^.y.11111 m~m ESSENTIALS OF AKITHMETIC ' "4. THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA LOS ANGELES OS ANGELES M. SCHOOL STATE NORMAL SCHOOL MW I I WENTWORTH-SM1TH MATHEMATICAL SERIES ESSENTIALS OF ARITHMETIC PEIMARY BOOK BY GEORGE WENTWORTH AND DAVID EUGENE SMITH GINN AND COMPANY BOSTON NEW YORK CHICAGO LONDON ATLANTA DALLAS COLUMBUS SAN FRANCISCO COPYRIGHT, 1915, BY GEORGE WENTWORTH AND DAVID EUGENE SMITH ALL RIGHTS RESERVED 515.8 gtbtnttum GINN AND COMPANY PRO- PRIETORS UOSTON U.S.A. PEEFACE This book is the first of a series of three intended to cover the essentials of arithmetic in the eight school years of the elementary course. It consists of five chapters, the first of which reviews the work usually done in the first and second grades, the others covering the work of the successive half grades through the fourth school year. If it is introduced in Grade II, the pupils should complete Chapter I in that year; but if it is first placed in the hands of the class in Grade III, it will suffice to take a rapid review of Chapter I, omitting such portions as may already be perfectly familiar to the children. A textbook for these grades can be constructed on any one of several definite plans, or, indeed, with little attention to any system- atic arrangement whatever. It may consist of a series of devices for teachers, such as games and dramatizations, all valuable in them- selves but not offering the material needed in a usable textbook. To be usable a book should suggest devices of this kind, which with many others the teachers may bring into their work, but it fails of its purpose if it uses most of its limited space in this manner. The primary purpose of a textbook in arithmetic is to furnish a large amount of material which the teachers would otherwise have to dic- tate, and to arrange this material in a systematic order. Teachers need hundreds of examples in addition, hundreds of examples in subtraction, and so on, and they should not be required to make up, arrange, and dictate this material. Teachers always welcome sugges- tions of games, of dramatizations of number relations, and of means to apply number facts to the daily experiences of the child, but such devices of teaching must necessarily come in large part from the teachers themselves. iv PKEFACE This book stands, in the first place, for good, well-arranged mathe- matics, and not for the scrappy presentation which always fails to give to the pupil that feeling of mastery of the subject- to which he is entitled ; and in the second place it appeals to the pupil's human interests by relating the subject to his personal needs and to the life in which he finds himself. It seeks to balance reasonably these two features, refraining on the one hand from devoting all its space to abstract drill, and on the other hand from failing, through the sacrifice of its space to methods of teaching, to give the amount Of drill that is necessary. It recognizes that the children who study its pages have already been in school from one to two years, that they not only possess a fair knowledge of number but that motives for study have already begun to be formed, and that the kindergarten stage is already passing out of their lives. Devices that are needed in Grade I are not necessary in Grade III; and the teachers, to a large extent, must be the judges as to how long they shall keep to the concrete introduction to the work, and as to the use they shall make of the numerous devices suggested in the book. It is the hope of the authors that teachers will find that the series furnishes exactly the essentials for good arithmetic work in the elementary schools and presents these essentials in the most usable manner. GEORGE WENTWORTH DAVID EUGENE SMITH CONTENTS CHAPTER I PAGE I. COUNTING TO TWELVE 1 II. ADDITION 5 III. ADDITION AND SUBTRACTION 10 IV. COUNTING TO 100 15 V. ADDITION 20 VI. SUBTRACTION 32 VII. USING WHAT YOU HAVE LEARNED 36 VIII. FRACTIONS . . . 38 IX. MEASURES 44 X. REVIEW DRILL 47 XI. USING WHAT YOU HAVE LEARNED 49 XII. LITTLE EXAMINATIONS . 52 CHAPTER II I. NUMBERS TO 1000 53 II. ADDITION 57 III. SUBTRACTION 64 IV. MULTIPLICATION AND DIVISION TABLES 71 V. MULTIPLICATION : 85 VI. USING WHAT YOU HAVE LEARNED 90 VII. DIVISION 93 VIII. FRACTIONS 97 IX. GENERAL REVIEW 102 X. USING WHAT YOU HAVE LEARNED 104 XI. LITTLE EXAMINATIONS 108 CHAPTER III I. READING AND WRITING NUMBERS 109 II. ADDITION 114 III. SUBTRACTION 120 v vi CONTENTS PAGE IV. MULTIPLICATION AND DIVISION 124 V. USING WHAT TOD HAVE LEARNED 145 VI. FRACTIONS 147 VII. MEASURES 149 VIII. REVIEW 153 IX. USING WHAT YOU HAVE LEARNED 164 X. LITTLE EXAMINATIONS 166 CHAPTER IV I. READING AND WRITING NUMBERS 167 II. ADDITION 169 III. SUBTRACTION 170 IV. MULTIPLICATION 172 V. USING WHAT you HAVE LEARNED 183 VI. DIVISION 187 VII. FRACTIONS 200 VIII. MEASURES 213 IX. REVIEW 218 X. USING WHAT YOU HAVE LEARNED 220 XI. LITTLE EXAMINATIONS 222 CHAPTER V I. READING AND WRITING NUMBERS . . . . ' 223 II. ADDITION 225 III. SUBTRACTION 226 IV. MULTIPLICATION 227 V. DIVISION 230 VI. MEASURES 233 VII. USING WHAT YOU HAVE LEARNED 246 VIII. FRACTIONS 248 IX. ALIQUOT PARTS 258 X. BILLS AND RECEIPTS 260 XI. GENERAL REVIEW 264 XII. USING WHAT YOU HAVE LEARNED 269 XIII. LITTLE EXAMINATIONS 272 XIV. WHAT THE PUPIL SHOULD KNOW WHEN HE HAS FINISHED THIS BOOK 273 TABLES FOR REFERENCE 279 INDEX . . 281 u\ ESSENTIALS OF " ARITHMETIC PRIMAKY BOOK CHAPTER I I. COUNTING TO TWELVE What You may have Learned. You have learned to count and to write numbers. Can you count to ten ? Are there twenty children in this room ? Can you tell how many children there are in this room ? Do you know what I mean when I speak of half the children in the room? Do you know how many cents there are in a dollar and a quarter, or a dollar and a half ? If your father has a dollar and spends seventy-five cents for you, do you know how much he will have left ? If you cannot tell now, you will be able to tell after you have studied this book. This page calls attention to some things that the children know, and to some that they have still to learn. The teacher will find it of advantage to suggest from time to time, in simple problems, the motives which should prompt the pupil to study further. The reading of some of the problems a few pages in advance is often a good stimulus for work. Notes in this type throughout the book are intended for the teacher. 1 COUNTING TO TWELVE ORAL EXERCISE 1. Here are some children playing with their pet donkey. How many children do you see? 2. How many children are riding on the donkey ? 3. How many girls are riding on the donkey ? 4. How many boys are riding on the donkey ? 5. How many children are on the ground ? 6. If the little girl without a hat should get off, how many children would be left on the donkey ? How many girls would be left on the donkey? 7. If both little girls should get off, how many children would be left on the donkey? Teachers should always be sure that new words do not obscure the meaning. Since this book is not intended for Grade I, the above words are probably all known, otherwise they should be explained. PLAYING STORE 3 ORAL EXERCISE 1. Let us play store. How many are there to play? 2. How many clerks shall we have in the store ? 3. How much shall we charge for apples ? 4. How many apples do you wish to buy ? 5. How much shall we charge for oranges ? 6. How many oranges do you wish to buy ? 7. How many bottles of milk are Q Q and Q fl J ? 8. Jack sells some blocks for building playhouses. How many blocks are g g g and g g ? 9. Rob sells some dolls. He sells 5 dolls to Mary and 1 doll to Kate. How many dolls does he sell ? 10. Kate buys some cups for the doll's table. How many cups are e 3 + 4=7 2 + 5 6 + 4 + 2 5+3 5+5 6 + 2 2 + 8 4 + 3 8+4 9+2 3 + 5 + 8 6 + 5 7+3 7 + 5 In drill work of this kind, number games may be used with discretion. For example, one of these number combinations may be placed on each step of a ladder drawn on the blackboard, and children may climb rapidly until they fall off by making an error. ADDITION ORAL EXERCISE 1. How many children are there in the picture ? 2. How many children are 4 children and 3 children ? 3. How many children are 5 children and 2 children ? Add these numbers and make problems about them : 4. 6136771199 1660217310 5. 5 2 WRITTEN EXERCISE Copy and add : 1. 3 + 5 + 3 7 + 2 6 + 3 5 + 4 2. + 3 3 + 5^ 2 + 7 3 + 6 6 + 3. 4 + 4 + 6 8 + 1 4 + 1 8 + 2 GAMES DRILL GAMES 1. Our class played the game of Numbers on the Hoop. The teacher put this picture on the blackboard. As Ruth pointed to the numbers on the hoop, we added 5 to each. Add 5 to each of these numbers : Change the number to be added and write the new number in the hoop, making a new game. The numbers must be chosen so that the sum, at this time, does not exceed 12. Similarly for Ex. 2 and other games. 2. We played Running the Square. The teacher put this picture on the blackboard. As John pointed to the numbers at the corners and on the ? 5 sides, we ran around the square with him and added 2 to each number. Add 2 to each of these numbers : 2 3. We also played Running the Triangle. The teacher put this picture on the blackboard, and we tried to see how fast we could run, adding each number to the one inside. Run around, beginning with 4. Run around, beginning with 9. Run around, beginning with 5. Run around, beginning with 6. Run around, beginning with 8. 10 ADDITION AND SUBTRACTION III. ADDITION AND SUBTRACTION ORAL EXERCISE 1. There are 6 children in a row. How many children must be added to this number to make 11 ? 2. Jennie wishes to buy a 5-cent paper. She has 2 cents in her pocket. How many more cents must she have ? 3. Jack has 8 marbles. How many more marbles must he get so as to have 11 marbles in all? 4. After we have studied 6 pages of this book, how many more must we study to make 10 pages in all? 5. What number must we add to 6 to make 9 ? to 3 to make 7 ? to 7 to make 10 ? to 10 to make 12 ? 6. What numbers must I put in place of the stars to have these additions all right ? 2365 733 9 * * * * #.# * * 5779H3412 7. Answer these questions : 5 and what number are 7 ? 7 and what number are 12 ? 6 and what number are 11 ? 8. Name the numbers to put in place of these stars : 5 + *= 10 4 + * = 6 * + 6 = 12 7 + *= 12 6 + * = 9 6 + *= 12 9 + * = 11 * + 4 = 6 7 + *= 11 SUBTRACTION 11 ORAL EXERCISE 1. Helen is counting her blocks. She has 7 blocks and takes away 3 blocks. How many blocks are left? 2. If Helen takes 4 blocks from 7 blocks, how many blocks are left? 3. How many blocks are 7 of these blocks less 3 of these blocks ? 4. How many blocks are 7 of these blocks less 4 of these blocks ? 5. If Helen has 7 cents and spends 4 cents, how' many cents has she left? Subtraction. Taking 3 blocks from 7 blocks is called subtraction. We subtract 3 blocks from 7 blocks. To show that we subtract 3 from 7 we write the work in a column as shown below in the margin. We may also show it by writing the numbers like this : 7-3 = 4, which we read in any one of these three ways : 7 less 3 is 4, 7 minus 3 equals 4, or 3 from 7 is 4. The pupil is now old enough to understand all these expressions, and he should use them interchangeably. The relation of3 + 4=7to7-r-4 = 3 and 73=4 should be understood by .the pupil. 12 ADDITION AND SUBTEACTION ORAL EXERCISE 1. Jennie is buying apples from Kate. If she buys 2 cents' worth, and gives Kate 10 cents, how much change should she get? 2. If she buys 5 cents' worth of candy, how much change should she get if she gives Kate 10 cents? 3. How much money should she pay Kate for 2 pop-corn balls if they cost 2 cents each ? What change should she get if she gives Kate a 5-cent piece. 4. If Jennie buys 3 apples, paying 1 cent for each, and a pop-corn ball for 2 cents, how much does she pay for all ? 5. If Jennie buys 2 apples at 1 cent each, and 5 cents' worth of candy, and 4 cents' worth of pop-corn balls, how much does she pay for all ? WRITTEN EXERCISE Copy and subtract : 1. 6 8 6 7 3 45211 2. 9 7 11 9 4 2 12 3 5 3 12 2 GAMES 13 DEVELOPMENT GAME 1. In school to-day we played the game of Climbing the Ladder. We climbed as fast as we could. When any one made a mistake he fell off. Climb the ladder in the picture. These numbers are 5-2, 4-2, 3-2, 8-2, 9-2, 7-2, and 6-2. Tell the answers as fast as you can. 2. Tell the answers for 9-2, 7-2, 5-2: Climb these ladders as fast as you can, beginning at the foot: 3. 4. 5. 6. 12 -3 10 -3 5O o 3 -3 8 _ 3 4 9 12 -4 10 -4 11 -4 7 -4 5 -4 9 -4 6 -4 10 -5 12 -5 11 -5 7 -5 5 -5 9 -5 8 -5 11 -6 10 -6 12 -6 7 -6 6 -6 8 -6 9 -6 14 ADDITION AXD SUBTRACTION ORAL EXERCISE Subtract rapidly : 1. 4 6 3 8 3 7 9 9 8 10 3 2 3 2 1 3 3 3 _3 2. 2 5 7 5 6 8 7 6 9 11 2 1 2 ? 3 5 1 8 10 WRITTEN EXERCISE Copy and subtract : 1. 4 5 6 7 8 9 10 11 12 12 4 4 4 4 4 4 4 4 4 J) 2. 5 6 7 8 9 10 11 12 12 11 5 5 5 5 5 _5 5 J> _1 _2 3. 6 7 8 9 10 11 12 12 12 10 6 6 6 6 _6 6 6 _3 2 J) 4. 7 8 9 10 11 12 11 11 11 12 7 7 7 7 7 7 1 11 12 5. If you have 10 cents and spend 4 cents, how many cents will be left? 6. If you have 12 apples and eat 2 of them, how many apples will be left? 7. If you have 7 roses and give away 5 of them, how many will you have left? 8. If 8 girls stand, and then 2 of them sit down, how many are left standing? COUNTING TO 100 15 IV. COUNTING TO 100 ORAL EXERCISE 1. How many books are there in the picture? If there were 10 more, how many would there be ? What name do we give to two 10's ? 2. How many blocks in the black and white pile? How many 10's in this pile? 3. There are 3 columns of smaller blocks. How many blocks in each column? How many in all? What name do we give to 3 tens ? 4. There are 4 bundles of splints in the picture, 10 in each bundle. How many splints in all? What name do we give to 4 tens ? 5. There are 5 packages of envelopes, 10 in each pack- age. How many envelopes are there ? What name do we give to 5 tens ? 6. Read these numbers : 10 20 30 40 50 60 70 80 90 100 7. How many tens are there in 20? in 30? in 70? in 40? in 50? in 90? in 100? 8. What name do we give to 9 tens ? to 6 tens ? to 8 tens ? to 7 tens? to 10 tens? 9. Tell how to write seventy on the blackboard. 16 COUNTING TO 100 ORAL EXERCISE 1. If you call 2 tens twenty and write it 20, and if you call 3 tens thirty and write it 30, what should you call 4 tens, and how should you write it? Tell the same for 5 tens, and so on up to 10 tens. 2. If ty in sixty means tens, then sixty means six tens. Then what does seventy mean? What does eighty mean? 3. State rapidly the sums : 2 2 tens 20 30 40 30 40 3 3 tens 30 40 50 60 20 United States Money. The table of United States money is as follows : 5 cents = l nickel 10 cents = 1 dime 100 cents = 1 dollar We write $ for cents, and $ for dollars, thus : 25$ means 25 cents, and $10 means ten dollars. 4. Subtract rapidly : 5 5 tens 50 70 90 90 60 2 2 tens 20 30 40 30 40 5. Read these numbers : 10 90 70 20 50 $10 40$ 60 80 30 40 100 $30 70$ COUNTING TO TWENTY 17 ORAL EXERCISE 1. Count from 1 to 10 ; then count by tens from 10 to 100. 2. How many splints are 10 splints and 1 splint ? 3. How many splints are 10 splints and 2 splints? The number after twelve is thirteen. It is written 13, which means 1 ten and 3 ones. The number after thirteen is fourteen. It is written 14, which means 1 ten and 4 ones. 4. \ififteen means five and ten, what does sixteen mean ? 5. Read these numbers and tell what each means : 10 14 15 16 30 18 19 6. Read these numbers and tell what each means : 17 12 10 40 20 13 11 7. How many pupils' desks are there in your row of desks ? 8. How many pupils are there in your row to-day ? 9. How many words are there in Exs. 7 and 8 together? 10. How many boys are there in your class ? 18 COUNTING TO 100 ORAL EXERCISE 1. Point to 10 splints and 3 splints in the picture. How much is 10 + 3 ? Write the number on the blackboard. 2. In each group, how many packages of 10 splints each, and how many splints over? Write the numbers. 3. Read the following : Twenty means 2 tens. Forty means. 4 tens. 4. Read the following : 21 means 20 and 1. 34 means 30 and 4. Read these numbers : 5. 21 62 53 84 65 86 77 6. 31 82 73 .64 75 96 68 7. What number comes after 26 in counting ? 8. What number comes before 35 ? 9. What number comes between 47 and 49 ? 10. Count from 20 to 30, and then from 30 back to 20. 11. Count from 20 to 40, and then from 40 back to 20. 12. Count from 1 to 50. 13. See if you can count from 1 to 100, speaking the words very clearly, in one minute. Maybe you can do it in less than one minute. 14. Count backwards from 100 to 90. ORDINAL NUMBERS 19 ORAL EXERCISE 1. What grade do children enter after the first grade in school ? What grade do they next enter ? 2. If the first day of the week is Sunday, what is the second day of the week ? 3. Which is the sixth day of the week ? 4. What day of the month is to-day ? 5. To-morrow will be what day of the month ? 6. Yesterday was what day of the month ? 7. Day after to-morrow will be what day of the month ? 8. Which is the first month of the year ? 9. In which month does Christmas come ? What is the number of that month ? 10. What is the number of this page that you are study- ing ? Then which page of the book is it ? 11. Which example on this page comes between the seventh example and the ninth example? WRITTEN EXERCISE 1. Write the numbers from 1 to 10. 2. Write the names of these numbers : 79824165 3. Write in figures : Seven Three Four Nine Eight 4. Write in figures the first number after 5 and the second number before 6. 20 ADDITION V. ADDITION ORAL EXERCISE 1. If you have 9< and earn 4$ more, how many cents do you then have ? 2. I think of two numbers whose sum is 13. Can you guess the numbers ? There are several correct guesses. 3. Tell what numbers to put in place of these stars : 9*8576*8* 4 _9 5 J* 6 _*_ _1_ _^_ _*_ * 13 * I3 * 13 13 13 13 4. If Carl is 8 years old and his brother is 6 years older, how old is his brother? 5. Tell what numbers to put in place of these stars : 987 10 7*38* * * * * * 14 14 14 14 14 WRITTEN EXERCISE Copy, add, and make a problem about each : 1. 4 8 9 7 10 7 9 6 12 9546J5758_2 2. 5 6 5 8 11 11 10 12 10 87 9 5 _2 J3 _5 J. _4 On this page the work centers about thirteen and fourteen as sums. The pupil is already familiar with sums to twelve. FIFTEEN AND SIXTEEN AS SUMS 21 ORAL EXERCISE 1. If Frank earned 9^ on Monday and 6< on Tuesday, how much did he earn in the two days? 2. If you found 7 eggs in the nests to-day and 8 eggs yesterday, how many have you found in the two days ? 3. Tell what numbers to put in place of these stars : 98*8'* 6*7* 6 1 J*. JH .1 _J> J 1 ! _! * * 15 15 15 15 15 15 15 4. Will is 7 years old and his sister is 9 years older. How old is his sister? 5. John has 8< and he earns 8$ more. How many cents has he then? 6. Tell what numbers to put in place of these stars : 98** 10 5 12** 78_9_8_6J*^_3_2 * * 16 16 * 16 * 16 16 WRITTEN EXERCISE Copy, add, and make a problem about each : 1. 6 7 -7 9 10 11 13 14 15 989 6_5jt_2_2_l 2. 8 9 8 11 12 10 12 14 13 877_5_4_6_3J._3 On this page the work centers about fifteen and sixteen as sums. 22 ADDITION ORAL EXERCISE 1. If there are 9 girls and 8 boys in a class, how many pupils are there in all ? 2. If Kate's score at bean-bag is 8 and Mollie's is 9, what is their total score? What does "total" mean? 3. Tell what numbers to put in place of these stars : 9 8 9 8 12' * * 15 14 8 9 * j* jj j) j| j* j* * *1717~^17l7l7l7 4. Ruth has 9 boys and 9 girls at her party. How many children are there in all ? 5. Tell what numbers must be put in place of these stars, and make a problem about each example : 11 + * =17 *+15 = 17 8 + * = 18 WRITTEN EXERCISE Copy, and add the following : 1. 14 15 12 17 2 10 1 8 2 _3_3_5_116J7161016 2. 4 16 16 7 10 11 7 5 13 13J.J211_8J>1013_4 On this page the work centers about seventeen and eighteen. The pupils have now learned all the combinations of two numbers whose sums are eighteen or less. On the next page[ this work is given in the form of tables, and the addition drill should be accompanied by subtraction drill. Drill also on adding and subtracting zero and one. TABLE 23 ADDITION TABLE 1 + 2 = 3 1 + 3 = 4 1 + 4 = 5 1 + 5 = 6 2 + 2 = 4 2 + 3 = 5 2 + 4 = 6 2 + 5 = 7 3 + 2 = 5 3 + 3 = 6 3 + 4 = 7 3 + 5 = 8 4 + 2 = 6 4 + 3 = 7 4 + 4 = 8 4 + 5 = 9 5 + 2 = 7 5 + 3 = 8 5 + 4 = 9 5 + 5 = 10 6 + 2 = 8 6 + 3 = 9 6 + 4 = 10 6 + 5 = 11 7 + 2 = 9 7 + 3 = 10 7 + 4 = 11 7 + 5 = 12 8 + 2 = 10 8 + 3 = 11 8 + 4 = 12 8 + 5 = 13 9 + 2 = 11 9 + 3 = 12 9 + 4 = 13 9 + 5 = 14 10 + 2 = 12 10 + 3 = 13 10 + 4 = 14 10 + 5 = 15 1 + 6 = 7 1 + 7 = 8 1 + 8 = 9 1 + 9 = 10 2 + 6 = 8 2 + 7 = 9 2 _i_ Q "TO 10 2 + 9 = 11 3 + 6 = 9 3 + 7 = 10 3 + 8 = 11 3 + 9 = 12 4 + 6 = 10 4 + 7 = 11 4 + 8 = 12 4 + 9 = 13 5 + 6 = 11 5 + 7 = 12 5 + 8 = 13 5 + 9 = 14 6 + 6 = 12 6 + 7 = 13 6 + 8 = 14 6 + 9 = 15 7 + 6 = 13 ' 7 + 7 = 14 7 + 8 = 15 7 + 9 = 16 8 + 6 = 14 8 + 7 = 15 8 + 8 = 16 8 + 9 = 17 9 + 6 = 15 9 + 7 = 16 9 + 8 = 17 9 + 9 = 18 10 + 6 = 16 10 + 7 = 17 10 + 8 = 18 10 + 9 = 19 The pupil is already familiar with these number facts. There is, how- ever, an advantage in reciting a table, as well as in being drilled upon the number combinations selected at random. The latter drill is provided on the next page and in the frequent reviews. 24 ADDITION ORAL EXERCISE Add the following : 1. 9 5 4 3 2 6 5 3 5 6 2 7 1 5 3 6 7 3 2. 8 6 4 7 7 5 5 3 8 2 6 7 4 7 6 8 9 4 1 3. 5 6 7 4 6 1 2 7 2 1 5 9 9 2 4 9 3 9 4. 3 8 4 9 8 1 3 2 9 5 1 9 3 5 1 5. 5 8 2 9 1 1 9 6 3 8 2 6 4 5 6 8 9 6. 5 7 3 1 9 1 6 2 7 4 8 6 7 1 7 6 4 7 1 7. 3 8 9 6 8 7 7 4 2 2 5 3 4 8 3 5 4 2 8 8. 4 9 5 4 6 2 5 4 3 5 6 2 8 6 2 3 7 9. 1 6 7 7 8 1 5 4 8 2 1 3 2 4 7 3 5 7 9 10. 9 9 4 6 1 8 1 9 3 2 4 8 1 3 9 2 8 1 8 All the fundamental combinations in addition are given on this page, and hence the page should be reviewed frequently. TROUBLESOME GROUPS 25 ORAL EXERCISE 1. Which number do you find easiest to add to another number ? Give four examples. 2. Which number do you find hardest to add to another number ? Give four examples. 3. Which two numbers of one figure each do you find hardest to add? The answers to these questions will reveal the " troublesome " groups, and these should receive attention until they are as familiar as the " easy " groups. In general the combinations given below are the ones that trouble children most. It will be noticed that the most difficult combinations are repeated several times. 5787 7 8 6'5 8873 7488 5865 867 6 6 86 7 5868 7775 6849 4597 8897 Add the following : 4. 8 6 5 7 5 8 5. 7 6 8 5 8 5 6. 5 8 8 7 8 7 7. 4 8 5 7 7 7 8. 5 6 7 6 8 5 9. 6 3 9 6 9 4 26 ADDITION DRILL GAME 1. The game we played to-day was Nimble Squirrel. The squirrel jumped from branch to branch and told the sums of the numbers. When he could not give the answers quickly he fell off. Be the nimble squirrel and tell these answers as quickly as you can : 7 + 2 5+6 6+7 8+9 4+8 9+7 Beginning at the bottom of each column, tell these sums as you jump from branch to branch : 2. 3. 4. 5. 6. 5 + 2 9 + 3 8 + 4 4 + 6 5 + 8 3 + 2 6 + 3 6 + 4 8 + 5 7 + 6 8 + 2 2 + 3 7 + 4 5 + 3 3 + 4 6 + 2 8 + 3 5 + 4 4 + 2 5 + 5 9 + 2 4 + 3 9 + 4 7 + 1 3 + 9 1 + 2 3 + 3 + 4 + 3 2 + 8 + 2 7 + 3 1 + 4 6 + 9 6 + 5 2 + 2 1 + 3 4 + 4 9 + 8 9 + 6 Add the following : 1. 1 11 21 31 2 2 2 2 2. 1 11 51 91 4 4 4 4 3. 2 12 22 42 6 6 6 _6 4. 4 14 24 14 7 7 7 8 DEILL WOEK 27 ORAL EXERCISE 1 11 41 61 3 _3 _3 _3 1 21 41 71 5 _5 _5 _5 3 23 43 73 5 _5 _5 J> 44 64 14 84 _8 _8 _9 _9 Add each of the numbers 4, 9, 7, 8, 6 to the following numbers ; read the results first by columns, then by roios : 5. 16 17 18 19 15 13 12 26 37 58 69 45 23 32 56 67 78 39 35 63 72 76 87 68 79 .,75 . 83 82 Drill means doing the same thing over and over again so as to secure mechanical efficiency, and the problem is to do this without making the work monotonous. Observe, for instance, that in Ex. 4 the numbers 4 and 7 are added three times, but always under different conditions. WRITTEN EXERCISE Add the following : 4 14 7 339 17 7 7 8 '18 9 19 1 1 29 9 9 28 ADDITION Column Addition. In adding 3, 5, and 7 we may arrange the numbers in a column, and begin with the lowest figure. Here we have 3 + 5 = 8, and 8 + 7=15. We see that 15 is the sum, and write it below the line. We make sure that the work is right by add- ing from the top down, thus : 7 + 5 = 12, and 12 + 3 = 15. We then say that we have checked the work, "because the two sums are the same. 7 5 _3 15 Teach the child to read a column as he reads a word, as far as this is possible. As he looks at this column he should think, " 3, 8, 15," thinking no other words. ORAL EXERCISE Add the following : 1.1 4 5 6 5 23211 32212 2. 5 4 9 9 9 8 8 3 4 1 1 2 1 2 4 1 1 8 WRITTEN EXERCISE Add the following : 1. 4 4 9 6 7 9 4 5 2 8 8 6 6 4 3 7 3 2 2 4 4 6 7 3 2. 2 7 9 7 7 6 9 1 5 4 1 9 3 2 1 8 5 6 9 1 6 4 3 8 GAMES DRILL GAME 1. To-day we played the game of Number Sprinters. If a boy did not give the right answer when he touched a. post, he was out of the game. See how much of a number sprinter you are, by telling the sums in the picture as fast as you can. Run over these courses, and time yourself for each course : 2. 1 3 3 2 2 2 3 4 1 3 2 2 2 2 3 4 4 4 2 1 5 1 2 4 4 4 4 4 9 5 3. 3 3 2 2 4 4 4 5 5 5 2 3 2 4 3 4 5 4 5 3 5 5 5 5 5 5 5 6 5 7 4. 3 3 3 5 6 3 1 1 1 3 3 4 2 2 3 7 7 8 1 1 7 7 7 8 7 7 8 8 9 9 ,30 ADDITION Column Addition. If you read 35 pages of a book on Monday and 41 pages on Tuesday, how many pages did you read on both days ? We see that we must add 35 and 41 to find the answer. 41 We write the numbers one under the other, 76 ones under ones and tens under tens. Adding the column at the right we have 6 ; adding the next column we have 7. We first write the 6 below the line in the ones' column. We then write the 7 below the line in the tens' column. The sum is 76, and so you read 76 pages in all. WRITTEN EXERCISE Add the following : 1. 20 21 21 23 23 24 28 30 30 35 35 45 52 71 2. 30 31 33 43 63 73 32 26 26 26 26 26 26 46 3. 40 41 43 53 64 64 38 34 34 34 34 34 35 50 4. 50 52 53 53 53 53 27 25 25 25 26 36 46 61 5. 60 61 61 62 63 63 39 16 16 26 26 26 36 60 6. 70 70 70 70 72 72 23 8 -18 28 ' 27 24 27 46 GAMES REVIEW GAMES 1. Some children played this number game. They placed a stick as shown in the picture, and marked an oblong and a circle on the garden sidewalk. They then rolled balls toward the stick. If a ball touches the stick, it counts 5 ; if it stops in the circle, it counts 4 ; if it stops on the oblong but does not touch the stick, it counts 3 ; if it stops anywhere else, it counts 0. If these were the scores, who won the game? John, 5, 4, 4, 3, 0, 3 Rob, 4, 4, 0, 0, 3, 5 Frank, 4, 5, 3, 0, 0, 5 2. The janitor made this ladder for a number game. The children tried to throw bean- bags through the spaces, each space counting as shown in the picture. If a bag strikes the ladder, it counts 0. These were three scores : Kate, 3, 2, 0, 0, 4, 1 Mary, 1, 1, 3, 2, 0, 2 Jennie, 4, 3, 2, 0, 0, 2 Who won the game ? \ SUBTRACTION VI. SUBTRACTION ORAL EXERCISE 1. How many cents must we add to 1$ to make 3$. 2. How many tens must we add to 1 ten to make 3 tens ? 3. How much must we add to 10 to make 30 ? 4. Name the number which belongs where each star is : 30 + * = 50 21 + * = 27 32 + * = 39 - x\ Column Subtraction. If a book has 68 pages and we have read 21 pages, how many pages have we left to read? We see that we must subtract 21 from 68. We write the smaller number below the larger number. We first think " 8 1 = 7," and write the 7 below the line, under the 1. We then think " 6 - 2 = 4," and write the 4 below the line, under the 2. The result is 47, and so we have 47 pages left to read. To make sure that the work is correct, that is, to check the work, we add 47 and 21, the result being 68. WRITTEN EXERCISE Subtract the following : 68 21 47 1. 9 90 60 50 55 75 86 7 70 30 10 10 20 50 2. 88 88 89 98 73 67 59 30 31 42 16 41 36 27 DEILL WORK 33 ORAL EXERCISE Subtract the following: 1. 9 90 99 96 87 76 86 3 30 33 32 43 32 36 2. 7 70 77 78 87 75 95 4 40 44 42 34 22 25 WRITTEN EXERCISE Copy and subtract 1. 98 89 93 64 55 63 75 73 46 31 24 21 52 25 2. 82 78 65 53 31 29 67 50 37 52 12 11 18 47 3. 68 79 84 86 73 81 39 11 21 30 22 22 30 J_ 4. 68 76 69 96 74 77 48 23 40 24 42 40 25 _3 5. 73 94 74 77 95 78 66 31 50 51 33 61 34 20 6. If Frank has 21 chickens, how many more must he get so as to have 34 chickens in all ? 7. If William has 43 marbles, how many more must he get so as to have 55 marbles in all ? 34 SUBTRACTION DRILL TEST. ADDING ONE-FIGURE NUMBERS Add, and state the ansioers rapidly : I. 1 7 6 2 8 9 7 3 9 1 2 1 2 1 2 1 2 1 2 2. 7 . 5 7 8 7 9 9 6 8 3 4 5 3 4 5 3 4 5 5 3. 9 7 8 5 8 9 4 9 7 6 5 6 7 6 6 7 5 6 7 8 Such tests may be used for both oral and written work. In the former case the results should be stated rapidly, with no hesitation ; in the latter case the numbers should be written neatly, with the answers, and a record kept of the time. The exercise should be repeated from week to week and a comparison made of the speed and accuracy. DRILL TEST. SUMS TO TWENTY Add, and state the answers rapidly : 1. 8 11 9 11 10 8 12 10 7 10 9 10 11 6 2. 8 13 7 6 14 7 14 12 5 12 13 2 13 _5 3. 14 15 16 5 16 3 16 _6 . 4 3 15 2 15 4 4. 2 18 3 2 19 1 17 1 17 18 17 19 DEILL TESTS 35 DRILL TEST. ADDITION Add, and state the answers rapidly : 1. 1 1 2 2 2 3 3 1 2 3 1 2 2 2 3 3 3 3 4 4 2 3 1 3 3 3 4 4 3 4 2. 4 4 4 5 5 5 5 5 5 4 4 3 4 2 5 3 5 6 4 5 5 5 4 5 6 6 6 5 3. 6 5 7 8 8 5 8 9 9 9 4 7 6 7 8 8 7 9 8 7 6 8 7 6 7 9 8 7 9 DRILL TEST. SUBTRACTION Subtract, and state thi ? answers rapidly : 1. 19 18 19 18 19 18 17 1 2 _3 6 7 _5 5 2. 17 16 15 17 16 15 14 6 3 _5 7. 8 7 _8 3. 14 13 12 14 13 12 14 9 9 7 6 8 6 _5 4. 12 11 10 12 11 10 11 5 4 7 8 6 3 7 For " Busy Work " encourage the pupils to write problems fitting such additions and subtractions as those given on this page. 36 USING WHAT YOU HAVE LEARNED VII. USING WHAT YOU HAVE LEARNED PROBLEMS ABOUT OUR CLASS 1. If there are 14 boys and 15 girls in our class, how many pupils are there in all ? 2. Using the numbers in Ex. 1, how many more girls than boys are there in the class ? 3. If 14 boys and 15 girls belong in our room, and 1 boy and 1 girl are absent, how many pupils are here to-day ? 4. If there are 29 pupils in our class, and 5 less in the class below ours, how many are there in that class ? 5. If there are 14 boys in our class, and 9 of them form a baseball team, how many boys of our class are not on the baseball team? APPLICATIONS 37 PROBLEMS ABOUT OUR STORE 1. Fred went to the store and bought a pencil for 5$ and a pad of paper for 6 $. How much did he pay for both ? 2. Mary bought an eraser for 5$, a ruler for 10$, and a penholder for 3 $. How much did she pay for all ? 3. The teacher bought a box of crayons for 30$ and a blackboard pointer for 8$. How much did she pay for both? 4. Jennie's mother sent her to the baker's for some little cakes. Jennie bought 6 of one kind and 8 of another kind. How many did she buy in all ? 5. I bought a bottle of ink for 10$, some pens for 8$, and a pencil for 5 $. How much did I pay for all ? 6. The teacher bought a box of colored crayons for 60$. She gave the dealer 75$. How much money did he give back to her? 7. Rob bought some candy for 5$, an apple for 2$, and an orange for 6$. How much did he pay for all? 7. 8. At our store they sell colored pencils for 15$ a box. If I buy a box and give the dealer 25$, how much money does he give back to me ? 9. Make up a problem about buying things at a store, using some of these prices : Bottle of black ink, 10$ Pens, 6 for 5$ Bottle of red ink, 10$ Pad of paper, 6$ or 8$ Penholder, 4$ Ruler, 10$ Pencil, 3$, 5$, or 8$ Box of toy money, 25$ 38 FRACTIONS VIII. FRACTIONS One Half. You may already know what we mean by one half of anything, or by one half of a number. This picture shows a sphere, and also shows a sphere cut in two halves. To find half of a number we divide the number by %. One half is written like this : ^. We write two halves, which equals 1, like this : f . If we cover a half sphere in the picture, we leave a sphere and a half. One and one half is written 1^, ORAL EXERCISE 1. How much is 1 of 4? i of 8? i of 10? 2. Divide 16 by 2 and so find ^ of 16. 3. How much is J of 14? 1 of 20? f of 18? 4. How much is \ of a pound and J of a pound? WRITTEN EXERCISE 1. "Write in figures : two and a half. 2. Write in figures : three and a half. Copy and add : 3- i + J 3J + 1 li + i 2 i + i 4. l+i 41 + J 5J + 1 61 + 1 5. Two halves are how many? Four halves are h6w many? 39 ORAL EXERCISE 1. What part of the sphere is (7? 2. B is how many times as large as (7? 3. If you write one half -|, how should you write one fourth? one third? 4. If you put two fourths of a sphere together, what part will you have ? 5. Add ^ of a sphere and \ of a sphere. Add sphere, \ of a sphere, and \ of a sphere. Fourths. We write \ for one fourth, |- for two fourths, and | for three fourths. B is |- of a sphere. You have now seen that = -f, and that = = f , and that One fourth is also called a quarter. J + J = f , and that J = WRITTEN EXERCISE 1. Draw a line. Divide it into halves. 2. Draw another line of the same length. Divide it into fourths. How many fourths do you find? 3. Draw a square. Divide it into fourths. How many fourths do you find ? 4. Draw a line. Divide it into halves and also into fourths. How many fourths do you find in one half? 40 FRACTIONS ORAL EXERCISE 1. Point to J of these squares. How many squares are \ of 8 squares? 2. Show that \ of this oblong equals 2 fourths, and also that 4 fourths of the oblong is the whole. 3. How many squares are J of 8 squares ? Point to them in two different groups. How many halves make the whole? WRITTEN EXERCISE 1. Draw a square 2 inches on a side. Divide it into squares each 1 inch on a side. Each small square is what part of the large one ? 2. Draw an oblong 1 inch high and 2 inches long. Divide it into squares each 1 inch on a side. Each square is what part of the oblong ? 3. If a square is 2 inches on a side, how far is it around the square? Draw the square and divide it into squares each 1 inch on a side. 4. Draw a square that is 1 inch high, and another that is 2 inches high. The first of these squares is what part as large as the second? 5. Draw a line and divide it into fourths. How much must you add to of the line to make the whole line ? 6. Draw an oblong like the one at the top of this page, , and divide it .into 8 squares. Put stars in three fourths of the squares. PAETS OF A GROUP 41 ORAL EXERCISE 1. How many marks are \ of 6 marks? Ill III 2. How many dots are ^ of 8 dots ? 3. How many stars are \ of 10 stars ? ***** 4. How many marks are \ of 12 marks ? 1 1 1 1 1 1 1 1 1 1 1 1 5. How many dots are J of 8 dots ? 2 ! Read and learn : 6. i of 2 is 1 1 of 6 is 3 of 10 is 5 7. 1 of 4 is 2 J of 8 is 4 \ of 12 is 6 8. i of 4 is 1 l of 8 is 2 J of 12 is 3 WRITTEN EXERCISE 1. Make 12 marks to show that J of 12 is 3. 2. Make 10 stars to show that \ of 10 is 5. 3. If John has 12 < and Rob has \ as much, how much has Rob? 4. If a boy 10 years old has a sister who is J as old, how old is the sister ? 5. If a man is 6 feet tall and his son is \ as tall, how tall is his son? 6. There are 12 inches in one foot. How many inches are there in ^ of a foot ? 7. How many inches are there in J of a foot ? Copy, and write the answers : 8. l of 8 \ of 10 l of 2 l of 6 1 of 1 9. l of 4 l of 12 J of 8 \ of 4 \ of 12 42 FRACTIONS ORAL EXERCISE 1. We call 12 things a dozen, and we write 1 doz. for one dozen. How many cubes make a dozen cubes ? 2. There are 12 inches in a foot. What other name can you give to a dozen inches ? 3. Name some things that are sold by the dozen. Can you tell the price ? 4. How many cubes make a half dozen cubes ? How many cubes make a quarter of a dozen cubes ? Point to the cubes in giving each answer. 5. How many fours do you see in a dozen? How many threes ? How many twos ? How many sixes ? Point to the cubes in giving each answer. 6. A hen sits on a dozen eggs and hatches all but two. How many chickens are hatched ? 7. When eggs are worth 40$ a dozen, how much does a half dozen cost ? 8. A newsboy buys a dozen papers for 8$, and sells them at a cent apiece. How much does he make ? 9. John had a dozen firecrackers. When they were lighted, all but J of them exploded. How many fire- crackers failed to explode ? How many exploded ? MEASURES 43 IX. MEASURES ORAL EXERCISE 1. What measure is Will using to find the length of the blackboard ? The measure is how many inches long ? 2. What measure is Mary using to find the height of the blackboard ? 3. How many feet in length is the yardstick? Measure it and see. 4. Measure the length of your own blackboard in feet ; in yards. 5. How many feet do you think the chalk rack is from the floor? Meas- ure the height and see. 6. If your height is 1 yard and 1 foot, how many feet tall are you? 7. How many feet are there in 1 yard and 2 feet ? Length. In measuring lengths, 12 inches = 1 foot 3 feet = 1 yard We write in. for inch or inches, ft. for foot or feet, yd. for yard or yards, 2 ft. 3 in. for 2 feet and 3 inches. EP 44 MEASURES MEASURING EXERCISE 1. A yard is how many times as long as a foot? 2. Measure the width of the room in yards, omitting parts of a yard. Measure this distance in feet. 3. Look at the foot rule. Point to 1 in. on the rule ; point to 6 in. How many inches are there in a foot ? 4. Draw a line one foot long and divide it into inches. How many inches are 6 in. and 6 in.? 5. Point to 3 in. How many inches are there in 1 ft. less 3 in.? How many inches are there in 1 ft. 3 in.? 6. Point to 4 in. How many inches are there in 1 ft. less 4 in.? How many inches are there in 1 ft. 4 in.? 7. Draw a line that you think is 1 ft. long. Measure it. 8. Draw a line that you think is 6 in. long. Measure it. 9. Is the edge of your desk more than a foot long or less than a foot long? Measure it. 10. Is your desk more than a foot high or less than a foot high? Measure it. 11. Cut a piece of string that you think is 1 yd. long. 12. Draw a line that you think is 1 in. long. Measure it. 13. How many inches are there in 1 ft. less 5 in. ? 14. How many inches are there in 1 ft. less 8 in.? 15. Draw a line that you think is 24 in. long. Measure it. The children should be given much practice in using real measures. They should also exercise their judgment in estimating lengths. A yard- stick and a ruler divided into inches, half inches, and quarter inches are desirable for this grade. LIQUID MEASURE 45 ORAL EXERCISE 1. Which is the pint measure in the picture, and which is the quart ? 2. How many pints make a quart? A pint is what part of a quart? ' 3. Tell me the names of several things that are sold by the pint and the names of others that are sold by the quart. 4. Draw a full-sized picture of a quart meas- ure. Draw a line across it, marking off 1 pint. 5. How much is 10 quarts + 1 quart + 1 quart + 1 quart? Liquid Measure. In measuring liquids, 2 pints = 1 quart We write pt. for pint or pints, and qt. for quart or quarts. A pint is \ of a quart. 6. How much does a quart of milk cost where we live ? How much does a pint of milk cost ? 7. If I have a quart of cream and a pint of cream, how many pints of cream do I have ? 46 MEASUKES ORAL EXERCISE 1. The children in the picture have a 2-pound weight and a ^-pound weight to balance the book. Tell me how much the book weighs. 2. Suppose the chil- dren should weigh 1 pt. of water and find that it weighs a pound, how much would 1 qt. weigh? 3. If one of your books weighs \ pound, another \ pound, and a third \ pound, how much do all three books weigh? 4. If the children had a pound of figs worth 2 dimes, how much would \ pound of these figs be worth? Pounds. "We write Ib. for pound or pounds. Thus, 2 Ib. means 2 pounds, and \ Ib. means \ of a pound. 5. Add 20 Ib., 10 Ib., and 1 Ib. 6. Add 9 Ib., 4 Ib., 2 Ib., and 1 Ib. 7. Find J of 4 Ib., 1 of 6 Ib., and 1 of 2 Ib. 8. From 69 Ib. subtract 4 Ib. and then add 1 Ib. 9. From 87 Ib. subtract 10 Ib., 6 Ib., and 1 Ib. It is desirable that children should weigh various objects, using the pound, half pound, and quarter pound. The table of pounds and ounces is taken up later. KEVIEW DRILL 47 X. REVIEW DRILL ORAL EXERCISE AA.WVV I 1. 31 /\A/\JI V Vf t. t/ 51 81 21 71 41 61 91 11 2. 42 82 22 72 52 12 2 32 62 3. 83 33 73 3 13 63 43 23 53 4. 64 44 74 4 34 84 14 54 24 5. 45 85 75 15 55 25 5 65 35 6. 56 46 6 36 66 26 76 16 86 7. 47 67 27 87 77 37 57 7 17 8. 58 48 78 18 88 68 28 8 38 9. 79 39 89 69 29 9 19 49 59 Subtract each of the numbers 2, 3, 4, 6 ; e, 7, 8, 9, from : 10. 40 70 90 10 50 80 20 60 30 11. 51 71 41 61 31 91 11 81 21 12. 72 52 12 42 82 62 22 92 32 13. 33 23 93 83 63 13 73 53 43 14. 64 14 44 74 54 24 84 34 94 15. 95 85 65 15 45 25 35 55 75 16. 96 46 86 56 36 66 16 76 26 17. 47 97 57 37 87 17 67 27 77 In exercises of this nature it is not expected that teachers will require all of the work. As soon as the pupils show themselves proficient in the additions and subtractions they should pass to the next topic. 48 REVIEW DRILL DRILL TEST. FRACTIONS AND MEASURES State the answers rapidly :. 1. i of 4 i of 2 J of 10 i of 6 1 of 8 2. 1 of 4 I of 8 1 of 12 | of 4 f of 4 3. l of 12 in. l of 1 doz. l of 8 ft. \ of $6 4. l of 12 in. l of 1 doz. l of 8 yd. \ of 6< 5. In 1 yd. there are (?) ft. A foot is (?) of a yard. 6. In 1 ft. there are (?) in.; in 2 ft. there are (?) in. 7. In 1 qt. there are (?) pt. A pint is (?) of a quart. 8. l of a pound and \ of a pound are (?) pound. 9.1 + 1 ll + l ll + l 21 + 1 10. l + l ll + l 2 + 1 2J + 1 11. % of a sphere and ^ of the same sphere make (?). 12. -| of a pound and ^ of a pound and \ of a pound make (?) pound. 13. In 1 qt. there are (?) pt. ; in 2 qt. there are (?) pt. 14. In 1 yd. there are (?) ft.; in 2 yd. there are (?) ft. 15. In 1 ft. there are (?) in.; in 2 ft. there are (?) in. 16. A foot is (?) in. more than 1 ft. 17. A yard is (?) ft. more than 1 ft. 18. A quart is (?) pt. more than 1 pt. 19. A nickel is (?) cents, and 2 nickels make (?) dime, or (?) cents. 20. In $1 there are (?) dimes, or (?) cents. 21. In 3 yd. there are (?) ft.; in 4 yd. there are (?) ft. USING WHAT YOU HAVE LEAKNED 49 XL USING WHAT YOU HAVE LEAENED ORAL EXERCISE 1. Fred's father gives him 30 an hour for weeding the garden. How much does Fred earn in 2 hours? 2. If Fred works long enough to earn 30$, and then buys a 25-cent ball, how much does he have left ? 3. If he wishes to buy an orange that costs 3 $, how long will he have to work to earn the money ? 4. How much does a good rubber ball cost? If Fred has 24$, is this too much or too little to buy the ball? 5. Fred has 1$ in his pocket. If he earns 3$ an hour, how long will it take him to earn 9$, so that he can buy 10$ worth of marbles? 50 USING WHAT YOU HAVE LEARNED 6. Julia's aunt wishes to show her what it means to earn money. She pays her 4$ an hour. Julia worked half an hour this morning before school. How much did she earn then? 7. After school Julia worked an hour. How much has she earned to-day? 8. Julia wished to earn enough to buy 15$ worth of ribbon. After she worked 2 hours at 4$ an hour had she enough ? Had she enough after she worked 3 hours ? How much did she then lack ? 9. After Julia had worked 4 hours she found she had earned more than enough for her ribbon. How much more ? There is always some advantage in letting a pupil do simple multi- plication by means of addition. It makes the subject of multiplication seem more valuable when it is reached. EEVIEW 51 10. Fred's father sent him to the store to buy a basket. He gave Fred a 25-cent piece. Fred paid 20$ for the basket. How much money did he have left? 11. Fred saw at the store a baseball mitt. He has saved 400 toward buying it. The mitt costs 500. How much more money must he have ? 12. Julia's aunt sent her to the store to buy a dozen eggs. Julia finds that they have only \ doz. to sell. How many eggs must she buy at another store to make up the dozen ? 13. Julia pays 200 for \ doz. eggs. How much would she have to pay for a dozen ? 14. Julia's aunt sends her to buy 2 qt. of milk. If Julia pays 80 for a quart, how much does she pay for 2 qt.? 15. Fred is sent to the store to buy \ doz. bananas. How many bananas does he buy ? 16. If Fred buys 1^ doz. oranges, how many oranges does he buy? First find how many oranges there are in a dozen, then in \ doz., and then in 1^ doz. 17. Fred pays 80 for some salt, and gives the storekeeper a dime. How much change does he get back ? 18. Julia is making some doll's clothes. She needs \ yd. of ribbon which costs 120 a yard. How much must she pay for \ yd.? 19. Julia's aunt asks her to find how much the breakfast cost. Julia found that the oatmeal cost 100, the milk 50, the bread and butter 40, and the meat 200. How much did she find that all these cost ? 52 LITTLE EXAMINATIONS XII. LITTLE EXAMINATIONS I. 1.3 + 9. 5. l of 8. 9. 2 pt. = (?) qt. 2. 17 - 8. 6. 1 of 12. 10. 1 yd. = (?) ft. 3. 22 + 6. 7. lof 80. 11. ll + l 4. 45 - 30. 8. l of 6^.. 12. 12 + 23 + 2. II. 1.5 + 8. 5. l of 8 ft. 9. 4 pt. = (?) qt. 2. 14 - 6. 6. l of 8 ft. 10. 1 ft. = (?) in. 3. 42 +10. 7. Jof 12. 11. 21 + 3. 4. 62 - 31. 8. l of 12. 12. 23 + 45 + 1. III. 1. 37 + 6. 5. Jof 100. 9. Ipt. = (?)qt. 2. 14 - 7. 6. 1 of 8 in. 10. 2 yd. = (?) ft. 3. 52 + 13. 7. l of 12 Ib. 11. 21 + 1. 4. 74 - 21. 8. l of 12 qt. 12. 51 + 6 + 11. IV. 1. 54 + 8. 5. l of 10. 9'. 6 pt. = (?) qt. 2. 13 - 5. 6. l of $10. 10. 2 ft. = (?) in. 3.38 + 20. 7. Jof 120. 11.3 + 21. 4. 66 - 22. 8. l of $12. 12. 31 + 22 + 12. V. 1. 77 + 7. 5. l of 20. 9. 2 qt. = (?) pt. 2. 13 - 6. 6. l of 14. 10. 6 ft. = (?)yd. 3. 73 + 14. 7. l of 12 Ib. 11. 31 + l 4.79-32.' 8.1 of 16. 12.33 + 40 + 1. These Little Examinations at the close of each chapter furnish excellent review drill work. The time should be recorded for each, and the pupils should endeavor to improve their records. This work may be used for review in the first part of the next chapter. CHAPTER II I. NUMBERS TO 1000 ORAL EXERCISE 1. Here are 4 bundles of splints, 10 in a bundle. How many splints are there ? Write the number on the blackboard. 2. If there are 5 such bundles of splints, how many splints are there in all? Write the number on the blackboard. 3. Here are 3 bundles of splints, 100 in a bundle. How many splints are there? Write the number on the blackboard. If there were 400 more, how many splints would there be? Write the number on the blackboard. 4. Here is a larger bundle of splints, containing as many splints as there are in 10 bundles of 100 each. How many splints are there in this bundle ? 5. How many 10's are there in 100? How many 100's are there in 1000? What is the name for ten 10' s? What is the name for ten 100's ? 53 54 NUMBERS TO 1000 ORAL EXERCISE 1. How many splints are there in the picture? 300 + 40 + 2 2. Read these numbers : 342 372 100 101 352 392 200 202 362 312 302 102 203 110 123 105 890 987 705 111 999 3. Open this book at page 146 ; at page 110. 4. The numbers below 10 are called ones. For example, 6 is six ones. We write the ones in the right-hand place. In the number 26 there are 2 tens and 6 ones. Where do we write the tens ? Where do we write the hundreds f 5. Name the figure in ones' place in 475 ; the figure in tens' place; the figure in hundreds' place. WRITTEN EXERCISE 1. Write in figures : Five hundred fifty-five Two hundred forty-nine One hundred twenty-one 2. Write in words : 242 207 520 634 Six hundred nine Three hundred three Eight hundred eighty 987 843 765 BEADING AND WEITING NUMBERS 55- ORAL EXERCISE Read these numbers : 1. 208 210 217 237 286 506 242 2. 348 376 407 473 530 721 346 3. 691 682 707 827 936 888 989 4. What is the ones' figure in 450 ? the tens' figure ? the hundreds' figure ? WRITTEN EXERCISE Write in figures : 1. One hundred one 2. Two hundred three 3. Three hundred six 4. Four hundred nine 5. Six hundred six One hundred fifty Two hundred seventy Three hundred ninety Five hundred forty Seven hundred eight Write in words : 6. 527 642 334 7. 708 860 901 Write in figures : 8. Forty-three 9. Twenty-one 10. Fifty-two 11. Seventy-eight 12. Five hundred 13. Six hundred 14. Seven hundred 456 777 678 800 909 750 742 630 830 400 303 1000 Eight hundred seventy-seven Seven hundred eighty-nine Nine hundred ninety-nine Six hundred seventy-eight Five hundred sixty-seven Six hundred seventy-three Seven hundred twenty-seven 56 NUMBERS TO 1000 ORAL EXERCISE 1. Read the figures on the clock. 2. Which hand tells the hours? Which tells the minutes? 3. How long does it take the hour hand to pass from I to II? How long does it take the minute hand to pass from I to II ? 4. How long does it take the hour hand to pass around from XII to XII again? How long does it take the minute hand? 5. What time is it by the clock in the picture? What time is it by the school clock? 6. How many minutes in an hour ? in ^ hour ? Roman Numerals. The figures often seen on clocks are called Roman numerals, and are as follows : I II III IHIorlV V VI VII VIII IX X XI XII 123 4 567 8 9 10 11 12 Time. Read and learn : 60 minutes = 1 hour 24 hours = 1 day We write min. for minute or minutes, hr. for hour or hours, da. for day or days, A.M. for forenoon, and P.M. for afternoon. We write 15 minutes after 2 in any of these three ways : 2 15, 2 : 15, or 2 hr. 15 min. ADDITION 57 II. ADDITION ORAL REVIEW DRILL Add the following: 1. 6 16 26 96 7 27 47 87 3 3 3 3 5 5 _5 _5 2. 4 14 34 64 5 37 55 25 7 7 _7 7 6 _6 6 _6 3. 8 28 48 78 3 13 33 53 4 4 _4 _4 8 _8 _8 8 4. 9 39 59 89 7 37 57 87 2 ' 2 2 2 9 _9 9 9 5. 3 43 43 65 2 35 48 62 9 _9 8 7 8 _6 _1_ _8 6. 7 37 58 58 8 68 52 63 8 8 8 J_ 6 _6 _9 9 7. 6 26 46 46 6 56 27 38 6 _6 6 _8 7 _7 _7 _7 8. 9 49 79 79 8 38 57 69 9 _9 9 _7 8 _8 _8 _8 9. 7 57 58 79 4 34 37 38 4 4 4 _5 9 _9 5 _6 10. 4 63 54 84 5 95 94 97 8 8 8 4 5 5 6 3 58 ADDITION . ORAL EXERCISE 1. If you have 12 marbles and 6 marbles, how many do you have in all ? 2. If you have 12 < and 10 <, how much do you have in all ? 3. If there are 11 girls and 10 boys in the class, how many children are there in all? Add the following : 4. 12 12 12 20 25 35 48 _6 _8 10 20 20 20 30 5. 50 51 57 58 67 22 35 30 30 30 40 30 11 11 WRITTEN EXERCISE Add the folloiving : 1. 30 32 32 42 45 87 40 40 45 35 32 _3 2. 33 33 63 63 64 76 60 66 30 36 35 4 3. 70 74 74 75 74 93 24 20 21 23 25 _7 4. 160 166 166 176 277' 342 200 210 213 223 322 523 5. 273 428 579 343 628 496 401 320 210 343 231 300 TWO-FIGUEE NUMBERS 59 Adding Two-Figure Numbers. 1. If I have 460 and 370, how much money have I in all ? I may think of 46 and 37 like this : 46 = 40 + 6, or 4 tens and 6 ones 37 = 30 + 7, or 3 tens and 7 ones The sum is 70 + 13, or 7 tens and 13 ones, or 83 46 37 13 = sum of ones 7 = sum of tens 83 = sum of numbers 46 37 83 The teacher should put the above solution on the blackboard, and should lead the pupils to see that they might add the ones and tens separately, as here shown. This is too long, however, and so we add without all this work. We add the numbers as shown below. We see that 7 ones and 6 ones are 13 ones, and we write the 3 in the ones' column and add the 1 to the tens. Then 1 + 3 + 4 = 8, and we write the 8 in the tens' column. The sum is 83, and so I have 830 in all. 2. If I have 24 marbles, 38 marbles, and 16 marbles, how many marbles have I in all? We add the numbers as here shown. We see that the sum of the ones is 6 + 8 + 4, or 18, and we write the 8 in the ones' column and add the 1 to the tens. Then 1 + 1 + 3 + 2 = 7, and we write the 7 in the tens' column. The sum is 78, and so I have 78 marbles in alL EP 24 38 16 78 60 ADDITION WRITTEN EXERCISE Add the following : 1. 24 23 23 21 25 35 65 36 37 38 39 39 17 25 2. 22 34 33 67 34 47 37 38 47 59 23 46 15 17 3. 32 24 36 26 58 29 53 48 28 36 37 25 16 38 4. 35 47 65 27 72 33 56 35 26 18 19 19 18 29 5. 48 56 39 47 55 78 74 27 39 29 38 19 16 18 6. 59 73 66 48 68 37 49 26 19 24 23 15 27 16 7. 29 52 29 35 19 27 58 48 29 39 45 39 46 18 8. 27 38 59 46 25 44 25 37 43 17 36 35 37 38 9. 21 36 45 37 56 49 47 19 18 15 17 18 29 36 10. 11 21 32 13 14 15 16 28 36 49 48 48 48 23 33 48 26 38 38 38 46 THREE-FIGURE NUMBERS 61 Adding Three-Figure Numbers. We often have to add numbers of three figures. John worked on Saturday for Mr. Eastman, the grocer. Mr. Eastman told John to look over two boxes of apples and throw away the bad ones. John found 156 good apples in one box and 117 in the other. How many good apples did he find in all? We see that we must add 156 and 117. 7 ones + 6 ones = 13 ones = 1 ten + 3 ones. We write the 3 in the ones' column and add the 1 to the tens. 1 ten + 1 ten + 5 tens = 7 tens. We write the 7 in the tens' column. 1 hundred + 1 hundred = 2 hundreds. We write the 2 in the hundreds' column. The sum is 273, and so John found 273 good apples. WRITTEN EXERCISE 1. There are 186 oranges in one box and 107 in an- other box. How many oranges are there in both boxes? 2. There are 127 boys and 134 girls in a school. How many pupils are there in the school ? 3. Sam tied 338 ft. of string and 125 ft. of string to- gether to make a kite string. How long was the kite string ? Add the following ', and check the work : 4. 5. 6. 7. 8. 9. 278 346 227 625 506 $329 104 229 347 135 206 225 62 ADDITION Addition Continued. Mr. Eastman told John to count the oranges which were left after the day's sale. In one box there were 172 oranges and in another box 156 oranges. How many oranges were left in the two boxes? We see that we must add 172 and 156. 6 ones + 2 ones = 8 ones. We write the 8 in the ones' column. 5 tens 4- 7 tens =12 tens = 1 hundred + 2 tens. We write the 2 in the tens' column and add the 1 to the hundreds. 1 hundred + 1 hundred + 1 hundred = 3 hundreds. We write the 3 in the hundreds' column. The sum is 328, and so there are 328 oranges left. The teacher will observe that on page 61 the sum of the ones (units) was more than 10, while on this page the sum of the tens is more than 10 (tens). On page 63 the general case is considered. WRITTEN EXERCISE 1. There are 140 sheep in one pasture and 174 sheep in another pasture. How many sheep are there in all ? 2. It is 143 miles from here to the place where Rob lives, and 162 miles further to the place where James lives. How far is it from here to the place where James lives ? Add the following, and check the work: 3. 4. 5. 6. 7. 8. 263 374 382 491 282 $473 142 251 166 275 370 264 THREE-FIGURE NUMBERS 63 Addition Continued. Mr. Forbes has a corner lot. He is building a picket fence on the sides facing the two streets. He needs 196 pickets on one side and 188 on the other side. How many pickets does he need in all? We see that we must add 196 and 188. 8 ones + 6 ones = 14 ones = 1 ten + 4 ones. We write the 4 in the ones' column and add the 1 to the tens. 1 ten + 8 tens + 9 tens = 18 tens, or 1 hundred + 8 tens. We write the 8 in the tens' column and add the 1 to the hundreds. 1 hundred + 1 hundred + 1 hundred = 3 hundreds. We write the 3 in the hundreds' column. The sum is 384, and so Mr. Forbes needs 384 pickets. WRITTEN EXERCISE 1. If Mr. Forbes needs 187 pickets for a fence on one side of his lot and 165 pickets for a fence on another side, how many pickets does he need for both sides ? Add the following, and check the ivork : 2. 3. 4. 5, 6. 7. 288 357 349 281 555 239 368 285 68 399 278 471 8. 9. 10. 11. 12. 13. 200 301 110 240 125 379 325 288 229 386 474 206 295 322 291 285 199 98 64 SUBTRACTION III. SUBTRACTION Subtraction Reviewed. If Louis has 7 marbles and loses 4 of them, he has 3 marbles left ; if he has 17 marbles and loses 4 of them, he has 13 marbles left ; and if he has 27 marbles and loses 4 of them, he has 23 marbles left. That is, 7-4= 3 27-4 = 23 47-4 = 43 17-4=13 37-4 = 33 57-4 = 53 This kind of drill on subtraction by endings is valuable. For example, because 8 - 6 = 2, we know that 18 - 6 = 12, 28 - 6 = 22, and so on. ORAL REVIEW DRILL Subtract the following : 1. 11 21 31 61 10 20 30 70 2 2 2 2 3 3 3 3 2. 12 22 32 82 13 23 33 93 4 4 4 4 5 5 5 5 3. 14 24 34 74 15 25 65 85 7 _7 7 7 6 6 6 6 4. 16 26 46 76 17 27 57 77 8 8 8 8 9 9 9 9 5. 18 28 48 98 16 36 56 86 _9 9 _9 9 _7 _7 7 7 6. 15 25 14 34 12 32 11 41 7 7 8 8 6 6 7 7 TWO-FIGURE NUMBERS 65 Subtraction Continued. When one number is subtracted from another, the larger number is called the minuend, the smaller number is called the subtrahend, and the result is called the difference or remainder. If there are 47 pupils in one room and 28 pupils in another, how many more are there in the first room? We subtract as here shown. We cannot take 8 ones from 7 . , -i , f ,, A Minuend, 47 ones, so we take 1 ten ot the 4 7 _ j -j. M.I. it. T bubtranend, tens and put it with the 7 ones, _. , . -. Difference, 19 making .17 ones. Then 17 ones 8 ones = 9 ones. Then 2 tens from the 3 tens remaining leaves 1 ten. The difference is 1 ten and 9 ones, or 19. This shows what we did, and also shows the check. 47 = 30+17 28 28 = 20+ 8 19 19 = 10+ 9 47 There are two leading methods of subtraction used in the business world. 1. We may think of the above numbers as follows : 47 = 40 + 7 or 30 + 17 28= 20+8 Subtracting, we have 10 + 9 = 19 This subtraction may be performed either directly, by taking 8 from 17, and 20 from 30 ; or indirectly, by thinking " 8 and 9 are 17, 2 and 1 are 3." 2. We may think of both numbers as increased by 10. Instead of 47 we shall have 40 + 17 Instead of 28 we shall have 30+8 Subtracting as before, we have 10 + 9 = 19 Either of these plans is allowable, and all are used in business. 66 SUBTRACTION WRITTEN EXERCISE Subtract, and clieck : 1. 53 61 72 81 65 91 83 28 32 28 53 37 56 25 2. 94 96 54 62 82 80 76 66 78 27 43 54 37 29 3. 74 63 73 83 55 63 95 46 47 39 65 39 29 38 4. 56 76 64 57 75 90 65 48 49 26 28 48 47 29 5. Frank has 28 marbles and Tom has 43. How many more marbles has Tom than Frank ? 6. A schoolroom is 42 ft. long and 28 ft. wide. It is how much longer than wide? 7. In playing a game John's score was 31 and Fred's was 19. Find the difference in their scores. 8. A boy is 12 years old and his father is 41 years old. How much older is the father than his son ? 9. A girl has a piece of cloth 41 in. long. She cuts off 27 in. for a doll's dress. How much has she left ? 10. There are 31 children in one class and 28 in another. How many more are there in one class than in the other ? 11. A man has 92 hens and sells 75 of them. How many hens has he left? THREE-FIGUKE NUMBERS 67 Subtracting Three-Figure Numbers. If there are 701 children in one city school and 240 in another, how many more are there in one school than in the other? We see that we must subtract 240 from 701. We write the numbers as here shown. We see that 10 = 1, and we write the 1 below the and the 1. We cannot take 4 tens from tens, so we take 1 hundred of the 7 hundreds, making 100, or 10 tens. Then 10 tens 4 tens = 6 tens, and we write the 6 below the 4 and the 0. The 7 hundreds is now 6 hundreds, because we took 1 hundred away. Then 6 hundreds 2 hundreds = 4 hundreds, and we write the 4 below the 2 and the 7. The difference is 461, and so there are 461 more children in one school than in the other. We check the work by adding 240 to 461. WRITTEN EXERCISE Subtract, and check the work : 1. 2. 3. 732 250 743 270 754 290 765 283 708 296 802 591 583 291 842 391 927 645 916 424 823 460 730 263 839 567 819 577 829 577 935 442 708 523 820 575 68 SUBTRACTION Further Work in Subtraction. If there are 731 pupils in one city school and 246 in another, how many more are there in the first school than in the second? We see that we must subtract 246 from 731. To subtract 246 from 731 we write the num- bers as here shown. We cannot take 6 from 1, so we take 1 ten of the 3 tens and put it with the 1, making 11. Then 11 6 = 5, and we write the 5 below the 6 and 1. The 3 tens are now 2 tens, because we took 1 ten away. We cannot take 4 tens from 2 tens, so we take 1 hundred of the 7 hundreds and put it with the 2 tens, making 120, or 12 tens. Then 12 tens 4 tens = 8 tens, and we write the 8 below the 4 and the 3. Then 6 hundreds 2 hundreds = 4 hundreds, and we write the 4 below the 2 and the 7. The difference is 485, and so there are 485 more pupils in the first school than in the second. Another Example. If there are 700 pupils in one school and 246 in another, how many more are there in the first school than in the second ? We see that we must subtract 246 from 700. We cannot take 6 from 0, or 4 from 0, so we think of 700 as 600 + 90 + 10. Then 10 6 = 4, 9 tens 4 tens = 5 tens, and 6 hundreds 2 hundreds = 4 hundreds. The difference is 454, and so there are 454 more pupils in the first school than in the second. THREE-FIGURE NUMBERS 69 WRITTEN EXERCISE Subtract, and check the work : 1. 2. 3. 4. 5. 6. 7. 911 385 621 384 722 388 645 387 523 287 821 642 713 396 925 456 632 469 617 438 927 679 731 496 515 296 651 392 834 688 722 485 722 433 832 468 735 268 913 688 536 398 643 288 635 388 936 428 912 335 834 495 826 237 925 358 813 426 914 769 716 328 814 227 841 356 922 488 833 539 644 298 113 4 103 4 203 4 413 104 703 205 703 215 J 8. If Robert picks 324 apples and Jack picks 187, how many more apples does Robert pick than Jack ? 9. In a city school of 523 pupils 267 are girls. How many pupils are boys ? 10. It is 660 ft. around a running track. After a boy has run 480 ft. of this distance, how much farther must he run to go all the way around? 70 SUBTRACTION ORAL REVIEW TEST Subtract each of the numbers 2, 3, 4, <5, 6, 7, 8, and 9 in turn from each of the following numbers : 1. 10 21 32 43 54 65 76 87 98 2. 62 72 41 20 97 52 61 40 83 3. 31 86 95 51 85 71 42 63 60 4. 96 30 70 82 50 92 73 53 81 5. 75 93 91 84 80 11 55 74 64 WRITTEN REVIEW TEST Subtract 468 from each of these numbers : 1 . 512. 2. 601. 3 . 725. 4. 836. 5. 957. Subtract 379 from each of these numbers : 6 . 425. 7. 536. 8 . 648. 9. 717. 10. 800. Subtract 254 from each of these numbers : 11 . 506. 12. 521. 13 . 632. 14. 703. 15. 812. Subtract 337 from eacA of these numbers : 16 . 425. 17. 502. 18 . 616. 19. 723. 20. 900. Subtract 576 from each of these numbers : 21 . 841. 22. 723. 23 . 900. 24. 811. 25. 612. Subtract 624 from each o/ 1 these numbers : 26 . 721. 27. 712. 28 . 801. 29. 813. 30. 900. If the check is insisted upon, it will give a review of addition. MULTIPLICATION TABLES BEGUN 71 IV. MULTIPLICATION AND DIVISION TABLES ORAL EXERCISE 1. Frank's father has sent him to buy 3 postage stamps for letters. How much must Frank pay for each stamp? How much must he pay for the 3 stamps ? 2. How much is 2 + 2 ? How much is 2 + 2 + 2 ? How much is 2 + 2 + 2 + 2? 3. If Frank's father sends him for 4 postage stamps for letters, how much money must he give him ? 4. If Frank's father has 5 letters to mail, how much do the stamps cost for all of these letters? Which is better, to add 2 + 2 + 2 + 2 + 2, or to know without adding how many five 2's are ? 5. Frank did not know how many five 2's are, and his father told him to count by 2's, like this : 2, 4, 6, and so on. Then Frank found how many five 2's are. How many are they? 6. How many are three 2's ? How many are four 2's ? 7. Can you count by 2's, beginning at 2 and ending at 10 ? Try it. 8. Can you count by 2's to 12 ? to 14 ? to 18 ? to 20 ? to 22 ? Try it. 9. Can you tell how much Frank would have to pay for ten 2$ stamps? It is advisable to introduce real, concrete problems of this nature when a new subject is begun, so as to show the purpose of the work. These prob- lems should relate to the home or school interests of the pupils. 72 MULTIPLICATION AND DIVISION TABLES 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ORAL EXERCISE 1. Add the columns of 2's, from one 2 to five 2's. 2. On the blackboard and on paper build more columns of 2's, until you have ten 2's in the last column. How many columns are there ? 3. Read the columns, thus : " One 2 is 2, two 2's are 4, three 2's are 6," and so on. 4. How many are five 2's ? six 2's ? seven 2's ? eight 2's ? nine 2's ? ten 2's ? 5. Read and learn this table of 2's, thus : " Two 2's are 4 " (or else " two times 2 are 4 "), and so on : 2x2 = 4 5x2 = 10 8x2 = 16 3x2 = 6 6x2=12 9x2=18 4x2 = 8 7x2 = 14 10x2=20 6. How much is 1x2? 2x1? 2x0? 0x2? 7. State these products : 2x3 2x7 2x8 2x5 2x6 2x4 2x9 2x10 The pupils should be made to see that if they know 6x2, they also know 2x6; therefore these inverse drills should be carried right along with the tables. 8. How much is 2 + 2 + 2? 3x2? 9. How much is 2 + 2 + 2 + 2? 4x2? 10. Read and learn : 11 x 2 = 22 ; 12 x 2 = 24. TABLE OF TWOS 73 ORAL EXERCISE 1. At 2 cents each, how much will 3 tablets cost? 2. At 2 cents each, how much will 4 pencils cost ? 3. At 2 cents each, how much will 7 papers cost ? At 2 cents each, find the cost of ike following : 4. 5 penholders. 8. 9 postage stamps. 5. 8 spools of thread. 9. 4 pictures. 6. 6 pears. 10. 9 calendars. 7. 7 yards of braid. 11. 8 newspapers. If 5 x % + 1 is equal to 10 + 1, state the values of: 12. 5x2 + 3. 15. 8 x 2 + 5. 18. 6 x 2 + 1. 13. 4 x 2 + 1. 16. 9 x 2 + 4. 19. 8 x 2 + 3. 14. 3 x 2 + 1. 17. 7 x 2 + 3. 20. 5 x 2 + 4. This carrying drill is of great importance in multiplication. WRITTEN EXERCISE Multiply the following : 1. 2242221902 2426893220 2. 2325261278 32527221-22 3. We have placed here 2 rows of four dots each, or 4 columns of 2 dots each. This shows easily that 2x4 dots = 4x2 dots. Draw 12 small squares, to show that 6x2 squares = 12 squares, and that 2x6 squares = 12 squares. 74 MULTIPLICATION AND DIVISION TABLES ORAL EXERCISE 1. How many 2's do you see in 4? How many 2's do you see in 6 ? 2. How many 2's do you see in 8 ? How many 2's do you see in 10 ? 3. 8 contains 2 how many times ? Division. The answer to Ex. 3, " 8 contains 2 four times," is written 8-2 = 4 2 2 2 2 4 2 2 2 6 2 2 2 2 8 2 2 2 2 2 10 2)8 4 In each case 8 is called the dividend, 2 is called the divisor, and 4 is called the quotient. The quotient multiplied by the divisor equals the dividend. The quotient is sometimes placed above the dividend, as in long division, and any school may require this arrangement. It is not, however, the busi- ness custom, and it is inconvenient in some advanced work. 4. State the values of the following : 4x2 5x2 6x2 2x4 2x5 2x6 8-^2 10-5-2 12-2 8-4 10-5 12 -H 6 5. Read and learn : 4-2 = 2 6-2 = 3 10-2 = 5 12 - 2 = 6 14 - 2 = 7 7x2 2x7 14-2 14 -s- 7 16-*- 2= 8 18 -H 2= 9 20 - 2 = 10 TABLE OF THREES 75 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ORAL EXERCISE 1. Add the columns of 3's, from one 3 to five 3's. 2. On the blackboard and on paper build more columns of 3's, until you have ten 3's in the last column. How many columns are there? 3. Read the columns, thus: "One 3 is 3, two 3's are 6, three 3's are 9," and so on. 4. How many are five 3's ? six 3's ? seven 3's ? eight 3's ? nine 3's ? ten 3's ? 5. Read and learn the table of 3's, thus : " Two 3's are 6 " (or else " two times 3 are 6 "), and so on. 2x3=6 5x3 = 15 8 x 3 = 24 3x3=9 6x3 = 18 9x3 = 27 4x3 = 12 7x3 = 21 10x3 = 30 6. How much is 1 x 3 ? 3x1? 3x0? 0x3? 7. State these products : 3x2 3x7 3x9 3x4 3x3 3x5 3x6 3x8 8. How much is 3 + 3 ? 2x3? 9. How much is 3 + 3 + 3? 3x3? 10. How much is 3 + 3 + 3 + 3? 4x3? Complete the following : 11. 2 x = 6. 12. 3 x = 9. 13. 14. x3=12. x3=15. 15. 2x3 16. 7x3 76 MULTIPLICATION AND DIVISION TABLES ORAL EXERCISE 1. Count by 3's from 3 to 36. 2. Repeat the multiplication table of 3's to 10 x 3. 3. Read and learn : 11 x 3 = 33 12 x 3 = 36 State the answers to the following : 4.4x34-1. 6.5x3 + 2. 8.6x3 + 2. 5. 7 x 3 + 5. 7. 8 x 3 +1. 9. 9 x 3 + 3. 10. How much is 3x0? 0x3? 2x0? 0x2? 11. If 1 orange costs 3 cents, how much will 6 oranges cost ? How much will 9 oranges cost ? 12. If 1 pencil costs 3 cents, how much will 7 pencils cost? How much will 8 pencils cost? 13. If 1 piece of burlap used in making a carpet for a doll's house costs 3 cents, how much will 8 pieces cost ? WRITTEN EXERCISE Copy and complete the following : 1. 4x =12 2x=6 x3 = 2. 6x =18 5x =15 x3 = 24 3. 9 x = 27 7 x = 21 x 3 = 18 4. 8 x = 24 11 x = 33 x 3 = 36 5. If 1 chair costs $3, how much will 7 chairs cost ? How much will 9 chairs cost? . If 1 school desk costs $3, how much will 12 school desks cost? How much will 11 school desks cost? TABLE OF THKEES 77 ORAL EXERCISE 1. How many 3's do you see in 6 ? How many 3's do you see in 9 ? 2. How many 3's do you see in 12 ? How many 3's do you see in 15 ? 3. How many more 3's are there in 15 than in 12 ? 4. State the values of : 4x3 5x3 3x4 3x5 12-3 15-3 12-4 15-5 5. How much is 8 x 3 ? 3x8? 24 6. How much is 6 x 3 ? 3x6? 18 in 6? 3 .12? 3 3 ? 3 3 3 3 3 3 3 here 333 3 3 369 12 15 7x3 9 x3 3x7 3 x9 21-3 27 -3 21-7 27 -9 3? 24-8? 3? 18-6? WRITTEN EXERCISE 1. At 3$ each, how many bananas can be bought for 9 ? for 150? for 240? for 300? 2. At 3 each, how many pencils can be bought for 120? for 180? for 210? for 270? 3. At 30 each, how many oranges can be bought for 90 and 120 together? 4. How many threes in a dozen ? in a half dozen ? 5. Copy and complete : -3 = 3 = 6 3 = 5 -3 = 8 -3 = 4 78 MULTIPLICATION AND DIVISION TABLES ORAL EXERCISE 1. At 3$ each, how many cakes can be bought for for 18#? for6$? for 9$? for 15$? 2. If 3 sheep cost $24, how much does each one cost ? 3. If a freight train goes a mile in 3 minutes, how many miles will it go in 30 minutes ? 4. A yard is 3 ft. How many yards in 30 ft. ? 5. How many yards of braid, at 3$ a yard, can be bought for 18$? 6. If you need 27 sheets of paper to make 3 notebooks, how many sheets will you need for 1 notebook ? 7. At 3$ each, how many oranges can be bought for 30$? for 21$? for 12$? for 18$? 8. If you need 3 yd. of cloth for each skirt, how many skirts of this kind can you make from 27 yd.? from 18 yd.? from 21 yd.? from 12 yd.? WRITTEN EXERCISE 1. Copy this table and learn it : 6-3 = 2 15-3 = 5 24 -3= 8 9-3 = 3 18-3 = 6 27 -3= 9 12 -3 = 4 21 -3 = 7 30 -3 = 10 Copy and complete the following : 2. 9- =3. 5. 6^ =3. 8. 12-2 = 3. 12 - = 6. 6. 6 - = 2. 9. 12 - 3 = 4. 12- =4. 7. 8-4-2= 10. 21- =7. TABLE OF FOURS 79 ORAL EXERCISE 1. Add the columns of 4's, from otie 4 to five 4's. 2. On the blackboard and on paper, build more columns of 4's, until you have ten 4's in the last column. Then read the columns, thus: "One 4 is 4, two 4's are 8," and so on. 3. Read and learn the table of 4's : 2x4= 8 5x4 = 20 3x4 = 12 6x4 = 24 4x4 = 16 7x4 = 28 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 8 x 4 = 32 9x4 = 36 10 x 4 = 40 4. How much is 1x4? 4x1? 4x0? 0x4? 5. How much is 4 + 4 + 4 + 4 + 4? 5x4? 6. State these products : 4x3 4x8 4x9 4x7 4x5 4x6 4x2 4x10 WRITTEN EXERCISE 1. There are 4 quarts in 1 gallon. How many quarts are there in 5 gallons ? in 7 gallons ? in 9 gallons ? 2. A square has 4 sides. How many sides have 8 squares ? 3. A cow has 4 feet. How many feet have 2 cows? 7 cows ? 6 cows ? 8 cows ? 10 cows ? 4. If a man can earn $4 a day, how many dollars can he earn in 9 da.? in 7 da.? in 8 da.? 80 MULTIPLICATION AND DIVISION TABLES ORAL EXERCISE 1. How many dots are there in each of these squares? How many squares are there in the upper row? How many dots are- there in the squares of the upper row? 2. How many dots are there in the squares of the lower row? How can you find this without adding all the dots in the squares of this row? 3. How many squares are there in all? How can you find the number of dots without adding ? How many dots are there in all ? State the answers to the following : 4. 5 x 4 + 1. 7. 8 x 4 + 3. 10. 3 x 4 + 2. 5. 7 x 4 + 3. 8. 9 x 4 + 2. 11. 2 x 4 + 1. 6. 6 x 4 + 2. 9. 4 x 4 + 3. 12. 8 x 4 + 2. WRITTEN EXERCISE 1. There are 4 stalks of corn in a hill. How many stalks are there in 7 such hills? 2. If there are 4 apples in each of 9 groups, how many apples are there in all the groups ? 3. How many shoes does it take to shoe 3 horses? to shoe 5 horses ? to shoe both 3 horses and 5 horses ? 4. One man has 3 horses to be shod, and another man has 4 horses to be shod. How many shoes are needed for all the horses? TABLE OF FOUES 81 ORAL EXERCISE 1. How many times does 8 contain 4? 2. How many 4's do you see in 12 ? in 20 ? in 16 ? in 4 ? 3. How many times does 16$ con- tain 4 $ ? 20 $ contain 4 < ? 4. State the values of : 2x4 7x4 9x4 4x2 4x7 4x9 8-4 28-4 36-4 8-2 28-7 36-9 4 4 4 4 8 4 4 4 12 4 4 4 4 16 4 4 4 4 4 20 5. If four boys have equal scores in a game and the total score is 12, what is each score? 6. Read and learn this table : 8-4 = 2 20-4 = 5 32 -4= 8 12-4 = 3 24-4 = 6 36 -4= 9 16 -4 = 4 28 -4 = 7 40 - 4 = 10 WRITTEN EXERCISE 1. In 1 gallon there are 4 qt. How many gallons are therein 28 qt.? in 36 qt.? 2. If 24 boys are marching, 4 in a line, how many lines of boys are there ? Copy and complete : 3. 24 - 4 = 16 - = 4 40 - 4 = 4. 32-4= 28- =7 36-4 = 82 MULTIPLICATION AND DIVISION TABLES 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ORAL EXERCISE 1. Add the columns of 5's, from one 5 to five 5's. 2. On the blackboard and on paper build more columns of 5's until you have ten 5's in the last column. Then read the columns, thus: "One 5 is 5, two 5's are 10," and so on. 3. Read and learn the table of 5's : 2x5 = 10 5x5 = 25 8x5 = 40 3x5 = 15 6x5 = 30 9x5 = 45 4x5 = 20 7x5 = 35 10x5 = 50 4. How much is 1x5? 5x1? 5x0? 0x5? 5x5? 5. State these products : 5x3 5x9 5x6 5x4 5x7 5x2 5x8 5x10 WRITTEN EXERCISE 1. If we go to school 5 days a week for 3 weeks, how many days are we in school ? 2. If it costs 5$ to telephone, and a man telephones 9 times, how much does it cost him? 3. If a class marches in rows of 5, and there are 7 rows, how many pupils are there in the class ? Copy and complete the folloiving : 4. 4x5 + 2= 6x5 + 3= 8x5 + 7 = 5.9x5 + 7= 5x5 + 4= 3x5 + 2 = TABLE OF FIVES 83 ORAL EXERCISE 1. How many 5's are there in 5 ? in 10 ? in 15 ? in 20 ? in 30 ? in 45 ? in 35 ? in 50 ? 2. State rapidly the results : 40-5 30-5 15-5 35-5 3. Read and learn this table : 10-5 = 2 25-5 = 5 40 -5= 8 15-5 = 3 30-5 = 6 45 -5= 9 20 -5 = 4 35 -5 = 7 50 ^-5 = 10 4. At 50 each, how many oranges can you buy for 200? for 40^? for 250? for 500? 5. At $5 a day, how many days must a man work in order to earn $30 ? WRITTEN EXERCISE Copy and complete the following : 1. 35- = 7 -5 = 4 15-*- 5 = 2. 45 - =9 -5 = 9 40-5 = 3. How many 5-yard lengths can be made from 45 yd. of cloth ? from 35 yd. ? from 25 yd. ? 4. At 50 each, how many oranges can you buy for 350? for 450? for 150? 5. At 50 each, how many bottles of mucilage can you buy for 400? for 500? for 200? 6. If it is 15 ft. around a flower bed, and each side is 5 ft. long, how many sides are there ? 84 MULTIPLICATION AND DIVISION TABLES ORAL REVIEW 1. There are 2 boys standing by each of 6 desks. How many boys are standing ? 2. There are 2 girls standing by each of 8 desks. How many girls are standing? 3. There are 2 pt. in a quart. How many pints are there in 9 qt.? How many pints are there in 10 qt.? 4. How many bananas at 2$ each can you buy for 16$? How many bananas can you buy for 18$? 5. At 4$ each, how many oranges can you buy for 12$? How many oranges can you buy for 32$? 6. If you have 20$, how many oranges can you buy at 3$ each, and how much money will you have left? WRITTEN REVIEW 1. If our class has 24 pupils in it, and they march in 4 lines, how many pupils will there be in each line ? 2. If there are 27 boys in school, how many baseball nines can be formed ? 3. If you buy a two-cent stamp, 3 one-cent stamps, and a one-cent postal card, how much will they all cost ? 4. If Mr. Wood earns $3 a day, how much will he earn in 9 days ? 5. If Mr. Wood earns $3 a day, how many days must he work to earn $24 ? 6. If Mr. Wood has $19 and earns $9 more, how much money does he have then ? MULTIPLICATION 85 V. MULTIPLICATION ORAL EXERCISE Multiply rapidly : 1. 2 3 4 5 4 2 3 5 2 3 2 4 5 2 3 3 9 3 9 5 2. 4 2 5 4 2 4 3 1 2 4 2 5 4 4 6 6 8 5 7 8 How to Multiply. If you have 23 marbles and John has three times as many, how many marbles has John ? To multiply 23 by 3 we see that 3x3 ones = 9 ones, and we write the 9 below the line, in the ones' column. Then 3x2 tens = 6 tens, and we write the 6 below the line, in the tens' column. The result is 69, so John has 69 marbles. o 23 is called the multiplicand 3 is called the multiplier 69 is called the product WRITTEN EXERCISE Multiply the following : 69 1. 13 41 42 23 24 32 322 2 2 2 2 2 2 2 2. 21 31 22 11 14 23 231 3 3 4 4 2 3 3 86 MULTIPLICATION ORAL EXERCISE 1. Count by 2's from 2 to 20. 2. Recite the multiplication table of 2's. 3. Count by 3's from 3 to 30. 4. Recite the multiplication table of 3's. 5. Recite the multiplication table of 4's. Find the following products : 6. 7. 8. 9. 10. 11. 21 51 63 52 41 63 222343 12. 72 4 14. Each side of a triangular park is 54 ft. long. How far is it around the park ? Look at this multiplication and tell what is the product of the ones. Tell what is the product of the tens. Tell what is the whole product. 15. In Ex. 14, what way do you see of mak- ing the work shorter ? 13. 81 5 54 _3 12 15 162 Further Multiplication. If there are 48 apple trees in each of 4 rows, how many trees are there in all? The short way of multiplying, and the one which we should always use, is shown here. We see that 4x8 ones are 32 ones. Write the 2 in the ones' place and add the 3 tens to the 4x4 tens, making 19 tens. The product is 192, so there are 192 trees. ONE-FIGUEE MULTIPLIER 87 ORAL EXERCISE 1. At 8$ a quart, what will 4 qt. of milk cost? 2. How much is 2 x 80? 3 x 80? 4 x 80? 3. At 90 each, what will 3 tablets cost? 4. At 1 7 each, what will 4 desks cost? Multiply the following: 2 8 9 2 7 9 3 4 5. 9 8 4 1 7 3 4 7 3 3 4 6. 3 6 1 8 4 7 4 9 9 3 4 WRITTEN EXERCISE Multiply the following : 1. 53 12 44 79 33 Jt _5 _7 2 8 2. 48 64 13 57 80 _4 _4 _5 3 4 3. 34 55 75 24 68 _3 _4 _2 1 4 4. 67 42 44 86 34 _2 jr _8 _3 _9 5. 89 78 56 31 97 3 2 3 6 4 22 222 3 3 12 4 32 322 __5 _3 21 211 _4 _4 63 231 4 4 88 MULTIPLICATION ORAL DRILL TEST. ADDITION Add rapidly : 1. 12 13 14 15 17 18 5 4 _5 _6 3 J7 2. 23 24 25 26 27 28 4 5 7 _5 _7 9 3. 32 33 34 45 56 67 _6 2 7 8 7 _9 4. 10 20 30 51 63 75 6 7 8 7 8 5 3 4 4 2 2 _9 ORAL DRILL TEST. SUBTRACTION Subtract rapidly 1. 18 17 15 25 25 35 5 7 8 8 18 18 2. 19 29 44 53 53 73 _4 14 14 4 14 14 3. 11 31 31 31 51 70 5 _5 15 25 25 20 4. 17 37 57 52 51 61 12 12 22 22 22 22 19 _8 29 _6 88 _7 82 8 9 75 18 93 24 70 25 71 23 DEILL TESTS 89 ORAL DRILL TEST. MULTIPLICATION Multiply rapidly : 1 .2x2 . 8. 3x2. 15. 3x 6. 22. 4x9. 2 .2x6 . ' 9. 3x8. 16. 4x 5. 23. 5x2. 3 .2x7 10. 3x3. 17. 3x 7. 24. 6x5. 4 .2x9 . 11. 4x6. 18. 4x 8. 25. 5x3. 5 .2x8 . , 12. 4x7. 19. 3x 5. 26. 5x4. 6 .2x5 . 13. 4x4. 20. 5x 5. 27. 8x5. 7 . 2 x 10. 14. 3x10. 21. 4x 10. 28. 5x10. State rapidly the answers : 29. 8x2 + 1. 33. 5 x3 + 2. 37. 6 x4 + 3. 30. 7x3 + 1. 34. 4 x3 + 1. 38. 8 x5 + 4. 31. 9x2 + 1. 35: 6 x2 + 1. 39. 9 x4 + 2. 32. 6x3 + 2. 36. 7 x 5 + 4. 40. 7 x5 + 3. ORAL DRILL TEST. DIVISION Divide rapidly : 1 . 8-2 . 9. 9-3 . 17 . 12 -4. 25. 25 -5. 2 . 6-3 . 10. 30- 3. 18 . 30 -5. 26. 36 -4. 3 . 6-2 . 11. 27- 3. 19 . 16 -4. 27. 40 -5. 4 . 16- 2. 12. 18- 3. 20 . 10 -5. 28. 50 -5. 5 . 20- 2. 13. 24- 3. 21 . 20 -4. 29. 32 -4. 6 . 18- 2. 14. 15- 3. 22 . 35 H-5. 30. 45 -5. 7 . 12 H- 2. 15. 21- 3. 23 . 15 -5. 31. 20 -5. 8 , 10- 2. 16. 12- 3. 24 . 24 -4. 32. 28 -4. 90 USING WHAT YOU HAVE LEAENED VI. USING WHAT YOU HAVE LEAENED NUMBERS USED IN PLAY 1. If each, of these three boys has 17 marbles, how many marbles have they in all ? 2. If each of the three boys should buy 12 more marbles, how many more marbles would they all have ? 3. If each of the three boys has 34 marbles, how many marbles do they all have ? 4. If you are playing. a game, and Fred's score is 29 and your score is twice as many, what is your score ? 5^ In a football game Jack's team scored 14 points and Rob's team scored this number multiplied by 3. How many points did Rob's team score? 6. Mr. Wilson's golf score was 88 and Mr. Brown's was 9 more. How much was Mr. Brown's score ? PROBLEMS 91 DRESSING THE DOLLS 1. Mollie has two dolls. One cost 35$ and the other cost 50$. How much did both cost? 2. Mollie bought 2 yd. of cloth at 25$ a yard to make dresses for her dolls. How much did the cloth cost ? 3. Mollie bought 3 yd. of lace for the dresses. The lace cost 12$ a yard. How much did the lace cost in all? 4. A doll's necklace was made by stringing beads. There were 8 beads to an inch. How many beads were there in 5 in. ? How many were there in 2 in. ? How many were there in \ in. ? 5. Mollie uses \ yd. of ribbon for sashes for her dolls. The ribbon costs 16$ a yard. How much must she pay for the \ yd. ? How do you find \ of 16 ? 6. Mollie uses \ yd. of ribbon on a doll's waist. If 1 yd. costs 16$, how much must she pay for the \ yd. ? 7. For one of her dolls Mollie buys a pair of shoes for 20$, a pair of stockings for 5$, a skirt for 15$, and a hat for 25$. How much does she pay for all? 8. Mollie buys 4 strings of beads for trimming. There are 48 beads on each string. How many beads has she ? 9. Mollie sees some strings of beads that the store- keeper says have 5 dozen beads on a string. How many beads are 5 dozen beads ? 10. Make a list of things for two dresses for a doll, and tell how much you think they would cost. This page may be used for the girls, and page 92 for the boys. 92 USING WHAT YOU HAVE LEAKNED PROBLEMS ABOUT GAMES 1. Ralph buys a baseball mitt for 50$ and a bat for 30$. How much does he pay for both ? 2. It is 90 ft. from the home base to first base, and 90 ft. from first base to second. How far does Ralph run in going from home base to first base and then to second base ? 3. How far does Ralph run in making a home run? 4. At one ball game in the school grounds there were 275 tickets sold, and at another 336 tickets. How many were sold for the two games ? 5. The girls played bean-bag. Jennie's score was 15, 20, 18, 34. What was her total score? 6. The boys played ring toss. Jack's score was 12, 18, 9, 17, 24. What was his total score? 7. Fred has a baseball mitt worth 75$ and John has a bat worth 30$. If they trade fairly, how much money should John give Fred in addition to the bat ? 8. If a top costs 6$, marbles 5$ a dozen, and a ball 25$, how much will a top, a ball, and a dozen marbles cost ? 9. How much must I pay for 24 marbles at 5$ a dozen ? 10. Cut nine squares of paper each small enough to fit in one of these little squares. On them write the nine figures 1, 2, 3, and so on to 9. Then see if you can put them in these squares so that the sum of any three numbers in the same row, in the same column, or in the same diagonal shall be 15. DIVISION 93 VII. DIVISION ORAL EXERCISE 1. How do you find half of 4 ? half of 8 ? half of 12 ? 2. If you wish to find one fourth of 8, how do you do it ? 3. If Mary has 24< in her bank and spends one fourth of it, how much money does she spend ? 4. If Mary wishes to buy \ of a yard of cloth that costs 16$ a yard, how much money must she spend? 5. Mary buys 20 buttons and uses one fourth of them. How many does she use ? How do you find out ? 6. If Mary has 24 hooks and eyes and uses one fourth of them, how many hooks and eyes does she use? 7. Mary bought 18 buttons and used half of them. How many buttons had she left? (j\ 8. If Mary has 28 in. of ribbon and cuts it into pieces that are 7 in. long, how many pieces will she have ? How do you find this number ? 9. If Mary should have 84 in. of ribbon and should cut it into pieces that are 7 in. long, how would you find the number of pieces ? Can you find it without pencil and paper ? Can you see how to find it with the help of pencil and paper ? Teachers will at once see that this exercise is intended to lead up to the necessity for knowing more about division. Ex. 9 should lead the pupil to see that he must now learn something new. If any pupils can work the example already, the teacher should make one that they cannot work. In this way they will feel the necessity for further study of division. 94 DIVISION How to Divide. John has 48 marbles and Robert has 'one fourth as many. How many marbles has Robert? We see that we must divide 48 by 4. To divide 48 by 4 we write the numbers as here shown. Then 4 tens -*- 4 = 1 ten, and we write the 1 in the tens' place. Then 8 ones -H 4 = 2 ones, and we write the 2 in the ones' place. The quotient is 12, and so Robert has 12 marbles. We check our work by multiplying the quotient by the divisor. If the product equals the dividend, the work is correct. Here 4 x 12 = 48. WRITTEN EXERCISE 1. Divide by 2 ; that is, find \ of : 24 28 42 48 66 82 84 844 2. Divide by 3 ; that is, find \ of : 33 36 60 69 39 96 66 666 3. Divide by 4 ; that is, find \ of : 44 40 80 88 84 24 48 444 4. Divide 63 by 3. Make a problem about 63 -*- 3. 5. There are 88 apple trees in 4 equal rows. How many apple trees are there in each row ? 6. At 3$ each, how many pencils can you buy with 36$ ? with 63 -**?-*} they used 2 snowballs in each row. How many snowballs did they use on each side? How many did they use on both sides? How many did they use for the whole fort? 18. For the snow fight Frank made 4 doz. snowballs, and his cousin made 3 doz. How many snowballs did each make? How many did they make together? 19. Frank coasted on his sled 428 ft., and his cousin coasted 35 ft. farther. How far did his cousin coast ? 20. Frank spent 5 min. in fixing his skates, and skated 25 min. Then he stopped 6 min. to fix his skates again. He skated 18 min. more and then went home. How many minutes was he skating and fixing his skates ? Omit Exs. 16-20 if the subjects are not familiar to the pupils. 21. Frank's father drove to town on Monday with 16 bushels of potatoes. On Tuesday he drove in with 18 bushels, and on Wednesday with 14 bushels. How many bushels did he take to town on these three days ? 22. Frank lives 4 miles from town. How many miles does his father drive in going to town and back? How many miles did he drive in the three days? State the following products : 1. 4 x 5. 6. 3 x 3. 11. 9x5. 16. 9 x 4. 2. 7 x 3. 7. 5 x 4. 12. 4x3. 17. 8 x 5. 3. 8 x 2. 8. 6 x 5. 13. 6x2. 18. 3 x 2. 4. 6 x 4. 9. 7 x 2. 14. 3x4. 19. 7 x 5. 5. 5x5. 10. 9x2. 15. 8 x 4. 20. 8x3. State the results of the following : 21. 6 x 3 + 2. 24. 5 x 2 + 1. 27. 3 x 4 + 1. 22. 9 x 2 + 1. 25. 2 x 5 + 1. 28. 4 x 4 + 3. 23. 3 x 5 + 2. 26. 8 x 3 + 2. 29. 9 x 5 + 4. The results of these 29 examples should be stated in 2 minutes or less. ORAL TIME TEST IN DIVISION State the following quotients : 1. 9-3. 10. 4-4. 19. 3 - 3. 28. 6-3. 2. 5-5. 11. 4-2. 20. 6 - 2. 29. 2-2. 3. 6-1. 12. 16-4. 21. 21-3. 30. 8-4. 4. 18 - 3. 13. 35 - 5. 22. 16 - 2. 31. 18 - 2. 5. 20-2. 14. 24-3. 23. 30-5. 32. 20-4. 6. 50-5. 15. 32-4. 24. 24-4. 33. 28-4. 7. 45-5. 16. 20 - 5. 25. 25 - 5. 34. 10 - 1. 8. 36-4. 17. 15-3. 26. 10-5. 35. 12-4. 9. 27-3. 18. 12-3. 27. 30-3. 36. 10-2. The results of these 36 examples should be stated in 1^ minutes or less. EP 108 LITTLE EXAMINATIONS XI. LITTLE EXAMINATIONS I. 1. 9 + 37. 5. 28- -4. 9. a of 636. 2. 50-4. 6. 3x 42. 10. 4 of 364. 3. XI = (?) 7. 7x 32. 11. 5 qt. = (?)pt. 4. 5x 4 + 2. 8. 56-4 -4. 12. 8 pt. , = (?)qt. II. 1. 7 + 45. 5. 24-* -3. 9. 2 of 36. 2. 45-7. 6. 24 -* -4. 10. 1 S of 36. 3. IX = (?) 7. 3x 24. 11. 4 of 360. 4. 7x 3 + 6. 8. 8x 24. 12. 3 ft. = (?)in. III. 1. 8 + 56. 5. 36-4. 9. i 2 of 72. 2. 56- -8. 6. 30-3. 10. 3" of 72. 3. VII .!=(?). 7. 4x 36. 11. 1 of 72. 4. 5x 2 + 4. 8. 4x 63. 12. 2 yd .-Oft IV. 1. 6 + 49. 5. 32-4. 9. "5" of 32. 2. 52-7. 6. 27-3. 10. of 312. 3. VII :=(?). 7. 4x 32. 11. 1 4 of 324. 4. 9x 4 + 7. 8. 8x 32. 12. 6 ft. = ( ? )yd. V. 1. 7 + 58. 5. 240 -4. 9. of 124. 2. 57-8. 6. 240 -2. 10. i of 124. 3. 2x 57. 7. 240 -3. 11. f of 123. 4. 3x 57. 8. 2x 240. 12. 1 yd . = (?) in. These Little Examinations at the close of each chapter furnish excel- lent review drill work. The time should be recorded for each, and the /pupils should endeavor to improve their records. CHAPTER HI I. BEADING AND WRITING NUMBERS 2000 + 300 + 40 + 2 ORAL EXERCISE 1. Ten 100's make one thousand, 1000. Count by 1000's from 1000 to 10,000. 2. How many splints are there in the picture? Write the number on the blackboard. 3. We read 2000 thus: "Two thousand." How do we read 3000? 4. We read 2200 thus : " Two thousand two hundred," or " twenty-two hundred." How do we read 3200 ? How do we read 4800 ? 5. We read 2004 thus: "Two thousand four." How do we read 3007? 3047? 3147? 5247? 6. Read the following numbers : 27 270 2700 271 2710 2713 35 350 3500 356 3560 3567 109 110 BEADING AND WKITING NUMBEES ORAL EXERCISE Read the following numbers : 1. 1000. 11. 3000. 21. 5000. 31. 7000. 2. 1200. 12. 3600. 22. 5005. 32. 7500. 3. 1230. 13. 3670. 23. 5050. 33. 7596. 4. 1235. 14. 3678. 24. 5055. 34. 8596. 5. 1435. 15. 3996. 25. 6000. 35. 8798. . 2000. 16. 4000. 26. 6600. 36. 9256. 7. 2400. 17. 4040. 27. 6606. 37. 9398. 8. 2460. 18. 4004. 28. 6666. 38. 9872. 9. 2465. 19. 4044. 29. 6756. 39. 9981. 10. 2578. 20. 4444. 30. 6897. 40. 9999. WRITTEN EXERCISE Write in figures : 1. One hundred one ; two hundred seven. 2. One thousand one ; five thousand four. 3. Two thousand one hundred one. 4. Three thousand two hundred seven. 5. Three thousand four hundred seventeen. 6. Four thousand seven hundred sixty-five. 7. Five thousand five hundred fifty-five. 8. Six thousand eight hundred nineteen. 9. Seven thousand eight hundred ninety. 10. Nine thousand nine hundred ninety-nine. 11. Three thousand three hundred thirty-three. ROMAN NUMERALS 111 ORAL EXERCISE 1. Read these numbers, which are found on the clock face : III IX XII I VII IY XI V X VI 2. Tell the time when the minute hand points to XII and the hour hand points to IX ; to XI ; to II ; to X ; to XII; to IIII; to I; to VI ; to VII. Use of Roman Numerals. The Roman numerals are often used for numbering the chapters of books. 1 to 5: I II III IV V 6 to 10: VI VII VIII IX X 11 to 15: XI XII XIII XIV XV 16 to 20: XVI XVII XVIII XIX XX 3. When you come to Chapter XIV in a book, how many chapters have you read ? 4. "When you have read Chapter IX of a book and the last chapter is XV, how many chapters have you to read ? WRITTEN EXERCISE 1. Write in Roman numerals : 15 8 11 17 13 9 5 10 14 2. Write in our ordinary numerals : XI IX XIX XIV XVII VII XVIII 3. Write the number of years of your age, both in ordi- nary numerals and in Roman numerals. 112 BEADING AND WRITING NUMBERS ORAL EXERCISE 1. These children are playing store. Jack buys 200 worth of candy and gives a quarter of a dollar. How much change is due ? 2. Fanny buys 10 < worth of bananas at 2 for a nickel. She buys how many bananas ? 3. The dealer says that oranges are sold at 3 for a dime. How much will half a dozen oranges cost ? 4. At 40 each, how much will 3 oranges cost Fanny? Writing Money. In writing dollars and cents we write $2.50 for 2 dollars and 50 cents, $15.05 for 15 dollars and 5 cents, and $0.75, $.75, or 750 for 75 cents. Write first the dollar sign ($), then the number of dollars, then a period (decimal point], and then the number of cents. Both $0.75 and $.75 are correct forms for 75 cents. When written by itself, $0.75 is the safer, for the decimal point in $.75 is easily overlooked ; but when written in a column, as in addition, there is no need for the 0. The teacher should also allow such forms as 75 ct. and 75 c. instead of 75 , because they are in common use and the pupils should know them. The pupils should be told that in addition and subtraction the dollar sign ($) is written only before the top number and before the result. 9. $19.05. 17. $231.00. 25. $219.36, 10. $21.00. 18. $217.81. 26. $246.95, 11. $32.01. 19. $329.75. 27. $318.86, 12. $75.56. 20. $831.08. 28. $981.99, 13. $65.00. 21. $106.75. 29. $152.50, 14. $46.73. 22. $415.50. 30. $524.25 15. $36.75. 23. $142.80. 31. $157.90 16. $40.02. 24. $300.75. 32. $423.86 UNITED STATES MONEY ORAL EXERCISE Read the following : 1. $1.25. 2. $2.07. 3. $3.00. 4. $5.75. 5. $4.00. 6. $5.65. 7. $5.50. 8. $7.00. WRITTEN EXERCISE Write in figures, with the proper signs for money : 1. 4 dollars 1 dollar and 75 cents 2. 16 dollars 3 dollars and 3 cents 3. 14 dollars 7 dollars and 25 cents 4. 18 dollars 16 dollars and 80 cents 5. 230 dollars 175 dollars and 75 cents 6. 100 dollars 248 dollars and 49 cents 7. 184 dollars 250 dollars and 49 cents 8. 200 dollars 500 dollars and 50 cents 9. 300 dollars 750 dollars and 85 cents 10. 400 dollars 286 dollars and 98 cents 11. Seven hundred sixty-eight dollars. 12. One hundred fifty dollars and ten cents. 13. Two hundred seventy-five dollars and ten cents. 114 ADDITION II. ADDITION Adding Long Columns. In adding long columns we may write the sum of each column separately. Business men often do this. We may add up the first time, and check the result by adding down. When you look at two figures, always think of the sum of the two numbers. Instead of saying " 3 and 4 are 7," simply look at 3 and 4 and think "7." When you look at the ones' column you should see the two 10's (3 + 5 + 2, and 7 + 3) at once, and you should see that the sum is two 10's and 6, or 26. Add rapidly; if you do so, you will usually make fewer mistakes. Uniting two or more numbers, called addends, so as to make a single number is called addition. The teacher should explain that the sign $, written before the first addend in a column, applies to all addends in the column. 76 83 67 92 55 43 26 39 416 sum WRITTEN EXERCISE Add the following : 1. 2. 3. 4. 5. 6. 7. 42 52 29 52 48 $39 $24 28 33 71 73 78 27 36 41 48 36 81 32 53 42 79 48 64 64 52 66 33 16 67 82 75 26 53 25 ADDING LONG COLUMNS 115 ORAL EXERCISE Add from the bottom to the top, group when possible, and check the work by adding from the top to the bottom : 1. 2. 3. 4. 5. 6. 7. 8. 9. 2 2 8 8 8 2 8 3 2 4 3 7 3 2 3 3 8 4 6 7 3 8 5 4 6 2 8 5 6 4 2 5 7 9 6 3 7 5 9 9 7 6 8 9 9 9 8 6 3 3 2 7 8 6 These are types of problems to be written on the board for rapid drill work. WRITTEN EXERCISE Add, checking the work as stated above : 1. 2. 3. 4. 5. 23 89 37 85 81 48 64 40 23 72 72 73 29 40 35 69 29 82 27 86 43 82 76 82 92 6. 7. 8. 9. 10. 128 834 823 828 348 932 281 204 926 492 486 342 896 349 687 529 907 480 877 402 348 602 320 492 374 726 270 981 681 200 116 ADDITION WRITTEN EXERCISE 1. George works after school for Mr. Forbes, the grocer. Mr. Forbes set him at work sorting oranges. George found 196 good oranges in one box and 188 in another box. How many good oranges did he find in both boxes ? 2. Mr. Forbes had George take the cans of fruit from the shelves so as to count them. He counted 97 cans of peaches, 86 cans of pears, and 47 cans of plums. How many cans were there of all three kinds? 3. George arranged some cakes of soap on the shelves. There were 127 cakes of one kind, 246 of another, and 144 of another. How many cakes of soap were there ? 4. George polished the eating apples so that they would sell better. He polished 98 apples of one kind, 139 of another, and 74 of another. How many apples did he polish? 5. Mr. Forbes paid George 15$ on Monday, 15 $ on Tues- day, 18$ on Wednesday, 20$ on Thursday, 15< on Friday, and 25< on Saturday. How many cents did he pay him that week ? 6. Mr. Forbes put $25 in the bank on Monday, $35 on Tuesday, $30 on "Wednesday, $36 on Thursday, $45 on Friday, and $48 on Saturday. How much money did he put in the bank that week ? 7. Mr. Forbes spent $35 one day and $18 another day. How much money did he spend altogether ? 8. If Mr. Forbes had $250 in the bank, and then put in $75 more, and then drew out $25, how much money was left in the bank ? COLUMN ADDITION 117 WRITTEN EXERCISE Add, timing yourself: 1. 2. 3. 4. 5. $217 246 276 329 $437 343 434 427 286 293 6. 7. 8. 9. 10. $127 142 326 463 $123 246 237 293 298 247 329 421 147 127 409 11. 12. 13. 14. 15. 106 213 106 132 222 287 129 219 167 333 109 308 137 207 111 16. 17. 18. 19. 20. 121 106 217 272 319 42 92 102 129 107 37 37 69 106 28 168 15 72 43 63 21. 22. 23. 24. 25. $136 $127 $147 $192 $400 42 38 29 37 125 81 25 108 91 30 92 172 32 82 19 237 81 129 263 16 148 69 70 109 128 118 ADDITION Addition of Money. Ruth put $2.70 in her bank in one month, $3.65 the next month, and $0.38 the first week of the following month. How much did she put in the bank in all ? We see that we must add $2.70, $3.65, and $0.38. We first write the numbers so that the dec- imal points are under one another. Then 8 cents + 5 cents = 13 cents = 1 dime + 3 cents. We write the 3 in the cents' column and add the 1 to the dimes. Then 1 dime + 3 dimes + 6 dimes + 7 dimes = 17 dimes = $1 + 7 dimes. We write the 7 in the dimes' column and add the 1 to the dollars. Then $1 + $3 + $2 = $6. We write the 6 in the dollars' column and put the decimal point under the decimal points. The sum is $6.73, so Ruth has put $6.73 in her bank. WRITTEN EXERCISE Add the following, and check the work : I. 2. 3. 4. 5. $4.83 $4.89 $5.90 $5.96 $8.92 5.64 5.66 2.75 2.78 5.78 9. ?9.22 .76 2.60 COLUMN ADDITION 119 WRITTEN EXERCISE 1. Robert helps in a grocery after school, and the grocer sometimes sets him at work to add the bills. Mrs. James has bought groceries costing $1.30, $1.20, $0.65, and $0.96. Robert adds these amounts. What is their sum ? 2. Robert finds that Mrs. Monroe has bought groceries costing $2,25, $1.60, $0.75, $1.32, $0.65, and $1.18. How much does she owe? The grocer gives Robert bills with the following items to add. Find the sum of each : 3. $1.42 .36 .48 .27 3.62 5. ^2.19 3.16 .42 3.27 1.68 6. 51.44 3.00 1.36 .42 1.07 7. $3.20 1.40 .39 1.86 .42 Robert finds that the bills are usually ruled, so that he does not have to write the dollar sign or the decimal point. He finds that the columns look like this. Add each bill: 8. 9. 10. 11. 12. 2 10 3 15 42 1 00 32 1 06 3 00 3 68 48 72 68 49 1 06 39 71 76 73 87 96 98 38 46 98 96 43 120 SUBTRACTION III. SUBTRACTION WRITTEN EXERCISE Subtract, timing yourself and checking the work : 1. 2. 3. 4. 5. 6. 236 342 409 527 400 326 129 273 263 329 192 178 7. 8. 9. 10. 11. 12. 409 600 725 908 752 360 237 482 536 809 429 290 13. 14. 15. 16. 17. 18. 728 342 801 712 801 902 299 139 236 348 296 327 19. 20. 21. 22. 23. 24. 711 628 $426 $304 $322 $209 344 439 278 265 148 168 25. 26. 27. 28. 29. 30. $387 $400 $925 $305 $492 $286 296 275 560 197 137 192 31. 32. 33. 34. 35. 36. $840 $927 $209 $325 $430 $535 726 109 110 186 345 287 37. 38. 39. 40. 41. 42. $415 $523 $816 $927 $862 $900 236 475 536 349 468 521 MAKING CHANGE 121 Making Change. If you owe the grocer 35$ and give him a 50-cent piece, he makes change by finding the amount which, added to 35$, makes 50$. He does this by saying, "35 and 5 are 40, and 10 are 50," taking up 5$ and 10$ as he says this. He then gives you 15$. If the school is provided with toy money it should be used at this time. The drill is valuable without this, however, for this is exactly the kind of work that we have to do mentally when we make purchases. ORAL EXERCISE 1. Make change for 50$, when you owe: 25$ 30$ 40$ 45$ 29$ 31$ 2. Make change for 25$, when you owe : 20$ 22$ 18$ 15$ 9$ 19$ 3. Make change for 75$, when you owe : 72$ 62$ 58$ 69$ 57$ 67$ 4. Make change for $1, when you owe : 95$ 85$ 68$ 52$ 36$ 91$ 75$ 80$ 55$ 65$ 20$ 25$ 5. Mary buys some ribbon for 18$ and gives the dealer 25$. How much change is due? 6. Rob buys a ball for 65$ and gives the dealer $1. How much change is due? 7. Harriet' buys some cloth for $1.20. She gives the dealer a 2-dollar bill. How much change is due? 122 SUBTRACTION Subtraction of Money. If Mr. Brown has $247.50 and spends $176.75 of it for some cattle, how much money has he left? We see that we must subtract $176.75 from $247.50. We write the numbers as here shown. 10 5 = 5. We write the 5 under cents. 14 7 = 7. We write the 7 under the dimes. We now write the decimal point. 6 6 = 0. We write the under the .dollars. 14 7 = 7. We write the 7 under the tens of dollars. 1 1=0, so there are no hundreds of dollars. The result is $70.75, and so Mr. Brown has $70.75 left. In subtracting United States money, write the numbers so that the decimal points are in a column and subtract in the usual way. WRITTEN EXERCISE Subtract) and check the work : 1. 2. $72.41 $29.84 24.92 12.97 5. .01 20.09 9. $341.65 120.40 10. $341.65 170.40 7. $90.08 25.19 11. $341.65 170.46 4. $60.70 55.81 8. $52.86 23.94 12. $341.65 173.46 UNITED STATES MONEY 123 ORAL EXERCISE Subtract the following : 1. $3.60 .10 2. $3.09 .04 9- $3.69 .14 4. $3.65 1.14 5. $5.75 2.14 6. $5.95 1.20 7. $4.65 1.10 8. $5.55 4.44 9. $8.75 .25 \ 10 ' $8.96 1.96 WRITTEN EXERCISE Subtract, check the work, and time yourself: 1. $76.29 75.37 2. $85.36 6.87 3. $76.29 62.89 4. $14.36 5.63 5. $70.24 10.65 6. $96.73 77.96 7. $88.41 79.52 8. $95.27 9.86 9. $33.42 9.29 10. $47.63 8.24 11. $26.96 17.27 12. $60.00 42.36 13. $21.40 17.52 14. $40.00 5.75 15. $90.00 36.27 16. $24.00 .78 17. $32.09 16.70 18. $41.32 28.75 19. $68.03 49.26 20. $75.00 .69 124 MULTIPLICATION AND DIVISION IV. MULTIPLICATION AND DIVISION ORAL EXERCISE 1. Minnie helps her mother make and care for the flower garden at their home. Minnie has planted some violets, 6 plants in each row. How many plants has she in 2 rows? 2. But Minnie has more than 2 rows of plants ; she has 4 rows. How do you find the number of plants in 4 rows ? How many plants are there ? 3. If Minnie sets out 2 more rows, she will have 6 rows in all. There are 6 plants in each row. How do you find the number of plants in all 6 rows ? 4. How much is 6 + 6 ? How much is 6 + 6 + 6 ? How much is 6 + 6 + 6 + 6? Which is easier, to add these, or to find the answers by multiplying ? 5. Howmuchis6 + 6? 12 + 6? 18 + 6? 24 + 6? Count by 6's from 6 to 30. 6. If Minnie sets out another row of violets, she will have 7 rows, and there will be 6 plants in each row. How do you find the number of plants in all? Is it easier to add 6+6 + 6 + 6 + 6 + 6 + 6, or to know without adding how many seven 6's are ? Do you know how much 7 x 6 is ? If you do not know, how can you find out ? The pupil is now about to begin the second half of the multiplication tables. By simple examples like those above he should be led to see the advantage of learning the tables. He should see that, although he could find his results by adding, it is much easier and quicker to use the mul- tiplication tables. TABLE OF SIXES 125 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ORAL EXERCISE 1. Add the columns of 6's, from one 6 to five 6's. 2. On the blackboard and on paper build more columns of 6's, until you have ten 6's in the last column. How many columns are there ? 3. Read the columns, thus: "One 6 is 6, two 6's are 12, three 6's are 18," and so on. 4. How many are five 6's ? six 6's ? seven 6's ? eight 6's ? nine 6's ? ten 6's ? 5. Read and learn this table of 6's, thus : " Two 6's are 12, " or " two times 6 are 12, " and so on: 2x6 = 12 5x6 = 30 8x6 = 48 3x6 = 18 6x6 = 36 9x6 = 54 4x6 = 24 7x6 = 42 10x6 = 60 6. How much is 1x6? 6x1? 6x0? 0x6? 7. How much is 6 + 6 + 6? 3x6? 8. How much is 6 + 6 + 6 + 6 + 6? 5x6? 9. State the values of the following : 2x6+1 3x6+2 5x6+1 3x6+1 4x6+3 5x6+2 10. State rapidly the following products : 6x1 6x8 6x4 6x3 6x5 6x7 6x2 6x9 1x6 8x6 4x6 9x6 5x6 7x6 2x6 0x6 126 MULTIPLICATION AND DIVISION One-Figure Multiplier. A dealer bought 6 automobiles. Including freight, they cost him $807 each. How much did they all cost? We see that they all cost 6 x $807. 6x7 ones = 42 ones = 4 tens + 2 ones. We write the 2 in the ones' place and add the 4 to the tens. 6x0 tens = tens ; but we have 4 tens already from the 42, so we write the 4 in the tens' place. 6x8 hundreds = 48 hundreds = 4 thousands + 8 hun- dreds. We write the 8 in the hundreds' place, and the 4 in the thousands' place. The product is 4842, and so the automobiles cost $4842. Teachers should note that the tables thus far learned are sufficient for any multiplication or any division in which either factor is less than 6. WRITTEN EXERCISE 1. How many " week days " are there in 31 weeks? 2. At 6$ a pound, how much will 21 Ib. of sugar cost? 3. At $6 apiece, how much will 30 lamps cost ? Multiply the following : 4. 5. 6. 7. 8. 9. 201 301 501 401 901 701 _6 _6 _6 _6 _6 _6 Copy and complete the following : 10. 5x6 + 3= 9x6 + 4= 6x6 + 4 = 11.7x6 + 6= 8x6 + 3= 3x6 + 2 = ONE-FIGURE MULTIPLIER 127 Multiplication Continued. We multiply 325 by 6 thus : 6x5 ones = 30 ones, or 3 tens and ones. We write the in the ones' place and add the 3 tens to the next product. 6x2 tens = 12 tens, and 12 tens + 3 tens = 15 tens, or 1 hundred and 5 tens. We write the 5 in the tens' place and add the 1 hundred to the next product. 6x3 hundreds = 18 hundreds, and we know that 18 hundreds + 1 hundred = 19 hundreds, or 1 thousand and 9 hundreds. We write the 9 in the hundreds' place and the 1 in the thousands' place. The product is 1950. WRITTEN EXERCISE Multiply the following : 1. 2. 3. 4. 5. 6. 120 125 234 325 425 275 2 2 2 2 2 2 7. 8. 9. 10. 11. 12. 320 321 325 343 446 453 3 3 3 3 3 3 13. 14. 15. 16. 17. 18. 206 216 265 236 326 525 4 5 6 7 8 9 19. 20. 21. 22. 23. 24. 406 461 416 466 566 728 5 5 5 7 8 3 128 MULTIPLICATION AND DIVISION ORAL EXERCISE 1. How many 6's are there in 6 ? in 12 ? in 18 ? in 42 ? 2. State rapidly the results : 54-6 30-6 48-6 36-6 3. Read and learn this table : 12-6 = 2 30-6 = 5 48 -6= 8 18-6 = 3 36-6 = 6 54 -6= 9 24 -6 = 4 42 -6 = 7 60 - 6 = 10 4. State rapidly the results : 5x6 7x6 54-6 3x6 6x5 6x7 54-9 18-6 30-6 42-6 48-6 6x6 30-5 42-7 8x6 36-6 WRITTEN EXERCISE 1. At 6$ a pound, how many pounds of sugar can you buy for 480? for 540? for 600? 2. At 6$ a box, how many boxes of crackers can you buy for 540? for 360? for 420? 3. At 60 a yard, how many yards of cloth can you buy for 240? for 300? for 660? 4. If the pupils of a class of 30 march in rows of 6, how many rows are there ? 5. Copy and complete : 36 - =6 -6 = 3 30-6 = DIVISION 129 Further Work in Division. We have already learned how to divide by a number of one figure, and we shall now consider the reasons more fully. For example, to divide 628 by 2 we write the numbers as here shown. We see that 6 hundreds 2 = 3 hundreds, and we write the 3 in the hundreds' place, below the dividend. Then 2 tens 2 = 1 ten, and we write the 1 in the tens' place, below the dividend. Then 8 ones 2 = 4 ones, and we write the 4 in the ones' place, below the dividend. The quotient is 314. WRITTEN EXERCISE Divide the following : 1. 648-2. 9. 846-2. 17. 468-2. 2. 639-3. 10. 693-3. 18. 936-3. 3. 444-4. 11. 448-4. 19. 840-4. 4. 884-4. 12. 848-4. 20. 888-8. 5. 555-5. 13. 550-5. 21. 505-5. 6. 666-6. 14. 660-6. 22. 868-2. 7. 600 - 6. 15. 500 - 5. 23. 777 - 7. 8. 448 - 2. 16. 336 - 3. 24. 999 - 9. 25. A man paid $360 for some lambs at $3 each. How many lambs did he buy ? 26. A dealer paid $408 for some coats at $4 each. How many coats did he buy ? 130 MULTIPLICATION AND DIVISION 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 ORAL EXERCISE 1. Add the columns of 7's, from one 7 to five 7's. 2. On the blackboard and on paper build more columns of 7's, until you have ten 7's in the last column. How many columns are there? 3. Read the columns, thus : " One 7 is 7, two 7's are 14," and so on. 4. How many are five 7's ? six 7's ? seven 7's ? eight 7's ? nine 7's ? ten 7's ? 5. Read and learn this table of 7's : 2x7 = 14 5x7=35 8x7=56 3x7=21 6x7=42 9x7=63 4x7=28 7x7=49 10x7=70 6. How much is 1x7? 7x1? 7x0? 0x7? 7. How much is 7 + 7 + 7 + 7 + 7 + 7? What short way is there of finding the answer ? 8. State rapidly the following products : 3x7 7x6 7x9 7x5 7x3 9x7 7x0 0x7 4x7 7x7 7x2 2x7 7x4 7x8 7x1 5x7 9. "What is the cost of 6 tables at $7 each ? 10. What is the cost of 7 desks at $3 each, and a teacher's desk at $7? 11. What is the cost of 9 yd. of calico at 7$ a yard ? of 2 yd. of trimming at 7$ a yard ? TABLE OF SEVENS 131 ORAL EXERCISE 1. Recite the table of 7's from 1 x 7 to 10 x 7. 2. At 7$ a yard, what will 8 yd. of ribbon cost? 3. At 70 a pound, what will 9 Ib. of sugar cost? State these products : 4. 4 x 7. 8. 8 x 7. 12. 6x7. 16. 2 x 7. 5. 9 x 7. 9. 7 x 7. 13. 7 x 1. 17. 1x7. 6. 7x3. 10. 3x7. 14. 5 x 7. 18. 0x7. 7. 7x2. 11. 7x5. 15. 10 x 7. 19. 7x4. State the answers : 20. 6 x 7 + 4. 23. 2 x 7 + 1. 26. 8 x 7 + 5. 21. 6 x 7 + 6. 24. 9 x 7 4- 5. 27. 9 x 7 + 2. 22. 4 x 7 + 3. 25. 5 x 7 + 2. 28. 7 x 7 + 3. WRITTEN EXERCISE Multiply the following : 1. 2. 3. 4. 5. 6. 101 102 112 132 335 227 7 7 7 7 7 7 7. 8. 9. 10. 11. 12. 200 204 224 324 368 362 7 7 7 7 7 7 13. 14. 15. 16. 17. 18. 400 409 419 439 489 777 7 7 7 7 7 9 132 MULTIPLICATION AND DIVISION ORAL EXERCISE 1. How many 7's are there in 7 + 7 4- 7 ? in 21 ? 2. How many 7's are there in 28 ? in 35 ? in 42 ? 3. State rapidly the results : 70-7 63-7 14-7 49-7 4. Read and learn this table : 14-7=2 35-7=5 56-7= 8 21-7=3 42-7=6 63-7= 9 28-7=4 49-7 = 7 70-7 = 10 5. State rapidly the results : 8x7 9x7 6x7 5x7 7x8 7x9 7x6 7x5 56-7 63-7 42-7 35-7 56-8 63-9 42-6 35-5 WRITTEN EXERCISE 1. There are 56 children marching in rows of 7. How many rows are there? 2. An open trolley car with 7 cross seats will seat 35 persons. How many persons can sit on each seat ? 3. Mary spent 42 < for 6 yards of calico. How much did she pay a yard ? 4. Kate spent 630 for 7 yards of ribbon. How much did she pay a yard ? 5. A dealer paid $42 for 7 tables. How much did he pay for each table ? DIVISION 133 Division Continued. A farmer bought 7 cows for $441. What was the average price per cow? We see that each cow cost $441 7. We see that 7 is not contained in 4, so we take 44 and divide it by 7. We know that 6 x 7 = 42, and so we see that 44 7 = 6, with a remainder of 2. Since we have divided 44 tens, we write the 6 in the tens' place. The remainder, 2, is tens ; so 2 tens + 1 = 21, and 21 7=3. We write the 3 in the ones' place. The quotient is 63, and so the average price was $63. Check. 1 x 63 = 441, the dividend. The teacher may ask the pupils to label the numbers in division, that is, to place the dollar sign before 441 and 63 ; but the business man would not do this in such a case. The fact that $6 -4- $2 = 3 and $6 + 2 = $3 makes the use of labels in division very difficult for children as early as this. It should be noticed that division by 8 and division by 9 are allowable on this page, provided the other factor in each separate division is 7 or less. WRITTEN EXERCISE 1. At $7 each, how many calves can a farmer buy with $364? with $371? with $378? with $714? 2. If there are 147 Boy Scouts marching in 7 equal squads, how many are there in each squad ? Divide the following , and check: 3. 651 -i- 7. 7. 726-6. 11. 725-5. 4.654-2. 8.567-7. 12.511-7. 5.648-4. 9.679-7. 13.456-8. 6. 635 - 5. 10. 434 - 7. 14. 909 - 9. 134 MULTIPLICATION AND DIVISION 8 8 ORAL EXERCISE 1. Add the columns of 8's from one 8 to five 8's. 2. Build more columns of 8's, until you have ten 8's in the last column. Then read the columns, thus : " One 8 is 8, two 8's are 16," and so on. 3. How many are five 8's? six 8's? seven 8's? eight 8's? nine 8's? ten 8's? 4. Read and learn this table of 8's : 2x8 = 16 5x8 = 40 8x8 = 64 3x8 = 24 6x8 = 48 9x8 = 72 4x8 = 32 7x8 = 56 10x8 = 80 5. How much is 1x8? 8x1? 8x0? 0x8? 6. How much is 8 + 8 + 8 + 8 + 8? What is the short way of finding the answer ? 7. State rapidly the following products : 5x8 8x2 7x8 8x9 8x5 3x8 8x6 6x8 4x8 8x0 2x8 8x7 8x4 8x3 8x8 8x1 8. At 8$ each, how much will 7 melons cost? 9. At $8 each, how much will 9 tables cost ? 10. At 8$ each, how much will 8 notebooks cost? 11. At 8 miles an hour, how far will a man drive a team of horses in 2 hours? 12. At 8$ each, how much will 6 grapefruits cost? TABLE OF EIGHTS 135 ORAL EXERCISE 1. Recite the table of 8's from 1 x 8 to 10 x 8. 2. Recite the table of 8's from 8 x 1 to 8 x 10. State the products : 3. 3 x 8. 7. 8 x 3. 11. 8x9. 15. 2 x 8. 4. 7 x 8. 8. 5 x 8. 12. 8x2. 16. 10 x 8. 5. 9 x 8. 9. 6 x 8. 13. 1x8. 17. 8 x 6. 6. 8x5. 10. 8x0. 14. x 8. 18. 4x8. State the answers : 19. 5 x 8 + 4. 21. 8 x 7 + 6. 23. 6 x 8 + 2. 20. 4 x 8 + 3. 22. 2 x 8 + 1. 24. 8 x 2 + 1. WRITTEN EXERCISE Multiply the following : 1. 2. 3. 4. 5. 6. 200 201 202 212 242 346 8 8 8 8 8 8 7. 8. 9. 10. 11. 12. 300 360 361 365 378 888 8 8 8 8 8 3 13. 14. 15. 16. 17. 18. 400 470 475 486 498 678 8 8 8 8 8 4 19. 20. 21. 22. 23. 24. 575 582 625 675 687 508 8 8 8 8 8 9 136 MULTIPLICATION AND DIVISION ORAL EXERCISE 1. How many 8's are there in 16 ? in 24 ? in 40 ? 2. State rapidly the results : 32-8 40-8 24-8 80-8 3. Read and learn this table : 16-8 = 2 40-8 = 5 64 -8= 8 24-8 = 3 48-8 = 6 72 -8= 9 32-8 = 4 56-8 = 7 80-8 = 10 4. How many 8's are there in 32 ? in 48 ? in 72 ? WRITTEN EXERCISE 1. At $8 each, how many rocking-chairs can be bought for $72? for $80? for $56? 2. At 8$ a quart, how many quarts of strawberries can be bought for 64 5> 6> 7, 8, and 9, in turn, giving quotients and remainders : 1. 125 243 627 481 936 829 2. 352 301 278 270 633 639 3. 473 486 907 842 568 781 4. 597 700 741 488 777 666 Teachers should clearly understand that drill pages of this kind are to be used only until the pupil has attained sufficient proficiency in the processes. The drill should then be discontinued and new work should be taken up. USING WHAT YOU HAVE LEARNED 145 V. USING WHAT YOU HAVE LEAENED HOW THE CITY BOY AND GIRL USE THEIR ARITHMETIC 1. Mollie pays 10$ a day for trolley fares in going to school. How much does she pay each week, if she goes every school day? How much does she pay in 2 weeks? 2. Rob's father took Rob and six of his friends to see the moving pictures. How many tickets did he buy in all ? How much did it cost at 10 $ each ? 3. Tom's father sent Tom to the post office to buy 25 two-cent stamps. How much did Tom pay for the stamps ? 4. Some children in a city school made these baskets out of raffia. The raffia for the three baskets cost 12$, and each took the same amount. What was the cost for each basket? What would be the cost for 15 baskets? 5. If each basket was sold for 10$, what was the gain on each? What was the gain on the three? What would be the gain on 15 baskets ? 6. Of these baskets the largest holds 8 pt. and the smallest holds 2 pt. The third holds half as much as the other two together. How much does the third hold ? 146 USING WHAT YOU HAVE LEARN-ED EARNING AND SPENDING 1. George is a newsboy. He pays 3$ for 5 papers. How much does he pay for 10 papers ? for 15 papers ? 2. Harold gets 25$ for mowing a lawn. If he mows it 4 times a month, how much does he get in a month ? 3. If it costs each pupil 60$ a year for schoolbooks, how much will it cost 3 pupils each year ? 4. Anna spends 5$ every week going to the moving pictures. There being 52 weeks in a year, how much would she save in a year if she did not go ? 5. John is in the third grade. His father buys him a reader for 40$, an arithmetic for 30$, a spelling book for 25$, and a language book for 35$. How much does he pay for all four books? 6. In Ex. 5, if John's father pays for the books with a $2 bill, how much change should he receive ? 7. If you earn 50$, 60$, 20$, and 70$, how many cents do you earn in all ? How many dollars is this ? 8. Frank earns 70$ and 50$. How many cents does he earn ? Write the answer also as dollars and cents. 9. Harold sold 140 copies of the Saturday Evening Post at 5$ each. How many cents did he receive? How many dollars is this ? Instead of multiplying 5 by 140, multiply 140 by 5. 10. Fred's father sent him to the post office for 125 two-cent stamps. How much did Fred have to pay for the stamps? FRACTIONS 14T VI. FRACTIONS ORAL EXERCISE 1. Miriam is making some doll's clothes for her little sister's doll. She has a piece of ribbon 16 in. long and uses ^ of it. How many inches of ribbon does she use ? / 2. If Miriam had used J of the 16 in. of ribbon, how many inches of ribbon would she have used ? 3. If Miriam had used f of the 16 in. of ribbon, how many inches of ribbon would she have used ? 4. How do you find J of a number? How do you find f of a number? 5. Miriam's mother has 24 yd. of calico, and she tells Miriam that she can have -| of it. How many yards does she let Miriam have ? 6. Can you tell me how many yards Miriam's mother had left after she gave Miriam ^ of the 24 yd.? How do you find this? 7. How do you find ^ of a number? After you have found ^ of a number, how can you find f of the number ? -| of the number ? - of the number ? 8. How do you find ^ of a number ? After this has been found, how can you find |- of the number ? How can you then find 1|- times the number ? The pupil is now beginning the study of harder fractions, and he should be led to see the need for the work. It is not necessary that he should be able to answer all of these questions ; indeed, it is better that he should not answer them too readily, if at all. The important thing is to let the pupil see the necessity of further work in fractions. 148 FRACTIONS ORAL EXERCISE 1. Tell the number of halves in : 1 11 2 21 3 3i 2. Tell the number of feet equal to 4ft. -6. ft 2" ib - 8 ft 2" It. 3. Tell the number of thirds in : 1 2 3 11 L 2 - 21 4. Tell the number of fourths in : fft. 10 ift 2 iu 3f 61 5. Which circles show you that J = J + 1 ? 6. How many sixths do you see in l of the circle ? 7. In the whole circle how many sixths do you see ? WRITTEN EXERCISE 1. Divide a circle into halves, fourths, and eighths, and show that 2" = f = -|- 2. Draw oblongs 4 inches long and 1 inch wide. Shade them to show that 1 J = f , l^f J? an( i i + i = \- 3. If a man has $1840 and spends \ of it, how much does he spend ? How much has he left ? MEASURES 149 VII. MEASURES ORAL EXERCISE 1. Name something that is sold by the bushel. 2. Name some kind of fruit that is sold by the peck. 3. How many pecks in a bushel ? 4. How many quarts in a peck ? 5. In the picture, point to the liquid pint, quart, and the measure called a gallon (gal.), which holds 4 qt. 6. Point to the dry quart, peck, and bushel. Dry Measure. The table of dry measure is as follows : 2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.) WRITTEN EXERCISE 1. If a boy feeds his pony 2 qt. of oats three times a day, how many quarts will he feed him a day ? 2. How many quarts in 2 pk. ? in 4 pk. ? in 1 bu. ? 3. How many pecks in half a bushel ? in 10 bu. ? 150 MEASURES ORAL EXERCISE 1. If you put a pound weight on one side of the scales, how many ounce weights must be put on the other side to balance it ? 2. Then how many ounces make a pound ? Then 1 ounce is what part of a pound? Weight. The table of weight is as follows : 16 ounces (oz.) = 1 pound (Ib.) If there are scales in the school, children should weigh various objects, and also find that 16 ounces = 1 pound. Children sometimes make bags of different sizes, putting in enough sand to make them weigh 1 Ib., Ib., and Ib. The weights are then told, the children's eyes being closed. 3. The average height and weight of children of your age is about as follows : Boys Girls Boys Girls 7yr. 44 in. 44 in. 48 Ib. 47 Ib. Syr. 46 in. 46 in. 52 Ib. 50 Ib. 9yr. 50 in. 49 in. 57 Ib. 55 Ib. Compare your height and weight with the average. WRITTEN EXERCISE 1. 579 Ib. + 927 Ib. 5. 981 Ib. - 264 Ib. 2. 648 Ib. + 879 Ib. 6. 923 Ib. - 478 Ib. 3. 737 Ib. + 578 Ib. 7. 961 Ib. - 389 Ib. 4. 998 Ib. + 287 Ib. 8. 800 Ib. - 126 Ib. SQUAEE MEASUEE 151 Area of a Square or Oblong. A square that is 1 in. on a side is 1 inch square. The area of such a square is 1 square inch. 1 square inch 1 sq. in. A square that is 1 ft. on a side is 1 foot square, and the area of such a square is 1 square foot. If an oblong is 4 ft. long and 2 ft. wide, its area is 8 square feet. There ^__^__ are 2 rows, with 4 square feet in a row ; that is, there are 2x4 square feet. We say that such an oblong is 2 ft. by 4 ft. The square inch and square foot should be drawn on the blackboard, and the idea of area should be made clear by numerous simple illustrations like the one given above. The pupils should ascertain the number of square inches in a square foot, and the number of square feet in a square yard. Square Measure. In square measure we use the following table : 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) WRITTEN EXERCISE 1. Draw a square yard, representing 1 yd. by 1 in. This is called drawing it to the scale of 1 in. to 1 yd. 2. Draw a square foot to the scale of 3 in. to 1 ft. 3. If an oblong is 3 in. long and 2 in. wide, how many square inches has it ? Draw the figure. 4. If a schoolroom is 10 yd. long and 7 yd. wide, how many square yards are there in the floor? 152 MEASUEES ORAL EXERCISE 1. The top of a box is an oblong 3 in. wide and 6 in. long. What is the area? 2. A sheet of paper is 4 in. by 7 in. What is the area ? 3. A pane of glass is 9 in. by 10 in. What is the area ? 4. An oblong is 7 in. long and 3 in. wide. What is the area ? What is the sum of all the sides ? 5. A square is 4 yd. on a side. Find the area, and the sum of all the sides. The teacher may introduce the word " perimeter," in place of " sum of all the sides," if desired. Practice should be given in estimating areas. WRITTEN EXERCISE 1. Draw an oblong 6 in. long and 4 in. wide. Find the area and the sum of all the sides. 2. Draw an oblong one half as long and one half as wide as the first oblong (Ex. 1). Find the area. 3. Find the area and the sum of all the sides of an oblong 8 ft. long and 5 ft. wide. 4. A square 6 yd. on a side contains how many square yards ? How many yards in the sum of all the sides ? 5. Measure the length and the width of your arithmetic. Each page contains how many square inches ? 6. Draw a 2-inch square. Draw a 4-inch square. The 2-inch square equals what part of the 4-inch square? Find the area and the sum of all the sides of the 2-inch square, and also of the 4-inch square. EEVIEW 153 VIII. REVIEW ORAL EXERCISE 1. How many school days in 1 week ? in 2 weeks ? 2. How many school days in 3 weeks ? in 5 weeks ? 3. How many school days in 7 weeks ? in 8 weeks ? 4. How many hours are you in school in the forenoon ? in the afternoon ? all day ? 5. How many hours are you in school in 5 days ? 6. 3 + 5. 11. 5 + 3. 16. 4 + 6. 21. 6 + 4. 7. 8-3. 12. 8-5. 17. 10-4. 22. 10-6. 8. 3x5. 13. 5x3. 18. 4x6. 23. 6x4. 9. 15 + 3. 14. 15 + 5. 19. 24 + 4. 24. 24 + 6. 10. 1 of 15. 15. i of 15. 20. 1 of 24. 25. J. of 24. WRITTEN EXERCISE Add the following : 1. 2. 3. 4. 5. $2.78 $4.87 $17.29 $26.48 $34.75 3.42 6.93 14.32 42.76 41.25 4.20 8.40 .18 39.37 6.00 6. 7. 8. 9. 10. $1.27 . $2.97 $19.37 $78.25 $57.32 2.43 3.23 23.48 49.75 49.68 4.09 5.71 4.29 33.33 81.93 .76 8.49 16.71 49.67 42.07 5.34 6.90 18.35 8.00 61.00 154 KEVIEW ORAL EXERCISE 1. If Mary finds that eggs cost 40$ a dozen, how much must she pay for 2 dozen eggs ? 2. If butter costs 40$ a pound, how much must Mary pay for 2 Ib. of butter ? 3. If oranges cost 5$ apiece, how much must Mary pay for 4 oranges ? 4. If cheese costs 20$ a pound, how much must Mary pay for 3 Ib. of cheese ? 5. Mary bought 2 cans of baking powder at 40$ a can. How much did she pay ? 6. 4 + 7. 11. 7 + 4. 16. 5 + 8 . 21. 8 + 5. 7. 11- 4. 12. 11- -7. 17. 13- 5. 22. 13-8. 8. 4x7 . 13. 7x 4. 18. 5x8 23. 8x5. 9. 28 - 4. 14. 28- -7. 19. 40-*- 5. 24. 40-8. 10. 1 of 28. 15. \ of 28. 20. 1 of 40. 25. 1 of 40. WRITTEN EXERCISE 1. How much must Mary pay for 3 Ib. of figs at 18$ a pound ? at 19 $ a pound ? 2. How much must Mary pay for 2 qt. of sirup at 46$ a quart ? at 48$ a quart ? 3. How much must Mary pay for 3 tins of wafers at 27$ a tin? at 24$ a tin? 4. How much must Mary pay for 3 Ib. of raisins at 25$ a pound ? at 23 $ a pound ? Add and check : REVIEW 155 WRITTEN EXERCISE 1. 2. 3. 4. 5. $8.26 $4.79 $6.87 $81.96 $78.92 9.42 3.42 4.91 32.88 81.36 3.82 5.39 5.73 56.42 47.57 1.23 2.27 1.06 41.60 37.43 6. 7. 8. 9. 10. $9.83 $7.35 $7.34 $27.42 $21.97 4.78 8.42 8.29 19.37 32.43 6.42 9.98 6.42 18.62 68.74 8.96 .67 4.31 5.34 42.96 Subtract and check : 11. ' 12. 13. 14. 15. $9.39 $8.72 $7.31 $15.78 $27.42 6.43 4.96 2.48 13.92 16.96 16. 17. 18. 19. 20. $8.21 $9.00 $8.10 $47.01 $68.75 4.32 4.76 3.92 22.43 49.96 21. 22. 23. 24. 25. $5.77 $9.11 $8.17 $37.82 $91.10 2.68 2.32 4.96 14.93 28.75 26. 27. 28. 29. 30. $9.07 $8.02 $6.00 $30.00 $90.04 6.49 3.70 4.27 6.94 27.70 156 EEVIEW WRITTEN EXERCISE Multiply the following : 1. $271 2 2. $486 3 3. $595 4 4. $643 5 5. $781 6 6. $842 7 7. $937 8 8. $249 9 9. $342 7 10. $873 8 11. $998 6 12. $843 7 13. $777 7 14. $398 8 15. $873 9 16. Divide each of these numbers by 2 and by 3 : 276 378 612 342 486 348 492 204 726 498 222 528 180 414 336 17. Divide each of these numbers by 4 and by 5 : 280 560 820 980 480 500 460, 340 740 220 900 620 18. Divide each of these numbers by 6 and by 7 : 420 840 462 210 294 378 546 882 504 252 336 924 19. Divide each of these numbers by 8 and by 9 : 720 360 288 504 648 936 792 216 432 576 864 144 EEVIEW 157 ORAL EXERCISE Find the cost of the following : 1. 2 doz. eggs at 40$ a dozen ; at 50$ a dozen. 2. 8 Ib. of crackers at 8$ a pound ; at 9$ a pound. 3. 2 Ib. of tea at 40$ a pound ; at 30 $ a pound. 4. 5 Ib. of prunes at 7$ a pound ; at 80 a pound. 5. 6 Ib. of starch at 9$ a pound ; at 10$ a pound. 6. 8 Ib. of rice at 8$ a pound ; at 9$ a pound. 7. 1 Ib. of figs at 20< a pound ; at 22 $ a pound. 8. 7 Ib. of crackers at 10$ a pound ; at 90 a pound. WRITTEN EXERCISE Find the cost of the following : 1. 2 Ib. of coffee at 35$ a pound ; at 37$ a pound. 2. 4 Ib. of raisins at 12$ a pound ; at 14$ a pound. 3. 2 Ib. of tea at 48$ a pound ; at 46$ a pound. 4. 2 doz. eggs at 47$ a dozen ; at 44$ a dozen. 5. 1 doz. oranges at 60$ a dozen; at 80$ a dozen. 6. l doz. bananas at 36$ a dozen; at 40$ a dozen. 7. 2 doz. bananas at 36$ a dozen ; at 38$ a dozen. Find the total cost in each example : 8. 2 Ib. of sugar at 6$ a pound; 3 Ib. of prunes at 8$ a pound ; 5 Ib. of rice at 8$ a pound. 9. 3 Ib. of starch at 9$ a pound ; 2 Ib. of crackers at 12$ a pound ; ^ doz. oranges at 40$ a dozen. 158 REVIEW WRITTEN EXERCISE 1. Write in figures : five thousand fifty-five ; eighteen hundred fifty-eight ; seven thousand three hundred forty- six ; nineteen hundred fourteen. 2. The rents for an office building for one month were as follows: first floor, $384; second floor, $290; third floor, $275; fourth floor, $186. What was the total rent? 3. Four coal trains left the mines loaded as follows : the first had 1100 tons of coal; the second, 1275 tons; the third, 998 tons; the fourth, 1822 tons. How many tons of coal did the four trains carry? It is legitimate to use the word " ton " as an indefinite term at the pres- ent time. Children hear such words used, and the teacher may explain them informally. Similarly for such words as " mile " and " year." 4. A merchant's receipts for one day were $298.85, $624.88, and $157.60. What were the total receipts? 5. A town has to-day 8967 inhabitants. It gained 1289 in ten years. How many were there ten years ago ? 6. A train started with 500 passengers and made four stops on a trip. At the first stop 89 passengers got off ; at the second, 78 ; at the third, 122 ; at the fourth, 55. How many passengers remained on the train? 7. By one way it is 411 miles from New York to Buffalo and 541 miles from Buffalo to Chicago. How far is it from New York to Chicago ? 8. A dealer offered $7.85 apiece for some suits of clothes, but $9.15 apiece was asked for them. How much more was asked than was offered for the suits ? PEOBLEMS 159 9. A farmer paid 60 a pound for some hogs. He kept them a week at no expense, during which time they gained 58 lb., and he then sold them for 6$ a pound. How many cents did he gain by keeping them ? How many dollars ? 10. If it costs $129 to run a locomotive one trip between two cities, how much will it cost for nine trips ? 11. A teacher receives $45 per month for 9 months. How much does she receive in all? 12. A mile contains 5280 ft. How many feet are there in half a mile ? 13. If milk costs 70 a quart and a family' uses 2 qt. a day, how much will be the milk bill for 7 da. ? 14. A man paid $487 for some land. He built on it a house costing $2225 and a barn costing $250. What was the total cost of the land and buildings ? 15. Ralph receives $55 a month for 7 months, and George $45 a month for 9 months. What is the total amount received by each? 16. What is the cost of 216 calves at $9 each? 17. A farmer paid $329 for 7 cows. How much did he pay for each cow ? 18. What is the cost of 564 tons of coal at $6 per ton? 19. What is the cost of 9 tables at $17 each ? 20. Frank pays a debt of $26.17, and gives in payment 3 ten-dollar bills. How much change should he receive ? 21. A bushel of oats weighs 32 lb. How many pounds do 8 bu. of oats weigh ? 160 REVIEW WRITTEN EXERCISE Add the following, and check : 1. 2. 3. 4. 5. $5.43 $9.34 AO f)rr |po.^ / $11.17 $13.37 1.27 2.18 9.36 25.25 - 72.26 3.19 6.25 10.19 37.37 87.19 6. 7. 8. 9. 10. $2.03 $8.12 $12.12 $14.05 $30.03 3.04 7.32 13.13 11.10 20.02 3.21 5.13 21.21 31.32 40.01 5.51 6.41 32.32 23.50 50.50 6.18 7.56 18.72 15.68 19.87 11. 12. 13. 14. 15. $4.06 $5.17 $13.78 $16.27 $15.76 2.98 6.24 14.26 18.42 8.24 3.74 8.19 19.16 27.96 24.16 2.45 3.32 12.04 11.34 14.26 6.17 4.46 18.75 12.19 18.91 9.63 8.75 22.67 19.84 22.68 16. 17. 18. 19. 20. $6.17 $2.99 $9.99 $10.06 $1.98 2.98 1.86 1.06 9.80 10.47 1.48 3.47 . 22.14 4.29 8.93 3.65 8.21 13.87 13.62 26.12 2.91 ' 1.69 20.16 8.75 10.89 1.64 5.16 7.98 22.10 37.16 7.49 8.22 10.00 41.09 9.48 DRILL WORK 161 Subtract the following, and check : 21. 22. 23. 24. 25. $7.45 $7.8? $8.59 $9.33 $36.55 5.03 4.63 5.26 7.29 28.00 * to i>-3 -3 26. 27. 28. 29. 30. $9.51 $5.65 $6.41 $6.73 $17.44 3.28 1.27 2.38 1.09 8.36 3 ^> \< u - > 3 ^> j f l ' 31. 32. 33. 34. 35. IjpO.DO . $7.11 $9.16 $8.92 $24.31 2.99 4.09 2.38 3.19 15.42 36. 37. 38. 39. 40. $9.17 $8.45 $6.07 $9.36 $46.18 6.29 4.56 3.08 4.07 20.09 Multiply the following : 41. 42. 43. 44. 45. $113 $224 $510 $1612 $1175 3 4 5 6 8 46. 47. 48. 49. 50. $950 $699 $907 $1128 $1750 7 5 9 _8 4 51. 52. *$ 53. 54. $675 $709 $812 $1050 8-7 9 9 162 KEVIEW 56. Divide each of these numbers by 2 : 468 456 372 331 634 972 326 253 214 547 418 905 57. Divide each of these numbers by 3 : 354 365 624 484 408 798 444 235 651 790 891 976 58. Divide each of these numbers by 4 : 924 824 955 564 592 918 752 912 734 723 961 513 59. Divide each of these numbers by 5 : 510 520 644 770 590 742 665 735 560 887 623 825 60. Divide each of these numbers by 6 : 666 636 732 727 822 924 624 725 746 810 845 933 61. Divide each of these numbers by 7 : 728 785 812 861 910 943 745 797 805 873 935 950 62. Divide each of these numbers by 8 : 728 656 592 392 928 111 744 672 512 304 984 222 63. Divide each of these numbers by 9 : 333 738 549 567 702 777 666 657 324 405 801 888 DEILL TESTS 163 DRILL TEST. MULTIPLICATION Write all the ansivers in two minutes or less : -1. 4x 6. 11. 6x 4. ^21. 7x 5. 31. 9 x6. 7x 3. 12. 4x 7. 22. 9x 9. 32. 3 x9. 3. 8x 2. 13. 8x 6. 23. 4x 8. 33. 8 x 7. 4. 5x 6. .X14. 7x 4. 24. 6x 5. 34. 4 x9. 5. 7x 7. ^15. 5x 7. 25. 7x 9. 35. 9 x8. 6. 6x 3. 16. 8x 3. 26. 9x 4. 36. 6 x6. 7. 8x 5. 17. 6x 8. 27. 5x 8. 37. 8 x8. 8. 9x 2. /18. 3x 8. 28. 9x 7. 38. 5 x9. 9. 6x 7. 19. 7x 8. ^ 29. 8x 4. 39. 7 x6. 10. 9x 5. 20. 9x 3. /30. 6x 9. 40. 8 x9. DRILL TEST. DIVISION Write all the answers in two minutes or less : 1.12-4. 11.18 + 6. 21.64 + 8. .31. 35 + '5. 2. 12 - 6. 12. 21 + 7. 22. 45 + 5. 32. 24 + 4. 3.32 + 8. 13.24 + 8. 23.24 + 6. 33.72+9. 4. 54 + 9. 14. 16 + 4. 24. 28 + 7. , 34. 27 + 3. 5. 36 + 4. 15. 48 + 8. 25. 63 + 9. 35. 42 + 6. 6. 63 + 7. 16. 54 + 6. 26. 27 + 9. ^6. 24 + 2. -7.48 + 6. 17.72 + 8 27.20 + 4. -37.56 + 7. -8.45 + 9. 18.35 + 7. 28.56 + 8. 38.18 + 9. 9. 28 + 4. 19. 36 + 9. 29. 36 + 6. . 39. 55 + 5. 10. 49 + 7. 20. 32 + 4. 30. 42 + 7. 40. 81 + 9. 164 USING WHAT YOU HAVE LEAENED IX. USING WHAT YOU HAVE LEAENED A BIRTHDAY PARTY * 1. Louise is having a birthday party. She bought 8 small candles at 2$ each and one larger candle for 3$. How much did she pay for all of the candles? 2. If Louise gave the storekeeper 25$ for the candles, how much change did she get back ? 3. Seven of her friends came. If she provided four pieces of cake for each one who came and four for herself, how many pieces did she provide ? 4. She made a cake, using 3 eggs worth 36$ a dozen, 3$ worth of sugar, 2$ worth of flour, and 2$ worth of other materials. How much did all the materials cost ? PROBLEMS 165 BUYING THINGS WE WOULD LIKE 1 . Frank can get an express wagon for 65 0. He has saved 480. How much more must he save to buy the wagon? 2. Fred wants a bicycle. He sees one that is marked $13.50. The dealer tells him he can have it for $1.25 less. How much will the bicycle cost him? 3. Kate wants a tricycle. Her father finds that one will cost $2.75. If he gives her $5 for her birthday, she can buy the tricycle and then have how much money left ? 4. Louise wants a pair of shears. She can buy them for 45$. If she gives the dealer a dollar bill, how much change should she receive ? 5. If you buy a box of water-color paints for 250, some brushes for 180, some colored crayons for 100, and some paper for 150, how much will it all cost? 6. Louise wants to weave some rugs for her doll house. She finds that a wooden loom will cost 350, some weaving needles 150, and some rug yarn 350. How much will it all cost? How much change should Louise rec,eive if she gives the dealer a dollar? 7. Kate wants a fountain pen. She can buy one for 900, but by paying 400 more she can buy the kind she wants. How much must she pay for the pen she wants ? How much change should she receive if she gives the dealer $1.50 ? 8. Kate's father promised her a hammock and a swing for her birthday. The hammock cost $2.65 and the swing cost $0.85. How much did the two cost? 166 LITTLE EXAMINATIONS X. LITTLE EXAMINATIONS I. 1. 39 + 7. 5. 26 + 37. 9. XX = (?). 2. 27 + 6. 6. 63 - 41. 10. $1.25 + $2.30. 3. 28 + 9. 7. 9x 6. 11. 4x6 + 2. 4. 37 + 4. 8. 2 x 808. 12. 369 -*- 9. II. 1. 46 + 9. 5. 72 - 36. 9. XVII = (?). % 2. 25 + 8. 6. 56 + 38. 10. $2.36 + $1.22. 3. 79 + 2. 7. 8 x 9. 11. 7x8 + 6. 4. 48 + 7. 8. 6 x 275. 12. 588 + 7. III. 1. 37 + 7. 5. 52-29. 9. XVI=(?). 2. 38 + 8. 6. 94 + 23. 10. $2.31 + $1.92. 3. 35 + 7. 7. 4 x 381. 11. 8x9 + 7. 4. 76 + 8. 8. 6 x 384. 12. 576 - 6. IV. 1. 49 + 6. 5. 63-48. 9. XIX = (?). ' 2. 56 + 7. 6. 7 x 8. 10. $3.42 + $1.73. 3. 47 + 8. 7. 7x223. 11. 9x6 + 4. 4. 58 + 6. 8. 7 x 225. 12. 9 ft. = (?) in. V. 1. 58 + 3. 5. 38 + 16. 9. XIV = (?). 2. 26 + 6. 6. 72 - 66. 10. 8 pt. = (?) qt. 3. 39 + 3. 7. 8 x6. 11. 8x8 + 2. 4. 67 + 9. 8. 9 x 288. 12. 512 -*- 8. These Little Examinations may be used on different days near the close of a term. Teachers should read the note on page 52. CHAPTER IV I. READING AND WRITING NUMBERS ORAL EXERCISE 1. Count by 10's from 10 to 100. 2. Count by 100's from 100 to 1000. 3. Count by 1000's from 1000 to 10,000. 4. Count by 10,000's from 10,000 to 90,000. The number 100,000 is read " one hundred thousand." In a number of five figures a comma (,) is written between the thousands and the hundreds. In 23,546 the 6 occupies the ones' place, the 4 occupies the tens' place, the 5 occupies the hundreds' place, the 3 occupies the thousands' place, . ' the 2 occupies the ten-thousands' place. Read the following : 5. 40,000. 6. 50,000. 7. 60,000. 8. 76,450. 9. 41,000. 10. 50,500. 11. 63,000. 12. 82,729. 13. 41,500. 14. 50,050. 15. 63,075. 16. 86,483. 17. 41,525 18. 50,005 19. 63,975 20. 99,999 167 168 BEADING AND WETTING NUMBERS Roman Notation. The Roman notation, used chiefly Sor numbering the chapters of books, employs seven capital letters, as follows : Letters, I V X L C D M Values, 1 5 10 50 100 500 1000 The first nine numbers are written thus : I II III IVorlHI V VI VII VIII IX The tens are written thus : X XX XXX XL L LX LXX LXXX XC The hundreds are written thus : C CC CCC CD D DC DCC DCCC DCCCC or CM The numbers from eleven to nineteen are written thus : XI XII XIII XIV XV XVI XVII XVIII XIX The following are examples of other numbers : XXIII = 23 XCVIII = 98 CLXVI = 166 XXXVI = 36 LXXVI = 76 CCCLIX = 359 MDCCCCXVII or MCMXVII = 1917 WRITTEN EXERCISE Write in common figures : 1. XI. 3. XXVI. 5. LXXII. 7. LXXVIL 2. LXIV. 4. LXVI. 6. XCVII. 8. XXXIV. Write in Roman numerals : 9. 31. 11. 42. 13. 67. 15. 175. 17. 1919. 10. 89. 12. 91. 14. 75. 16. 150. 18. 1920. ADDITION 169 II. ADDITION. - WRITTEN EXERCISE Copy, add, and check in five minutes or less 1. 2. 3. 4. 3 45 72 1 86 2 17 .94 5 28 82 4 64 26 3 25 7 33 1 56 21 4 74 36 9 48 89 7 17 51 10 52 Copy, add, and check in six minutes or less 6. 7. 8. 9. 10 87 1 45 2 32 19 80 17 3 15 12 08 13 47 10 26 41 80 20 45 12 16 13 18 24 72 15 65 16 17 28 45 13 92 11 15 8 78 5. 12 35 6 10 14 65 79 8 20 10. 13 96 8 44 19 27 21 13 12 68 11. A farmer sold milk on four days as follows : Monday, 224 qt.; Tuesday, 246 qt. ; Wednesday, 238 qt,; Thursday, 228 qt. How many quarts did he sell in all ? 12. When Ethel's father went to Chicago he paid $12.80 for his ticket, $7.75 at the hotel, $24.75 in shopping, and $875 for an automobile. How much did he spend in all ? 13. On the first day of the fair 7214 tickets were sold ; on the second day 8112 tickets, and on the third day 6125. tickets. How many tickets were sold on the three days ? 170 SUBTRACTION III. SUBTRACTION WRITTEN EXERCISE 1. How much more is 224 ft. than 187 ft. ? 2. How many less are 224 men than 301 men? 3. How much more is the sum of 426 and 182 than the sum of 97 and 58 ? 4. How much less is the sum of 196 and 259 than the sum of 437 and 296 ? 5. A farmer who had 235 chickens sold 86 of them. How many had he left? He then bought 52 more. How many chickens did he then have ? 6. A farmer had 68 sheep. After buying 75 more, how many did he have ? If he then sold 40 sheep, how many did he then have ? 7. A man's income for a year is $1500 and $280, and his expenses are $1275. How much does he save? 8. A man's salary is $1400 a year, and he receives $180 from a house which he rents. His expenses for the year are $1142. How much does he save ? 9. How many more Boy Scouts are there in a regiment made up of 76 boys under twelve years of age and 89 boys over twelve years of age than there are in a regiment of 144 boys ? 10. A boy had a kite string 428 ft. long. He tied on 856 ft. more, and later lost 68 ft. in a tree. How many feet of string did he have left? DRILL WORK 171 ORAL EXERCISE If you owe the following sums, how much change should you receive from $1 in each case? 1. 900 950 800 850 700 750 880 920 810 2. 300 600 450 380 490 620 360 430 770 3. 100 200 250 350 410 330 660 790 890 If you owe the folloiving sums, how much change should you receive from $2 in each case ? 4. $1.25 $1.50 $1.75 $1.80 $1.90 $1.95 5. $1.35 $1.38 $1.62 $1.56 $1.88 $1.17 6. $1.82 $1.61 $0.75 $1.20 $1.32 $1.44 If you owe the following sums, how much change should you receive from $5 in each case ? 7. $2.25 $3.25 $4.75 $2.80 $3.50 $1.50 8. $3.80 $4.10 $2.60 $1.40 $2.10 $4.15 9. $2.78 $3.75 $4.60 $3.90 $2.01 $3.07 WRITTEN EXERCISE Subtract, and check the work : 1. 2. 3. 4. 5. $281.42 $691.75 $298.30 $427.20 $532.60 135.02 208.02 107.60 109.32 237.62 6. 7. 8. 9. 10. $532.65 $281.92 $409.72 $672.35 $491.63 206.39 192.60 286.58 148.39 269.75 172 MULTIPLICATION IV. MULTIPLICATION Terms Used. We have already learned that when we take a number 2 times we multiply it by 2, that when we take it 3 times we multiply it by 3, and so on. Pupils are not expected to learn formal definitions at this stage. We have also learned (page 85) the names of the terms used in multiplication. These are multiplicand, multiplier, and product, and are seen in the next example. Multiplying Money. If a bookseller sells 7 books at $1.25 each, how much money does he receive for them? We see that we must multiply $1.25 multiplicand We first see that 7x 5< = 35<1 ,,. ,. j. ,- v 7 multiplier or 6 dimes and 5 cents, and we ^o nr -, _ . , $8.75 product write the 5 in the cents place and add the 3 to the dimes. Then 7x2 dimes = 14 dimes, and 14 dimes + 3 dimes = 17 dimes, or $1.70. We write the 7 in the dimes' place and add the 1 to the dollars. We then write the decimal point, to separate the dollars from the dimes. Then 7 x $1 = $7, and $7 + $1 = $8, and we write the 8 in the dollars' place. The product is $8.75, and so the bookseller receives $8.75 for the 7 books. Therefore, to multiply United States money, multiply as with other numbers, placing the decimal point in the product below the decimal point in the multiplicand. DRILL WOKK 173 WRITTEN EXERCISE Multiply the following : 1. 2. 3. 4. 5. 135 $1.35 275 $12.75 $10.20 2 2 2 2 4 6. 7. 8. 9. 10. $3.75 $1.35 $7.25 $18.60 $20.30 2 3 3 4 5 11. 12. 13. 14. 15. $9.30 $8.95 $2.33 $23.42 $24.70 4 4 5 5 6 16. 17. 18. 19. 20. $4:81 $4.09 $7.28 $43.00 $36.75 6 6 6 7 5 21. 22. 23. 24. 25. $3.09 $3.59 $4.86 . $71.93 $49.78 7 7 8 8 6 26. 27. 28. 29. 30. $6.32 $2.13 $12.75 $14.75 $82.86 9 9 9 9 8 31. At $2.25 a yard, how much will 2 yd. of silk cost? 32. At $3.25 each, how much will 7 desks cost ? . , 33. At $6.50 each, how much will 6 tables cost? 34. At $7.35 each, how much will 8 boys' suits cost? . 174 MULTIPLICATION ORAL EXERCISE 1. How much is 10 x 2? 10 x 20? 2. To multiply by 10, how many zeros do you annex ? 3. How much is 10 x 25? 10 x 47? Multiply by 10: 4. 7 70 73 26 27 33 82 52 5. 34 48 29 66 87 41 79 99 6. How much is 10 x $3 ? 10 x $3.00 ? 7. How much is 10 x $7 ? 10 x $7.50 ? 8. How much is 10 x $15? 10 x $15.75? 9. How much is 10 x $21.50 ? 10 x $100 ? Multiplying by Tens. To multiply by 10, annex a zero. If there is a decimal point, move it one place to the right. Thus 10 x 75 = 750, and 10 x $7.50 = $75.00. The result of both 10 x $3 and 10 x $3.00 is $30. We may write this as $30, or as $30.00. The product of 10 x $1.25 is $12.50, not $12.5, it being the custom to put a zero at the right in such a case. To multiply by 100, annex two zeros. Move any decimal point two places to the right. To multiply by 20, multiply by 2 and annex a zero. To multiply by 200, multiply by 2 and annex two zeros. 25 32 20 300 500 9600 We write the numbers and express the work as shown above in the multiplication of 25 by 20 and of 32 by 300. MULTIPLYING BY TENS 175 WRITTEN EXERCISE Multiply ~by 10 : 1. $2.75 $12.75 $22.75 $25.50 2. $26.00 $48.30 $53.25 $69.73 3. $82.96 $100.00 $200.00 Multiply ~by 20 : 4. 42 36 81 53 67 5. 39 $1.20 $2.20 $3.50 $2.23 6. $4.50 $5.70 $4.90 $7.75 $9.65 Multiply by 100 : 7. 4 22 45 50 81 75 42 86 8. 77 36 83 87 63 66 29 99 Multiply ly 200: 9. 5 8 7 9 6 15 18 25 10. 35 41 48 55 46 60 67 75 11. At $2 each, how much will 30 chairs cost? 12. At $3 each, how much will 40 tables cost ? 13. At $5 each, how much will 50 desks cost ? 14. At $6 each, how much will 70 coats cost ? 15. At $32 each, how much will 20 bedroom sets cost ? 16. At $60 each, how much will 30 cows cost? 17. At $3.50 each, how much will 20 hats cost? 18. At $17.50 each, how much will 20 office desks cost? 19. At $22.75 each, how much will 30 overcoats cost? 176 MULTIPLICATION WRITTEN EXERCISE 1. How much will 10 doe. pencils cost at 30$ a dozen? at 36$ a dozen? at 42$ a dozen? 2. How much will 10 boxes of crayons cost at 35$ a box? at 38$ a box? at 43$ a box? 3. At 10$ apiece, how much will 2 doz. blackboard pointers cost? How much will 3 doz. cost? 4. At 10$ a small package, how much will half a dozen small packages of pens cost ? 5. How many fingers have the pupils in a class of 27? How many toes ? How many fingers and toes ? 6. If an arithmetic costs 35$, how much must be paid for 10 arithmetics ? for 2 arithmetics ? 7. If a book costs $1.25, how much must be paid for 10 such books ? for 20 such books ? for 30 such books ? 8. At $12.75 each, how much must a dealer pay for 40 suits of boys' clothes ? for 60 suits ? 9. At $38.25 each, how much must a dealer pay for 30 bedroom sets ? for 40 sets ? for 60 sets ? 10. At $62.50 an acre, how much must a farmer pay for 80 acres of land ? for 90 acres ? for 70 acres ? 11. At $45.50 each, how much must a furniture dealer pay for 50 dining-room sets? for 20 sets? for 40 sets? 12. At $37.75 each, how much must a dealer pay for 80 office desks? for 70 desks? for 30 desks? 13. At $87.50 each, how much must a dealer pay for 20 Texas ponies ? for 30 Texas ponies ? TWO-FIGURE MULTIPLIER 177 Two-Figure Multiplier. To multiply 35 by 21, we write the numbers as here shown. We first multiply by 1, the product being 35. We write the 5 below the ones. 21 We then multiply by 2 tens, the product being 70 tens. We write this so that the right-hand figure (0) is below the multiplier (2), in the tens' place. 35 70 Adding, the total product is 735. WRITTEN EXERCISE 1. At $32 each, how much will a merchant pay for 21 suits of clothes? for 31 suits? 2. At $43 each, how much will a dealer pay for 21 bed- room sets? for 31 sets? for 41 sets? 3. Multiply by 21: 46 53 65 76 83 38 52 94 60 4. Multiply by 31 and by 41, in turn : 27 52 74 39 85 41 28 63 96 Multiply ~by 52, 62, and 72, in turn : 5. 33 46 57 44 35 68 55 79 82 6. 47 69 25 71 93 36 84 58 95 Multiply the following : 7. 63 x 95 63 x 84 83 x 88 93 x 97 8. 74 x 96 84 x 98 94 x 99 64 x 88 178 MULTIPLICATION Two-Figure Multiplier. To multiply $2.75 by 54, we write the numbers as here shown. We multiply in the usual way, first by 4 units and then by 5 tens. In the product we place the decimal point between dollars and dimes. The product is $148.50. Teachers who feel that the class needs a more com- plete explanation may refer back to page 172. WRITTEN EXERCISE Multiply the following : 1. $4.82 by 15. 6. 2. $4.09 by 19. 3. $2.81 by 38. 4. $2.99 by 27. 5. $0.69 by 73. 7. 8. 9. 11. $3.27 by 62. 12. $3.96 by 28. 13. $1.39 by 39. 14. $1.75 by 68. 15. $0.75 by 89. ..23 by 12. 5.17 by 32. ;.41 by 29. L80 by 36. 10. $5.60 by 71. 16. At $24 a dozen, how much will 24 silver tablespoons cost ? How much will 24 doz. cost ? 17. At $36 a dozen, how much must a dealer pay for 4 cut-glass vases? for 26 doz. ? for 15 doz. ? 18. At $7 each, how much will 12 armchairs cost ? What will be the cost of 25 ? of 38 ? of 46 ? Multiply the following : 19. 23 x $2.56. 22. 41 x $3.45. 20. 28 x $3.91. 23. 43 x $3.05. 21. 75 x $4.00. 24. 75 x $4.50. 25. 52 x $2.86. 26. 75 x $3.08. 27. 36 x $5.50. TWO-FIGURE MULTIPLIER 179 WRITTEN EXERCISE In solving these examples in multiplication see how large a score you can make in five minutes, counting every correct result 1, and subtracting 2 for every incorrect result : 1. 2. 3. 4. 5. 6. $2.50 $3.65 $4.80 $5.25 $12.50 $27.62 31 22 34 42 44 20 7. 8. 9. 10. 11. 12. $4.60 $7.95 $5.92 $9.37 $13.75 $52.96 22 26 36 39 64 30 13. 14. 15. 16. 17. 18. $5.80 $8.34 $8.75 $9.99 $48.70 $99.99 75 27 48 99 82 90 19. A clothing dealer bought 75 suits of clothes at $12.25 each. How much did he pay for the lot? 20. A dealer bought 48 automobiles at $427.50 each. How much did he pay for the lot? Multiply the following : 21. 22. 23. 24. 25. $425.25 $275.05 $162.73 $421.11 $228.96 32 34 36 71 30 26. 27. 28. 29. 30. $326.45 $241.36 $432.47 $225.25 $600.09 28 35 26 88 80 180 MULTIPLICATION $348 234 1392 1044 696 $81432 Three-Figure Multiplier. 1. A city dealer buys 234 auto- mobiles at $348 per car. How much do the cars cost him? We see that we must multiply $348 by 234. We multiply by 4, and write the product, 1392, so that the right-hand figure (2) is in the ones' place. We then multiply by 3, and write the product, 1044, so that the right- hand figure (4) is in the tens' place. We then multiply by 2, and write the product, 696, so that the right-hand figure (6) is in the hundreds' place. The product is $81,432, and this is the cost of the cars. 2. If the dealer buys 240 cars at $720 each, how much do all the cars cost him? To multiply by 240 is the same as to multiply by 10 x 24. We multiply by 10 by annexing 0, and so we may multiply $720 by 24 and annex as here shown. The product is $172,800, the total cost. WRITTEN EXERCISE Multiply the following : 1. 2. 3. 4. 5. 6. 231 231 439 575 $575 $356 111 123 123 ,222 322 550 7. 8. 9. 10. 11. 12. 243 348 329 426 $527 $481 126 241 423 178 136 670 THREE-FIGURE MULTIPLIER 181 Multiplication Continued. A maker sells 204 wagons at $116.67 per wagon. How much money does he receive? We see that he receives 204 x $116.67. We multiply as on page 180, except that there is no need to multiply by 0. We multiply by 4, and write the 204 j rt / GO product, 46668, so that the right-hand figure (8) is in the ones' place. We mul- $23800 68 tiply by 2, and, because we are multiply- ing by hundreds, we write the product so that the right-hand figure (4) is in the hundreds' place. The product is $23,800.68, and this is the money received. The pupils are already familiar with multiplication involving money, and they know where to place the decimal point. * WRITTEN EXERCISE 1. At $85 an acre, how much must a farmer pay for 104 acres of land ? for 107 acres ? for 109 acres ? 2. At $37.50 a head, how much will 102 head of cattle cost? 143 head? 107 head? 109 head? Multiply the following : 3. 4. 5. 6. 7. $481.20 $502.75 $681.39 104 109 102 $217.42 206 $321.50 371 8. 9. 10. 11. 12. $491.76 $482.75 $536.47 381 243 308 $671.70 426 $879.90 897 182 MULTIPLICATION REVIEW DRILL Find the cost of the following : 1. 6 books at 31$. 13. 8 yd. of carpet at 70$. 2. 3 Ib. of tea at 42$. 14. 5 cans of cocoa at 3. 4 cows at $41. 15. 9 gallons of oil at 4. 6 Ib. of steak at 21 $. 16. 7 tennis balls at 20$. 5. 7 collars at 21$. 17. 3 writing tablets at 15$. 6. 6 flags at 15$. 18. 7 Ib. of butter at 30$. 7. 6 Ib. of figs at 15$. 19. 2 bu. of wheat at 90$. 8. 12 pencils at 3$. 20. 8 Ib. of walnuts at 15$. 9. 9 Ib. of meat at 20$. 21. 21 yd. of ribbon at 9$. 10. 15 trout flies at 8$. 22. 3 Ib. of cheese at 32$. 11. 9 Ib. of sugar at 6$. 23. 18 doz. buttons at 5$. 12. 9 cans of soup at 12$. 24. 4 sewing machines at Find the cost of the following , and the change due: 25. 6 Ib. of roast beef at 20 t $. Paid $1.25. 26. 7 writing tablets at 12$. Paid $1. 27. 2 pencils at 5$ and 3 tablets at 12$. Paid 50$. 28. 3 cows at $40 and 2 sheep at $6. Paid $140. 29. 2 horses at $125 and a carriage at $100. Paid 30. 5 acres of land at $90 and 2 acres at $50. Paid $600 31. 7 cows at $50 and 6 cows at $40. Paid $600. 32. 5 tables at $15 and 20 desks at $4. Paid $160. 33. 8 chairs at $2 and a table at $9. Paid $30. Exs. 1-24 may be taken for oral work. USING WHAT YOU HAVE LEAKNED 183 V. USING WHAT YOU HAVE LEAENED BUYING PRESENTS FOR CHRISTMAS 1. If some children pay 45$ for a Christmas tree and give the dealer 50$, how much change is due ? 2. If Maude buys 9 candy canes, at 8$ each, how much do they cost ? How much change should she get from 75 $ ? 3. If Mollie buys her mother 4 handkerchiefs at 25$ each, how much do they cost? 4. If Jack buys 10 colored balls at 4$ each, how much do they cost? 5. Sue buys 5 strings of tinsel at 12$ a string. How much does the tinsel cost? 6. How much will 2 doz. candles cost at 18$ a dozen ? 7. The children bought some toys costing 10$, 20$, 32$, 30$, 10$, 25$. How much did these all cost? 184 GOING TO THE PQST OFFICE % 1. It costs 2$ for a stamp for a letter weighing 1 oz. or less. How much will stamps for a dozen letters cost ? In the examples, each letter may be taken as weighing 1 oz. 2. A postal card costs 1$. How much will it cost you to buy a half dozen postal cards and 8 stamps for letters ? 3. If you have a friend living in Italy, a postage stamp for a letter to be sent there will cost 5$. How much will it cost for postage if you write a letter every month for the twelve months of a year ? 4. If you send a newspaper by mail, the postage is 1$ for each 4 oz. or less. How much will it cost to send a letter, 3 postal cards, and a newspaper weighing 4 oz. ? 5. You can send parcels through the post office. If your cousin lives about 100 miles away, and you wish to send him a book weighing 2 lb., the postage will be 6 $. How much will it cost to send him such a book, a letter, and a newspaper as heavy as the one in Ex. 4 ? 6. If you are in a hurry to have your letter delivered, you may put on a special-delivery stamp, costing 10$, besides the postage on the letter. How much will it cost you to send a special-delivery letter? 7. If you are sent to the post office to buy 2 doz. 2-cent stamps, 5 postal cards, and a special-delivery stamp, how much money must you take with you? The pupils should be asked to state problems from their own experience similar to the above. PROBLEMS 185 A DAY IN THE CITY 1. Irene's father took her to the city. Their railroad tickets cost $2.10. They paid 50$ for street-car fares and $1.50 for luncheon. They paid 75$ for a cab to make a call. How much money did they spend ? 2. Irene's father gave her the money for some Christ- mas presents. She bought a doll for $1.25, a pair of skates for $1.50, a bat and a glove to give to her brother Fred for $1.25, and some handkerchiefs for her mother for 75$. How much did she spend in all ? . 3. At a fruit stand Irene saw the sign, "Apples, 3 for 5$." How many apples could she buy for 10$? 4. Irene's father owed three bills in the city. The amounts were $125, $16.50, and $48.25. She went with him when he paid them. How much did he pay in all ? 5. Irene's father sent a telegram of 16 words. It cost him 40 $ for the first ten words, and 3 $ for each additional word. How much did he pay for sending the telegram? 6. Irene did some shopping for her mother. She bought two pairs of gloves at $1.50 a pair, and three handkerchiefs, at 25$ each. How much did she pay for them all? 4,3 *}:$ 7. Irene's father bought for her brother Fred a story book costing 75$, a tennis racket costing $1.50, and a ball costing 45$. How much did all three cost?" ,3, V ^ 8. A football team in their town had asked Irene's father to find what their suits would cost. He found that the price was $3.50 each. How much will 11 suits cost? How much will 22 suits cost?$ 3 A- O 1 1 1 "T 1 3 10337 * -39 3> 3' ' TOT' TIT- l *' 16~> 16"' T6- s- ili - IF? re? re- * i> i> f- 9 - i. I- 1- i*- A. *> A- 5. J, i, }. 10. A, A, T V 15. A, i, ^. Add, as explained in the oral exercise on page 205 : 16. 1,1 20. If 24. If. 28. 11 + 1 17. 1 |. 21. 1,J. 25. l,f 29. 21 + 1 18. J, J. 22. 1 l. 26. |, |. 30. 71 + 3J. 19. If 23. If 27. f,f 31. 5l + 2f. It is not expected that pupils will be able to reduce the results to lowest terms at this time. ADDITION 211 WRITTEN EXERCISE 1. If we have 21 yd. of cloth in one piece and IJyd. in another, how much have we in both? 2. If we buy 1^ yd. of one kind of ribbon and |- yd. of another kind, how much do we buy in all? Add tlie following : 3. 31 + 1 8. 3J + |. 13. 3J + f. 4. 3f + 2f . 9. 7-|- + 9f . 14. 6 J + 7|, 5.21 + 1 10.21 + 31. 15. 3l + 2f 6. 31 + 2J, 11. 3| + 2f 16. 9| + 6f 7. 4f + 6f. 12. 3f + 5J. 17. 4f + 6|. 18. If a desk is 21 ft. long and 1^ ft. wide, what is the sum of the length and width of the desk ? Add the f allowing : 19. 21 + 11 25. 21 + 11 31. 41 + 11 20. 31 + 51. 26. 41 + 61. 32. 51 21. 8f + 5. 27. 6f + 81. 33. 3J 22. 4| + 6^-. 28. 7| + 2|. 34. 6J + 71. 23. 9f + 2f . 29. 61 + 5|. 35. 7-J- + If. 24. 5| + 2lf 30. 3f + 81. 36. 2f + 5f . 37. If you place a board | in. thick on a plank that is If in. thick, what is the total thickness ? 38. If you place a plank 1|- in. thick on a beam that is 8J in. thick, what is the total thickness ? 212 FRACTIONS Subtraction. 1. In making a picture frame Louis cut a piece of molding 5f in. long from a piece 8J in. long. How long was the piece that was left ? We see that 8$ - 5f = 3f We know from the pictures on page 209 that f = J, and so 3^ = 3^. That is, Louis has 3^- in. 'of molding left. 2. How much picture molding will Louis have left if he takes 2-| in. from 8 in. ? We know that 8 = 7f , because f = 1. We see that 7-f 2-J = 5|-, and so Louis has 5-| in. left. 3. How much picture molding will Louis have left if he takes 2J in. from 8J in. ? We see that } is greater than ^, and so we cannot take } from J. - _ - _ - We see that 8J = 7 + 11 = 7|. Z * " 2 * " ** We know that f = f . So we can take 2} from 7}. The answer is 5}, and so Louis has 5} in. left. WRITTEN EXERCISE 1. If from 10 yd. of cloth we cut 21 yd., how much cloth is left? 2. If from 15 yd. of ribbon we cut 5} yd. and 1J yd., how much ribbon is left ? Subtract the following : 3. 5l-f. 5.5-11 7.2-}. 9.71-5}. 4. 7| - f 6. 7 - 31 8. 51 - 31. 10. 81 - 4}. MEASURES 213 VIII. MEASURES ORAL EXERCISE 1. How many pints are there in a quart? 2. A pint is what part of a quart ? Liquid Measure. The table of liquid measure is as follows 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal.) Express the following as pints : 3. 2qt. 5. 5qt. 7. 7 qt. 9. 10 qt. 4. 11 qt. 6. Iqt. 8. 1J qt. 10. 21 qt. Express the following as quarts : 11. 2pt. 13. 4pt. 15. 8pt. 17. 10 pt. 12. 20 pt. 14. 1 gal. 16. 2 gal. 18. 4 gal. Illustrative Problems. 1. Express 7 qt. as pints. Since 1 qt. = 2 pt., therefore 7 qt. = 7 x 2 pt., or 14 pt. 2. Express 36 qt. as gallons. Since 1 qt. = \ gal., therefore 36 qt. = 36 x l gal., or 9 gal. Pupils at this stage of their work are not expected to explain such reductions very elaborately. The above forms are accurate, but a pupil might properly think, for example, that there are 4 qt. in 1 gal., and in 36 qt. there are as many gallons as 36 -f- 4, or 9 gal. 214 MEASUEES WRITTEN EXERCISE Express the following as quarts: 1. 75 gal. 3. 48 pt. 5. 175 gal. 7. \ gal. 2. 145 gal. 4. 98 pt. 6. 180 pt. 8. 11 gal. Express the following as gallons : 9. Sqt. 11. 96 qt. 13. 168 qt. 15. 240 qt. 10. 36 qt. 12. 96 pt. 14. 168 pt. 16. 240 pt. 17. If Martha's mother buys 2 qt. of milk to-day and pays 8$ a quart, how much does the milk cost ? How much is she paying for each pint of milk that she buys ? How much would a gallon of milk cost? 18. If Mr. Lane, the grocer, buys 60 gal. of vinegar, and puts it up in quart bottles for sale, how many quart bottles can he fill ? How many pint bottles could he fill ? 19. If the milkman charges 30 a pint for cream, how much does he charge a quart ? If he has a gallon of cream and sells it all, how much does he get for it ? 20. If mother buys a gallon of molasses and uses a pint each day in cooking, how long will the molasses last ? 21. How many pint bottles can a dealer fill from 75 qt. of milk? Oral and written work of this kind should be given to show the relations of the parts of each table, one to another. This textbook furnishes plenty of such abstract work, but the teacher may profitably supplement it by home problems made by the class and representing prices in the community. There should also be given simple exercises in estimating the capacity of boxes, glasses, pitchers, and the like, in the schoolroom. TIME MEASURE 215 Time Measure. The table of time is as follows : 60 seconds (sec.) = 1 minute (min.) 60 minutes = 1 hour (hr.) 24 hours = 1 day (da.) 7 days = 1 week (wk.) About 4 weeks = 1 month (mo.) 12 months = 1 year (yr.) 100 years = 1 century The days of the week are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday. The months of the year and the number of days in each month are as follows : January, 31 da. July? 31 da. February, 28 or 29 da. August, 31 da. March, 31 da. September, 30 da. April, 30 da. October, 31 da. May, 31 da. November, 30 da. June, 30 da. December, 31 da. Thirty days has September, April, June, and November. February has 28 days except in a leap year, when it has 29 days. Until the year 2100, every fourth year is a leap year; that is, 1916, 1920, 1924, and so on, are leap years. Ordinary years have 365 days ; leap years have 366 days. There are 52 weeks and 1 day in an ordinary year. Every morning the teacher should have some of the pupils write on the blackboard the day of the week and the day of the month. 216 MEASURES ORAL EXERCISE 1. What month is this ? What was last month ? 2. What is next month ? the month after that ? . 3. Name the months of the year. 4. Name the days of the week. What day is this ? 5. What months have thirty days ? 6. How many days are there in this month ? 7. What day of the month is this ? 8. On what days of the week do you go to school ? The pupil should be taught to understand the calendar, and the calendar for the month should be hung in the schoolroom. WRITTEN EXERCISE 1. How many days are 5 da. + 2 da.? How many weeks do they make ? 2. How many days are 7 da. + 7 da.? How many weeks do they make ? 3. How many weeks are 7 da. + 7 da. + 7 da. ? How many days in 2 wk.? in 3 wk.? 4. How many seconds are 2 x 30 sec.? How many minutes in 60 sec.? in 120 sec.? 5. How many seconds are 40 sec. + 20 sec. ? How many minutes ? How many minutes in 360 sec.? 6. How many seconds are 60 sec. + 60 sec. ? How many minutes? How many minutes in 600 sec.? 7. How many more days in January than in February of this year? MEASUEES 217 PROBLEMS WITHOUT NUMBERS 1. How do you multiply by a number of two figures, the right-hand figure being zero ? 2. How do you multiply a number representing dollars and cents by a number ending in zero ? 3. How do you divide a number ending in zero by a two-figure number ending in zero? 4. If a division is exact, the dividend is the product of what two numbers ? 5. How do you check the work in exact division? 6. How do you find a fourth of any number ? How do you find three-fourths of the number ? 7. How do you find three-fifths of any number ? 8. How do you add fourths and eighths ? fourths and halves ? halves and eighths ? 9. If you know how many quarts a can will hold, how do you find the number of pints ? 10. If you know the number of gallons a pail will hold, how do you find the number of quarts ? 11. How do you change pints to quarts? quarts to gallons ? 12. How would you find the number of seconds in an hour ? the number of hours in a week ? 13. How would you find the number of minutes in a day? in a week? in a year? 14. If you know the cost of milk by the quart, how do you find the cost by the gallon ? 218 EEVIEW IX. REVIEW WRITTEN REVIEW 1. A fruit train of 19 cars was loaded with oranges. If there were 324 boxes in each car, how many boxes were in the whole train? > 2. A bushel of corn weighs 56 Ib. How many bushels are there in 1792 Ib. of corn ? 3. A dealer sold 28 building lots at an average price of $366. How much did he receive for the lots? 4. If 27 typewriters cost a dealer $1701, how much does the dealer pay for each typewriter? 5. If a man spends $48 a year for cigars, how much will he spend for cigars in 25 yr. ? 6. A farmer raised 4212 bu. of corn on 78 acres. How many bushels did he raise per acre ? 7. If a man earns $3.20 a day, how much will he earn in 28 da. ? 8. How many square feet are there in a lot 120 ft. long and 58 ft. wide ? 9. How many steel rails each 33 ft. long will be re- quired for 5940 ft. of track? Remember that a track has two lines of rails. 10. In an orchard containing 1440 trees there are 45 rows of trees. How many trees are there in a row? 11. A man saved, $1260 in 28 months. How many dollars did he save a month? WRITTEN REVIEW 219 WRITTEN REVIEW Add the following : 1. 2. 3. 4. 5. 2473 2975 $2.75 $12.82 $25.85 4826 8372 3.86 4.96 17.68 6. 7. 8. 9. 10. 3426 5383 $4.75 $32.75 $53.42 4289 2468 2.68 18.26 26.89 2976 9289 3.42 4.98 14.93 Subtract the following : 11. 12. 13. 14. 15. 4012 9235 $7.61 $11.72 $91.26 3746 6842 2.95 6.85 13.41 Multiply or divide as 'indicated : 16. 17 x $2.75. 21. 14,620-37. 26. 228x228. 17. 23 x $1.86. 22. 42,836 + 74. 27. 346 x 482. 18. 48 x $12.62. 23. 53,000 -*- 75. 28. 527 x 693. 19. 56 x $27.35. 24. 48,125 + 25. 29. 648 x 987. 20. 74 x $68.75. 25. 81,348 - 46. 30. 209 x 209. Find the answers to the following : 31. | of 162. 34. of 275. 37. 16 qt. = (?) pt. ' 32. f of 168. 35. f of 176. 38. 16 gal. =(?)qt. 33. f of 225. 36. of 352. 39. 28 da. = (?) wk. EP 220 USING WHAT YOU HAVE LEARNED X. USING WHAT YOU HAVE LEARNED TAKING A TRIP 1. Arthur's father took him on a trip from Indianapolis to Chicago. They left at half past eleven in the morning and arrived at five in the afternoon. How long were they in taking the trip ? 2. It is 109^- miles from Cincinnati to Indianapolis, and 303| miles from Cincinnati to Chicago. How far is it on the trip that Arthur and his father took to Chicago ? 3. If the railroad charged for 195 miles, at 2$ a mile, how much did Arthur's father pay for a ticket for himself ? 4. They bought, for luncheon on the train, 8 sandwiches at 10$ each, 6 cookies at 10$ a dozen, and 4 oranges at 5$ each. How much did the luncheon cost ? 5. They left Chicago at 15 min. before one and reacheql Indianapolis at 6 o'clock. How long did this take ? PROBLEMS 221 6. Arthur and his father saw these prices at the lunch counter in the station : Sandwiches, 10 Cookies, 30 Coffee, 100 Oranges, 60 Milk, 100 Bananas, . 40 Oatmeal, 200 Apples, 30 Bread and milk, 150 Pies, 100 Cold ham, 250 Soup, 200 Cold beef, 250 Ice Cream, 200 From this list select five things that you would like to eat for luncheon, and find the cost. 7. If Arthur's father took 2 sandwiches, a cup of coffee, some cold beef, and an orange, what did his luncheon cost ? Use the above list in Exs. 7, 8, and 9. 8. If Arthur took a sandwich, a glass of milk, a piece of pie, and 2 cookies, how much did his luncheon cost ? 9. A man sat beside Arthur and ordered some oatmeal, a cup of coffee, some cold ham, and 2 bananas. How much did his luncheon cost ? 10. If Arthur's father paid 750 for a drive in a taxi, $1 for two rides in a bus, and 500 for delivering a trunk which he brought home, how much did he pay for all ? 11. Find the cost of a trip on which a man paid the following: ticket, $2.70; baggage, 500; luncheon, 650. 12. Find the cost of a trip on which a man paid the following : ticket, $7.60; sleeper, $1.75; dining car, $1.25; porter, 250; taxi, $1.25; hotel bill, $12.50. 222 LITTLE EXAMINATIONS XL LITTLE EXAMINATIONS L 1. 578 + 296. 5. 428 x 324. 9. 2568 - 321. 2. $2.75 + $3.69. 6.509x672. 10. l ft. = (?) in, 3.342-196. 7. 7344-36. 4. 24x86. 8. XC = (?). II. 1. 983 + 432. 5.286x981. 2. $4.87 + $3.73. 6.870x392. 3.481-296. 7.5304-26. 4.48x94. 8. LXXI = (?) III. 1.887 + 556. 5.534x787. 2. $2.88 + $1.97. 6.508x667. 3. 513-234. 7. 3968-31. 4.33x69. 8. XLI = (?). IV. 1. 789 + 987. 6. 609 x 770. 11. 240 min. = (?)sec. 2. $4.47 + $2.89. 7. 6952 - 44. 12. 40 qt. = (?) pt. 3. 812 - 296. 8. LXIV = (?). 13. 1 - f . 9. 4500-375. 14. l of 352. 10. 360x430. 15.6087-45. 6. 783 x 892. 7. 340 x 820. 8. 6336-48. 9. XCI = (?). 10. cix=m. 4. 77 x 98. 5. 642 x 889. V. 1. 276 + 688. 2. $3.39 + $2.47. 3. 723-465. 4. 64 x 39. 5. 680 x 732. 11. 60 gal. = (?)qt. 12. l of 729. 9. 2830-283. 10. 1200ft.= (?)yd. 11. 60qt.= (?)gal. 12.1 + 1 + 1 9. 6084-432. 10. 888ft. = (?)yd. 11. 40 pt. = (?)qt. 12.1 + 1 - 11. 8536-194. 12. 240sec. = (?)min. 13. 4 Ib. = (?) oz. 14. 64 oz. = (?)lb. 15. 300 x 5280. Teachers should read the note on page 52. CHAPTER V I. READING AND WRITING NUMBERS ORAL EXERCISE 1. Name the places from right to left as you have learned them in writing a number of five figures. 2. What is the smallest number and the largest number that can be written with five figures ? 3. If you add one to 99,999, what is the sum ? 4. Read these numbers : 1,000 10,000 100,000 200,000 300,000 900,000 125,000 275,000 468,921 237,630 342,275 407,507 WRITTEN EXERCISE Write in figures : 1. Seventy-five thousand, sixteen. 2. Two hundred thousand, four hundred six. 3. Five hundred fifty-five thousand, seven. 4. Nine hundred ninety-nine thousand, nine hundred. Write in ivords : 5. 125,050. 7. 500,005. 9. 100,100. 6. 304,004. 8. 101,010. 10. 123,456. 223 224 READING AND WRITING NUMBERS Million. There is a special name for a thousand thousand. This number is called a million, and is written 1,000,000. We count millions just as we count thousands. That is, 5,000,000 is 5 million, 273,000,000 is 273 million, and 170,050,270 is 170 million, 50 thousand, 270. For easy reading we separate by commas the figures of a large number into groups of three, always beginning at the right, thus : 175,926,284. All these groups must have three figures, except the left-hand one ; thus : 1,275,340 30,000,000 425,000,723 21,426,580 120,000,000 196,481,278 The name of the first group at the right is ones ; of the second group, thousands ; of the third group, millions. ORAL EXERCISE Head these large numbers : 1. 1,253,429 28,276,390 126,289,000 2. 2,426,000 43,070,001 342,428,476 WRITTEN EXERCISE Write in figures : 1. Sixteen million, two thousand, nine. 2. Seventy-one million, five hundred seventy. 3. Sixty-two million, four thousand, six. 4. Four hundred seventy-nine million. 5. Five hundred fifteen million, three hundred. 6. Six million, ninety-three thousand, seventeen. ADDITION 225 II. ADDITION ORAL EXERCISE To each of the following numbers add 2, 3, 4, 5, 6, 7, 8, and 9, in turn : 1. 27 26 45 74 33 52 21 96 2. 82 83 38 62 17 15 34 61 To each of the following add 10, 11, and 20, in turn : 3. 4 12 49 24 14 23 16 21 4. 7 20 13 38 19 27 66 90 WRITTEN EXERCISE 1. Indiana contains 36,350 square miles ; Iowa contains 56,025 square miles; Illinois, 56,650 square miles. What is the combined area of these states ? 2. A farmer sells six loads of hay. The first weighs 2430 lb.; the second, 2350 lb.; the third, 2160 lb.; the fourth, 1960 lb.; the fifth, 2140 lb.; the sixth, 1860 lb. How much do the six loads weigh together ? Add the following numbers : 3. 4. 5. 6. $227.75 $476.68 $883.60 $342.98 184.84 204.69 445.38 38.28 68.09 30.84 268.84 194.45 224.65 26.85 97.25 230.68 80.75 342.68 684.06 49.95 226 SUBTRACTION III. SUBTRACTION ORAL EXERCISE 1. State rapidly the remainders: 37 37 37 37 37 46 52 _7 10 17 _8 18 18 22 From 92 subtract tlie following numbers : 2. 10 20 40 52 62 47 3. 12 22 42 53 64 14 27 4. Louise spent 64 < for Christmas and Clara spent 32$. How much more did Louise spend than Clara ? 5. Grandfather is 85 years old and father is 50 years old. How much older than father is grandfather ? WRITTEN EXERCISE Subtract and check : 1. 2. 3. 4. $994.83 $607.64 $813.80 $970.50 538.80 249.89 396.78 448.68 5. 6. 7. 8. $765.08 $376.30 $940.60 $880.60 259.69 267.95 430.54 479.95 9. 10. 11. 12. $972.58 $896.20 $878.69 $890.25 348.99 798.43 362.90 86.09 MULTIPLICATION 227 IV. MULTIPLICATION ORAL EXERCISE 1. Recite the multiplication table of 5's. 2. Recite the multiplication table of 6's. 3. Recite the multiplication table of 7's. 4. Recite the multiplication table of 8's. 5. Recite the multiplication table of 9's. 6. If 1 doz. cans of soup cost $2, what will 42 doz. cans cost ? What will 50 doz. cans cost ? 7. If 1 doz. jars of meat extract cost $8, what will 30 doz. jars cost ? What will 40 doz. jars cost ? 8. If 1 doz. cans of lobster cost $3, what will 22 doz. cans cost ? What will 33 doz. cans cost ? WRITTEN EXERCISE Multiply the following : 1. $243 by 22. 11. $924 by 43. 21. $723 by 64. 2. $315 by 73. 12. $672 by 94. 22. $825 by 35. 3. $465 by 54. 13. $941 by 85. 23. $732 by 45. 4. $572 by 25. 14. $682 by 69. 24. $417 by 53. 5. $485 by 62. 15. $617 by 82. 25. $525 by 64. 6. $564 by 47. 16. $426 by 91. 26. $812 by 14. 7. $259 by 57. 17. $324 by 28. 27. $476 by 42. 8. $538 by 38. 18. $416 by 29. 28. $385 by 74. 9. $467 by 59. 19. $675 by 25. 29. $416 by 46. 10. $635 by 92. 20. $530 by 24. 30. $625 by 62. 228 MULTIPLICATION Three-Figure Multiplier. Mr. Greene bought three farms, the first containing 120 acres ; the second, 116 acres ; and the third, 102 acres. If he paid $125 an acre for all the land, how much did each farm cost him ? We see that we must find three products, 120 x $125, 116 x $125, and 102 x $125. We learned on pages 180 and 181 how to multiply by three-figure numbers. Study these three multipli cations : $125 120 $125 116 $125 102 2500 125 750 125 125 250 125 $15000 $12750 $14500 We see that the first farm cost $15,000; the second, $14,500 ; and the third, $12,750. WRITTEN EXERCISE Multiply the following : 1. 115 x 136. 2. 225 x 475. 3. 142 x 387. 4. 268 x 491. 5. 380 x 662. 6. 132 x 390. 7. 243 x 487. 8. 161 x 296. 9. 314 x 417. 10. 180 x 672. 11. 201 x 325. 12. 208 x 362. 13. 405 x 488. 14. 507 x 983. 15. 16. 17. 18. 19. 20. 21. 708 x 807. 263 x 482. 478 x 298. 309 x 286. 440 x 555. 908 x 687. 693 x 447. THREE-FIGURE MULTIPLIER 229 WRITTEN EXERCISE Multiply the following : 1. 131 x 427. 7. 362 x 648. 13. 375 x 702. 2. 101 x 363. 8. 407 x 942. 14. 406 x 1475. 3. 242 x 787. 9. 387 x 682. 15. 368 x 3209. 4. 303 x 525. 10. 805 x 377. 16. 402 x 2008. 5. 575 x 766. 11. 994 x 782. 17. 498 x 2007. 6. 909 x 999. 12. 809 x 698. 18. 909 x 1009. 19. What will 225 acres of land cost' at $125 an acre? 20. A man buys 15 acres of land at $62.50 an acre, and 125 acres at $87.50 an acre. What does all the land cost? Find the cost of the following : 21. 121 locomotives at $9875 each. 22. 216 passenger cars at $3950 each. 23. 162 yd. of Wilton carpet at $1.65 a yard. 24. 272 yd. of silk at $1.15 a yard; at $1.25 a yard. 25. 112 building lots at $1375 each; at $1250 each. 26. 135 automobiles at $2450 each ; at $1875 each. 27. 102 farm wagons at $87.50 each ; at $92.25 each. Multiply the following : 28. $28.75 by 100 ; by 101 ; by 106 ; by 108 ; by 109. 29. $43.50 by 200 ; by 207 ; by 208 ; by 306 ; by 309. 30. $67.56 by 400 ; by 406 ; by 409 ; by 403 ; by 405. 31. $29.30 by 500; by 504; by 507; by 508 ; by 509. 32. $35.25 by 600 ; by 609 ; by 807 ; by 808 ; by 987. 230 DIVISION V. DIVISION ORAL EXERCISE 1. How many 10's in 30 ? in 100 ? in 700 ? in 1000 ? 2. How many 20's in 40 ? in 400 ? in 800 ? in 2000 ? 3. How many 100's in 300 ? in 700 ? in 1000 ? in 8000 ? 4. Divide the following : 500-10 500 -,50 500-100 500-500 Divisors Ending in Zeros. To divide 24,000, 24,357, and 25,357 by 2000, we proceed as follows : 2000)24000 2000) 240W 2000) 25gW 12 That is, we cancel (cross out) the zeros at the right of the divisor and cancel as many figures at the right of the divi- dend as we cancel zeros of the divisor, writing the complete remainder over the divisor. Canceling three figures divides by 1000, and because we divide the rest by 2, we really have divided by 2000. WRITTEN EXERCISE Divide the following : 1. 6000 - 300. 6. 4000 -* 200. 2. 6007 - 300. 7. 4009 -*- 200. 3. 6107 - 300. 8. 4109 -*- 200. 4. 60,107 - 300. 9. 102,107 - 6000. 5. 69,107 - 300. 10. 147,111 + 7000. THEEE-FIGURE DIVISOR 231 Three-Figure Divisor. To divide 12,525 by 501 we write the numbers in the same way as in other cases of division. Since 12 5 is a little more than 2, we see that 1252 -*- 501 is also more than 2, but less than 3. np- Since 2 x 501 = 1002, we subtract, and r r,-, N-io^ there is a remainder of 250 tens. 1002 2505 2505 Since we divided 1252 tens, we write the 2 in the quotient over the tens. Bringing down the next figure as usual, we have 2505. Since 2505 501 = 5, we write the 5 as the next figure. The quotient is therefore 25. Check. 25x501 = 12,525. If the quotient figure is taken too large, the partial prod- uct will be greater than the corresponding part of the dividend. In this case, try a smaller quotient figure. If the quotient figure is taken too small, the remainder will be greater than the divisor. In this case, try a larger quo- tient figure. WRITTEN EXERCISE Divide the following : 1. 1284-321. 7. 7398-274. 13. 2250-375. 2. 5733 - 273. 8. 3675 - 525. 14. 7446 - 219*. 3. 1415 - 283. 9. 3552 - 888. 15. 9174 - 278. 4. 8450 - 325. 10. 1926 - 321. 16. 7896 - 329. 5. 9683 - 421. 11. 3024 - 432. 17. 8536 - 388. 6. 9541 - 329. 12. 7011 - 171. 18. 5136 - 642. 232 DIVISION WRITTEN EXERCISE Divide the following 1. 15,000-125. 2. 29,000-125. 3. 17,250-125. 4. 25,984-116. 5. 77,604-116. 6. 86,229-201. 7. 76,708-302. 8. 50,470 - 245. 9. 93,632-176. 10. 87,143-211. 11. 93,860 - 247. 12. 91,739-199. 13. 85,158-249. 14. 87,648-249. 15. 87,318-231. 16. 91,791 - 217. 18. 84,300 - 281. 19. 17,000-125. 20. 16,875-125. 21. 29,375-125. 22. 51,736-116. 23. 52,576-212. 24. 28,644 - 231. 25. 70,512 - 226. 26. 32,568-236. 27. 79,442-314. 28. 69,834-226. 29. 72,670-215. 30. 79,692-229. 31. 82,450-194. 32. 79,808-5-232. 33. 78,200-184. 34. 69,687-267. ,594, what is the cost of 17. 65,649-237. 35. If 98 machines cost each machine? 36. If 175 tons of hay cost $2975, what is the cost of the hay per ton ? 37. If 405 sewing machines cost a dealer $14,175, how much did he pay for each machine ? MEASURES 233 VI. MEASURES ORAL EXERCISE 1. How many inches in 1 ft. ? in ^ ft. ? 2. How many feet in 1 yd. ? in -J- yd. ? in 1 J yd. ? 3. There is a measure called the rod. It is 16^- ft. long. How much does this lack of being 20 ft. ? It is how much more than 15 ft. ? Length. The following is the table of length : 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 16| feet = 1 rod (rd.) 5280 feet = 320 rods = 1 mile (mi.) The teacher should assist the pupils to visualize these basal units. In cities the number of blocks to the mile, the number of feet or rods in the width of the streets, and the average size of building lots should be known. In the country the rod and the mile are of particular importance in meas- uring the size of fields and the distance to the village. WRITTEN EXERCISE 1. How many feet in 3 yd. ? How many inches ? 2. How many feet in 1 mi.? in ^ mi.? in ^ mi.? 3. How many rods in ^ mi. ? in nii.? in mi. ? 4. How many inches in 1 yd.? in 1 rd.? in 1 mi.? 5. How many miles in 640 rd.? in 5440 rd.? 6. How many yards in 792 ft.? in 1065 ft.? 234 MEASURES ORAL EXERCISE 1. Estimate the length and the width of this room. 2. How high is the chalk rack from the floor ? 3. How high do you think the door is ? 4. How wide do you think the street is in front of the schoolhouse ? 5. How many inches do you step in taking a long step ? 6. Tell some place that is about a mile from the school- house. Teachers should make sure that the pupils have a definite idea of the value of each item in the various tables, and should fix these ideas of values by frequent reviews and drills in which the words are used concretely. They should use the blackboard, the schoolroom, floor, and the school yard to illustrate distances and areas. The pupils should learn to pace dis- tances. The distance from the school to some well-known point should be fixed as a standard mile to which the pupils can refer in making estimates. Much practice in estimating should be given, and the estimates should be followed by actual measurements. WRITTEN EXERCISE 1. Find the number of ounces in 14 Ib. 2. Find the number of pounds in 98 oz. 3. Find the number of quarts in 17 gal. 4. Find the number of gallons in 17 qt. 5. Find the number of pecks in 28 bu. 6. Find the number of bushels in 28 pk. 7. If you weigh 52 Ib., how many ounces do you weigh ? 8. If a street is 66 ft. wide, what is its width in yards ? SQUARE MEASURE 235 ORAL EXERCISE 1. A square is 3 ft. on a side ; what is the area? 2. What is the area of a square that is 12 int on a side? 3. How many feet in 1 yd. ? Then 1 ft. is what part of 1 yd. ? How many square feet in 1 sq. yd. ? Square Measure. The following is the table of square measure : 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30j square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) In the country special care should be taken to visualize the acre by pointing out fields that contain an acre or a definite number of acres. The teacher should review page 151 at this time. WRITTEN EXERCISE 1. How many times is 9 sq. ft. contained in 144 sq. ft.? How many square yards in 144 sq. ft.? 2. How many square yards in an oblong 30 yd. long and 8 yd. wide ? Draw the figure, using J in. to a yard. We speak of such, a rectangle as being 8 yd. by 30 yd. in size. Find the areas of the following rectangles: 3. 32 ft. by 52 ft. 6. 19 yd. by 37 yd. 4. 58 yd. by 63 yd. 7. 43 ft. by 98 ft. 5. 16 ft. by 121 ft. 8. 69 ft. by 248 ft. 236 MEASURES ORAL EXERCISE 1. If you were to speak of the length of your state, would you speak of it by miles or by feet? 2. If you were to measure your schoolroom, would you measure by miles, or by feet, or by inches ? 3. If you were to measure your finger, would you meas- ure by yards, or by feet, or by inches ? 4. If asked your age, would you answer in years or in weeks ? If asked how long before you go home to-day, how would you answer ? Unit of Measure. When we measure anything by feet we call the foot the unit of measure. So if we measure weight by the pound, the pound is the unit of measure. In measuring great lengths we use the mile as the unit. For lengths less than 1 mi. we often use the rod or the yard. For short lengths we often use the foot or the inch. MEASURING 1. Measure the length of the room, using 1 ft. as the unit ; using 1 yd. as the unit. 2. Measure the length of the desk, using 1 ft. as the unit ; using 1 in. as the unit. 3. Measure the height of the desk, using 1 ft. as the unit ; using 1 in. as the unit. 4. Imagine a square 36 in. on a side. Find its area, using 1 sq. ft. as the unit ; also using 1 sq. yd. as the unit ; also using 1 sq. in. as the unit. DBA WING TO SCALE 237 DRAWING TO SCALE 1. If we draw a picture of a doll's house, and make it \ as long and ^ as high as the house, we say that we draw the picture to the scale of 1 to 4, or to the scale ^. Every inch in length is then represented by J in. We may draw to other scales. If we represent 1 ft. by 1 in., we say that we draw to the scale of 1 in. to 1 ft. Since there are 12 in. in 1 ft. we also say that we draw to the scale of 1 to 12, writing this as the scale y 1 ^-. A B i i The line AB drawn to the scale ^. i I The line AB drawn to the scale ^. I I The line AB drawn to the scale J. I 1 2. If we draw to the scale ^-, by what length shall we represent a line 4 in. long ? 3. If we draw to the scale ^, by what length shall we represent a line 12 in. long? a line 15 in. long? 4. If we draw to the scale ^-, by what length shall we represent a line 40 in. long? a line 36 in. long? 5. Draw a line to the scale \ to represent 16 in. Draw lines to the given scales to represent these lengths : 6. 10 in., \, 9. 24 in., J. 12. 20 in., ^ 7. 15 in., l. 10. 24 in., l. 13. 30 in., ^ 8. 12 in., 1. 11. 24 in., f 14. 36 in., f We frequently write 4' for 4 ft., 4" for 4 in., 4' 8" for 4 ft. 8 in., and so on. 238 MEASURES ORAL EXERCISE 1. Here is a rectangle 2" long by 1" wide. It is di- vided into eight squares, each of which is ^" on a side. If we make a drawing of this rectangle, making each line half as long as it is _ _ _ _ _ here, we have the lower rectangle. We then say that we have drawn the rectangle to the scale ^, or 1 to 2, or 1" to 2". 2. A plan of a box lid is drawn to the scale ^. The drawing is 4" long. What is the length of the box lid ? 3. In a plan of a room the scale is 1" to 1'. The plan is 14" by 16". What is the size of the room ? 4. A drawing is made of a leaf of a notebook. The drawing is 2" by 3" and the scale is ^. What are the di- mensions of the leaf ? 5. A drawing is made of the cloth back used in binding a book. The drawing is 1" by 3" and the scale is J. What are the dimensions of the cloth ? WRITTEN EXERCISE 1. Make the drawing mentioned above in Ex. 2. 2. Make the drawing mentioned above in Ex. 3. 3. Make the drawing mentioned above in Ex. 4. 4. Make the drawing mentioned above in Ex. 5. AREAS 239 ( r 1 ^ WRITTEN EXERCISE Find the areas of the following rectangles : 1. 6 ft. by 17 ft. 8. 19 ft. by 72 ft. 2. 12 ft. by 27 ft. 9. 32 in. by 47 in. 3. 21 in. by 53 in. 10. 67 in. by 82 in. 4. 12 yd. by 25 yd. 11. 33 yd. by 47 yd. 5. 26 yd. by 48 yd. 12. 54 ft. by 96 ft. 6. 22 yd. by 75 yd. 13. 29 in. by 38 in. 7. 23 rd. by 75 rd. 14. 43 mi. by 62 mi. 15. Draw a picture of a square 2 ft. on a side, using ^ in. to represent a foot. This is called drawing to a scale of |- in. to 1 ft. 16. Draw a picture of a rectangle 2 yd. wide and 3 yd. long, on a scale of 1 in. to the yard. 17. It is 32 in. around a square. What is the length t#^~ of each side? How many square inches does the square contain ? 18. A farmer has a field 40 rd. long and 16 rd. wide. How many square rods does it contain? 19. A sidewalk is 95 ft. long and 5 ft. wide. How many square feet of area in the walk ? 20. A garden is 14 rd. long and 7 rd. wide. What is its area in square rods ? If the class has not learned the meaning of right angle, acute angle, and obtuse angle, these should be explained before proceeding to page 240. The terms "horizontal," " vertical," and "perpendicular" should also be explained at this time. 240 MEASURES ORAL EXERCISE 1. Which of these three triangles has an obtuse angle ? What kind of a triangle is it ? 2. Which of these triangles has a right angle ? Point to the right angle. What kind of a triangle is it ? 3. In which of the triangles are all of the angles acute ? What kind of a triangle is it ? 4. What kind of a triangle can you make with three narrow strips of paper 3 in., 4 in., and 5 in. long ? Triangles. A triangle having a right angle is a right triangle. A triangle having an obtuse angle is an obtuse triangle. A triangle having three acute angles is an acute triangle. The pupils should have plenty of practice in drawing these figures. WRITTEN EXERCISE 1. How far is it around a triangle whose sides are 14 ft., 12 ft., and 12 ft.? 2. Draw any acute triangle with two of its sides 2 in. and 3 in. Measure the third side and find how far it is around the triangle. 3. Draw a right triangle with the shortest side 1 J in., and the next longer side 2 in. Measure and find the length of the longest side. VOLUMES 241 ORAL EXERCISE 1. How many cubic inches are there in a block 1 in. long, 1 in. wide, and 1 in. high ? 2. How long is the edge of a cube which con- tains 1 cu. in. ? How long is the edge of a cube which contains 1 cu. ft. ? We write cu. in. for cubic inches and cu. ft. for cubic feet. 3. How many cubic inches are there in a block 3 in. long, 1 in. wide, and 1 in. high ? The teacher should use three 1-inch cubes, or should draw the figure. 4. How many cubic inches are there in a block 3 in. long, 2 in. wide, and 1 in. high ? The teacher should use six 1-inch cubes, or should draw the figure. 5. How many cubic inches are there in a block 3 in. long, 2 in. wide, and 4 in. high ? Since a block 1 in. long, 1 in. wide, and 1 in. high contains 1 cu. in., a block 3 times as long contains 3 x _ 1 cu. in., or 3 cu. in., and a block 2 times as wide contains 2 x 3 cu. in., or 6 cu. in., and a block 4 times as high contains 4 x 6 cu. in., or 24 cu. in. That is, 2 x 3 x 4 cu. in. = 24 cu. in. 6. How many cubic inches are there in a block 3 in. long, 2 in. wide, and 2 in. high ? The teacher should see that the pupils understand informally the mean- ing of the words cube, solid, volume, and dimensions, and should state to the class that the blocks and boxes which we shall measure have square cor- ners. Such a long term as rectangular solid need not be used at this time. 242 MEASURES ORAL EXERCISE 1. The cube A is how many times the block .5? 2. The block B is how many times the cube C ? 3. A cube that is 3 ft. on an edge is how many times as large as a cube that is 1 ft. on an edge? 4. How many feet in 1 yd.? Then how many cubic feet in 1 cubic yard ? 5. How would you find the number of cubic inches in 1 cu. ft. ? Multiply on the blackboard and find this number. Cubic Measure. The following is the table of cubic measure : 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) WRITTEN EXERCISE 1. A bin is 3 ft. by 5 ft. by 2 ft. It holds how much more than 1 cu. yd. ? 2. A box is 8 in. by 20 in. by 10 in. It holds how much less than 1 cu. ft. ? 3. How many cubic yards in a bin 6 ft. by 9 ft. by 3 ft. ? Find the volume of solids whose dimensions are : 4. 12 in., 19 in., 14 in. 6. 6 ft., 138 ft., 2 ft. 5. 27 in., 43 in., 32 in. 7. 2 yd., 698 yd., 1 yd. VOLUMES 243 ORAL EXERCISE 1. How many cubic feet in 10 cu. yd. ? 2. How many cubic yards in a cellar 5 yd. by 10 yd. by 2 yd. ? in a cellar 4 yd. by 5 yd. by 3 yd. ? 3. How many cubic inches in a box 3 in. by 4 in. by 5 in. ? in a box 4 in. by 5 in. by 7 in. ? 4. How many cubic inches in a cube 2 in. on an edge ? State the volume of boxes of the following dimensions : 5. 2 in., 3 in., 5 in. 9. 4 in., 5 in., 6 in. 6. 3 in., 4 in., 10 in. 10. 5 in., 7 in., 6 in. 7. 2 in., 5 in., 10 in. 11. 4 in., 5 in., 10 in. 8. 2 in., 4 in., 6 in. 12. 3 in., 5 in., 10 in. WRITTEN EXERCISE 1. How many cubic inches in an aquarium 16 in. long, 8 in. wide, and 9 in. deep ? 2. How many cubic feet in a wall 36 ft. long, 30 ft. wide, and 2 ft. thick ? 3. A cistern is 6 ft. square at the bottom and 5 ft. deep. How many cubic feet of water will it contain ? 4. A water tank is 8 ft. long, 6 ft. wide, and 4 ft. deep. How many cubic feet of water will it contain? 5. A cellar is to be dug 19 ft. by 25 ft. by 6 ft. How many cubic feet of earth must be taken out ? 6. A coal bin is 22 ft. long, 15 ft. wide, and 7 ft. deep. How many cubic feet of coal will it contain? 244 MEASURES ORAL EXERCISE 1. This boy is 4 ft. tall. Estimate the dimensions of this woodpile. Do you know the name of this amount of wood? 2. A pile of wood is 8 ft. long, 4 ft. wide, and 4 ft. high. How do you find the number of cubic feet it contains ? Read and learn this table : 128 cubic feet = 1 cord (cd). Wood is sold by the cord. Stand 8 ft. from the front of the room and 4 ft. from the side, and hold your hand 4 ft. from the floor, so as to show the size of a cord. 3. How much will 9 cd. of wood cost at $4 a cord? 4. How much will 7 cd. of wood cost at $5 a cord ? 5. How many cords of wood in a pile 16 ft. long, 4 ft. wide, and 8 ft. high ? MEASURES OF WEIGHT 245 ORAL EXERCISE 1. Meat is sold by the pound. Candy is sold by the pound. Pepper is sold by the ounce. Do you know how coal is sold ? Do you know how hay is sold ? 2. Can you name anything else that is sold by the ounce ? by the pound ? by the ton ? 3. How many ounces are there in a pound? How many pounds in a ton ? Weight. The following is the table of weight : 16 ounces (oz.)=l pound (Ib.) 2000 pounds =1 ton (T.) The ton is used in weighing substances sold in heavy loads, like coal, hay, building stone, and iron. WRITTEN EXERCISE 1. At $12.75 a ton, what will 17 T. of hay cost? 2. At $5.50 a ton, what will 34 T. of coal cost? 3. At $36.60 for 6 T., what will 1 T. of coal cost? 4. When coal is worth $7.25 a ton, what will 9 T. cost? 5. When hay is worth $13.25 a ton, what will 7 T. cost ? 14T.? 19 T.? 28T.? 37T.? 49T.? 6. What will 17 T. of coal cost at $4.75 a ton ? 7. What will 26 T. of coal cost at $4.95 a ton ? at $5.30 a ton? at $5.80 a ton? at $6.25 a ton? 8. What does hay cost a ton when 9 T. cost $116.10? 9. What is hay worth when 21 T. cost $270.90 ? 246 USING WHAT YOU HAVE LEARNED VII. USING WHAT YOU HAVE LEAKNED A BOY SCOUT CLUB 1. These Boy Scouts earned the money for their uni- forms. The hats cost $1.15 each, the coats $1.25, the trousers $1, the leggings 55$, and the shirts $1. Find the cost of the suits for the five boys shown in the picture. 2. The patrol leader decided to add to his outfit a belt at 40$, a canteen at 50$, and a haversack at 75$. He handed the salesman a $2 bill. What change was due ? 3. For their hikes they bought a stewpan at 80$, a water pail at 25$, a coffeepot at 60$, and a ring stand at 20$. How much did they pay for all these ? 4. For luncheon one day they took Frankfurters at 30$, buns at 18$, mustard at 5$, pie at 20$, and 2 qt. of milk at 8$ a quart. Each boy paid 10$ for car fares. How much did the five boys pay in all ? SCOUT CAMP 247 GOING TO SCOUT CAMP 1. The patrol of a Scout company consists of 8 boys. They raised money by an entertainment to go into camp for two weeks. They took in $62.40, and their expenses were $4.80. How much was left for going to camp ? What was each boy's share? How much more must each boy earn to start out with $12 ? 2. Each boy's expenses were as follows: railway fare, $1.04; fare on the boat, $1; street car, 15$; meals, going and returning, 78$; camp fee, $7.84. What was the total cost for each boy ? What was the total cost for the patrol ? 3. If each boy started with $15, how much had he left for spending money after paying his share as found in Ex. 2 ? 4. One boy lost a $5 bill on the way to camp. You have found in Ex. 2 the total cost for each boy. Now tell how much he must borrow from the others to make up his expenses. 5. One of the boys became ill and had to return home at the end of a week. How much should he receive back on his camp fee ? 6. There were 84 boys in camp. If the fee of each was $7.84, what was the total amount paid in camp fees? 7. The boys walked 3|- mi. from the station to the camp grounds at Scout pace, which is 1 mi. in 12 min. How long did it take to go this distance ? Find 3 x 12 min., then f of 12 min., and then add the results. 8. If a patrol starts on a hike at 15 min. before 10 and returns at 10 min. after 12, how long are the boys out ? 248 FRACTIONS VIII. FRACTIONS Terms of a Fraction. To take | of this rectangle, we divide the rectangle into 8 equal parts and take 3 of these parts. In the fraction f, the number 3 is O 9 called the numerator, and it tells how many equal parts we take. In the same fraction 8 is called the denominator, and it tells the number of equal parts into which the rectangle has been divided. 3 = numerator 8 = denominator The numerator and denominator are called the terms of the fraction. The terms of the fraction -| are 3 and 8. A whole number, like 2, 7, or $10, is called an integer. An integer and a fraction together are called a mixed number; as 2|, $4|. A fraction that is less than 1 is called a proper fraction; QQ 1 3. 2 aS 2> 4> 5"' A fraction that is equal to 1 or greater than 1 is called an improper fraction ; as ^, |-, f, ^. "We see that we can write improper fractions as whole numbers or as mixed numbers. For example, | = 1 f = ll J = l | = 1J 6=1 = ! This work in fractions covers what is usually given in Grade IV. It is slightly more extended than that required by the minimum course of study in some places and may, therefore, be shortened if the teacher desires. It is given in this form so that teachers who wish the material need not go outside the textbook to find it. FRACTION COLUMNS ORAL EXERCISE 249 4 5 6 7 4 4 5 5 6 6 7 7 444 555 666 777 4444 5555 6666 7777 4 81216 5 10 15 20 6 12 18 24 7 14 21 28 If we look at these columns and the sums, we see that 4 is \ of 8, 12 is f- of 16, and so on. Point to the columns representing the following numbers, and tell the answers in all cases : 1. 10, 1 of 10, f of 10. 2. 15, i of 15, | of 15. 3. 14, 1 of 14, | of 14, | of 14. 4. 21, 1 of 21, | of 21, f of 21. 5. 28, 1 of 28, f (or 1) of 28, f of 28. 6. 12, 1 of 12, f of 12, 1 of 12. 7. 18, 11 times 18, 1 of 18, f of 18. 8. Think of J of each of the following numbers, and then state - of each: 9 6 12 3 21 30 33 36 9. Think of \ of each of the following numbers, and then state f of each : 32 40 12 24 20 28 36 44 250 FRACTIONS ORAL EXERCISE 1. How much is -| of 12 ? f of 12 ? 2. How much is J- of 20? f of 20 ? f of 20? 3. How much is 1 of 12 ? f of 12 ? l of 12 ? Find j, and then j, of 'the following : 4. 18. 5. 15. 6. 24. 7. 39. 8. 33. 9. 60. Find j, and then j, of the following : 10. 15. 11. 25. 12. 35. 13. 45. 14. 50. 15. 55. WRITTEN EXERCISE 1. Find l of 75, and then find f of 75. 2. Find l of 72, and then find f of 72. 3. Find l of 81, and then find f of 81. Find j, and then j, of the following : 4. 27. 5. 45. 6. 63. 7. 42. 8. 54. 9. 66. Find J, and then | and | , of the following : 10. 65. 11. 30. 12. 85. 13. 40. 14. 80. 15. 95. Using a ruler, or the edge of a piece of paper on which inches have been marked, draw lines of the following lengths, and then mark off the parts stated : 16. 2 in., J of 2 in. 19. 1J in., f of 1J in. 17. 11 in., f of 11 in. 20. 2J in., l of 21 in. 18. 21 in., f of 21 in. 21. 4J in., f of 4J in. FRACTIONAL PAKTS 251 ORAL EXERCISE 1. How many fourths of a square in 1 square? How many fourths of an apple in 1 apple? How many fourths in 1 ? 2. How many fourths of a square in ^ of the square? How many fourths of anything in 1 of it? in | of it? in f of it? 3. How much is 1 of 24 ? of 24 ? l of 24 ? How does f compare with \ ? with f ? 4. How do you find \ of a number ? Then how do you find % of it ? |- of it ? Is there any easier way of finding of a number ? 5. How much is 1 of 16 ? of 16 ? J of 16 ? 6. How much is 1 of 48 ? 4 of 48 ? l of 48 ? o O 7. How much is 1 of 36 ? f of 36 ? i of 36 ? 8. Which will buy the more candy, a half dollar, two quarters, or five dimes ? Why is this ? WRITTEN EXERCISE Draw lines and divide them into parts to show that : 7. = - 10- = - squares and divide them into parts to show that : 13.1 = }. 15. 1 = 4. 17. l = f 19. |=f 14. f = . 16. f = . 18. f = . 20. | = f. EP 252 FBACTIONS ORAL EXERCISE 1. Look at figure A and state how many sixths you see in one half. 2. Look at figure B and state how many eighths you see in one half ; in three quarters. 3. Look at figure C and state how many tenths you see in one half ; in one fifth ; in four fifths. Reduction. We see that f can be obtained from \ by multiplying both terms by 2, and that \ can be obtained from fy by dividing both terms by 5. That is, Both terms of a fraction may be multiplied by the same number without changing the value of the fraction. Both terms of a fraction may be divided by the same number without changing the value of the fraction. When we change the value of the terms without chang- ing the value of a fraction we reduce the fraction. When both terms cannot be divided by the same number, the fraction is said to be in lowest terms. To reduce a fraction to lowest terms, divide by the largest number that will divide both terms without a remainder. 8 8^4 2 ^77 = -7^ j = -^ , lowest terms. 1Z 1Z -v- 4 o In this example, 4 is said to be canceled from both terms when the work is written as here shown. REDUCTION 253 WRITTEN EXERCISE 1. Reduce the following fractions to halves : 2. Reduce the following fractions to fourths J2 4 16 10 20 18 8 8 ~8~ ~8~ ~8~ ~S~ 3. Reduce the following fractions to eighths 1 1 s. A 6. 1 _2_ JL. 2444 4 2 16 16 4. Reduce the following fractions to twelfths : 1111 2. 1 5. _2_ 2443 3 6 6 24 5. Reduce the following fractions to lowest terms : 2. 4. 1_0 JL 3- 4. 6. 5 488 10 6 6 8 TO" 6. Express ^ in. and -| in. as sixths of an inch, and tell which is the greater. 7. Express -| in. and ^ in. as twelfths of an inch, and tell which is the greater. 8. Express as sixths : -|, -|-, and J-. 9. Express as tenths : ^-, ^, |-, J-, and |-. 10. Express as fifteenths : -J, J, f, |-, f , and f. 11. Express as sixteenths : -|, |-, -|-, |-, -|, and |-. 12. Express -| as halves ; as fourths ; as sixteenths. 13. Reduce f to halves ; to fourths ; to sixteenths. 14. How many fourths in | ? in -| ? in -| ? 15. How many eighths in -| ? in ^ ? in 1 ? 16. How many tenths in ^ ? in \ ? in 1 ? 254 FRACTIONS Addition. If we ask for the sum of 3 boys and 2 girls, the answer cannot be boys alone, or girls alone. But we say, 3 boys = 3 children 2 girls = 2 children 5 children in all In adding, we think of things as having the same name. In the same way, if we wish to find the sum of J and |, we must think of these as f and J, the sum being f , or 1 J. In adding fractions we think of them as having the same name. ORAL EXERCISE 1. Express ^ as eighths. To the result add f . 2. If you are making the supports for a bookshelf and fasten a strip of molding J in. thick to a strip of wood f in. thick, how thick are the two together ? 3. Express as tenths. To the result add ^j-. 4. If you lay an arithmetic that is in. thick on a note- book that is ^j- in. thick, how thick are the two together ? 5. Express $ as sixths. To the result add . 6. If you sew a piece of cloth f yd. wide to a strip J yd. wide, how wide will the new piece be ? WRITTEN EXERCISE Reduce to the same denominator and add : I- i, t- 3. J, f 5. J, f 7. i, J. 2. J, f . 4. J, f . 6. J, J. 8. J, f . ADDITION 255 Addition of Fractions. Margaret had a lily given to her when it was only 3f in. tall. After it had grown to be 7f in. taller, how tall was the lily ? We see that we must add 3|^ in. and 7-| in. We found on page 254 that we must think of the frac- tions as having the same denominator. Teachers may, if they choose, speak of reducing the fractions to the least common denominator, or to fractions having the least common de- nominator. It is well, however, to use simple language at this time. In adding 3| and 7-|, we might think of both fractions as 12ths or as 24ths. But to save work it is better to use fractions having as small a denom- inator as possible. 64- = 9 If we think of the numbers which can be exactly divided by both 4 and 6, we see that the smallest is 12. We know this be- cause no number less than 12 is exactly divisible by 4 and 6. Therefore the smallest denominator that both fractions can have is 12. We also see that = 3^- and that f = JJ, because we may multiply both terms of by 3, and both terms of f by 2. Then the sum is 10^|, which equals 10 + 1^, or ll^. So the lily grew to be H^ m - The pupil is not expected to explain an example like this at present. Gradually, as here and on page 211, he should be led to add fractions in cases where the least common denominator can be seen by inspection. Unusual denominators, such as 7, 11, and 13, should not be used at this time. Even the illustrative problem given above, desirable as it is for purposes of illustration, is more difficult than is usually needed in business. 256 FEACTIONS WRITTEN EXERCISE 1. Add 21 lb., 61 lb, and 1J Ib. 2. Add 11 yd, 11 yd, and 21 yd. 3. The top of a teacher's desk is 41 ft. long and 3 ft. wide. What is the perimeter, that is, the distance around the top of the desk ? 4. Some boys built a hut 7J- ft. long and 5 ft. wide. What was the perimeter? 5. If a boy in this class weighs 66|- lb, and his dog 20 J lb, how much do they weigh together? 6. A lady bought three pieces of cloth, containing 17f yd, 16 J yd, and 23 J yd, respectively. How many yards did she buy ? 7. One pole is 10 J ft. long, another 10 J ft, a third 10^- ft, and a fourth 3 ft. What is their total length when placed end to end? 8. A man has 168J acres of land. He buys 3J acres from one neighbor and 49^ acres from another. How many acres does he then own ? 9. A kite string was broken, and four parts were saved. The first was 751 ft. long, the second 127f ft, the third 261 ft, and the fourth 89J ft. Allowing 1 ft. for tying, how long was the string when all four were tied together ? 10. Five cans of sirup were measured carefully and the first was found to contain 21 qt, the second 2f qt, the third 2^ qt, the fourth 2f qt, and the fifth 2J qt. How many quarts were there in all ? SUBTRACTION 257 Subtraction of Fractions. Mollie had a little rosebush given to her. It was then only 3^ in. tall. After it had grown to be 18|- in. tall her mother asked her how much it had grown. What should Mollie answer? We see that Mollie must subtract 3J in. from 18|- in. In subtraction, as in addition, we must think of the fractions as having the same denominator. The smallest denominator that we can use is 12. We see that |- = ^|, and that |- = ^-. 18f = 18if '12 Then 18| - 3f = 18fJ - 3 & = 15^. So Mollie should say that her bush had grown 15^ in. WRITTEN EXERCISE 1. If from a board ^|- in. thick we plane off -^ in., how thick is the board then ? 2. If a notebook is -^ in. thick and the cover is ^ i n - thick, how thick is the book without the cover? 3. If from a board |- in. thick we plane off \ in., how thick is the board then ? Subtract the following : 4. 1-1. 9. l-i. 14. 3f in. -11 in. 5. 1-1 10. f -1 15. 4|in.-2fin. 6.1-1 11. I- i- 16. 51 yd. -21 yd. 7.1-1 12. l-l 17. 7|yd.- 3| yd. 8. f-l 13.|-l 18. 8f in. -41 in. 258 ALIQUOT PAETS IX. ALIQUOT PAETS WRITTEN EXERCISE 1. Multiply 246 by 5. Divide 2460 by 2. Compare the results. 2. Instead of multiplying by 5, you may annex how many zeros and divide by what number ? 3. Multiply 224 by 25. Divide 22,400 by 4. Compare the results. 4. Instead of multiplying by 25, you may annex how many zeros and divide by what number? To multiply by 5, annex a zero and divide by . To multiply by 25, annex two zeros and divide by 4. 5. Divide 240 by 5. Multiply 24 by 2. Compare the results. 6. Instead of dividing tens by 5, you may cut off how many zeros and multiply by what number ? 7. Divide 300 by 25. Multiply 3 by 4. Compare the results. 8. Instead of dividing hundreds by 25, you may cut off how many zeros and multiply by what number ? To divide tens by 5, cut off a zero and multiply by 2. To divide hundreds by 25, cut off two zeros and mul- tiply by 4. MULTIPLICATION" 259 ORAL EXERCISE Multiply the following : 1. 86 by 5. 3. 84 by 25. 5. 88 by 25. 2. 44 by 25. 4. 48 by 25. 6. 124 by 5. Divide the following : 7. 110-5. 8. 320-5. 9. 800-25. Aliquot Part. An integer or a mixed number that will exactly divide a number is called an aliquot part of that number. Thus, $0.50 is l of $1 $0.331 i s l of $1 $0.25 is l of $1 $0.66| is f of $1 $0.121 i s i O f $1 $0.20 is J of $1 Hence, instead of multiplying $0.121 by 16 ? we ma y simply multiply $J- by 16, which is much easier. Teachers should show the pupils that 16 X $$ gives the same answer as \ of $16, and is an easier operation. They should also recognize that it is not necessary to label the numbers except when it adds to the clearness of a solution. That is, we may write " 16 x \ = 2," the number of dollars. WRITTEN EXERCISE Multiply the following : 1. 32 x $0.121 6. 120 x $0.66f . 2. 64 x $0.121 7. 375 x $0.331 3. 56 x $0.50. 8. 336 x $0.25. 4. 72 x $0.25. 9. 336 x $0.331 5. 96 x $0.331. 10. 666 x $0.331. 260 BILLS AND EECEIPTS X. BILLS AND RECEIPTS ORAL EXERCISE 1. What is meant by charging goods at a store ? 2. What is meant by having an account at a store ? 3. What is meant by a bill of goods bought at a store ? 4. What does this item mean: " 8 doz. eggs @ 30$"? Making out Bills. To foot a ~bill means to add the amounts and find the total cost. To receipt a bill means to stamp or write the words " Paid " or " Received Payment," followed by the date and by the name of the one to whom it is due. This is a receipted bill : Newark, N.J., March 1, 1919 Mr. David Brownson Bought of CHARLES DUNHAM Feb. \ 5 I 6 cans soup @ 20? \\ 1 \ 20 Received Payment, March 3, 1916 5. Study the bill and answer these questions : What does @ mean? What is the amount of the bill? When were the goods bought? When was the bill paid? Who was the buyer ? Who was the seller ? 6. What does the receipt show ? The teacher should encourage the pupils to make out bills of goods at prices current in the place where they live. The meaning of the term "debtor" and the abbreviation "Dr." should be explained. BILLS AND EECEIPTS WRITTEN EXERCISE 261 Copy, fill, foot, and receipt each of the following bills, dating it and the receipt at the place where you live, and signing your name as the clerk who received the money : 1. Mr. Robert Lee Bought of GEORGE HALL Jan. 9 & 9 doz. eggs 32? 9 Ib. butter 33? 5 6 Ib. cheese 22? Mr. James Keene Received Payment 2. Bought of B. S. OSBORNE & CO Oct. 3 12 yd. silk @ $1.00 9 yd. lace @ 75? 8 yd. ribbon, @ 30? 3. Mr. R. S. Bell Bought of McCLINTOCK & CO. Apr. 6 3 yd. silk @ 80? 2 doz. buttons @ 45? 15 12 yd. calico 7? 5 yd. lace @ 40? May 10 9 yd. linen @ 60? 2 yd. ribbon 75? 262 BILLS AND RECEIPTS Copy, fill, foot, and receipt the following, as on page 261: 4. [Name of place, and date] 19 M [Name] Bought of [Name] , Dealer in Meats and Poultry .[Date] 6 lb. roast beef @ 84? 6 lb. chicken @ 25? [Receipt] 5. [Name of place, and date] 19 _ M [Name] Bought of [Insert name of some grocer] , Grocer [Date] 4 lb. powdered sugar @ 7? 8 doz. eggs @ 85? | doz. oranges @ 60? [Receipt] 6. [Name of place, and date] 19 M [Name] Bought of [Name] , Grocer .[Date] 2 heads lettuce @ 5? 6 lb. butter @ 82? 4 gal. oil @ 18? " 8 lb. raisins @ 12? " 8 lb. coffee @ 80? [Receipt] BILLS OF GOODS 263 WRITTEN EXERCISE Make out bills for the following : 1. 15 Ib. granulated sugar @ 5$, 3 pk. fancy potatoes @ 25$, 4 cans salmon @ 8$. 2. 7 Ib. butterine @ 25$, 4 jars New Orleans molasses @ 20$, 2 packages raisins @ 9$, 5 boxes matches @ 4$. 3. 84 gro. bone buttons @ 18$, 694yd. cambric @ 17$, 72 doz. pearl buttons @ 9$, 364 yd. cashmere @ 82$. 12 dozen = 1 gross (gro.). Therefore 144 = 1 gro. 4. 8 doz. combs $1.95, 4 doz. brushes $18.37, 3 doz. atomizers @ $19.25, 4 gro. toothbrushes @ $9.35, ^ gro. nailbrushes $27.50. 5. 480 yd. matting 18$, 375 yd. matting @ 19$, 284 yd. carpet 48$, 8 rugs @ $7.33, 4 doz. doormats @ $6.75. 6. 9 dining-room sets @ $62.50, 16 rockers $5.35, 8 sideboards @ $32.50, 6 card tables @ $8.75, 4 china closets @ $17.50. 7. 325 yd. carpet @ 48$, 520 yd. matting @ 22$, 16 rugs $6.40, 4 rugs @ $12.50, 3 doz. doormats $7.30, 328 yd. calico @ 6$. 8. 8 doz. hatchets $10.75, 6 doz. pairs hinges $4.35, 5 doz. carpenter's squares @ $34.50, \ gro. locks $42.50, 8 doz. files $6.25. 9. 75 M (75,000) envelopes $2.30, 75 Ib. paper 22$, 4 doz. fountain pens $23.50, 10 doz. bottles ink @ 42$, 6 dictionaries @ $5.50. 264 GENERAL REVIEW XL GENERAL REVIEW WRITTEN EXERCISE 1. Frank's father had $1250 in a bank. He drew out $533 and afterwards $265. How many dollars did he still have in the bank ? 2. Charles has 250 chickens. In one yard he has 46 chickens ; in another, 35 ; and in another, 53. How many chickens has he that are not in these yards ? 3. Mary bought 8 yd. of cloth at 5< a yard. How much change should she receive if she gave the storekeeper a half dollar? 4. If 62 acres of land cost $992, how much will 1 acre cost ? How much will 40 acres cost ? 5. One house is valued at $7270 and another house at three times as much. How much are both together worth ? 6. If 6 overcoats cost $144, how -many overcoats can be bought for $1320 ? (First find the cost of one overcoat.) 7. Mr. Jackson had $700. How much money will he have left after buying a horse for $150, a wagon for $45, and 4 cows at $35 each ? 8. What is the cost of 15 yd. of velvet at $1.25 a yard and 5 yd. of ribbon at 37$ a yard ? 9. I have 63 bu. of corn in one bin, 54 bu. in another, 37 bu. in a third, and 29 bu. in a fourth. How many pecks of corn do I have ? Teachers will observe that the problems in this exercise are two-step problems. This type of problem has been approached gradually. PROBLEMS 265 10. What is the cost of 16 barrels of flour at $6.25 a barrel and 7 barrels of apples at $2.50 a barrel? 11. From a bin containing 516 bu. of oats, 65 bu. were sown and 73 bu. have been fed to horses. How many bushels of oats are left? 12. What is the cost of fencing a park 36 rd. long and 14 rd. wide at $2.50 a rod? 13. If a man having $1000 buys 5 horses at $152 each and spends the rest of his money for cows at $40 apiece, how many cows does he buy ? Take 5 x $152 from $1000, and then divide by $40. 14. At a rent of $23 a month for a house and $12 a month for a stable, what is the rent of both for 1 yr.? 15. What is the cost of 9 horses at $175.75 each and 76 tons of hay at $18.50 a ton? 16. Find the area of a field 40 rd. long and 24 rd. wide. Draw a plan of the field on the scale of \ in. to 4 yd. 17. A mile of gas pipe is laid at a cost of $5 a rod. What is the cost of laying the pipe? 18. At 40$ a dozen, what will 30 lemons cost ? 19. How many yards of braid will be required to bind a rug 5 ft. long and 3 ft. wide ? 20. If a man travels 70 mi. a day, how many days will it take him to make a trip of 1470 mi. ? Find how many times 70 is contained in 1470. 21. At $40 an acre, what will 2 eighty-acre farms cost? 22. How many Quarts in 248 pt.? How many gallons? 266 GENEKAL KEVIEW 23. A milk dealer sells every day 16 cans of milk, each holding 2 gal. How many quarts does he sell ? 24. A grocer bought 4 bu. of apples at 800 a bushel and sold them at 250 a peck. How much did he gain? 25. What is the price of a dozen oranges at the rate of 3 oranges for a dime? 26. A man earns 350 an hour and works 2 da. of 8 hr. each. How much does he receive ? 27. At 20^ a square yard, what will it cost to oil a floor 6 yd. long and 4 yd. wide ? 28. Draw a plan of the floor in Ex. 27 on the scale of \ in. to 1 yd. Find the perimeter of the room. 29. A carload of coal containing 30,000 Ib. was sold at $6 a ton. How much was received ? 30. How many cubic feet of stone in a wall 20 ft. long, 4 ft. high, and 2 ft. thick ? 31. Walter has 100 inch cubes. They are built into a solid 10 in. long and 2 in. wide. How high is the solid ? 32. How many pint packages can a seedsman fill from 2pk. 2qt. of seeds? 33. If a man earns $2 a day, how many days will it take him to earn $24 ? to earn $36 ? to earn $96 ? 34. A boy bought 4 doz. pencils at 350 a dozen and sold them at 40 apiece. How much did he gain ? 35. A peddler in a city buys a pushcart for $22. He has $14.75 of his own and borrows $3.50 from his brother. How much more does he borrow to buy the pushcart? PROBLEMS 267 36. A peddler bought 6 doz. oranges at 150 a dozen and sold them at 20 apiece. How much did he make on all the oranges? 37. A man bought 4 bunches of bananas. The first bunch contained 120 bananas; the second, 176; the third, 160; and the fourth, 240. He sold the bananas at the rate of 4 for 50. How much did he receive for them? 38. A workman in a factory makes 9 doz. caps a day. How many caps can he make in the 6 working days of a week ? How many can he make in 7 wk.? 39. If a workman uses 2 buttons on each cap that he makes, how many caps can be trimmed with 12 doz. buttons? How many can be trimmed with 24 doz. buttons? 40. A newsboy pays 30 for 5 newspapers. How much money must he have in order to buy 75 newspapers ? 41. A grocer sells 8 eggs marked 360 a dozen. How much change should he give for 250? 42. A boy runs on errands for a grocer. He gets his car fare and also 50 for each errand. How much does he get if he runs on 9 errands and pays 200 for car fare ? 43. A workman's wages are $2.50 a day, and he usually works 6 da. each week. This week he stays at home 2 da. How much will he find in his pay envelope at the end of the week? 44. Our class has 28 children. The teacher and the chil- dren go on a picnic and pay 100 each for car fare. They have $8.75 for the picnic. How much money is left for luncheon after paying all the car fares? 268 GENERAL EEVIEW PROBLEMS WITHOUT NUMBERS 1. If you know the cost of each of two different things, how do you find the cost of both together ? 2. If you know the number of feet in a piece of string, and cut off a part of the string, how do you find the length of what is left ? 3. If you know the cost of one yard of cloth, how do you find the cost of a given number of yards ? 4. If you have a certain number of inches of cloth of a certain width, and a book cover requires a certain number of inches of this width, how do you find the number of books you can cover with all the cloth? 5. If you know the number of quarts of milk in a can, how do you find the number of pints ? 6. If you know the length of a piece of picture molding in feet, how do you find the length in inches ? 7. How do you multiply a number of two figures by a number of one figure ? 8. What do you mean by drawing a line to a given scale, say, to the scale of 1 in. to a foot ? 9. How do you draw a rectangle to a given scale ? 10. How do you find the area of a rectangle ? Draw a rectangle to explain your answer. 11. Draw this page of the book to some scale, and write below the plan the scale that you have used. 12. Draw a plan of the top of your desk to some scale, and write below the plan the scale that you have used. USING WHAT YOU HAVE LEARNED 269 XII. USING WHAT YOU HAVE LEARNED THE SURPRISE PARTY 1. Fanny will be 9 years old next week, and the class is going to give her a surprise party. There are 17 boys and 19 girls besides Fanny. The boys agree to put in 150 apiece and the girls 100 apiece. How much will the boys put in ? How much will the girls put in ? 2. How much money will the boys and girls put in for Fanny's surprise party in Ex. 1 ? 3. They take out 750 for flowers. How much does that leave ? 4. With what is left, after taking out the money for the flowers, they think of buying a present for Fanny. They spend some of it, however, for candles for the cake, and have $3.50 left. How much did they spend for candles ? 5. They priced a watch and found that this would use half of the $3.50. What was the price of the watch? If they buy it, how much money will they have left ? 6. They bought the watch and then bought a silver bracelet for $1.50, and decided to give the rest to a poor woman whom Fanny liked. How much money did they give to the woman? 7. At the night of the party each of the 19 girls took 4 little cakes to the party. How many did they all take ? 8. Since the boys wanted to do their share, each one took 6 apples. How many apples did the 17 boys take ? 270 USING WHAT YOU HAVE LEABNED CAMP FIRE GIRLS 1. Camp Fire Girls are over 12 yr. old. In how many years and months, to the nearest month, will each girl in your class be old enough to be a member ? 2. A group of girls, not less than six nor more than twenty in number, can form a Camp Fire. In a certain town there are 7 Camp Fires, averaging 14 girls each. How many Camp Fire Girls are there in the town? 3. A Camp Fire of 14 girls found that they could buy their gowns for $2.50 each, or could buy the materials for $1.70 each. How much would they save in all by buying the materials and making their gowns? 4. There are three, ranks of Camp Fire Girls, the Wood Gatherer, the Fire Maker, and the Torch Bearer. In our camp there are 7 Wood Gatherers, each paying $1.70 for the materials for a gown. How much do the seven pay ? CAMP FIRE GIRLS 271 5. There were 4 Fire Makers in the camp. Each paid $1.50 for a Fire Maker's bracelet, $1.70 for materials for a gown, and $1.25 for a pair of moccasins. How much did each Fire Maker pay in all ? How much did all four pay ? 6. There were 3 Torch Bearers in the camp. Each paid $1.50 for a Torch Bearer's pin, 25$ for a Camp Fire hat- pin, 65$ for materials for bloomers, 30$ for a dozen Camp Fire buttons, and 25$ for a Torch Bearer's emblem. How much did each pay in all ? How much did all three pay ? 7. The Camp Fire Girls have many honors. For Home Craft Honors a girl must do things about the house. Among other things she must plan refreshments for a party of 10 girls, not spending more than $1. Make such a plan and bring the list, with prices, to school to-morrow. 8. For Hand Craft Honors a girl must do things with her hands, such as make a skirt. Find out how much the materials for a school skirt would cost, and bring the list, with prices, to school to-morrow. 9. The Camp Fire Girls often go out to camp. Eight of them, besides the Guardian of the Fire (making nine in all), went camping. They spent 40$ each for trolley fares, $1.60 each for railway tickets, $5.40 for the rent and car- riage of the tents for the party, and $24.44 for food and camp expenses for the party. How much did they spend in all ? How much should each contribute if the Guardian of the Fire had her expenses paid by the rest of the girls ? To many girls this subject of the Camp Fire Girls is of great interest. For such pupils these two pages are especially intended. Through the kind- ness of the national organization the illustration on page 270 is printed. 272 LITTLE EXAMINATIONS XIII. LITTLE EXAMINATIONS I. 1. 4856 + 9237. 6. 300 x $1.75. 2. 7902 - 5919. 7. 72 x $3.75. 3. $40.73 + $20.96. 8. 475 x 582. 4. $50.13 - $32.75. 9. 25,984 - 58. 5. 7 x $2.96. 10. 2 cu. ft. = (?) cu. in. II. 1. 8346 + 9078. 6. 400 x $2.40. 2. 3709 - 2963. 7. 38 x $4.22. 3. $30.82 + $52.86. 8. 287 x 496. 4. $52.32 -$29.56. 9. 7500-125. 5. 8 x $2.85. 10. 4 cu. ft. = (?) cu. in. III. 1. 4283 + 6296. 7. 68 x $5.37. 2. 4132 - 2876. 8. 394 x 498. 3. $40.27 + $32.96. 9. 14,500-125. 4. $60.01 -$19.83. 10. 288 sq. in. = (?) sq.ft. 5. 9 x $3.27. 11. 17bu. = (?)pk. 6. 520 x $3.04. 12. of 64. IV. 1. 7129 + 3786. 7. 49 x $7.72. 2. 5235 - 2868. 8. 778 x 642. 3. $23.49 + $87.62. 9. 38,802-116. 4. $52.29 -$26.60. 10. 9 sq. ft. = (?) sq. in. 5. 6 x $4.72. 11. 40 pt. = (?) qt. 6. 760 x $4.60. 12. | of 96. Teachers should read the note on page 52. WHAT THE PUPIL SHOULD KNOW 273 XIV. WHAT THE PUPIL SHOULD KNOW WHEN HE HAS FINISHED THIS BOOK YOU SHOULD ADD QUICKLY AND ACCURATELY Copy and add, timing yourself on each set often examples. 1. 4136 + 9287. 21. $52.43 + $48.76. 2. 3092 + 4768. 22. $524.30 + $48.76. 3. 4381 + 8092. 23. 5243 + 4876. 4. 5276 + 8397. 24. 8179 + 9283. 5. 4855 + 8762. 25. $81.79 + $92.83. 6. 3984 + 9876. 26. $817.90 + $928.30. 7. 8237 + 4583. 27. $54.62 + $87.96. 8. 5692 + 8173. 28. $78.37 + $49.87. 9. 8494 + 9877. 29. $70.36 + $89.09. 10. 4086 + 3790. 30. $37.49 + $98.97. 11. 6842 + 9382. 31. 428 + 396 + 987. 12. 7209 + 9089. 32. 629 + 438 + 909. 13. 8778 + 8296. 33. 778 + 896 + 408. 14. 4009 + 8999. 34. 539 + 683 + 997. 15. 6872 + 1983. 35. $5.28 + $4.96 + $3.74. 16. 4849 + 2183. 36. $52.80 + $4.96 + $37.40. 17. 7680 + 9398. 37. $52.80 + $4.96 + $3.74. 18. 4777 + 8643. 38. $128.90 + $34.76 + $48.23. 19. 5273 + 8556. 39. $12.89 + $34.76 + $48.23. 20. 4196 + 3784. 40. $12.89 + $347.60 + $428.30. Efficiency tests of this kind are helpful throughout the course, and many of them are provided in this book. 274 WHAT THE PUPIL SHOULD KNOW YOU SHOULD SUBTRACT QUICKLY AND ACCURATELY Copy and subtract, timing yourself on each set of ten examples : ^ 1. 7830^296^ 21. $29.60 -$3.48. 2. SlfeVfSSOl 22. $128.30 -$26.37. 3. 6209-4836. 23. $201.40 - $52.33. 4. 7108-2987. 24. $280.30 - $29.46. 5. 5633-1987. 25. $310.02 - $38.36. 6. 4206 - 1899. 26. $401.01 - $56.75. 7. 3837-1968. 27. $126.37 - $109.48. 8. 9001-2983. 28. $630.02 - $427.63. 9. 8002-3093. 29. $702.23 - $426.48. 10. 6277-4968. 30. $523.41 - $239.68. 11. 5307-2836. 31. $429.83 - $327.60. 12. 6612-4833. 32. $527.75 - $209.09. 13. 4702 - 3685. 33. $607.07 - $421.36. 14. 5211 - 2033. 34. $528.28 - $492.99. 15. 4787-2939. 35. $800.70 - $528.36. 16. 2192 - 1998. 36. $602.73 - $478.64. 17. 6070 - 3841. 37. $281.32 - $193.82. 18. 5791 - 2992. 38. $1026.00 - $873.75. 19. 6280 - 5691. 39. $2000.00 - $1482.60. 20. 2936 - 1987. 40. $2172.30 - $1986.45. In computing the time, the pupil should include the time of copying. In practical business we have to write the numbers as well as subtract them, and this is part of the training. The pupil should learn to write the numbers neatly and accurately as well as quickly. EFFICIENCY TESTS 275 YOU SHOULD MULTIPLY QUICKLY AND ACCURATELY Copy and multiply, timing yourself on each set of ten examples : 1. 29 x 38. 21. 121 x 342. 41. 2 x $48.72. 2. 42 x 70. 22. 426 x 809. 42. 3 x $96.80. 3. 63 x 96. 23. 707 x 556. 43. 5 x $40.75. 4. 45 x 84. 24. 432 x 487. 44. 7 x $36.42. 5. 32 x 29. 25. 562 x 809. 45. 4 x $80.92. 6. 86 x 98. 26. 977 x 844. 46. 9 x $78.82. 7. 70 x 93. 27. 555 x 876. 47. 6 x $68.08. 8. 80 x 90. 28. 743 x 201. 48. 7 x $98.74. 9. 68 x 86. 29. 529 x 826. 49. 9 x $56.43. 10. 44 x 88. 30. 432 x 481. 50. 8 x $80.96. 11. 14 x 236. 31. 26 x 3478. 51. 15 x $2.78. 12. 43 x 309. 32. 43 x 8296. 52. 28 x $3.46. 13. 57 x 877. 33. 21 x 8477. 53. 56 x $4.09. 14. 92 x 379. 34. 30 x 9872. 54. 42 x $9.81. 15. 64 x 909. 35. 62 x 8907. 55. 77 x $8.75. 16. 83 x 888. 36. 48 x 7460. 56. 48 x $21.36. 17. 47 x 926. 37. 38 x 9080. 57. 37 x $92.08. 18. 35 x 875. 38. 65 x 2178. 58. 56 x $90.09. 19. 44 x 557. 39. 36 x 8472. 59. 78 x $89.86. 20. 63 x 892. 40. 27 x 9628. 60. 96 x $86.79. In giving such efficiency tests the teacher may find it of advantage to give on one day Exs. 1-10 on page 273, Exs. 1~10 on page 274, Exs. 1-10 on page 275, and so on ; and on another day Exs. 11-20 on the same pages. 276 WHAT THE PUPIL SHOULD KNOW YOU SHOULD DIVIDE QUICKLY AND ACCURATELY Copy and divide, writing both quotient and remainder, timing yourself on each set of ten examples : 1. 428 -H 26. 21. 2173 + 42. 41. $144 * 12. 2. 378-24. 22. 5683-85. 42. $288-24. 3. 526-28. 23. 8093-92. 43. $17.28-4. 4. 875 - 43. 24. 9062 - 77. 44. $1728 - 12. 5. 920-37. 25. 8112-92. 45. $1728-24. 6. 801-49. 26. 3984-46. 46. $1331-11. 7. 676-33. 27. 5085-^-70. 47. $7007-11. 8. 494 - 19. 28. 3700 - 69. 48. $2626 - 13. 9. 962 - 32. 29. 4008 - 90. 49. $2756 - 13. 10. 488-27. 30. 7782-56. 50. $4575-25. 11. 1283 - 38. 31. 5434 - 82. 51. $1270 - 12. 12. 4072 - 56. 32. 4848 - 49. 52. $3250 - 14. 13. 5710-29. 33. 6209-80. 53. $1236-21. 14. 8209-37. 34. 5000-91. 54. $2238-33. 15. 9108-43. 35. 3707-86. 55. $4756-42. 16. 9807-46. 36. 5200-35. 56. $4020-45. 17. 5055 - 75. 37. 4801 - 29. 57. $5005 - 72. 18. 8026 - 93. 38. 8237 - 92. 58. $6172 - 36. 19. 9071-85. 39. 5781-86. 59. $4856-29. 20. 9002 - 96. 40. 4000 - 99. 60. $3792 - 18. In practical work in division there is usually a remainder. When the pupil studies a more advanced book he can carry the quotient as far as may be necessary by means of decimal fractions. At present he should merely indicate the remainder or write a common fraction in the quotient. EFFICIENCY TESTS 277 YOU SHOULD BE ABLE TO REDUCE, ADD, AND SUBTRACT THE ORDINARY COMMON FRACTIONS OF BUSINESS, AND FIND A FRACTIONAL PART OF A WHOLE NUMBER Copy, and perform the operations indicated, timing your- self on each set of ten examples : 1. 1 = 6- 21. i 2 r* 41. Jof 428. 2. f = "8' 22. 3 T ~ 2' 42. tof 828. 3. i = ' 23. } -f 43. fof 624. 4. 8 = T6' 24. *-* 44. Jof 624. 5. 1 = T6" 25. 1 -i 45. fof 736. 6. i~ = * 26. 7 3 46. 8 968. 7. i = - 27. | ~ 2' 47. fof 256. 8. i = "9- 28. f ~ 3' 48. fof 496. 9. i = T6' 29. 2 3 1 2" 49. f 584. 10. f = "3^' 30. f ~ 3 ' 50. 1 of 475. 11. * + 3 31. 1 + i + 8' 51. 2* + 3f. 12. i _j_ 1 32. \ + i + 8- 52. 3|- 2$. 13. 4 + 33. \ + i + -. 53. 4| + 3J- 14. 1 + i 34. a + i + f 54. 4f- 31 15. 7 t i i r 2' 35. 3" + i + i- 55. 6-2- + U 3 n 24- 16. "3 i 1 r 2' 36. i + 4 + 1- 56. 6 f- 2i- 17. 2 3 + i- 37. i + i + 1- 57. 4f + H- 18. i + 1- 38. 5" + i "*~ 3"' 58. 4f- !f 19. 2 3 + 8 " 39. 1 + i + 3- 59. 7| + 2J. 20. * + 4. 40. * + * + * 60. 7| 24. 278 WHAT THE PUPIL SHOULD KNOW THE COMMON TABLES OF MEASURES, AND HOW TO USE THEM Copy, and complete each statement, timing yourself on each set of ten examples : 1. 1ft. = (?)in. 21. llb. = (?)oz. 2. 7 ft. = (?) in. 22. | Ib. = (?) oz. 3. 9 ft. = (?) in. 23. 2J Ib. = (?) oz. 4. lyd. = (?)ft. 24. 16oz. = (?)lb. 5. 7 yd. = (?) ft. 25. 144 oz. - (?) Ib. 6. 31 yd. = (?) ft! 26. 288 oz. = (?) Ib. 7. lyd. = (?)in. 27. 1 T. = (?) Ib. 8. 21yd. = (?)in. 28. 3J T. = (?) Ib. 9. 1 rd. = (?) ft. 29. 1 qt. = (?) pt. 10. 2 rd. = (?) ft. 30. 71 qt. = (?) pt. 11. 1 rd. = (?) yd. 31. 1 gal. = (?) qt. 12. 9 rd. = (?) yd. 32. 3f gal. = (?) qt. 13. 1 mi. = (?) rd. 33. 4| gal. = (?) pt. 14. 4mi. = (?)rd. 34. 1 bu. = (?) pk. 15. 1 mi. = (?) yd. 35. 1\ bu. = (?) pk. 16. \ mi. - (?) yd. 36. 1 pk. = (?) qt. 17. 1 mi. = (?) ft. 37. 5J pk. = (?) qt. 18. 3J mi. = (?) ft. 38. 7 sq. ft. = (?) sq. in. 19. | mi. = (?) ft. 39. 7 sq. yd. = (?) sq. ft. 20. | mi. = (?) ft. 40. 7 hr. = (?) min. Teachers should remember that we no longer use such numbers as 4 mi. 17 rd. 3 yd. 2 ft. 2 in. TABLES FOR REFERENCE 279 LENGTH 12 inches (in.) = 1 foot (ft.) 3 feet = 1 yard (yd.) 161 feet = 1 rod (rd.) 5280 feet, or 320 rods = 1 mile (mi.) SQUARE MEASURE 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq. yd.) 30J square yards = 1 square rod (sq. rd.) 160 square rods = 1 acre (A.) 640 acres = 1 square mile (sq. mi.) CUBIC MEASURE 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) 128 cubic feet = 1 cord (cd.) WEIGHT 16 ounces (oz.) = 1 pound (Ib.) 2000 pounds = 1 ton (T.) LIQUID MEASURE 4 gills (gi.) = 1 pint (pt.) 2 pints = 1 quart (qt.) 4 quarts = 1 gallon (gal.) DRY MEASURE 2 pints (pt.) = 1 quart (qt.) 8 quarts = 1 peck (pk.) 4 pecks = 1 bushel (bu.) 280 TABLES FOR REFERENCE MULTIPLICATION TABLE 1x2= 2 2x2= 4 3x2= 6 4x2= 8 5x2 = 10 6x2 = 12 7x2 = 14 8x2 = 16 9x2 = 18 10x2 = 20 11x2 = 22 12x2 = 24 1x3= 3 1x4= 4 1x5= 5 2x3= 6 2x4= 8 2x5 = 10 3x3= 9 3x4 = 12 3x5 = 15 4x3 = 12 4x4 = 16 4x5 = 20 5x3 = 15 5x4 = 20 5x5 = 25 6x3 = 18 6x4 = 24 6x5 = 30 7x3 = 21 7x4 = 28 7x5 = 35 8x3 = 24 8x4 = 32 8x5 = 40 9x3 = 27 9x4 = 36 9x5 = 45 10 x 3 = 30 10x4 = 40 10x5 = 50 11x3 = 33 11x4 = 44 11x5 = 55 12x3 = 36 12x4 = 48 12x5 = 60 1x6= 6 2x6 = 12 3x6 = 18 4x6 = 24 5x6 = 30 6x6 = 36 7x6 = 42 8x6 = 48 9 x 6 = 54 10x6 = 60 11x6 = 66 12x6 = 72 1x7= 7 2x7 = 14 3x7 = 21 4x7 = 28 5x7 = 35 6x7 = 42 7x7 = 49 8x7 = 56 9x7 = 63 10x7 = 70 11x7 = 77 12x7 = 84 1x8= 8 1x9= 9 2x8 = 16 2x9= 18 3x8 = 24 3x9= 27 4x8 = 32 4x9= 36 5x8 = 40 5x9= 45 6x8 = 48 6x9= 54 7x8 = 56 7x9= 63 8x8 = 64 8x9= 72 9x8 = 72 9x9= 81 10x8 = 80 10x9= 90 11x8 = 88 11x9= 99 12x8 = 96 12x9 = 108 INDEX PAGE Acute triangle 240 Addend 114 Addition, 5, 20, 57, 114, 118, 169, 225 check on 28, 114 defined 114 table 23 Aliquot part 259 Area 151 Average 191, 199 Bills 119, 260 Birthday party ....... 164 Boy Scouts 246 Buying things we would like . . 165 Camp Fire Girls 270 Cancel 252 Change, making 121, 171 Check on addition 28, 114 on division 74, 188 on subtraction 32 Christmas problems 183 City, a day in the 185 City boy and girl 145 Counting 1, 15 Country boy and girl 104 Cubic measure . . 242 PAGE Dividend 74, 188 Division ... 71, 93, 124, 187, 230 check on . 74, 188 defined 74 Divisor 74, 188 Dramatization explained . . . 3, 6 Dressing the dolls 91 Drill explained 27 Drill tests, 7, 24, 25, 27, 34, 35, 47, 48, 57, 70, 88, 89, 107, 115, 143, 144, 163, 169, 171, 186, 193 Dry measure 149 Earning money 116, 146 Efficiency tests 273 Equals 5 Exact division 95 Footing a bill .260 Fractional parts . . . 101, 205, 251 Fractions. . . 38,97,147,200,248 addition of 202, 254 reduction of 252 subtraction of .... 203, 257 Games, 6, 9, 13, 26, 29, 31, 37, 91, 92 General review . 102, 154, 218, 264 Debtor 260 Hundreds 54 Denominator 248 Difference 65 Improper fraction 248 Dimensions 241 Integer 248 281 282 INDEX PAGE Length 43, 233 Liquid measure 45, 213 Little Examinations, 52, 108, 166, 222, 272 Long division 191 Lowest terms 252 Measures, 43, 45, 56, 149, 150, 151, 213, 215, 233, 235, 242, 244, 245 Millions 224 Minuend 65 Minus 11 Mixed number 248 Money . . 16, 112, 118, 122, 172, 198 Multiplicand 85, 172 Multiplication . 71, 85, 124, 172, 227 defined 172 tables 71, 124, 280 Multiplier 85, 172 Numbers to 1000 53 used in play 90 Numerator 248 Obtuse triangle 240 Perimeter 152 Playing store 3, 12, 37 Plus 5 Post office 184 Problems about our class ... 36 about our store 37 about games 92 without numbers . . . 217,268 Product 85,172 Proper fraction 248 Quotient 74, 188 Reading and writing numbers, 53, 109, 167, 223 PAGE Receipt 260 Receipting a bill 260 Reduction of fractions .... 252 Remainder 65, 95 Right triangle 240 Roman numerals . . . 66, 111, 168 Scale, drawing to . . . . 151, 237 Scout camp 247 Square measure 151, 235 Store problems 37 Subtraction . . .10, 32, 64, 120, 170, 226 check on 32 defined 11 methods of 65 Subtrahend x . . . 65 Sum 6 Surprise party 269 Tables .... 23, 71, 124, 279, 280 Taking a trip 220 Terms of a fraction 248 Thousands 224 Time 56, 215 Triangle 240 Troublesome groups 25 Unit 172 of measure 236 United States money .... 16, 112 Using what you have learned, 36, 49, 90, 104, 145, 164, 183, 220, 246, 269 Volume 242 Weight 46, 150, 245 What the pupil should know . . 273 Wood measure 244 ANSWEKS Page 54. 1..555; 249; 121; 609; 303; 880. 2. Two hundred forty-two; two hundred seven ; five hundred twenty ; six hundred thirty-four ; nine hundred eighty-seven ; eight hundred forty-three ; seven hundred sixty-five. Page 55. 1. 101; 150. 2. 203; 270. 3. 306; 390. 4. 409; 540. 5. 606; 708. 6. Five hundred twenty-seven ; six hundred forty-two ; three hundred thirty-four ; four hundred fifty-six ; six hundred seventy-eight ; nine hundred nine ; seven hundred forty-two ; eight hundred thirty ; three hundred three. 7. Seven hundred eight ; eight hundred sixty ; nine hundred one; seven hundred seventy-seven; eight hundred; seven hundred fifty; six hundred thirty ; four hundred; one thousand. 8. 43; 877. 9. 21; 789. 10. 52; 999. 11. 78; 678. 12. 500; 567. 13. 600; 673. 14. 700; 727. Page 58. 1. 70; 72; 77; 77; 77; 90. 2. 93; 99; 93; 99; 99; 80. 3. 94; 94; 95; 98; 99; 100. 4. 360; 376; 379; 399 ; 599 ; 865. 5. 674; 748; 789; 686; 859; 796. Page 60. 1. 60; 60; 61; 60; 64; 52; 90. 2. 60; 81; 92; 90; 80; 62; 54. 3. 80; 52; 72; 63 ; 83 ; 45 ; 91. 4. 70; 73 ; 83 ; 46 ; 91 ; 51 ; 85. 5. 75; 95; 68; 85; 74; 94; 92. 6. 85; 92; 90; 71; 83; 64; 65. 7. 77; 81; 68; 80; 58; 73; 76. 8. 64; 81; 76; 82; 60; 81; 63. 9. 40; 54; 60; 54; 74; 78; 83. 10. 72; 105; 107; 99; 100; 101; 85. Page 61. 1. 293. 2. 261. 3. 463 ft. 4. 382. 5. 575. 6. 574. 7. 760. 8. 712. 9. $554. Page 62. 1. 314. 2. 305 miles. 3. 405. 4. 625. 5. 548. 6. 766. 7. 652. 8. $737. Page 63. 1. 352. 2. 656. 3. 642. 4. 417. 5. 680. 6. 833. 7. 710. 8. 820. 9. 911. 10. 630. 11. 911. 12. 798. 13. 683. Page 66. 1, 25; 29; 44; 28; 28; 35; 58. 2. 28; 18; 27; 19; 28; 43; 47. 3. 28; 16 ; 34; 18; 16 ; 34 ; 57. 4. 8; 27; 38; 29; 27; 43; 36. 5. 15. 6. 14ft. 7. 12. 8. 29 yr. 9. 14 in. 10. 3. 11. 17. EP 515.7 1 2 ESSENTIALS OF AEITHMETIC Page 67. 1. 482; 473; 464; 482; 412; 211. 2. 292; 451; 282; 492; 363; 467. 3. 272; 242; 252; 493; 185; 245. Page 69. 1. 526; 237; 334; 258; 236; 179. 2. 317; 469; 163; 179; 248; 235. 3. 219; 259; 146; 237; 289; 364. 4. 467; 225; 138; 355; 247; 508. 5. 577; 339; 589; 567; 387; 145. 6. 388; 587; 485; 434; 294; 346. 7. 109 ; 99 ; 199 ; 309 ; 498 ; 488. 8. 137. 9. 256. 10. 180 ft. Page 70. 1. 44. 2. 133. 3. 257. 4. 368. 5. 489. 6. 46. 7. 157. 8. 269. 9. 338. 10. 421. 11. 252. 12. 267. 13. 378. 14. 449. 15. 558. 16. 88. 17. 165. 18. 279. 19. 386. 20. 563. 21. 265. 22. 147. 23. 324. 24. 235. 25. 36. 26. 97. 27. 88. 28. 177. 29. 189. 30. 276. Page 73. 1. 4; 8; 8; 12; 16; 18; 3; 18; 0; 0. 2. 6) 6; 10; 10; 14; 12; 2; 2; 14; 16. Page 76. 1". 3; 3; 0. 2. 3; 3; 8. 3. 3; 3; 6. 4. 3; 3; 12. 5. $21; $27. 6. $36; $33. Page 77. 1. 3; 5; 8; 10. 2. 4; 6; 7; 9. 3. 7. 4. 4; 2. 5. 27; 21; 18; 15; 24; 12. Page 78. 2. 3. 3. 2. 4. 3. 5. 2. 6. 3. 7. 4. 8. 6. 9. 4. 10. 3. Page 79. 1. 20; 28; 36. 2. 32. 3. 8; 28; 24; 32; 40. 4. 36; 28; 32. Page 80. 1. 28. 2. 36. 3. 12; 20; 32. 4. 28. Page 81. 1. 7; 9. 2. 6. 3. 6.; 4 ; 10. 4. 8; 4; 9. Page 82. 1. 15. 2. 45 f 3. 35. 4. 22; 33; 47. 5. 52; 29; 17. Page 83. 1. 5; 20; 3. 2. 5 ; 45 ; 8. 3. 9; 7; 5. 4. 7; 9; 3. 5. 8 ; 10; 4. 6. 3. Page 84. 1. 6. 2. 3. 3. 6f 4. $27. 5. 8. 6. $28. Page 85. 1. 26; 82; 84; 46; 48; 64; 644. 2. 63; 93; 88; 44; 28; 69; 693. Page 87. 1. 212; 60; 308; 158; 264; 66; 666. 2. 192; 256; 65; 171; 320; 48; 484. 3. 102; 220; 150; 24; 272; 160; 966. 4. 134; 294; 352; 258; 306; 84; 844. 5. 267; 156; 168; 186; 388; 252; 924. Page 90. 1. 51. 2. 36. 3. 102. 4. 58. 5. 42. 6. 97. Page 91. 1. 85 . 2. 50. 3. 36^. 4. 40; 16; 4. 5. 8$. 6. 4^. 7. 65f 8. 192. 9. 60. Page 92. 1. 80f 2. 180ft. 3. 360ft. 4. 611. 5. 87. 6. 80. 7. 45. 8. 36f 9. 10. EF ANSWERS 3 Page 94. 1. 12 ; 14 ; 21 ; 24 ; 33 ; 41 ; 42 ; 422. 2. 11 ; 12 ; 20 ; 23 ; 13; 32; 22; 222. 3. 11 ; 10; 20 ; 22 ; 21 ; 6 ; 12 ; 111. 4. 21. 5. 22. 6. 12; 21; 30. Page 95. 1. ll,rem. 2$. 2. 10, rem. 3$. 3. 12, rem. 1$. 4. 22, rem. 1. 5. 11, rem. 2. 6. 22, rem. 2. 7. 33, rem. 1. 8. 11, rem. 1. 9. 31, rem. 1. 10. 31, rem. 1. 11. 21, rem. 1. 12. 31, rem. 2. 13. 40, rem. 1. 14. 32, rem. 1. 15. 22, rem. 1. Page 96. 1. 16; 17; 26; 29; 36; 48; 22; 224. 2. 24 ; 8 ; 29 ; 18 ; 16; 27; 21; 121. 3. 14; 13; 16; 18; 24; 23; 9; 91. 4. 13. 5. 30; 28; 26; 19; 331. 6. 22; 21; 31; 19; 333. 7. 25. 8. 18. Page 97. 3. 2. 4. 3. 5. 6. Page 98. 1. f. 2. f , or 1. 3. 0. 4. f 5. 2. 6. 3. Page 99. 1. f 3. 8. Page 102. 1. 595; 655; 661; 779; 772; 587. 2. 881; 795; 935; 807; 875; 937. 3. 674; 864; 921; 855; 920; 920. 4. 642; 860; 784; 901; 760; 735. 5. 355; 295; 345; 285; 187; 198. 6. 259; 258; 404; 473; 592; 248. 7. 288; 307; 628; 157; 385; 513. 8. 376; 459; 389; 604; 295; 448. 9. 83; 78; 299; 54; 312; 414. 10. 50; 66; 28; 72; 90; 99. 11. 123; 92; 160; 128; 215; 135. 12. 110; 155; 126; 252; 120; 118. 13. 238 ; 308 ; 264 ; 400 ; 405 ; 228. 14.92. 15. $72. 16.14; 23; 26; 11; 17; 29; 20; 8. 17. 19; 31; 35; 15; 23; 39; 27; 11. 18; 30 ; 34 ; 14 ; 22 ; 38 ; 26 ; 10. 18. 24 ; 39 ; 44 ; 19 ; 29 ; 49 ; 34 ; 14. 23 ; 38; 43; 18; 28; 48; 33; 13. 22 ; 37; 42 ; 17 ; 27; 47 ; 32; 12. 19. 16; 21 ; 26 ; 31 ; 36, rem. 1 ; 37, rem. 1. 20. 17 ; 19 ; 23 ; 25 ; 26, rem. 2 ; 30, rem. 1. 21. 12 ; 14 ; 18 ; 20, rem. 1 ; 21, rem. 3 ; 23, rem. 1. 22. 13 ; 15 ; 14, rem. 2 ; 16, rem. 3 ; 19 ; 19, rem. 4. Page 104. 1. 85. 2. 34. 3. 90 f 4. 75$. 5. 30. 6. 84 $. 7. 37$. 8. Yes; 12$. 9.70$. 10.80$. 11. $1.00. 12.42$. 13.52$. 14.48$. 15. $17. 16.18. 17. 6; 12; 30. 18. 48 ; 36 ; 84. 19.463ft. 20.54. 21. 48. 22. 8; 24. Page 110. 1. 101; 207. 2. 1001; 5004. 3.2101. 4.3207. 5.3417. 6. 4765. 7. 5555. 8. 6819. 9. 7890. 10. 9999. 11. 3333. Page 111. 1. XV; VIII; XI; XVII; XIII; IX; V; X; XIV. 2. 11; 9; 19; 14; 17; 7; 18. EP 4 ESSENTIALS OF AKITHMETIC Page 113. 1. $4.00; $1.75. 2. $16.00; $3.03. 3. $14.00; $7.25. 4. $18.00; $16.80. 5. $230.00; $175.75. 6. $100.00; $248.49. 7. $184.00; $250.49. 8. $200.00; $500.50. 9. $300.00; $750.85. 10. $400.00; $286.98. 11. $768.00. 12. $150.10. 13. $275.10. Page 114. 1. 206. 2. 248. 3. 282. 4. 345. 5. 236. 6. $238. 7. $160. Page 115. 1. 255. 2. 337. 3. 264. 4. 257. 5. 366. 6. 3149. 7. 3236. 8. 3704. 9. 4153. 10. 2503. Page 116. 1. 384. 2. 230. 3. 517. 4. 311. 5. 108. 6. $219. 7. $53. 8. $300. Page 117. 1. $560. 2. 680. 3. 703. 4. 615. 5. $730. 6. $702. 7. 800. 8. 766. 9. 888. 10. $779. 11. 502. 12. 650. 13. 462. 14. 506. 15. 666. 16. 368. 17. 250. 18. 460. 19. 550. 20. 517. 21. $736. 22. $512. 23. $515. 24. $774. 25. $718. Page 118. 1. $10.47. 2. $10.55. 3. $8.65. 4. $8.74. 5. $14.70. 6. $5.39. 7. $12.50. 8. $15.70. 9. $12.58. 10. $12.35. Page 119. 1. $4.11. 2. $7.75. 3. $6.15. 4. $14.29. 5. $10.72. 6. $7.29. 7. $7.27. 8. $4.69. 9. $6.19. 10. $5.77. 11. $6.91. 12. $5.21. Page 120. 1. 107. 2. 69. 3. 146. 4. 198. 5. 208. 6. 148. 7. 172. 8. 118. 9. 189. 10. 99. 11. 323. 12. 70. 13. 429. 14. 203. 15. 565. 16. 364. 17. 505. 18. 575. 19. 367. 20. 189. 21. $148. 22. $39. 23. $174. 24. $41. 25. $91. 26. $125. 27. $365. 28. $108. 29. $355. 30. $94. 31. $114. 32. $818. 33. $99. 34. $139. 35. $85. 36. $248. 37. $179. 38. $48. 39. $280. 40. $578. 41. $394. 42. $379. Page 122. 1. $47.49. 2. $16.87. 3. $17.78. 4. $4.89. 5. $29.92. 6. $5.45. 7. $64.89. 8. $28.92. 9. $221.25. 10. $171.25. 11. $171.19. 12. $168.19. Page 123. 1. $0.92. 2. $78.49. 3. $13.40. 4. $8.73. 5. $59.59. 6. $18.77. 7. $8.89. 8. $85.41. 9. $24.13. 10. $39.39. 11. $9.69. 12. $17.64. 13. $3.88. 14. $34.25. 15. $53.73. 16. $23.22. 17. $15.39. 18. $12.57. 19. $18.77. 20. $74.31. Page 126. 1. 186. 2. $1.26. 3. $180." 4. 1206. 5. 1806. 6. 3006. 7. 2406. 8. 5406. 9. 4206. 10. 33; 58; 40. 11. 48; 51; 20. Page 127. 1. 240. 2. 250. 3. 468. 4. 650. 5. 850. 6. 550. 7. 960. 8. 963. 9. 975. 10. 1029. 11. 1338. 12. 1359. 13. 824. 14. 1080. EP ANSWERS 5 15. 1590. 16. 1652. 17. 2608. 18. 4725. 19. 2030. 20. 2305. 21. 2080. 22. 3262. 23. 4528. 24. 2184. Page.128. 1. 8; 9; 10. 2. 9; 6; 7. 3. 4; 5; 11. 4. 5. 5. 6; 18; 5. Page 129. 1. 324. 2. 213. 3. 111. 4. 221. 5. 111. 6. 111. 7. 100. 8. 224. 9. 423. 10. 231. 11. 112. 12. 212. 13. 110. 14. 110. 15. 100. 16. 112. 17. 234. 18. 312. 19. 210. 20. 111. 21. 101. 22. 434. 23. 111. 24. 111. 25. 120. 26. 102. Page 131. 1. 707. 2. 714. 3. 784. 4. 924. 5. 2345. 6. 1589. 7. 1400. 8. 1428. 9. 1568. 10. 2268. 11. 2576. 12. 2534. 13. 2800. 14. 2863. 15. 2933. 16. 3073. 17. 3423. 18. 6993. Page 132. 1. 8. 2. 5. 3. 7$. 4. 9. 5. $6. Page 133. 1. 52; 53; 54; 102. 2. 21. 3. 93. 4. 327. 5. 162. 6. 127. 7. 121. 8. 81. 9. 97. 10. 62. 11. 145. 12. 73. 13. 57. 14. 101. Page 135. 1. 1600. 2. 1608. 3. 1616. 4. 1696. 5. 1936. 6. 2768. 7. 2400. 8. 2880. 9. 2888. 10. 2920. 11. 3024. 12. 2664. 13. 3200. 14. 3760. 15. 3800. 16. 3888. 17. 3984. 18. 2712. 19. 4600. 20. 4656. 21. 5000. 22. 5400. 23. 5496. 24. 4572. Page 136. 1. 9; 10; 7. 2. 8; 9. 3. 8; 8; 16. 4. 16; 24; 32. 5. 8. 6. 80. 7. 111. 8. 110. 9. 60. 10. 71. 11. 70. 12. 101. Page 137. 2. $70; $90; $60. 3. $72. 4. 72 . Page 138. 1. 2187. 2. 2880. 3. 3654. 4. 5148. 5. 7767. 6. 6678. 7. 2946. 8. 4945. 9. 8181. 10. 5274. 11. 4295. 12. 4608. 13. 4104. 14. 5274. 15. 2445. 16. 3234. 17. 5873. 18. 8847. 19. 47 . Page 139. 1. 6885. 2. 7218. 3. 6588. 4. 6102. 5. 4464. 6. 6183. 7. 2412. 8. 2385. 9. 2655. 10. 2475. 11. 5283. 12. 6472. 13. 3591. 14. 3357. 15. 3483. 16. 1854. 17. 2786. 18. 7024. Page 140. 1. 3. 2. 4. 3. 6. 4. 20. 5. 31. 6. 41. 7. 51. 8. 21. 9. 60. 10. 40. 11. 50. 12. 100. 13. 110. 14. 111. 15. 101. Page 142. 4. 2; 3; 4; 5; 6; 7; 8; 9; 10. Page 143. 1. 2238. 2. 4145. 3. 5463. 4. 5352. 5. 3896. 6. 6881. 7. 836. 8. 3612. 9. 4185. 10. 6084. 11. 2679. 12. 2862. 13. 5504. 14. 3968. 15. 3123. 16. 3648. 17. 7497. 18. 5168. Page 145. 1. 50^; $1.00. 2. 8; 80^. 3. 50. 4. 4; 60^. 5. 6; 18; 90. 6. 5pt. 6 ESSENTIALS OF ARITHMETIC Page 146. 1. 6$; 9$. 2. 100$, or $1. 3. 180$, or $1.80. 4. 260$, or $2.60. 5. 130$, or $1.30. 6. 70$. 7. 200$, or $2. 8. 120$, or $1.20. 9. 700$, or $7. 10. $2.50. Page 148. 3. $460; $1380. Page 149. 1. 6. 2. 16; 32; 32. 3. 2; 40. Page 150. 1. 1506 Ib. 2. 1527 Ib. 3. 1315 Ib. 4. 1285 Ib. 5. 717 Ib. 6. 445 Ib. 7. 572 Ib. 8. 674 Ib. Page 151. 3. 6. 4. 70. Page 152. 1. 24sq.in.; 20 in. 2. 6 sq. in. 3. 40 sq.ft.; 26ft. 4. 36; 24. 6. \ ; 4 sq. in. ; 8 in. ; 16 sq. in. ; 16 in. Page 153. 1. $10.40. 2. $20.20. 3. $31.79. 4. $108.61. 5. $82.00. 6. $13.89. 7. $27.30. 8. $82.20. 9. $219.00. 10. $292.00. Page 154. 1. 54$; 57$. 2. 92$; 96$. 3. 81$; 72$. 4. 75$; 69$. Page 155. 1. $22.73. 2. $15.87. 3. $18.57. 4. $212.86. 5. $245.28. 6. $29.99. 7. $26.42. 8. $26.36. 9. $70.75. 10. $166.10. 11. $2.96. 12. $3.76. 13. $4.83. 14. $1.86. 15. $10.46. 16. $3.89. 17. $4.24. 18. $4.18. 19. $24.58. 20. $18.79. 21. $3.09. 22. $6.79. 23. $3.21. 24. $22.89. 25. $62.35. 26. $2.58. 27. $4.32. 28. $1.73. 29. $23.06. 30. $62.34. Page 156. 1. $542. 2. $1458. 3. $2380. 4. $3215. 5. $4686. 6. $5894. 7. $7496. 8. $2241. 9. $2394. 10. $6984. 11. $5988. 12. $5901. 13. $5439. 14. $3184. 15. $7857. 16. 138; 174; 111; 189; 246; 264; 306; 102; 90; 171; 363; 207; 243; 249; 168; 285; 144; 480. 92; 116; 74; 126; 164; 176; 204; 68; 60; 114; 242; 138; 162; 166; 112; 190; 96; 320. 17. 70; 115; 140; 85; 205; 185; 245; 55; 120; 225; 125; 155. 56; 92; 112; 68; 164; 148; 196; 44; 96; 180; 100; 124. 18. 70; 91; 140; 147; 77; 84; 35; 42; 49; 56; 63; 154. 60; 78; 120; 126; 66; 72; 30; 36; 42; 48; 54; 132. 19. 90; 99; 45; 27; 36; 54; 63; 72; 81; 108; 117; 18. 80; 88; 40; 24; 32; 48; 56; 64; 72; 96; 104; 16. Page 157. 1. 70$; 74$. 2. 48$; 56$. 3. 96$; 92. 4. 94$; 88$. 5. 30$; 40$. 6. 18$; 20$. 7. 72$; 76$. 8. 76$. 9. 71$. Page 158. 1. 5055; 1858; 7346; 1914. 2. $1135. 3. 5195. 4. $1081.33. 5.7678. 6.156. 7. 952 miles. 8. $1.30. 9. 348$; $3.48. 10. $1161. 11. $405. 12. 2640. 13. 98$. 14. $2962. 15. $385; $405. 16. 17. $47. 18. $3384. 19. $153. 20. $3.83. 21. 256. ANSWERS 7 Page 160. 1. $9.89. 2. $17.77. 3. $27.82. 4. $73.79. 5. $172.82. 6. $19.97. 7. $34.54. 8. $97.50. 9. $95.65. 10. $160.43. 11. $29.03. 12. $36.13. 13. $100.66. 14. $106.02. 15. $104.01. 16. $26.32. 17. $31.60. 18. $85.20. 19. $109.71. 20. $105.03. 21. $2.42. 22. $3.26. 23. $3.33. 24. $2.04. 25. $8.55. 26. $6.23. 27. $4.38. 28. $4.03. 29. 30. $9.08. ' 31. $5.64. 32. $3.02. 33. $6.78. 34. $5.73. 35. 36. $2.88. 37. $3.89. 38. $2.99. 39. $5.29. 40. $26.09. 41. 42. $896. 43. $2550. 44. $9672. 45. $9400. 46. $6650. 47. 48. $8163. 49. $9024. 50. $7000. 51. $5400. 52. $4963. 53. $7308. 54. $9450. 55. $8550. 56. 234; 163; 228; 126, rem. 1; 186; 107; 165, rem. 1; 273, rem. 1; 317; 209; 486; 452, rem. 1. 57. 118; 148; 121, rem. 2; 78, rem. 1; 208; 217; 161, rem. 1; 263, rem. 1; 136; 297; 266; 325, rem. 1. 58. 231; 188; 206; 228; 238,rem.3; 183, rem. 2; 14.1; 180, rem. 3; 148; 240, rem. 1; 229, rem. 2; 128, rem. 1. 59. 102; 133; 104; 147; 128, rem. 4; 112; 154; 177, rem. 2; 118; 124, rem. 3; 148, rem. 2; 165. 60. Ill; 104; 106; 120, rem. 5; 122; 124, rem. 2; 121, rem. 1; 135; 137; 140, rem. 5; 154; 155, rem. 3. 61. 104; 106, rem. 3 ; 112, rem. 1; 113, rem. 6; 116; 115; 123; 124, rem. 5; 130; 133, rem. 4; 134, rem. 5 ; 135, rem. 5. 62. 91; 93; 82; 84; 74; 64; 49; 38; 116; 123; 13, rem. 7; 27, rem. 6. 63. 37; 74; 82; 73; 61; 36 ; 63 ; 45; 78 ; 89 ; 86, rem. 3; 98, rem. 6. Page 164. 1. 19 . 2. 6f 3. 32. 4. 16 f Page 165. 1. 17^. 2. $12.25. 3. $2.25. 4. 55^. 5. 6S. 6. 85; 15. 7. $1.30; 20f 8. $3.50. Page 168. 1. 11. 2. 64. 3. 26. 4. 66. 5. 72. 6. 97. 7. 77. 8. 34. 9. XXXI. 10. LXXXIX. 11. XLII. 12. XCI. 13. LXVII. 14. LXXV. 15.CLXXV. 16. CL. 17.MDCCCCXIX,orMCMXIX. 18. MDCCCCXX, or MCMXX. Page 169. 1. $9.14. 2. $14.25. 3. $14.20. 4. $28.57. 5. $42.09. 6. $34.61. 7. $80.76. 8. $86.16. 9. $78.47. 10. $75.48. 11. 936. 12. $920.30. 13. 21,451. Page 170. 1. 37 ft. 2. 77 men. 3. 453. 4. 278. 5. 149 ; 201. 6. 143 ; 103. 7. $505. 8. $438. 9. 21. 10. 716. Page 171. 1. $146.40. 2. $483.73. 3. $190.70. 4. $317.88. 5. $294.98. 6. $326.26. 7. $89.32. 8. $123.14. 9. $523.96. 10. $221.88. Page 173. 1. 270. 2. $2.70. 3. 550. 4. $25.50. 5. $40.80. 6. $7.50. 7. $4.05. 8. $21.75. 9. $74.40. 10. $101.50. 11. $37.20. 12. $35.80. EP 8 ESSENTIALS OF AEITHMETIC 13. $11.65. 14. $117.10. 15. $148.20. 16. $28.86. 17. $24.54. 18. $43.68. 19. $301. 20. $183.75. 21. $21.63. 22. $25.13. 23. $38.88. 24. $575.44. 25. $298.68. 26. $56.88. 27. $19.17. 28. $114.?5. 29. $132.75. 30. $662.88. 31. $4.50. 32. $22.75. 33. $39. 34. $58.80. Page 175. 1. $27.50; $127.50; $227.50; $255. 2. $260; .$483; $532.50; $697.30. 3. $829.60; $1000; $2000; $5000. 4. 840; 720; 1620 ; 1060 ; 1340. 5. 780 ; $24 ; $44 ; $70 ; $44.60. 6. $90 ; $114 ; $98 ; $155; $193. 7. 400; 2200; 4500; 5000; 8100; 7500; 4200; 8600. 8. 7700; 3600; 8300; 8700; 6300; 6600; 2900; 9900. 9. 1000; 1600; 1400; 1800; 1200; 3000; 3600; 5000. 10. 7000; 8200; 9600; 11,000; 9200; 12,000; 13,400; 15,000. 11. $60. 12. $120. 13. $250. 14. $420. 15. $640. 16. $1800. 17. $70. 18. $350. 19. $682.50. Page 176. 1. $3; $3.60; $4.20. 2. $3.50; $3.80; $4.30. 3. $2.40; $3.60. 4. 60. 5. 270 ; 270 ; 540. 6. $3.50 ;70f 7. $12.50 ; $25 ; $37.50. 8. $510; $765. 9. $1147.50; $1530; $2295. 10. $5000; $5625; $4375. 11. $2275- $910; $1820. 12. $3020; $2642.50; $1132.50. 13. $1750; $2625. Page 177. 1. $672; $992. 2. $903; $1333; $1763. 3. 966; 1113; 1365 ; 1596 ; 1743 ; 798 ; 1092 ; 1974 ; 1260. 4. 837 ; 1612 ; 2294 ; 1209 ; 2635; 1271; 868; 1953; 2976. 1107; 2132; 3034; 1599; 3485; 1681; 1148; 2583; 3936. 5. 1716; 2392; 2964; 2288; 1820; 3536; 2860; 4108 ; 4264. 2046 ; 2852 ; 3534 ; 2728 ; 2170 ; 4216 ; 3410 ; 4898 ; 5084. 2376; 3312; 4104; 3168; 2520; 4896; 3960; 5688; 5904. 6. 2444; 3588; 1300; 3692; 4836; 1872; 4368; 3016; 4940. 2914; 4278; 1550; 4402; 5766; 2232; 5208; 3596; 5890. 3384; 4968; 1800; 5112; 6696; 2592; 6048; 4176; 6840. 7. 5985; 5292; 7304; 9021. 8. 7104; 8232; 9306; 5632. Page 178. 1. $72.30. 2. $77.71. 3. $106.78. 4. $80.73. 5. $50.37. 6. $14.76. 7. $69.44. 8. $98.89. 9. $172.80. 10. $397.60. 11. $202.74. 12. $110.88. 13. $54.21. 14. $119. 15. $66.75. 16. $48; $576. 17. $12; $936; $540. 18. $84; $175; $266; $322. 19. $58.88. 20. $109.48. 21. $300. 22. $141.45. 23. $131.15. 24. $337.50. 25. $148.72. 26. $231. 27. $198. Page 179. 1. $77.50. 2. $80.30. 3. $163.20. 4. $220.50. 5. $550. 6. $552.40. 7. $101.20. 8. $206.70. 9. $213.12. 10. $365.43. 11. $880. 12. $1588.80. 13. $435. 14. $225.18. 15. $420. 16. $989.01. 17. $3993.40. 18. $8999.10. 19. $918.75. 20. $20,520. 21. $13,608. 22. $9351.70. ANSWERS 9 23. $5858.28. 24. $29,898.81. 25. $6868.80. 26. $9140.60. 27. $8447.60. 28. $11,244.22. 29. $19,822. 30. $48,007.20. Page 180. 1. 25,641. 2. 28,413. 3. 53,997. 4. 127,650. 5. $185,150. 6. $195,800. 7. 30,618. 8. 83,868. 9. 139,167. 10. 75,828. 11. $71,672. 12. $322,270. Page 181. 1. $8840; $9095; $9265. 2. $3825; $5362.50; $4012.50; $4087.50. 3. $50,044.80. 4. $54,799.75. 5. $69,501.78. 6. $44,788.52. 7. $119,276.50. 8. $187,360.56. 9. $117,308.25. 10. $165,232.76. 11. $286,144.20. 12. $789,270.30. Page 182. 1. $1.86. 2. $1.26. 3. $164. 4. $1.26. 5. $1.47. 6. 900. 7. 900. 8. 360. 9. $1.80. 10. $1.20. 11. 540. 12. $1.08. 13. $5.60. 14. $2.05. 15. $1.89. 16. $1.40. 17. 450. 18. $2.10. 19. $1.80. 20. $1.20. 21. $1.89. 22. 960. 23. 900. 24. $168. 25; $1.20; 50. 26. 840; 160. 27. 460; 40. 28. $132; $8. 29. $350; $50. 30. $550; $50. 31. $590; $10. 32. $155 ; $5. 33. $25 ; $5. Page 183. 1. 50. 2. 720; 30. 3. $1.00. 4. 400. 5. 600. 6. 360. 7. $1.27. Page 184. 1. 240. 2. 220. 3. 600. 4. 60. 5. 90. 6. 120. 7. 630. Page 185. 1. $4.85. 2. $4.75. 3. 6. 4. $189.75. 5. 580. 6. $3.75. 7. $2.70. 8. $38.50; $77. Page 186. 1. 3552. 2. 3552. 3. 4984. 4. 64,296. 5. 85,869. 6. 37,093. 7. 72,928. 8. 66,123. 9. 26,461. 10. 72,720. 11. 75,336. 12. 39,001. 13. 64,218. 14. 677,329. 15. 96,933. 16. 90,873. 17. 282,492. 18. 390,656. 19. 360,675. 20. 357,414. 21. 387,816. 22. 312,900. 23. 434,600. 24. $51. 25. $190.56. 26. $771.44. 27. $605.64. 28. $388.85. 29. $592.02. 30. $335. 31. $367.36. 32. $498.96. 33. $396.48. 34. $473.04. 35. $327.36. 36. $214.38. 37. $235.17. 38. $284.34. 39. $711.75. 40. $455.76. 41. $289.56. 42. $657.72. 43. $383.13. 44. $307.80. 45. $645. 46. $821.30. 47. $367.36. 48. $592.02. 49. $1844.64. 50. $967.98. 51. $1444.85. 52. $1504.80. 53. $1257.62. 54. $1976.32. 55. $4635.68. 56. $2031.74. 57. $2621.88. 58. $4174.08. 59. $5236.59. 60. $5077.26. 61. $4016.04. 62. $2173.94. 63. $3432.52. 64. $6229.66. 65. $6646.96. 66. $2426.88. 67. $5308.82. 68. $3684.20. 69. $3410.68. Page 187. 1. 6; 7; 9; 13; 19; 27; 39. 2. 4; 8; 12; 13; 14; 15; 16. 3. 17; 19; 21; 23; 24; 27; 32. 4. 12. 5. 14. 6. 15. 7. 6. 8. 12. 9. 16. 10. 24. 11. 26. 12. 41. 13. 20. 14. 2. 15. 12. EP 10 ESSENTIALS OF ARITHMETIC Page 188. 1. 914*-. 2. 10431-. 3. 1226f 4. 706f 5. 1170f 6. 321f 7. 360f 8. 13741. 9. 2058f 10. 584$. 11. 1698$, 12. 2063f 13. 1390. 14. 1856f 15. 1170f 16. 529f 17. 388f 18. 13071. 19. i641f. 20. 408f. 21. 1620f. 22. 466f 23. 718f 24. 1690f. 25. 621f 26. 1096|. 27. 1306 1. 28. 823 T V 29. 624^. 30. 918 T V 31. 298-ft. 32. 876^. 33. 376 T y Page 191. 1. 11. 2. 12. 3. 13. 4. 111. 5. 112. 6. 141. 7. 121. 8. 131. 9. 351. 10. 431. 11. 321. 12. 212. 13. 231. 14. 717. 15. 155. 16. 65; 66; 76. 17. 22; 32; 33. 18. 58 Ib. Page 193. 1. 23. 2. 45. 3. 25. 4. 116. 5. 133. 6. 16. 7. 23. 8. 19. 9. 37. 10. 111. 11. 144. 12. 66. 13. 99. 14. 51. 15. 21. 16. 24; 33. 17. 21; 31. Page 194. 1. 62. 2. 102. 3. 120. 4. 62. 5. 303. 6. 532. 7. 51. 8. 64. 9. 402. 10. 111. 11. 102. 12. 102. 13. 222. 14. 109. 15. 107. Page 195. 1. 121. 2. 111. 3. 39^. 4. 58/ T . 5. 59f . . 6. 138f . 7. 31ff 8. 88|f. 9. 16 7 V 10. 139$f 11. 47|f 12. 89|f 13. 69ff 14. 79||. 15. 66|7. is. 85 . Page 196. 1. 9. 2. 7. 3. 7. 4. 6. 5. 4. 6. 8. 7. 9. 8. 8. 9. 6. 10. 7. 11. 8. 12. 8. 13. 7. 14. 9. 15. 8. 16. 66. 17. 88. 18. 82. 19. 102, rem. 1. 20. 81. 21.- 109, rem. 3. 22. 112. 23. 71, rem. 8. 24.66. 25. 77, rem. 1. 26.104. 27.66. 28. 81, rem. 5. 29.113. 30. 243. 31. 219, rem. 3. 32. 91. 33. 73, rem. 4. 34. 82. 35. 132. 36. 123, rem. 2. 37. 110, rem. 8. 38. 51. 39. 71. 40. 87. 41. 29. 42. 114. 43. 112. 44. 372. 45. 365. 46. 82. 47. 93. 48. 117ff. 49. 113o. 50. 138-fa. 51. 141^. 52. 222/ r 53. 171fi. 54. 85. 55. 28. 56. 201-jY 57. 141|f 58. 149|f. 59. 88ff. 60. 109ff. Page 197. 1. $45. 2. $21. 3.35. 4. $11. 5. 21; 22. 6. 43 mi. 7. 46. 8. $33. 9. 66. 10. 23 ; $10. 11. 606. 12. 324. 13. 328. 14. 792. 15. 1632. 16. 648. l7. 925. 18. 933. 19. 506. Page 198. 1. $1.40. 2. $0.54. 3. $2.16. 4. $2.88. 5. $0.45. 6. $0.36. 7. $0.36. 8. $0.32. 9. $2.70. 10. $5.40. 11. $0.27. 12. $0.48. Page 199. 1. 125. 2. $2.50. 3. $9. 4. $0.16. 5. $75. 6. $850. 7. $3.80. 8. 32. 9. 6. 10. 32. 11. 4. 12. 24. 13. 30. 14. 49. 15. 50. 16. 54. 17. 31f|. 18. 121. 19. 96. 20. $1.40. 21. 22. 4474f 23. 612^. 24. 810. 25. 964. EP ANSWERS 11 Page 202. 1. 8. 2. 34. 3. 10. 4. 13. 5. 58. 6. 21. 7. 47. 8. 58|. 9. 7f. 10. 12. 11. 92. 12. 85. 13. 82. 14. 113f. ' Page 203. 1. 8 in. 2. 15$ in. 3. 5f 4. 2f 5. 6|. 6. 4. 7. 12f. 8. 17f 9. 3. 10. 4. 11. 6. 12. 4. 13. 7|. 14. llf. 15. 7|. 16. 7. 17. 6f. 18. 6f. 19. 12f. 20. 13f. Page 204. 1. 177; 118f 2. 177; 117. 3. 971$; 286. 4. 707; 109. 5. 557; 164. 6. 588 ; 252f 7. 54l; 142. 8. 557; 297. 9. 456; 197. 10. 849; 311. 11. 730; 471f 12. 778; 240. 13. 631; 175. 14. 953; 407. 15. 1508; 411. 16. 1449; 352. 17. 975; 424. 18. 896; 303f. 19. 927; 672. 20. 834; 588. 21. 469; 333. 22. 349; 251. 23. 1010^; 811. 24. 828; 773. 25. 1265; 376. 26. 1476; 437. 27. 1053;564f 28. 993 ; 502f 29. 1477; 178f. 30. 999; 441f. 31. 927$; 275$. 32. 1367; 77|. 33. 1035|; 564. 34. 1104; 379. 35. 1123; 188$. Page 206. 2. 12. 3. 24. 4. 36. 5. 22. 6. 33. 7. 10. 8. 20. 9. 40. 10. 66. 11. 100; 125; 150. Page 207. .1. 6; 12; 7; 14 ; 20. 2. 4 ; 12; 8; 24 ; 30. 3. 5 ; 10 ; 15; 30; 40. 4. 2; 10; 3; 15; 10. 5. 2; 6; 10; 10; 50. Page 208. 1. 42; 84. 2. 110; 220. 3. 150; 300. 4. 170; 340. 5. 213; 426. 6. 241; 482. 7. 32; 96. 8. 56; 168. 9. 82; 246. 10. 86; 258. 11. 131; 393. 12. 168; 504. 13. 45; 90. 14. 135; 180. 15. 67; 268. 16. 290; 519. 17. 56; 280. 18. 121; 605. 19. 41; 123. 20. 205; 287. 21. 180; 305. 22. 21; 242. 23. 123; 168. 24. 360; 400. 26. 39. 27. 18. 28. 8yd. 29. 287ft. 30. $450; $270. Page 210. 1. 1. 2. 1. 3. f. 4. f 5. 1. 6. If 7. T V 8. f 9. If 10. 1 T V 11. ft. 12. if 13. ^. 14. T r 15. 1,V 16. f. 17. If 18. f 19. f 20. If 21. If. 22. f 23. f 24 f 25. If 26. If 27. 14. 28. 2. 29. 2|. 30. 11. 31. 8. a * Page 211. 1. 4yd. 2. 2yd. 3. 3f. 4. 6f. 5. 3. 6. 6. 7. 11. 8. 4. 9. 17f 10. 6. 11. 6f 12. 9. 13. 4f 14. 14|. 15. 5f 16. 16f 17. lOf 18. 3|ft. 19. 3f 20. 8f 21. 13|. 22. 10} f 23. 12 T V 24. 8}f 25. 3f. 26. lOf. 27. Hf 28. lOf 29. llf 30. 12. 31. 5|. 32. 12f. 33. 9f. 34. 14f 35. 9f 36. 8f 37. 2f in. 38. 10| in. Page 212. 1. 1\ yd. 2. 7f yd. 3. 4f . 4. 6f 5. 3f 6. 3f . 7. If 8. If. 9. If. 10. 3f. 12 ESSENTIALS OF ARITHMETIC Page 214. 1. 300 qt. 2. 580 qt. 3. 24 qt. 4. 49 qt. 5. 700 qt. 6. 90 qt. 7. 2qt. 8. 6qt. 9. 2 gal. 10. 9 gal. 11. 24 gal. 12. 12 gal. 13. 42 gal. 14. 21 gal. 15. 60 gal. 16. 30 gal. 17. 16$; 4$; 32$. 18. 240; 480. 19. 60$; $2.40. 20. 8 da. 21. 150. Page 216. 1. 7; 1. 2. 14; 2. 3. 3; 14; 21. 4. 60; 1; 2. 5. 60; 1; 6. 6. 120; 2; 10. Page 218. 1. 6156. 2. 32. 3. $10,248. 4. $63. 5. $1200. 6. 54. 7. $89.60. 8. 6960. 9. 360. 10. 32. 11. 45. Page 219. 1. 7299. 2. 11,347. 3. $6.61. 4. $17.78. 5. $43.53. 6. 10,691. 7. 17,140. 8. $10.85. 9. $55.99. 10. $95.24. 11. 266. 12. 2393. 13. $4.66. 14. $4.87. 15. $77.85. 16. $46.75. 17. $42.78. 18. $605.76. 19. $1531.60. 20. $5087.50. 21. 395/ 7 . 22. 578f 23. 706fg. 24. 1925. 25. 1768f. 26. 51,984. 27. 166,772. 28. 365,211. 29. 639,576. 30. 43,681. 31. 108. 32. 126. 33. 135. 34. 220. 35. 66. 36. 220. 37. 32 pt. 38. 64 qt. 39. 4wk. Page 220. 1. 5hr. 2. 194| miles. 3. $3.90. 4. $1.05. 5. 5i.hr. 7. 61$. 8. 36$. 9. 63$. 10. $2.25. 11. $3.85. 12. $24.60. Page 223. 1. 75,016. 2. 200,406. 3. 555,007. 4. 999,900. 5. One hundred twenty-five thousand, fifty. 6. Three hundred four thousand, four. 7. Five hundred thousand, five. 8. One hundred one thousand, ten. 9. One hundred thousand, one hundred. 10. One hundred twenty-three thousand, four hundred fifty-six. Page 224. 1. 16,002,009. 2. 71,000,570. 3. 62,004,006. 4. 479,000,000. 5. 515,000,300. 6. 6,093,017. Page 225. 1. 149,025 square miles. 2. 12,900 Ib. 3. $786.08. 4. $1081.74. 5. $2379.13. 6. $856.34. Page 226. 1. $456.03. 2. $357.75. 3. $417.02. 4. $521.82. 5. $505.39. 6. $108.35. 7. $510.06. 8. $400.65. 9. $623.59. 10. $97.77. 11. $515.79. 12. $804.16. Page 227. 1. $5346. 2. $22,995. 3. $25,110. 4. $14,300. 5. $30,070. 6. $26,508. 7. $14,763. 8. $20,444. 9. $27,553. 10. $58,420. 11. $39,732. 12. $63,168. 13. $79,985. 14. $47,058. 15. $50,594. 16. $38,766. 17. $9072. 18. $12,064. 19. $16,875. 20. $12,720. 21. $46,272. 22. $28,875. 23. $32,940. 24. $22,101. 25. $33,600. 26. $11,368. 27. $19,992. 28. $28,490. 29. $19,136. 30. $38,750. ANSWERS 13 Page 228. 1. 15,640. 2. 106,875. 3. 54,954. 4. 131,588. 5. 251,560. 6. 51,480. 7. 118,341. 8. 47,656. 9. 130,938. 10. 120,960. 11. 65,325. 12. 75,296. 13. 197,640. 14. 498,381. 15. 571,356. 16. 126,766. 17. 142,444. 18. 88,374. 19. 244,200. 20. 623,796. 21. 309,771. Page 229. 1. 55,937. 2. 36,663. 3. 190,454. 4. 159,075. 5. 440,450. 6. 908,091. 7. 234,576. 8. 383,394. 9. 263,934. 10. 303,485. 11. 777,308. 12. 564,682. 13. 263,250. 14. 598,850. 15. 1,180,912. 16. 807,216. 17. 999,486. 18. 917,181. 19. $28,125. 20. $11,875. 21. $1,194,875. 22. $853,200. 23. $267.30. 24. $312.80; $340. 25. $154,000; $140,000. 26. $330,750; $253,125. 27. $8925; $9409.50. 28. $2875; $2903.75; $3047.50; $3105; $3133.75. 29. $8700; $9004.50; $9048; $13,311; $13,441.50. 30. $27,024 ; $27,429.36 ; $27,632.04 ; $27,226.68 ; $27,361.80. 31. $14,650; $14,767.20; $14,855.10; $14,884.40; $14,913.70. 32. $21,150; $21,467.25; $28,446.75; $28,482; $34,791.75. Page 230. 1. 20. 2. 20 3 ^. 3. 20|ft, 4. 200^. 5. 230^7. 6 . 20 . 7. 20^. 8. 20UR. 9- ^Mr 10 - 21 TVVV Page 231. 1. 4. 2. 21. 3. 5. 4. 26. 5. 23. 6. 29. 7. 27. 8. 7. 9. 4. 10. 6. 11. 7. 12. 41. 13. 6. 14. 34. 15. 33. 16. 24. 17. 22. 18. 8. Page 232. 1. 120. 2. 232. 3. 138. 4. 224. 5. 669. 6. 429. 7. 254. 8. 206. 9. 532. 10. 413. 11. 380. 12. 461. 13. 342. 14. 352. 15. 378. 16. 423. 17. 277. 18. 300. 19. 136. 20. 135. 21. 235. 22. 446. 23. 248. 24. 124. 25. 312. 26. 138. 27. 253. 28. 309. 29. 338. 30. 348. 31. 425. 32. 344. 33. 425. 34. 261. 35. $353. 36. $17. 37. $35. Page 233. 1. 9; 108. 2. 2640; 1320; 660. 3. 160; 80; 40. 4. 36; 198; 63,360. 5. 2; 17. 6. 264; 355. Page 234. 1. 224. 2. 6^. 3. 68. 4. 4. 5. 112. 6. 7. 7. 832. 8. 22. Page 235. 1. 16; 16. 2. 240. 3. 1664 sq.ft. 4. 3654 sq.yd. 5. 1936 sq.ft. 6. 703 sq.yd. 7. 4214 sq. ft. 8. 17,112 sq. ft. Page 236. 4. 9 sq. ft. ; 1 sq. yd. ; 1296 sq. in. Page 239. 1. 102 sq. ft. 2. 324 sq. ft. 3. 1113 sq. in. 4. 300 sq. yd. 5. 1248 sq. yd. 6. 1650 sq. yd. 7. 1725 sq. rd. 8. 1368 sq. ft. 9. 1504 sq. in. 10. 5494 sq. in. 11. 1551 sq. yd. 12. 5184 sq. ft. 13. 1102 sq. in. 14.2666sq.ini. 17. 8 in.; 64. 18.640. 19.475. 20.98. Page 240. 1. 38 ft. 3. 2 in. EP 14 ESSENTIALS OF ARITHMETIC Page 242. 1. Bcu.it. 2. 128cu.in. 3. 6. 4. 3192cu.in. 5. 37,152 cu.in. 6. 1656 cu. ft. 7. 1396 cu. yd. Page 243. 1. 1152. 2. 2160. 3. 180. 4. 192. 5. 2850. 6. 2310. Page 245. 1. $216.75. 2. $187. 3. $6.10. 4. $65.25. 5. $92.75 ; $185.50; $251.75; $371; $490.25; $649.25. 6. $80.75. 7. $128.70; $137.80; $150.80; $162.50. 8. $12.90. 9. $12.90. Page 246. 1. $24.75. 2. $0.35. 3. $1.85. 4. $1.39. Page 247. 1. $57.60; $7.20; $4.80. 2. $10.81; $86.48. 3. $4.19. 4. $0.81. 5. $3.92. 6. $658.56. 7. 45 min. 8. 2 hr. 25 min. Page 250. 1. 15; 30. 2. 12; 60. 3. 27; 54. 4. 9; 18. 5. 15; 30. 6. 21; 42. 7, 14; 28. 8. 18; 36. 9. 22; 44. 10. 13; 39; 52. 11. 6; 18; 24. 12. 17; 51; 68. 13. 8; 24; 32. 14. 16; 48; 64. 15. 19; 57; 76. Page 253. 1. ; J; f ; f ; f ; f ; f ; y. 2. f ; $; f ; f ; *; Y; f ; V- 3 4-2.6.8.12.28.1.2 4. 6- 3- 9- 4- 8. 2. 10- 1 K 1 . * f t T> fi Tf TT* f ' r ** l ft W'lfc T> 1 t! t' J> ? ' | t t 1 f f ! 6. in. ; in. ; in. is the greater. 7. -^ in. ; ^ in. ; i in. is the greater. 8. f;f;f 9. T