IN MEMORIAM FLORIAN CAJORI dc ^< i 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; (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; . $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.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 //v--> ■■» THE UNIVERSITY OF CALIFORNIA LIBRARY