12 
 
 4x1= 4 
 
 4x 2= 8 
 
 4x 3 = 12 
 
 4x 4 = 16 
 
 5x1= 5 
 
 5x 2 = 10 
 
 5x 3 = 15 
 
 5x 4 = 20 
 
 6x1= 6 
 
 6x 2 = 12 
 
 6x 3 = 18 
 
 6x 4 = 24 
 
 7x1= 7 
 
 7x 2 = 14 
 
 7x 3 = 21 
 
 7x 4 = 28 
 
 8x1= 8 
 
 8x 2 = 16 
 
 8x 3 = 24 
 
 8x 4 = 32 
 
 9x1= 9 
 
 9x 2 = 18 
 
 9x 3 = 27 
 
 9x 4 = 36 
 
 10 X 1 = 10 
 
 10 x 2 = 20 
 
 10 X 3 = 30 
 
 10 X 4 = 40 
 
 11x1 = 11 
 
 11 X 2 = 22 
 
 11 X 3 = 33 
 
 11 X 4 = 44 
 
 12 X 1 = 12 
 
 12 x 2 = 24 
 
 12 X 3 = 36 
 
 12 X 4 = 48 
 
 1X5= 5 
 
 IX 6= 6 
 
 Ix 7= 7 
 
 Ix 8= 8 
 
 2 X 5 = 10 
 
 2x 6 = 12 
 
 2x 7 = 14 
 
 2x 8 = 16 
 
 3x5 = 15 
 
 3x 6 = 18 
 
 3x 7 = 21 
 
 3x 8 = 24 
 
 4 X 5 = 20 
 
 4x 6 = 24 
 
 4x 7 = 28 
 
 4x 8 = 32 
 
 5 X 5 = 25 
 
 5x 6 = 30 
 
 5x 7 = 35 
 
 5x 8 = 40 
 
 6 X 5 = 30 
 
 6x 6 = 36 
 
 6x 7 = 42 
 
 6x 8 = 48 
 
 7 X 5 = 35 
 
 7X 6 = 42 
 
 7x 7 = 49 
 
 7x 8 = 56 
 
 8x5 = 40 
 
 8x 6 = 48 
 
 8x 7 = 56 
 
 8x 8 = 64 
 
 9x5 = 45 
 
 9x 6 = 54 
 
 9X 7 = 63 
 
 9x 8 = 72 
 
 10x5 = 50 
 
 lOx 6 = 60 
 
 10 X 7 = 70 
 
 10 X 8 = 80 
 
 11x5 = 55 
 
 11 X ^ = 66 
 
 11 X 7 = 77 
 
 11 X 8 = 88 
 
 12 X 5 = 60 
 
 12 X 6 = 72 
 
 12 X 7 = 84 
 
 12x 8 = 96 
 
 1x9= 9 
 
 1x10= 10 
 
 1x11= 11 
 
 1x12= 12 
 
 2x9= 18 
 
 2x10= 20 
 
 2x11= 22 
 
 2x12= 24 
 
 3x9= 27 
 
 3x10= 30 
 
 3x11= 33 
 
 3x12= 36 
 
 4x9= 36 
 
 4x10= 40 
 
 4x11= 44 
 
 4x12= 48 
 
 5x9= 45 
 
 5x10= 50 
 
 5x11= 55 
 
 5 X 12 = 60 
 
 6x9= 54 
 
 6 x 10 = 60 
 
 6x11= 66 
 
 6x12= 72 
 
 7x9= 63 
 
 7x10= 70 
 
 7x11= 77 
 
 7x12= 84 
 
 8x9= 72 
 
 8x10= 80 
 
 8x11= 88 
 
 8x12= 96 
 
 9x9= 81 
 
 9x10= 90 
 
 9x11= 99 
 
 9x12 = 108 
 
 10x9= 90 
 
 10x10 = 100 
 
 10x11 = 110 
 
 10x12 = 120 
 
 11x9= 99 
 
 11x10 = 110 
 
 11x11=121 
 
 11x12 = 132 
 
 12x9 = 108 
 
 12x10 = 120 
 
 12x11 = 132 
 
 12 x 12 = 144 
 
122 FOURTH YEAR [Oral 
 
 MULTIPLIERS ENDING IN NAUGHT 
 
 1. Annex a naught to the right of 3; then multiply 
 3 by 10. Is there any difference in the result ? 
 
 Annexing a naught to the right of a number multiplies 
 it by 10. 
 
 2. Multiply by 10: 40; 20; 60; 800; 300; 700; 900. 
 
 3. Multiply 3 by 100 ; 8 by 100 ; 9 by 100 ; 20 by 100. 
 How many times greater has each of the numbers 
 become? How many naughts were added to each? 
 
 Annexing two naughts to the right of a number multi- 
 plies it bylQO, 
 
 4. Find: 
 
 100x4 100x15 100x50 100x75 
 
 100x7 100x95 100x85 100x12 
 
 100x5 100x37 100x91 100x36 
 
 5. What is the difference between 1000 x 3 and 3 x 
 1000? between 1000x6 and 6x1000? How many 
 naughts were annexed to 3 ? to 6 ? How many times 
 greater has each become? 
 
 Annexing three naughts to the right of a number multi- 
 plies it by 1000. 
 
 6. From what you have learned make a rule for 
 multiplying any number by 10 ; 100; 1000; 10000. 
 
 7. Multiply: 
 
 8 by 1000; 7 by 1000; 9 by 1000; 4 by 1000; 13 by 
 1000; 12 by 10000; 14 by 1000; 19 by 1000; 25 by 
 100; 36 by 10; 95 by 100; 72 by 10; 72 by 10000. 
 
Oral and Written] MULTIPLICATION 123 
 
 1. How many cents are there in 100 dimes? 
 
 2. How many cents are there in $6? 
 
 Find the weight of: 
 
 3. 1000 two-pound packages of rolled oats. 
 
 4. 1000 five-pound boxes of starch. 
 
 5. 25 one hundred-pound kegs of nails. 
 
 6. 100 lambs at an average of 45 lb. each. 
 
 7. Find the cost of 1000 one-cent postal cards and 
 100 two-cent stamps. 
 
 a Multiply 63 by 2000. 
 
 Write the 2 of the multiplier under the figure 
 63 in ones' place of the multiplicand. 2 x 63 is 
 
 2000 126. Annex three naughts to the right of 126, 
 126000 making 1 26000. 1000 x 63 = 63000 ; 2000 x 
 63 = 126000. 
 
 Multiply, and read the product: 
 
 9. 71 10. 85 11. 245 12. 715 
 
 200 3000 4000 700 
 
 13. 347 by 20 is. 293 by 500 23. 481 by 2000 
 
 14. 409 by 30 19. 786 by 700 24. 894 by 4000 
 
 15. 715 by 60 20. 184 by 400 25. 906 by 7000 
 
 16. 329 by 80 21. 796 by 600 26. 728 by 9000 
 
 17. 475 by 90 22. 832 by 200 27. 365 by 1200 
 
124 FOUKTH YEAH [Oral 
 
 DIVISORS ENDING IN NAUGHT 
 
 1. Divide 60 by 10. Remove from 60. 60 is Low 
 many times 6? 
 
 2. Compare 40 and 4; 30 and 3; 2 x 10 and 20 ^ 10. 
 What effect has the removing of naught from the right 
 of a number upon the value of the number? 
 
 3. Divide by 10: 20; 900; 350; 470; 530; 260; 740. 
 
 4. Howmany are 100x6? 100x9? 600^100=? 
 900-^100=? How many naughts are removed from 
 the right of 900 when it is divided by 100? from the 
 right of 600? What effect has the removing of two 
 naughts from the right of a number upon the value of 
 the number ? 
 
 5. Find 1000x9; 1000x3; 9000^1000; 3000-^ 
 1000. How many naughts are removed from the riglit 
 of 9000 when it is divided by 1000 ? from the right of 
 3000 ? What effect has the removing of three naughts 
 from the right of a number upon the number ? 
 
 Removing one naught from the right of a number 
 divides the number hy 10; removing tivo naughts, divides 
 it hy 100 ; removing three naughts, divides it hy 1000, etc. 
 
 Find quotients : 
 
 6. 30^10 10. 300^100 14. 4000^100 
 
 7. 90-^10 11. 600 -^ 100 15. 5000^1000 
 
 8. 70^10 12. 700 -^ 100 16. 9000-^1000 
 
 9. 200-^10 13. 900 -f- 100 17. 7000 -f- 1000 
 
Oral and Written] DIVISION 125 
 
 1. Divide 1460 by 20. 
 
 2^ )146 ^ Cutting off naught, or the same 
 
 73 number of naughts, from hoth dividend 
 
 2iS)i^)146(J^ and divisor does not change the quo- 
 
 "~73 tient. 
 
 Find the quotients : 
 
 2. 80-^-20 6. 900^100 10. 12000^1000 
 
 3. 60-^30 7. 1000-^100 11. 12000^2000 
 
 4. 90^-10 8. 6000^200 12. 18000^3000 
 
 5. 40-^20 9. 8400^400 13. 16000^4000 
 
 14. How many 10-gallon cans will a dealer use in 
 shipping 200 gallons of milk ? 
 
 15. How many 20-lb. packages can be made from 
 1000 lb. of coffee ? 
 
 16. 2000 pounds of crackers were shipped in 400 
 boxes. How many poimds did each box contain ? 
 
 17. How many $20 coats must be sold to realize 
 $2400? 
 
 18. A man bought a house for $3500. How many 
 months will it take to pay for it at $100 a month ? 
 
 Give quotients at sight : 
 
 19. 160-^40 24. 200 
 
 20. 360^30 25. 480 
 
 21. 900^90 26. 480 
 
 22. 750-^30 27. 220 
 
 23. 850-^50 28. 240 
 
 50 
 
 29. 
 
 750-4- 15 
 
 80 
 
 30. 
 
 300^ 60 
 
 60 
 
 31. 
 
 250^ 25 
 
 110 
 
 32. 
 
 600-4- 50 
 
 120 
 
 33. 
 
 700 + 140 
 
126 
 
 FOURTH YEAR 
 
 [Written 
 
 MULTIPLICATION BY TWO-FIGURE NUMBERS 
 
 1. Multiply 64 by 23. 
 
 Multiplicand 
 
 64 
 
 64 
 
 Multiplier 
 
 23 
 
 23 
 
 1st partial product 
 
 192= 3x64 
 
 192 
 
 2d partial product 
 
 1280 = 20x64 
 
 128 
 
 Entire product 
 
 1472 = 28x64 
 
 1472 
 
 In practice the in the second partial product is 
 omitted, and 1280 is written as 128 tens by placing 
 the right-hand figure of that product in tens' place. 
 
 2. 
 
 3. 
 
 
 4. 
 
 
 5. 
 
 327 
 
 203 
 
 
 6004 
 
 
 3060 
 
 35 
 
 42 
 
 
 73 
 
 
 89 
 
 1635 
 
 406 
 
 18012 
 
 
 27540 
 
 981 
 
 812 
 
 42028 
 
 
 24480 
 
 11445 
 
 8526 
 
 438292 
 
 
 272340 
 
 Multiply : 
 
 
 
 
 
 
 a 
 
 6 
 
 c 
 
 
 d 
 
 e 
 
 6. 63 
 
 645 
 
 863 
 
 
 765 
 
 806 
 
 24 
 
 32 
 
 24 
 
 
 35 
 
 43 
 
 7. 98 
 
 346 
 
 609 
 
 
 963 
 
 863 
 
 23 
 
 54 
 
 15 
 
 
 41 
 
 51 
 
 8. 604 
 
 861 
 
 867 
 
 
 763 
 
 867 
 
 43 
 
 32 
 
 45 
 
 
 54 
 
 36 
 
Written] MULTIPLICATION 127 
 
 Multiply : 
 
 1. 426 by 23 ii. 634 by 37 21. 9006 by 48 
 
 2. 372 by 41 12. 298 by 73 22. 2694 by 75 
 
 3. 256 by 33 13. 604 by 48 23. 8002 by 38 
 
 4. 307 by 32 i*. 729 by 40 24. 4293 by 67 
 
 5. 269 by 43 15. 903 by 86 25. 9128 by 39 
 
 6. 307 by 27 le. 694 by 79 26. 2807 by 74 
 
 7. 538 by 36 17. 928 by 89 27. 6293 by 56 
 
 8. 736 by 63 ' is. 726 by 75 28. 4060 by 13 
 
 9. 487 by 52 19. 349 by 28 29. 2734 by 27 
 10. 994 by 35 20. 723 by 14 30. 4169 by 32 
 
 31. Announce products at sight : 
 
 50x90 90x70 20x80 70x60 70x40 
 
 80x70 60x50 40x30 30x30 90x90 
 
 3x3 = 9; 9 is the square of 3. 6 x 6 = 36 ; 36 is the 
 square of 6. 
 
 To find the square of a numher, we multiply it by itself. 
 
 32. Find the squares and memorize : 
 
 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 
 19, 20, 21, 22, 23, 24, 25. 
 
 Multiply : 
 
 33. 463 by 73 37. 9869 by 84 4i. 8693 by 28". 
 
 34. 938 by 84 38. 3278 by 93 42. 9281 by 39 
 
 35. 697 by 95 39. 9009 by 49 43. 7375 by 47 
 
 36. 893 by 96 40, 6075 by 74 44, 4069 by §9 
 
128 FOURTH YEAR [Written 
 
 MULTIPLICATION OF CONCRETE NUMBERS 
 
 Which of the following numbers are abstract f Which 
 are concrete f Why ? 
 
 1. 8 ; 6 days ; $ 4 ; 5^ ; 25 ; 4 feet ; 8 horses. 
 
 2. Name the multiplier and the multiplicand in each 
 problem : 
 
 $ 8 64 days 81 horses 72 oranges 
 
 X 5 X 4 . 2<_7 X 3 
 
 3. Observe in each of the above, problems that the 
 product must have the same name as the multiplicand. 
 
 The multiplier is always an abstract 7iiimber. 
 
 4. When two numbers are multiplied, the number in 
 the product remains the same in whatever order the 
 numbers are taken; thus: 7 x 12 = 12 x 7. 
 
 5. How much do I earn in 125 days at $ 3 per day ? 
 In problems like this where the multiplier has more 
 
 figures than the multiplicand, the product of the num- 
 bers may be found thus : 125, but the analysis of the 
 
 3 
 375 
 problem should be given in this way : 
 I earn in one day, $3. 
 I earn in 125 days, 125 x $3, or $375. 
 
 Find the cost of : How many : 
 
 6. 319 days' work @ $ 3 lo. Pints in 327 qt. ? 
 
 7. 817 tons coal @ $ 5 ii. Inches in 845 ft. ? 
 
 8. 198 lb. meal @ 9f^ 12. Pecks in 164 bu. ? 
 
 9. 345 doz. buttons @ S^ 13. Ounces in 375 lb. ? 
 
Written] MULTIPLICATION" 129 
 
 PRACTICAL PROBLEMS 
 
 Find the cost of : 
 
 1. 28 pounds of raisins 
 
 2. 46 J gallons of vinegar 
 
 3. 196 pounds of sugar 
 
 4. 48 J^ pounds ol butter 
 
 5. 64.1^ pounds of meat 
 . 6. 85 dozen oranges 
 
 7. 27 gallons of molasses 
 
 8. 58^ bushels of potatoes 
 
 9. 25 dozen eggs 
 
 10. 54 barrels of flour 
 
 11. 27 barrels of apples 
 
 12. 34 tons of coal 
 
 13. 148 J pounds of tea 
 
 14. 144 dozen eggs 
 
 15. 48 yards of cloth 
 
 16. 36 J tons of hay 
 
 17. The frontage on a city street is 176 feet. How- 
 much is it worth at $ 65 a front foot ? 
 
 18. A grocer sold 18 firkins of butter, each contain- 
 ing 56 pounds, at 24^ a pound. How much did he 
 receive for the butter ? 
 
 19. A boy works 8 hours a day. How many hours 
 does he work in 28} days ? 
 
 @ 
 
 15^. 
 
 @ 
 
 24^. 
 
 @ 
 
 6^. 
 
 @ 
 
 27^. 
 
 @ 
 
 16^. 
 
 @ 
 
 35)^. 
 
 @ 
 
 48^. 
 
 @ 
 
 60 A 
 
 @ 
 
 23^. 
 
 @ 
 
 $5.25. 
 
 @ 
 
 $2.35. 
 
 @ 
 
 $ 6.75. 
 
 @ 
 
 50 >^. 
 
 @ 
 
 26 (^. 
 
 @ 
 
 87^. 
 
 @ $16.70. 
 
130 FOURTH YEAR [Oral and Written 
 
 COMPARISON 
 
 In the following comparisons the first number is to 
 be divided by the second: 
 
 1. Compare 12 and 4 ; 12 and 3 ; 16 and 4. 
 
 2. Compare 5 and 15. 
 
 3. Compare : 
 
 18 and 6 16 and 4 . 6 and 12. 
 
 20 and 5 45 and 9 6 and 30. 
 
 4. When 3 oranges cost 10 cents, how much will 12 
 oranges cost ? 
 
 Note. — 12 oranges equal 4x3 oranges ; hence they will cost 
 4 X 10 cents, or 40 cents. 
 
 5. At 6 melons for 25 cents, how much will 24 cost ? 
 
 6. At 12 lemons for 15 cents, how much will 72 cost ? 
 
 7. If 8 tons of coal cost $54, how much will 40 tons 
 cost ? 
 
 8. If 3 collars cost 35 cents, how much will 24 collars 
 cost? 
 
 9. When 12 cords of wood cost $48, how much will 
 3 cords cost ? 
 
 10. How much will 4 qt. of milk cost when 16 qt. 
 cost $1.28? 
 
 11. When 7 tons of hay sell for $91, how much will 
 a farmer receive for 35 tons ? 
 
 12. If 96 acres of land are worth $2592, how much 
 are 12 acres worth ? 
 
f 
 
 I Oral] 
 
 DIVISION 
 
 131 
 
 REVIEW OF SHORT DIVISION 
 
 Answer at sight : 
 
 1. 2}32 3}48 4)44 5)35 5)75 
 
 2. 6^ 7 )147 8 )872 9 )3699 8 )4056 
 
 Give answers quickly 
 
 3. 1 of 16 
 
 4. 1 of 24 
 
 5. 1 of 48 
 
 6. I- of 60 
 
 7. 1 of 72 
 
 8. i of 84 
 
 9. I of 96 
 
 10. 1 of 108 
 
 11. 3-VoflOO 
 
 12. 
 
 Ir of 132 
 
 TT 
 
 13. iVofl44 
 
 Divide and test : 
 
 14. 11 )6303 11 )2244 
 
 ; 18 
 
 ; 26 
 
 ; 28 
 
 ; 32 
 
 ; 36; 
 
 ; 27 
 
 ; 36 
 
 ; 18 
 
 ; 60 
 
 , 90; 
 
 ; 24 
 
 60 
 
 ; 72 
 
 ; 36 
 
 , 44; 
 
 ; 55; 
 
 100, 
 
 150; 
 
 75; 
 
 45; 
 
 ; 96; 
 
 84; 
 
 24; 
 
 48; 
 
 240; 
 
 ; 91 
 
 ; 49 
 
 63 
 
 ; 105 
 
 ; 350; 
 
 ; 72 
 
 , 640 
 
 ; 960 
 
 ; 560 
 
 ; 120; 
 
 ; 135 
 
 , 360 
 
 ; 720 
 
 ; 54 
 
 ; 7209; 
 
 ; 120, 
 
 130 
 
 , 190 
 
 ; 1250 
 
 , 1950; 
 
 ; 88, 
 
 09, 
 
 77 
 
 , 1100, 
 
 1320; 
 
 ; 288; 
 
 96. 
 
 84 
 
 ; 960. 
 
 , 840; 
 
 40. 
 120. 
 
 56. 
 
 65. 
 
 36. 
 2100. 
 880. 
 1080. 
 1780. 
 1210. 
 1080. 
 
 11 )2882 11 )6699 
 
 15. 12 )96840 1 2)89640 1 2)6072 12 )9060 
 
 Give quotients at sight : 
 
 8)96 9)72 10)190 
 
 16 
 
 11)121 
 
 12)96, 
 
132 ' FOURTH YEAR [Written 
 
 LONG DIVISION 
 1. Divide 240 by 15. 
 
 16 Quotient. In long division tlie quotient 
 
 Divisor 15)240 Dividend, is placed over the dividend. 15 
 
 15 is contained in 24, 1 time. 
 
 90 Write the 1 in the quotient 
 
 90 over the 4. Multiply 15 by 1, 
 
 placing the product, 15, under 
 
 24. Subtract 15 from 24. The remainder is 9. Bring 
 
 down the next figure, 0. 15 is contained in 90, 6 times. 
 
 Multiply 15 by 6, placing the product, 90, under 90. As 
 
 there is no remainder, the quotient is IG. 
 
 Divide : 
 
 21 Ans. 
 
 23 Ans. 209 Ans, 
 
 2. 13)273 
 
 3. 14)322 4. 25)5225 
 
 26 
 
 28 50 
 
 13 
 
 42 225 
 
 13 
 
 42 225 
 
 5. How many 
 
 times is 21 contained in 504 ? 
 
 24 
 
 Steps : 
 
 L)504 
 
 1. Divide 50 by 21. 
 
 42 
 
 2. Write quotient figure. 
 
 «4 
 
 3. Multiply 21 by 2. 
 
 ■M 
 
 4. Subtract 42 from 50. 
 
 
 5. Bring down next figure. 
 
 Test. — 24x21 = 504. 
 
 6. Divide 441 
 
 by 21 ; 672 by 21 ; 903 by 21. 
 
Written] DIVISION 133 
 
 FINDING THE QUOTIENT FIGURE IN DIVISION 
 
 Think how many times the first figure of the divisor 
 is contained in the first figure of the dividend. The 
 number will be the first figure of the quotient. 
 
 1. 252-^21 4. 714 -f- 21 7. 504-^21 
 
 2. 525-^21 5. 651-^21 8. 2398^21 
 
 3. 861 H- 21 6. 357^21 9. 2625^21 
 Think how many times the first figure of the divisor 
 
 is contained in the first figure, or in the first two figures, 
 
 of the dividend. The number will be the first figure 
 of the quotient. 
 
 7061^23 18. 6831 -^ 33 
 
 9269^23 19. 1984^32 
 
 5028-^42 20. 2272^32 
 
 1344^42 21. 1683^51 
 
 22. Divide 819 by 21. 
 
 . . 39 
 
 Since the product of the divisor 
 
 and quotient is greater than 81, the ^ 
 
 ^ quotient figure is too large. Try a y— 
 
 — smaller quotient figure. 
 
 189 
 
 23. Divide 651 by 21. 
 
 2 . -^ 
 
 o-j YprT Since the remainder is greater than 21) 651 
 
 .0 the divisor, the quotient figure is too 63 
 
 00 small. Try a larger quotient figure. 21 
 
 21 
 
 10. 
 
 713^31 
 
 14. 
 
 11. 
 
 899-^31 
 
 15. 
 
 12. 
 
 6727-^31 
 
 16. 
 
 13. 
 
 8323-^41 
 
 17. 
 
134 
 
 
 FOUKTH YEAR 
 
 
 [Written 
 
 Divide and tesi 
 
 1 \ 
 
 
 
 
 
 1. 21)882 
 
 13. 
 
 23)575 
 
 25. 
 
 33)462 
 
 37. 
 
 43)1333 
 
 2. 21)903 
 
 14. 
 
 23)736 
 
 26. 
 
 33; 858 
 
 38. 
 
 43)6880 
 
 3. 21)504 
 
 15. 
 
 23)966 
 
 27. 
 
 33)561 
 
 39. 
 
 43)9460 
 
 4. 21)819 
 
 16. 
 
 23)138 
 
 28. 
 
 33)627 
 
 40. 
 
 43)1376 
 
 5. 21)315 
 
 17. 
 
 31)775 
 
 29. 
 
 41)943 
 
 41. 
 
 51)1683 
 
 6. 21)567 
 
 18. 
 
 31)744 
 
 30. 
 
 41)2296 
 
 42. 
 
 51)3672 
 
 7. 21)399 
 
 19. 
 
 31)899 
 
 31. 
 
 41)1107 
 
 43. 
 
 51)3264 
 
 8. 21)441 
 
 20. 
 
 31)217 
 
 32. 
 
 41)1435 
 
 44. 
 
 51)1428 
 
 9. 22)814 
 
 21. 
 
 32)672 
 
 33. 
 
 42)1008 
 
 45. 
 
 52)1508 
 
 10. 22)638 
 
 22. 
 
 32)928 
 
 34. 
 
 42)1596 
 
 46. 
 
 52)2288 
 
 11. 22)352 
 
 23. 
 
 32)160 
 
 35. 
 
 42)1680 
 
 47. 
 
 53)2385 
 
 12. 22)660 
 
 24. 
 
 32)192 
 
 36. 
 
 42)1722 
 
 48. 
 
 53)1908 
 
 49. A butcher paid $1476 for 41 head of cattle. 
 How much was that per head? 
 
 50. If a railroad trackman walks 16 miles each day, 
 how long will he be in walking 832 miles ? 
 
 51. If there are 496 ounces in 31 pounds, how many 
 ounces are there in 1 pound ? 
 
 52. If 24 barrels of oil cost $ 44.40, what is the price 
 of 1 barrel ? 
 
 53. If a bushel of oats weighs 32 lb., how many 
 bushels will weigh 28640 lb. ? 
 
 54. How long will it take a train that travels 35 
 miles an hour to go a distance of 315 miles ? 
 
 55. At 38 ^ a word, how many words can I cable from 
 New York to Sweden for $3.04? 
 
Written] 
 
 
 DIVISIOK 
 
 
 135 
 
 
 
 LONG DIVISION 
 
 
 
 
 1. Divide 7416 by 
 
 25. 
 
 
 
 
 29616 
 
 Quotient Write the remainder 
 
 
 25)7416 
 
 
 over i 
 
 the 
 
 divisor, and 
 
 
 50 
 
 
 annex 
 
 it to the right 
 
 
 241 
 
 
 of the 
 
 quotient. 
 
 
 225 
 
 
 Test 
 
 
 296 X 25 = 
 
 
 166 
 
 
 7400; 
 
 7400 
 
 + 16 = 7416. 
 
 
 150 
 
 
 
 
 
 
 16 remainder -^ 25 = J|-. 
 
 
 
 
 Divide and test : 
 
 
 • 
 
 
 
 2. 
 
 2397 by 51 
 
 13. 
 
 1281 by 21 
 
 24. 
 
 6938 by 94 
 
 3. 
 
 3888 by 86 
 
 14. 
 
 1703 by 27 
 
 25. 
 
 7159 by 39 
 
 4. 
 
 1302 by 21 
 
 15. 
 
 3034 by 46 
 
 26. 
 
 8697 by 28 
 
 5. 
 
 2945 by 38 
 
 16. 
 
 4697 by 61 
 
 27. 
 
 4910 by 45 
 
 6. 
 
 3213 by 51 
 
 17. 
 
 4368 by 98 
 
 28. 
 
 3682 by 73 
 
 7. 
 
 1827 by 27 
 
 18. 
 
 4544 by 76 
 
 29. 
 
 4918 by 94 
 
 8. 
 
 3007 by 36 
 
 19. 
 
 2867 by 61 
 
 30. 
 
 8168 by 86 
 
 9. 
 
 6256 by 81 
 
 20. 
 
 2058 by 27 
 
 31. 
 
 7369 by 69 
 
 10. 
 
 5096 by 95 
 
 21. 
 
 2668 by 31 
 
 32. 
 
 8925 by 28 
 
 11. 
 
 2542 by 41 
 
 22. 
 
 3592 by 43 
 
 33. 
 
 8010 by 65 
 
 12. 
 
 3567 by 87 
 
 23. 
 
 2047 by 83 
 
 34. 
 
 9102 by 98 
 
 35. How many suits, at $32 each, can be bought for 
 $1095, and what amount will be left ? 
 
 36. Find the number of barrels of oil, 51 gallons each, 
 that can be filled from a vessel containing 408 gallons. 
 
136 FOURTH YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. At $.25 each, how many books can you buy for 
 $6.25? 
 
 $6.25 = 625^ $.25 = 25^ 
 
 2o No. of books. 
 Cost of 1 book 25 ^) 625 ^ money spent. 
 50 
 
 125 
 125 
 
 2. At 16 cents each, how many belts can be bought 
 for $4.80? 
 
 3. Mary paid 24 cents a pound for butter. The 
 amount of her bill was $3.12. How many pounds did 
 she buy ? 
 
 4. How many gallons equal 652 quarts ? 
 
 5. I bought silk at 75 cents a yard and paid $13.50. 
 How many yards did I buy ? 
 
 6. In how many months will a man save $1120, if 
 he saves $32 a month ? in how many years? 
 
 7. How many bars of iron, weighing 56 lb. each, are 
 equal in weight to a bar weighing 18200 lb. ? 
 
 8. A man sold land for $45 an acre, receiving 
 $7200 for it. How many acres did he sell? 
 
 9. An orchard contains 4032 trees, planted in 32 
 rows. How many trees are there in a row ? 
 
 10. A farm of 174 acres was sold for $12970. What 
 was the selling price per acre ? 
 
Oral and Written] DIVISION AND PARTITION 137 
 
 DIVISION AND PARTITION 
 
 Division is the process of finding how many times one 
 number contains another, or of separating a number into 
 equal parts. 
 
 1. How many times is $ 3 contained in $ 15 ? 
 
 This problem gives the size of the equal parts ($3) 
 into which the dividend ($15) is to be divided, and 
 asks for the number of equal parts. $15-^-$3 = 5, the 
 numher of equal parts. 
 
 2. What is the quotient of $ 15 divided by 3 ? 
 
 This problem gives the numher of equal parts (3) into 
 which the dividend ($15) is to be divided, and asks for 
 the size of each part. | of $ 15= $ 5, the size of each 
 part. This kind of division is called partition. 
 
 First state whether each problem calls for the numher 
 of equal parts or the size of each part, and then give 
 answers : 
 
 3. 144 in. -^ 12 in. 7. 192 bu. ^ 16 bu. 
 
 4. 125 yd. ^5 8. 108 in. -^9 
 
 5. $132^ $11 9. ^oi $250 
 
 6. 150 ft. -f- 10 10. i of 128 da. 
 
 11. At 45^ a bushel, how many bushels of com will 
 sell for $17.55? 
 
 12 If 28 Stanhope buggies are sold for $ 2912, what 
 is the average price ? 
 
 13. If a train runs 1036 miles in 37 hours, how far 
 will it run in one hour ? 
 
138 
 
 FOURTH YEAR 
 
 [Written 
 
 REVIEW 
 
 Find the cost of: 
 
 1. 131 lb. of butter at 25^ a lb. 
 
 2. 64 suits at $81 each. 
 
 3. 32 pairs of shoes at $2 a pair. 
 
 4. 400 lb. of sugar at 4^ a pound. 
 
 5. 36 overcoats at $13.25 each. 
 
 6. 3000 envelopes at $12 a thousand. 
 
 7. 172 yards of cloth at 87^ a yard. 
 
 8. 2500 lb. of coffee at 20/ a pound. 
 
 9. 128 hogs at $161 each. 
 
 10. 37 hats at $2.25 each. 
 
 11. 451 yards of silk at 80/ a yard. 
 
 12. 1 gross pencils at 60/ a dozen. 
 
 13. 32 cows at $32 each. 
 
 14. 125 tons of hay at $14.75 a ton. 
 
 15. 72 bbl. of flour at $5.25 a barrel. 
 
 16. 14 bolts of ribbon at 75/ a bolt. 
 
 17. 78 bu. of wheao at 87/ a bushel. 
 
 18. 47| bu. of oats at 40/ a bushel. 
 
 19. 25 bu. of corn at 50/ a bushel. 
 
 20. 25 lb. of meat at 25/ a pound. 
 
 21. 21 doz. pairs of gloves at $1 a pair. 
 
 22. 36 J yd. of cloth at 18/ a yard. 
 
 23. 2 gross penholders at 50/ a dozen. 
 
 Add; 
 
 24. 
 
 25. 
 
 26. 
 
 27. 
 
 $463.75 
 695.42 
 
 1937.86 
 947.75 
 678.93 
 
 $6937.85 
 596.27 
 
 8346.39 
 326.42 
 
 2186.75 
 495.38 
 
 $9612.73 
 693.85 
 
 2928.46 
 478.74 
 
 8569.93 
 195.84 
 
 $3762.95 
 
 661.43 
 
 99.87 
 
 875.67 
 
 989.86 
 
 4987.19 
 
Written] PRACTICAL WORK 139 
 
 PRACTICAL WORK 
 
 Market Report 
 
 Potatoes, 75^ per bu. Corn, 46^ per bu. 
 
 Beans, .$1.25 per bu. Baked beans, 95^ per doz. cans. 
 
 Butter, Print,38^ per lb. Celery, 25^ per doz. 
 
 Dairy, 25^ per lb. Eggplant, 75^ per doz. 
 
 Sugar, 100 lb. bag, $5.50. Watercress, 40 f per doz. 
 
 Flour, per bbl., $5.80. Blackberries, per crate, $3.20. 
 
 From the market report find the cost of each of the 
 following : 
 
 1. 
 
 7 bu. potatoes. 
 
 7. 
 
 8 bu. corn. 
 
 2. 
 
 15 lb. prmt butter. 
 
 8. 
 
 10 bags sugar. 
 
 3. 
 
 12 doz. celery. 
 
 9. 
 
 25 bbl. flour. 
 
 4. 
 
 25 doz. watercress. 
 
 10. 
 
 2 doz. cans baked beans. 
 
 5. 
 
 5 bu. beans. 
 
 11. 
 
 7 doz. eggplant. 
 
 6. 
 
 12 lb. dairy butter. 
 
 12. 
 
 3 crates blackberries. 
 
 J 
 
 ^.t 121 ^ each find the cost of : 
 
 13. 
 
 72 lb. of meat. 
 
 18. 
 
 176 cards of buttons. 
 
 14. 
 
 144 books. 
 
 19. 
 
 272 pecks of potatoes. 
 
 15. 
 
 64 vases. 
 
 20. 
 
 128 baskets of tomatoes. 
 
 16. 
 
 168 cups. 
 
 21. 
 
 96 watermelons. 
 
 17. 
 
 256 yd. of lawn. 
 
 22. 
 
 152 yd. of ribbon. 
 
 23. If it is 8 miles from A to B, and 4^ times as far 
 from B to C, how far is it from A to C ? 
 
 24. James bought 10 lb. of sugar at 5 J cents a pound ; 
 41 lb. of butter at 20 cents a pound ; 6 lemons at 3 for 
 5 cents ; and two 8-cent loaves of bread. He gave the gro- 
 cer a two-dollar bill. How much change did he receive? 
 
140 rOUETH YEAR [Written 
 
 PRACTICAL PROBLEMS 
 
 1. A farmer has 28 cows in three fields. If there 
 are 12 in the first, and 9 in the second, how many cows 
 are there in the third field ? 
 
 2. The farmer values his cows at an average of $ 35 
 each. What is the value of all ? 
 
 3. The fields over which they graze contain 24 acres, 
 18 acres, and 14 acres. How much grazing land is there, 
 and what is the value of this land at $ 35|- an acre ? 
 
 4. If the farmer receives 21560 gallons of milk a 
 year, how much is it worth at 1 2 cents a gallon ? 
 
 5. His Jersey cow yields 350 lb. of butter a year, 
 which he sells at 28 cents a pound. How much does he 
 receive for it ? 
 
 6. He sold 5 of the cows at an average price of 
 $ 48.50. How much did he receive for them ? 
 
 7. He keeps 2 men at $ 22 J a month, to work on 
 the farm. How nnich does the labor for the year cost ? 
 
 8. He sold 14 calves for $ 98. How much did he 
 receive, on an average, for each ? 
 
 9. His grocery bill averaged $ 36J per month. Find 
 his bill for the year. 
 
 10. He purchased 2 horses, one at $ 125, and one at 
 $ 150 ; and 2 wagons at $ 85 each. Repairs on the 
 farm cost $ 87.50. Find the amount paid. 
 
 11. He bought 1^ doz. milk cans at $1.25 each. 
 How much did they cost ? 
 
Oral and Written] 
 
 MEASURES 
 
 141 
 
 MEASURES OF TIME 
 
 1. Write the days of the week 
 and the months of the year, with their 
 abbreviations. 
 
 2. Observe that the second hand 
 moves over 60 small or second spaces, 
 while the minute hand moves over 
 one minute space. 
 
 3. Memorize this table : 
 
 60 seconds ( 
 
 sec.) = 1 minute 
 
 (min.) 
 
 60 minutes = 
 
 = 1 hour (hr.) 
 
 
 24 hours = 1 
 
 day (da.) 
 
 
 365 days = l 
 
 year (yr.) 
 
 
 September, November, April, and June have each 
 30 days. All the others except February have 31 days 
 each. February usually has 28 days. A year that 
 has 366 days is called a leap year. In leap year 
 February has 29 days. 
 
 4. Memorize this rhyme : 
 Thirty days have September, 
 April, June, and November. 
 All the rest have thirty-one, 
 Save February, which alone 
 Has twenty-eight ; and one day more 
 We add to it one year in four. 
 
 Change : 
 
 5. 3 min. to sec. 
 
 6. 6 da. to hours. 
 
 7. 7 hr. to minutes. 
 
 8. 3 da. 6 hr. to hr. 
 
 9. 10 wk. 6 da. to da. 
 
 10. How many days are there in April, May, and 
 June ? in November, December, and January ? 
 
142 
 
 FOURTH YEAR [Oral and Written 
 
 MEASURES OF WEIGHT 
 
 1. Name some arti- 
 cles bought by the ounce 
 (oz.) ; by the pound. 
 
 2. How many ounces 
 are there in 1 pound ? in 
 10 pounds ? 
 
 Coal, hay, sand, plas- 
 ter, etc., in large quanti- 
 ties, are sold by the ton 
 of 2000 pounds. 
 
 3. Memorize the table : 
 
 16 oz. = 1 pound (lb.) 
 2000 pounds = 1 ton (T.) 
 
 4. A dealer buys 150 bales of hay, averaging 90 
 pounds to the bale. How many tons and pounds over 
 does he buy ? 
 
 5. At 3 cents an ounce, how much will 1 pound of 
 mustard cost ? 
 
 6. Find the cost of six kegs of nails, each keg weigh- 
 ing 100 lb., at 5|- cents a pound. 
 
 7. 2 tons of rolled oats were packed in pound pack- 
 ages. How many packages were there ? 
 
 8. How many ounces are there in a ton ? 
 
 • 9. A load of hay weighed 3000 pounds. How many 
 tons did it weigh ? What was its value at $ 14 a ton ? 
 
Oral and Written] MEASURES 143 
 
 MEASURES OF LENGTH OR DISTANCE 
 
 1. Name the measures that you have already learned. 
 
 2. A foot = inches. 
 
 3. A yard = feet. 
 
 4. What measure should you use to measure the 
 length of your book ? of your desk ? the width oi your 
 schoolroom ? the length of the blackboard ? 
 
 5. Measure b^ yards or W^ feet along the street or 
 on the school ground. Call it one rod. 
 
 6. Secure a tape measure 5| yards long, and with 
 it measure the length and the width of your school 
 grounds in yards and feet. 
 
 7. With a pole or a tape, a rod in length, measure the 
 distance in rods and feet around a square or a field. 
 
 8. 20 city blocks, each 16 rods in length, are 320 
 rods long. This is called one mile. 1 mile = 320 rods. 
 
 9. 320 X 161 ft. = feet. (Why do we multi- 
 ply 16| ft. by 320 ?) 
 
 10. 5280 ft. ^ 3 = yards. (Why do we divide 
 
 5280 ft. by 3 ?) 
 
 11. Memorize this table : 
 
 
 12 
 
 inches 
 
 (in.) = 1 foot (ft.) 
 
 
 3 
 
 feet 
 
 = 1 yard (yd.) 
 
 5l yards, 
 
 or 161 feet 
 
 = 1 rod (rd.) 
 
 
 320 
 
 rods 
 
 = 1 mile (mi.) 
 
 1760 yards 
 
 5 = 1 
 
 mile 
 
 5280 feet = 1 mile 
 
144 FOURTH YEAR [Oral 
 
 MEASURES OF LENGTH OR DISTANCE 
 
 Change : 
 
 1. 60 ft. to yd. 7. 5 ft. to in. 
 
 2. 27 rd. to ft. 8. 120 in. to ft. 
 
 3. 16 ft. to in. 9. 72 ft. to yd. 
 
 4. 42 in. to ft. 10. 420 in. to ft. 
 
 5. 320 rd. to ft. 11. 1250 yd. to ft. 
 
 6. 1760 yd. to ft. 12. 120 rd. to ft. 
 
 13. How many feet of fence are required for a garden 
 in the form of an oblong 26 yards long and 12 yards 
 wide ? 
 
 14. James lives 180 rods from the schoolhouse. How 
 many feet does he travel in going to and coming from 
 school each day ? 
 
 15. A boy travels 135 yards each day in carrying the 
 mail. How many yards does he travel in 6 days? 
 How much less than a mile does he travel? 
 
 MEASURES OF SURFACE 
 
 1. Draw a square inch. What two things show 
 that it is a square inch ? 
 
 2. Draw on the blackboard one square foot. What 
 two things show that it is a square foot ? 
 
 3. Separate each side of a square foot into 12 equal 
 parts. Connect these points by straight lines. What 
 is the size of each square ? the name of each square ? 
 How many square inches equal one square foot ? 
 
Oral] 
 
 MEASURES 
 
 145 
 
 144 square inches = 1 square foot 
 
 4. Draw on the blackboard a square yard. What 
 two things show that it is a square yard ? 
 
 Let one inch represent a foot. How long, then, is 
 the side of the square that represents a square yard? 
 
 5. Represent a square yard by a square, each side 
 of which is f inch. Then, \ inch represents 1 foot. 
 How long is each side of a square yard ? 
 Measure the surface of the square yard by 
 1 square foot. How many square feet are 
 there in the upper row ? in the second row? 
 in the three rows ? 
 
 w, 
 
 
 
 
 
 
 
 
 
 9 sq. ft. = 1 sq. yd. 
 
 ^^/S- 
 
 
 
 
 
 
 
 
 6. This drawing represents 
 an oblong 4 yards long and 2 
 yards wide. Measure the sur- 
 face by 1 square yard. How 
 many square yards are in one 
 row ? in both rows ? 
 
 In 1 row there are 4 sq. yd. 
 
 In 2 rows there are 2 x 4 sq. yd. or 8 square yards. 
 
 7. How many square yards are there in an oblong 
 5 yd. long and 4 yd. wide ? 
 
 The number of square inches, square feet, or square 
 yards a surface contains is called its area. 
 
146 FOURTH YEAR [Written 
 
 MEASURES OF SURFACE 
 
 Find the area in square inches of: 
 
 1. An oblong 6 in. by 4 in. 5. An 8-in. square 
 
 2. A square 7 in. on each side. 6. A 12-in. square 
 
 3. A page 8 in. by 5 in. 7. A 9-in. square. 
 
 4. A slate 10 in. by 12 in. 8. A 10-in. square. 
 9. Draw a figure to represent an oblong 5 in. long 
 
 and 3 in. wide. Find its area. Find the distance 
 around the oblong. 
 
 The distance around a figure is called the perimeter. 
 
 10. Find the perimeter, iii inches, of each figure de- 
 scribed in problems 1 to 9. 
 
 Represent the following figures by a scale of 1 inch to 
 the foot, and find the area and the perimeter : 
 
 11. A 6-ft. square. i3. A wall 9 ft. by 6 ft. 
 
 12. A rug 9 ft. by 4 ft. i4. A table 6 ft. by 5 ft. 
 
 Find the area and the perimeter. Represent on a 
 scale of 1 inch to a yard : 
 
 15. A schoolroom 10 yd. long and 8 yd. wide. 
 
 16. A hall 15 yd. long and 3 yd. wide. 
 
 17. A sidewalk 12 yd. long and 2 yd. wide. 
 
 18. Matting for a room 5 yd. long and 4 yd. wide. 
 
 19. Measure, in even yards, the length and width of 
 your schoolroom floor, and draw the figure on a scale 
 of 1 in. to the yard 3 1 in. to the foot. 
 
Oral, Written] READING AND WRITING NUMBERS 14T 
 
 READING AND WRITING NUMBERS 
 
 1. How are large numbers pointed off before being 
 read? 
 
 2. Name the periods of numbers up to millions. 
 
 3. Read 2,028,375. Notice that in reading a num- 
 ber the units' period is not named. Thus this number 
 is read 2 millioriy 28 thousa7id, 375; no ^375 units. 
 
 The next period after millions is called billions* period. 
 Copy, point off, and read: 
 a 
 
 4. 2405 
 
 5. 3065 
 
 6. 7005 
 
 7. 8900 
 
 8. 6666 
 
 9. 3050 
 
 10. 9580 
 Write : 
 
 11. Six thousand six hundred six. 
 
 12. Two billion ten million four. 
 
 13. Seventy-five thousand nine hundred six. 
 
 14. One billion eight million seventy-five. 
 
 15. Eighty-four million six hundred five thousand. 
 Twenty-five thousand thirty-eight. 
 Nine hundred million nine hundred ninety-nine. 
 Two million six thousand thirty. 
 
 b 
 
 c 
 
 d 
 
 30670 
 
 6800907 
 
 8645742689 
 
 49007 
 
 400745 
 
 750680009 
 
 40074 
 
 8790007 
 
 406009807 
 
 87090 
 
 4057042 
 
 6804704924 
 
 90703 
 
 3012890 
 
 9000000250 
 
 65002 
 
 7000002 
 
 8057000000 
 
 73200 
 
 9050601 
 
 5700809563 
 
 16. 
 17. 
 18. 
 19. 
 
 One billion one million one thousand. 
 
148 FOUKTH YEAR [Written 
 
 REVIEW 
 
 
 1. Begin with 9 and count by 9's to 126. 23. 2. 2134 
 
 
 2. Begin with 1 and count by 9's to 118. 
 
 s. 2124 
 
 
 Add by columns and by lines : 
 
 4. 2110 
 
 
 a b 
 
 c d e f 
 
 6. 2124 
 
 3. 
 
 42 + 74 + 39= 8. 24 + 32 + 65 = 
 
 6. 2124 
 
 4. 
 
 36 + 93 + 61= 9. 39+86 + 92 = 
 
 7. 2064 
 
 5. 
 
 27 + 81 + 87= 10. 94 + 39 + 19= . 
 
 9. 2123 
 
 €. 
 
 49 + 64 + 
 
 49= 11. 28 + 76 + 85 = 
 
 10. 2128 
 
 7. 
 
 38 + 72 + 
 
 86= 12. 63 + 15 + 84 = 
 
 11. 2124 
 
 
 + + 
 
 = + + = 
 
 12. 2109 
 
 
 a 
 
 6 c d 
 
 13. 2114 
 
 13. 
 
 $42.35+^ 
 
 $24.63 + $36.74 + $82.95 = 
 
 U> 2063 
 
 14. 
 
 18.69 + 
 
 32.78+ 6.27+ 2.39 = 
 
 16. 2110 
 
 15. 
 
 2.41 + 
 
 41.65+ .96+ 49.85 = 
 
 17. 2124 
 
 16. 
 
 36.74 + 
 
 59.83+ 18.49+ 13.74 = 
 
 18. 2124 
 
 17. 
 
 8389 + 
 
 43.62+ 9.37+ 26.48 = 
 
 19. 2124 
 
 20. 2124 
 
 21. 2062 
 
 
 + 
 
 + + = 
 
 18. 
 
 $57.35 + 
 
 $75.15+ $72.26+ $275.25 = 
 
 23. 2128 
 
 19. 
 
 63.27 + 
 
 64.23+ 17.83+ 375.65 = 
 
 24. 2124 
 
 20. 
 
 54.86 + 
 
 81.37+ 27.64+ 825.45 = 
 
 25. 2124 
 
 21. 
 
 83.74 + 
 
 76.45+ 36.21+ 963.75 = 
 
 26. 2124 
 
 22. 
 
 83.64 + 
 
 22.68+ 73.56+ 856.87 = 
 
 27. 2124 
 
 
 + 
 
 + + = 
 
 28. 2058 
 
 
 23. From the numbers at the right repre- 
 
 1 tin DC thp rJa.ilv p.iro.nla.tinn of a r>;q,Tipr- find 
 
 30. 2120 
 
 31. 2127 
 
 its circulation for July. 
 
Written] ADDITION AND SUBTRACTION 
 
 149 
 
 BANK DEPOSITS 
 
 A bank is an institu- 
 tion that receives and 
 loans money. 
 
 1. A bank received 
 as follows 
 $4126.50 
 $2842.35 
 $5045.60 
 $3862.41 
 $6065.70 
 $7564.72. 
 
 deposits 
 
 Monday, 
 
 Tuesday, 
 
 \Yednesday, 
 
 Thursday, 
 
 Friday, 
 
 Saturday, 
 
 Find the total deposits 
 
 for the week. 
 
 2. It paid out during 
 the week $24862.43. 
 How much more was received than was paid out ? 
 
 3. On June 1, F. G. Bishoff had a balance on hand 
 of $4232.44. During the month he deposited $1642.80, 
 and checked on his account to the amount of $2214.60. 
 What was his balance in bank July 1 ? 
 
 Find the balances : 
 
 4. 
 
 Deposits 
 
 Payments 
 
 Deposits 
 
 Payments 
 
 $216443.62 
 
 $111861.74 
 
 5. $15419.21 
 
 ^14000.00 
 
 112384.76 
 
 210987.65 
 
 16987.91 
 
 9044.89 
 
 211129.82 
 
 2940.74 
 
 6456.75 
 
 1055.20 
 
 114781.64 
 
 172.67 
 
 14381.50 
 
 10105.00 
 
 122046.95 
 
 127642.94 
 
 3102.62 
 
 2056.98 
 
 336847.68 
 
 1654.87 
 
 10000.00 
 
 8401.40 
 
50 
 
 FOURTH 
 
 YEAR 
 
 [Written 
 
 
 REVIEW OF 
 
 ADDITION 
 
 
 Add (when written) 4 problems in IJ minutes : 
 
 a 
 
 b 
 
 c 
 
 d 
 
 1. $751.04 
 
 $146.80 
 
 $345.75 
 
 1187.90 
 
 690.20 
 
 12.96 
 
 187.60 
 
 64.72 
 
 404.72 
 
 842.90 
 
 962.45 
 
 124.87 
 
 812.42 
 
 950.45 
 
 878.72 
 
 671.82 
 
 900.25 
 
 2.75 
 
 964.54 
 
 48.96 
 
 10.48 
 
 24.87 
 
 12.68 
 
 702.84 
 
 2. $964.77 
 
 $420.41 
 
 $862.41 
 
 $864.12 
 
 844.76 
 
 703.45 
 
 742.87 
 
 246.98 
 
 99.75 
 
 802.60 
 
 368.23 
 
 107.64 
 
 184.65 
 
 12.87 
 
 467.28 
 
 963.66 
 
 209.87 
 
 908.72 
 
 643.82 
 
 478.23 
 
 84.72 
 
 885.88 
 
 782.95 
 
 682.87 
 
 104.88 
 
 225.12 
 
 328.15 
 
 478.24 
 
 84.91 
 
 380.96 
 
 841.62 
 
 332.85 
 
 3. $844.62 $10642.83 $321.62 $12891.42 
 256.48 469.27 41.68 117.68 
 
 741.87 
 
 184.64 
 
 769.62 
 
 49.64 
 
 369.73 
 
 926.48 
 
 186.47 
 
 961.41 
 
 108.42 
 
 12.93 
 
 524.93 
 
 87.83 
 
 957.68 
 
 193.67 
 
 834.71 
 
 113.22 
 
 87.64 
 
 446.72 
 
 221.34 
 
 487.64 
 
 123.96 
 
 689.38 
 
 455.26 
 
 923.06 
 
p 
 
 Written] SUBTRACTION 151 
 
 REVIEW OF SUBTRACTION 
 
 Write, subtract, and test 4 problems in 2i- minutes : 
 
 1. 
 
 a 
 
 $843.87 
 632.17 
 
 6 
 $376.47 
 248.02 
 
 C 
 
 $48892.00 
 15079.63 
 
 d 
 
 $2498.73 
 519.71 
 
 2. 
 
 $600.01 
 289.81 
 
 $246.91 
 19.17 
 
 $32171.19 
 16693.40 
 
 $7739.82 
 7015.09 
 
 3. 
 
 $940.09 
 16.41 
 
 $1497.63 
 900.75 
 
 $45269.79 
 27319.27 
 
 $9999.86 
 1305.17 
 
 4. 
 
 $ 632.25 
 245.19 
 
 $741.20 
 523.18 
 
 $37461.27 
 19842.07 
 
 $5020.37 
 2456.78 
 
 5. 
 
 $ 95.33 
 49.27 
 
 $61.05 
 37.97 
 
 $649.08 
 500.16 
 
 $27004.49 
 19017.63 
 
 6. 
 
 $82.36 
 19.36 
 
 $79.87 
 27.93 
 
 $532.98 
 403.61 
 
 $75009.75 
 69135.92 
 
 7. 
 
 $80.16 
 25.31 
 
 $65.32 
 13.27 
 
 $763.55 
 300.01 
 
 $97382.99 
 39853.75 
 
 8. 
 
 $67.35 
 59.32 
 
 $51.27 
 27.75 
 
 $983.27 
 742.19 
 
 $32148.91 
 14269.90 
 
 9 
 
 $90.00 
 37.17 
 
 $86.95 
 14.75 
 
 $836.92 
 775.48 
 
 $33197.84 
 19057.55 
 
152 
 
 FOURTH YEAE 
 
 [Written 
 
 DRILL WORK 
 
 Multiply and test : 
 
 1. 8465 
 
 
 a 22 
 
 
 
 2. 7645 
 
 
 6 45 
 
 
 
 3. 8741 
 
 
 c50 
 
 Form 100 problems by mul- 
 
 4. 9860 
 
 
 d86 
 
 tiplying each multiplicand by 
 
 5. 8425 
 
 6. 9654 
 
 by 
 
 e76 
 /98 
 
 each multiplier, 
 la 22x8465 = 
 
 as: 
 
 7. 7869 
 
 
 5-66 
 
 Id 86x8465 = 
 
 = ? 
 
 8. 9765 
 
 
 h 69 
 
 6 e 76 X 9654 = 
 
 = ? 
 
 9. 4875 
 
 
 t97 
 
 
 
 10. 8420 
 
 
 i89 
 
 
 
 11. Divide 969 by 23. 
 
 12. Divide 969 by 24. 
 
 42* 
 
 
 40^ 
 
 23)969 
 
 
 24)969 
 
 92 
 
 
 96 
 
 49 
 
 
 9 
 
 46 Test. — 42 x 
 
 23 = 966 
 
 
 3 966 
 
 + 3 = 969 
 
 
 Divide and test : 
 
 
 
 13. 84765 
 
 1 
 
 a 86 
 
 
 
 14. 57672 
 
 
 &78 
 
 Form 64 
 
 problems by 
 
 15. 80720 
 
 
 c91 
 
 dividing eacL 
 
 I of the divi- 
 
 16. 50724 
 
 17. 60925 
 
 •by 
 
 ^59 
 
 'e72 
 
 dends by each of the divi- 
 sors, thus : 
 
 18. 86412 
 
 
 /67 
 
 13 a 84765^ 
 
 -86=? 
 
 19. 76412 
 
 
 ^82 
 
 13 c 84765^ 
 
 -91 = ? 
 
 20. 83456 
 
 
 /i65 
 
 18 e 86412 ^ 
 
 -72=? 
 
Written] 
 
 FRACTIONS 
 
 153 
 
 I 
 
 ADDITION AND SUBTRACTION OF HALVES 
 AND FOURTHS 
 
 Halves Fourths 
 
 I equal one whole unit ; 
 
 h+i 
 
 or 1. 
 
 f equal one whole unit; 
 
 +i + i + i = | or 1. 
 
 /2 
 
 = \y4 
 
 = 1 
 
 4 
 
 + 1 
 
 ^ 4 
 
 4 ' 
 
 l4-l=-l- 1+14-1 = 1 
 2^4 4'2~4~4 4' 
 
 ^■2 4 4'4 2 4'4 
 
 First add, then subtract : 
 
 3. 51 4. 9| 5. 
 
 3^ 8J ■ 
 
 
 V4 
 
 6. 51 
 
 7. 8f 
 
 2J 
 
 Add: 
 8. 31 
 
 iH 
 
 671 
 
 10. 
 
 651 
 
 11. 
 
 25| 
 9i 
 
 12. 
 
 561 
 8i 
 
 Tn example 8, |+} = | or 1 ; 1 + 1 = 11 Write the 
 fraction J and add the 1 to the whole number. 
 
154 
 
 FOURTH YEAR 
 
 [Written 
 
 HALVES, FOURTHS, AND EIGHTHS 
 
 Halves Fourths Eighths 
 
 1- i = t = t- f + l + i = t- _ s 
 
 2. Compare ^ and J of the same circle. 
 
 3. Compare ^ and ^ of the same circle. 
 
 4. J is what part of ^ ? f = ^ = i- 
 
 e 1— i.. 1 — -L- 1.4.1 4.1 — r- i_i_i. 
 
 ^- 2~'8J4:~~8'2^8^4:"~8?2 8~"8* 
 
 6. Into how many eighths can the whole circle be 
 divided? into how many fourths? 
 Add: 
 
 7. 3J 
 
 H 
 
 ii 
 
 8. 7f 
 
 9. 61 
 9| 
 
 10. 
 
 9i 
 11 
 
 6^ 
 
 11. 5J 
 
 121 
 31 
 
 12- | + f + f = f, or 
 many whole units ? 
 Subtract, then add : 
 
 2 whole units; 
 
 t+l 
 
 + f = how 
 
 13. lOf 
 
 5i 
 
 14. 121 
 6i 
 
 15. 27f 
 
 «8 
 
 16. 
 
 191 
 6i 
 
 17. 361 
 
 16| 
 
 18. 62f 
 
 31| 
 
 19. 63| 
 39^ 
 
 20. 26| 
 
 24| 
 
 21. 
 
 18| 
 
 22. 40| 
 
 20i 
 
Written] 
 
 FRACTIONS 
 
 155 
 
 THIRDS, SIXTHS AND NINTHS 
 
 Thirds Sixths Ninths 
 
 i 
 
 1 
 
 = 
 
 f 
 
 
 1- i+f = |; 
 
 2- i+l + i = 
 
 4 or— unit; J + 
 
 9=?; 2 = 
 
 
 i+i=f 
 
 First add and then subtract : 
 
 
 
 
 3. 15| 
 10| 
 
 4. 29^ 
 13^ 
 
 5. 81| 
 
 20* 
 
 
 6. 42| 
 13i 
 
 7. 62f 
 12i 
 
 8. 15f 
 12| 
 
 9. 16J 
 
 lOi 
 
 
 10. 19| 
 
 12i 
 
 11. Mrs. Clark bought If dozen lemons and used IJ 
 dozen. How many remained ? 
 
 12. Henry studies 41 hours a day, and James 6J 
 hours. How much longer does James study each day 
 than Henry? 
 
 13. A flower bed is 4i ft. long and 2| ft. wide. Find 
 the distance aground it. 
 
 14. If it takes Henry 3J hours to walk a certain dis- 
 tance, or 11 hours to ride it on his bicycle, how much 
 time does he save by riding ? 
 
156 FOURTH 
 
 YEAR 
 
 MULTIPLICATION 
 
 1. Multiply 794 by 
 
 326. 
 
 
 694 
 
 
 694 
 
 326 
 
 
 326 
 
 4164= 6x694 
 
 
 4164 
 
 13880= 20x694 
 
 
 1388 
 
 208200 = 300x694 
 
 
 2082 
 
 [Written 
 
 226244 = 326 x 694 226244 
 
 When multiplying by 3 hundreds, write the partial 
 product as 2082 hundreds by placing the first figure of 
 that product under hundreds. 
 
 Multiply : 
 2. 462 3. 283 4. 619 5. 543 
 
 375 * 243 128 264 
 
 6. $40.75 7. $26.73 8. $38.27 9. $46.75 
 325 364 918 842 
 
 10. 465 by 327 17. 5382 by 147 24. $46.75 by 275 
 
 11. 289 by 943 is. 2493 by 316 25. $83.94 by 843 
 
 12. 568 by 769 19. 9875 by 827 26. $76.15 by 972 
 
 13. 987 by 938 20. 7341 by 695 27. $39.85 by 867 
 
 14. 478 by 783 21. 9386 by 783 28. $48.57 by 984 
 
 15. 925 by 867 22. 6294 by 894 29. $ 96.78 by 786 
 
 16. 387 by 591 23. 9387 by 619 30. $39.74 by 815 
 31. Announce products at sight : 
 
 20x40 50x50 12x12 80x80 
 
Written] MULTIPLICATION 
 
 MULTIPLICATION 
 1. Multiply 273 by 304. 
 
 273 
 304 
 
 157 
 
 1092 
 000 
 819 
 
 82992 
 
 273 
 
 304 
 1092 
 
 819 
 
 82992 
 
 Do not multiply by as in the first illustration. 
 
 When multiplying by 3 hundreds, write the partial 
 
 product as 819 hundreds by placing the right hand 
 figure of that product in hundreds' place. 
 
 2. 
 
 3. 
 
 
 4. 
 
 402 
 
 $30.60 
 
 
 ■ $20.75 
 
 x503 
 
 X2040 
 
 
 xl05 
 
 1206 
 
 122400 
 
 
 10375 
 
 2010 
 
 6120 
 
 
 2075 
 
 202206 
 
 $62424.00 
 
 
 $2178.75 
 
 5. 316 
 
 6. 275 
 
 7. 428 
 
 8. 506 
 
 x502 
 
 x306 
 
 x405 
 
 x30V 
 
 9. 243 
 
 10. 709 
 
 11. 608 
 
 12. 705 
 
 x308 
 
 x504 
 
 x209 
 
 x804 
 
 ks. $8.08 
 
 14. $40.75 15. 
 
 $90.70 
 
 16. $38.04 
 
 1 x607 
 
 x603 
 
 x504 
 
 x703 
 
158 
 
 
 FOURTH YEAR 
 
 
 [Written 
 
 How many are 
 
 
 
 
 
 1. 
 
 704x3096 
 
 6. 
 
 309 X 4039 
 
 11. 
 
 803 X $40.70 
 
 2. 
 
 809 X 9409 
 
 7. 
 
 907 X 7008 
 
 12. 
 
 709x$75.2£ 
 
 3. 
 
 609 X 7320 
 
 8. 
 
 408 X 6007 
 
 13. 
 
 304 x$ 68.07 
 
 4. 
 
 507 X 8060 
 
 9. 
 
 502x9103 
 
 14. 
 
 508 x$ 70.95 
 
 5. 
 
 608 X 3724 
 
 10. 
 
 903 X 7030 
 
 15. 
 
 806 x$ 48.57 
 
 Multiply : 
 
 
 
 
 
 16. 
 
 8945 by 643 
 
 26. 
 
 6785 by 904 
 
 36. 
 
 5078 by 206 
 
 17. 
 
 3089 by 136 
 
 27. 
 
 7856 by 685 
 
 37. 
 
 9067 by 508 
 
 18. 
 
 4506 by 275 
 
 28. 
 
 9786 by 607 
 
 38. 
 
 8906 by 379 
 
 19. 
 
 3875 by 609 
 
 29. 
 
 7869 by 783 
 
 39. 
 
 6709 by 806 
 
 20. 
 
 5783 by 382 
 
 30. 
 
 6778 by 579 
 
 40. 
 
 6076 by 927 
 
 21. 
 
 3296 by 907 
 
 31. 
 
 9868 by 632 
 
 41. 
 
 8405 by 403 
 
 22. 
 
 7395 by 834 
 
 32. 
 
 5846 by 597 
 
 42. 
 
 6035 by 876 
 
 23. 
 
 3837 by 958 
 
 33. 
 
 6484 by 460 
 
 43. 
 
 8708 by 804 
 
 24. 
 
 6574 by 687 
 
 34. 
 
 9676 by 329 
 
 44. 
 
 7083 by 705 
 
 25. 
 
 8936 by 706 
 
 35. 
 
 6798 by 376 
 
 45. 
 
 5067 by 770 
 
 46. Mr. Watson had 2475 boxes of soap. Each con- 
 tained 175 cakes. Find the entire number of cakes. 
 
 47. A factory averages 2485 articles for 310 days of 
 the year. What is the entire number made ? 
 
 48. Mrs. Thompson raised 246 turkeys and sold them 
 at $ 1.75 each. How much did she receive for them? 
 
 49. A suit factory manufactured 3685 suits during the 
 season. At $ 28.50 each, how much was received for 
 them? 
 
Oral and Written] MULTIPLICATION 159 
 
 PARTS OF NUMBERS 
 
 1. Find I of 24. 
 
 ^ f 94. • Q . How do we find ^ of a mim- 
 
 I of '24 = 2 xl ov 16. ^'' ^ i °f ^ j'T)'' • * t ' 
 
 •^ number, etc. ? | ot a number 
 
 of the number. # of a number = 3 x ^ of the 
 
 'AX 
 
 number, etc. 
 
 Give rapidly. 
 
 2. i of each number: 16, 24, 36, 44, 48, 50. 
 
 3. J and I of each number : 15, 18, 24, 36, 45. 
 
 4. 
 
 i and f of each number : 16, 20, 28, 3 
 
 2, 48. 
 
 5. 
 
 h h h ^^d 1 
 
 of each number : 20, 35, 
 
 45, 40, 80. . 
 
 
 Find: 
 
 
 
 
 
 6. 
 
 iofl8 
 
 12. 
 
 foflS 
 
 18. fof21 
 
 24. |of75 
 
 7. 
 
 lof24 
 
 13. 
 
 f of 28 
 
 19. fof20 
 
 25. |-of75 
 
 8. 
 
 lofl6 
 
 14. 
 
 |of 56 
 
 20. f of 40 
 
 26. |of96 
 
 9. 
 
 lof 42 
 
 15. 
 
 iof 64 
 
 21. J of 24 
 
 27. i of 144 
 
 10. 
 
 fof24 
 
 16. 
 
 lof 63 
 
 22. f of 65 
 
 28. f of 160 
 
 11. 
 
 fof 25 
 Find: 
 
 17. 
 
 |of 63 
 
 23. |of48 
 
 29. 1 of 255 
 
 30. 
 
 1 of $24 
 
 
 35. f 1 
 
 3f 12 lb. 40. 
 
 ^ of $8.20 
 
 31. 
 
 |of $16 
 
 
 36. f ( 
 
 Df 9 ft. 41. 
 
 ^of $12.60 
 
 32. 
 
 1 of $50 
 
 
 37. 1. 
 
 Df 12 yd. 42. 
 
 1 of $20.40 
 
 33. 
 
 f of $18 
 
 
 38. f 1 
 
 oi 16 gal. 43. 
 
 1 of $15.90' 
 
 
 1 of $20 
 
 
 39. f of 8 bu. 44. 
 
 1 of $24.20' 
 
160 FOURTH YEAR [Written 
 
 MULTIPLICATION BY MIXED NUMBERS 
 1. Multiply 36 by 6f. 
 36 
 
 2. 
 
 means that f of 36 is to 
 
 21^ 
 
 ; = 6 x36 be added 1 
 
 24C 
 
 ) = 6f 
 
 x36 
 
 Multiply 
 
 
 2. 
 
 72 
 
 by8| 
 
 3. 
 
 126 
 
 by9f 
 
 4. 
 
 324 
 
 byl2J 
 
 5. 
 
 872 
 
 by25f 
 
 6. 
 
 966 
 
 by 124| 
 
 7. 
 
 848 
 
 by 238f 
 
 8. 
 
 489 
 
 by 372^ 
 
 9. 
 
 1248 
 
 by 309f 
 
 10. 
 
 2530 
 
 by 842f 
 
 11. 
 
 3575 
 
 by 909f 
 
 12. 
 
 8496 
 
 by 890f 
 
 13. 
 
 3660 
 
 by 780J 
 
 14. 
 
 8575 
 
 by 197J 
 
 15. 
 
 8496 
 
 by 875f 
 
 16. 
 
 9639 
 
 by 976f 
 
 17. 
 
 8472 
 
 by 865i 
 
 18. 
 
 8436 
 
 by 345i 
 
 19. 
 
 9764 by 876| 
 
 20. 
 
 9972 by 984| 
 
 21. 
 
 8848 by 787f 
 
 22. 
 
 7266 by 719f 
 
 23. 
 
 8755 by 394f 
 
 24. 
 
 9875 by 485f 
 
 25. 
 
 9672 by 872§ 
 
 26. 
 
 6488 by 797| 
 
 27. 
 
 7465 by 864f 
 
 28. 
 
 7280 by 6201 
 
 29. 
 
 4860 by 701f 
 
 30. 
 
 5050 by 500| 
 
 31. 
 
 6006 by 303| 
 
 32. 
 
 9608 by 490f 
 
 33. 
 
 8570 by 809f 
 
 34. 
 
 6099 by 789f 
 
 35. 
 
 7085 by 804| 
 
Oral] PARTS OF A DOLLAR 161 
 
 FRACTIONAL PARTS OF A DOLLAR 
 
 $.50= ^of $1.00 
 
 $.12|= iof $1.00 
 
 $.25= |of $1.00 
 
 $.06i=Xof $1.00 
 
 $.20= Iof $1.00 
 
 $.33|=|of $100 
 
 $.10 = ^of $1.00 
 
 $.16|= |of $1.00 
 
 $.40= |of $1.00 
 
 $.75 = |of $1.00 
 
 Give at sight the cost of : 
 
 1. 6 bushels of apples at $ .50 a bushel. 
 Hint. — 6x^1 = ^1 = ^3. 
 
 2. 8 gallons of vinegar at $ .25 a gallon, 
 
 3. 8 yards of silk at $ .50 a yard. 
 
 4. 8 pounds of meat at $ .121 a pound. 
 
 5. 10 dozen eggs at $ .20 a dozen. 
 
 6. 9 yards of muslin at $ .10 a yard. 
 
 7. 6 pecks of pears at $.25 a peck. 
 
 8. 12 pictures at $ .75 each. 
 
 9. 10 yards of lawn at $ .10 a yard. 
 
 10. 6 gallons of vinegar at $ .50 a gallon. 
 
 11. 8 gallons of oil at $ .25 a gallon. 
 
 12. 12 dozen oranges at $ .25 a dozen. 
 
 13. 6 bushels of apples at $ .50 a bushel. 
 
 14. 16 pounds of rice at $ .121 a pound. 
 
 15. 10 pecks of peaches at $ .20 a peck. 
 
 16. 8 gallons of milk at $ .12|^ a gallon. 
 
16 
 
 2 
 
 FOUETH 
 
 YEAR 
 
 [Oral and Written 
 
 
 
 
 DIVISION 
 
 
 
 
 Give quotients at sight : 
 
 
 
 
 1. 
 
 a 
 100^ 
 
 10 280- 
 
 h140 
 
 c 
 
 993^ 
 
 331 315 + 
 
 105 
 
 2. 
 
 500^ 
 
 50 930- 
 
 ^310 
 
 645^ 
 
 129 972-+ 
 
 324 
 
 3. 
 
 300^ 
 
 30 860- 
 
 -172 
 
 951h- 
 
 317 725 + 
 
 145 
 
 4. 
 
 250^ 
 
 50 396- 
 
 i-132 
 
 284H- 
 
 142 932 H- 
 
 466 
 
 5. 
 
 400-^ 
 
 80, 960- 
 
 h320 
 
 788 H- 
 
 197 260 + 
 
 130 
 
 €. 
 
 844-^211 990- 
 
 -330 
 
 882^ 
 
 126 775 + 
 
 155 
 
 7. 
 
 Divide 
 
 175608 by 
 
 324. 
 
 8. Divide 793320 by 
 
 264. 
 
 
 542 
 324)175608 
 1620 
 1360 
 1296 
 
 
 3005 
 
 264)793320 
 
 792 
 
 1320 
 
 1320 
 
 
 
 
 648 
 
 648 , 
 do 
 
 Since 264 is lar 
 we write in the 
 
 ger than 13, what 
 quotient ? 
 
 
 Divide 
 
 
 
 
 
 
 9 
 
 63596 
 
 a 
 
 by 126 
 
 46785 
 
 6 
 by 135 
 
 c 
 13940 by 
 
 340 
 
 10 
 
 78563 
 
 by 341 
 
 78568 
 
 by 244 
 
 81282 by 
 
 408 
 
 11 
 
 . 48842 
 
 by 144 
 
 65375 
 
 by 255 
 
 23674 by 
 
 726 
 
 12 
 
 . 26786 
 
 by 354 
 
 78634 
 
 by 184 
 
 83765 by 
 
 415 
 
 13 
 
 . 46785 
 
 by 165 
 
 79673 
 
 by 263 
 
 27854 by 
 
 129 
 
 14 
 
 . 83761 
 
 by 219 
 
 86572 
 
 by 196 
 
 76348 by 
 
 366 
 
Written] PRACTICAL PROBLEMS 163 
 
 PROBLEMS OF TWO OPERATIONS 
 
 1. A dairyman has 137 cows in one herd and 47 less 
 in another. How many cows has he ? 
 
 Study of Problem 
 137 No. cows in one herd. 1. What is given in this 
 
 47 No. less in 2d herd. problem ? 
 
 ~90 No. cows in 2d herd. «• The number of 
 
 cows in one herd. 
 137 cows + 90 COWS =227 cows. h. The difeerence in 
 
 the number in the two 
 herds. 
 
 2. What is required in the problem ? 
 a. The number in the second herd. 
 h. The number in both herds. 
 
 3. How can you find what is required from what is given ? 
 
 a. By subtracting the difference from the number in the 
 
 first herd. 
 6. By adding the number of cows in the two herds. 
 
 Note. — The purpose of these studies is threefold : 
 
 1. To train the pupil to see and understand the conditions of 
 the problem. 
 
 2. To give a logical grasp of the conditions of the problem. . 
 
 3. To direct the teacher in his efforts to attain these ends. 
 
 2. A man has 267 sheep in one field and 88 less in 
 another. How many sheep has lie ? 
 
 3. A merchant has $496 in the safe and $175.25 
 less in the bank. How much money has he in both 
 places ? 
 
 4. A man sold a farm for $7625 and gained $1685. 
 How much would he have received for it if the gain 
 had been $2675? 
 
164 FOURTH YEAR [Written 
 
 5. A man's salary is $950 per year. He pays $260 
 for board, $136 for clothing, and $115.75 for other 
 expenses. How much has he left ? 
 
 6. A grocer deposited in bank dm-ing the week the 
 following sums : $495.65, $283.75, $693.29, $75.80, 
 $249.89, and $375.77. After making the last deposit, 
 lie found there was a balance to his credit of $1265.15. 
 How much had he withdrawn ? 
 
 7. If a freight car costs $475, and a locomotive 
 $14625, what is the value of a train containing 27 cars 
 and a locomotive ? 
 
 8. A woman sold at a store 16 doz. eggs at 18^ a 
 dozen, 13J lb. of butter at 28^ a pound, and 27 lb. of 
 dressed chicken at 16^ a pound. How much did she 
 receive for all ? 
 
 9. A lady bought at a store : 
 
 8 lb. of coffee® 28^; 
 9^1b. of rice® 8^; 
 
 24 lb. of sugar ® 5^; 
 
 8 cans tomatoes ® 13^; 
 20 cans beans @ 19 ^. 
 
 Find the amount of her purchases. 
 
 10. Find the cost of : 
 
 271 lb. of cheese ® 18^; 
 14| lb. of lard ® 12^; 
 17 Ib.of butter ® 27^; 
 
 25 bottles ammonia ® 8 ^ ; 
 12 cans peas ® 18 ^. 
 
$ 2.75 
 
 
 
 3.65 
 
 
 
 4.75 
 
 
 
 6.75 
 
 
 
 1.75 
 
 
 
 12.75 
 
 
 
 6)§32.40 
 
 in 6 days. 
 
 
 $5.40 ; 
 
 average each 
 
 day. 
 
 Written] PEOBLEMS OF TWO OPERATIONS 165 
 
 11. A man earned each day in one week as follows : 
 $2.75, $3.65, $4.75, $6.75, $1.75, $12.75. Find his 
 average daily earnings. 
 
 Study of Problem 
 
 1. What is given in this 
 problem ? 
 
 2. What is required ? 
 
 3. What is the first step 
 in the solution ? the second ? 
 
 4. Why do you divide by 
 6 to find the average ? 
 
 5. Show that the answer 
 is correct. 
 
 12. Two men contribute equal amounts to buy a lot for 
 £875; to build a storeroom for $4860; for furniture, 
 $520; and for goods to begin business, $5785. How 
 much does each pay ? 
 
 13. A creamery received milk for six days as follows : 
 7640 gallons, 8675 gallons, 9634 gallons, 8432 gallons, 
 8763 gallons, and 8604 gallons. What were the 
 average daily receipts? 
 
 14. If Helen received 85 in arithmetic, 79 in gram- 
 mar, 89 in history, 92 in geography, 86 in physi- 
 ology, and 85 in writing, what was her average in these 
 studies ? 
 
 15. The attendance at a school was 604 on Monday, 
 607 on Tuesday, 598 on Wednesday, 603 on Thursday, 
 598 on Friday. What was the average daily attend- 
 ance for the week ? 
 
166 FOUKTH YEAR [Written 
 
 16. 39 ladies' suits, each requiring 12 yards, were made 
 from a lot of cloth containing 576 yards. How many 
 yards were left ? 
 
 Study of Problem 
 
 12 yd. in 1 suit. 
 
 on 1. State this problem in 
 0\j number of suits. ,, 
 another way. 
 
 J-^^ 2. What operation is em- 
 
 36 ployed in the first step in the 
 
 468 yd. in 39 suits. solution ? in the second ? 
 
 3. Prove that the answer 
 
 576 yd. - 468 yd. = 108 yd. i, eorrect. 
 
 17. A boy sold 16 books at 20 cents each, and 36 toys 
 at 26 cents each. How much more did he receive for 
 the toys than for the books ? 
 
 18. Mr. Boyd's mail route is 23J^ miles, and Mr. Bur- 
 ton's is 17|^ miles. How much farther does Mr. Boyd 
 travel in 84 days than Mr. Burton ? 
 
 19. A school term is 180 days. If James attends ^ 
 of the term, how many days is he absent from school ? 
 
 20. A bookkeeper receives $150 a month, and saves 
 $68 a month. How much does he spend in a year? 
 
 21. Harry works 48|^ hours after school each month, 
 at 12 cents per hour, and Henry 52| hours at 16 cents 
 per hour. Find the difference in their wages. 
 
 22. What is the difference between the cost of 17 
 horses at $156 each, and 69 cows at 137 each? 
 
 23. A merchant buys 28 bbl. of sugar at $23 a barrel, 
 and 36 bbl. at $24 a barrel. If he sells all for $1856, 
 how much does he gain ? 
 
Written] PROBLEMS OF TWO OPERATIONS 167 
 
 24. A merchant paid $420.48 for carpet, and sold it 
 for $569.40. If he gained 17^ on each yard, how- 
 many yards did he buy ? 
 
 Study of Problem 
 
 $569.40 selling price of all. 1. What do you mean 
 
 " 9 
 
 420.48 cost price of all. ^j the terra " cost 
 
 $~~TJq~(vo r^^ir. r.( r^^ 2. What (lo vou mean 
 
 148.9 J gam of all. • „o u 
 
 by " selling price " f by 
 
 Gain on 
 
 " gain " ? 
 
 3. How do you find the 
 1yd. $. 17 ) S 148.92 gain on all. total gain ? 
 
 876 times, or yd. 4. Prove that the an- 
 
 swer is correct. 
 
 25. I bought land for $1850, and sold it for $2294, 
 thereby gaining $6 an acre. How many acres did I 
 buy? 
 
 26. A drover bought cows for $1500, and sold them 
 for $2250. If he gained $15 on each, how many did 
 he buy ? 
 
 27. Mr. Kinney paid $2640 for a city lot, and sold it 
 for $4560. If he gained $24 a front foot, how many 
 front feet did he sell ? 
 
 28. The population of a town was 8675 in 1900, 
 and 12635 by a special census taken in 1905. What 
 was the average yearly increase ? 
 
 29. Mr. Beggs paid $288 rent last year. This year 
 he pays $36 less. What is his rent per month ? 
 
 30. A jeweler bought rings for $140 and sold them 
 for $160. If he gained $.50 on each, how many did he 
 buy? 
 
$1.60 daily wages. 
 
 16 number of days worked. 
 
 9 60 
 
 16 
 
 $25.60 total wages. 
 
 Price of 40 times, or bushels, 
 
 168 FOURTH YEAR [Written 
 
 31. A laborer worked 16 days at $1.60 a day, and 
 with his earnings bought potatoes at 64)2^ a bushel. 
 How many bushels did he receive ? 
 
 Study of Problem 
 
 1. State this problem 
 in another way. 
 
 2. How can we find 
 the total amount earned? 
 
 3. What operation io 
 involved in the first step 
 of the solution ? in the 
 second step ? 
 
 1 bu. $.64)$25.60 total wages. 4. Prove that the an- 
 
 swer is correct. 
 
 32. If 124 bags of coffee, each weighing 48 lb., were 
 bought for $729.12, what was the price per pound ? 
 
 33. At 20 i^ per hour how long will it take a laborer 
 to earn $80, working 8 hours per day? 
 
 34. If 96 bu. of corn sell for $60.48, what is the 
 value of 250 bushels at the same price ? 
 
 35. A trackman averages 2 miles per hour for 8 
 hours each day. His record book shows 960 miles 
 walked. Find the number of days. 
 
 36. If a dozen lemons cost $.36, how much will 840 
 lemons cost ? 
 
 37. If 25 bbl. of flour weigh 4900 lb., how much will 
 56 bbl. weigh ? 
 
 38. If 23 carriages cost $4025, how much are 84 
 such carriages worth ? 
 
Written] PKOBLEMS OF TWO OPERATIONS 169 
 
 39. If 600 bu. of shelled corn weigh 33,600 lb., how 
 much will 468 bu. weigh ? 
 
 40. When 9 bales of cotton, weighing 325 lb. each, 
 sell for $ 731.25, what is the price per pound ? 
 
 41. If a peach basket holds 2 pecks, how many- 
 bushels are there in 12. carloads, each containing 456 
 baskets ? 
 
 42. How many books each 2 inches thick can be 
 placed in a bookcase containing 4 shelves, each shelf 
 of which is 3 ft. in length ? 
 
 43. If 123 tons of coal cost $725.70, how much will 
 16 tons cost ? 
 
 44. 24 cords of wood cost $90; how much will 18 
 cords cost at the same rate ? 
 
 45. If a newsboy earns $19.98 in 18 days, how much 
 will he earn at the same rate in 360 days ? 
 
 46. When 525 gallons of milk sell for $84, for how 
 much will 715 sell ? 
 
 47. Mary bought 16 pounds of coffee at 14^ a pound, 
 8 lb. of butter at 28^ a pound, and 12 cans of corn at 
 15^ a can. She gave the merchant in payment a $10 
 bill. How much change should she receive ? 
 
 48. A drover sold 56 sheep at $4 each, 8 cows at 
 $36 each, and 48 hogs at $12 each. If he received 
 $275 on the day of the sale, how much is still due him ? 
 
 49. A lady had $100. If she bought 4 chairs at $6 
 each, a couch for $28, and a rocking chair for $16, 
 how much had she left? 
 
170 FOURTH YEAR [Written 
 
 50. I bought 57 yards of cloth at 25)^ a yard, and 16 
 yards of matting at 2%P a yard. Find the cost of both. 
 
 51. A lady sold 6 doz. eggs at 18 cents a dozen, and 
 8 lb. of butter at 27 cents a pound. How much did she 
 receive for both ? 
 
 52. A merchant bought 546. bbl. of pork at $ 16.25 a 
 barrel, and sold it so as to gain $1638. At what 
 price per barrel did he sell the pork ? 
 
 53. James earned $ 1.50 per day and saved 85 cents. 
 If his savings were $ 33.15, how many days did he work ? 
 
 54. A farmer bought 4 horses at $ 137 each, 7 cow^s 
 at $27 each, and 38 sheep at $6.50 each. Find tlie 
 cost of all. 
 
 55. What will be the cost of 108 lb. of ham at 16i 
 cents a pound, and 48 lb. of breakfast bacon at 18 cents 
 a pound ? 
 
 56. Two automobile parties travel in opposite direc- 
 tions, one at an average of 127 miles, the other at 78 
 miles a day. How far apart will they be in 16 days ? 
 
 57. A factory employs 56 men at $ 1.75 a day, and 
 12 men at $ 2.25 a day. Other expenses are $ 125 a day. 
 How much does it cost to run the factory 26 days ? 
 
 58. A man paid $ 165 for a carriage, and 3| times as 
 much for a span of horses. How^ much did he pay for 
 both? 
 
 59. Mr. Hall deposited in the bank $ 24 a month 
 for 8 months, and $ 27 a month for 4 months. How 
 much did he deposit in the year ? 
 
ritten] 
 
 DIVISION 
 
 
 
 REVIEW OF 
 
 DIVISION 
 
 Divide and test : 
 
 
 
 1. 
 
 84563 by 224 
 
 13. 
 
 95846 by 675 
 
 2. 
 
 45675 by 125 
 
 14. 
 
 37846 by 332 
 
 3. 
 
 46752 by 236 
 
 15. 
 
 92846 by 124 
 
 4. 
 
 84252 by 342 
 
 16. 
 
 45983 by 475 
 
 5. 
 
 78654 by 375 
 
 17. 
 
 32841 by 243 
 
 6. 
 
 98740 by 425 
 
 18. 
 
 92384 by 752 
 
 7. 
 
 97601 by 438 
 
 19. 
 
 66008 by 300 
 
 8. 
 
 98700 by 508 
 
 20. 
 
 15899 by 122 
 
 9. 
 
 80070 by 710 
 
 21. 
 
 77443 by 224 
 
 10. 
 
 81704 by 508 
 
 22. 
 
 59823 by 525 
 
 11. 
 
 99999 by 999 
 
 23. 
 
 78912 by 640 
 
 12. 
 
 50321 by 637 
 
 24. 
 
 93408 by 825 
 
 Find 
 
 quotients and test : 
 
 
 
 25. 
 
 136425^405 
 
 35. 
 
 604325 -^ 304 
 
 26. 
 
 246840 -^ 476 
 
 36. 
 
 708546-^222 
 
 27. 
 
 332468^332 
 
 37. 
 
 125745^125 
 
 28. 
 
 948562-^450 
 
 38. 
 
 985432^112 
 
 29. 
 
 476352^221 
 
 39. 
 
 756342^102 
 
 3b. 
 
 789324 -^ 552 
 
 40. 
 
 354725^256 
 
 31. 
 
 569239 -f- 334 
 
 41. 
 
 498075^401 
 
 32. 
 
 159909^115 
 
 42. 
 
 987260 -^- 200 
 
 33. 
 
 550550-^155 
 
 43. 
 
 800745-^310 
 
 34. 
 
 889034-^324 
 
 44. 
 
 584972 -^ 226 
 
 171 
 
172 FOURTH YEAR [Oral and Written 
 
 COMBINING PROCESSES 
 
 1. 6 + 4 + 8-7 + 4-9 = ? 
 
 2. 7 + 6-5-4 + 9-6 = ? 
 
 The parenthesis ( ) indicates that all numbers in- 
 closed by it are to be considered as one number ; thus, 
 (7 + 9) - (4 + 5) means that the sum of 4 and 5 is to be 
 taken from the sum of 7 and 9. 
 
 The vinculum ( ) is sometimes used instead of 
 
 the parenthesis ; thus, 7 + 9 — 4 + 5 = 7. 
 
 Solve : 
 
 3. 9 + 8- (6 + 6) + 7-3 = ? 
 
 4. 8 + 6 + 16-7-8 + 6 = ? 
 
 5. 26 + 38 -(48 -23) + 16 = ? 
 
 6. 87-42 + 96-72 + 26 = ? 
 
 7. (97 -35) -26 + 14 + 78 = ? 
 
 8. 86-48 + 56-28-47 = ? 
 
 COUNTING BY MIXED NUMBERS 
 
 1. Count by 2^ to 40 ; by 3^ to 40 ; by 61 to 50. 
 
 2. Announ 
 
 ce at sight : 
 
 
 
 11x4 
 
 Ux 6 
 
 11x6 
 
 lix4 
 
 2Jx4 
 
 21 X 6 
 
 21x6 
 
 21x4 
 
 31x4 
 
 3Jx6 
 
 31x6 
 
 31x4 
 
 4ix 4 
 
 4|x6 
 
 41x6 
 
 4| x4 
 
 o. 
 
 Build similar tables with 1-|, 1^, and 1|-. 
 
Oral] ANALYSIS 173 
 
 ANALYSIS 
 
 1. Find the cost of 3 doz. oranges at 20 ^ per dozen. 
 1 doz. oranges cost 20 ^; 3 doz. cost 3 times 20 ^ = 60 ^. 
 
 2. At 12 cents a quart for berries, how much will 
 8 quarts cost ? 
 
 3. At 30 ^ a peck, how much will a bushel of beans 
 cost? 
 
 4. When peaches are 50 cents a basket, how much 
 will 7 baskets cost ? 
 
 5. A ton of coal costs $5. How much will 9 tons 
 cost? 
 
 6. A boy rides his w^heel 6 miles in one hour. How 
 far will he ride in 7 hours ? 
 
 7. When 5 boxes of matches cost 50^, how much 
 will 1 box cost ? 
 
 Cost of 5 boxes = 50 ^ ; 
 
 Cost of 1 box = i of 50^, or 10^. 
 
 8. A boy bought 4 balls for 80 cents. How much 
 was that apiece ? 
 
 9. When 8 yards of velvet cost $24, how much will 
 1 yard cost ? 
 
 10. A box of shoes containing 12 pairs costs $36. 
 Find the cost per pair. 
 
 11. Six cows were sold for $246. What was the 
 average selling price ? 
 
 12. When a telegram of 10 words costs 40 cents, 
 what is the average cost of each word ? 
 
174 FOURTH YEAR [Oral 
 
 ANALYSIS 
 
 1. When 1 pencil costs 10 ^, how many can you buy 
 
 for 60 ^ ? 
 
 When 1 pencil costs 10 ^, for 60 ^ you can buy as many pen- 
 cils as 10 ^ is contained in 60 ^. 
 
 2. At 12 ^ per yard, how many yards of ribbon can 
 be bought for 96^? 
 
 3. Cherries are 8 ^ a quart. How many quarts can 
 be bought for 72 ^ ? 
 
 4. When 3 tons of coal cost $18, how much will 7 
 
 tons cost ? Cost of 3 tons = 118; 
 
 Cost of 1 ton = 1 of $ 18, or $6; 
 Cost of 7 tons = 7 X $6, or $42. 
 
 5. How much will 9 dozen lemons cost when 3 
 dozen sell for 45 cents ? 
 
 6. Three men earn $30 in a certain time. How 
 much will 8 men earn in the same time ? 
 
 7. When 1 a bushel of potatoes sells for 25 cents, 
 
 how much will 3 bushels cost ? 
 
 Cost of ibu.= 25^; 
 
 Cost of i bu. = 2 X 25^, or 50^; 
 
 Cost of 3 bu. =3 X 50^, or $1.50. 
 
 8. At 20 cents a peck, how much will 2 bushels of 
 apples cost ? 
 
 9. When milk is selling at 5 ^ a quart, how much will 
 3 gallons cost ? 
 
 10. If J of a yard of velvet costs 60 ^, how much will 
 2 yards cost ? 
 
Oral and Written] COMPARISON 175 
 
 COMPARISON 
 
 1. Compare 80 and 20 ; 60 and 30 ; 90 and 10. 
 
 2. 2-1 is what part of 5 ? of 10 ? of 15 ? of 20 ? 
 
 3. 31 is what part of 10 ? of 20? of 30? of 6f ? 
 
 4. Compare 3-% and ^^ ; y% and ^ ; ^-g and y^^. 
 
 5. What part of 25 is 5 ? is 6^ ? is 21 ? is 8I ? 
 
 6. What part of 6 pk. is 2 pk.? of 10 gal. is 2 gal.? 
 
 7. 3 pk. is what part of 1^ bn. ? of 21 bu. ? 
 
 8. 8 oz. of butter is what part of 2 lb. ? of 21 lb. ? 
 
 9. When 21 pounds of butter cost 90 cents, how 
 much will 9 pounds cost ? 
 
 9 pounds equal 4 x 2 J pounds ; hence, 9 pounds will cost 4 x 90 
 cents, or $3.60. 
 
 10. If J a ton of hay costs $7.50, how much will 4 
 tons cost ? 
 
 11. When 2 pecks of potatoes cost 50 cents, how 
 much will 1^ bushels cost ? 
 
 12. When butter is selling at 3 pounds for $|, how 
 much will 15 pounds cost ? • 
 
 13. When 2^ dozen buttons sell for 30 cents, how 
 much will 7J dozen cost ? 
 
 14. If 61 tons of coal cost $37.50, how much will 
 25 tons cost ? 
 
 15. If 7^ yards of velvet cost $11.40, how much will 
 15 yards cost ? How many yards can be bought for 
 $22.80? 
 
176 FOURTH YEAR [Written 
 
 16. A boy picked 18 quarts of chestnuts and sold 
 them at the rate of 2 quarts for 25 cents. How much 
 did he receive for them ? 
 
 17. If 3 pounds of steak cost 48 cents, how much 
 will 10 pounds cost ? 
 
 18. A farmer raised 40 bushels of shelled corn per 
 acre on 7^ acres. At the same rate, how many bushels 
 «^^ould he raise from 22| acres ? 
 
 Find the cost of : 
 
 19. 288 chairs, when 9 chairs cost $6.75. 
 
 20. 350 rings, when 7 rings cost $ 19.74. 
 
 21. 285 fans, when 5 fans cost $ 1.75. 
 
 22. 144 knives, when 6 knives cost $ 5.04. 
 
 23. 78 vases, when 6 vases cost $ 17.76. 
 
 24. 248 hats, when 8 hats cost $ 15.68. 
 
 25. 24 pictures, when 4 pictures cost $ 18.92. 
 
 26. 48 lamps, when 16 lamps cost $34.56. 
 
 27. 54 clocks, when 27 clocks cost $ 72.63. 
 
 28. 28 desks, when 14 desks cost $ 173.32. 
 
 29. 78 rockers, when 26 rockers cost $ 196.30. 
 
 30. 36 watches, when 18 watches cost $702. 
 
 31. 36 cords of wood, when 6 cords cost $ 35.04. 
 
 32. 128 tons of coal, when 8 tons cost $57.60. 
 
 33. 180 quarts of milk, when 18 quarts cost $ 1.08. 
 
 34. 56 crates of melons, when 8 crates cost $ 28.80. 
 
 35. 328 books, when 8 books cost $ 1.44. 
 
Written] 
 
 BILLS 
 BILLS 
 
 17V 
 
 Pittsburg, Pa., ^ee. /, 1907. 
 
 Mu L. m. ^ka^yu^, 
 
 67 S^&oaI ^t. 
 
 aSotigfjt 0! C. H. MORRISON & CO., 
 
 Terms : Cash. 1854 PENN AVENUE. 
 
 
 
 2 {yu.. a.j}.^t^, @ $0.76 
 
 3 da^. tqcfo., @ .26 
 
 / 
 
 60 
 76 
 
 
 
 
 
 2 6~U. (Cauv, @ 6. 60 
 
 /3 
 
 00 
 
 
 26 
 
 
 
 16 
 
 Observe that this bill shows : (1) the jplace and the 
 date; (2) who hought the goods; (3) who sold the 
 goods; (4) the name of the goods sold and the ^rzce and 
 the amount of each sale. 
 
 The abbreviation @ for ^^ at *' should always be used 
 in making out a bill. 
 
 To foot a bill means to add the cost of all the separ- 
 ate articles. 
 
 The word total means the amount of the sales. 
 
 Make bills of the following sales, using a schoolmate's 
 name as purchaser, and your grocer as the one who sells 
 the goods. 
 
 1. 2 lb. butter, @ 25^ 
 6 lb. meat, @ 15^ 
 3 bars soap, @ 10^ 
 
178 FOURTH YEAR [Written 
 
 2. 
 
 4. 
 
 5. 
 
 6. 
 
 7. 
 
 8. 
 
 9. 
 
 10. 
 
 FOURTH YEAR 
 
 [ 
 
 b bills as suggested on previous page. 
 
 3 skeins yarn, @ 
 
 $0.08 
 
 4 papers needles, @ 
 
 .05 
 
 6 yd. ribbon, @ 
 
 .50 
 
 5 bu. potatoes, @ 
 
 $0.75 
 
 3 boxes peaches, @ 
 
 1.50 
 
 12 doz. lemons, @ 
 
 .40 
 
 4 spools thread, @ 
 
 $0.05 
 
 6 papers pins, @ 
 
 .10 
 
 5 cards hooks and eyes, @ 
 
 .02 
 
 5 lb. roast beef, @ 
 
 $0.15 
 
 3 lb. pork chops, @ 
 
 .15 
 
 4 lb. lamb chops, @ 
 
 .18 
 
 7 silver forks, @ 
 
 $2.00 
 
 3 sterling spoons, @ 
 
 1.75 
 
 4 napkin rings, @ 
 
 3.25 
 
 4 nickel sponge racks, @ 
 
 $2.25 
 
 5 hairbrushes, @ 
 
 2.00 
 
 6 nickel towel rods, @ 
 
 .75 
 
 4 doz. linen writing paper, @ $0.20 
 
 4 doz. linen envelopes, @ 
 
 .15 
 
 12 stamps, @ 
 
 .02 
 
 12 pkgs. flax seed, @ 
 
 $0.05 
 
 3 oz. cologne, @ 
 
 .10 
 
 5 lb. paint, @ 
 
 .20 
 
 2 music cabinets, @ 
 
 $15.00 
 
 5 rocking chairs, @ 
 
 5.00 
 
 3 medicine cabinets, @ 
 
 3.00 
 
Oral and Written] MEASURES 179 
 
 REVIEW OF MEASURES 
 
 1. Give the table used for measuring liquids. 
 
 2. Name some articles sold by liquid measure. 
 
 3. Give the table used for measuring dry and bulky 
 articles. 
 
 4. Name the most common articles sold by the peck 
 or the bushel. 
 
 5. Give the table of measures of weight. 
 
 6. Name the most common articles sold by the ounce; 
 the pound ; the ton. 
 
 7. Give the table used for measuring time. 
 
 8. Give the table of measures of length. What 
 measures are used for measuring short distances? long 
 distances ? 
 
 9. Give the table of measures of surface. 
 
 10. Write the names of the measures on blackboard 
 or paper, and write each of the following under its 
 proper measure : oil, cheese, oats, hay, beans, potatoes, 
 coal, cloth, molasses, sugar, rice, the surface of the 
 blackboard, the width of the room, the length of the 
 blackboard. 
 
 11. Draw a diagram to show the number of square 
 inches in an oblong 4 in. by 3 in. 
 
 12. Show by diagram that 9 square feet equal one 
 
 » square yard. 
 13. Show by a diagram on a scale of -^ inch to the 
 foot that 144 square inches equal one square foot. 
 
180 rOUETH YEAR [Written 
 
 MEASURES 
 
 Change : 
 
 1. 16 pt. to gallons. 8. 74 pk. to bushels. 
 
 2. 24 bu. to pecks. 9. 3750 yd. to feet. 
 
 3. 3 sq. ft. to sq. inches. 10. 3 in. to feet. 
 
 4. 17 yd. to feet. 11. 6 mi. to rods. 
 
 5. 120 ft. to inches. 12. 360 ft. to yards. 
 
 6. 50 lb. to ounces. 13. 4860 in. to feet. 
 
 7. 6 T. to pounds. 14. 6966 sq. ft. to sq. yd. 
 
 15. How many dozen oranges, and how many over 
 are there in a box containing 143 oranges? 165 oranges? 
 195 oranges? 
 
 16. Find the number of square inches in a flower bed 
 4 feet long and 3 feet wide. 
 
 17. The slate blackboard is 3 feet wide and 26 feet 
 long. Find its surface in square feet. 
 
 18. A fruit dealer buys chestnuts at $3 per bushel, 
 and sells them at $.10 per quart. Find his profit. 
 
 19. The schoolroom floor is 36 feet long and 28 feet 
 wide. Find the number of square feet in the floor ; in 
 the ceiling. 
 
 20. James walks to school every morning, 600 yards. 
 How many feet does he walk each day, in going to and 
 coming from school? 
 
 21. A huckster sells 10 bushel-crates of peaches at 20 
 cents per quarter peck. Find the amount from the sale 
 of the peaches. 
 
Written] 
 
 PRACTICAL WORK 
 
 181 
 
 I 
 
 I 
 
 
 
 
 
 PRACTICAL WORK 
 
 
 
 
 240 ft 
 
 
 
 it 
 
 
 
 
 
 
 t 
 
 
 o 
 
 
 
 
 
 
 O 
 
 
 ■"^ 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 ^ 
 
 -c 
 
 5 
 1 
 
 
 B 
 
 C 
 
 D 
 
 E 
 
 ' 1 
 
 S>i 
 
 Q) 
 
 •< 
 
 
 
 
 
 ^ 
 
 ^^ 
 
 5 
 CO 
 
 
 
 
 
 
 5 
 to 
 
 
 
 30ft 
 
 40 ft 
 
 40 ft 
 
 40 ft 
 
 40ft. 
 
 50ft 
 
 
 
 
 Sidevs/alk lOft 
 
 
 
 MAIN STREET 
 
 Tl 
 
 1. Mr. Stokes, a real estate agent, purchased this 
 plan of lots at $70 per front foot on Main Street. Find 
 the cost of the plan of lots. 
 
 2. Mr. R. M. Holland purchased lot A at $110 per 
 front foot, and built on it a house for $6450. Find the 
 cost of Mr. Holland's property. 
 
 3. Mr. Remington purchased lots B and C for $8000. 
 He put an iron fence around his lots at $1.10 per foot. 
 Find, the cost of the fence. 
 
 4. The concrete sidewalk on Main St. is 10 ft. in 
 width. Find the cost of Mr. Remington's walk at 19^ 
 per square foot. 
 
 5. Mr. Stokes sells lots D, E, and F to L. F. Holtz- 
 man for $9500. Find his profits on these lots. 
 
182 
 
 FOURTH YEAR 
 
 [Written 
 
 Divide and test : 
 a 
 
 1. 16434 by 64 
 
 2. 34643 by 28 
 
 3. 19603 by 88 
 
 4. 94432 by 62 
 
 5. 26341 by 74 
 
 6. 36236 by 37 
 
 7. 42624 by 41 
 
 8. 76342 by 36 
 
 9. 64283 by 24 
 
 10. 55022 by 82 
 
 11. 44302 by 74 
 
 12. 16792 by 81 
 
 13. 28644 by 73 
 
 14. 74305 by 37 
 
 15. 83265 by 87 
 
 16. 78325 by 75 
 
 17. 85679 by 41 
 
 18. 39410 by 52 
 
 19. 80624 by 68 
 
 20. 73102 by 74 
 
 21. 81103 by 85 
 
 22. 77777 by 96 
 
 23. 88888 by 72 
 
 REVIEW 
 
 b 
 
 28792 by 270 
 
 75639 by 770 
 66041 by 602 
 77006 by 784 
 60424 by 603 
 90328 by 735 
 76028 by 344 
 84605 by 766 
 16248 by 860 
 74637 by 450 
 68026 by 360 
 84132 by 770 
 70066 by 880 
 50468 by 480 
 66399 by 790 
 24166 by 670 
 12345 by 154 
 67890 by 221 
 89765 by 336 
 43210 by 742 
 34786 by 819 
 57602 by 745 
 80703 by 613 
 
 33467 by 890 
 77304 by 860 
 44384 by 280 
 35690 by 761 
 88762 by 892 
 56044 by 883 
 76428 by 444 
 23688 by 985 
 55624 by 666 
 34632 by 555 
 99240 by 461 
 36002 by 880 
 45676 by 390 
 76324 by 302 
 25321 by 440 
 65436 by 784 
 70504 by 621 
 62131 by 905 
 88776 by 860 
 54340 by 408 
 82107 by 329 
 62434 by 752 
 93785 by 607 
 
Written] 
 
 EEVIEW 
 
 188 
 
 » 
 
 PAID ADMISSIONS TO A FAIR 
 
 TICKETS 
 
 Price 
 
 TUES. 
 
 Wed. 
 
 Thubs. 
 
 Fri. 
 
 Total 
 Receipts 
 
 Children 
 Adults 
 
 One-horse vehicles 
 Two-horse vehicles 
 
 15^ 
 50^ 
 
 864 
 
 2864 
 
 376 
 
 212 
 
 1865 
 
 3245 
 
 364 
 
 216 
 
 1226 
 
 2764 
 
 176 
 
 144 
 
 1285 
 
 3768 
 
 472 
 
 224 
 
 
 
 
 
 
 
 
 
 IV 24. Find total admissions of each class, and the 
 receipts in money from each in the 4 days. 
 
 25. Find the receipts in money each day. 
 
 26. Add daily receipts; add total receipts for each 
 class. 
 
 27. A dealer pays $ 312.50 for 25 children's bicycles. 
 How much is that apiece? 
 
 28. A merchant pays $ 17.28 for 4 dozen boys' caps. 
 Find the cost of each cap. 
 
 29. At $ 84 per dozen, how much does a jeweler pay 
 for 15 watches ? 
 
 30. A concrete walk 80 ft. long and 4 ft. wide costs 
 $ 57.60. How much is that a square foot? 
 
 31. A ranchman clipped 4|- pounds of wool on an 
 average from each of 2175 sheep. How much is it 
 worth at 40^ per pound? 
 
 32. John's books weigh 2|- lb., and he weighs 58^ lb. 
 How much does he weigh with the books in his hand ? 
 
 33. There are 1232 pupils in a school, and fare girls. 
 Find the number of girls in school ; the number of boys. 
 
 ■ 
 
184 FOURTH YEAR [Written 
 
 34. A student buys a dictionary for $15, paying 50>^ 
 down, and the balance in weekly installments of 25^. 
 How many weeks will it take to cancel the debt? 
 
 35. James picked 4 bu. 3 pk. of berries, and sold 
 them at 8^ a quart. How much did he receive? 
 
 36. A lamp in a lighthouse consumes 2 gallons 1 
 quart of oil daily. Find the cost of the oil for Septem- 
 ber, October, and November at 18^ per gallon. 
 
 37. Make out the bill for the following: 3 pk. of 
 potatoes at 20^ a peck, 12 lb. of sugar at 7^ a pound, 
 5 qt. of molasses at 15^ a quart, 2 lb. of cheese at 
 25^ a pound. How much change should be received 
 from $5? 
 
 38. A dealer buys three paintings at auction for 
 S 544. If he sells one for $ 250, another for $ 275, and 
 the third for $375, how much does he gain? 
 
 39. Find the. cost of 2 bushels 2 pecks of nuts at 15 
 cents a peck. 
 
 40. In one season a pear orchard of 384 trees 
 averaged If bu. of pears to the tree. Find their value 
 at $ 1.25 a bushel. 
 
 41. How much do I gain on a box of fine soap cost- 
 ing $ 1.80 and containing a dozen cakes, if I sell the 
 soap at 20)2^ a cake? 
 
 42. A building lot 144 feet long is J as wide. 
 How wide is it ? How many square feet does it contain ? 
 
 43. Find the cost of 3 bu. of cherries at 6^ a quart. 
 
Written] REVIEW 185 
 
 44. There are 30 passengers seated and 13 standing 
 in a car, in which the conductor has collected $ 4.15 in 
 5^ fares. How many people have left the car? 
 
 45. An oblong field is 80 rods long and 25 rods wide. 
 How many rods of fence will it take to inclose it? 
 
 46. How many square yards are there in the floor of 
 a room 18 feet long and 15 feet wide? 
 
 47. In Ex. 46 find the perimeter of the room in yards; 
 in feet; in inches. 
 
 48. A newsboy buys Leaders at the rate of 5 for 3^, 
 and News at the rate of 7 for 10^. How much does he 
 gain on the sale of 65 Leaders at 1^ each, and 35 News 
 at 2^ each? 
 
 49. Find the perimeter in feet, and the area in square 
 inches, of an oblong 26 inches long and 18 inches 
 wide. 
 
 50. By selling a horse for $ 260, I lost $ 35. How 
 much should I have gained by selling it for $310? 
 
 51. A lady bought 4 pairs of kid gloves at $1.50 a 
 pair, 18J yd. of cambric at 15^ a yard, 8 yd. of muslin 
 at 12^^ a yard, and |- dozen linen napkins at $4 a 
 dozen. Find the cost of all. 
 
 52. The population of the United States increased 
 from 9,633,822 in 1820 to 84,907,156 in 1906. Find 
 the increase in this time. 
 
 53. A boy earns $ 1.25 each working day, and his ex- 
 penses are S 4.25 a week. Find his profits in 4 weeks. 
 
PART lY — FIFTH YEAR 
 FRACTIONS 
 
 Review Pages 107, 108, 147, 54, 55, 148 to 152, 119, 120, 156 to 160, 
 132 to 137, 163 to 170, and 172 to 182. 
 
 Fractional equivalents of halves, fourths, and eighths. 
 1 unit = |. 
 
 1 unit = |. 
 
 1 unit = |. 
 
 J^^^ 
 
 'V8\ 
 
 
 /'/6\ 
 
 ^^ 
 
 
 i = I = I 
 
 1. The first circle is divided? into how many equal parts ? 
 What is each part called ? 
 
 2. The second circle is divided into how many equal 
 parts? What is each part called ? 
 
 3. The third circle is divided into how many equal parts ? 
 What is each part called ? 
 
 4. \ of the first circle = | of the second circle. \ of the 
 first circle = | of the third circle. 
 
 5. How many halves of a circle are there in one circle ? 
 how many fourths of a circle ? how many eighths of a circle ? 
 
 6. Change \ to fourths ; thus, J = |. 
 
 7. Change \ to eighths ; J to eighths. 
 
 8. How many units are there in f ' I' f ^ 
 
 9. \ of the first circle 4- | of the first circle = how many 
 times the first circle ? Then l + l = how many ? 
 
 186 
 
FRACTIONS 187 
 
 10. J of the second circle + ^ of the second circle = what 
 part of the second circle ? Then -J + | = how many ? 
 
 11. I of the second circle + | of the second circle = how 
 many times the second circle ? Then | -f- 1 = how many ? 
 
 12. I of the third circle = | of the same circle. Then 
 
 4 _ ? _ ? 
 ^ - 2 - 1- 
 
 J-'i. :f — -J J 2 — "5 — 1* 
 
 14. Change | and | each to eighths. 
 
 15. I of an orange = | = |^ of the same orange. 
 
 16. VoMT boys each have $^. How many dollars have they ? 
 
 17. .i;i+ii = f|; ||+f^i=||; iday + l day = | day. 
 
 18. if + i J = 8 J ; $1 = how many dollars ? 
 
 19. I days = — days ; | days = 1 day and | days. 
 
 20. ij + IJ = it; ij + ^i- + i^ + ^| =*!• 
 
 21. Write in order of their size ^ of the first circle ; | of 
 the second circle, and | of the third circle. 
 
 A unit is any one thing. 
 
 A fraction is one or more of the equal parts of a unit. 
 
 22. Write in figures one half ; one fourth. How many 
 figures are needed to express a common fraction ? In the 
 fraction | what does the 4 show ? the 3 ? 
 
 23. ReadJ; J; |; |; f; f; ^. 
 
 24. Write seven eighths ; thirteen twenty-fourths. 
 
 The denominator of a fraction, which is written below the 
 line, shows into how many equal parts the unit is divided. 
 
 The numerator of a fraction, which is written above the 
 line, shows how many equal parts of the fraction are taken. 
 
 The terms of a fraction are the numerator and denominator. 
 
 Fractions are said to be equivalent when they have the 
 same value. Thus, ^, |, and | are equivalent fractions. 
 
188 
 
 FIFTH YEAR 
 
 Fractional equivalents of thirds, sixths, and ninths. 
 1 unit = |. 1 unit = |. 1 unit = |. 
 
 1. Into how many parts is the first circle divided ? the 
 second circle ? the third circle ? 
 
 1 of a circle = | of the circle = | of the circle. 
 
 I of a circle = J of the circle 
 
 of the circle. 
 
 |- of a circle = J of the circle = | of the circle. 
 
 1j_2_?. l4.3_?. Ir3_? 
 3^6~6> 3^9—9' 3^6 — 6* 
 
 6. J of an hour + J of an hour = | of an hour. 
 
 7. I of a day + | of a day = | of a day. 
 
 ®- 3 + 6~ '3 + 9~ >2+6~ '4 + 8=" * 
 
 9. Add| + l + i; I + I + I4-I + I + I; 1 + 1. 
 
 10. Draw an oblong and show that ^ of the oblong = f of 
 the oblong = f of the oblong. 
 
 11. Change to equivalent fractions in eighths : J, J, |, |. 
 
 no 1—1. 2.-1. 2_1.8_? 
 "^^- 3~6» 3"~6' 3~"9' ?~"8' 
 
 13. How many fourths of a pie = | of a pie ? 
 
 14. Draw squares and show that ^ = ^ ; that f = f ; that 
 J = f;that| = f. 
 
 15. How many halves equal one unit ? how many thirds ? 
 how many fourths ? how many sixths ? how many ninths ? 
 
 16. I = how many units ? ^= how many units ? | = how 
 many units ? | = how many units ? 
 
FRACTIONS 189 
 
 Fractional equivalents of the yard and the foot, and their 
 sum. 
 
 One foot. One yard. 
 
 1. A foot is what part of a yard ? 
 
 2. 2 feet are what part of a yard ? 
 
 3. Into how many parts is the yard divided ? 
 
 4. How many feet equal ^ of a yard? | of a yard? 
 I of a yard ? 
 
 I 5. Measure a yard on the blackboard. Divide the yard 
 into feet. Divide a foot into inches. 
 
 6. How many inches equal |^ of a foot? | of a foot? 
 I of a foot ? 11 feet ? 21 feet ? 
 
 7. 6 inches are what part of a foot ? of 2 feet ? of a yard ? 
 
 8. 4 inches are what part of a foot ? of 2 feet ? 
 
 9. llft. + ljft.= —ft. 
 
 11. 1 J ft. + 1 ft. = how many ft. ? 1| + J = — • 
 
 12. iyd. + iyd. +Jyd.= — yd. =— ft. 
 
 13. 21 ft. + 3| ft. = — ft. = — yd. 
 
 14. |ft. + ift.= —ft.; |ft.4-|ft.+|ft.= —ft. 
 
 15. I ft. = — ft. ; I ft. = — ft. ; f ft. = — ft. 
 
 Add: 
 
 16. 2f in. 17. 5| yd. 18. 
 
 H in. 81yd. 
 
 20. 3^ ft. 21. 7J yd. 22. 
 
 2f ft. 61 yd. 
 
 31 ft. 5J yd. 
 
 
 19. 2J ft. 
 
 8|ft. 
 
 2fft. 
 
 J ft. 
 
 23. lO^ft, 
 lof ft. 
 20^ ft. 
 
190 
 
 FIFTH YEAR 
 
 Fractional equivalents of fifths, tenths, and fifteenths, and 
 their sum and difference. 
 
 1 unit = |. 
 
 1 unit = 1^. 1 unit = if. 
 
 i 
 
 _2__ 
 
 10 
 
 1. Into how many parts is the first circle divided ? the 
 second circle ? the third circle ? 
 
 2. Observe the parts of each circle that are not shaded. 
 
 ■J 9 9 
 
 6 - 10 - T"^- 
 
 3. Then | = ^^^ = ^^^ ; f = iV = iV » I = iV = l^- 
 
 4. Each of five boys had ^ of a dollar. How many 
 dollars did they have ? 
 
 5. What is meant by J of a circle ? | of a circle ? | of a 
 circle ? -^^ of a circle ? -j^ of a circle ? 
 
 6. f of a circle + f of the same circle = | of the circle. 
 
 Then| + | = |; t-f = i;^-f = |. 
 
 7. How many parts of a unit are there in "1+ ^ + 3-? 
 in| + |?in32_ + _5^ + _.^Mn,3^ + ,^ + ^3_?in^8^-^;? 
 
 8. 4 + ^V=^V; i + TV=i%; i + i 
 
 15- 
 
 9. 1 + 1 = 1? Then ^ = how many units ? 
 
 10. I = how many units and f remaining ? 
 
 11. ^^ = how many units and | remaining ? 
 
 12. If = how many units and ^^ remaining ? 
 
 13. Change to units and parts of units : |, |, ^, -J-J-. 
 
If Add; 
 
 14. 12^ 
 
 M 
 
 18. 241 mi. 
 
 41| mi. 
 
 Subti'act : 
 
 H 
 
 2tV 
 
 I 
 
 22. 
 
 FRACTIONS 
 
 15. 25| mi. 
 
 19. 1231 
 3U 
 
 23. 25i hr. 
 
 16. 111^ 
 
 20. 50| 
 
 4| 
 
 24. il4f 
 
 191 
 
 17. 5^^ 
 
 4i 
 
 21. 24Jda. 
 
 3| da. 
 
 25. 78f min. 
 42^V min. 
 
 Fractional equivalents of halves, fourths, and sixteenths, 
 and their sum and difference. 
 
 1 unit = |. 
 
 1 unit = |. 
 
 1 unit = 1|. 
 
 B 
 
 
 ■ 
 
 
 ^ 
 
 I 
 
 T^ 
 
 1. How do these three units compare in size ? 
 
 2. Into how many parts is the first square divided ? the 
 second square ? the third square ? 
 
 3. I of the first square = — fourths of the second square 
 = — sixteenths of the third square. 
 
 14. I = — units ; | = — units ; | = — units ; |f= — units* 
 5. 2=i=i =16' 
 
 6- i=l 
 
 16 ' 
 
 Iff- 
 
)2 
 
 
 FIFTH YEAR 
 
 
 
 ■>■ 1=1 = 
 8- f=TV = 
 9. i+i + 
 
 16 5 
 
 _ ? . 
 
 - 1' 
 
 4 = 
 
 O 9 9 
 
 4 ? ? . 6 
 
 5-16-2' I 
 
 A 
 
 tV = f 
 
 = \& > i°5 - i = 
 
 _ 1 
 
 
 Add: 
 
 
 
 
 
 
 
 10. SJft. 
 61ft. 
 2Jft. 
 3|ft. 
 
 
 11. 16J ft. 
 
 20J ft. 
 17J ft. 
 10^ ft. 
 
 
 12. 12{ 
 
 10| 
 12J 
 
 13. 
 
 10| 
 
 6| 
 8^ 
 
 Subtract : 
 
 
 
 
 
 
 
 14. «12J 
 8i 
 
 
 15. 28| yd. 
 
 ISjL yd. 
 
 
 16. 18| mi. 
 9^2^ mi. 
 
 17. 
 
 68| 
 
 18. A flower bed is 4 ft. 6 in. long and 3 ft. 4 in. wide. 
 Find the distance around it. 
 
 19. The school ground is in the form of a square, 13 J rd. 
 on a side. Find the distance in rods around it. 
 
 Fractional equivalents of sixths, twelfths, and eighteenths, 
 and their sum and difference. 
 
 
 
 
 1 unit = 
 
 = l = ii 
 
 = \ 
 
 !• 
 
 
 '/3 
 
 '/l2 
 
 '/l2 
 
 '/,2 
 
 'Az 
 
 Via 
 
 '/,8 
 
 Vm 
 
 '/la 
 
 'Aa 
 
 'Aa 
 
 yi2=y3 
 
 ^/,a=y3 
 
 1. Into how many thirds can the oblong be divided? 
 into how many twelfths? into how many eighteenths? 
 

 I 
 
 FRACTIONS 198 
 
 9 1 — JL — _? • 2 _ _?_ _ _? 
 ^- 3 — 12 "~ 1^' 3 "~ 12 ■" 1^- 
 
 3. I of a day = how many 9ths of a day? how many 
 8ths of a day ? 
 
 4. 1 hour = ^2 of an hour ; = -^^ of an hour. 
 
 5. Change to 18ths : J, |, |. 
 
 6. Change to 16ths : J, |, f . 
 
 7. I = how many units? ^^- = how many units? 
 
 8. Change to 3ds : ■{-^, f , ||, f . 
 
 9. Draw oblongs and show that J = | ; | = J ; i^g = J 5 
 
 il = f; ^\^i- 
 
 
 
 
 10. 1| = how 
 
 many units? 
 
 2 _ ^Q^ man^ 
 
 ^ units and ^^^ 
 
 remaining? 
 
 
 
 
 11. Change to units and parts of units : |, 
 
 |. \h if. If 
 
 I. ¥. ¥' ii 
 
 Add: 
 
 
 
 
 12. 29J 
 
 32i 
 
 45A 
 
 13. 7tV 
 
 lOf 
 
 25J 
 
 14. 39| 
 
 42A 
 28i^ 
 
 15. 5| 
 
 12^ 
 
 16. 27| ft. 
 
 17. 16^ mi. 
 
 18. U\ bu. 
 
 19. 12J da. 
 
 45| ft. 
 25,% ft. 
 
 29^ mi. 
 31J mi. 
 
 19^ bu. 
 16| bu. 
 
 10^ da. 
 18,^ da. 
 
 Subtract : 
 
 
 20. ^ 
 
 1 ^ 
 
 21. 17| 
 
 22. 14| 
 
 12tV 
 
 23. 32^ 
 
 30J 
 
 24. 7| in. 
 
 2S. 9f bu. 
 
 26. lOJ lb. 
 
 27. 15|J da. 
 
 6,^ in. 
 
 1^ bu. 
 
 6,^ lb. 
 
 5| da. 
 
194 
 
 FIFTH YEAR 
 
 Fractional equivalents of sixths, twelfths, and twenty- 
 fourths, and their sum and difference. 
 
 1 unit = Jl 
 
 i2 
 '12 
 
 24 
 
 '/6 
 
 
 '/6 
 
 
 'A2 
 
 7/2 
 
 
 //2 
 
 'Az 
 
 ^As^/e 
 
 •/24 
 
 y24. 
 
 y^A. . 
 
 ^4 
 
 
 y24. 
 
 y24. 
 
 ^4 
 
 y24. 
 
 Y4*=y6 
 
 1. What part of the oblong = f of it ? ^^ of it ? if of it ? 
 
 2. J of the oblong = y^ of the oblong; equals ^-^ of it. 
 
 3. ^ of the oblong = | of the oblong ; equals -j^ of it. 
 
 4. 1+1 + 1 + 1=6' equals how many units ? 
 
 5. Any unit can be divided into how many halves? 3ds? 
 4ths? 5ths? 6ths? 7ths? 8ths? 16ths? 24ths, etc.? 
 
 6. Add I and -^^ ; -^^ and ^^. From f^ take ^V* 
 
 7. From If subtract J ; t^ ; f ; i^. 
 
 8. I means that a unit (|) and a part of a unit (|) have 
 been added. What does | mean ? § ? 
 
 Add: 
 
 10. 154 bu. 11. 
 
 9. 181- in. 
 20^V in- 
 
 39^1 
 
 m. 
 
 27 J^ bu. 
 4ll j bu. 
 
 Subtract : 
 13. 91 yd. 
 
 14. 
 
 14* 
 
 da. 
 
 19J 
 
 20^ 
 
 IS. 28^2 
 
 12. 40^5 
 30,V 
 18* 
 
 16. 39f 
 
 lis. 
 
FRACTIONS 195 
 
 REDUCTION OF FRACTIONS 
 
 1. Notice in the diagram on p. 30 that J = ^^. By what 
 number are both numerator and denominator of -J- multiplied 
 to change it to -^^ ? Is there any difference in value between 
 i- and -^-^ ? Notice that the terms in ^-^ are larger or higher 
 than in J. The change of J to the equal fraction ^^ is 
 
 Ifcalled changing or reducing J to higher terms. 
 
 2. By what number must both terms of i^^ be divided to 
 change g*^ to i ^ Is there any difference in value between 
 2*^ and i ? Which fraction has the lower terms ? The 
 change of ^^ to \ is called reducing -^^ to lower terms. 
 
 3. Notice in the diagram that /^ = t2 = 6 • When ^^ is 
 changed to ^2_ it is reduced to lower terras but not to its 
 lowest terms, since -^ can be changed to still lower terms, J. 
 Can 1 be reduced to still lower terms ? The change of -^^ 
 to J is called reducing -^-^ to its lowest terms. 
 
 4. By what number must both terms of |- be multiplied 
 to change it to the equal fraction J? By what number 
 must both terms oi'^-Q be divided to change it to the equal 
 fraction |? Is | in its lowest terms ? 
 
 Multiplying or dividing both terms of a fraction by the same 
 number does not alter its value, 
 
 5. Reduce to higher terms : | ; | ; | ; f ; | ; | ; f ; yo • 
 
 6. Reduce to lowest terms : | ; | ; | ; -f ; ^^ '■> -f^. 
 Fractions like -J, |, and |, which have the same denomina- 
 tor, are said to have a common denominator. 
 
 Similar fractions are fractions tliat have a common denom- 
 inator. 
 
 7. Change to similar fractions ^ and | ; ^ and J ; ^ and -^^ ; 
 |, j, and |. 
 
196 FIFTH YEAR 
 
 Written Work 
 
 1. Change f and | to similar fractions having the common 
 denominator 12. 
 
 Since the denominator 3 in | must be multiplied by 4 
 2x4 8 to produce 12, the numerator must also be multiplied by 
 
 o X 4 lZ 4, so as not to change the value of the fraction. ^ a.= 19' 
 
 3x3 9 Cilice the denominator 4 in | must be multiplied by 3 to 
 
 A v^ Q ~ To produce 12, the numerator 3 must also be multiplied by 3. 
 
 3x3 9 
 
 - o = 7^- Hence the similar fractions are A and A. 
 
 4 X 3 12 12 T^ 
 
 Change to similar fractions : 
 
 2. J and I 4. I and | 6. l |, and | 8. J, |, and -^-^ 
 
 3. I and I 5. I and \ 7. |, J, and f 9. f , f, and ^^ 
 
 10. Reduce ^^ to its lowest terms. 
 
 g_j_Q 9 2 — 2 1 ^^ ^^^ divide both terms, 6 and 24, of the 
 
 ^TT ^ Q = Q» o . 9^^T fraction /j by 3 without changing the value 
 *^ * ' *^ of the fraction. The result is f. We can 
 
 then divide both terms 2 and 8 of the fraction 2 by 2. The result is \. 
 
 Reduce to lowest terms : 
 
 11. i^ 13. If 15. If 17. If 19. 1| 
 
 12. -/^ 14. ^% 16. 1^ 18. If 20. if 
 
 21. Change |^ to units. Thus, 1 unit = 2 halves. In 
 4 halves there are 4 -^ 2, or 2, units. Change IgO- to units. 
 
 22. Change ^- to units and parts of units. Thus, 1 = 3 
 thirds. In 10 thirds there are 10 -^ 3, or 3, units and J re- 
 maining; that is, 3 J. 
 
 To cJiange a fraction to units and parts of units ^ divide the 
 numerator hy the denominator. 
 
 Change to units and parts of units : 
 
 23. Y 24. -I32. 25. Jg^- 26. ^^- 27. J^ 
 
FRACTIONS 197 
 
 ADDITION OF FRACTIONS 
 
 1. Can you add J and J without change ? Can you add 
 fj and ^ ? What change must be made in J and J before they 
 5an be added ? 
 
 2- ^ — TO' 5 — TXT' f — 1X>» 5—10- 
 
 o 1_ ? . Ill— ? . 111 — ?. l_l_l_?? 
 
 4. Can you add \ and J without change? Change both 
 [to tenths. Can they then be added ? 
 
 5. Can you add \ and \ without change ? Change both 
 to sixths. Can they then be added ? 
 
 6. When I and \ are to be added, to what similar fractions 
 
 •should they be changed ? 
 
 7. What are the denominators of the fractions in exam- 
 ple 4? To what like or common denominators (c. d.) did 
 you change both fractions ? 
 
 8. What are the denominators of the fractions in example 
 5 ? To what denominator did you change the fraction |^ ? J ? 
 Why? 
 
 9. After two or more fractions are changed to like, or 
 common denominators^ that is, after they have been made 
 similar^ what is the second step in adding them f 
 
 in Afhliii- 11- 1 ^- 11 1- 11 1 
 J.U. ^(lUg^g, g, :j, ^, 5' TfT' 3'¥'T2> 3' ^' T^* 
 
 11. Observe that in problem 10, |^+ J4- i = |, or 1, and 
 thatJ+i+iV = A'Orf. 
 
 12. What is the third step in adding fractions ? 
 Why is the first step not necessary in the following? 
 
 13- l + J 
 
 "■ i + f 
 
 17. 
 
 J + f + f + 1 
 
 "• 4 + f 
 
 16. f + ^ 
 
 18. 
 
 tV + tV + A + -i% 
 
198 FIFTH YEAR 
 
 Give the sums at sight : 
 19. i + i + i 28. Jj + ^+^j + ^ 
 
 20- i + i+i 29. ^2_ + _3^4._5^+^^ 
 
 21. 
 
 i + i + i 
 
 
 30. 
 
 ^+A+A+A 
 
 22. 
 
 l + i + i 
 
 
 31. 
 
 tV + t'6 + i\ + t\ 
 
 23. 
 
 i+l+i+l 
 
 
 32. 
 
 2V+2V+2'o + 2V 
 
 24. 
 
 Hf + f + f 
 
 
 33. 
 
 A + A+iV+A 
 
 25. 
 
 tV + t% + ^ + 
 
 A 
 
 34. 
 
 2^5+A + A+2V 
 
 26. 
 
 iV+iV + A 
 
 
 35. 
 
 tV + l\ + 1 V + tV 
 
 27. 
 
 Hf+f+l 
 
 
 36. 
 
 t\ + tV + tV + ^ 
 
 37. A boy spent | of his money for a knife, ^ of it for a 
 ball, and ^ of it for his lunch. What part of his money 
 did he spend ? 
 
 38. After cutting off |^ of a foot and | of a foot from a 
 bgard, the part remaining was | of a foot long. How long 
 was the whole board ? 
 
 39. I paid |Jq for milk, f^2_ f^^ lettuce, andi^3_ for but- 
 ter. What part of a dollar did I pay for all ? 
 
 40. David paid f of a dollar for a fishing rod, and ^ of a 
 dollar for a line. How much did he pay for both ? 
 
 Adding fractions that are not similar. 
 
 Written Work 
 
 The fractions must first be made simi- 
 lar. They may be changed to the com- 
 mon denominator twelfths. Multiplying 
 both terms of | by 4 changes it to ^%, and 
 multiplying both terms of ^ by 3 changes 
 it to jV The sum of ^V and j\ is ^^. 
 
 Fractions must he made similar before they can he added. 
 
 1. 
 
 Addf 
 
 and ^. 
 
 
 12 = c, 
 
 . d. 
 
 
 2x4 
 
 8 
 
 
 3x4" 
 
 12 
 
 
 1x3 
 
 4x8" 
 
 3 
 12 
 
FRACTIONS 199 
 
 Add, using a pencil; then orally: 
 
 2. J and J 8. J and 1 14. J and J 
 
 3. I and ^ 9. I and | 15. ^ and 1 
 
 4. J and J 10. I and ^ 16. ^ and J^ 
 
 5. J and ^ 11. ^ and ^ 17. | and ^ 
 
 6. J and ^ 12. |^ and ^ 18. J and i 
 
 7. I and -J- 13. J and ^ 19. J and J^ 
 
 20. Henry had J of a dollar, and found | of a dollar. 
 How much had he then? 
 
 21. Mary bought ^ of a yard of red ribbon, | of a yard of 
 blue ribbon, and J of a yard of white ribbon. How many 
 yards of ribbon did she buy ? 
 
 22. What is the total cost of a ball at | of a dollar, a pen- 
 knife at ^ of a dollar, and a book at |^ of a dollar ? 
 
 A mixed number is a number expressed by a whole num- 
 ber and a fraction ; as, 5J, 3J, 11^. 
 
 Adding mixed numbers when the sum of the fractions is less 
 than a whole unit. 
 
 Written Work 
 1. Add 2^ and 3i. 
 
 12 = c. d. ^ and ^ may each be changed to twelfths. Write 
 
 21 _ 2-4- the common denomiuator (c. d.), 12, above the frac- 
 
 3 "^12 1x4 41x3 3 
 
 H = ^1% *io^s- 3x4^12' 4x3^ l2* The sum of the frac- 
 
 3 "T" 4 12 tions is 3^2 and the sum of the integers is 5 ; 5 + ^'^^ = ^i^* 
 
 Add: 
 
 2. 5J 3. 121 
 
 6i 14J 
 
 H 
 
 5. 35J 
 
 201 
 
 60J 
 
 8iV 
 
 422V 
 
200 
 Add 
 
 6. 
 
 10. 
 
 
 FIFTH : 
 
 iEAR 
 
 
 18tV 
 
 7. 20J 
 
 24i 
 
 28iV 
 
 8. IIH 
 
 i 
 
 9. 20^ 
 
 145,V 
 230J 
 
 lOOJ 
 
 80iV 
 205^ 
 
 11. 351 
 
 H 
 
 12. 12J 
 
 13. 128| 
 34 
 
 14. A man walked 3^ miles one hour, 3J miles the second 
 hour, and 2J miles the third hour. How far did he walk ? 
 
 15. A farmer sold corn for $ 14^, wheat for $ 37^, and rye 
 for $ 15^^Q. How much did he receive for all ? 
 
 Adding mixed numbers when the sum of the fractions is 
 greater than a whole unit. 
 
 
 
 Written Work 
 
 
 
 1. Add 8f and 12f . 
 
 
 
 15 = 
 
 12f = 
 
 c. d. 
 1%^ 
 
 f and 1 may each be cha 
 2x5_10. 3x3_ 9 
 3x5 15' 5x3 15* 
 T»5 is ^f, which equals l^^s 
 to the sum of 12 and 8, 
 with rV makes 21x*5. 
 
 mged to fifteenths. 
 The sum of {^ and 
 . The 1 is added 
 
 8f + 12| = 
 
 20l| or 
 21tV 
 
 making 21, which 
 
 Add: 
 
 
 
 
 
 2. 7| 
 
 3. 
 
 150f 4. 
 
 m 
 
 5. 321 
 
 !i 
 
 
 68f 
 
 18f 
 
 60^^, 
 
 6. 175^ 
 161 
 
 7. 
 
 350,:^ 8. 
 
 267| 
 
 419| 
 
 22J 
 
 9. 17| 
 
 ^ 
 
FRACTIONS 
 
 201 
 
 Add: 
 fio. 80J 
 
 181 
 42f 
 
 12A 
 
 11. 
 
 17| 
 71| 
 
 12. 20| 
 
 120| 
 
 268H 
 
 13. 
 
 1351 
 
 122t^ 
 
 118,V 
 
 14. Mary bought a reader for f of a dollar, a slate for -^ 
 of a dollar, and a grammar for J of a dollar. How much 
 did they all cost ? 
 
 15. A clerk spent $18 J a month for board, i9| for a 
 room, and 14^ for clothes. How much did he spend in one 
 month ? 
 
 16. I sold J of an acre of land to one man, 2^ acres to an- 
 other, and If acres to another. How many acres did I sell ? 
 
 17. Find the perimeter of a sheet of paper 9J in. by 5J in. 
 
 SUBTRACTION OF FRACTIONS 
 
 
 'A 
 
 ■ 
 
 
 fi 
 
 B 
 
 i 
 
 1. 1 sq. in. — 1 sq. in = — sq. in. 
 
 2. 1 sq. in. — ^ sq. in. = — sq. in. 
 
 3. 1 sq. in. — :| sq. in = — sq. in. 
 
 4. I sq. in. — j4g sq. in. = — sq. in. 
 
 5. ^ sq. in. — -^q sq. in. = — sq. in. 
 
 6. |-i = i; f- 
 
 H ' 10 
 
 io — ilF* 
 
202 FIFTH YEAR 
 
 7. Give answers to the following: y| — 1^2^ ii— i\; 
 t\ ~ 1*1 ' 2 ~ 10 » 2 & "" 2 5- 
 
 8. What do you notice about the denominators of the 
 fractions you have subtracted in example 7 ? 
 
 In subtraction of fractions, just as in subtraction of whole 
 numbers, the minuend must be larger than the subtrahend. 
 
 9. When the denominators are alike, what do we sub- 
 tract ? 
 
 10. Could you subtract \ from J without change ? How 
 may these fractions be made similar ? 
 
 11. When the denominators are unlike^ what is the first 
 step 9 What is the second step P What is the third step ? 
 
 Subtract: 
 
 12. fj-*i; I ft. -J ft.; I yd. -I yd.; ^ift.-|ft. 
 
 13- ^-|; M-f; \\-h \-h ll-h \-\- 
 
 Subtracting similar mixed numbers. 
 Written Work 
 
 Since | cannot be subtracted from ^, 
 we take 1 or | from 3, and add it to ^, 
 thus changing 3^ to 2f . Tlien \ from 
 I leaves | and 1 from 2 leaves 1. Hence, 
 the answer is If. 
 
 7. SS^-aj- 5^ 
 
 8. 17if-1.3,\ 
 
 9. \\\ - 9f 
 
 10. 7f - 2| 
 
 11. 18f - 9f 
 
 1. 
 
 From %\ 
 
 ; take If. 
 
 ^- 
 
 ■1| = 1* 
 
 
 Find the differences : 
 
 2. 
 
 ^ - 
 
 H 
 
 3. 
 
 H - 
 
 ^ 
 
 4. 
 
 Hh- 
 
 61% 
 
 S. 
 
 20H-i^H 
 
 6. 
 
 I6M-II2V 
 
I 
 
 FKACTIONS 203 
 
 I 
 
 12. If a boy buys papers at f of a cent each, and sells 
 them at 1 cent each, how much does he gain on each paper ? 
 
 13. I bought a bushel of potatoes for -^q of a dollar, and a 
 bushel of corn for -f^ of a dollar. How much more did I pay 
 for the potatoes than for the corn ? 
 
 14. William bought a hat for $2|, and a pair of shoes for 
 ^2^. How much more did he pay for the hat than for the 
 shoes ? 
 
 15. From a piece of ribbon 16^7^ inches long was cut a piece 
 J inches long. What was the length of the piece remaining ? 
 
 16. One farmer owns 124^^1 acres of land, and another 
 owns llli% acres. How many more acres does the one 
 farmer own than the other? 
 
 Subtracting fractions or mixed numbers that are not similar. 
 Written Work 
 
 1. From I take |. Before they can be subtracted the fractions 
 
 20 = c. d. must be made similar. Change them both to 
 
 1 _ 1 twentieths, i = ^ and ^ = ^. Subtracting, 
 
 Fractions must be made similar before they can be subtracted. 
 Subtract, using a pencil ; then orally: 
 
 I 
 
 2- i-i 
 
 9- i-i 
 
 16. J-t1j 
 
 3- \-\ 
 
 10. I-} 
 
 17. i-i 
 
 4- i-i 
 
 "• \-\ 
 
 "• \-\ 
 
 5- J-i 
 
 12- i-i 
 
 19. \-i 
 
 «• \-\ 
 
 13. \-\ 
 
 20. I-tV 
 
 ->■ i-T^ 
 
 "• i-i 
 
 21. \-\ 
 
 «• i-i 
 
 "• i-^ 
 
 22. t-J 
 
204 FIFTH YEAR 
 
 23. From a piece of cloth containing J of a yard, ^ of a 
 yard was sold. What part of a yard remained ? 
 
 24. From a city lot containing | of an acre, -^^ of an acre 
 was sold. What part of an acre remained ? 
 
 25. A man traveled ^ of a certain distance the first hour, 
 and I of the distance the second hour. What part of the 
 distance farther did he travel the first hour than the second? 
 
 26. From 7 take |. 
 
 7 = 6| Change 7 into 6f . Subtracting | from 
 
 1—2. I gives I, which added to 6 gives 6^. 
 
 Subtract, using a pencil; then orally: 
 
 27. 3-1 34. 22-1^ 
 
 28. 12-2 35. 7_J 
 
 29. 18 -J 36. 28 -ij 
 
 30. 9-| 37. 55 -if 
 
 31. 3-f 38. 4- If 
 
 32. 100 -^9^ 39- 125 -J^ 
 
 33. 18 --If 40. 10- I 
 
 48. Albert had $2 and spent $|- for skates, 
 money had he remaining ? 
 
 49. A vessel contained 8 gallons of oil. After |^ of a gal- 
 lon had leaked out, how much remained ? 
 
 50. A grocer who had bought 10 bushels of potatoes, sold 
 I of a bushel. How many bushels remained ? 
 
 51. From 12| take 10 J. 
 
 4 = c. d. Change I to fourths, i = |. 
 
 12| = 12# I ^''""^ f = i which added to 12 
 
 101 =102 less 10, or 2, gives 2^. 
 
 12|-10i= 2i 
 
 41. 
 
 133- 
 
 -1 
 
 42. 
 
 44- 
 
 -A 
 
 43. 
 
 11- 
 
 -f 
 
 44. 
 
 40- 
 
 -f 
 
 45. 
 
 7- 
 
 -i\ 
 
 46. 
 
 51- 
 
 -iV 
 
 47. 
 
 48- 
 
 -i 
 
 . How much 
 
I 
 
 FRACTIONS 205 
 
 Find differences: 
 
 52. 4f - 3J 62. 80| - 14J 
 
 53. 7| - 41 63. 98f - 321 
 
 54. lOf - 31 64. 45|f- 30f 
 
 55. 101 _ 2f 65. 25| - 12} 
 
 56. 12^ - 5f 66. 1001 _ 521 
 
 57. 24f,-llf 67. 78| - 35f 
 
 58. 3111 -18f 68. 50|- - 40J 
 
 59. 79i|_26| 69. 1243-\-112i 
 
 60. 9Ti{-35f 70. 24011-2001 
 
 61. 121f -66f 71. 15|- - 8i 
 
 72. From a lot containing 17| acres, 5| acres were sold. 
 How many acres remained? 
 
 73. One motorman's trip takes 4| hours, and another's 2| 
 hours. How much longer is the first motorman's trip than 
 the second motorman's trip ? 
 
 74. A man bought two suits of clothes, one costing $35| 
 and the other i28J. How much more did the one suit cost 
 than the other ? 
 
 75. James lives 1^ miles from the schoolhouse, and Sam- 
 uel If miles away. How much farther does Samuel have to 
 walk to school than James ? 
 
 REVIEW 
 
 1. A newsboy earned If one day, $-^ another day, and 
 $1 a third day. How much did he earn in the 3 days ? 
 
 2. A stick was broken into two pieces — one 3| ft. long 
 and the other 1| ft. long. How long was the whole stick ? 
 
 I 3. If a man earns 1 3| a day, and a boy S| a day, how 
 much more does the man earn in a day than the boy ? 
 
206 FIFTH YEAR 
 
 4. What will be the total cost of 1 sack of flour $1|, 
 sugar i^, dried beef 1^^^, and corned beef |i? 
 
 5. A boy is 4 ft. 5 in. tall. His sister is 3 ft. 5 in. tall. 
 How much taller is the boy than his sister ? 
 
 6. The top of a door is 12|- feet above the ground, and 
 the bottom of it is 4| feet above the ground. How high is 
 the door? 
 
 7. Four loads of coal weighed as follows: 2 tons, 1| tons, 
 2 J tons, and 2J tons. How much did the four loads weigh ? 
 
 8. The rainfall in April was 4 Jq inches, in May 3| inches, 
 and in June 4^ inches. What was the total rainfall for the 
 three months ? 
 
 9. From a barrel containing 51J gallons of oil, 17|^ gallons 
 were sold in one day, and 25J gallons another day. How 
 many gallons remained unsold ? 
 
 10. A station agent who was paid 860 per month spent 
 in one month il2| for groceries, $7j^ for meat, and |15| 
 for other expenses. How much did he save ? 
 
 11. A farmer drives in one day 12| miles, then 6J miles, 
 and then 9J miles. How far does he drive ? 
 
 12. To the sum of 22|^ and 15J add their difference. 
 
 13. From 38/^ take the sum of 16 J and 12i^. 
 
 14. The feed for a horse cost 85| per month; for a cow, 
 $4:^ per month. If a man has 2 horses and 2 cows, how 
 much will it cost to feed them a month ? 
 
 15. A boy walked from his home east along a certain road 
 IJ miles. He then walked to a place 2^ miles west of his 
 home. How far had he walked when he got home ? 
 
 16. A man purchased a chair for -f 4^, a stove for $6 J, a 
 table for i8J, and a bookcase for $12.00. How much did 
 they cost ? 
 
FRACTIONS 
 
 20T 
 
 17. When a grocer receives a $10 bill in payment for sugar 
 
 $|, vegetables f 1^^, fruits l|, rice I J, and cakes $1^, how 
 much change does he give ? 
 
 18. A student in the city in one month paid 1 4^^ for car 
 fare, 1 18 J for board, i7| for room, $2| for laundry, and $61 
 for books. How much did his expenses amount to during 
 that month ? 
 
 19. During the same month he earned $30 by tutoring, 
 $18 J by selling books, and $12| by chemical work. How 
 much did he have left after paying expenses ? 
 
 20. In 3 days in June the sun shone in New York Ill- 
 hours, 14^ hours, and 14l| hours. How many hours of 
 sunshine were there in these 3 days ? How many hours 
 without sunshine were there? 
 
 MULTIPLICATION OF FRACTIONS 
 Multiplying a fraction by a whole number. 
 
 IT 
 
 IL 
 
 H 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 8. 
 
 3 feet - I yard 
 
 Into how many halves is the square divided ? 
 
 Two times |- the square = square. 
 
 Two times $J=- 
 Four times $J=- 
 Five times $J = - 
 
 dollar. 
 - dollars. 
 • dollars. 
 
 Into how many feet is the yard divided ? 
 What is one of these parts called ? 
 What are two parts called ? 
 
208 FIFTH YEAR 
 
 9. 2 X J of a yard = yard. 
 
 10. 6 X J of a yard = yards. 
 
 11. 6 X 1^ of a circle = circles. 
 
 12. 12 X J of a circle = circles. 
 
 13. 4 X J is the same as |^ + ^ + |^ + J. 
 
 14. 6 X I = |, or 3. Therefore to multiply ^ by 6, we say 
 six times | = |, or 3. 
 
 Give products: 
 
 15. 8 X J 20. 9 X f 25. 7 X f 30. 3 X ^^^ 
 
 16. 12 X J 21. 8 X f 26. 12 X f 31. 12 X I 
 
 17. 6 X I 22. 9 X -^Q 27. 4 X -^^ 32. 5 X | 
 
 18. 7 X I 23. 6 X I 28. 8 X f 33. 6 X f 
 
 19. 10 X I 24. 8 X f 29. 11 X J 34. 6 X | 
 
 Finding fractional parts of whole numbers. 
 
 1. ^ of 1 unit = unit. 
 
 2. J of 2 units = unit. 
 
 3. J of 12 = dollar. 
 
 We have learned that we may divide a unit into any num- 
 ber of parts and then take any number of these parts; thus, 
 I of $60 means that $60 (60 units) is divided into 4 equal 
 [>arts of $15 each and that 3 of these parts, or 845, are taken. 
 
 
 Since!- of $60 = $15, 
 
 1 of $60=3 X $15, or $45. 
 
 
 
 Find the following: 
 
 
 4. 
 
 f of $24 
 
 8. 1 of 36 minutes 12. 
 
 J of 72 cents 
 
 5. 
 
 j\ of 60 horses 
 
 9. 11 of $144 13. 
 
 ^\ of 99 
 
 €. 
 
 1 of 36 days 
 
 10. -f^ of 78 miles 14. 
 
 T% of 75 
 
 7. 
 
 1 of 20 hours 
 
 11. -fj of 44 rods 15. 
 
 f of 84 
 
FRACTIONS 20& 
 
 16. If I wish to find J of 4, into how many parts do I 
 divide 4? How do I find one of these parts? Divide 
 4 by 3. 
 
 17. Explain what you mean by ^ of a number ; by | of 
 a number ; by | of a number. 
 
 18. Find I of 4. 
 
 Solution. — i of 4 = f , and f of 4 = 2 x |, or | = 2f 
 
 Find the following : 
 
 19. 
 
 |of7 
 
 25. 
 
 T% of 12 
 
 31. 
 
 f of 20 
 
 20. 
 
 |of9 
 
 26. 
 
 11 of 8 
 
 32. 
 
 f of 6 
 
 21. 
 
 |ofl2 
 
 27. 
 
 i\of8 
 
 33. 
 
 iof9 
 
 22. 
 
 |of8 
 
 28. 
 
 |of9 
 
 34. 
 
 f of 11 
 
 23. 
 
 f of 10 
 
 29. 
 
 3- of 12 
 
 35. 
 
 loflO 
 
 24. 
 
 |of3 
 
 30. 
 
 fof7 
 
 36. 
 
 t of 12 
 
 37. Multiply I by 8. Which number is the multiplier? 
 Which number is the multiplicand? Observe that | of 8 
 gives the same result. 
 
 We find a fractional part of a number by partition. 
 
 If the sign of multiplication is written after a fractional 
 multiplier, it may be read "of." Thus, | X 12 may be 
 read "f of 12." 
 
 Read the following problems : 
 
 38. I X 9 39. I X 6 40. I X 4 41. f X 6 
 
 Written Work 
 
 1. A merchant owing $1200 gave his check for | of the 
 amount. For how much did he write his check ? 
 
 2. Three men own 2500 acres of land. The first owns | of 
 it, the second | of the remainder, and the third the remainder. 
 How many acres does each own ? 
 
210 FIFTH YEAR 
 
 3. If a laborer works ^ of the days in a common year, how 
 many days does he work ? 
 
 4. A student's expenses at college are $480 per year. If 
 board and tuition cost | of that amount, how much is spent 
 for room rent, books, etc. ? 
 
 5. A contractor agrees to erect a building for $24,570. 
 Labor costs J of the amount, material J of the remainder. 
 Find his profit. 
 
 6. I of the entire enrollment of 14,720 in school are girls. 
 Find the number of girls and the number of boys. 
 
 7. -^Q of I960 is paid in a year for rent. Find the monthly 
 rent bill. 
 
 8. An automobile cost $3456 and the expenses and repairs 
 for one year were -^q of the cost. Find the expenses. 
 
 9. A western farmer bought a farm of 160 acres at $25 
 an acre. He erected a house costing -^^ as much as the 
 land, and a barn costing ^ as much as the house. Find the 
 total cost of the property. 
 
 Finding a number when a fractional part of it is given. 
 
 1. f of a flock of sheep are 40. Find the number in the 
 flock. 
 
 Solution. — Since two thirds of the flock equal 40 sheep, one third of 
 the flock equals I of 40 sheep, or 20 sheep, and three thirds, or the flock, 
 equal 3 x 20 sheep, or 60 sheep. 
 
 Find the number when : 
 
 2. I of a number = 12 7. |^ of a number = 12 
 
 3. I of a number =9 8. ^j of a number = 36 
 
 4. ^ of a number = 15 9. ^| of a number = 60 
 
 5. I of a number = 21 10. |^ of a number = 45 
 •6. f of a number = 18 11. -f^ of a number = 54 
 
FRACTIONS 211 
 
 Written Work 
 
 1. There are 18 girls in a school. This number is | of all 
 the pupils in the school. How many pupils are there in the 
 school ? 
 
 2. James deposited 818 in a savings bank, which was | of 
 wliat he earned during the month. How much did he earn 
 in the month ? 
 
 3. May spelled correctly 27 words, which were ^^^ of all 
 the words given. How many words were given ? 
 
 4. A farmer sold 42 lambs, which were |- of his flock. 
 How many lambs had he at first ? 
 
 5. John has attended school 40 days, which are | of the 
 number of days in the term. Find the number of days in 
 the term. 
 
 6. Mr. Tanner pays $30 each quarter for his telephone* 
 At the same rate, how much does he pay in a year ? 
 
 7. i500 is I of a teacher's salary. Find her salary. 
 
 5 of the six parts of her salary = $500. 
 
 1 part = 1 of $500, or $100. 
 6 parts, or her salary = 6 x $100 = $600. 
 
 8. Mr. Arnold bought a horse and a cow. He paid 850' 
 for the cow, which was ^ of what the horse cost. How much 
 did they both cost? 
 
 9. A traveling salesman drove 18 miles one day. This, 
 was ^ as far as he rode on a train. How far did he ride on 
 the train ? 
 
 10. The cost of a barn was | as much as the cost of a 
 house. If the barn cost 8920, how much did they both 
 cost ? 
 
212 FIFTH YEAR 
 
 11. The distance from New York to Harrisburg, Pa., ia 
 195 miles. This is J| of the distance from New York to 
 Pittsburg. What is the latter distance ? 
 
 12. A steel rail is 30 feet long. This is -^^ of the length 
 of a Pullman car. What is the length of a Pullman ? 
 
 Multiplying a mixed number by an integer. 
 
 Analyze these problems : 
 
 1. Find the cost of 6 eggs at 3J cents a piece. 
 
 2. Find the cost of 4 qt. of oil at 4| cents per qt. 
 
 3. How much will 8 lb. of rice cost at 6J cents per lb. ? 
 
 4. Find the cost of 12 lb. of sugar at 6J cents per lb. 
 
 5. When berries are sold for 8|- cents per basket, find 
 the cost of 6 baskets. 
 
 6. A man earns $lf per day. How much does he earn 
 in 6 days? 
 
 7. When apples are sold for $1| per bushel, find the cost 
 of 8 bushels. 
 
 8. Mary pays 8| for music lessons and takes two lessons 
 per week. How much do her music lessons cost her in 4 
 weeks ? 
 
 9. John makes f of a cent on each paper and averages 
 40 papers each day for six days. Find his profit. 
 
 10. We pay 7J^ per qt. for milk. How much is our milk 
 bill in 4 weeks, if we use 2 qt. per day ? 
 
 Suggestion. — Find the bill for each day ; then for each week ; and 
 then for the number of weeks. 
 
 11. By buying 25 cents worth of street car tickets, each 
 ticket costs me 4J cents. Find the cost of 12 tickets. 
 
FRACTIONS 213 
 
 12. A storekeeper makes IJ cents on each can of corn. 
 How much does he make on 18 cans ? 
 
 13. John works for 5 J cents per hour. If he works 3 
 hours a day, how much does he earn m 2 days ? 
 
 14. Mary uses 1| yd. of ribbon for a bow. How much 
 does it take for 9 such bows ? 
 
 15. Find the cost of a dozen eggs at 3J cents apiece. 
 
 16. I pay i55| for a boy's suit. Find the cost of 4 such 
 suits. 
 
 17. 3 baskets of cherries cost 25 cents. How much will 
 12 baskets cost ? 
 
 Suggestion. — 12 baskets will cost how many times the cost of 3 
 baskets ? 
 
 1. Find 6 
 
 H 
 
 6 
 
 xli. 
 
 Written Work 
 
 
 This means that 6 x | is 
 
 to be added to 6 x 1. 
 
 ? = 6xJ 
 
 6 
 
 6x 
 
 i = S 
 
 or 3 ; 6x1 = 6 
 
 ; and 3 + 6 = 9. 
 
 9 
 
 Find the value of 
 
 , 
 
 
 
 2. 8 X 41 
 
 
 11. 
 
 10x2f 
 
 20. 125xl8f 
 
 3. 10x41 
 
 
 12. 
 
 12x3| 
 
 21. 72 X 24| 
 
 4. 9 X 2f 
 
 
 13. 
 
 20x5f 
 
 22. 100x14^0 
 
 5. 12x3f 
 
 
 14. 
 
 45 X 12^ 
 
 23. 132 X 5^\ 
 
 6. 11 X 3^ 
 
 
 15. 
 
 120 X 22| 
 
 24. 168xl0^\ 
 
 7. 14x22 
 
 
 16. 
 
 154 X llf 
 
 25. 20 X 18| 
 
 8. 12x8i 
 
 
 17. 
 
 96 X 6f 
 
 26. 90 X 15| 
 
 9. 6 X 81 
 
 
 18. 
 
 144 X 91 
 
 27. 50 X 16J 
 
 10. 5 X 3f 
 
 
 19. 
 
 80x41" 
 
 28. 200 X 15^ 
 
214 FIFTH YEAR 
 
 29. A book dealer purchases 125 books at wholesale at 
 f 1 J each. Find the cost. 
 
 30. The car fare from Pittsburg to Chicago on the Ft. 
 Wayne is $10 J. Find the amount received from the sale of 
 50 tickets. 
 
 31. A newsdealer buys 300 papers at 1| cents each and 
 sells them at 2 cents each. Find the cost and the gain. 
 
 32. A huckster buys 20 dozen bananas at 10 cents per dozen 
 and sells them at the rate of 2 cents each. Find his gain. 
 
 33. A fruit dealer buys a barrel of apples for $4|^. The 
 barrel contains 240 apples. He sells one half of them at 
 the rate of 2 for 5 cents and the remainder at the rate of 
 3 for 5 cents. Find his profit. 
 
 34. A merchant buys a roll of calico containing 40 yards 
 at 5| cents per yard. Find the cost. 
 
 35. The merchant retails the calico at 7| cents per yard. 
 Find the amount received for the roll. 
 
 36. A boy lives If miles from his school and attends 150 
 days in the term. How many miles does he walk in a term 
 both to and from school ? 
 
 37. A department store employs 100 cash girls at f 2| per 
 week and 120 other clerks at $4| per week. Find the 
 amount paid to all. 
 
 38. If a man can cut an average of 2 J cords of wood in a 
 day, how many cords can he cut in 44 days ? 
 
 39. A dealer in feed finds that a car load of 600 bushels 
 of oats, after paying freight, damage, etc., costs 42 J cents 
 per bushel. Find the cost. 
 
 40. A contractor buys 20 thousand feet of lumber at 
 $20| per thousand and 16 thousand bricks at il6^ per 
 thousand. Find his bill. 
 
FKACTIONS 215 
 
 41. Find the cost of 24,000 railroad ties at 62| ^ each. 
 
 42. When lead pencils are selling at $1| per gross (144), 
 find the cost of 3550 gross. 
 
 43. Find the cost of sewing buttons on 72 suits, at 1|^ a 
 suit. 
 
 44. A contractor averages 6| rd. a day in digging a sewer. 
 How long is the sewer if it takes him 39 days to dig it ? 
 
 45. A rural mail carrier travels 23J miles for each delivery. 
 Find the number of miles traveled in 310 deliveries. 
 
 46. An ocean steamer burns on an average 201^^ tons of 
 coal in a day. How much coal will it consume in a voyage 
 of 7 days ? 
 
 Multiplying an integer by a mixed number. 
 
 Analyze these problems : 
 
 1. Multiply 12 by 6| ; 10 by 7|. 
 
 2. 7 1 times 8 hours are how many hours? 
 
 3. How much do 2| pounds of candy cost at 40 cents 
 a pound? 
 
 4. I bought 4J yards of ribbon at 40 cents a yard. 
 How much did it cost? 
 
 5. A boy walks 3 miles in an hour. How far can he 
 walk at the same rate in 2f hours ? 
 
 6. James is 6 years old. His mother is 4| times as old. 
 How old is she? 
 
 7. How much will 10| pounds of meat cost at 16 cents a 
 pound? 
 
 8. A man bought 7J gallons of oil at 12^ a gallon. 
 How much did he pay for it? 
 
216 FIFTH YEAR 
 
 9. When gas costs 25 cents per thousand feet, what is 
 my bill for 10| thousand feet? 
 
 10. If a lot cost $200 and a house 6|- times as much, how 
 much did the house cost? 
 
 11. A man worked 20| days in a month for $2 a day. 
 How much did he earn? 
 
 12. How many inches equal 9| feet? 
 
 13. At 60 cents a bushel, how much will 2J bushels of 
 wheat cost? 
 
 14. I bought Ij dozen collars at $2 per dozen. How 
 much did they cost? 
 
 15. At 12 cents a pound, how much will 15| pounds of 
 raisins cost? 
 
 16. How much will 5| bu. raspberries cost at $2 a bushel ? 
 
 17. If a plumber is paid 75 cents per hour, how much does 
 he receive in 3| hours? 
 
 18. How far will an automobile travel in 2| hours if it 
 travels 18 miles in one hour ? 
 
 19. If the freight from New York to Albany on a ton of 
 merchandise is 33 cents, how much will it be on 5^^^ tons? 
 
 20. A gallon of water weighs 8 pounds. How much do 
 10| gallons weigh? 
 
 Written Work 
 1. Multiply 12 by 181. 
 12 
 
 181 
 
 2 = 1 X 12 18| times 12 means that I of 12 is to be added 
 
 9^ ^ to 18 X 12. i of 12 = 2, whicii added to 18 x 12 
 
 12 =218. 
 
 218 
 
FRACTIONS 217 
 
 2. Multiply 12 by 14|. 
 
 12 
 
 8 = f of 12 
 48 
 12 
 
 176 
 
 14f times 12 means 
 to 14 X 12. 1 of 12 = 
 = 176. 
 
 that f of 12 is to be added 
 : 8, which added to 14 x 12 
 
 Find products : 
 
 
 
 
 
 3, 71 X 6 
 
 17. 
 
 2O2V X 100 
 
 31. 
 
 116f X 54 
 
 4. 151 X 9 
 
 18. 
 
 42^L X 55 
 
 32. 
 
 112^ X 50 
 
 5. 271 X 12 
 
 19. 
 
 64J^ X 39 
 
 33. 
 
 88f X 28 
 
 6. 120 J X. 40 
 
 20. 
 
 72J^ X 42 
 
 34. 
 
 30| X 160 
 
 7. 216^0 X 50 
 
 21. 
 
 102Jg X 80 
 
 35. 
 
 19^2 X 24 
 
 8. 731 X 15 
 
 22. 
 
 124^^ X 120 
 
 36. 
 
 3,^x60 
 
 9. 1401 X 28 
 
 23. 
 
 12f X 9 
 
 37. 
 
 145^^ X 55 
 
 10. 100^0 X 60 
 
 24. 
 
 14| X 10 
 
 38. 
 
 48f X 84 
 
 :ii. 95-1 X 45 
 
 25. 
 
 20| X 12 
 
 39. 
 
 21f X 16 
 
 12. 811 X 21 
 
 26. 
 
 35f X 18 
 
 40. 
 
 40| X 25 
 
 13. 1201 X 81 
 
 27. 
 
 951 X 42 
 
 41. 
 
 121f X 49 
 
 14. 1441 X 108 
 
 28. 
 
 lOOf X 20 
 
 42. 
 
 lOf X 18 
 
 15. 150^V X 60 
 
 29. 
 
 1241 X 120 
 
 43. 
 
 14J X 24 
 
 16. 180^8 X 18 
 
 30. 
 
 65| X 32 
 
 44. 
 
 20^2 X 84 
 
 45. If the rate of sailing of a vessel is 18 miles an hour, 
 
 how far will it sail in 24 J hours ? 
 
 46. Find the cost of 12^ tons of coal at $6 a ton. 
 
 47. Find the cost of 16| yards of silk at 11.50 a yard. 
 
 48. A farmer sold 5J acres of land at $ 40 an acre. How 
 much did he receive for it ? 
 
218 FIFTH YEAR 
 
 49. If ribbon is sold at 24 cents a yard, how much will 7| 
 yards cost ? 
 
 50. At 16 cents a pound, how much will 10|^ pounds of 
 
 cheese cost ? 
 
 51. If clover seed is selling at i 8 a bushel, how much will 
 11| bushels cost ? 
 
 52. Find the cost of 5J yards of point lace at $ 24 a 
 yard. 
 
 53. When hay is selling for 812 a ton, how much must I 
 pay for 16| tons ? 
 
 54. If a boy walks 18 miles in a day, how far can he walk 
 in 36| days ? 
 
 55. Mr. Penrose sold his farm containing 85| acres at $ 56 
 an acre. How much did he receive for it ? 
 
 56. Find the cost of 15| yards of velvet at $ 5 a yard. 
 
 Multiplying a fraction by a fraction. 
 
 1. What is J of 6 feet ? | of 6 feet ? 
 
 2. What is 1^ of 6 sevenths ? f of f ? 
 
 3. J of 1^ means that we are to take ^ of 6 equal parts of 
 a unit that has been divided into 7 equal parts. 
 
 4. ^ of 1^ = how many sevenths ? 
 
 5. J of 1^ = |, and I" of f = 2 times f , or ^. 
 
 Find: 
 
 6. loff 9. f off 12. f oflf 
 
 7. J of I 10. foff 13. I of If 
 
 8. i of I 11. f of f 14. I of fl 
 
FRACTIONS 219 
 
 15. What is I of f? 1 of 1 = 1, and I of f= 2 times i 
 
 or f . 
 
 16. • Observe that | of | = ? ^ | = f 5, or |. 
 
 0X0 
 
 Written Work 
 
 1. Find I of f This means | x f = Jf 
 Find products : 
 
 2. 
 
 |x| 
 
 6. 
 
 fxA 
 
 10. 
 
 fxt 
 
 3. 
 
 f x| 
 
 7. 
 
 f X ^ 
 
 11. 
 
 ftx| 
 
 4. 
 
 fx|- 
 
 8. 
 
 |xf 
 
 12. 
 
 fxf 
 
 5. 
 
 fxf 
 
 9. 
 
 ix| 
 
 13. 
 
 fX^TT 
 
 14. Find H X 1|. Change to improper fractions. Thus, 
 llxl| = |x^ = ^,or2|. 
 
 15. If X 21 19. IJ X 21 23. 6J X 9| 
 
 16. U X 2f 20. 3| X 11 24. 121 X 4J 
 
 17. 31x11 21. 4fx7i 25. 10fx3^ 
 
 18. 41x21 22. 9|xl2l 26. 121x121 
 
 27. Find the cost of 3 J quarts of milk at 7J^ per quart. 
 
 28. A lady bought 18 1 yards of gingham at 8|y per yard. 
 Find the cost. 
 
 29. When copper is selling at 16|^ per pound, find the 
 cost of 8| pounds. 
 
 REVIEW 
 
 1. Find the cost of 2 dozen cans of tomatoes at 8^ cents 
 per can. 
 
 2. How much does a motorman earn in 13J hours at 22^ 
 per hour ? 
 
220 FIFTH YEAR 
 
 3. When copper is selling at 16| cents per pound, find 
 the cost of 36 pounds. 
 
 4. If platinum is selling at l|19| per ounce, find the cost 
 of 7 ounces. 
 
 5. Find the cost of 21 tons of anthracite coal at f 6| per 
 ton. 
 
 6. A load of soft coal contains 50 bushels. How much is 
 it worth at 7| ^ per bushel ? 
 
 7. When apples are selling at $.64 a bushel, find the cost 
 of 12| bushels. 
 
 8. At 8| cents per pound, how much is the express- 
 age on a package weighing 48 pounds ? 
 
 9. If a bale of cotton weighs 475| pounds, how much is 
 it worth at 8 cents per pound ? 
 
 10. How much will 17J quarts of ice cream cost at 
 20 cents per quart ? 
 
 11. When hay is selling at 88| per ton, find the cost of 
 34| tons. 
 
 12. From a piece of carpet containing 61 yd., 19| yd. were 
 sold at 70^ a yard, 17 J yd. at 65^ a yard, and the remainder 
 at 65 ^ a yard. For how much was the whole piece sold ? 
 
 13. If the above piece of carpet cost 45 ^ a yard, find the 
 entire gain. 
 
 14. Find the weight of 14 bags of coffee if each bag 
 weighs 47| pounds. 
 
 15. At 8| miles per hour, how far does a steamboat travel 
 in 16 hours ? 
 
 16. The rate in example 15 is the rate downstream. Up- 
 stream the rate is 2| miles per hour less. How far would 
 the boat travel upstream in 24 hours ? 
 
FRACTIONS 221 
 
 CANCELLATION 
 
 1. Find |- of ^. In changing y^^ to | both terms of the frac- 
 
 divide 
 2x3 
 
 2 V 3 _ 6 r»v 2 tion are divided by 3. Hence, in finding the 
 
 3 ^ 5 ~ 15' ^^ 5 
 
 2 X $ 2 value of - — - the work may be shortened by 
 
 — L_ :3s _ O y, O 
 
 p X O 5 rejecting the factor 3 from both dividend and 
 
 divisor, as indicated in the second model. 
 
 Cancellation is the process of shortening operations by 
 striking out equal factors from both dividend and divisor. 
 Cancel equal factors from both dividend and divisor when 
 
 5 
 
 possible ; thus, | x 71 x 3 = | x ^ x | = ^ = 15. 
 
 p f 1 1 
 
 2. I X 2f X 2 9. 51 X 21 X 4 
 
 3. If x4| xli 10. I of I X 61 
 
 4. 4 X 21 X 11 11. J X 8 X 12f 
 
 5. J X 3 X 41 12. ^% of 3| X 10 
 
 6. 3 X I of I 13. 51 X 2^2_ X 31 
 
 7. 51 X 31 x4 14. 5 x3i X 3| 
 
 8. 61 X 8 X 2f 15. 161 X 41 X 3 
 
 16. At 8| cents per pound, how much is the expressage on 
 a package weighing 64 pounds ? 
 
 17. At $9| a pair find the cost of 15 pairs of lace cur- 
 tains. 
 
 18. At the rate of 33 1 miles an hour how far will a train 
 travel in 10| hours ? 
 
 19. If a load of coal weighs 5| tons, find the cost at $6| 
 per ton. 
 
 20. Where hay is selling at S12| per ton, find the cost of 
 6^ tons. 
 
222 
 
 FIFTH YEAR 
 
 DIVISION OF FRACTIONS 
 
 
 '/z 
 
 l'^'/z=2 
 
 Dividing a whole number by a fraction. 
 
 1. How maDj halves are there in this 
 square ? 
 
 2. How many times is \ contained in 1 ? 
 
 3. How many times is %\ contained in f 1? 
 
 in $2? insB4? 
 
 4. What is the quotient of tivo halves 
 divided by one half? of f h- |- ? What is the 
 quotient oifour halves divided by two halves ? 
 
 of 4. ^ 2 9 f)f 6 ^ 2 ') 
 Ui. 2 • 2 • ^2 • 2 • 
 
 5. How many fourths are there in this 
 square ? What, then, is the quotient of 1 
 divided by J ? 
 
 6. How many I J are there in $1 ? in $3 ? 
 
 7. What is the quotient of four fourths divided by one 
 fourth? of |-5-:f? What is the difference between the 
 quotients of l-^\ and |-i? of 2 -- J and f-i? of 3-^J 
 and -152.^ J? 
 
 
 'A 
 
 
 
 1^/4 = 4 
 
 8. Explain how 1-i- 1 = 1 H-^; 2-i-J = |H-J; 3 -s- 
 
 ¥^i;|- 
 
 ^i 
 
 = ll 
 
 -^A; 1- 
 
 ■-\ = 
 
 li-/5- 
 
 
 
 Give quotients: 
 
 
 
 
 
 
 9. 2^1 
 
 
 15. 
 
 5- 
 
 -l 
 
 21. 
 
 12-J 
 
 27. 
 
 15-1 
 
 10. 4-i-l 
 
 
 16. 
 
 6- 
 
 -\ 
 
 22. 
 
 10^1 
 
 28. 
 
 2-i 
 
 11. 5.:- J 
 
 
 17. 
 
 6- 
 
 -* 
 
 23. 
 
 9^1 
 
 29. 
 
 4-^i 
 
 12. 2^1 
 
 
 18. 
 
 8- 
 
 -i 
 
 24. 
 
 6^i 
 
 30. 
 
 5^i 
 
 13. 4^1 
 
 
 19. 
 
 5- 
 
 -i 
 
 25. 
 
 12^* 
 
 31. 
 
 16 -f- 1- 
 
 14. 3^1 
 
 
 20. 
 
 4- 
 
 -I 
 
 26. 
 
 4-J 
 
 32. 
 
 lO^i 
 
FRACTIONS 223 
 
 33. Change 1, 2, 8, 4, 5, 6, 7, 8, 9, 10 each to 4ths ; to 6ths ; 
 to 8ths ; to lOths. Thus, 1 = | = | = f = ^. 
 
 34. What change must be made in ^ and | before they can 
 be added or their difference taken ? 
 
 35. What change did we make in the problem 1 -?- 1 before 
 we divided 1 by ^ ? 
 
 36. What change did we make in the fractions in exam- 
 ple 8 before one fraction was divided by another fraction? 
 This is the first step. 
 
 37. When the fractions have been made similar what is 
 the second step in dividing the fractions ? the third step ? 
 
 An7/ number may he divided by a fraction hy changing both 
 numbers to similar fractions and then dividing the numerators. 
 
 Thus, 
 
 8^ 
 
 l = ¥*4=*o^ 
 
 h 4 = 10. 
 
 
 i^ 
 
 i = H-'-A = i5H 
 
 -8= IJ. 
 
 38. Give 
 
 quotients : 
 
 
 4 . 1 
 
 
 S . 1 
 
 20 _t. 1 
 
 ■5^5 
 
 
 liJ^¥ 
 
 jr~7 
 
 8^i 
 
 
 i%^i 
 
 i*^f 
 
 j\-^i 
 
 
 M^i 
 
 H-i 
 
 fj^i 
 
 
 M-i 
 
 1^^^ 
 
 ii^l 
 
 
 iJ-i 
 
 f-^A 
 
 il^i 
 
 
 il-i 
 
 1^1% 
 
 39. Give 
 
 quotients : 
 
 
 4--i 
 
 
 1^* 
 
 i^i 
 
 6^1 
 
 
 ii^l 
 
 i^^i 
 
 2^f 
 
 
 U^l 
 
 i-i 
 
 li^l 
 
 
 M-i 
 
 i-i 
 
 if^i 
 
 
 -J!-f 
 
 f^l 
 
 12^1 
 
 
 l-A 
 
 i%^l 
 
 M-f 
 
 -H 
 
 -A 
 
 J- 
 
 -1^ 
 
 iV^ 
 
 -A 
 
 J-^ 
 
 ■A 
 
 |-^^2 
 
 1- 
 
 ^i 
 
 i- 
 
 ^f 
 
 i- 
 
 ^+ 
 
 !• 
 
 ^i 
 
 ^' 
 
 ^iV 
 
 if 
 
 -^1 
 
224 
 
 FIFTH YEAR 
 
 Dividing a whole number or a mixed number by a fraction. 
 
 An improper fraction is a fraction whose numerator is equal 
 to or greater than its denominator; as, |, |, |, J. 
 
 A proper fraction is a fraction whose numerator is less 
 than its denominator; as, |, |, |. 
 
 Change 4J, 5J, 2|-, 51, 7J, to improper fractions. 
 
 1. Divide 41 by |. 
 
 4 = c. d. 
 
 1^1 = 
 
 ¥--- 
 
 6 
 
 Written Work 
 
 Change 4| to the improper fraction f . 
 Change f and | to similar fractions. 
 
 Divide 
 2. 6 
 
 4 
 
 2i 
 
 21-1 
 
 H 
 
 8. 
 
 9. 
 10. 
 11. 
 12. 
 13. 
 
 1|^ 
 
 10 -4- 
 
 12 
 
 12 _^ 
 -^3 • 
 
 1 
 
 3i 
 
 4 
 5 
 
 14. 
 15. 
 16. 
 17. 
 18. 
 19. 
 
 i 
 
 21 
 
 6 
 
 - f 
 
 
 20. How much are eggs per dozen when 36 cents are paid 
 for 2^ dozen ? 
 
 21. A man's wages amounted to 46 dollars for 9J days' 
 work. How much did he receive per day ? 
 
 22. A piece of ribbon containing 10 yards is cut into 
 badges each |^ of a yard in length. How many badges can 
 be cut from the piece ? 
 
 23. A merchant sold 81 cents' worth of ribbon. If he 
 sold 6 J yards, what was the price per yard ? 
 

 8. 
 
 m^H 
 
 14. 
 
 H - 
 
 -9| 
 
 9. 
 
 14f^2f 
 
 IS. 
 
 8|- - 
 
 -8^ 
 
 10. 
 
 ^^^ 
 
 16. 
 
 8f - 
 
 -6f 
 
 11. 
 
 6f^4i 
 
 17. 
 
 9| - 
 
 -H 
 
 12. 
 
 H^H- 
 
 18. 
 
 s-^- 
 
 ^2| 
 
 13. 
 
 H^n 
 
 19. 
 
 H - 
 
 -^1 
 
 FRACTIONS 225 
 
 Dividing a mixed number by a mixed number. 
 Written Work 
 
 1. Divide IJ by 14 First change the mixed numbers 
 
 ^ _ 1 to improper fractions, then make the 
 
 — — — '- — •* fractions similar, and divide the nu- 
 
 ^^2 "^ ^^ merator of the dividend by the nu- 
 
 I -H I = 9 -f- 8, 1 or 1^ merator of the divisor. 
 
 2. 71^21 
 
 3. 6|^1| 
 
 4. 5|H-lf 
 
 5. 8| + 2i 
 
 6. 7J-^1| 
 
 7 31-^^1 
 /. 03 . -2 
 
 20. At 2| dollars each, how many vests can be bought 
 for 142 ? 
 
 21. At $1^ apiece, how many pictures can be bought for 
 $10| ? 
 
 22. I paid 1 28 1 for cloth at f 1| a yard. How many 
 yards did I buy ? 
 
 23. I spent |17f for molasses at f lyg- a gallon. How 
 many gallons did I buy ? 
 
 24. At $1^ each, how many straw hats can be bought for 
 |14f ? 
 
 25. A merchant purchases $50^ worth of gas lamps at 
 84^ a piece. Find the number purchased. 
 
 26. When 3| bushels of apples cost $2|, how much will 
 one bushel cost? 
 
 27. A man earns $ 16 1 in 5 J days. How much is this per 
 day? 
 
 28. At $2^ per pair, how many pairs of shoes can be bought 
 for $11 1? 
 
226 FIFTH YEAR 
 
 Dividing any number by a fraction by inverting the terms 
 of the divisor. 
 
 1. How many times is ^ inch contained in 1 inch? ^ yard 
 in 1 yard? ^ foot in 1 foot? Draw figures to illustrate. 
 
 When the fraction |- is changed to |, the fraction is said to 
 be inverted. It then shows how many times the fraction is 
 contained in 1. 
 
 2. 1^1= 1-^1= 1-1= 
 
 3. 1^1 = 1^1 = . 1^1= 
 
 Observe that in each of the above problems the quotient 
 equals 1 x the fraction inverted. 
 
 Thus : 1 - § = 1 X 2, or 2 ; 1 -- i =1 x f, or 4. 
 
 4. Since 1 -f- i = 1 x f , or 2, then 1 -^ | = 1 x |, or 2. 
 
 How many times is | contained in 1? |? -f^? |? f ? |? 
 
 The number of times each of the above fractions is con- 
 tained in 1 equals the number of times the numerator of 
 each fraction is contained in its denominator. 
 
 Find quotients by inverting the divisor and multiplying: 
 Thus: 3-| = 3xf= V = 3!. 
 
 5. 
 
 l^i 
 
 12. 
 
 2-1 
 
 19. 
 
 8-1 
 
 26. 
 
 15^1 
 
 6. 
 
 1-1 
 
 13. 
 
 B-f 
 
 20. 
 
 16-f 
 
 27. 
 
 16-1 
 
 7. 
 
 1-1 
 
 14. 
 
 4-1- 
 
 21. 
 
 24-1 
 
 28. 
 
 12-1 
 
 8. 
 
 1-1 
 
 15. 
 
 5-f 
 
 22. 
 
 20-f 
 
 29. 
 
 8-f. 
 
 9. 
 
 1-1 
 
 16. 
 
 6-^J 
 
 23. 
 
 15-f 
 
 30. 
 
 7-i\ 
 
 10. 
 
 1-f 
 
 17. 
 
 9-fo 
 
 24. 
 
 30-1 
 
 31. 
 
 6-1 
 
 11. 
 
 1-f 
 
 18. 
 
 10-1 
 
 25. 
 
 12-f 
 
 32. 
 
 9-i 
 
FRACTIONS 227 
 
 Written Work 
 1. Divide 128 by -If. 
 
 o Since l^ is contained in 1, f | times, 
 
 ^^R ^— = n^ X — = 200 ^3 i^ contained in 128, 128 x f |, or 200 
 " * 25 ;^ times. 
 
 Ani/ number may he divided by a fraction hy inverting the 
 terms of the divisor and multiplying. 
 
 Divide : 
 
 2. 18 by I 9. 63 by J 16. 288 by ^4. 
 
 3. 25 by I 10. 72 by I 17. 400 by J^- 
 
 4. 28by^ 11. 84by|i 18. 285 by J^^. 
 
 5. 21byf 12. 90 by If 19. 546 by |l 
 
 6. 36 by ^9^ 13, 108 by If 20. 425 by -fl 
 
 7. 42byfi 14. 84 by ^2 21. 378 by || 
 
 8. 54byf 15. 96byf 22. 324 by ^^^ 
 
 23. Divide 36 by 3|. 
 
 Suggestion. — Change the divisor to an improper fraction. 
 
 Divide: 
 
 24. 27by2i 30. 84by4J 36. 780 by 7| 
 
 25. 33by3f 31. 75by2f 37. 355 by 8 1 
 
 26. 44 by 4| 32. 90 by 3| 38. 295 by 6| 
 
 27. 60by3f 33. 92 by 2^3^ 39. 748 by 3| 
 
 28. 76by4f 34. 85 by 1 1 40. 549 by 8f 
 
 29. 60by6f 35. 245by5f 41. 620 by 7|' 
 
 Divide : 
 
 42. Ilfby3f 45. 4-^5 by If^ 48. 10fby2f 
 
 43. 6|byl| 46. 7t^2byl| 49. 15|by2i 
 
 44. 10| by 2^2- 47. 7f by 2f 50. 12| by o| 
 
228 FIFTH YEAR 
 
 MISCELLANEOUS PROBLEMS 
 
 Divide : 
 
 1. SJybySf 5. 9fTby8| 9. 27f by 8^ 
 
 2. 9f by 4f 6. 65f by 3f 10. 48i by IQi- 
 
 3. 16^by6| 7. 4fby6i 11. Wf by U 
 
 4. ai^byWJj 8. 14Jby5t 12. 29f^ by 21| 
 
 Problem 12 may be expressed in this way ^'^^ -, but it is 
 solved in the same way. ^ 
 
 Solve: 
 
 13. ^ 19. " ^ ^^ 25. ^ ^ -^'^ 
 If 
 
 14. 1^ 20. "' -^ :: "^ 26. 
 
 23- 
 
 3f 
 
 2x 
 5}x 
 
 
 5t- 
 
 ^ 
 
 3|-x 
 8| X 
 
 
 6|-- 
 
 21 
 
 _ 95 
 
 101 
 
 15. ^ 21. '1': ~' ^ 27. 
 
 2 X 21 
 
 16. -— -^ 22. ^V^^^ 28. 
 
 17. ^i_^ 23. ^4 --3 29. 
 
 18. MjhI 24. ^Qx^i 
 
 21 8i 31x2 
 
 31. Mr. Ames sold 630|- pounds of wool at 32i ^ per pound. 
 How much did he receive for it ? 
 
 32. A farmer cut 3J tons of hay per acre from 13J acres. 
 Find the value of the hay at S 1 2| per ton. 
 
 33. Mr. Anderson sold |- of 66^ acres of land at f 47|- per 
 acre. For how much did he sell the land ? 
 
 34. How many badges 6| inclies long can be cut from 23|- 
 yards of ribbon ? 
 
I 
 
 FRACTIONS 229 
 
 35. I of I of Mr. Adams's farm was 32 acres. If he sold 
 the farm at >j)105 per acre, how much did he get from the 
 sale ? 
 
 36. How many ribbons | of a yard long can be cut from 
 46| yards of ribbon ? 
 
 37. Two boys buy a sled. One pays for | of the cost and 
 the other ^ of the cost. If the boy that paid | of the cost 
 paid 90^, how much did the sled cost? 
 
 38. If any two factors in a division are given, how may we 
 obtain the third factor ? Make problems to illustrate. 
 
 39. The dividend is 163|, the quotient is 2181. Find the 
 divisor. 
 
 40. IJ is the product of 6 and what other number ? 
 
 41. I of the length of a flag pole is 60 feet. What is the 
 length of I of the pole ? 
 
 42. I of I of the time I worked for Mr. Ward is 12 days. 
 Find my pay for the whole time at f 2.50 per day. 
 
 43. The length of a certain city square is 338 1 feet. Find 
 its length in rods. 
 
 44. An automobile ran Q^^^ miles in 2| hours. Find the 
 average rate per hour. 
 
 45. James weighs 160| lb., Sara 108Jg lb., John 135| lb., 
 Mary 121| lb., and Henry 121| lb. Find | of their com- 
 bined weight. 
 
 46. Paul averages 2|- feet at a step. How many steps 
 does he take in going 1 mile ? 
 
 47. The lead lining in a tank weighs 3| pounds to the 
 square foot. How many pounds will be necessary to line 
 a tank containing 275J square feet of inside surface ? 
 
230 FIFTH YEAR 
 
 COMPARISON — WHOLE NUMBERS AND FRACTIONS 
 
 1. 1 = J ; I = |. Then how do J and | compare? 
 
 2. If a unit is first divided into halves and then each 
 half into halves, into how many parts is the unit divided ? 
 Is ^ of a unit larger or smaller than J of a unit ? 
 
 3. Divide a unit into halves, fourths, eighths, and six- 
 teenths, and show how many sixteenths of a unit it takes to 
 make ^ of the unit ; J of the unit ; J of the unit ; ^ of the 
 unit. 
 
 4. Draw equal squares to show that J = | or ^^g-. 
 
 5. Compare | and | ; | and ^- ; | and f. 
 
 6. How does I of 20 compare with J of 20 ? J of 16 
 with I of 16 ? I of 50 with ^ of 20 ? 
 
 7. A has 40 acres of land, and B 60 acres. How does A's 
 farm compare in size with B's ? 
 
 8. 8 is what part of 12, 16, 24, 32, 48, 72? 
 
 Suggestion. — Make 8 the numerator in each case and the other 
 numbers the denominators and reduce the fractions to their lowest terms. 
 Thus, y\ = 1; j\ = ^; .«? = h etc. 
 
 9. If 5 quarts of milk cost 45 cents, how much will 10 
 quarts cost ? 15 quarts ? 20 quarts ? 
 
 10. Elizabeth buys 3J yards of ribbon for 35 cents. At 
 the same rate, how much would she pay for 10 J yards ? 
 
 Suggestion. — How many times 3^ is 10^ ? 
 
 11. A woodsman cuts 15 cords of wood in 6 days. How 
 many cords, at the same rate, could he cut in 48 days ? 
 
 12. Compare 8 and 2 ; 6 and 4 ; 2 and 8 ; 5 and 10. 
 
 13. Compare J and ^ ; ^ and J ; J and -^^. 
 
 14. Compare 24 with 4, 6, 8, 48, 72, 16, 20. 
 
I 
 
 FRACTIONS 231 
 
 15. Draw a square inch and show that | of it = ^ of it; 
 that ^ of it = Y^g of it. 
 
 16. If I of a man's weekly wages is 12.75, how much is 
 J of his weekly wages ? 
 
 Suggestion. — I is how many times \7 
 
 17. 3| pounds of rice cost 35 cents. At that rate how 
 much will 7 pounds cost ? 
 
 18. If |- of my money is f 10, and George has 6 times my 
 money, how much has George ? 
 
 19. In New York 9J inches of rain fell in 3 months. At 
 that rate how much will fall in a year ? 
 
 20. If a man pays 13675 for 60 acres of land, at the same 
 rate how much should he pay for 120 acres ? 
 
 21. My telephone bill is 112.85 a month. At that rate 
 how much should I pay in 2| years ? 
 
 22. My coal bill for 5|- tons is 811. What is the bill of 
 my neighbor who buys 27 J tons at the same rate ? 
 
 23. If 30 bushels of oats sell for 113.20, how much will 60 
 bushels sell for ? 
 
 24. If a boy receives $7.50 for two weeks' work, how 
 much should he receive for 12 weeks' work? 
 
 25. How much will a clerk earn in a year if he earns flSO 
 in 3 months? 
 
 26. If 4 tons of coal cost $8|, how much will 16 tons cost ? 
 
 27. When 5 books cost 117.50, how much will 25 such 
 books cost ? 
 
 28. A man walked 11| miles in 3 hours. At the same 
 rate, how far would he walk in 6 hours ? 
 
232 FIFTH YEAR 
 
 REVIEW OF FRACTIONS 
 
 1. A boy earns |2| a week and spends |1|. If he puts 
 the remainder in bank, what will his bank account be in 
 19 weeks ? 
 
 2. May went to the store with 120. If she spends |2| 
 for a pair of shoes and $4| for a hat, how much change will she 
 receive ? 
 
 3. From a web of muslin containing 60 yards, 19| yd. 
 were sold to one customer, 13J yd. to another, and 9^ yd. 
 to another. How many yards remained ? 
 
 4. A dealer sold 2 loads of coal at 17.20 a ton. If the 
 first load contained 2| T., and the second d^ T., how much 
 did he receive ? 
 
 5. How many yards of muslin can be bought for 75^, 
 if 3 yards cost 25^? 
 
 6. If John weighs 96| lb. and Mary weighs 361 lb. less 
 than John, how much do they both weigh ? 
 
 7. A farmer bought 480 acres of land. He sold 148J 
 acres to one man, and 125-| acres to another. What was the 
 remainder worth at f'20 an acre? 
 
 8. How many days will it take a man to earn $126|, if 
 he earns 1 2| a day ? 
 
 9. A man dies leaving 14440. He leaves J^ ^f it to his 
 son, J of it to his daughter, | of it to his widow, and the rest 
 to a hospital. How much does each receive ? 
 
 10. John bought 3 pieces of cloth containing 19 J yd., 26^ 
 yd., and 35| yd. respectively. How many yards did he buy? 
 
 11. A man worked 43| hr. one week, and 36^^ hr. the 
 next. How many hours did he work in the two weeks ? 
 
I 
 
 FRACTIONS 233 
 
 12. A man paid ^ of his indebtedness one year, J of the 
 remainder the second year, and J of what then remained the 
 third year. Then he owed $ 516. How much did he owe at 
 first ? 
 
 13. From a certain number 2| + 3 J was subtracted, leav- 
 ing a remainder of lO^^^^. What was the number ? 
 
 14. One fifth of a certain number, minus 2|, equals 87|-. 
 What is the number ? 
 
 15. Mrs. Smith bought 4 pieces of lace containing 4| yd., 
 6| yd., 5 J yd., and 9 J yd., respectively. How much were 
 they worth at 12| ^ a yard? 
 
 16. If an acre of land is worth f 32, how much is | of an 
 acre worth? 
 
 17. A man paid f 45 for | of a quantity of grain. Find 
 the value of the entire quantity at the same rate. 
 
 18. How many poor families can be supplied with |^ of a 
 ton of coal each from 9 J tons ? 
 
 19. Find the cost of 36 J pounds of tea at 32^ a pound. 
 
 20. If I of a yard of silk cost 45 cents, what is the value 
 of 6| yards at the same rate ? 
 
 21. What number taken from the sum of 16 J and 28f will 
 leave 19J ? 
 
 22. What is the cost of | of a yard of muslin at 12^ a half 
 yard ? 
 
 23. The sum of two numbers is 126|, and the larger 
 number is 94|. What is the smaller number ? 
 
 24. A man spends i6J for board, 812| for clothing, $3^ 
 for books, and has $12 left. How many dollars and cents 
 had he at first ? 
 
234 FIFTH YEAR 
 
 25. If 75)^ is the cost of | of a yard of cloth, what is the 
 cost of 5 yards ? 
 
 26. il.50 is the value of | of a yard of broadcloth. How 
 many yards can be bought for $20 ? 
 
 27. I of a number is 9. What is the number ? 
 
 28. In traveling 72 miles a man went | of the distance 
 the first day, ^ of the distance the second day, and the re- 
 mainder the third day. How far did he travel the third 
 day? 
 
 29. From a farm of 225| acres there were sold 150^ acres. 
 How many acres were left? 
 
 30. How much must be paid for 16 tables at $7J each? 
 
 31. At $f each, how many books can I buy for $36 ? 
 
 32. A man bought a hat for f 5|, a pair of shoes for i6-|-, 
 a pair of gloves for 13 J, and a suit for $22^. How much did 
 he pay for all ? 
 
 33. A clerk earns $75 a month and spends i36|. How 
 much has he left? 
 
 34. At $.87 J a bushel, what is the cost of 56 bushels of 
 grain ? 
 
 35. How many chairs, at $5J each, can be bought for 
 $2621? 
 
 36. A lady bought | of a yard of narrow lace. If yards of 
 medium width lace, and 2J yards of wide lace. How many 
 yards did she buy in all ? 
 
 37. From a piece of muslin containing 40 yards there were 
 sold 25 1 yards. How many yards remained? 
 
 38. At $.12^ a yard, what is the cost of 42 yd. of muslin? 
 
 39. How many pencils, at ^^ each, can be bought for 
 $1.16? 
 
FRACTIONS 235 
 
 40. One coat requires 2|- yards. How many coats can be 
 made out of S5^ yards? 
 
 41. Jolm weighs 124|^ pounds, and Ned weighs 18| pounds 
 less. How many pounds does Ned weigh? 
 
 42. A farmer sold 35| bushels at one time, and 21 J 
 bushels at another time. How many bushels did he sell? 
 
 43. A tailor uses 9| yards of cloth for a suit. How many 
 yards will it take for 32 suits? 
 
 44. John and James cut 3| cords of wood in one day. In 
 how many days can they cut 84:| cords? 
 
 45. A man raised 236J bushels of oats, and sold 129| 
 bushels. How many bushels had he left? 
 
 46. A man exchanged with a grocer 2^ bushels of pota- 
 toes at 60^ a bushel, for 6| pounds of bacon. How much did 
 the grocer charge per pound for the bacon ? 
 
 47. A merchant sold some grain for $63 which was J of 
 its cost. What was the cost of the grain? 
 
 48. I of a building is valued at $300? What is the value 
 of the whole building? 
 
 49. 11 lb. of butter cost 30^. Find the cost of 2f lb. ' 
 
 50. A owns 160 sheep and B owns ^ as many as A. 
 C owns J as many as B. How many sheep do all own ? 
 
 51. Show that multiplying or dividing both terms of a 
 fraction by the same number does not change its value. 
 
 52. How many potatoes are there in 12 barrels, if one 
 barrel contains 2 bushels 3 pecks? 
 
 53. 48-121 = ? 12|-5f = ? 10f-l| = ? 
 
 54. For 5 cents one can buy 3 oranges. How much must 
 be paid for 12 oranges? 
 
DECIMALS 
 
 Decimal parts of the dollar. 
 
 1. How many dimes equal a dol- 
 lar? Then what part of a dollar is 
 a dime? 
 
 2. How many cents equal a dol- 
 lar ? Then what part of a dollar is a cent ? 
 
 3. Ten mills equal one cent. How many mills equal a 
 dollar? Then what part of a dollar is a mill? 
 
 Mills are not coined, but are used for exactness in computations. 
 
 When we think of a dollar as dimes, it has 10 equal parts ; 
 when we think of a dollar as cents, it has 100 equal parts ; 
 when we think of a dollar as mills, it has 1000 equal parts. 
 A mill is yl(j of a cent ; a cent 3^ of a dime ; and a dime J-^y of 
 a dollar. 
 
 This division of the dollar into tenths, hundredths, thou- 
 sandths, etc., we call decimal parts of the dollar. 
 
 The decimal point is the point separating dollars and cents. 
 Thus, in $2.75 the point separates 2 dollars from 75 cents. 
 
 4. What decimal part of a dollar are 5 dimes? 6 dimes? 
 
 8 dimes? 9 dimes? 
 
 5. What decimal part of a dollar are 5 cents? 8 cents? 
 
 9 cents? 10 cents? 
 
 236 
 
DECIMALS 237 
 
 The first place to the right of the decimal point is occupied 
 by dimes or tenths of a dollar ; the second place, by cents or 
 hundredths of a dollar; the third place, by mills or thour 
 sandths of a dollar. 
 
 Thus, 8 dimes, 5 cents = 85 cents. Cents occupy the first two places 
 to the right of the decimal point. Observe that dimes, cents, and mills 
 can always be written as decimal parts of a dollar ; thus, 8 dimes = f .80 ; 
 2 mills = $ .002. 
 
 6. In $1,256, state what each figure represents. 
 
 7. Name the parts of a dollar, first as tenths, hundredths, 
 and thousandths; then as cents and mills: $.65, $S.05, 
 $2,005, $.50, $.75, $.80, $.705. 
 
 8. Write in figures : six dollars, five cents ; ten dollars, 
 fifty cents ; three mills ; five cents ; five mills. 
 
 We may also find tenths, hundredths, thousandths, etc., of 
 any unit. 
 
 READING AND WRITING DECIMALS 
 
 One tenth inay be written .1 as well as -^-^ ; one hundredth 
 may be written .01 as well as ^^^ ; and one thousandth may 
 be written .001 as well as y^Vo- 
 
 1. Read: .8 ft., .5 lb., .7 pk., .5 ft., .7 mi. 
 
 A decimal point is a period placed before tenths. 
 
 A decimal fraction is any number of lOths, lOOths, lOOOths, 
 etc., of a unit. When expressed after a decimal point and 
 without a written denominator it is usually called a decimal. 
 
 The first place to the right of the decimal point is called 
 tenths, the second place hundredths, and the third place thou- 
 sandths. 
 
 2. In 55.55, the 5 hundredths is what part of the 5 tenths ? 
 the 5 tenths is what part of the 5 units? the 5 units is 
 
 . what part of the 5 tens? 
 
238 FIFTH YEAR 
 
 In any number, whether a whole number or a decimal, the 
 "Value of a figure in any place is -^^ of the value of the same 
 figure standing one place to the left. 
 
 3. What is the largest decimal division of a unit? the 
 second largest ? the third largest ? 
 
 4. 
 
 .06 = y|^ = 10^ 
 
 7. 
 
 •^ — TO — TOO — TTFTT-O" 
 
 5. 
 
 •-^ = Tto = loVo 
 
 8. 
 
 .025- ^(^00 - 100(5-(F 
 
 6. 
 
 •^5= ito =ToVo 
 
 9. 
 
 .349 = ^0^0 =ToW 
 
 Observe that a decimal is always less than a unit. 
 
 tC H O P H W H 
 
 5 2 5-256 
 
 This number is read, five hundred twenty-five and two hun- 
 dred fifty-six thousandths. 
 
 10. What do we call the decimal point when we read a 
 number? What word, then, always joins the whole number 
 and the decimal ? 
 
 Observe that we express every number as units, or ones, and parts of a 
 unit. Thus : 525.256 is 525 units and .256 of a unit. 
 
 As the first decimal division of a unit is tenths, we always 
 begin to enumerate the decimal at tenths' place ; thus : 
 tenths hundredths thousandths 
 .0 5 
 
 11. At what place do we begin to enumerate whole numbers ? 
 
 12. Read the following: .25, .025, 25.005, 7.05, 321.1, 
 0.875, 1.008, 100.001, 0.001. 
 
 13. Write as decimals: -f^, ^J^, ^ff^, J^, ^-^f^, j-^2_^, 
 26-1^^, lOO^J^O' 1t!^' 703-V^. 
 
DECIMALS 2S9' 
 
 Write decimally : 
 
 14. Two thousandths. 
 
 15. Two and two thousandths. 
 
 16. Five hundredths. 
 
 17. Two hundred and two thousandths. 
 
 18. Two hundred two thousandths. 
 
 19. Three and five tenths. 
 
 20. Seventy-five hundredths. 
 
 21. Five hundred and five thousandths. 
 
 22. Thirty-three thousandths. 
 
 23. Ninety-five thousandths. 
 
 24. Two hundred and five hundredths. 
 
 25. Six and nine tenths. 
 
 26. Six hundred and six hundredths. 
 
 COMPARISON OF COMMON FRACTIONS AND DECIMALS 
 
 1- t^-tVo = AVo; .5 = .50 = .500. 
 
 2. Do naughts at the right of a decimal affect its value? 
 Annexing naughts to the right of a decimal does not affect its 
 
 value, 
 
 3. What is a fractional unit? 
 
 4. What is the largest fractional unit that may be ex- 
 pressed decimally? the second largest? the third largest? 
 
 5. Change -f^-^ to tenths. 
 
 6. Express .25, .45, .75, .025, each in the form of a com- 
 mon fraction. 
 
 7. Change .5 to equivalent decimals expressed in hun- 
 dredths and thousandths. Thus, .5 = .50 = .500. 
 
240 FIFTH YEAR 
 
 8. Name the three largest fractional units in their order; 
 the three largest decimal fractional units. 
 
 9. Change y^ to an equivalent decimal. 
 
 Changing a decimal to a common fraction. 
 
 1. Change .75 to a common fraction in its lowest terms. 
 
 Expressed in the form of a common fraction 
 ^75 = r^Q = 1 .75 = j^5(j. By dividing both numerator and denomi- 
 nator of r^ by 25, we reduce it to its lowest terms, |. 
 
 To change a decimal to a common fraction, write the decimal, 
 omitti7ig the decimal point, place the decimal denominator be- 
 neath it, and change the fraction to its lowest terms. 
 
 Change to fractions : 
 
 2. .15 4. .9 6. .75 8. .125 
 
 3. .825 5. .325 7. .025 9. .425 
 
 10. Memorize the following equivalents : 
 
 J=.5or.50 1 = .2 or .20 | = .8or.80 
 
 . i = .25 
 
 
 1= 
 
 .4 or .40 
 
 i= 
 
 .125 
 
 | = .75 
 
 
 1= 
 
 .6 or .60 
 
 f= 
 
 .375 
 
 11. Change 
 
 to tenths : ^ 
 
 ; i; 
 
 I; I; t- 
 
 
 
 12. Express as decimal hundredths : J ; f ; 
 
 i;f. 
 
 
 Change to fractions and reduce to lowest terms : 
 
 
 13. .45 
 
 19. .20 
 
 
 25. .40 
 
 31. 
 
 .075 
 
 14. .625 
 
 20. .60 
 
 
 26. .48 
 
 32. 
 
 .025 
 
 15. .75 
 
 21. .125 
 
 
 27. .150 
 
 33. 
 
 .12 
 
 16. .65 
 
 22. .90 
 
 
 28. .50 
 
 34. 
 
 .225 
 
 17. .375 
 
 23. .96 
 
 
 29. .025 
 
 35. 
 
 .700 
 
 18. .80 
 
 24. .72 
 
 
 30. .08 
 
 36. 
 
 .800 
 
DECIMALS 241 
 
 ADDITION OF DECIMALS 
 
 1. What kind of fractions can be added or subtracted? 
 
 In adding or subtracting decimals, like units must always 
 be written under one another; thus, .8+ .85 + .096 may be 
 written thus: .8 .8-f .8 = 1.6 
 
 Added .85 Test: .05 + .09= .14 
 
 .096 .006= .006 
 
 T7f46 1.746 
 
 2. In how many of the decimals are there tenths to be 
 added? hundredths? thousandths? 
 
 3. Why must tenths be written under tenths, hundredths 
 under hundredths, etc. ? 
 
 A mixed decimal is a whole number and a decimal united j 
 thus, 4 + .05, or 4.05, is a mixed decimal. 
 
 Written Work 
 
 1. Add 45.5 + 6.005 + 40. 
 45.5 
 
 6.005 Keep the decimal points and units of the same order in a 
 
 ^Q column, and add as in whole numbers, placing the decimal 
 
 Q-j rr.r poiut in the sum under the points above. 
 
 Find the sums of the following : 
 
 2. .1 + . 2 + .35 + .365 = ? 
 
 3. .02 + .05 + .095 + .056 = ? 
 
 4. .05 +.007 + .089 +.11 = ? 
 
 5. 1.2 + 3.4 + 4.5 = ? 
 
 6. 3.04 + 4.05 + 6.099 = ? 
 
 7. .005 + .007 + .009 + .0101 = ? 
 
 8. 2.006 + 7.009 + 9.012 = ? 
 
 9. .001 + .001 + .0902 = ? 
 
242 
 
 
 FIFTH 
 
 YEAR 
 
 
 
 , 
 
 10. 
 
 10 + 2.1 + 14.9 + 17.85 = ? 
 
 
 
 
 11. 
 
 .9 + .85 + .005 + .25 + .895 = 
 
 :? 
 
 
 Add: 
 
 
 
 
 
 
 12. 1.45 
 
 
 13. .424 
 
 14. .7 
 
 15. 
 
 11.111 
 
 3.7 
 
 
 8.2 
 
 .425 
 
 
 3.06 
 
 10.01 
 
 
 6.16 
 
 18.54 
 
 
 .635 
 
 2.005 
 
 
 19.009 
 
 7.011 • 
 
 
 .000 
 
 16. 18.002 
 
 
 17. .040 
 
 18. 89.400 
 
 19. 
 
 .707 
 
 2.056 
 
 
 48.010 
 
 75.800 
 
 
 101.101 
 
 121.114 
 
 
 .708 
 
 761.612 
 
 
 96.086 
 
 2,02 
 
 
 89.010 
 
 1245.000 
 
 
 27.409 
 
 20. Find the sum of 15.38, 9.17, 3.07, and 20.35. 
 
 21. A boy picked on Monday, .75 of a bushel of berries ; 
 on Tuesday, .875 of a bushel; on Wednesday, 1.125 of a 
 bushel. How many bushels did he pick in the three days ? 
 
 22. Helen paid $.25 for a handkerchief, $2.75 for a pair 
 •of shoes, S.45 for lace, and ff 1.49 for a waist. How much 
 •did they all cost ? 
 
 23. A train runs the first hour 19.625 miles ; the second 
 hour, 20.5 miles ; the third hour, 20.75 miles ; the fourth 
 hour, 21.225 miles. How far does it run in the four 
 hours ? 
 
 24. Find the number of pounds in the following purchases : 
 1.25 lb. of cheese, 3.5 lb. of sugar, .5 lb. of cloves. 
 
 25. The distance from Harrington to Houston is 4.31 
 miles, thence to EUendale 11.25 miles, thence to George- 
 town 8.37 miles. How far is it from Harrington to 
 ^Georgetown ? 
 
DECIMALS 24a 
 
 SUBTRACTION OF DECIMALS 
 Find differences : 
 
 1. 
 
 .5".3 = ? 
 
 5. .008 -.002 = ? 
 
 2. 
 
 .9-. 8-=? 
 
 6. .014 -.011 = ? 
 
 3. 
 
 15.8-11.7 = ? 
 
 7. .08 + .09 -.12 + .04 +.02 = ? 
 
 4. 
 
 4.7-3.2 = ? 
 
 8. .009 + .003 -.007 -.004 = ? 
 
 Written Work 
 1. From 16.35 subtract 11.76. 
 
 ■*^"*"^ Keep the decimal points in a column and sub* 
 
 11.76 tract as in whole numbers, placing the decimal 
 
 4.59 point in the difference under the points above. 
 
 2. 7. 3. 16. 4. 1.101 5. 265.36 
 
 1.21 3.046 .796 84.468 . 
 
 6. 25.2 7. 151.003 8. 954.1 9. 36.291 
 
 9.18 78.076 258.375 17.456. 
 
 10. 144.001 11. 300. 12. 86.59 13. 728.3 
 
 12.256 261.385 53.594 619.333: 
 
 14. Warren had 17.50 and spent 13.75. How much had 
 he remaining ? 
 
 15. The distance between two towns is 9 miles. After 
 I have walked 3.625 miles, how far have I yet to walk ? 
 
 16. A man having 120 acres of land, sold to one man 
 28.75 acres, and to another, 35.5 acres. How many g,cres 
 had he left ? 
 
 17. If I pay i 1.25 for car fare, |.65 for dinner, and |.90 
 for an umbrella, how much change have I left from a five- 
 dollar bill ? 
 
2U FIFTH YEAR 
 
 18. The second floor of a house is 18.78 feet above the 
 floor of the celhir, and the first floor is 7.92 feet above it. 
 How far is it from the first floor to the second? 
 
 19. Four lots measure in width 128.08 ft. Three of them 
 are respectively 25 ft., 32.72 ft., and 36.9 ft. wide^ What is 
 the width of the fourth ? 
 
 20. A boy having 84.25 spent for skates 81.25, for a caj 
 f .50, and for a hockey stick $.45. How much had he leff^ 
 
 21. A lady having 25.75 pounds of butter sold to one; 
 customer 3.25 pounds, to another 8.5 pounds, to another 
 7.25 pounds, and the balance to a fourth customer. Hc^. 
 many pounds did the fourth customer buy? 
 
 22. From a ham weighing 18.125 lb. a butcher sold 3.25 lb., 
 4.501b., 2.75 lb., and 2.5 lb. How many pounds had he left ? 
 
 23. A fisherman brought home four trout weighing respec- 
 tively 1.25 pounds, .875 pounds, 1.375 pounds, and 1.125 
 pounds. How much less than 5 pounds did they all weigh? 
 
 24. A farmer cut 40 tons of hay in 1905. He sold 6.85 
 tons to one man, and 5.55 tons to another. He fed the rest 
 to his stock. How many tons did he feed to his stock? 
 
 25. A lady bought 4.75 yards of woolen cloth, 11.625 
 yards of cotton cloth, and 6.875 yards of silk. How many 
 yards less than 30 yards did she buy ? 
 
 26. A man having 120 spent 14.75 for board, $2.80 for 
 a room, f .88 for laundry, $1.75 for a pair of gloves, and $3.50 
 for a pair of shoes. How much had he left? 
 
 27. A merchant purchased the following: coffee $15.25, 
 sugar $18.35, cakes $11.65, fruit $27.75, canned corn $8.45, 
 canned peaches $12.30, and vegetables $21.90. How much 
 less than $ 120 was the amount of his bill? 
 
DECIMALS 245 
 
 MULTIPLICATION OF DECIMALS 
 
 Multiplying a decimal by an integer. 
 
 1. X .3 means that .3 is taken as an addend 6 times. 
 Thus, .3 -h .3 + .3 -f .3 + .3 = 15 tenths or 1.5. 
 
 By multiplication 5 x .3 = 1.5. 
 
 2. 5 X .03 means that .03 is taken as an addend 5 times. 
 Thus, .03 + .03 + .03 + .03 + .03 = 15 hundredths or .15. 
 
 By multiplication 5 x .03 = .15. 
 
 3. 5x1.007 means that 1.007 is taken as an addend 5 
 times. Thus, 1.007 4- 1.007+1.007 + 1.007 + 1.007 = 5.035. 
 
 By multiplication 5 x 1.007 = 5.035. 
 
 4. In each problem above, how many decimal places are 
 there in the multiplicand ? how many in the product ? 
 
 Observe that in multiplying a decimal by an integer^ the 
 product contains the same number of decimal places as the 
 multiplicand. 
 
 Written Work 
 1. Multiply 5.75 by 6. 
 
 6x5 hundredths = 30 hundredths, or 3 tenths and 
 
 5.75 no hundredths. Write naught in hundredths' place 
 
 g and carry the 3 tenths. 6x7 tenths = 42 tenths ; 
 
 - 42 tenths + 3 tenths = 45 tenths, or 4 units and 5 
 
 tenths. Write 5 in tenths' place and carry the 4 
 
 units. Place the decimal point. 6x5 units = 30 
 
 units; 30 units + 4 units = 34 units. 
 
 Find products : 
 
 2. 8 X .015 6. 7 X .97 10. 86 x .861 14. 55 x .066 
 
 3. 9 X .005 7. 12 X .025 ii. 74 x .037 15. 39 x .467 
 
 4. 8 X .17 8. 6 X .604 12. 67 x .92 ' 16. 48 x .095 
 
 5. 11 X .207 9. 9 X .054 13. 44 x .705 17. 36 x .081 
 
246 FIFTH YEAR 
 
 18. How mucli will 7 arithmetics cost at 1.82 apiece? 
 
 19. At $ .35 apiece, how much will 24 chickens cost ? 
 
 20. A rod is 16.5 feet. How many feet are there in 9 rods ? 
 
 21. When a man earns f 3.65 per day, how much does he 
 earn in 26 days ? 
 
 22. A pound of cream cheese costs $ .115. How much do 
 126 pounds cost ? 
 
 23. If an automobile averages 17.75 miles an hour, how far 
 will it travel in 14 hours ? 
 
 Multiplying a decimal by a decimal. 
 
 1. Multiply 1.5 by 4. When a decimal is multiplied by 
 an integer, what do you observe about the number of decimal 
 places in the product ? 
 
 2. Multiply .1 by .01 ; ^^ x i^o = loViT = -^^l- ^Mti- 
 ply 1.5 by .5; 1.5= if; ii X -^%=^\= .lb. When a 
 decimal is multiplied by a decimal, what do you observe 
 about the number of decimal places in the product ? 
 
 Written Work 
 
 1. Multiply .75 by .3. 
 
 Since there are two decimal places in the multiplicand and 1 in the 
 multiplier, point off 3 decimal places in the product, making the answer 
 .225. 
 
 • ^^ Test : .75 = xVo, and .3 = ^. ^o\ x ^ = iWu 
 
 »3 or .225, a decimal. 
 
 ^225 
 
 Multiply as in integers^ pointing off as many decimal places 
 in the product as there are decimal places in both factors. 
 
1 
 
 IT 
 
 
 DECIMALS 
 
 
 2 
 
 
 Find products : 
 
 
 
 
 
 2. 
 
 .8X.27 
 
 8. 
 
 7.24 X 8 
 
 14. 
 
 .025x124 
 
 3. 
 
 .5X.45 
 
 9. 
 
 .011 X 42 
 
 15. 
 
 22.5 X 4.04 
 
 4. 
 
 .15 X. 256 
 
 10. 
 
 .57X.15 
 
 16. 
 
 .75 X .624 
 
 5. 
 
 6.5x10 
 
 11. 
 
 2.03 X .4 
 
 17. 
 
 1.44 X 5.5 
 
 6. 
 
 5.7x9.4 
 
 12. 
 
 .145x48 
 
 18. 
 
 2.4 X 64 
 
 7. 
 
 3.21x4.5 
 
 13. 
 
 11.4 X 150 
 
 19. 
 
 1.33 X 44 
 
 24T 
 
 20. Find the cost of 11.5 yards of cloth at 12|^ cents a 
 yard. 
 
 21. Mrs. Crane bought 3.5 pounds of steak at f .16 per 
 pound, 6 pounds of sugar at f .05 per pound, 4 pounds 
 of coffee at i .28 per pound, and 3 quarts of cranberries at 
 $.10 per quart. She gave in payment 3 one-dollar bills. 
 How much change should she receive ? 
 
 22. How much will 41.25 yards of linoleum cost at $1.25 
 per yard ? 
 
 23. A train between Los Angeles and San Francisco runs 
 13.5 hours at the rate of 35.7 miles per hour? What is the 
 distance between the two cities ? 
 
 24. A mail carrier averages 3.25 miles per hour while de- 
 livering mail. If lie spends 5.25 hours delivering each day 
 how far does he walk per day ? 
 
 25. Find the cost of 5.125 yards of silk at $1.75 a yard. 
 At the same price per yard find the cost of 8.875 yards. 
 
 26. At $2.50 per day, how much will 4 men earn in 6.5 
 days ? 
 
 27. A cubic foot of water weighs 62.5 pounds. How 
 much do 12.75 cubic feet of water weigh ? 
 
248 FIFTH YEAR 
 
 DIVISION OF DECIMALS 
 Dividing a decimal by an integer. 
 
 Written Work 
 
 4') 84 
 
 1. Divide .84 by 4 in this way : ^^^ 
 
 Divide and test, placing a decimal point in the quotient 
 before beginning to divide: 
 
 2. 6 )M 5. 7 ). 714 8. 7 ). 847 
 
 3. 3 ). 96 6. 5). 535 9. 6 ). 936 
 
 4. 8 ). 808 7. 4 ). 848 10. 8 ). 896 
 
 11. Explain why adding naughts to the right of a decimal 
 does not change its value ; thus, .8 = .80, .05 = .050. 
 
 It is sometimes necessary to add naughts to the right of 
 the dividend to complete the division. 
 
 12. Divide .12 
 
 by^ 
 
 5. 5).12 = 5).120 
 .024 
 
 
 
 Find the quotients 
 
 and test : 
 
 
 
 
 13. 4). 3 
 
 14. 
 
 8). 6 15. 
 
 61 
 
 ^ 
 
 16. 5). 28 
 
 17. .6^2 
 
 
 25. .024^ 6 
 
 
 33. 
 
 .108^ 3 
 
 18. .9-3 
 
 
 26. .102- 3 
 
 
 34. 
 
 .08 -^ 2 
 
 19. .12-6 
 
 
 27. .039^13 
 
 
 35. 
 
 .125^ 5 
 
 20. .005 -r- 5 
 
 
 28. .144-12 
 
 
 36. 
 
 .16^ 4 
 
 21. .008-^4 
 
 
 29. .015-^ 3 
 
 
 37. 
 
 .35-^ 7 
 
 22. .27 -^ 9 
 
 
 30. .063-^ 7 
 
 
 38. 
 
 .077 -h 11 
 
 23. .2-4 
 
 
 31. .904^ 8 
 
 
 39. 
 
 .022- 2 
 
 24. .24-8 
 
 
 32. .72-10 
 
 
 40. 
 
 .036 -f- 6 
 
DECIMALS 249 
 
 Dividing a mixed decimal by an integer. 
 
 Written Work 
 
 Divide in this way : 
 
 1. 6 )6.648 2. 8)24.600 3. 9 )729.83 
 
 1.108 3.075 81.09| 
 
 Observe that in dividing a decimal or a mixed decimal by 
 an integer, the dividend is simply separated or partitioned 
 into equal parts. 
 
 4. Divide 39.25 by 25. 5. Divide 12.648 by 24. 
 
 1.57 
 
 .527 
 )12.648 
 12 
 64 
 
 48 
 
 168 
 
 168 
 
 
 25)39.25 24; 
 25 
 14.2 
 12.5 
 
 1.75 
 
 1.75 
 
 How many times is 25 contained 
 in 39? in 14.2? in 1.75? 
 
 In practice, we simply divide as 
 in the division of integers. Since 
 24 is larger than 12.648, the quo- 
 tient must be a decimal. 
 
 Place a decimal point directly above or below the decimal 
 point in the dividend, before beginning to divide; then divide 
 as in the division of integers. 
 
 Divide and test : 
 
 
 
 6. 69.92 --23 
 
 14. 
 
 .945 --35 22. 8.437^59 
 
 7. 29.54 --14 
 
 15. 
 
 60.32-52 23. 233.32-38 
 
 8. 195.2-32 
 
 16. 
 
 .968^44 24. 283.88-^47 
 
 9. 401.4-18 
 
 17. 
 
 .828-5-23 25. 6.497-^73 
 
 10. 3.434-34 
 
 18. 
 
 5.18^37 26. 16.150^34 
 
 11. 156.4-46 
 
 19. 
 
 .0833 --49 27. 55.660-92 
 
 12. 1.014-26 
 
 20. 
 
 1.566-^54 28. 5.460^84 
 
 13. 5.084^41 
 
 21. 
 
 2.546 -J- 67 29. 1.6272-18 
 
250 FIFTH YEAR 
 
 30. Divide 12 by 16. 
 12-^-16 = 12.00^16. 
 
 _^ 12 is equal to 12.00, wJiich divided by 16 
 
 16)12.00 equals .75. 
 
 112 ^ decimal point must be placed after an 
 
 oQ integer before naughts are annexed. 
 
 80 
 Divide : 
 
 31. 20 -i- 75 35. 44 -4- 99 39. 605 by 1210 
 
 32. 60^150 36. 110^220 40. 513 by 2052 
 
 33. 24-^228 37. 340 -f- 1700 41. 208 by 1664 
 
 34. 30 -f- 375 38. 510 -i- 1020 42. Ill by 8888 
 
 Dividing any number by a decimal. 
 
 1. In .5, .25, .025 move the decimal point one place to the 
 right and read the result; two places to the right; three 
 places to the right. 
 
 2. In what short way, then, may a decimal be multiplied 
 by 10? by 100? by 1000? 
 
 3. Multiply each of the following numbers first by 10 and 
 read the results. Then by 100. Then by 1000 : 
 
 .2, 2.5, .25, .04, .025, .002, .020, .001, 40.25, 4.05, 200, 21.0, 
 .012, 1.001, 10.1, 400.1, 04.04, 50.0, 4.004. 
 
 Explain why : 
 
 4. .2).24 = 2)2.4 ; .04 ).0164 = 4 )1.64 ; 1. 6)25.6 = 16)256 
 
 5. .6)18 = 6)180; .12 )144 = 12 )14.4 ; .08).48 = 8)48 
 
 6. .09)8.1 = 9)810; .25 )2.25 = 2 5)225 ; .05)5 = 5)500 
 /. Observe that when both the dividend and the divisor 
 
DECIMALS 251 
 
 of ^ are multiplied by 10, thus, i|>^ ^^ = |, the quotient 
 
 remains the same. 
 
 8. Tell the number of places the decimal point must 
 be moved to the right in both dividend and divisor in each 
 of the following problems, in order to make the divisor an 
 integer ; then give quotients : 
 
 9. .5 ). 25 .2 )2.6 4 )4.4 .6)66 8 )8.08 
 
 10. .03). 15 .12). 96 .07). 21 .09). 81 .05). 05 
 
 Written Work 
 
 1. Divide .025 by .0«5. Make the divisor an integer by moving 
 
 Qc-N Qoc 5 ^2 5 *^^ decimal point two places to the right 
 
 ^ = ' fv~r A in both dividend and divisor. Then solve 
 
 ' ' * as in dividing a decimal by an integer. 
 
 A decimal is divided by a decimal hi/ moving the decimal 
 point in both dividend and divisor the number of places to the 
 rif/ht necessary to make the divisor a whole number, and divid- 
 ing as in the division of a decimal by an integer. 
 Divide : 
 
 2.538 by .27 20. .0095 by .19 
 .5655 by .65 21. 20.25 by .45 
 .6150 by .82 22. 6.192 by .72 
 
 27.93 by .57 23. 3.360 by .35 
 
 52.51 by .59 24. 2.016 by .72 
 
 6.216 by .74 25. 826.5 by .95 
 
 .6225 by .75 26. 375.2 by .56 
 
 8.930 by .94 27. 7.728 by .84 
 
 440.8 by .58 28. 8.025 by .25 
 
 2. 
 
 .325 by .5 
 
 11. 
 
 3. 
 
 .756 by .9 
 
 12. 
 
 4. 
 
 6.96 by .8 
 
 13. 
 
 5. 
 
 .444 by .6 
 
 14. 
 
 6. 
 
 .888 by .12 
 
 15. 
 
 7. 
 
 1.445 by .17 
 
 16. 
 
 8. 
 
 2.695 by .35 
 
 17. 
 
 9. 
 
 3.528 by .42 
 
 18. 
 
 10. 
 
 3.034 by .37 
 
 19. 
 
252 
 
 FIFTH YEAR 
 
 Find quotients : 
 
 
 
 29. .005^5 
 
 39. 
 
 40.098-^1.23. 
 
 30. .625^.05 
 
 31. 5.55-^5 
 
 
 
 1.23)40.098 = 123.)4009.?5 
 
 32. 17.28^.12 
 
 40. 
 
 55.968 -i- 1.32 ' 
 
 33. 3.036^.06 
 
 41. 
 
 97.875^2.61 
 
 34. 3.728-?- .016 
 
 42. 
 
 437.836-5.32 
 
 35. .864-^.24 
 
 43. 
 
 214.302-3.82 
 
 36. 3.654-^.21 
 
 44. 
 
 46.695-1.65 
 
 37. 10.044 -.36 
 
 45. 
 
 139.956 H- 3.21 
 
 38. 8.007 ^ .03 
 
 46. 
 
 86.784-^2.26 
 
 REVIEW OF DECIMALS 
 
 1. At f 8.25 per ton, how many tons can be bought for 
 141.25? 
 
 2. From five hundred eighty and sixty-seven ten-thou- 
 sandths take ninety-six and forty-nine tliousandths. 
 
 3. John has .75 of i2 and spends .3 of it. How much 
 does he save ? 
 
 4. If a car conductor earns f 1.75 a day, how long will it 
 take him to earn 1638.75? 
 
 5. If 8.75 tons of coal cost $44.80, how many tons can be 
 bought for $21.76? 
 
 6. If I paid 1720 for land at $37.50 an acre, how many 
 acres did I purchase ? 
 
 7. How many tons are there in 272^ tons, 15.7 tons, 9^ 
 tons, and 33.5 tons? 
 
 8. To the sum of 14.5 and 9.7 add their difference. 
 
 9. What is the value of 7.5 tons of hay at $18.75 per ton? 
 
DECIMALS 253 
 
 10. The distance from Pittsburg to San Francisco is 
 2747.9 miles, and from Pittsburg to Chicago, 507.1 miles. 
 How far is it from Chicago to San Francisco ? 
 
 When possible, express the numbers in the following deci- 
 mally : 
 
 11. A girl sent 27 pieces to a laundry that charged her 
 seventy-five cents a dozen for washing and ironing them. 
 What was her bill ? 
 
 12. Mrs. Rorer mixed 15.5 lb. of fat with 2.25 lb. of potash 
 and made soap which she cut into pieces weighing one eighth 
 of a pound each. How many pieces of soap had she ? 
 
 13. The weight of a diamond before it was cut was 3.875 
 carats. After it was cut, its weight was 2.50 carats. How 
 much was lost in the cutting ? 
 
 14. Each of two pillows weighs 4.75 pounds, and a bolster 
 weighs 7| pounds. Find the weight of all. 
 
 15. At $2|^ a ton, how many tons of ice can be bought for 
 
 $3.75 ? 
 
 16. If I bought 2 gallons of gasoline and used .75 of it to 
 clean a dress, how many quarts did I use ? 
 
 17. A merchant bought 1200 gas fixtures at $.08^ each 
 and sold them at f .10 each. How much did he gain? 
 
 18. A 24 story city building averages 14.75 ft. to a story. 
 How high is the building ? 
 
 19. Find the value of 17,745 bricks at 17.50 per M. 
 
 20. A merchant bought oil at 89.43 per barrel. He sold 
 it at 8 11.48 a barrel, and gained -1451. How many barrels 
 did he have ? 
 
 21. Divide 5 pounds by .005 of a pound. 
 
PERCENTAGE 
 
 In Common Fractions we learned that a number may be 
 divided into any number of equal parts and any number of 
 these may be taken. 
 
 Thus, f of 60 means that 60 is divided into 4 equal parts and 3 of 
 these parts are taken. 
 
 In Decimal Fractions we learned that a number may be 
 divided into 10, 100, 1000, etc., equal parts, and that any 
 number of these parts may be taken. 
 
 Thus, .9 of 60 means that 60 is divided into 10 equal parts and that 9 
 of these equal parts are taken. 
 
 We now come to a subject that divides a number into 100 
 equal parts only. We call this subject Percentage. 
 
 In common fractions we compute by halves^ thirds^ fourths^ 
 sixths^ etc. ; in decimal fractions we compute by tenths, hun- 
 dredths, thousandths, etc. ; but in percentage we compute by 
 hundredths only. 
 
 Another name for hundredths is per cent, usually writ- 
 ten "%." 
 
 We may now write any number of hundredths in three 
 different ways, thus: j^-q, .08, 8% ; -ff^, .25, 25%. 
 
 Percentage is simply an application of decimal fractions. 
 
 1. Write the following numbers as per cents : 
 
 .05 .03 .15 .20 .25 .40 .06 .75 
 
 2. Write the following as decimals: 
 
 5% 20% 7% 15% 25% 16% 18% 24% 50% 75%. 
 
 254 
 
PERCENTAGE 
 
 255 
 
 3. Show by equivalent decimals that naughts added to the 
 riglit of a decimal do not affect its value. 
 
 4. Write as decimals, and as per cents : 
 
 i f sV A iV f I f 
 
 5. What is the difference between .05 of $100 and 5% of 
 
 iioo? 
 
 6. 5 % = 2V ^^ ^ number ; 10 % =-j^ of a number. 
 
 7. 25 % of $100 may be found in two ways : (a) 25 % = J 
 J of $100 = $25. (5) 25% =.25; .25 x $100 = $25. 
 
 Learn the following : 
 
 50 %=J 
 
 m%=i 
 
 75 % = f 
 
 331%= J 
 
 12|%=i 
 
 40 % = | 
 
 25 0/0=1 
 
 10 %=tV 
 
 80 % = t- 
 
 20 %=i 
 
 5 % = 2V 
 
 371% = ! 
 
 Give per cents at sight : 
 
 8. 20% of $50 
 
 9. 25% of $60 
 
 10. 10% of $40 
 
 11. 50% of $80 
 
 12. 40% of $75 
 
 13. 5% of $40 
 
 14. 6% of $6 
 
 15. 75% of $20 
 
 16. 12i% of $72 
 
 17. 331% of 30 days. 
 
 18. 50% of 60 minutes. 
 
 19. 75% of 100 books. 
 
 20. 40% of 20 rods. 
 
 21. 5% of 40 weeks. 
 
 22. 16|% of 100 pounds- 
 
 23. 10% of 70 bushels. 
 
 24. 25% of 24 hours. 
 
 25. 12-1% of 800 bushels. 
 
256 FIFTH YEAR 
 
 Written Work 
 
 1. Find 28% of 7500 bushels of oats. 
 7500 bu. 
 
 OQ 
 
 • " Since percentage is simply so many hundredths of 
 
 60000 anything, 28 o/^ of 7500 bushels equals .28 of 7500 
 
 15000 bushels, or 2100 bushels. 
 :ilOO#bu. 
 
 Find : 
 
 2. 27% of $395 7. 35% of 190.60 12. 75% of 1605 
 
 3. 14% of $478 8. 40% of $20.50 13. 37% of $2005 
 
 4. 24% of $527 9. 10% of $2004 14. 45% of $6745 
 
 5. 6% of $57.40 10. 5% of $200.60 15. 80% of $905 
 
 6. 5% of $90.80 11. 7% of $500.50 16. 98% of $7008 
 
 17. Mr. Jordon bought a horse for $175 and sold it for 
 90% of the cost. For how much did he sell the horse ? 
 
 18. Raymond has $165 in the savings bank and Bertha 
 has 80 % as much. How much more money has Raymond 
 in the bank than Bertha ? 
 
 19. The distance between two cities is 1080 miles. 
 After 45% of the distance is traveled, how much of the 
 distance remains to be traveled? 
 
 20. Mr. Watson earned $1580 in a year, and his son 
 Henry (j5% as much. Find the amount Henry earned. 
 
 21. The salary of a school teacher last year was 
 and this year her salary was increased 25% of last year's 
 salary. Find her present salary. 
 
PERCENTAGE 257 
 
 22. Paul lives 560 rods from the schoolhouse and David 
 72 % as far. Find the number of rods David lives from the 
 schoolhouse. 
 
 23. Mr. Adams borrows $365 for one year, and pays 6% 
 for the use of the money for the time. How much money 
 will pay the debt when due ? 
 
 24. Mr. Brown has loaned 11200 to one party and 81600 
 to another party. How much does Mr. Brown get each year 
 for the use of the money if each party pays him 5 % of the 
 amount borrowed? 
 
 25. Find 5% of 20; of 40 ; of 50; of 60; of 80. 
 
 26. A newsboy sells $18 worth of papers and gets 40% 
 for selling. How much does he earn ? 
 
 27. Mary has $ 24 in the savings bank, and deposits 25 % 
 as much as she has in the bank. Find the amount deposited. 
 
 28. A boy borrows $200 to go to school, and pays the 
 lender 5% for the use of the money for one year. How 
 much does he pay for its use ? 
 
 29. A boy bought a pony and a cart. The pony cost % 80, 
 and the cart 60 % as much as the pony. Find the total cost. 
 
 30. A man had 400 sheep. On Monday he sold 25 % of 
 them. On Tuesday he sold 25 % of the remainder. How 
 many sheep had he then ? 
 
 31. In a spelling test of 30 words, James missed 20%. 
 How many words did he spell correctly? 
 
 32. \ = y^o = ? %. Compare \ and .20 ; \ and 20 %. 
 
 33. A man bought a house for $2800. He paid 78% of 
 the amount cash, and gave his note for the balance. For 
 how much did he give his note ? 
 
 34. A merchant sold in one year $25,375 worth of goods. 
 His profits were 20 % of the sales. Find his profits. 
 
258 FIFTH YEAR 
 
 INTEREST 
 
 1. Mr. James Adams borrows $200 from Mr. John 
 Buchanan for 2 years to send his son to school, and agrees 
 to pay Mr. Buchanan 6 % of the money for the use of it 
 each year. How much does it cost Mr. Adams for the use 
 of the money the first year? How much does it cost Mr. 
 Adams for the use of the money for the 2 years ? 
 
 2. If Mr. Adams settles with Mr. Buchanan at the end of 
 two years, how much in all does he give Mr. Buchanan ? 
 
 Interest is money paid for the use of money. 
 
 The principal is the sum of money on which the interest 
 is paid. 
 
 The rate of interest is a certain number of hundredths of 
 the principal paid for the use of the principal for 1 year. 
 
 The amount is the sura of the principal and the interest. 
 
 In finding interest it is always necessary to know the time. 
 The interest for 2 yr. equals 2 times the interest for 1 yr. ; 
 the interest for 6 mo. equals J the interest for 1 yr. ; the 
 interest for 2 mo. equals J the interest for 1 yr. 
 
 3. In Prob. 1 what is the principal ? the rate of inter- 
 est ? the interest for 1 yr. ? the interest for 2 yr. ? the 
 amount at the end of 2 yr. ? 
 
 How much is the interest at 6 % on: 
 
 4. $ 100 for 11 yr. ? 10. $ 150 for 3 mo. (J yr.) ? 
 
 5. I 200 for 21 yr. ? li. $ 80 for 2 yr. ? 
 
 • 6. I 300 for 11 yr. ? 12. $ 200 for f yr. ? 
 
 7. $250for6mo. (lyr.)? 13. $ 100 for 2^ yr. ? 
 
 8. $400 for If yr.? 14. $900 for 1| yr. ? 
 
 9. $ 800 for 2| yr ? 15. $ 750 for 1 1 yr. ? 
 
INTEREST 
 INTEREST FOR YEARS AND MONTHS 
 
 259 
 
 1. What part of a year are 6 months? 4 months'* 
 3 months ? 2 months ? 1 month ? 
 
 Written Work 
 
 1. What is the interest on $ 200 for 2|- years at 6% ? 
 f 200 principal 
 
 .06 rate 
 
 $ 12.00 interest for one year 
 
 21 
 
 $ 30.00 interest for 2 J years 
 
 The interest for 1 year is .06 
 of the principal, or $ 12. The in- 
 terest for 2| years is 2^ x $ 12, or 
 ^30. 
 
 Multiply the principal hy the rate and the product hy the 
 number of years. 
 
 Find the interest on ; 
 
 2. $200 for 1 year at 5%. 
 
 3. 1 900 for 2 years at 8%. 
 
 4. $150 for 3 years at 6%. 
 
 5. 1 700 for 4 years at 4 % . 
 
 6. $150 for 11 years at 4%. 
 
 7. $96 for 2 years at 8%. 
 
 9. $150 for 41 years at 5%. 
 
 10. $ 190 for 21 years at 6 % . 
 
 11. $ 600 for 2 J years at 4 % . 
 
 12. $950 for 9 mo. at 6%. 
 
 13. $ 940 for 2f years at 7 % . 
 
 14. $650forf year at 6%. 
 
 15. $225for |year at 8%. 
 
 8. $75 for 3| years at 7%. 
 Find the interest and amount at 6 % of : 
 
 16. $200 for 6 months. 19. $620 for 3 mo. 
 
 17. $400 for 4 months. 20. $270 for 8 mo. 
 
 18. $150 for 2 yr. 2 mo. 21. $350 for 9 mo. 
 
 22. Frank loaned Mr. Brown $250 for 2 years and 6 
 months at 6 % interest. How much money will it take to 
 pay the loan ? 
 
OPERATIONS WITH UNITED STATES MONEY 
 
 10 
 
 mills = 
 
 I cent 
 
 10 
 
 cents = 
 
 I dime 
 
 10 
 
 dimes = 
 
 = I dollar 
 
 10 
 
 dollars 
 
 = I eagle 
 
 1. From tlie above table tell why United States money is 
 called a decimal system of money. 
 
 2. How many cents equal a dollar ? What part of a dol- 
 lar is 1 cent ? 
 
 3. A cent is what part of a dime ? A dime is what part 
 of a dollar ? Cents are written as hundredths of a dollar. 
 
 4. Read as hundredths of a dollar : 
 
 $0.01 $0.02 10.03 15.07 $9.09 $8.07. 
 
 Note. — 1 cent may be written either $0.01 or | .01 ; 25 cents may be 
 written either -10.2.5 or $.25, etc. The naught preceding the decimal 
 point does not affect the result, and is sometimes written to show more 
 prominently that cents and not dollars are represented. 
 
 5. How many mills equal $1? What part of a dollar 
 is 1 mill ? Mills are written as thousandths of a dollar. 
 Thus, 1 mill is written $0,001. $0,005 may be read one 
 half cent. Why? 
 
 Mills are not coined, but are used for convenience in computations. 
 In final results any part of a cent is usually regarded by the seller as 
 a whole cent. Thus, for a bill amounting to $0,565, we pay $0.57. 
 
 6. How does moving a number one place to the right affect 
 its value? one place to the left? 
 
 200 
 
OPERATIONS WITH UNITED STATES MONEY 261 
 
 The rules for addition, subtraction, multiplication, and 
 division of decimals apply to United States money since it 
 is a decimal system. 
 
 Written Work* 
 
 I. Find the cost of 27 yards of silk at S 0.87J a yard. 
 
 ^^•^^^ Study of Problem 
 
 ^i~9c !• Why do we change ^^ to 5 mills? 
 
 2. What is the name of the right-hand place in 
 '^"^^ the product ? 
 
 $ 23.625 3. What is the business answer to this problem. 
 
 • Find the cost of : 
 
 2. 4 yd. of lace @ 10.37^. 5. 8 lb. of roast @ llj ^. 
 
 3. 6 bu. of potatoes @ 1 0.62^-. 6. 25 bu. apples @ i \\. 
 
 4. 9 doz. eggs @ 1 0.12|. 7. 36 cords of wood @ -fSf . 
 
 Find the amount of : 
 
 8. 23 yd. of cloth @ 121 ^. 9. 14 cakes of soap @ 21 ^ 
 14 boxes corn starch @ 8 ^. 37 boxes macaroni @12|^. 
 
 31 lb. of raisins @ 30 ^. 14 cans of soup @ 10 ^. 
 
 10. At $ 1.50 each, how many readers can be bought with 
 $6.00? 
 
 150^)600)^(4 times or readers. ^^^^° the divisor contains 
 ^^-. cents, both dividend and divisor 
 may be changed before dividing. 
 
 II. At il.25 each, how many pairs of gloves can be 
 bought for $57.50? 
 
 12. A farmer sold potatoes at 2 bushels for $ 1.50. He 
 received $ 87.50. How many bushels did he sell ? 
 
 * For short methods of performing operations of this kind, see p. 175, 
 
262 
 
 FIFTH YEAR 
 
 13. Walters & Company sold sleds at 65 cents each. 
 They received $ 31.20. How many dozen sleds did tiiey sell ? 
 
 14. Find the cost of boarding for 12 weeks at 17.50 a week. 
 
 15. A merchant bought ^ dozen pairs of shoes at $2.75 
 a pair. How much was paid for all ? 
 
 16. A bookseller sold 56 books at 80.12i each, 37 books 
 at $0.40 each, and 75 books at 10.25 each. How much 
 money did he receive for all ? 
 
 17. At $.02| each, how much will 1 gross of tablets cost ? 
 
 18. A man paid $43.75 for carpet at $1.75 a yard. How 
 many yards did he buy ? 
 
 BILLS 
 
 The following is a common form of hill. 
 
 1 
 
 Boston, Mass., M. fO, 1907. 
 
 iVi'Ui/. fayyv&Qy B'baw-n, 
 
 38fliiigj^t 0f Morris Bros. & Co., 
 
 175 BEACON ST. 
 
 TERMS : Cash. phone 365. 
 
 
 
 /O yd. ^\Utiyv(f @ f0.06\ 
 fO " ^umA @ 0.06-^ 
 20 " €cdUo- @ 0.0 7\ 
 
 f 
 / 
 
 66 
 63 
 
 60 
 
 i 
 
 78 
 
 
 
BILLS 263 
 
 Who sold the goods ? Who purchased the goods ? When 
 and where was the purchase made ? What words show that 
 the bill has been paid ? 
 
 The words "Received payment, Morris Bros. & Co.," 
 are called the receipt of the bill. Who received the money ? 
 When a clerk receives payment for a bill, he always writes 
 the receipt of the firm, per his own name or initials. The 
 receipted bill should be kept by the buyer to show that the 
 bill has been paid. 
 
 Every bill should show : (a) the place and date of purchase; 
 (6) fhe names of the buyer and the seller; (<?) the quantity^ 
 the price, and the cost of each item, and the amount of the 
 bill. 
 
 1. Mrs. James Robinson, on a certain day, buys from 
 Morris Bros. & Co., 12 cans of Acme corn @ ^0.12J, 18 
 pounds sugar for $ 1.00, 3 pecks potatoes @ $0,25. 
 
 Make out the receipted bill. 
 
 Make out receipted bills for the following sales, using your 
 father's name as buyer, and the name of your local merchant 
 as seller : 
 
 2. 3|- lb. rice @ $ 0.08. 3. 12 yd. muslin @$0.09. 
 10 lb. prunes @ 0.121 lo yd. lace @ 0.12J. 
 
 2 bags salt @ 0.10. 2 pair socks @ 0.35. 
 
 4. William Thomas bought of J. A. Crawford & Co., New 
 Castle, Pa., Oct. 10, 1905, 15 lb. butter at 28^ per lb. ; 10 doz. 
 eggs at 24^ per doz.; 35 lb. lima beans at 11^ per lb. 
 Make out receipted bill, representing yourself as clerk. 
 
 5. Mrs. J. M. Rowe bought of Johnston & Son, Buffalo, 
 N.Y., Dec. 22, 1905, 2 dressed turkeys weighing 12J lb. and 
 13 lb. respectively, at 22^ per lb. ; 5 lb. of lamb chops at 
 Idff per lb. Clerk, James Brown. 
 
264 
 
 FIFTH YEAR 
 
 6. W. M. Hays & Son, Baltimore, Md., dealers in general 
 merchandise, sold to Frank N. Clark, Jan. 12, 1905, the fol- 
 lowing bill of goods : 
 
 7| lb. butter @ 24/ ; 6 lb. cheese @ 11 J /; 14 yd. calico @ 
 7^/; 1 can lard, weighing 8| lb., @ 12/. 
 
 Supposing that you are the clerk and some neighbor is the 
 buyer, make out receipted bills for the following purchases 
 at your local stores : 
 
 7. 81 lb. lard @ lO/; 6 cans corned beef @ 15/; 81 lb. 
 ham @ 14|/; 8 lb. sausage @ 12i/. 
 
 8. 3 hassocks @ 98/; 6 chairs @ f 1.25; 12 yd. carpet @ 
 $1.10; 2 rockers® -12.90; 1 lamp @ f 1.65. 
 
 9. 1 saw @ 75/; 3 gas heaters @ 14.90; 3J doz. screws 
 @ 12/; lOi lb. lawn seed @ 20/; 8 joints stove pipe @ 
 30/; 2 elbows @ 40/. 
 
 Another form of bill is commonly used when services have 
 been rendered, as well as material furnished. For example : 
 
 Akron, Ohio, June 1, 1907. 
 3^a R. la. f(yyvtc., h^. 
 
 
 
 a (A. cAalU @ 0.06 
 R. la. fa^&a.. 
 
 f9 
 / 
 
 00 
 60 
 ¥■8 
 
 10 
 
 98 
 
 
 
 
BILLS 265 
 
 The creditor is the person who sells the goods or does the 
 work. 
 
 The debtor is the person who buys the goods or for whom 
 the work is done. 
 
 In the bill on p. 98 Mrs. Brown is debtor to Morris Bros., 
 since she owes for the goods purchased, and Morris Bros, are 
 tlie creditors, since they furnished the goods. In the last 
 bill on p. 264 Mr. Burroughs is the debtoj' for work received, 
 and Mr. Jones is the creditor for work he has done. 
 
 1. T. S. Ball owes Dr. S. N. Pool, Lloyd Building, Pitts- 
 burg, Pa., for services as follows : Jan. 1, 1907, to 1 call, $2 ; 
 Jan. 12, 1907, to 1 call, $2; Jan. 14, 1907, office, $1; 
 Jan. 16, 1907, to 1 call, 82. Make out and receipt the 
 bill if paid Feb. 1, 1907. 
 
 2. Boydson & Co. owe Charles Frampton, Detroit, Mich., 
 for services as follows : 
 
 March 10, 1907, 6 hr. delivering goods @ f 0.20 
 
 March 11, 1907, trip to country 2.00 
 
 March 12, 1907, " " " 2.00 
 
 March 13, 1907, " " " 2.00 
 
 March 14, 1907, repairs to wagon 3.75 
 
 Write the receipted bill of Boydson & Co., if paid April 
 1, 1907. 
 
 3. James Brown owes Stamm Bros, for labor and materia] 
 as follows: June 1, 1907, 189 ft. lumber at 8^ per foot; 
 June 4, 1907, 50 lb. cement at 4^ per pound ; June 8, 1907, 
 15 days labor at 84.50 per day. 
 
 Receipt this bill if paid July 1, 1907. 
 
DENOMINATE NUMBERS 
 Liquid Measures 
 
 A gallon, a quart, and a pint measure should be brought into 
 Pupils should measure, and thus learn the relative capacities. 
 
 Liquid measures are used iu measuring liquids. 
 
 2 pints 
 
 = 1 quart (qt.) 
 
 4 quarts 
 
 = 1 gallon (gal.) 
 
 311 gallons 
 
 = 1 barrel (bbl.) 
 
 63 gallons 
 
 = 1 hogshead (hhd.) 
 
 1 gallon 
 
 = 231 cubic inches 
 
 1 gal. = 4 qt. 
 
 = 8pt.=32gi. 
 
 1. How many pints equal a gallon ? a half gallon ? 
 
 2. How man}' quarts equal 16 pints ? 24 pints ? 36 pints ? 
 
 3. How many gallons equal 28 quarts ? 12 qt. ? 32 qt. ? 
 
 266 
 
4 gal. = 4 X 8 pt. 
 2 qt. =2x2 pt. 
 1 pt. 
 
 = 32 pt. 
 = 4pt. 
 = 1 pt. 
 
 4 gal. 2 qt. 1 pt. 
 Change : 
 
 = 37 pt. 
 
 DENOMINATE NUMBERS 267 
 
 Written Work 
 
 1. Change 4 gal. 2 qt. 1 pt. to pints. 
 
 Since there are 8 pints in 1 gal- 
 lon, in 4 gallons there are 4 times 
 8 pints or 32 pints. Since there are 
 2 pints in 1 quart, in 2 quarts there 
 are 2 times 2 pints, or 4 pints. 32 
 pints -f 4 pt. + 1 pt. = 37 pt. Hence, 
 4 gal. 2 qt. 1 pt. = 37 pt. 
 
 2. 6 gal. 1 pt. to pints. 4. 4 gal. 3 qt. to pints. 
 
 3. 8 gal. 1 qt. 1 pt. to pints. 5. 5 gal. 2 qt. 1 pt. to pints. 
 
 6. Change J gal. to pints. 
 
 7. Mary bought S^ gallons of cream at 10^ a pint. How 
 much did it cost her ? 
 
 8. A grocer sold 6^ gallons of vinegar at 8 ^ a pint. How 
 much did he receive for it ? 
 
 9. Change 127 pt. to gallons, etc. 
 
 OM 07 f • + Since 2 pints = 1 quart, there 
 
 J)1J7, no. ot pints. ^ill ^^ ^ ^g ^^^^ ^^^^^^ ^^ p. ^^^ . ^j^^^ 
 
 4)63, no. of qt. -f 1 pt. is, 63 qt. + 1 pt. Since 4 quarts = 
 
 15, no. of gal. + 3 qt. 1 gallon, there will be ^ as many 
 
 127 pt. = 15 gal. 3 qt. 1 pt. ^^^^^""^ ^' "^""^^^^ ' *^^^ '^ ^^ ^^^' + 
 
 3 qt. 
 
 Note. — The numbers in the operation must be regarded as abstract. 
 Do not say 127 pints -^ 2 = 63 quarts -\- 1 pint. It is evident that 127 
 pints -^ 2 would equal 63^ pints. 
 
 Change : 
 
 10. 375 pt. to quarts, etc. 14. 469 qt. to gallons, etc. 
 
 11. 846 pt. to quarts, etc. 15. 875 qt. to pints. 
 
 12. 278 pt. to gallons, etc. 16. 13 gal. to quarts. 
 
 13. 675 pt. to gallons, etc. 17. 144 gal. to pints. 
 
268 
 
 FIFTH YEAR 
 
 Dry Measures 
 
 
 Dry measures are used in measuring grain, fruit, roots, and 
 other dry articles. Name five articles sold bv the bushel. 
 
 2 pints (pt.) 
 
 = 1 quart (qt.) 
 
 8 quarts 
 
 = 1 peck (pk.) 
 
 4 pecks 
 
 = 1 bushel (bu.) 
 
 1 bushel 
 
 = 2150.42 cubic inches 
 
 1 bu. = 4 pk. 
 
 = 32 qt. = 64 pt. 
 
 1. Find, by measuring, how many pecks equal a bushel. 
 
 2. How many quarts will fill a peck measure ? 
 
 3. How many quarts will fill a bushel measure? 
 
 4. How many bushels do 16 pecks equal? 64 quarts? 
 
 Written Work 
 Change : 
 
 1. 3 bu. 2 pk. 6 qt. to pints. 4. ^b pk. to bushels. 
 
 2. 96 pt. to bushels. 5. 8 bu. 3 pk. 1 pt. to pints. 
 
 3. 1200 qt. to bushels. 6. 1500 pt. to bushels. 
 
DENOMINATE NUMBERS 
 
 269 
 
 Avoirdupois Weight 
 
 The teacher should secure a scale and weights, and have pupils weigh 
 articles of different kinds. 
 
 Avoirdupois weight is used in weighing heavy articles ; 
 as, groceries, coal, grain, and metals, except gold and silver. 
 
 16 ounces (oz.) 
 
 
 = 1 pound (lb.) 
 
 100 pounds 
 
 
 = 1 hundredweight (cwt.) 
 
 20 hundredweight 
 2000 pounds 
 
 
 = lton(T.) 
 
 2240 lb. 
 
 
 = 1 long ton 
 
 1 T. = 20 cwt. 
 
 
 = 2000 lb = .32,000 oz. 
 
 The long ton is used at the United States custom houses, and in 
 wholesale transactions in coal and iron. 
 
 The avoirdupois pound contains 7000 grains, and the avoirdupois 
 ounce, 437| grains. 
 
 The unit of avoirdupois weight is the pound. 
 
 1. Name several kinds of articles sold by the pound; by 
 the ton. 
 
 2. How many tons equal 6000 pounds? 24,000 pounds? 
 
 3. Find the cost of 2^ tons of hay at 1 14 a ton. 
 
270 
 
 FIFTH YEAR 
 
 Change : 
 
 1. G lb. 5 oz. to ounces. 
 
 2. 3 T. 8 cwt. to pounds. 
 
 3. 4 cwt. 3 lb. to ounces. 
 
 4. 5|- cwt. to ounces. 
 
 5. 3600 lb. to cwt. 
 
 Written Work 
 
 6. 2 T. 5 lb. to ounces. 
 
 7. 544 oz. to pounds. 
 
 8. 6000 lb. to tons. 
 
 9. 128 oz. to pounds. 
 10. 810 oz. to lb. and oz. 
 
 Time Measures 
 
 Time measure is used in measuring time. There ^ are two 
 standard units of time, the day and the year. 
 
 60 seconds (sec.) 
 
 = 1 minute (min.) 
 
 60 minutes 
 
 = 1 hour (hr.) 
 
 24 hours 
 
 = 1 day (da.) 
 
 7 days 
 
 = 1 week (wk.) 
 
 1 year = 12 mo. 
 
 = 365 or 366 days = 
 
 52 wk. 1 da 
 
 L. or 52 wk. 2 da. 
 
DENOMINATE NUMBERS 271 
 
 1. How many hours is it from midnight on Tuesday to 
 midnight on Wednesday? 
 
 2. At what time does the new day begin? 
 
 3. How many times in a day does the hour hand pass 
 around the face of the clock? 
 
 4. What part of an hour are 10 minutes? 45 min.? 
 
 5. What part of a minute are 15 seconds? 30 sec? 
 
 6. What do you mean by A.M. ? by p.m. ? by M. ? 
 
 7. Read the time on each of the clocks in the picture. 
 
 8. A man leaves home at 6:30 A.M. and returns at 
 5:45 P.M. How long is he away from home? 
 
 9. A train leaves the station at 11:10. It requires 25 
 minutes to reach the station. At what time must one leave 
 home in order to catch this train? 
 
 10. Harry leaves for school at 8:30, and reaches school 
 at 3 minutes before 9 o'clock. How long is he on the way? 
 
 11. The morning session of school begins at 9 A.M. and 
 closes at 11:30 a.m. The afternoon session begins at 1 P.M. 
 and closes at 3:45 p.m. How long are both sessions? 
 
 12. How many months have 31 days each? 30 days each? 
 28 days? When has February 29 days? 
 
 Written Work 
 
 Change: 
 
 1. 3 hr. 6 min. to seconds. 5. 12 wk. 6 da. to hours. 
 
 2. 144,000 sec. to days. 6. 336 hr. to weeks. 
 
 3. 5 da. 3 hr. to minutes. 7. 5760 min. to days. 
 
 4. 108 mo. to days. 8. 30 days to seconds. 
 
 9. If the school is in session 5J hours, how many seconds 
 is it in session? 
 
272 
 
 FIFTH YEAR 
 
 10. At $1J a day, how much will a boy earn in 14 days? 
 
 11. If a motorman receives 20 ^ an hour, what is his pay 
 for 6 days of 9 hours each? 
 
 12. A clerk pays f 4.50 a week for board. How much will 
 his board cost him for September, October, and November ? 
 
 13. At the rate of f | a day, how much can a boy earn 
 during the month of February? 
 
 Distance 
 
 The teacher should bring into the class a yard stick and a 50-foot 
 measuring line. Each pupil should be provided with a 12-inch ruler, 
 with inches and half inches clearly marked. 
 
 Linear measure is used in measuring lines and distances. 
 
 12 inches (in.) 
 3 feet 
 
 5| yards | 
 lel feet J 
 320 rods 
 
 = 1 foot (ft.) 
 = 1 jkrd (yd.) 
 
 = 1 rod (rd.) 
 
 = 1 mile (mi.) 
 
 1 mi. = 320 rd. = 1760 yd. =5280 ft. 
 
DENOMINATE NUMBERS 
 
 273 
 
 1. Measure the length of a book ; of a desk ; of a table. 
 
 2. Measure the yard stick with the ruler. How many- 
 feet equal a yard? A foot is what part of a yard? 
 
 3. With the measuring line mark off 16| ft., or 1 rod, on. 
 the blackboard. 
 
 4. How many yards are there in 16J ft. ? in 320 rd. ? 
 
 Change : 
 
 1. 33 ft. to inches. 
 
 2. 12 yd. to feet. 
 
 3. 28 rd. to yards. 
 
 4. J mi. to inches. 
 
 Written Work 
 
 5. 3 yd. 2 ft. 6 in. to inches. 
 
 6. 4 rd. 3 yd. 1 ft. to fest. 
 
 7. 1728 in. to yards. 
 
 8. 198 in. to rods. 
 
 Miscellaneous Measures 
 
 There are 12 dozen in a gross. 
 
 1. How much will 1 gross buttons cost at 15^ a dozen? 
 
 2. A stationer bought 12 quires of paper for f 1.20 and 
 sold it at a cent a sheet. How much did he gain? 
 
 3. Find the cost of 40 lemons at 15 ^ a dozen. 
 
274 FIFTH YEAR 
 
 REVIEW 
 
 1. A bicycle wheel is 7 feet 4 inches in circumference. 
 How many turns will it make in going 6 miles ? 
 
 2. How much will 3J bushels of plums cost at 9 ^ a quart ? 
 
 3. How much fence will be needed to inclose a square 
 field, each side of which is 22 rods ? 
 
 4. If 9 boxes weigh 27 pounds, how mucb will 36 boxes 
 weisfh ? How mucli will 3 boxes weis'h? 
 
 5. George has a can of milk containing 10 gallons. If he 
 sells 10 quarts to his first customer, 4 quarts to the second 
 customer, 3 gallons to the third customer, and 2 gallons 
 1 pint to the fourth, how much has he left in the can ? 
 
 6. How much are 5 J miles of telegraph wire worth at 
 to. 005 afoot? 
 
 7. Our grocer found that 9 hams weighed 82| pounds. 
 What was the average weight ? 
 
 8. How much must be paid for 15 gross of lead pencils 
 at 35 ^ a dozen ? 
 
 9. Walter picked 4| bushels of blackberries and sold 
 them to a grocer for 6 ^ a quart. He took in exchange eggs 
 at 24 ^ a dozen. How many dozen did he receive ? 
 
 10. A butcher sold 30^ pounds of lard at »! 0.12 a pound, 
 and purchased with the money flour at $0.03 per pound. 
 How much flour did he buy ? 
 
 11. 500 bushels of peaches were packed in baskets, each 
 holding 2 pecks. How many baskets were needed ? 
 
 12. 20 hundredweight of starch was packed into boxes, 
 each containing 5 pounds. How much was received, if each 
 box was sold for 6^ ^ ? 
 
DENOMINATE NUMBERS 275 
 
 13. Count the change from a five-dollar bill for 8 pounds 
 of steak at 18^ a pound, 3 cans of tomatoes at 9B^ a dozen, 
 and 2 gallons of gasoline at 15^ a gallon. 
 
 14. What is my January milk bill, if I use 5 pints every 
 day, at 8 ^ a quart ? 
 
 15. If f of a ton of coal costs 13.75, how much will 3 J 
 tons cost ? 
 
 16. How many pint cans can be filled from 26 gallons of 
 tomato soup ? 
 
 17. The Bell Telephone Co. charges me $40 a year for 
 600 calls. How much is that per month ? how much for 
 each of the calls ? 
 
 18. Find the amount of the following sales: 
 1 dozen boxes of cocoa at 15 ^ a box, 
 
 8 cans of tomatoes at $ 1 a dozen, 
 
 3 boxes of figs at 8 3 a dozen, 
 
 11 J pounds turkey at 22 ^ a pound. 
 
 19. Five girls weigh 75 pounds, 86 pounds, 93 pounds, 
 69' pounds, and 72 pounds respectively. What is their 
 average weight ? 
 
 20. There are 20 quires in a ream. At $1.20 a ream, find 
 the cost of 3 reams, 3 quires of paper. 
 
 21. How old is a man who is threescore years and ten ? 
 
 22. The Adams Coal Company sold 8 loads of coal as fol- 
 lows : 2470 lb., 3680 lb., 1974 lb., 2985 lb., 1741 lb., 3161 lb., 
 3749 lb., and 4278 lb. Find the number of tons, hundred 
 weight, and pounds sold. 
 
PRACTICAL MEASUREMENTS 
 
 LENGTHS AND SURFACES 
 
 Lines that meet, making a square corner, form a right 
 angle. 
 
 A figure that has four straight sides and four right angles 
 is called a rectangle. 
 
 A rectangle having its four sides equal is called a square. 
 
 Rectangles that are not squares are sometimes called oblongs. 
 
 144 
 
 sq. 
 
 in. 
 
 = 1 
 
 sq. 
 
 ft. 
 
 9 
 
 sq. 
 
 ft. 
 
 = 1 
 
 sq. 
 
 yd. 
 
 4 in. 
 
 The perimeter is the distance around a surface. 
 
 What is meant by drawing a surface on a scale ot 
 1 inch to 2 feet ? On what scale is this surface drawn ? 
 
 What is the unit -of 
 measure ? How many 
 units are there in the 
 
 C WM^I^ ^^^^ ^^^ ^^ squares ? in 
 
 cvj the second? How many 
 
 square inches are there 
 in the rectangle, or what 
 is its area ? 
 
 H 
 
 
 
 
 
 
 
 
 2x4x1 
 
 8 sq. in., area. 
 
 The area of a rectangle is a number of square units equal to 
 the product of its two dimensions when expressed in like units. 
 
 Thus, if the dimensions of a rectangle are 2 inches and 4 inches, the 
 area is 8 square inches; if the dimensions are 2 feet and 4 feet, the area 
 is 8 square feet. 
 
 276 
 
PKACTICAL MEASUREMENTS 277 
 
 Written Work 
 
 1. If a pane of glass is 10 inches by 12 inches, how many- 
 square inches does it contain ? 
 
 2. How many square feet of glass equal 32 such panes ? 
 
 3. A garden is 73 feet by 50 feet. How many square 
 feet does it contain ? 
 
 4. The page of a book is 1\ inches by 5 inches. How 
 many square inches are there on the page ? 
 
 5. How many square inches are there in a page of your 
 book? 
 
 6. Measure the blackboard in your schoolroom and find 
 how many square feet it contains. 
 
 Note. — Reduce inches to the fraction of a foot; as, 8 ft. 6 in. 
 
 = 8^ ft. 
 
 7. How many square inches are there in the surface of 
 your schoolroom door ? 
 
 8. At i 1^ per square yard, how much will it cost to 
 cover a floor 12 feet by 15 feet with linoleum ? 
 
 9. A plate glass window is 9 feet 8 inches wide and 12 
 feet 3 inches long. How much will such a window cost at 
 f 0.36 per square foot? 
 
 10. Brussels carpet is 2i feet wide. How many square feet 
 are there in a yard of it ? 
 
 11. A room is 16 feet long and 14 feet wide. How much 
 will it cost to paint the ceiling of this room at 12 ^ per square 
 yard? 
 
 12. Which is the larger, a surface 26 in. long and 5 in. 
 wide or a surface 20 in. long and 12 in. wide ? 
 
 13. At 15^ per square foot, how much does a sidewalk 
 50 feet long and 5 feet wide cost ? 
 
278 FIFTH YEAR 
 
 14. At 12 ^ per square foot, how mucli will it cost to 
 cement the floor of a cellar 28 ft. 4 in. by 22 ft. 6 in. ? 
 
 15. At 81.05 per square yard, how much will it cost to 
 pave the street in front of a 50-foot lot, the street being 33 
 feet wide between the curbs ? 
 
 16. Compare a square 1 inch on a side with a square 2 
 inches on a side. Prove your work by drawing the required 
 squares and dividing tliem into square inches. 
 
 17. Compare a rectangle 2 inches by 8 inches with a rec- 
 tangle 4 inches by 16 inches. 
 
 18. Show that a square 4 inches on a side is 16 times as 
 large as a square 1 inch on a side. 
 
 19. Name and draw the figures you have learned in which 
 all the angles are right angles. 
 
 20. What other name is sometimes given to a rectangle ? 
 Is a square a rectangle ? When is a rectangle not a square ? 
 Draw figure to illustrate. 
 
 21. Name the different measures of length. 
 
 22. Lines have what dimensions ? Surfaces have what 
 dimensions ? Illustrate each. 
 
 VOLUME 
 
 1. What is the length of the 
 figure? the width? the height? 
 
 2. How many dimensions 
 has it ? 
 
 3. How many sides or faces 
 has it ? 
 
 4. Show that each side is a 
 square. 
 
PRACTICAL MEASUREMENTS 
 
 279 
 
 5. How many square surfaces has it ? 
 
 A solid with six equal squal-e surfaces is a cube. 
 
 6. Look at the figure and tell how many edges it has. 
 What is the length of each edge ? 
 
 A cube whose edge is 1 inch is called a cubic inch. 
 
 7. Draw on paper or on the blackboard a square foot. 
 
 8. Divide each side into 12 equal parts and connect them 
 by straight lines. 
 
 9. How many square inches equal a square foot ? 
 
 10. The base of a 1-inch cube has how many square inches ? 
 
 11. 144 cubes 1 inch on an edge can be placed on a sur- 
 face of 1 square foot thus : 
 
 ift. 
 
 ((((((((\(c 
 
 12. What is the height of 12 such layers of cubes ? How 
 many cubic inches are there in the first layer ? in 12 layers ? 
 
 13. How many cubic inches can be placed in the cube ? 
 
 1728 cubic inches (cu. in.)= 1 cubic foot (cu. ft.) 
 
280 
 
 FIFTH YEAR 
 
 SURFACES AND VOLUMES 
 
 3 ft. 
 
 1. How many feet on an edge is the cube in the figure 
 above ? 
 
 2. How many cubes 1 foot on an edge are there in the 
 first layer ? 
 
 3. How many cubes 1 foot on an edge are there in the 
 3 layers? 
 
 27 cu. ft. = 1 cubic yard (cu. yd.) 
 A cart load of earth = 1 cu. yd. 
 
 The contents, or volume, of any body that has six rectangular 
 surfaces is a number of cubic units equal to the product of its 
 three dimensions when expressed in like units. 
 
 4. A schoolroom is 30 ft. wide, 40 ft. long, and 16 ft. 
 high. Find the number of cubic feet of air in it. 
 
 5. Find the number of cubic yards of air in the room. 
 
 6. A piece of timber is 1 ft. square at the end and 12 ft. 
 long. How many cubic feet are there in it ? 
 
PRACTICAL MEASUREMENTS 
 
 281 
 
 7. How many l-in. cubes are necessary to make a rec- 
 tangular solid 12 in. long, 8 in. wide, and 4 in. high ? 
 
 8. A box is 4 ft. long, 2 ft. wide, and 2 ft. high. Find 
 the number of square feet in its six surfaces. 
 
 9. Find the number of cubic inches in the box. 
 
 10. A bin for grain is 12 ft. long, 8 ft. wide, and 5 ft. deep. 
 Find the number of cubic feet in it. 
 
 11. If there are 2150.42 cu. in. in a bushel of wheat, find 
 the number of bushels of wheat the bin will hold. 
 
 12. A water tank is 8 ft. long, 4 ft. wide, and 3 ft. deep. 
 If a cubic foot of water weighs 62| lb., find the weight of the 
 water when the tank is full. 
 
 13. A stone wall is 4ft ft. long, 4 ft. high, and 2 ft. thick. 
 Find the number of cubic feet of stone in it. 
 
 14. Measure the dimensions 
 of your schoolroom and find the 
 number of cubic feet of air in it. 
 
 15. A rectangular solid is 
 1 ft. square and 4 ft. long. Find 
 the surface of its six faces. 
 
 16. Cut from cardboard a 
 surface as shown in the draw- 
 ing. Fold along the dotted 
 lines into a box; find the sur- 
 face of the six faces and the 
 contents of the box in cubic 
 inches. 
 
 17. Measure the walls and ceiling of your schoolroom and 
 find the cost of plastering them at 27 cents per square yard. 
 
 18. Cut from cardboard a diagram to show a rectangular 
 box 18 in. long, 12 in. wide, and 8 in. deep. 
 
 
 lin. 
 
 
 
 
 
 
 • 
 
 
 
 
 
 
 
282 
 
 FIFTH YEAR 
 
 How many cubic 
 How many cubic 
 How many cubic 
 
 19. Find the number of cubic inches in the box/ 
 
 20. Measure the surface of your schoolroom floor, and 
 find the cost of oiling it at 12 cents per square yard. 
 
 21. What is the difference in cubic feet between 9 cubic 
 feet and a cube 3 feet on an edge ? 
 
 To THE Teacher. — Get, if possible, 141 cubical blocks 1 inch on an 
 3dge. 
 
 22. Build a cube 3 blocks on an edge. 
 Inches are there in the cube ? 
 
 23. Build a cube 4 blocks on an edge, 
 inches are there in the cube ? 
 
 24. Build a cube 2 blocks on an edge, 
 inches are there in the cube ? 
 
 25. The cube 4 blocks on an edge is how many times the 
 cube 2 blocks on an edge ? 
 
 26. Build a rectangular solid as 
 shown in the figure. How many 
 cubic inches are there in the solid ? 
 
 27. Show that the solid in problem 
 24 has 6 rectangular surfaces. Find 
 the surface of each rectangle. 
 
 28. Build a cube 5 inches on an edge. How many more 
 than 100 cubes are needed ? 
 
 29. Find the cost, at 30 cents a cart load (1 cubic yard), 
 for excavating the ground for a cellar 30 ft. in length, 20 ft. 
 in width, and 4 ft. in depth. 
 
 30. A laborer digs a ditch 100 ft. long, 18 in. wide, 
 and 2J ft. deep in 1 day. Find the number of cart loads of 
 3arth removed, and the cost at 30 cents a load. 
 
 3 in. 
 
GENERAL REVIEW 
 
 1. A clerk bought a gross of penholders for 80 cents and 
 sold them at 2 cents each. How much did he gam ? 
 
 2. I paid $3.65 for groceries, $1.75 for dry goods, and 
 87 cents for sundries. What was the cost of all ? 
 
 3. Write one hundred two thousand, seven hundred. 
 
 4. Find the cost of 30 gross of writing tablets at 37J cents 
 a dozen. 
 
 5. If 11| is subtracted from a certain number 1^ will 
 remain. What is the number ? 
 
 6. A merchant pays 6|^ a yard for muslin and sells it 
 for 7^^ a yard. What is his gain on 24 yards ? 
 
 7. I can make 3 aprons in 6 hours. How many aprons 
 can I make in 12 hours ? 
 
 8. Write in words 4006.015. 
 
 9. A man bought J of a farm containing 800 acres and 
 sold .25 of his share. How many acres had he left ? 
 
 10. If 8 loads of hay cost $80, what is the cost of 24 loads ? 
 
 11. Change 12 gallons, 2 quarts, 1 pint, to pints. 
 
 12. Robert rides 14.75 miles north on his pony, and his 
 brother James rides 20.25 miles south. How far apart are 
 they at the end of the ride ? 
 
 13. At Home's sale a customer bought three remnants of 
 silk, containing respectively 16 J yd., 12 yd., and 9^ yd. 
 How many yards of silk did the customer buy ? 
 
 283 
 
284 FIFTH YEAR 
 
 14. There are 5280 feet in a mile. How many feet is it 
 from Albany to New York, a distance of 143 miles ? 
 
 15. 6 is y^2 of what number ? 
 
 16. At 150 a month rent, what is the income to the owner 
 on 24 houses for 12 months ? 
 
 17. At 95 cents per square yard, how much will it cost to 
 cement the floor of a cellar 10 yards long and 6 j^ards wide ? 
 
 18. Find the cost of 144 lb. of raisins at 8|^ a pouncj^. 
 
 19. Add 8 bu. 1 pk. 3 qt. 
 
 4 bu. 3 pk. 2 qt. 
 2 bu. 1 pk. 5 qt. 
 
 20. Find the interest on a loan of $ 250 made for 2 years 
 and 9 months at 6 % . 
 
 21. Explain why it is wrong to say 12 times 325 yards. 
 
 22. How many feet of picture molding will be required 
 for a room 18 ft. long and 12 ft. wide? At 6^/ a foot, how 
 much will it cost ? 
 
 23. Change |, |, and -j^ to 24ths. 
 
 24. Add |, |, J, and ^^, 
 
 25. Add by 3's to 64. 
 
 26. 32 x9| yards = ? 
 
 27. Change 8 square rods to a fraction of an acre ; to a 
 
 decimal of an acre. 
 
 28. Each of 8 boxes holds 5 pounds, 4 ounces of meal. 
 How much do all the boxes hold ? 
 
 29. What is the cost of 8 barrels of vinegar, averaging 41 
 gallons 3 quarts per barrel, at 18^ a gallon? 
 
 30. In a warehouse there are 15 pillars 2 ft. by 18 in., and 
 20 ft. high. How many cubic feet are there in the pillars ? 
 
GENERAL REVIEW 285 
 
 31. How much will it cost, at 27^ a square yard, to paint 
 a floor that is 18 ft. long and 16 ft. wide ? 
 
 32. In the first column find the number of yards ; in the 
 second, the number of gallons ; and in the third, the number 
 of bushels. 
 
 Cost 
 
 Price 
 
 Cost 
 
 Price 
 
 Cost 
 
 Price 
 
 
 per yd. 
 
 
 per gal. 
 
 
 per bu. 
 
 $3.20 
 
 6i^ 
 
 $45.00 
 
 62-J^ 
 
 $9.00 
 
 75^ 
 
 $6.72 
 
 12J^ 
 
 $36.60 
 
 16f/ 
 
 $15.00 
 
 m^ 
 
 $8.40 
 
 20^ 
 
 $40.50 
 
 m 
 
 $21.75 
 
 37 J/ 
 
 33. Charles spent at a sale 5 half dollars, 6 quarters, 3 
 dimes, 4 nickels, and 3 pennies. How much did he spend in 
 all? 
 
 34. A motorman worked 8 J hours one day, and 10|- hours 
 another day. At 24^ an hour, how much did he receive for 
 the two days' work ? 
 
 35. If 12 T. of hay cost $144, how much will 24 T. cost ? 
 
 36. How many pounds of sugar, at $0.06 a pound, can be 
 exchanged for 9 pounds of butter at $0.32 a pound, and 12 
 dozen eggs at $0.18 a dozen ? 
 
 37. William works 6| hours on each of 36 Saturdays. 
 Find the amount earned at 12 ^ per hour. 
 
 38. John earned $350 and loaned it for 1 yr. and 8 mo. at 
 5 % interest. What was the amount when due ? 
 
 39. If it takes 16 J yards to make a dress, how many yards 
 will it take to make 12 dresses? 
 
 40. How much will 128 clocks cost if 8 clocks cost $104? 
 
 41. A lady sold some butter at $0.32 a pound and with 
 the sum received bought 16 yards of cloth at 90^ a yard, 4 
 hats at $3 each, 4 ties at 24^ each, and 4 pairs of gloves 
 at 55^ each. How many pounds of butter did she sell? 
 
^86 ■ FIFIH YEAR 
 
 42. A father having 8105.06 gave 197.08 to his son. If 
 he divided the remaining amount equally between his two 
 daughters, how much did each receive ? 
 
 43. Find the cost of 81.25 acres of land at $46.75 an acre. 
 
 44. At $0,525 per bushel, how much corn can be bought 
 for 152.50? 
 
 45. A dressmaker had 40 yd. of cloth. She used 12^ 
 yd. for a dress, 3| yd. for a coat, and S^ yd. for a waist. 
 How many yards had she left ? 
 
 46. Mr. White owned | of a farm. He sold J of his share 
 at 160 an acre. If the entire farm contained 80 acres, how 
 much money did he receive ? 
 
 47. At 121 cents a dozen, how much will | of 16 dozen 
 buttons cost? 
 
 48. If I of a dozen oranges cost 20 cents, how much will 
 5J dozen cost ? 
 
 49. A company of four men leased a tract of West Vir- 
 ginia land and drilled an oil well. It flowed for a time 
 at the rate of 100 barrels a day. If oil was selling at $1.68 
 a barrel, how much did each realize per day ? 
 
 50. I paid $6.30 for ribbon. If I paid 60^ for f of a yard, 
 how many yards did I buy ? 
 
 51. A farmer lent his nephew $450 for 2 years and 6 
 months at 6%. Find the interest. 
 
 52. A bought a horse for $100, a cow for $45-|-, and a 
 wagon for $78|. What was the cost of all ? 
 
 53. $65 is the value of |- of an acre of land. At this rate 
 how many acres of land can be bought for $ 6396 ? 
 
 54. Change 27000 pounds to tons. 
 
 55. One side of a square is 18 ft. 8 in. What is the dis- 
 tance around it ? 
 
GENERAL REVIEW 287 
 
 56. If I spend $ I for an inkstand, $| for a book, and $^ 
 for paper, how much do I spend in all ? 
 
 57. Lucy has 1^, and Mary $|. Which has the larger 
 sum, and how much larger is it ? 
 
 58. Charles earned il7J, John 120}, and William i25J. 
 How much more must they earn to have $ 75 in all? 
 
 5x3 75 
 
 59. Perform the operations indicated : — - — '-^—^. 
 
 60. On Jan. 1, 1906, Mr. Blethrow bought of T. C. Jen- 
 kins & Co., the following: 
 
 25 bbl. of flour, @ $ 5.25 
 
 20 bbl. of sugar, @ 14.50 
 
 29 hams, @ 1.85 
 
 112 lb. of bacon, @ 0.10 
 
 Find total, and receipt the bill, acting as clerk for T. C. 
 Jenkins & Co. yourself. 
 
 61. How many pecks are there in 17J bushels ? 
 
 62. (.5 + .75)-i-.00125=? 
 
 63. In an orchard there are 144 trees ; 18 are cherry, 36 
 are apple, and ^ of the remainder are peach trees. How 
 many are peach trees? 
 
 64. How many pecks are there in 25 bu. 3 pk. ? 
 
 65. Find the cost of 21 1 bushels wheat at 80 ^ a bushel. 
 
 66. 1 ton of coal will cost how many times as much as 5 
 hundredweight? as 600 pounds? as 60 pounds? 
 
 67. A haystack contains 9000 pounds of hay. How much 
 is it worth at $ 15 a ton? 
 
 68. A grocer bought 5 barrels of cider at $6.50 a barrel, 
 and sold it at $ 0.10 a quart. How much did he gain ? 
 
288 FIFTH YEAR 
 
 69. A farmer exchanged 45 pounds of butter, at 30 cents a 
 pound, for sugar, at 5 cents a pound. How many pounds 
 of sugar did he receive ? 
 
 70. How many cubic feet of air are there in a room 12 ft. 
 long, 10 J ft. wide, and 9 ft. high? 
 
 71. What is the cost of 48 gal. oil at 5 cents a quart ? 
 
 72. For i 20^, how many barrels, at $ 2^ a barrel, can be 
 bought ? 
 
 73. A boy lost J of his marbles one day, ^ of them the next 
 day, and had 44 marbles left. How many had he at first ? 
 
 74. John had 120 marbles. He gave Louis | of them, and 
 Henry J of the remainder. How many had he remaining ? 
 
 75. If a boy pays $2.50 a hundred for papers, and sells 
 them for 5 cents apiece, how much does he gain on 300 
 papers ? 
 
 76. A field contains 25 rows of corn. If each row yields 
 6 bu. 3 pk., how much corn will the field yield? 
 
 77. What will be the cost of painting the ceiling and the 
 floor of a kitchen 14 ft. long and 12 ft. wide, at iO.lO per 
 square yard ? 
 
 78. Mary has §175. How mtich will it amount to in 3 
 years and 10 months at 6 % ? 
 
 79. How many loads of earth will be removed in excavating 
 a cellar 24 ft. long, 18 ft. wide, and 6 ft. deep? 
 
 80. Add one and one tenth, one and one thousandth, one 
 hundred and one thousandth, ten and five hundredths, and 
 six tenths. 
 
 81. Frank worked 2J hours for five days each week and 
 12 hours each Saturday. Find his earnings for 10 weeks 
 at 12^ an hour. 
 
ANSWEKS 
 
 THIRD YEAR 
 
 Page 32. — 2. a. 994 ; &. 820 ; c. 781 ; <?. 1204 ; e. 831 ; /. 755. 
 3. a. 1005; b. 853; c. 1733; d. 1442; e. 1490; /. 1932. 4. a. 908; 
 
 b. 962; c. 954; d. 1334; e. 189; f. 757. 6. a. 1397; b. 1©06 ; 
 
 c. 1338; d 1292; e. 1414; /. 1757. 
 
 Page 33. — 1. a. 38; &. 44; c. 34; d. 32; e. 30; /. 38; ^. 41; 
 
 h. 41 ; I. 42 ; j. 32 ; k. 45 ; Z. 46 ; m. 34 ; n 32. 2. a. 784 ; 6. 1118 ; 
 
 c. 2040; d. 1196; e. 553; /. 1235; ^. 561. 3. a. 2050; &. 1397;. 
 
 c. 1433; d 1609; e. 1509; /. 1695; gr. 994. 4. a. 1411; 6. 2020; 
 c. 1325; (Z. 838; e. 1654; /. 706; ^. 1037. 
 
 Page 34. — 2. a. 3095; ft. 3494; c. 7421; d 1763; e. 10,388. 
 
 3. a. 7783; b. 5778; c. 10,805; d. 14.553; e. 11,997. 4. a. 12,640; 
 
 b. 13,239; c. 9715; d. 5610; e. 12,803. 6. 27. 6. 26. 7. 33. 8. 35. 
 Page 35. — 1. 600. 2. 1044. 3. 4631. 4. 3004. 5. 1305. 6. 800. 
 
 7. 834. 8. 1175^. 9. 8654. 10. 187 pt. 11. 1159 qt. 12. 1109 pk. 
 13. 1330 in. 14. 4364 dimes. 15. 5627 hr. 16. 2239 min. 17. 3153 gal. 
 18. 3882 da. 
 Page 36. — 1. 22,595. 2. 19,999. 3. 14,177. 4. 19.265. 5. 15,189. 
 
 6. 24,973. 7. 22,;-).:7. 8. 23,289. 9. 23,320. 10. 15.873. 11. 36 men. 
 12. $676. 13. 774 mi. 14. 787 bii. 15. $678. 
 
 Page 41.-5. 87 boys. 6. 27 chickens. 7. 209 mi. 8. 7 ft. 9. 167 mi. 
 
 Page 42. — 1. 3749 pupils. 2. 8625. 3. 3712 ft. 4. 4385 people. 
 
 5. 1511 boys. 6. 5437 flags. 7. 430 steps. 8. 390 fares. 
 
 Page 54. — 2. 86.06; 85 60; 84.49; 86.07; 85.68. 3. $22.35. 
 
 4. $23.54. 6. $24.73. 1st col. : $9.62 ; 2d col. : $10.92 ; 3d col. : $11.87 ; 
 4th col.: $13.93; 5th col. : $8.24; 6th col.: $16.04. 6. a. $2.21; b. $.51; 
 
 c. $.85; (Z. $3.46; c. $2.48. 7. a. $.96; &. $1.79; c. $1.25; d. $.85; 
 e. $2.57. 8. $6.89. 9. $5.78. 10. $3.90. 11. $4.82. 
 
 Page 55. — 1. a. $913.87; &. $2489.87 ; c. $2269.27; f7. $2624.92. 
 2. a. $1444.03; 6. $1521.75; c. $1347.07; <?. $902.09. 3. $1671.24. 
 4. $873.44. 5. $1292.77. 6. $835.82. 1st col. : $1412.07; 2d col. : 
 $172.80; 3d col. : $1244.99; 4th col.: $ 1843.41. Total, $4673.27. 
 
 7. a. $279.08; b. 8256.29; c. 8242.91; d. $626.04. 8. a. $97.77; b. $28.39; 
 
 c. $167.51; d. $138.60. 9. $71.62. 10. $65.82. 
 
 Page 63. — 1. a. 16,910; b. 20.524; c. 19,634; d. 18,184; e. 13,022. 
 2. a. 18,330; b. 15,900; c. 16,996'; d. 22,750; e. 21,607. 3. a. 21,010; 
 b. 24,150; c. 24,153; d. 26,261; e. 26,350. 
 
 Page 64.-2. a. 3136; b. 5591; c. 3239 ; d. 1812; e. 2541. 3. a. 1084; 
 
 6. 22i>3; c. 4986; d. 1766; e. 3844. 4. a. 3939; b. 2814; c. 1285; 
 
 d. 1832 ; e. 4809. 5. a. 3226 ; 6. 1778 ; c. 1343 ; d. 2244 ; e. 950. 
 
 e. a. 3058 ; b. 206 ; c. 2429 ; d. 2291 ; e. 2215. 7. 6908 ; 6921. 
 
290 ANSWERS 
 
 Page 65. — 1. a. 1869; b. 819; c. 2(589; d. 3479; e. 659. 2. n. 1706 
 
 6. 1599; c. 1888; d. 494; e. 408. 3. a. 2059; Z>. 1505; c. 8699 
 d 948 ; e. 955. 4. a. 3579 ; b. 4065 ; c. 489 ; d. 995 ; e. 2764. 5. a. 749 
 b. 947; c. 2105; (Z. 3805; e. 3736. 6. a. 3676; b. 487; c. 4405 
 d. 4006 ; e. 4798. 7. a. 4098 ; 6. 769 ; c. 526 ; d. 2069 : e 1854.' 
 8. a. 3657 ; 6. 999 ; c. 604 ; d. 892 ; e. 3775. 
 
 Page 73. — 1. a. $1447.28; b. $984.34; c. $1180.93; d. $1572.63. 
 2v a. $154.56; b. $97.75; c. $76.78; d. $140.21. 3. $9737.98. 
 
 4. $1098.36. 5. $982.04. 6. a. $57.18; 6. $145.71; c. $174.67; 
 
 d. $90.51; e. $216.72. 7. a. $356.59; 6. $93.58; c. $37.98; d. $733.47; 
 
 e. $90. 8. $190.35. 9. $250.78. 10. $272.27. 11. $261.62. 
 12. $119.37. 13. $89.91. 
 
 Page 74.-4. 4i gal. 5. 7 bu. 6. 10 yd. 7. 4 qt. 9. 35i. 10. 55i. 
 11. 79^. 12. 133. 13. 6; 8; 1; 4; 9; 9A. 14. 3* ; U ; 2 ; 2 ; 7 ; 8. 
 1£. 17 ; 8 ; 7 ; 13 ; 25^ ; 23. 
 
 Page 75.-3. a. 7 ; 6. 8 ; c. 9i ; d 13f ; e. 17. 4. a. 31 ; 6. 23 ; c. 23; 
 
 d. 22 ; c. 30. 5. 3 ; 5i ; 5| ; 3^ ; 3. 6. 4f ; 3^ ; 5 ; 13 ; 8. 7. 3 inches. 
 
 Page 76.— 2. $3. 8. 6^. 4. 7 gal. 5. 5f pk. 6. 9 bu. 7. 9 hr. 
 
 8. a. 11 ; b. 23; c. 36| ; d. 20f ; e. 27; /. 30. 9. a. 52i ; b. 57; c. 90; 
 d. 2; e. 29; f. 60. 10. 5^. 11. 2. 12. 5. 13. 4. ^14. 7. 15. 6i. 
 16. H. 17. 'll^. 18. 16. 19. H. 20. 9. 21. 1. 22. 12^. 23. 8^. 
 24. 7|. 
 
 Page 77. —1. 6 tons. 2. 6^ gallons. 3. 1625| gallons. 4. 59 bu. 
 
 5. 2ibu. 6. 11 yards. 7. 8 yards. 8. $288. 9. 92 1b. 10. U gal. 
 11. 69 ft. 
 
 Page 81. —1. 120 feet. 2. $20. 3. $26. 4. $156. 6. 41. 6. $36. 
 
 7. $400. 8. $22.24. 
 
 Page 84. — 2. 60. 3. 84. 4. 408. 5. 714. 6. 390. 7. 990. 8. 2464. 
 
 9. 1023. 10. 2576. 11. 2322. 12. 1476. 13. 1728. 14. 2223. 15. 1591. 
 16. 6045. 17. 2530. 18. 2009. 19. 3776. 20. $1.02. 21. $5. 22. $9.90. 
 23. $1.20. 24. $1.50. 25. $3.51. 26. $2.03. 27. $2.70. 28. $1.68. 
 29. $2.64. 30. $1.04. 31. $2.90. 32. 50)^. 33. $2.55. 
 
 Page 89. — 1. 28 yd. 2. $2.24. 3. 19 caps. 4. 30 pupils. 5. $1.26. 
 €. $5.74. 7. $4.45. 
 
 Page 91.— 1. a. $75.06; b. $87.08; c. $66.01; d. $75.26; e. $52.03. 
 
 2. a. Mon. $163.61; b. Tues. $181.53; c. Wed. $156.05; d. Thurs. 
 $241.92; e. Fri. $255.09. Total, $998.20. Corn: $323.45; oats: 
 $128.76; bran: $35.95; chop: $69.89; meal: $46.40; flour: $393.75. 
 
 3. $3595.55. 4. $11.55. 
 
 Page 92.-3. a. 2987 ; b. 2695 ; c. 1197 ; d. 991 ; e. 172. 4. a. 6503 ; 
 
 b. 240; c. 1791; d. 5098; e. 1363. 5. a. 1100; b. 3631; c. 3619; 
 
 d. 1414; e. 203. 6. a. 3695; 6. 1070; c. 1192 ; d. 2504; e. 4893. 
 7. a. 2097 ; 5. 2802 ; c. 295 ; d. 1308 ; e. 1503. 
 
ANSWERS 291 
 
 Page 93.— 28. a. 18,808; h. 21,710; c. 32,740; d. 27,171; e. 27,189. 
 3. «. 20,327 ; b. 26,902 ; c. 34,134 ; d. 30,398 ; e. 24,095. 
 
 Page 94. — 1. 104 feet. 2. $38.60. 3.14.05. 4. 320 minutes. 
 
 6. $5.25. 6. §32.25. 
 
 Page 95.— 28. 2143. 29. 6639. 30. 3332. 31. 1553. 32. 1002. 
 
 33. 6168. 34. 5770. 35. 2522. 36. 2226. 37. 917. 38. 2042. 
 
 39. 2660. 40. 4791. 41. 4414. 42. 4563. 43. 1494. 44. 3357. 
 
 45. 1963. 46. 4207. 47. 1055. 48. 3042. 49. 3523. 60. 3274. 
 61. 741. 58. 4584. 53. 2120. 54. 3809. 
 
 Page 97.— 7. 40^. 8. 824. 9. $12. 10. 30j^. 12. $960. 13. $30. 
 
 14. $195. 15. $9. 16. $255. 
 
 Page 102. — 1. $20. 2. $1.26. 3. $2.75. 4. $2.24. 5. $15.75. 
 6. .S48.60. 7. $2. 8. $6.80. 9. $15.75. 10. $16.87|. 11. $1.96. 
 12. $14.25. 13. $12. 14. $9.96. 15. $114.50. 16. $3.74. 
 
 Page 103. — 1. 288 pints. 2. 2.34 miles. 3. $2.64. 4. 3 hours. 5. 55^. 
 6. 23 pounds. 7. 21 plants. 8. 34 weeks. 9. 340 sheep. 10. $2.16. 
 11. 99 bushels. 12. 99 gallons. 13. 131 tons. 14. 32 quarts, or 8 gallons. 
 
 Pagel04. — 15. 209 boxes. 16. $125. 17. 41 weeks. 18. 38 days. 
 19. 13 cents. 20. 18 yards. 21. 6 cents. 22. $2.25. 23. $24. 
 
 24. $63. 25. 56^. 26. $16. 27. $1. 28. $21. 29. $31.50. 30. 96/?. 
 31. $27. 32. 60^ 33. $4. 34. 80^ 35. $20. 36. $1200. 
 
 PagelOS. — 37. 7 hours. 38. 1152 sq. in. 39. $52.50. 40. 99^. 
 41. $38. 42. $15.75. 43. $124. 44. 114 palings. 45. $1.36. 
 
 46. $9.60. 47. $2. 48. $286. 49. $2700. 
 
 PagelOe. — 50. $2.45. 51. $1275. 52. 1008 pounds. 53. $38.25. 
 54. $4.25. 55. 288 pupils. 56. $270. 57. $4.08. 58. $17.60. 
 59. 32f ; 48^ 60. $17.76. 
 
 FOURTH YEAR 
 
 PagelOS.- 1. 42.000. 2. 66,004. 3. 75,050. 4. 39,122. 5. 210,350. 
 
 6. 565,100. 7. 1,125,000. 8. 3,600,035. 9. 26,009,026. 10. 80,026,064. 
 11. 900,009. 12. 46,004,016. 13. 110,000,500. 14. .336,000,104. 
 
 15. 607,005,006. 16. 17,003,075. 17. 1,002,704. 18. 1,104,186. 
 19. 21,110,109. 20. 604,622,468. 21. 101,010,010. 
 
 Pagel09.— 4. $1050.27. 5. $904.60. 6. a. $108.08; 5. $228.47; 
 
 c. $121.79; d. $46.3.51. 7. a. $602.92; b. $766.69; c. $437.07; 
 
 d. $622.92. 
 
 Page 110. — 2. 846 bu. 3. $103. 4. 184 da. 5. $16,995. 6. $6572. 
 
 7. 108 ft. 8. 444 mi. 9. $66.91. 
 
 Pagelll. — 2. 56 yr. in 1907. 3. $10,906. 4. 8847 votes. 5- $4234. 
 6. 8224 bu. 7. 6199. 8. $739. 9. 196 1b. 10. 2669 votes. 
 
292 ANSWERS 
 
 Page 114. —3. First col. 5580; 5115. 6552 ; 6006. 9408 ; 8624. 
 9420 ; 8635. 11,736 ; 10,758. Second col. 2832 ; 2596. 9396 ; 8613. 
 11,244; 10,307. 6168 ; 5654. 8328 ; 7684. Third col. 9468 ; 8679. 
 11,136 ; 10,208. 8316 ; 7623. 11,256 ; 10,318. 3552 ; 3256. 
 
 2. 408. 3. 672. 4. 990. 5. 1140. 6. 609. 7. 1331. 8. 2800. 
 
 Page 116.— 4. 248, rem. 10. 5. 754. 6. 185, rem. 1. 7. 632, rem. 2. 
 8. 362, rem. 4. 9. 273, rem. 4. 10. 811, rem. 2. 11. 196, rem. 2 
 12. 732, rem. 5. 13. 6341, rem. 2. 14. 6642, rem. 3. 15. 8188, rem. 6. 
 19. 306, rem. 6. 20. 344, rem. 7. 21. 581, rem. 1. 22. 594. 
 
 23. 391, rem. 1. 24. 651, rem. 5. 25. 244, rem. 8. 26. 769, rem. 10. 
 27. 391, rem. 5. 28. 782. 29. 3516. 30. 6781, rem. 6. 31. 6162, rem. 1. 
 32. 6888, rem. 3. 33. 3108. 34. 7656, rem. 3. 35. 2060, rem. 6. 
 36. 5696, rem. 7. 37. 6813, rem. 7. 38. 7697. 
 
 Page 117. — 1. $27. 2. $420. 3. $36.50. 4. $15. 5. $255. 
 6. $15.75. 7. $7.50. 8. $23.90. 9. $950. 10. $24.75. 11. $52.25. 
 
 12. $52.50. 13. $4.50. 14. $54. 15. $4.25. 16. $8.12. 17. $1.95. 
 
 18. $4.50. 19. 8 3.25. 20. $7.20. 21. $4.85. 22. $3. 23. $2.25. 
 
 24. $.12. 25. $3.25. 26. $1.25. 27. $3.09. 28. $.25. 29. $.15. 
 30. $3.55. 31. $.04. 32. $.18. 33. $.12. 34. $.75. 35. $.25. 
 36. $3.50. 37. $.22. 38. $.20. 39. $3.75. 40. $1.75. 41. $.11. 
 42. $.20. 43. $3.25. 44. $.20. 
 
 Page 118. — 1. 54 mi. 2. $33.25. 3. 96 times. 4. $482. 5. 110 1b. 
 
 6. $7.20. 7. $3.70. 8. $1427. 9. 410 boys. 
 
 Page 119.— 1. a. $35,538.46; h. $28,736.60; c. $30,106.56. 
 
 2. a. $21,464.87; h. $24,836.37; c. $20,168.03. 3. a. $20,184.93; 
 
 h. $21,878.20; c. $24,181.02. 
 
 Page 120.— 1. a. $681.83; 6. $748.19; c. $614.96; <?. $681.68. 
 
 2. a. $286.42; h. $159.46; c. $800.99; d. $511.68. 3. a. $304.49; 
 
 ft. $713.35; c. $195.01; cZ. $366.44. 4. «. $784.66; 6. $812.60; 
 c. $32.45; cZ. $233.45. 5. a. $412.34 ; 5. $444.45; c. $611.70; d $ 2.32. 
 
 6. a. $611.78; &. $256.77 ; c. $730.87; <?. $663.09. 7. o. $642.19; 
 7>. $775.47; c. $732.60; d $137.96. 8. a. $364.93; 6. $176.05; 
 c. $386.08; d. $453.11. 
 
 Pagel23. — 9. 14,200. 10. 255,000. 11. 980,000. 12. 500,500. 
 
 13. 6940. 14. 12,270. 15. 42,900. 16. 26,320. 17. 42,760. 18. 146,500. 
 
 19. 550,200. 20. 73,600. 21. 477,600. 22. 166.400. 23. 962,000. 
 24. 3.576,000. 25. 6,342,000. 26. 6,652,000. 27. 438,000. 
 
 Page 125. -2. 4. 3. 2. 4. 9. 5. 2. 6. 9. 7. 10. 8. 30. 9. 21. 
 10. 12. 11. 6. 12. 6. 13. 4. 14. 20 cans. 15. 50 packages. 
 16. 5 1b. 17. 120 coats. 18. 35 mo. 
 
 Page 126. — 6. a. 1612 ; &. 20,640 ; c. 20,712 ; d 26,775 ; e. 34,668. 
 
 7. a. 2254; h. 18,684; c. 9136; d. 39,483; e. 44,013. 8. a. 25,972. 
 b. 21,bb2 ; c. 39,015 ; d. 41,202 ; e. 31,212. 
 
 Page 127.— 1. 9798. 2. 15,252. 3. 8448. 4. 9824. 5. 11,567. 
 6. 8289. 7. 19,368. 8. 46,368. 9. 25,324. 10. 34,790. 11. 23,458. 
 
13. 
 18. 
 
 27. 
 34. 
 
 ANSWERS 
 
 28,992. 14. 29,160. 
 
 54,450. 19. 9772. 
 
 23. 304,076. 24 
 
 362,408. 28. 52,780. 
 78,792. 35. 66,215. 
 
 15. 77,658. 
 20. 10,122. 
 287,631. 
 
 29. 73,818. 
 36. 85,728. 
 
 293 
 
 16. 54,826. 
 21. 432,288. 
 25. 355,992. 
 30. 133,408. 
 37. 828,996. 
 
 441,441. 40. 449,550. 41. 243,404. 42. 361,959. 
 
 346,62.; 
 
 44. 227,864. 
 
 Page 128. — 5. 
 10. 3270 pt. 11. 
 
 8 175. 6. 
 10,140 in. 
 
 $957. 7. $4085. 8. $17.82. 
 12. 656 pk. 13. 6000 oz. 
 
 9. $27.60. 
 
 Page 129. —1. $4.20. 2. $11.16. 3. $11.76. 4. $13.05. 5. $10.32. 
 6. $29.75. 7. $12.96. 8. $34.95. 9. $5.75. 10. $283.50. 11. $63.45. 
 12. $229.50. 13. $83.16. 14. $37.44. 15. $41.76. 16. $609.55. 
 17. $11,440. 18. $241.92. 19. 226 hr. 
 
 7. $270. 
 
 8. $2.80. 
 
 9. $12 
 
 Page 130. — 5. $1. 6. $.90. 
 
 10. $.32. 11. $455. 12. $324. 
 
 Page 132. — 6. 21 ; 32 ; 43. 
 
 Page 133.— 1. 12. 2. 25. 3. 41. 4. 34. 5. 31. 6. 17. 7. 24. 
 8. 114, rem 4. 9. 125. 10. 23. 11. 29. 12. 217. 13. 203. 14. 307. 
 15. 403. 16. 119, rem. 30. 17. 32. 18. 207. 19. 62. 20. 71. 21. 33. 
 
 Page 134.— 1. 42. 2. 
 
 43. 3. 24. 4. S 
 
 8. 21. 9. 37. 10. 29. 
 
 11. 16. 12. 30. 
 
 16. (5. 17. 25. 18. 24. 
 
 19. 29. 20. 7. 
 
 24. 6. 25. 14. 26. 26. 
 
 27. 17. 28. 19. 
 
 33. 35. 33. 24. 34. 38. 
 
 35. 40. 36. 41. 
 
 40. 32. 41. 33. 42. 44. 
 
 43. 45. 44. 64. 
 
 48. 72. 49. $36. 50. 
 
 62 da. 51. 16 oz. 
 
 54. 9 hr. 55. 8 words. 
 
 
 39. 5. 15. 6. 27 
 13. 25. 14. 32. 
 
 7. 19. 
 
 15. 42. 
 
 21. 21. 22. 29. 23. 6. 
 
 29. 23. 30. 56. 31. 27. 
 
 37. 31. 38. 160. 39. 220. 
 
 46. 28. 46. 29. 47. 36. 
 
 52. $1.85. 53. 895 bu. 
 
 Page 135. — 2. 47. 3. 45, rem. 18. 4. 62. 5. 77, rem. 19. 6. 63, 
 7. 67, rem. 18. 8. 83, rem. 19. 9. 77, rem. 19. 10. 53, rem. 61. 
 
 11. 62. 12. 41. 13. 61. 14. 63, rem. 2. 15. 65, rem. 44. 16. 77. 
 17. 44, rem. 56. 18. 59, rem. 60. 19. 47. 20. 76, rem. 6. 21. 86, rem. 2. 
 22. 83, rem. 23. 23. 24, rem. 55. 24. 73, rem. 76. 25. 183, rem. 22. 
 2G. 310, rem. 17. 27. 109, rem. 5. 28. 60, rem. 32. 29. 52, rem. 30. 
 
 30. 94, rem. 84. 31. 106, rem. 55. 32. 318, rem. 21. 33. 
 'Jl. 92, rem. 86. 35. 34 suits ;$ 7 left. 36. 8 bbl. 
 
 123, rem. 15. 
 
 Page 136.-2. 30 belts. 3. 13 lb. 4. 163 gal. 5. 18 yd. 
 -!i|yr. 7. 325 bars. 8. 160 A. 9. 126 trees. 10. $74.64+. 
 
 6. 35 mo. ; 
 
 Page 137.— 11. 39 bu. 12. $104. 13. 28 mi. 
 
 
 Page 138. —1. $3.37.^ 2. $628. 3. $64. 4. $16. 
 3. $36. 7. $149.64. 8. $600. 9. $2080. 10. $83.25. 
 12. $7.20. 13. $1024. 14. $1843.75. 15. $378. 
 17. $67.86. 18. $19. 19. $12.50. 20. $6.25. 
 22. $6.57. 23. $12. 24. $4723.71. 25. $18,889.06. 26. 
 27. $11,376.97. 
 
 5. $477. 
 11. $36.40. 
 16. $10.50. 
 
 21. $30 
 $22,479.55 
 
294 ANSWERS 
 
 Page 139. — 1. $5.25. 2. .$4.95. 3. $3. 4. $10. 5. $6.25. 
 6. .$8. 7. $3.60. 8. $50. 9. $145. 10. $1.90. 11. $5.25. 
 
 12. $9.60. 13. $9. 14. $18. 15. $8. 16. $21. 17. $32. 18. $22. 
 
 19. $ 34. 20. $ 16. 21. $ 12. 22. $ 19. 23. 44 mi. 24. $ .29. 
 
 Page 140. — 1. 7 cows. 2. $980. 3. 56 A ; $1988. 4. $2587.20. 6. $98. 
 6. $242.50. 7. $540. 8. $7. 9. $435. 10. $532.50. 11. $22.50. 
 
 Page 141.— 5. 180 sec. 6. 144 hr. 7. 420 min. 8. 78 lir. 9. 76 da. 
 
 10. 91 da. ; 92 da. 
 
 Page 142. — 4. 6 T.+ 1500 lb. 5. $.48. 6. $33. 7. 4000 packages. 
 8. 32,000 oz. 9. l^T. ; $21. 
 
 Page 144. — 1. 20 yd. 2. 445Ut. 3. 192 in. 4. 3^ ft. 
 
 6. 5280 ft. 6. 5280 ft. 7. 60 in. " 8. 10 ft. 9. 24 yd. 10. 35 ft. 
 
 11. 3750 ft. 12. 1980 ft. 13. 228 ft. 14. 5940 rd. 16. 810 yd. ; 2850 ft. 
 
 Page 146. — 1. 24 sq. in. 2. 49 sq. in. 3. 40 sq. in. 4. 120 sq. in. 
 5. 64 sq. in. 6. 144 sq. in. 7. 81 sq. in. 8. 100 sq. in. 9. 15 sq. 
 in. ; 16 in. 10. 20 in. ; 28 in. ; 26 in. ; 44 in. ; 32 in. ; 48 in. ; 36 in. ; 40 in, 
 
 11. 36 sq. ft. ; 24 ft. 12. 36 sq. ft. ; 26 ft. 13. 54 sq. ft. ; 30 ft. 14. .30 
 sq. ft. ; 22 ft. 15. 80 sq. yd. ; 36 yd. 16. 45 sq. yd. ; 36 yd. 17. 24 sq. 
 yd. ; 28 yd. 18. 20 sq. yd. ; 18 yd. 
 
 Page 147.— 11. 6606. 12. 2,010,000,004. 13. 75,906. 
 
 14. 1,008,000,075. 15. 84,605,000. 16. 25,038. 17. 900,000,999. 
 18. 2,006,030. 19. 1,001,001,000. 
 
 Page 148.— 3. 155. 4. 190. 5. 195. 6. 162. 7. 196; a. 192; 
 
 b. 384 ; c. 322. Total, 898. 8. 121. 9. 217. 10. 152. 11. 189. 
 
 12. 162. d. 248; e. 248; f. 345. Total, 841. 13. $186.67. 14. $60.13. 
 
 15. $94.87. 16. $128.80. 17. $163.36. a. $184.08; 1). $202.51; 
 
 c. $71.83; d. $175.41. Total, $633.83. 18. $480.01. 19. $520.98. 
 
 20. $989.32. 21. $1160.15. 22. $1036.75. a. $342.86; b. $319.88; 
 c. $227.50; d. $3296.97. Total, $4187.21. 23. 54,938. 
 
 Page 149. — 1. $29,507.28. 2. $4644.85. 3. $3660.64. 4. $658,373.86. 
 
 5. $21,684.52. 
 
 Page 150. — 1. a. $3569.11; 6. $1980.73; c. $3351.74 ; c?. $1801.11. 
 2. «. $2578.31; b. $4340.01; c. $5037.33; d. $4154.59. 3. a. $3490.40; 
 
 b. $1.3,565.92; c. $3355.63; d. $15,631.90. 
 
 Page 151. — 1. a. $211.70; b. $128.45; c. $3.3,812.37; d. $1979.02. 
 2. a. $310.20; b. $227.74; c. $15,577.79; d. $724.73. 3. a. $923.68: 
 
 6. $596.88; c. $17,950.52; d. $8694.69. 4. a. $387.06; b. $218.02. 
 
 c. $17,619.20; d. $2563.59. 5. a. $46.06; b. $2-3.08; c. $148.92; 
 
 d. $7986.86. 6. a. $63; b. $51.94; c. $129.37; d. $5873.8-3. 
 
 7. a. $54.85; b. $52.05; c. $463.54; d. $57,529.24. 8. a. $8.03; 
 
 b. $23.52; c. $241.08; d. $17,879.01. 9. a. $52.83; b. $72.20; 
 
 c. $61.44; d. $14,140.29. 
 
ANSWERS 
 
 295 
 
 Page 152. — 
 
 1. a. 186,230; h. 
 f. 829,570; g. 
 
 2. a. 168,190; h. 
 f. 749,210; g. 
 
 3. a. 192,302; 6. 
 /. 856,618; g. 
 
 4. a. 216,920 ; h. 
 f. 966,280; g. 
 
 5. a. 185,350 ; b. 
 f. 825,650; g. 
 
 6. a. 212,388 ; b. 
 f. 946,092; g. 
 
 7. a. 173,118; b. 
 f. 771,162 ; g. 
 
 8. a. 214,830 ; b. 
 f. 956,970; g. 
 
 9. a. 107,250 ; b. 
 f. 477,750; g. 
 
 10. a. 185,240 ; b. 
 J. 825,160; g. 
 
 13. a. 985, rem. 55 ; 
 e. 1177, rem. 21 ; 
 
 14. a. 670, rem. 52 ; 
 e. 801 ; 
 
 15. a. 938. rem. 52 ; 
 e. 1121, rem. 8; 
 
 16. a. 589, rem. 70 ; 
 e. 704, rem. 36 ; 
 
 17. a. 708, rem. 37 ; 
 e. 846, rem. 13 ; 
 
 18. a. 1004, rem. 68 ; 
 e. 1200, rem. 12 ; 
 
 19. a. 888, rem. 44 ; 
 e. 1061, rem. 20 ; 
 
 20 a. 970, rem. 36 ; 
 e. 1159, rem. 8 ; 
 
 380,925 ; 
 474,040 ; 
 344,025 ; 
 428,120 ; 
 393,345 ; 
 489,496 ; 
 443,700 ; 
 552,160; 
 379,125; 
 471,800 ; 
 434,430 ; 
 540,624 ; 
 354,105 ; 
 440,664 ; 
 439,425 ; 
 546,840 ; 
 219,375 ; 
 273,000 ; 
 378,900 ; 
 471,520 ; 
 b. 1086, 
 /. 1265, 
 
 c. 423,250 
 h. 584,085 
 c. 382,250 
 h. 527,505 
 c. 437,050 
 A. 603,129 
 c. 493,000 
 h. 680,340 
 c. 421,250 
 h. 581,325 
 c. 482,700 
 h. 666,126 
 
 393,450 
 
 542,961 
 
 488,250 
 
 673,785 
 
 243,750 
 
 336,375 
 c. 421,000 
 h. 580,980 
 
 c. 931, 
 
 739, 
 860, 
 1034, 
 1204, 
 650, 
 757, 
 781, 
 909, 
 1107, 
 1289, 
 979, 
 1140, 
 b. 1069, 
 /. 1245, 
 
 rem. 5/ ; 
 rem. 10 ; 
 rem. 30 ; 
 rem. 52 ; 
 rem. 68 ; 
 rem. 52 ; 
 rem. 24 ; 
 rem. 5 ; 
 rem. 7 ; 
 rem. 22 ; 
 rem. 66 ; 
 rem. 49 ; 
 rem. 50 ; 
 rem. 32 ; 
 rem. 74 : 
 
 d. 727,990; 
 
 i. 821,105; 
 
 d. 657,470; 
 
 i. 741,565; 
 
 d. 751,726; 
 
 i. 847,877; 
 
 d. 847,960; 
 
 i. 956,420; 
 
 d. 724,550; 
 
 i. 817,225; 
 
 d. 830,244; 
 
 i. 936,438; 
 
 d. 676,734; 
 
 i. 763,293; 
 
 d. 839,790; 
 
 i. 947,205; 
 
 d. 419,250; 
 
 i. 472,875 ; 
 
 d. 724,120; 
 
 i. 816,740; 
 
 1033, 
 633, 
 703, 
 887, 
 984, 
 557, 
 618, 
 669, 
 742, 
 949, 
 g. 1053, 
 c. 839, 
 g. 931, 
 c. 917, 
 
 rem. 41 ; g. 1017, 
 
 rem. 44 
 rem. 59 
 rem. 69 
 rem. 26 
 rem. 3 
 rem. 32 
 rem. 37 
 rem. 48 
 rem. 46 
 rem. 81 
 rem. 53 
 rem. 66 
 rem. 63 
 rem. 70 
 rem. 9 
 rem. 62 
 
 e. 
 
 J- 
 e. 
 
 J- 
 e. 
 
 J- 
 e. 
 
 J- 
 e. 
 
 J- 
 e. 
 
 J- 
 
 e. 
 
 J- 
 e. 
 
 J- 
 e. 
 
 J- 
 
 e. 
 
 J- 
 
 1436, 
 
 1304, 
 
 977, 
 
 887, 
 
 1368, 
 
 1241, 
 
 859, 
 
 780, 
 
 1032, 
 
 937, 
 
 1464, 
 
 1329, 
 
 1295, 
 
 1175, 
 
 1414, 
 
 1283, 
 
 643,340 ; 
 753,385. 
 581,020; 
 680,405. 
 664,316; 
 777,949. 
 749,360 ; 
 877,540. 
 640,300 ; 
 749,825. 
 733,704 ; 
 859,206. 
 598,044 ; 
 700,341. 
 742,140; 
 869,085. 
 370,500; 
 433,875. 
 639,920 ; 
 749,380. 
 rem. 41 ; 
 rem. 5. 
 rem. 29 ; 
 rem. 17. 
 rem. 8 ; 
 rem. 55. 
 rem. 43 ; 
 rem. 24. 
 rem. 37 ; 
 rem. 20. 
 rem. 36 ; 
 rem. 27. 
 rem. 7 ; 
 rem. 37. 
 rem. 30 ; 
 rem. 61. 
 
 Page 153.— 3. Sum 8| ; diff. 2^. 4. Sum 18J ; diff. 1|. 5. Sum 13; 
 diff. 6. 6. Sum 9J ; diff. 1^. 7. Sum llj; diff. 6^. 9. 79J. 10. 82J. 
 
 11. 43|. 12. 72. 
 
 Page 154. — 7. 10|. 8. 25|. 9. 23. 10. 26|. 11. 20|. 13. Diff. 5^; 
 sum lof. 14. Diff^Of; sura 18f. 15. Diff. 19|; sum36i. 16. Diff. 13| ; sum 
 25|. 17. Diff. 20^ ; sura 52|. 18. Diff. 31|; sum 94. 19. Diff. 24^; sura 
 103^. 20. Diff. 2| ; sum 51|. 21. Diff. 9| ; sum 28^. 22. Diff. 20^ ; sum 60|. 
 
 Pagel55. — 3. Sum 25| ; diff. 5|. 4. Sum 42J ; diff. 16|. 5. SumlOlf; 
 diff. 61^. 6. Sura 56| ; diff. 29f. 7. Sura 74| ;^ diff. 50|. 8. Sum 28^; 
 diff. 3^. 9. Sura 27^ ; diff. 6f. 10. Sum 31| ; diff. 7^. 11. ^ doz. 
 
 12. 21 hr. 13. 14 ft. 14. 2| hr. 
 
296 ANSWEES 
 
 Page 156. — 2. 178,250. 3. 68,769. 4. 79,232. 5. 143,352. 
 
 6. .$13,243.75. 7. $9729.72. 8. $35,131.86. 9. $39,363.50. 10. 152,055. 
 
 11. 272,527. 12. 436,792. 13. 925,806. 14. 374,274. 15. 801,975. 
 16. 2:>8,717. 17. 791,154. 18. 787,788. 19. 8,166,625. 20. 5,101,995. 
 
 21. 7,349,238. 22. 5,626,836. 23. 5,810,553. 24. $12,856.25. 
 
 25. $70,761.42. 26. $74,017.80. 27. $34,549.95. 28. $47,792.88. 
 
 29. $76,069.08. 30. $32,388.10. 
 
 Page 157.— 5. 158,632. 6. 84,150. 7. 173,340. 8. 155,342. 
 
 9. 74,844. 10. 357,336. 11. 127,072. 12. 566,820. 13. $4904.56. 
 14. $24,572.25. 15. $45,712.80. 16. $26,742.12. 
 
 Page 158. — 1. 2,179,584. 2. 7,611,881. 3. 4,457,880. 4. 4,086,420. 
 
 5. 2,264,192. 6. 1,248,051. 7. 6,356,256. 8. 2,450,856. 9. 4,569,706. 
 
 10. 6,348,090. 11. $82,682.10. 12. $53,352.25. 13. $ 20,693.28. 
 14. $36,042.60. 15. $39,147.42. 16. 5,751,635. 17. 420,104. 
 18. 1,239,150. 19. 2,859,875. 20. 2,209,106. 21. 2,989,472. 
 
 22. 6,167,430. 23. 3,675,846. 24. 4,516,338. 25. 6,308,816. 
 
 26. 6,133,640. 27. 5,381,360. 28. 5,940,102. 29. 6,161,427. 
 
 30. 3,924,462. 81. 6,236,576. 32. 3,490,062. 33. 2,982,640. 
 34. 3,183,404. 35. 2,556,048. 36. 1,046,068. 37. 4,606,036. 
 38. 3,375,374. 39. 5,407,454. 40. 5,6.32,452. 41. 8,387,215. 
 42. 5,286,660. 43. 7,001,232. 44. 4,998,515. 45. 3,901,590. 
 46. 433,125 cakes. 47. 907,025 articles. 48. $430.50. 49. $105,022.50. 
 
 Page 160.— 2. 630. 3. 1218. 4. 4050. 5. 22,454. 6. 120,428. 
 
 7. 202,460. 8. 182,152|. 9. 386,568. 10. 2,131,272. 11. 3,251,105. 
 
 12. 7,567,812. 13. 2,857,240. 14. 1,690,990. 15. 7,440,372. 
 16. 9,414,090. 17. 7,334,634. . 18. 2,912,529. 19. 8,558,146. 
 
 20. 9,819,096. 21. 6,970,012. 22. 5,229,098. 23. 3,454,723. 
 24. 4,793,325. 25. 8,440,432. 26. 5,175,802. 27. 6,452,746. 
 28. 4,515,420. 29. 3,410,505. 30. 2,527,020. 31. 1,823,822. 
 32. 4,715,126. 33. 6,938,272. 34. 4,816,177. 35. 5,699,174. 
 
 Page 162. — 9. a. 504, rem. 92; 6. 346, rem. 75; c. 41. 10. a. 230, 
 rem. 133 ; h. 322 ; c. 199, rem. 90. 11. a. 339, rem. 26 ; 6. 256, rem. 
 95 ; c. 32, rem. 442. 12. a. 75, rem. 236 ; h. 427, rem. m ; c. 201, rem. 
 350. 13. a. 283, rem. 90; 6. 302, rem. 247; c. 215, rem. 119. 
 
 14. a. 382, rem. 103 ; h. 441, rem. 136 ; c. 208, rem. 220. 
 
 Page 163. — 2. 446 sheep. 3. $816.75. 4. $8615. p 296 
 
 Page 164. — 5. $438.25. 6. $909. 7. $27,450. 8. $ 10.91. 9. $9.04. 
 10. $15.47. 
 
 Page 165. — 12. $6020. 13. 8624| gal. 14. 86. .15. 602. 
 
 Page 166. — 17. $6.16. 18. 525 mi. 19. 36 da. 20. $984. 
 
 21. $2.62. 22. $99. 23. $348. 
 
 Pagel67. — 25. 74 A. 26. 50 cows. 27.80 ft. 28.792. 29. $21. 
 30. 40 rings. 
 
 Page 168. — 32. $.121. 33. 50 da. 34. $157.50. 35. 60 da. 
 
 36. $25.20. 37. 10,976 1b. 38. $14,700. 
 
AKSWEKS 297 
 
 Pagel69. — 39. 26,2081b. 40. $.25. 41. 2736 bu. 42. 72 books. 
 43. $94.40. 44. $67.50. 45. $399.60. 46. $114.40. 47. $3.72. 
 48. $813. 49. $32. 
 
 Page 170. — 50. $18.73. 51. $3.24. 52. $19.25. 53. 39 da. 
 
 54. $984. 56. $26.46. 66. 3280 mi. 57. $6500. 58. $726. 
 
 59. $300. 
 
 Page 171. —1. 377, rem. 115. 2. 365, rem. 50. 3. 198, rem. 24. 
 4. 246, rem. 120. 5. 209, rem. 279. 6. 232, rem. 140. 7. 222, rem. 365. 
 
 8. 194, rem. 148. 9. 112, rem. 550. 10. 160, rem. 424. 11. 100, rem. 
 90. 12. 78, rem. 635. 13. 141, rem. 671. 14. 113, rem. 330. 15. 748, 
 rem. 94. 16. 96, rem. 383. 17. 135, rem. 36. 18. 122, rem. 640. 
 19. 220, rem. 8. 20. 130, rem. 39. 21. 345, rem. 163. 22. 113, 
 rem. 498. 23. 123, rem. 192. 24. 113, rem. 183. 25. 336, rem. 345. 
 26. 518, rem. 272. 27. 1001, rem. 136. 28. 2107, rem. 412. 29. 2155, 
 rem. 97. 30. 1429, rem. 516. 31. 1704, rem. 103. 32. 1390, rem. 
 59. 33. 3551, rem. 145. 34. 2743, rem. 302. 35. 1987, rem. 277. 
 36. 3191, rem. 144. 37. 1005, rem. 120. 38. 8798, rem. 56. 39. 7415, 
 rem. 12. 40. 1385, rem. 165. 41. 1242, rem. 33. 42. 4936, rem. 60. 
 43. 2583, rem. 15. 44. 2588, rem. 84. 
 
 Page 172. — 1. 6. 2. 7. 3. 9. 4. 21. 5. 55. 6. 95. 7. 100. 8. 19. 
 
 Page 173.— 2. 96^. 3.81.20. 4. $3.50. 5. $45. 6. 42 mi. 8. 20j?. 
 
 9. $3. 10. $3. 11. $41. 12. 4^. 
 
 Page 174. — 1. 6 pencils. 2. 8 yd. 3. 9qt. 5. $1.36. 6. $80. 
 8. $1.60. 9. 60^. 10. $4.80. 
 
 Page 175. — 10. $60. 11. $1.50. 12. $2|. 13. $.90. 14. $150. 
 15. $22.80; 15 yd. 
 
 Pagel76.— 16. $2.25. 17. $1.60. 18. 900 bu. 19. $216. 20. $987. 
 21. $99.75. 22. $120.96. 23. $230.88. 24. $486.08. 25. $113.52. 
 26. $103.68. 27. $145.26. 28. $346.64. 29. $588.90. 30. $1404. 
 31. $210.24. 32. $921.60. 33. $10.80. 34. $201.60. 35. $69.04. 
 
 Page 177. — 1. $1.70. 
 
 Page 178. — 2. $2.94. 3. $13.05. 4. $ .90. 5. $1.92. 6. $32.26. 
 7. $23.50. 8. $1.64. 9. $1.90. 10. $64. 
 
 Page 180. —1. 2 gal. 2. 96 pk. 3. 432 sq. in. 4. 61ft. 5. 1440 in. 
 6. 800 oz. 7. 12,000 1b. 8. 18| bu. 9. 11,250 ft. 10. J ft. 11. 1920 rd. 
 12. 120 yd. 13. 405 ft. 14. 774 sq. yd. 15. 11 doz. + 11 ; 13 doz. + 9 ; 
 16 doz. + 3. 16. 1728 sq. in. 17. 78 sq. ft. 18. S .20 profit per bu. 
 
 19. 1008 sq. ft. in floor ; 1008 sq. ft. in ceiling. 20. 3600 ft. 21. $32. 
 
 Page 181. — 1. $16,800. 2. $9750. 3. .$440. 4. $162. 5. 8400. 
 
298 
 
 
 ANSWERS 
 
 
 
 Page 182.— 
 
 
 
 
 
 
 1. a. 
 
 256, rem. 50 
 
 ; &• 
 
 106, rem. 
 
 172 
 
 c. 
 
 37, rem. 537. 
 
 2. a. 
 
 1237, rem. 7 
 
 6. 
 
 98, rem. 
 
 179 
 
 c. 
 
 89, rem. 764. 
 
 3. a. 
 
 236, rem. 15 
 
 6. 
 
 109, rem. 
 
 423 
 
 c. 
 
 158, rem. 144. 
 
 4. a. 
 
 1523, rem. 6 
 
 h. 
 
 98, rem. 
 
 174 
 
 ; c. 
 
 46, rem. 684. 
 
 5. a. 
 
 355, rem. 71 
 
 b. 
 
 100, rem. 
 
 124 
 
 c. 
 
 99, rem. 454. 
 
 6. a. 
 
 979, rem. 13 , 
 
 b. 
 
 122, rem. 
 
 658 
 
 c. 
 
 63, rem. 415. 
 
 7. a. 
 
 1039, rem. 25 
 
 b. 
 
 221, rem. 
 
 4 
 
 c. 
 
 172, rem. 80. 
 
 8. a. 
 
 2120, rem. 22 
 
 b. 
 
 110, rem. 
 
 345 
 
 c. 
 
 24, rem. 48. 
 
 9. a. 
 
 2678, rem. 11 
 
 b. 
 
 18, rem. 
 
 768, 
 
 c. 
 
 83, rem. .346. 
 
 10. a. 
 
 671; 
 
 b. 
 
 165, rem. 
 
 387 
 
 c. 
 
 62, rem. 222. 
 
 11. a. 
 
 598, rem. 50 
 
 b. 
 
 188, rem. 
 
 346 
 
 c. 
 
 215, rem. 125. 
 
 12. a. 
 
 207, rem. 25 
 
 b. 
 
 109, rem. 
 
 202 
 
 c. 
 
 40, rem. 802. 
 
 13. a. 
 
 392, rem. 28 
 
 b. 
 
 79, rem. 
 
 546 
 
 c. 
 
 117, rem. 46. 
 
 14. a. 
 
 2008, rem. 9 
 
 b. 
 
 105, rem. 
 
 68 
 
 > c. 
 
 252, rem. 220 
 
 15. a. 
 
 957, rem. 6 
 
 b. 
 
 84, rem. 
 
 39 
 
 c. 
 
 57, rem. 241 
 
 16. «. 
 
 1044, rem. 25 
 
 b. 
 
 36, rem. 
 
 46 
 
 c. 
 
 83, rem. 364 
 
 17. a. 
 
 2089, rem. .30 
 
 b. 
 
 80, rem. 
 
 25 
 
 , c. 
 
 113, rem. 331 
 
 18. a. 
 
 757, rem. 46 
 
 b. 
 
 307, rem. 
 
 43 
 
 c. 
 
 68, rem. 591 
 
 19. a. 
 
 1279, rem. 47 
 
 b. 
 
 267, rem. 
 
 53 
 
 c. 
 
 103, rem. 196 
 
 20. a. 
 
 987, rem. 64 
 
 b. 
 
 58, rem. 
 
 174 
 
 c. 
 
 133, rem. 76. 
 
 21. a. 
 
 954, rem. 13] 
 
 b. 
 
 42, rem. 
 
 388 
 
 c. 
 
 249, rem. 186. 
 
 22. a. 
 
 810, rem. 17; 
 
 b. 
 
 77, rem. 
 
 237 
 
 ; c. 
 
 83, rem. 18 
 
 23. a. 
 
 1234, rem. 40 
 
 b. 
 
 131, rem. 
 
 400 
 
 c. 
 
 154, rem. 307. 
 
 Page 183. —24. Children, 5240 ; $ 786 ; adults, 12,641 ; $ 3160.25 ; 
 one-horse vehicles, 1-388; $485.80 ; two-horse vehicles, 796, $398 ; total, 
 $4830.05. 25. Tiies. $ 1083.20 ; Wed., $ 1326.40 ; Thurs., $1008.50; 
 
 Fri., $1411.95. 26. $4830.05 ; $4830.05. 27. $12.50. 28. $.36. 
 
 29. $105. 30. $.18. 31. $4060. 32. 61^ lb. 33. 770 girls, 
 
 462 boys. 
 
 Page 184. — 34. 58 wk. 35. $12.16. 36. $36.86|. 37. $2.31. 
 
 38. $356. 39. $1.50. 40. $840. 41. $.60. 42. 36ft.; 
 
 5184 sq. ft. 43. $5.76. 
 
 Page 185.— 44. 40 people. 45. 210 rd. 46. 30 sq. yd. 47. 22 yd.; 
 66 ft. ; 792 in. 48. $.46. 49. 7^ ft. ; 468 sq. in. 50. $15. 51. $11.77^. 
 52. 75,273,334. 53. $13. 
 
ANSWERS 299 
 
 FIFTH YEAR 
 
 Page 189. -16. 6 J in. 17. 13| yd. 18. 2| ft. 19. llj ft. 20. 9|ft. 
 21. lUyd. 22. 4 ft. 23. 46| ft. 
 
 Page 191.-14. -^S^V 15. 294 mi. 16 $16^. 17. 9|. 18. 34^ mi. 
 19. $62i^V 20. 90^. 21. 321 da. 22. $1^. 23. 12^^ hr. 24. ^ij\. 
 
 25. 36/j min. 
 
 Page 192.-10. 14| ft. 11. 64^^^ ft. 12. 49|. 13. 30H. 14. $4^. 
 15. oHyd. 16. 45p5mi. 17. 16^^. 18. 15| ft. 19. 54 rd. 
 Page 193. -12. 106f. 13. 43^- 14. 104||. 15. 24f. 16. 98i| ft. 
 
 17. 75fmi. 18. 50 bu. 19. 35f da. 20. 2^. 21. 2j%. 22. 2j\. 
 23. 2^2. 24. 2T'^in. 25. 2^| bu. 26. 4^ lb. 27. 10| da. 
 
 Page 194. -9. 77^\ in. 10. 84|| bu. 11. 7H|. 12. 88i|. 13. 2^2 yd. 
 
 14. 7TVcla. 15. 15f. 16. 3H|. 
 
 Page 196.-2. x^^,xV ^. j% {I ^-Ihih 5- ^h -h- 6. f , |, |. 
 7. hhl- 8- iVA,tV 9- M'ifi»3^- 11- h 12. h 13. I 14. h 
 
 15. i. 16. f 17. f. 18. |. 19. i. 20. f. 23. 2. 24. i^. 25. If. 
 
 26. 9. 27. 4^. 
 
 Page 199.-2. f. 3. |. 4. ,V 5. f. 6. if. 7. j\. 8. yV 9. f. 
 
 10. ^V 11. A. 12. ii. 13. f. 14. A. 15. H. 16. rV 17- tV 
 
 18. f. 19. i 20. ^^\. 21. l^J^yd. 22. $^. 
 2. ]2|. 3. 28rV 4. 29f. 5. 137i. 
 
 Page 200. -6. 58f. 7. 72^. 8. 148f 9. 3953!g. 10. 385|. 
 
 11. 1582^. 12. 23|i 13. 140f. 14. 8f mi. 15. $66^. 
 
 2. 16'-. 3. 21 9f. 4. 99.K 5. 92 H- 6. 192. 7. 1038. 8. 43,5^. 
 
 9. 50?. 
 
 Page 201. -10. 153. 11. 109}^. 12. 671f 13. 470^8^. 14. I If 
 15. $33. 16. 4|A. 17. 28f in. 
 
 Page 202. -2. IJ. 3. 3J. 4. 3^\. 5. 9}. 6. 5f 7. 30,^. 
 8 4jSp 9. 2f. 10. 5f 11. 4f. 
 
 Page 203.-12. f^. 13. $3^. 14. $J. 15. 9^ in. 16. 13^^ A. 
 
 2. f 3. ^V- 4. tV- 5- f. 6. /x- 7. ^V- 8- tV «• A- 
 
 10. ^V- 11 ^^- 12. |. 13. 3j3^. 14. ^V 16. ^5. 16. i. 
 17. i. 18. ^V. 19. 1^3^- 20. ^V 21. ^^. 22. ^V 
 
 Page 204. - 23. | yd. 24. ^V A. 25. ^^ of the distance. 27. 2f 28. llf 
 
 29. 17f 30. 81. 31. 2f. 32. 99iV. 33. 17 ^V 34. 21t^. 
 
 35. 6|. 36. 27t\. 37. 54^^. 38. ^^jj. 39. 124^|. 40. 9f 
 
 41. 132f 42. 43||. 43. lOJ. 44. 39f. 46. 6^^. 46. SOjV 
 
 47. 47f 48. i^lf 49. 7^ gal. 50. 9| bu. 
 
300 ANSWERS 
 
 Page 205. — 52.* 1 J. 53. 3i. 54. 7i. 55. 8i. 56. 7|. 57. 13 jV 
 58. la^L- 59- 53t6- 60. 622V 61. 55^^ 62. 66f 63. 66f. 64. ld^\. 
 66. 13^5. 66. 4S^\. 67. 43^^. 68. 10 1?^. 69. 12/^. 70. 40 j%. 71. 7|. 
 12. 12f A. 73. 2/5 hr. 74. .$7^. 75. ^^ mi. 
 
 1. $lf 2. 5ift. 3. $2^^. 
 
 Page 206.— 4. $2|f. 5. 1ft. 6. 7| ft. 7. 8J T. 8. 12^V '«• 
 
 6. 8igal. 10. S24^||. 11. 291 mi. 12. 45f. 13. 8xV 14. aiDj?^. 
 
 15. 8^ mi. 16. .$30if. 
 
 Page 207. — 17. ^S^^^. 18. $29^^. 19. .|21ii. 20. 43^% hr. ; 28fi- hr. 
 
 Page 209. — 1. $900. 2. 1000 A.; 1000 A.; 500 A. 
 
 Page 210. — 3. 292 da. 4. $160. 5. $5460. 6. 9200 girls; 
 5520 boys. 7. $35. 8. $648. 9. $5800. 
 
 Page 211. — 1. 27 pupils. 2. $24. 3. 30 words. 4. 49 lambs. 
 5. 180 da. 6. $120. 7. $600. 8. $225. 9. 66 mi. 10. $5060. 
 
 Page 212. — 11. 442 mi. 12. 72 ft. 
 
 Page 213. — 2. 36. 3. 45. 4. 24. 5. 45. 6. 36. 7. 32. 8. 102, 
 9. 51. 10. 18. 11. 24. 12. 45. 13. 108. 14. 575. 15. 2685. 
 
 16. 1826. 17. 640. 18. 1320. 19. 360. 20. 2325. 21. 1768. 
 22. 1470. 23. 720. 24. 1760. 25. 376. 26. 1425. 27. 825. 28. 3030. 
 
 Page 214. — 29. $150. 30. $525. 31. $.3.75 cost; $2.25 gain. 
 32. $2.80. 33. $.50. 34. $2.30. 35. $3. 36. 500 mi. 37. $845. 
 38. 99 cd. 39. $257.25. 40. $679. 
 
 Page 215. — 41. $15,000. 42. $5680. 43. $1.35. 44. 2681 rd. 
 45. 74011 mi. 46. 1409^^ T. 
 
 Page 217.— 3. 45. 4. 138. 5. 326. 6. 4806. 7. 10,806. 8. 1100. 
 9. 3927. 10. 6006. 11. 4284. 12. 1704. 13. 9729. 14. 15,606. 
 15. 9004. 16. 3241. 17. 2005. 18. 2315. 19. 2499. 20. 3027. 
 21. 8165. 22. 14,885. 23. 114. 24. 144. 25. 249. 26. 64-5. 27. 3996. 
 28. 2012. 29. 14,895. 30. 2092. 31. 6276. 32. 5615. 33. 2476. 
 34. 4900. 35. 470. 36. 208. 37. 7990. 38. 4104. 39. 348. 40. 1020. 
 41. 5971. 42. 196. 43. 357. 44. 1687. 45. 438 mi. 46. $73.50. 
 47. $24.75. 48. $220. 
 
 Page 218. — 49. $1.86. 50. $1.74. 51. $94. 52. $138. 53. $201. 
 54. 660 mi. 55. $4809. 56. $78f. 
 
 Page 219.-2. ff. 3. ||. 4. H- »• H- 6. |§. 7. ff 8. if. 
 9. If. 10. fe. 11. ^V 12. if. 13. U' 15. 4i. 16. 8|. 17. 4|. 
 18. 10^. 19. 21^. 20. 5|. 21. 33^^- 22. 1205. 23. 60i|. 24. 52|. 
 25. 33 J. 26. 156^. 27. 261^. 28. 159f^. 29. 142|^. 
 
 1. $2. 2. $2.97. 
 
 Page220. — 3. $6.03. 4. $138^. 5. $141f. 6. $3.76. 
 
 7. $8.16. 8. $4.02. 9. $38.06. 10. $3.50. 11. $301|. 
 12. $38.26^. 13. $10,811. 14. 663^ lb. 15. 142 mi. 16. 147 mi. 
 
ANSWERS 301 
 
 Page 221.— 2. 2S. 3. 9|. 4. 12. 6. 10|. 6. IJ. 7. 7U. 
 8 106. 9. 49. 10. 3^. 11. 85. 12. 33f. 13. 37i. 14. 54. 
 1&. iW*^. 16. $5|. 17. $144. 18. 364|mi. " 19. |34§. 
 
 20. ^%>^. 
 
 Page 224.— 2. 18. 3. 5f. 4. 10. 5. 3|. 6. 4^. 7. 16 
 
 8. 2. 9. 40. 10. 12. 11. 3|. 12. 1\. 13. 2^. 14. 2 
 
 15. 2}^. 16. 9. 17. 4. 18. 7 J. 19. 3i. 20. $.16. 21. $5. 22. 30. 
 
 23. $.12. 
 
 Page i25.^2. 3. 3. 4. 4. 3. 5. 4. 6. 6^. 7. li. 8. 2. 9. 5. 
 
 10. liV 11. Iff. 12. 11. 13, If. 14. \. 15. ItV 16. If 17. 2^f. 
 
 18. 11. 19. l|f 20. 16 vests. 21. 7 pictures. 22. 24 yd. 23. 16 gal. 
 
 24. 12 hatri. 25. 12 lamps. 26. ^-f. 27. 3. 28. 7. 
 
 Page 227.-2. 27. 3. 40. 4. 36. 5. 49. 6. 40. 7. 77. 
 8. 63. 9. 72. 10. 81. 11. 100. 12. 96. 13. 117. 14. 144. 15. 108. 
 
 16. 60. 17. 225. 18. 171. 19. 910. 20. 204. 21. 405. 22. 504. 
 
 23. 10. 24. 12. 25. 9. 26. 10. 27. 16. 28. 16. 29. 9. 30. 20. 
 31. 27. 32. 24. 33. 40. 34. 45. 35. 42. 36. 100. 37. 40. 38. 45. 
 39. 204. 40. 63. 41. 80. 42. 3f. 43. 3|. 44. 4|. 45. 3f 46. 4^. 
 47. 3^. 48. 4f 49. 5f. 50. 2\. 
 
 Page 228.^1. 1^ 2. 2. 3. 2\. 4. \\. 5. \^^. 6. 152|. 7. ||. 
 8. 2\. 9. 3^. 10. 4f 11. 12|. 12. If. 13. \\\. 14. 2^^. 15. 3^. 
 
 16. f. 17. li- 18. 2^V 19. ^. 20. 121. 21. 7. 22. ^^i^. 23. |f. 
 
 24. 43yV. 2a. 42|. 26. 8y%. 27. 13|. 28. i\. 29. 2||. 30. ^V 
 31. $205.03xV. 32. $631f 33. $2105f. 34. 126 badges. 
 
 Page 229.^^35. $11,340. 36. 70. 37. $1.35. 39. |. 40. \\. 
 
 41. 50 ft. 42. $60. 43. 20^ rd. 44. 25f| mi. 46. 434»V lb. 
 
 46. 2112 steps. 47. 929 [f lb. 
 
 Page 232.-1. $18^V- 2. $12|. 3. 17 J yd. 4. $40.50. 5. 9 yd. 
 
 6. 157 1b. •:. $4125. 8. 46 da. 9. $370, son; $ 1480, daughter; 
 $ 1665, widow; $ 925, hospital. 10. 81^ yd. 11. 100^ hr. 
 
 Page 233. — 12. $4128. 13. 16. 14. 450. 15. $3.31^. 16. $24. 
 
 17. $54. 18. 79 families. 19. $11.60. 20. $3.90. 21. 25^. 
 22. $.18. 23. 31 J;^. 24. $35.95. 
 
 Page 234.— 25. $5. 26. 8^ yd. 27. 12. 28. 15 mi. 29. 75i A. 
 30. 8124. 31. 48 books. 32. $38. 33. $38^. 34. $49. 35. 50 chairs. 
 36. 4|yd. • 37. 14^ yd. 38. $5.25. 39. 232 pencils. 
 
 Page235. — 40. 15 coats. 41. 105f lb. 42. 57f bu. 43.312 yd. 
 44. 25^ da. 45. 106f bu. 46. $.20. 47. $81. 48. $800. 49. $.55. 
 50. 220 sheep. 62. 33 bu. 53. 35^;2^^;6|. 54. $.20. 
 
 Page 240.-2. ^V 3. f^ 4^ ^^. 5. if 6. f. 7. ^V- 8- i- 9- \l 
 
 12. .25; .75; .125; .375. 13. ^V 14. f. 15. f. 16. ^f. 17. |. 18. |. 
 
 19. 1. 20. |. 21. i. 22. jV 23. ff. 24. if. 25. f 26. i?. 27. ^V 
 28. h 29. ^L. 30. ^2^. 31. ^-^. 32. ^V 33. ^\. 34. ^%. 35. ^V- 36. f. 
 
 Page 241.— 2. 1.015. 3. .221. 4. .256. 5. 9.1. 6. 13.189. 
 
 7. .0311. 8. 18.027. 9. .0922. 
 
302 ANSWERS 
 
 • 
 
 Page 242.-10. 44.85. 11.2.9. 12.17.165. 13.38.793. 14.26.676. 
 
 15. 14.806. 16. 143.192. 17. 137.768. 18. 2171.812. 19. 225.303. 
 
 20. 47.97. 21. 2.75 bu. 22. $4.94. 23. 82.1 mi. 24. 5.25 1b. 
 
 25. 23.93 mi. 
 
 Page 243.-2. 5.79. 3. 12.954. 4. .305. 5. 180.892. 6. 16.02. 
 
 7. 72.927. 8. 695.725. 9. 18.835. 10. 131.745. 11. 38.615. 12. 32.996. 
 
 13. 108.967. 14. $3.75. 15. 5.375 mi. 16. 55.75 A. 17. •'$2.20. 
 
 Page 244.-18. 10.86 ft. 19. 28.46 ft. 20. $2.05. 21. 6.75 1b. 
 
 22. 5.125 1b. 23. .375 1b. 24. 27.6 T. 25. 6.75 yd. 26. $6.32. 27. $4.35. 
 
 Page 245. -2. .12. 3. .045. 4. 1.36. 5. 2.277. 6. 6.79. 7. .3. 
 
 8. 3.024. 9. .486. 10. 74.046. 11. 2.738. 12. 61.64. 13. 31.02. 
 
 14. 3.63. 15. 18.213. 16. 4.56. 17. 2.916. 
 
 Page 246.-18. $5.74. 19. $ 8.40. 20.148.5 ft. 21. $94.90. 
 
 22. !$ 14.49. 23. 248.5 mi. 
 
 Note. In business problems count 5 mills or more as an additional 
 cent. 
 
 Page 247.-2. .216. 3. .225. 4. .0384. 5.65. 6.5.3.58. 7.14.445. 
 8. 57.92. 9. .462. 10. .0855. 11. .812. 12. 6.960. 13. 1710. 14. 3.1. 
 
 15. 90.9. 16. .468. 17. 7.92. 18. 153.6. 19. 58.52. 20. $1.44. 21. $.72. 
 22. $51.56. 23. 481.95 mi. 24. 17.0625 mi. 25. $8.97; $15.53. 
 
 26. $65. 27. 796.8751b. 
 
 Page 248. -2. .11. 3. .32. 4. .101. 5. .102. 6. .107. 7. .212. 
 
 8. .121. 9. .156. 10. .112. 13. .075. 14. .075. 15. .045. 16. .056. 
 17. .3. 18. .3. 19. .02. 20. .001. 21. .002. 22. .03. 23. .05. 24. .03. 
 
 25. .004. 26. .034. 27. .003. 28. .012. 29. .005. 30. .009. 31. .113. 
 32. .072. 33. .036. 34. .04. 35. .025. 36. .04. 37. .05. 38. .007. 
 39. .011. 40. .006. 
 
 Page 249.-6. 3.04. 7. 2.11. 8. 6.1. 9. 22..3. 10. .101. 11. 3.4. 
 
 12. .039. 13. .124. 14. .027. 15. 1.16. 16. .022. 17. .036. 18. .14. 
 
 19. .0017. 20. .029. 21. .038. 22. .143. 23. 6.14. 24. 6.04. 25. .089. 
 
 26. .475. 27. .605. 28. .065. 29. .0904. 
 
 Page 250. -31. .266+. 32. .4. 33. .105+. 34. .08. 35. .444+. 36. .5. 
 37. .2. 38. .5. 39. .5. 40. .25. 41. .125. 42. .0124+. 
 
 Page 251.-2. .65. 3. .84. 4. 8.7. 5. .74. 6. 7.4. 7. 8.5. 8. 7.7. 
 
 9. 8.4. 10. 8.2. 11. 9.4, 12. .87. 13. .75. 14. 49. 15. *89. 16. 8.4. 
 17. .83. 18. 9.5. 19. 760. 20. .05. 21. 45. 22. 8.6. 23. 9.6. 24. 2.8. 
 25. 870. 26. 670. 27. 9.2. 28. 32.1. 
 
 Page 252.-29. .001. 30.12.5. 31.1.^1. 32.144. 33.50.6. 34.233. 
 35. 3.6. 36. 17.4. 37. 27.9. 38. 266.9. 39. 32.6. 40. 42.4. 41. 37.5. 
 42. 82.3. 43. 56.1. 44. 28.3. 45. 43.6. 46. 38.4. 
 
 1. 5. 2. 48.3.9577. 3. $1.05. 4. 365 da. 5. 4.25 T. 6. 19.2 A. 
 7. 85.375 T. 8. 29. 9. $140.63. 
 
 Page 253.-10. 2240.8 mi. 11. $1.69. 12. 142 pieces. 13. 1.376 carats. 
 14. 16.625 1b. 15. 1.5 T. 16. 6 qt. 17. $20. 18.354 ft. 19. $133.09. 
 
 20. 220 bbl. 21. 1000. 
 
ANSWERS 303 
 
 Page 256. — 2. 8106.65. 3. .^66.92. 4. $126.48. 5. $3.44. 6. $4.54. 
 
 7. a31.71. 8. $8.20. 9. $200.40. 10. $10.03. 11. $35.04. 12. $453.75. 
 
 13. $741.85. 14. $3035.25. 15. $724. 16. $6867.84. 17. $157.50. 
 18. $33. 19. 594 mi. 20. $1027. 21. $50. 
 
 Page 257. — 22. 403.2 rd. 23. $386.90. 24. $140. 25. 1 ; 2 ; 2.5 ; 3 ; 4. 
 26. $7.20. 27. $0. 28. $10. 29. $128. 30. 225 sheep. 31. 24 words. 
 33. $616. 34. $5075. 
 
 Page 259. — 2. $10. 3. $144. 4. $27. 5. $112. 6. $9. 7. $15.36. 
 
 8. $lt).25. 9. $33.75. 10. $28.50. 11. $56. 12. $42.75. 13. $180.95. 
 
 14. $29.25. 15. $15.75. 16. $6; $206. 17. $8; $408. 18. $19.50; 
 $169.50. 19. $9.30; $629.30. -20. $10.80; $280.80. 21. $16.75; 
 $365.75. 22. $287.50. 
 
 Page 261.— 2. $1.50. 3. $3.75. 4. $1.13. 5. $.92. 6. $28.13. 
 7. $121.50. 8. $13.30. 9. $6.38. 11. 46 pairs. 12. 116| bu. 
 
 Page 262.— 13. 4 doz. 14. $90. 15. $16.50. 16. $40.55. 17. $3.60. 
 18. 25 yd. 
 
 Page 263. — 1. $3.25. 2. $173. 3. $3.0.3. 4. $10.45. 5. $6.56. 
 
 Page 264.— 6. $4.65. 7. $3.98. 8. $31.09. 9. $21.17. 
 
 Page 265. —1. $7. 2. $10.95. 3. $84.62. 
 
 Page 267.-2. 49 pt. 3. 67 pt. 4. 38 pt. 5. 45 pt. 6. 7 pt. 
 7. $2.80. 8. $4. 10. 187 qt. 1 pt. 11. 423 qt. 12. 34 gal. 3 qt. 
 13. 84 gal. 1 qt. 1 pt. 14. 117 gal. 1 qt. 15. 1750 pt. 16. 52 qt. 
 
 17. 1152 pt. 
 
 Page 268. — 1. 236 pt. 2. H bu. 3. 37^ bu. 4. 16i bu. 5. 561 pt. 
 6. 23^5 bu. 
 
 Page 270. — 1. 101 oz. 2. 6800 1b. 3. 6448 oz. 4. 8800 oz. 
 
 6. 36 cwt. 6. 64,080 oz. 7. 34 lb. 8. 3 T. 9. 8 lb. 10. 50 lb. 10 oz. 
 
 Page 271.- 1. 11,160 sec. 2. l|da. 3. 7380 min. 4. 3240 da. 
 
 5. 2160 hr. 6. 2 wk. 7. 4 da. 8. 2,592,000 sec. 9. 19,800 sec. 
 
 Page272. — 10. $21. 11. $10.80. 12. $58.50. 13. $21. 
 
 Page 273. — 1. 396 in. 2. 36 ft. 3. 154 yd. 4. 31,680 in. 
 
 6. 138 in. 6. 76 ft. 7. 48 yd. 8. 1 rd. 
 
 Page 274.— 1. 4320 turns. 2. $10.08. 3. 88 rd. 4. 108 1b.; 91b. 
 5. 1 gal. 1 qt. 1 pt. 6. $145.20. 7. 9^^ lb. 8. $63. 9. 34 doz. 
 10. 1211b. 11. 1000 baskets. 12. $25. 
 
 Page 275. — 13. $3.02 change. 14. $6.20. 15. $21. 16. 208 cans. 
 17. $3^; $.06|. 18. $5.75. 19. 791b. 20. $3.78. 21. 70 yr. 
 
 22. 12 T. 41 lb. 
 
30^ ANSWERS 
 
 Page 277. —1. 120 sq. in. 2. 26f sq.ft. 3. 3650 sq. ft. 4. 36i 
 sq. in. 8. 824. 9. ^42.63. 10. 6| sq. ft. 11. |2.99. 12. Second 
 is 110 sq. in. larger. 13. ^37.50. 
 
 Page 278. — 14. $76.50. 15. $192.50. 16. :J of it. 17. ^ as large. 
 
 Page280. — 4. 19,200 cu. ft. 5. 711^ cu. yd. 6. 12 cu. ft. 
 
 Page 281.— 7. 384 cubes. 8. 40 sq. ft. 9. 27,648 cu. in. 10. 480 
 cu. ft. 11. 385.7106+ bu. 12. 6000 Ibi 13. 320 cu. ft. 15. 18 sq. ft. 
 
 Page 282. — 19. 1728 cu. in. 21. 18 cu. ft. 22. 27 cu. in. 23. 64 
 cu. in. 24. 8 cu. in. 25. 8 times. 26. 24 cu. in. 27. 4 sq. in. 
 
 28. 25 more. 29. $26.07. 30. l3| loads ; $4.17. 
 
 Page 283.— 1. |2.08. 2. $6.27. 3. 102,700. 4. $135. 5. 12^. 
 6. $.18. 7. 6 aprons. 8. Four thousand six and fifteen thousandths. 
 9. 75 A. 10. $240. 11. 101 pt. 12. 35 mi. 13. 37| yd. 
 
 Page 284. — 14. 755,040 ft. 15. 24. 16. $ 14,400. 17. $57. 
 
 18. $12.00. 19. 15 bu. 2 pk. 2 qt. 20. $41.25. 22. $3.75. 23. if ; 
 ^1; ^f. 24. 21^. 26. 312 yd. 27. ^ A. ; .05 A. 28. 42 1b. 
 
 29. $60.12. 30" 900 cu. ft. 
 
 Page 285.— 31. $8.64. 32. (1) 51.2 yd. ; 53.76 yd. ; 42 yd. ; (2) 72 
 
 pal.; 219.6 gal. ; 27 gal. ; (3) 12 bu. ; 45 bu. ; 58 bu. 33. $4.53. 
 
 34. $4.62. 35. $288. 36. 84 1b. 37. $28.80. 38. $379.17. 
 
 39. 195 yd. 40. $1664. 41. 92f lb. 
 
 Page 286.— 42. $3.99. 43. $3798.44. 44. 100 bu. 46. 204 yd. 
 46. $600. 47. $1.50. 48. $1.60. 49. $42. 50. 7 yd. 61. $67.50. 
 62. $ 224^. 53. 82 A. 54. 13| T. 55. 74| ft. 
 
 Page 287. — 56. $ H. 67. Mary, $i^. 58. $llf. 59. 4. 60. $486.10. 
 61. 70 pk. 62. 1000. 63. 72. 64. 103 pk. 65. $17.40. 66. 4 times ; 
 3^ times; 331 times. 67. $67.50. 68. $30.50. 
 
 Page 288.— 69. 2701b. 70. 1134 cu. ft. 71. $9.60. 72. 9 bbl. 
 73. 80 marbles. 74. 32 marbles. 75. $7.50. 76. 143 bu. 3 pk. 
 
 77. $3.73. 78. $215.25. 79. 96 loads. 80. 112.752. 81. $29.40. 
 
H IC KS'S C HAM PI ON 
 SPELLING BOOK 
 
 By WARREN E. HICKS, Assistant Superintendent of 
 Schools, Cleveland, Ohio 
 
 Complete, $0.25 - Part One, $0.18 - Part Two, $0.18 
 
 THIS book embodies the method that enabled the pupils 
 in the Cleveland schools after two years to win the Na- 
 tional Education Association Spelling Contest of 1908. 
 ^ By this method a spelling lesson of ten words is given each 
 day from the spoken vocabulary of the pupil. Of these ten 
 words two are selected for intensive study, and in the spelling 
 book are made prominent in both position and type at the head 
 of each day's lessons, these two words being followed by the 
 remaining eight words in smaller type. Systematic review is 
 provided throughout the book. Each of the ten prominent 
 words taught intensively in a week is listed as a subordinate 
 word in the»next two weeks; included in a written spelling 
 contest at the end of eight weeks ; again in the annual contest 
 at the end of the year ; and again as a subordinate word in the 
 following year's work; — used five times in all within two 
 years. 
 
 ^ The Champion Spelling Book consists of a series of lessons 
 arranged as above for six school years, from the third to the 
 eighth, inclusive. It presents about 1,200 words each year, 
 and teaches 3 i 2 of them wdth especial clearness and intensity. 
 It also includes occasional supplementary exercises which serve 
 as aids in teaching sounds, vowels, homonyms, rules of spell- 
 ing, abbreviated forms, suffixes, prefixes, the use of hyphens, 
 plurals, dictation work, and word building. The words have 
 been selected from lists, supplied by grade teachers of Cleve- 
 land schools, of words ordinarily misspelled by the pupils of 
 their respective grades. 
 
 AMERICAN BOOK COMPANY 
 
STEPS IN ENGLISH 
 
 By A. C. McLEAN, A.M., Principal of Luckey School, 
 Pittsburg; THOMAS C. BLAISDELL, A.M., Pro- 
 fessor of English, Fifth Avenue Normal High School, 
 Pittsburg; and JOHN MORROW, Superintendent of 
 Schools, Allegheny, Pa. 
 
 Book One. For third, fourth, and fifth years ^0.40 
 
 Book Two. For sixth, seventh, and eighth years 60 
 
 THIS series presents a riew method of teaching language 
 which is in marked contrast with the antiquated systems 
 in vogue a generation ago. The books meet modern 
 conditions in every respect, and teach the child how to ex- 
 press his thoughts in language rather than furnish an undue 
 amount of grammar and rules. 
 
 ^ From the start the attempt has been made to base the work 
 on subjects in which the child is genuinely interested. Lessons 
 in writing language are employed simultaneously with those in 
 conversation, while picture-study, the study of literary selec- 
 tions, and letter-writing are presented at frequent intervals. 
 The lessons are of a proper length, well arranged, and well 
 graded. The books mark out the daily work for the teacher 
 in a clearly defined manner by telling him what to do, and 
 when to do it. Many unique mechanical devices, e. g., a 
 labor-saving method of correcting papers, a graphic system of 
 diagramming, etc., form a valuable feature of the work. 
 ^ These books are unlike any other series now on the 
 market. They do not shoot over the heads of the pupils, 
 nor do they show a marked effort in writing down to 
 the supposed level of young minds. They do not contain 
 too much technical grammar, nor are they filled with what 
 is sentimental and meaningless. No exaggerated attention is 
 given to analyzing by diagramming, and to exceptions to ordi- 
 nary rules, which have proved so unsatisfactory. 
 
 AMERICAN BOOK COMPANY 
 C81) 
 
RODDY'S GEOGRAPHIES 
 
 By JUSTIN RODDY, M.S., Department of Geography, 
 First Pennsylvania State Normal School, Millersville, Pa. 
 
 Elementary Geography . ^0.50 
 
 Complete Geography . . j^l.oo 
 
 THIS "information** series meets a distinct demand for 
 new geographies which are thoroughly up to date, and 
 adapted for general use, rather than for a particular use 
 in a highly specialized and organized ideal system. While 
 not too technical and scientific, it includes sufficient physio- 
 graphic information for the needs of most teachers. 
 ^ An adequate amount of material is included in each book 
 to meet the requirements of those grades for which it is designed. 
 This matter is presented so simply that the pupil can readily 
 understand it, and so logically that it can easily be taught by 
 the average teacher. 
 
 ^ The simplicity of the older methods of teaching this subject 
 is combined with just so much of the modern scientific methods 
 of presentation as is thoroughly adapted to elementary grades. 
 Only enough physiography is included to develop the funda- 
 mental relations of geography, and to animate and freshen the 
 study, without overloading it in this direction. 
 ^ The physical maps of the grand divisions are drawn to the 
 same scale, thus enabling the pupil to form correct concepts 
 of the relative size of countries. The political and more de- 
 tailed maps are not mere skeletons, giving only the names 
 which are required by the text, but are full enough to serve 
 all ordinary purposes for reference. In addition, they show 
 the principal railroads and canals, the head of navigation on 
 all important rivers, and the standard divisions of time. 
 ^ The illustrations are new and fresh, reproduced mostly 
 from photographs collected from all parts of the world. 
 Formal map studies or questions accompany each map, direct- 
 ing attention to the most important features. 
 
 AMERICAN BOOK COMPANY ' 
 
 Clio) 
 
BROOKS'S READERS 
 
 By STRATTON D. BROOKS, Superintendent 
 of Schools, Boston, Mass. 
 
 FIVE BOOK SERIES 
 
 First Year $0.25 
 
 Second Year 35 
 
 Third Year 40 
 
 Fourth and Fifth Years . .50 
 Sixth, Seventh, and 
 
 Eigjith Years . . . .60 
 
 EIGHT BOOK SERIES 
 
 First Year i^o.25 
 
 Second Year . *. , . .35 
 
 Third Year 40 
 
 Fourth Year 40 
 
 Fifth Year 40 
 
 Sixth Year 40 
 
 Seventh Year 40 
 
 Eighth Year 40 
 
 THESE readers form a good all-round basal series, suit- 
 able for use in any school ; but they will appeal to 
 teachers particularly, because of their very easy gradation. 
 Both in thought and expression, the books are so carefully 
 graded that each selection is but slightly more difficult than 
 the preceding one, and there is no real gap anywhere. 
 ^ Although a wide variety of reading matter is provided, 
 good literature, embodying child interests, has been considered 
 of fundamental importance. Lessons of a similar nature are 
 grouped together, and topics relating to kindred subjects recur 
 somewhat regularly. All are designed to quicken the child's 
 observation, and increase his appreciation. 
 ^ By the use of this series, the child will be taught to read in 
 such a manner as will appeal to his interests, and at the same time 
 he will be made acquainted with the masterpieces of many fa- 
 mous writers. He will gain a knowledge of many subjects, and 
 acquire pure and attractive ideals of life and conduct. His imagi- 
 nation will be cultivated by pleasing tales of fancy, and he will 
 also be taught a love of country, and given glimpses into the 
 life of other lands. 
 
 ^ The books are very attractive in mechanical appearance, 
 and contain a large number of original illustrations, besides 
 reproductions of many celebrated paintings. 
 
 AMERICAN BOOK COMPANY 
 
 •liO 
 
CARPENTER'S READERS 
 
 By FRANK G. CARPENTER 
 GEOGRAPHICAL READERS 
 
 North America . . ^0.60 
 
 South America . , .60 
 
 Europe . . . . .70 
 
 As:a . . . . .60 
 
 Africa .... j55o.6o 
 Australia, Our Colonies, 
 and Other Islands of the 
 Sea . . . . .60 
 
 READERS ON COMMERCE AND INDUSTRY 
 How the "World is Fed . $0.60 I How the World is Clothed $0.60 
 
 CARPENTER'S Geographical Readers supplement the 
 regular text-books on the subject, giving life and interest 
 to the study. They are intensely absorbing, being 
 written by the author on the spots described, and presenting 
 an accurate pen-picture of places and peoples. The style is 
 simple and easy, and throughout each volume there runs a 
 strong personal note which makes the reader feel that he is 
 actually seeing everything with his own eyes. 
 \\ The books give a good idea of the various peoples, their 
 strange customs and ways of living, and to some extent of their 
 economic condition. At the same time, there is included a 
 graphic description of the curious animals, rare birds, wonder- 
 ful physical features, natural resources, and great industries of 
 each country. The illustrations for the most part are repro- 
 ductions of photographs taken by the author. The maps show 
 the route taken over each continent. 
 
 ^ The Readers on Commerce and Industry give a personal 
 and living knowledge of the great world of commerce and 
 industry. The children visit the great food centers and see 
 for themselves how the chief food staples are produced and 
 prepared for use, and they travel in the same way over the 
 globe investigating the sources of their clothing. The journeys 
 are along geographical lines, and while studying the industries 
 the children are learning about localities, trade routes, and the 
 other features of transportation and commerce. 
 
 AMERICAN BOOK COMPANY 
 
 _ 
 
WEBSTER'S 
 SCHOOL DICTIONARIES 
 
 Revised Editions 
 
 T 
 
 HESE Dictionaries have been thoroughly revised, 
 entirely reset, and made to conform to that great stand- 
 ard authority — Webster's International Dictionary. 
 
 WEBSTER'S PRIMARY SCHOOL DICTION- 
 ARY ^0.48 
 
 Containing over 20,000 words and meanings, with over 
 400 illustrations. 
 
 WEBSTER'S COMMON SCHOOL DICTION- 
 ARY ^0.72 
 
 Containing over 25,000 words and meanings, with over 
 500 illustrations. 
 
 WEBSTER'S HIGH SCHOOL DICTIONARY, $0.98 
 
 Containing about 37,000 words and definitions, and an 
 appendix giving a pronouncing vocabulary of Biblical, 
 Classical, Mythological, Historical, and Geographical proper 
 names, with over 800 illustrations 
 
 WEBSTER'S ACADEMIC DICTIONARY 
 
 Cloth, ^1.50; Indexed ;^i.8o 
 
 Half Calf, ;^ 2.75 ; Indexed 3.00 
 
 Abridged directly from the International Dictionary, and 
 giving the orthography, pronunciations, definitions, and 
 synonyms of about 60,000 words in common use, with an 
 appendix containing various useful tables, with over 800 
 illustrations. 
 
 SPECIAL EDITIONS 
 
 Webster's Countinghouse Dictionary. Sheep, 
 
 Indexed ^2.40 
 
 Webster's Handy Dictionary 15 
 
 Webster's Pocket Dictionary 57 
 
 The same. Roan, Flexible .... .69 
 
 The same. Roan, Tucks -7^ 
 
 The same. Morocco, Indexed ... ^90 
 
 AMERICAN BOOK COMPANY 
 
 (104) 
 
UNITED STATES HISTORIES 
 
 By JOHN BACH McMASTER, Professor of American 
 History, University of Pennsylvania 
 
 Primary History, ^0.60 School History', $i.oo Brief History, ^i-oo 
 
 THESE Standard histories are remarkable for their 
 freshness and vigor, their authoritative statements, 
 and their impartial treatment. They give a well- 
 proportioned and interesting narrative of the chief events 
 in our history, and are not loaded down with extended 
 and unnecessary bibliographies. The illustrations are his- 
 torically authentic, and show, besides well-known scenes 
 and incidents, the implements and dress characteristic of the 
 various periods. The maps are clear and full, and well 
 executed. 
 
 ^ The PRIMARY HISTORY is simply and interestingly 
 written, with no long or involved sentences. Although brief, 
 it touches upon all matters of real importance to schools in 
 the founding and building of our country, but copies beyond 
 the understanding of children are omitted. The summaries 
 at the end of the chapters, besides serving to emphasize the 
 chief events, are valuable for review. 
 
 ^ In the SCHOOL HISTORY by far the larger part of 
 the book has been devoted to the history of the United States 
 since 1783. From the beginning the attention of the student 
 is directed to causes and results rather than to isolated events. 
 Special prominence is given to the social and economic 
 development of the country. 
 
 «[[ In the BRIEF HISTORY nearly one-half the book 
 is devoted to the colonial period. The text proper, while 
 brief, is complete in itself; and footnotes in smaller type 
 permit of a more comprehensive course if desired. Short 
 summaries, and suggestions for collateral reading, are provided. 
 
 AMERICAN BOOK COMPANY 
 
 4"6) 
 
APPLIED PHYSIOLOGIES 
 
 By FRANK OVERTON, A.M., M.D., late House 
 Surgeon to the City Hospital, New York City 
 
 Primary Physiology . . . ^o.-30 Intermediate Physiology . $0.50 
 
 Advanced Physiology . . ^0.80 
 
 OVERTON'S APPLIED PHYSIOLOGIES form a 
 series of text-books for primary, grammar, and high 
 schools, which departs radically from the old-time 
 methods pursued in the teaching of physiology- These books 
 combine the latest results of study and research in biological, 
 medical, and chemical science whh the best methods of 
 teaching. 
 
 ^ The fundamental principle throughout this series is the 
 study of the cells where the essential functions of the body 
 are carried on. Consequently, the study of anatomy and 
 physiology is here made the study of the cells from the most 
 elementary structure in organic life to their highest and most 
 complex form in the human body. 
 
 ^ This treatment of the cell principle, and its development 
 in its relation to life, the employment of laboratory methods, 
 the numerous original and effective illustrations, the clearness of 
 the author* s style, the wealth of new physiological facts, and the 
 logical arrangement and gradation of the subject-matter, give 
 these books a strength and individuality peculiarly their own. 
 ^ The effects of alcohol and other stimulants and narcotics 
 are treated in each book sensibly, and with sufficient fullness. 
 But while this important form of intemperance is singled out, 
 it is borne in mind that the breaking of any of nature's laws 
 is also a form of intemperance, and that the whole study of 
 applied physiology is to encourage a more healthful and a 
 more self-denying mode of life. 
 
 ^ In the preparation of this series the needs of the various 
 school grades have been fully considered. Each book is well 
 suited to the pupils for whom it is designed. 
 
 AMERICAN BOOK COMPANY 
 
THE ELEANOR SMITH 
 MUSIC COURSE 
 
 By ELEANOR SMITH, Head of the Department of 
 Music, School of Education, University of Chicago, 
 Director of Hull House Music School. 
 
 First Book 
 Second Book 
 
 $0.25 
 •30 
 
 Third Book .... $0.40 
 Fourth Book 50 
 
 THIS rrxusic series, consisting of four books, covers the 
 work of the primary and grammar grades. It contains 
 nearly a thousand songs of exceptional charm and 
 interest, which are distinguished by their thoroughly artistic 
 quality and cosmopolitan character. The folk songs of many 
 nations, selections from the works of the most celebrated 
 masters, numerous contributions from many eminent Ameri- 
 can composers, now presented for the first time, are 
 included. 
 
 ^ The Eleanor Smith Music Course is graded in sympathy 
 with the best pedagogical ideas — according to which every 
 song becomes a study, and every study becomes a song. 
 Technical points are worked out by means of real music, 
 instead of manufactured exercises; complete melodies, instead 
 of musical particles. Each technical point is illustrated by a 
 wealth of song material. A great effort has been made to 
 reduce to the minimum the number of songs having a very 
 low alto. 
 
 ^ The course as a whole meets the demands of modern 
 education. Modern life and modern thought require the 
 richest and best of the past, combined with the richest and 
 best of the present, so organized and arranged as to satisfy 
 existing conditions in the school and home. The series 
 is world wide in its sources, universal in its adaptation, 
 and modern in the broadest and truest sense of the 
 word. 
 
 AMERICAN BOOK COMPANY 
 
 (140) 
 
ATTRACTIVE SONG BOOKS 
 
 FOR ELEMENTARY AND 
 
 HIGH SCHOOLS 
 
 $0.50 
 .65 
 
 .70 
 
 • 15 
 .15 
 
 • 15 
 .15 
 .65 
 
 Aiken's Music Course. In one book 
 
 Part Songs for Mixed Voices . 
 Betz's Gems of School Song (Complete) 
 
 Songs of Home and Pleasure . 
 
 Songs of Nature 
 
 Songs of the Seasons 
 
 Songs for Morning, Evening, and Night 
 Birge's Choruses and Part Songs for High Schools 
 Brewster & Thomas's Song Stories and Songs for 
 
 Children .60 
 
 Franklin Square Song Collection. Nos. i, 2, 3, 
 
 4» 5> 6, 7, and 8 . . . Each, .60 
 
 Gantvoort's High School Ideal .60 
 
 Johnson's Songs Every One Should Know ... .50 
 
 Jones's Songs of Seasons .25 
 
 Loomis's Progressive Glee and Chorus Book . . .84 
 
 MacConnell's Standard Songs and Choruses for 
 
 High Schools .75 
 
 Mathews's Songs of All Lands .50 
 
 McCaskey's Favorite Songs and Hymns .... .80 
 
 Natural Advanced Music Reader 1.09 
 
 Natural Music Leaflets : Prices from 2c. to 8c. each. 
 
 Special list on application. 
 Neidlinger's Earth, Sky, and Air in Song: 
 
 Book I 
 
 Book II 
 
 Shirley's Part Songs for Girls' Voices 
 
 Part Songs for Mixed Voices . 
 
 School and Festival Songs 
 Siefert's Choice Songs. Book I 
 
 Book II. Revised edition 
 
 AMERICAN BOOK COMPANY 
 
 (141) 
 
SCHOOL EDITIONS OF 
 STANDARD FICTION 
 
 Defoe's Robinson Crusoe (Stephens) .... ^0.50 
 Defoe's Robinson Crusoe. (Adapted for children by 
 
 Baldwin) .35 
 
 Dickens's Story of Little Nell— From The Old Curi- 
 osity Shop (Gordon) 50 
 
 Dickens's Tale of Two Cities (Kirk) 50 
 
 Dickens's Twelve Christmas Stories (Gordon) — A 
 Christmas Carol; The Child's Story; The 
 School-boy's Story ; Our School ; The Seven 
 Poor Travelers ; The Holly-Tree Inn ; A 
 Christmas Tree; Mugby Junction ; The Ghost 
 in Master B's Room; Little Bebelle ; A Child's 
 Dream of a Star ; and The Detective Police . .50 
 Dickens's Child's Oliver Twist and David Copper- 
 field (Severance) 40 
 
 Lambs' Tales from Shakespeare — Comedies (Rolfe) . .50 
 Lambs' Tales from Shakespeare — Tragedies (Rolfe) . .50 
 
 Stories from the Arabian Nights (Clarke) 60 
 
 Scott's Kenil worth (Norris) 50 
 
 Scott's Quentin Durward (Norris) 50 
 
 Scott's Talisman (Dewey) ojo 
 
 Scott's Ivanhoe 50 
 
 THESE masterpieces of English literature should be 
 famihar to every child. Not only will they prove ab- 
 sorbing and interesting in themselves, but they will also 
 create a love for good literature, and awaken in children a 
 desire to read others of these authors' works. 
 ^ In their present editions, the original narratives have been 
 altered only so much as was necessary to make them compre- 
 hensible to children. Unessential passages have been omitted, 
 and in some cases the wording has been slightly changed. 
 
 AMERICAN BOOK COMPANY 
 
 (26) 
 
A SYSTEM OF PEDAGOGY 
 
 ■ By EMERSON E. WHITE, A.M., LL.D. 
 
 Elements of Pedagogy $l.oo 
 
 School Management and Moral Training . , i.oo 
 
 Art of Teaching i.oo 
 
 BY the safe path of experience and in the light of modern 
 psychology the ELEMENTS OF PEDAGOGY 
 points out the limitations of the ordinary systems of 
 school education and shows how their methods may be har- 
 monized and coordinated. The fundamental principles of 
 teaching are expounded in a manner which is both logical 
 and convincing, and such a variety and wealth of pedagogical 
 principles are presented as are seldom to be found in a single 
 text-book, 
 
 ^ SCHOOL MANAGEMENT discusses school govern- 
 ment and moral training from the standpoint of experience, 
 observation, and study. Avoiding dogmatism, the author 
 carefully states the grounds of his views and suggestions, and 
 freely uses the fundamental facts of mental and moral science. 
 So practical are the applications of principles, and so apt are 
 the concrete illustrations that the book can not fail to be of 
 interest and profit to all teachers, whether experienced or 
 inexperienced. 
 
 ^ In the ART OF TEACHING the fundamental princi- 
 ples are presented in a clear and helpful manner, and after- 
 wards applied in methods of teaching that are generic and 
 comprehensive. Great pains has been taken to show the 
 true functions of special methods and to point out their limita- 
 tions, with a view to prevent teachers from accepting them 
 as general methods and making them hobbies. The book 
 throws a clear light, not only on fundamental methods and 
 processes, but also on oral illustrations, book study, class 
 instruction and management, written examinations and pro- 
 motions of pupils, and other problems of great importance. 
 
 AMERICAN BOOK COMPANY 
 
 (200) 
 
- ^- ;.^^■■■v..^../v.:■..-^^v.<vw^>wi«t:vv.»i.- 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.00 ON THE SEVENTH DAY 
 OVERDUE. 
 
 
 
 AU6 .;a 1945 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 LD 21-100m-12,'43 (8796s) 
 
>VA.-L^V^ 
 
 
 7;il;^i 
 
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 THE UNIVERSITY OF CALIFORNIA LIBRARY