ORAL EXERCISES in NUMBER By Anna L, Rice z M- . GIFT OF R-D -L1NQUIST 1 EDUCATION DEPT. ORAL EXERCISES IN NUMBER FOR USE IN GRADES FOUR TO EIGHT INCLUSIVE BY ANNA L. RICE PRINCIPAL OF LINCOLN SCHOOL, SPRINGFIELD MASSACHUSETTS AUTHOR OF "OUTLINES IN DICTIONARY STUDY " THE GREGG PUBLISHING COMPANY NEW YORK CHICAGO BOSTON SAN FRANCISCO LONDON COPYRIGHT, 192 1, BY THE GREGG PUBLISHING COMPANY Gift R.D .LINQUIST EDUCATION DEPT. PREFACE Though educators differ as to just how much knowledge of arithmetic is essential to a common-school education, the necessity of teaching certain fundamental facts of number is unquestioned. Children must be taught to add, subtract, multiply, and divide, whole numbers. They must understand common fractions, and be able to perform the same operations with these as with whole numbers. Some knowledge of decimals is necessary, in order that they may be able to use United States money. They must be acquainted with the common facts of denominate num- bers, and know the elements of percentage. This elementary knowledge of number is essential not only to a common-school education, but as a foundation for all advanced work in mathematics. If this foundation is weak, the work built upon it will be weak; for it is clear that no problem can be correctly solved if the simple operations which it involves are incorrectly performed. Nor should we be satisfied with accuracy alone. The facts of number are not in any true sense learned until they can be quickly, as well as accurately, recalled. If the teaching of the fundamental facts of number is to be effective — if these simple number combinations, which are the very alphabet of all mathematical work, are to be mastered — systematic training must be given. No royal road to the accomplishment of this end has yet been found. Mastery of these tools of the mind, like the mastery of a musical instrument, comes through long-continued practice only. In other words, drill is indispensable. Drill in arithmetic, to be effective, must be regular. A few minutes daily should be devoted to it in each grade. It must be '^cro ^ a iv PREFACE thorough ; that is, the facts need to be presented over and over again. The method of presenting these facts must also be varied from day to day, in order to maintain interest. To provide for this daily drill, an abundance of material is necessary. The textbook in arithmetic, however excellent it may be, cannot fully supply this need. Oral Exercises in Number is intended to supplement any basal textbook in arithmetic, and is adapted for use from the fourth grade to the high school. It is not assumed that the book will be used for more than ten minutes daily in any grade. This daily period of drill, if begun in the fourth grade, should enable pupils to master the essential facts of number by the time they reach the seventh or the eighth grade. It is not necessary to lengthen the arithmetic period to allow for this work, for pupils will soon be able to do their written arithmetic more rapidly as the result of this daily oral drill. As they gain in accuracy and speed, and the time now so unprofitably spent in looking for and correcting mistakes is gradually eliminated, less time will be re- quired to teach the topics of the higher grades, and children will take greater interest and pleasure in their work. For every one enjoys doing the things he can do well, while failure is discouraging to us all. As indicated by the spacing the exercises on most of the pages are graded, the first group of exercises on each page being the simplest. It is not possible, however, to say definitely what exercises should be used in a given grade. This must be de- termined by the ability of the children, and by what has already been mastered. In using these graded pages, teachers should be guided by the following rule : " Master the first group of exercises on any page before taking the second, and master the second group before taking the third.' ' The ungraded pages are of about equal difficulty throughout, and require no explanation. PREFACE V It is expected that teachers will use the exercises suited to their grades not simply once or twice, but many times. The same exercise should not, however, be used on two or more consecutive days. This would mean loss of interest, and possible memorizing of answers. Since one exercise affords as good mental drill as another, the power gained by spending ten minutes on any exercise will help pupils to master any other. After going through an exercise once or twice leave it for a different one, coming back to it from time to time until children have no further need of it. A study of the mistakes made by children in their arithmetical work shows that some number facts are remembered with greater difficulty than others. The most troublesome combinations occur most frequently on the pages of this book. Since variety is as important a factor in effective drill as repe- tition, the same old number facts are dressed in new costumes and introduced under different headings, such as " United States Money/' " Denominate Numbers," " Percentage," etc. An im- portant by-product of this method of drill will be the familiarity thus acquired by pupils with the elements of these subjects. While the object of these exercises is to develop both accuracy and speed, teachers should never lose sight of the fact that chil- dren are to be trained to accuracy first. Do not confuse them by trying to secure speed and accuracy at the same time. An exercise should be well learned before children are timed in recit- ing it. Much interest can be aroused in number-drills, and the value of these drills will be in proportion to the interest and enthusiasm of the class. An appeal to the play instinct meets with instant re- sponse from children, who love to compete with each other in doing mental, as well as physical, stunts. Teachers will find these ex- ercises well adapted for group work, and class drills should be sup- plemented by much work of this kind. A few suggestions for making the drills interesting will be found on another page. VI PREFACE The author gratefully acknowledges her indebtedness to Dr. James H. Van Sickle, Superintendent of Schools, Springfield, Massachusetts; to Dr. G. M. Wilson, Professor of Education, Iowa State College; and to Miss Sarah J. Lee, formerly teacher of mathematics in the High School, Riverside, California, for their courtesy in reviewing this text and for their many helpful criticisms and suggestions. A. L. R. HOW NUMBER-DRILLS MAY BE MADE INTERESTING Hints to Teachers The purpose of this book, as stated in the preface, is to supply teachers in elementary and junior high schools with material for oral drill in the fundamental facts of number. Since the value of this drill will depend largely upon the way in which the book is used, it is hoped that teachers will first of all read the preface, in order to acquaint themselves with the principles upon which the book is based, the arrangement of material, and the manner in which the exercises are intended to be used. It is suggested that teachers supplement class drill by much group work. This method of study is particularly interesting and effective when used as a means of preparation for the one- minute exercises and speed tests suggested further on. As a rule, only exercises which have been studied in class should be assigned for group work, and the leader of each group should be a pupil who has accurately recited the exercise chosen for study. Any member of the group may, however, question the correctness of an answer accepted by the leader, and the group as a whole must be convinced that the answer finally accepted is right. The value of group work depends upon the keen participation of each member of the group in the work being done, and each pupil should feel a sense of personal responsibility for noticing errors. Considerable freedom is t therefore necessary, but no disorder. It is quite possible for several groups to work at the same time without disturbing one another or the teacher in the least. It will add to the independence of pupils if they learn where to find, in their textbook in arithmetic, the multiplication Vlll HINTS eTO TEACHERS tables and the tables of denominate numbers, and form the habit of referring to these tables whenever in doubt about the facts which are to be found stated in them. On pages 84 and 124 will be found a few suggestions for one- minute exercises and speed tests, indicating ways in which almost any exercise may be used after it has been sufficiently practiced. Pupils should frequently be allowed to choose the exercise for study. A few minutes' drill on this exercise will show each member of the class where his own weakness lies, and after a period of study — preferably in groups — individuals may be timed in reciting either the whole exercise or some part of it. Or, a row of pupils, each in turn answering one question, may compete with another row reciting in the same manner. Another suggestion is that a boy* be chosen by the boys and a girl by the girls to compete with each other, answering ques- tions alternately from a given exercise. If the boy makes a mistake the girls win, and vice versa. If neither one makes a mistake, it is a tie. Another boy and girl are then chosen, and the game proceeds as before. Still another suggestion is that a game like the old-fashioned spelling match be made of these exercises, the pupils being evenly divided on "sides." The teacher should choose simple exercises for this game, and should put the questions herself. As teachers become familiar with the contents of this book, they will develop methods of drill better suited, perhaps, to the needs of their classes than any here suggested. The important fact to keep in mind is that the only good drill is a lively one. The success of any drill is measured by the degree of interest aroused. CONTENTS PAGE Whole Numbers 1 to 60 Addition 1 Subtraction 18 Addition and Subtraction . . . . . . . 23 Multiplication 26 Facts of the Multiplication Tables 37 Multiplication and Addition 38 Multiplication and Subtraction ....... 39 Division 40 Facts of the Division Tables 48 Multiplication and Division . . . . . . .49 Practice in Interpreting Signs Quickly 50 Relation of Numbers 53 Cancellation 54 Factoring 58 Numbers — Prime and Composite 59 Factors and Multiples . 60 Common Fractions 61 to 83 Reduction ' 61 Comparison 66 and 76 Addition 67 Subtraction 70 Addition and Subtraction 73 Multiplication 74 Fractional Parts of Numbers 79 Division 81 Special One-minute Exercises . . . . . . .84 United States Money 85 to 96 U. S. Coins 85 Addition 86 Finding Amount of Purchases 87 ix X CONTENTS PAGE Subtraction — Making Change . . . . . . .88 Fractional Parts of One Dollar 91 The Number Twenty-Five 96 Decimal Fractions 97 to 108 Addition 97 Subtraction 100 Multiplication ..103 Division 106 Denominate Numbers 109 to 113 Reckoning Time 113 Percentage . 114 to 119 Percentage and Denominate Numbers 120 to 123 Speed Tests in Percentage 124 Areas and Perimeters 125 Appendix 126 to 135 Reading of Whole Numbers 127 Reading Exercise : U. S. Money 129 Reading Exercise : Roman Numerals . ... . . 130 Months and Dates 131 Relation of Numbers, or Ratio 132 Questions for Leisure Moments 133 WHOLE NUMBERS ADDITION 1. 1 and 2 2. 4 + 3 3. 3 and 4 4. 6 + 5 5 and 2 7 + 3 5 and 4 2 + 5 4 and 2 3 + 3 1 and 4 1 + 5 7 and 2 8 + 3 and 4 7 + 5 3 and 2 9 + 3 6 and 4 8 + 5 9 and 2 + 3 8 and 4 3 + 5 8 and 2 2 + 3 2 and 4 9 + 5 2 and 2 6 + 3 9 and 4 + 5 6 and 2 1 + 3 4 and 4 4 + 5 and 2 5 + 3 7 and 4 5 + 5 5. 10 + 4 6. 20 + 2 7. 30 + 5 8. 40 + 3 11 + 3 21 + 5 31 + 2 41 + 4 12 + 3 22 + 2 32 + 4 42 + 5 13 + 4 23 + 3 33 + 2 43 + 5 14 + 2 24 + 5 34 + 3 44 + 4 15 + 5 25 + 2 35 + 4 45 + 3 16 + 2 26 + 3 36 + 5 46 + 4 17 + 5 27 + 4 37 + 3 47 + 2 18 + 3 28 + 5 38 + 2 48 + 4 19 + 4 29 + 3 39 + 5 8 49 + 2 Id: 9. 5 6 4 3 6 10. 7 3 6 2 4 6 8 9 5 6 8 7 5 9 2 7 7 8 2 9 4 8 9 11. 3 9 6 3 5 12. 3 2 7 6 9 7 5 4 7 9 2 3 7 6 8 9 7 8 9 7 3 8 7 13. 1 3 2 1 2 14. 6 5 8 4 7 2 4 5 8 6 7 5 4 7 8 9 5 9 6 1 6 5 8 4 7 2 WHOLE NUMBERS ADDITION 1. 6 plus 6 2. 3 + 7 3. 5 and 8 4. 1 + 9 plus 6 6 + 7 9 and 8 4 + 9 3 plus 6 9 + 7 1 and 8 + 9 1 plus 6 2 + 7 7 and 8 9 + 9 5 plus 6 4 + 7 2 and 8 6 + 9 2 plus 6 8 + 7 8 and 8 2 + 9 9 plus 6 1 + 7 3 and 8 8 + 9 8 plus 6 5 + 7 and 8 3 + 9 7 plus 6 7 + 7 4 and 8 7 + 9 4 plus 6 + 7 6 and 8 5 + 9 5. 50 + 8 6. 60 + 9 7. 70 + 6 8. 80 + 7 51 + 6 61 + 7 71 + 8 81 + 9 52 + 7 62 + 8 72 + 9 82 + 6 53 + 7 63 + 8 73 + 9 83 + 6 54 + 9 64 + 7 74 + 6 84 + 8 55 + 7 65 + 9 75 + 6 85 + 8 56 + 6 66 + 8 76 + 9 86 + 7 57 + 8 67 + 7 77 + 6 87 + 9 58 + 9 68 + 8 78 + 7 88 + 6 59 + 6 69 + 9 79 + 8 89 + 7 Add: 9. 5 3 9 2 5 10 6 3 8 7 9 4 8 4 1 7 2 7 1 2 6 7* 7 6 6 5 8 9 2 2 1 8 9 7 8 7 8 2 11. 2 3 7 8 6 12 9 3 2 3 9 8 5 7 8 6 2 5 2 8 6 6 9 4 3 4 9 8 4 9 8 9 4 3 7 8 5 2 1 WHOLE NUMBERS ADDITION 3 1. 1 2 3 4 5 2. 6 7 8 9 6 5 4 5 8 5 9 9 2 7 3. 1 2 3 4 5 4. 6 7 8 9 6 4 9 6 9 7 7 6 4 4 6 5. 1 2 3 4 5 6. 6 7 8 9 7 6 5 2 9 8 7 8 3 9 7. 1 2 3 4 5 8. 6 7 8 9 7 8 7 8 4 1 9 4 7 9 2 9. 8 9 3 4 5 10. 7 2 5 1 6 2 1 7 6 5 3 8 5 9 4 11. 3 7 4 5 5 12. 4 2 1 9 3 3 2 4 3 4 2 8 6 4 1 2 2 1 6 6 1 1 1 13. 7 3 4 8 6 14. 3 9 8 9 4 5 1 2 • 7 6 5 4 5 6 9 2 9 6 3 3 3 4 7 3 7 15. 7 9 3 4 8 16. 5 8 7 6 4 8 2 4 7 8 4 2 3 8 5 6 5 6 5 2 5 3 5 6 8 17. 2 5 6 5 3 18. 6 2 4 6 1 8 9 1 3 8 9 8 3 8 3 7 4 7 2 4 1 5 2 4 1 2 8 7 8 9 7 5 4 7 19. 5 7 8 4 2 20. 6 5 3 7 3 8 9 6 6 2 4 8 7 9 7 5 1 3 8 3 5 3 2 6 6 3 9 7 9 3 9 n 4 5 WHOLE NUMBERS ADDITION 1. 1 + 6 2. 1 + 4 3. 1 + 7 4. 1 + 9 2 + 5 2 + 8 2 + 6 2 + 7 3 + 4 3 + 6 3 + 5 3 + 8 4 + 6 4 + 9 4 + 8 4 + 4 5 + 8 5 + 2 5 + 3 5 + 5 6 + 4 6 + 7 6 + 8 6 + 9 7 + 9 7 + 3 7 + 2 7 + 4 8 + 6 8+4 8 + 5 8 + 7 9 + 2 9 + 5 9 + 4 9 + 9 + 7 + + 9 + 2 Add: 5. 13 24 49 27 6. 12 39 73 44 5 6 8 6 2 5 8 7 7. 65 34 19 51 8. 77 66 55 13 _8 5 6 5 7 6 8 7 9. 33 42 87 91 10. 75 69 25 48 _8 8 5 7 4 8 6 4 11. 5 3 8 6 4 12. 6 2 6 5 3 67031 78083 02873 17382 49428 35802 51^52 12 14 4 13. 3 4 7 8 6 14. 7 3 2 1 9 90836 84 4 30 86152 05658 26902 36072 2 3 295 77814 WHOLE NUMBERS ADDITION 5 1. 1 + 5 2. 5+1 3. 8 + 8 4. 2 + 3 9 + 7 2 + 4 1 + 8 7 + 5 4 + 5 6 + 5 9 + 6 9 + 1 3 + 7.. 7 + 7 7 + 6 3 + 9 2 + 9 8+1 5 + 9 8 + 9 5 + 6 9 + 8 2 + 3 6 + 3 8 + 3 4 + 7 4 + 3 4 + 2 7 + 8 3 + 2 6 + 2 7 + 5 4+1 5 + 7 3 + 3 5 + 4 6 + 6 7+1 8 + 2 9 + 3 Add: 5. 24 16 44 57 6. 42 50 29 19 12 32 22 30 26 18 10 50 7. 75 38 73 61 8. 15 46 64 70 11 40 24 17 31 12 33 25 9. 25 16 80 21 10. 15 35 49 36 42 31 19 23 51 42 30 41 11. 7 8 3 6 2 12. 9 1 3 4 2 4 8 9 3 4 3 2 8 9 8 5 4 7 4 6 5 2 7- 2 4 6 5 3 5 3 1 6 3 4 3 7 4 3 1 4 2 5 1 2 2 8 2. 1 7 2 9 3 2 1 13. 4 6 5 3 5 14. 8 7 1 2 6 1 4 8 3 5 6 2 7 8 2 7 6 5 9 8 3 8 1 8 2 3 9 6 3 5 2 8 5 7 6 5 7 4 6 9 4 6 3 5 8 7 5 2 7 4 6 4 1 6 WHOLE NUMBERS ADDITION Add: 1. 9 7 3 8 6 2. 5 8 4 2 9 8 6 4 2 9 5 6 5 7 5 3. 7 5 6 8 9 4. 9 8 5 6 4 9 4 6 3 9 3 7 9 7 5. 8 7 4 2 5 6. 1 8 5 6 7 8 7 6 9 8 9 7 5 3 13 + 4 10 7. 8. 62 plus 2 9. 17 + 7 . 36 + 6 27 + 9 45 plus 4 19 + 6 22 + 7 84 + 6 37 plus 3 38 + 5 33 + 8 55 + 8 89 plus 7 23 + 4 44 + 9 31 + 5 52 plus 5 14 + 9 55 + 8 42 + 8 21 plus 9 66 + 8 66 + 7 26 + 5 93 plus 8 43 + 7 77 + 6 57 + 7 64 plus 6 29 + 3 88 + 5 45 + 3 33 plus 5 34 + 5 19 + 4 78 + 6 88 plus 8 50 + 6 26 + 3 Add: 11. 50 30 60 4C ) 20 12. 70 80 10 90 50 10 20 80 4( ) 50 10 20 40 20 50 13. 55 37 64 43 22 14. 74 83 14 95 58 10 20 30 40 50 10 20 40 20 50 15. 55 37 64 43 22 16. 74 83 14 95 58 13 21 32 44 56 12 25 44 22 51 17. 64 81 45 73 26 18. 18 54 83 44 75 35 16 24 15 32 31 32 16 30 11 WHOLE NUMBERS ADDITION 7 1. 15 + 2 2. 64 + 3 3. 52 + 4 4. 75 + 5 21 + 2 27 + 3 25 + 4 48 + 5 36 + 2 35 + 3 44 + 4 33 + 5 45 + 2 91 + 3 88 + 4 56 + 5 18 + 2 84 + 3 16 + 4 67 + 5 57 + 2 36 + 3 22 + 4 71 + 5 64 + 2 72 + 3 53 + 4 74 + 5 33 + 2 29 + 3 92 + 4 39 + 5 12 + 2 43 + 3 37 + 4 82+5 49 + 2 48 + 3 41 + 4 54 + 5 Add: 5. 67 24 36 50 28 6. 41 54 65 63 19 3 2 4 5 3 5 2 4 2 5 7. 37 45 92 69 11 8. 84 94 37 81 35 A A A A A A A A A A 9. 49 27 38 16 27 10. 39 58 87 76 92 45354 23453 11. 78 37 89 93 56 12. 68 77 88 29 18 5 4 5 2 3 5 4 _3 2 _5 13. 44 81 25 52 14. 88 39 42 53 36 49 36 39 52 17 29 38 15. 53 49 68 48 16. 57 72 95 81 25 27 33 44 12 33 55 47 17. 25 37 82 58 18. 24 36 54 28 58 70 35 37 47 63 45 69 19. 19 28 39 56 20. 45 82 16 44 34 63 29 36 37 94 65 37 8 WHOLE NUMBERS ADDITION 1. 15 + 6 2. 64 + 7 3. 52 + 8 4. 75 + 9 21 + 6 27 + 7 25 + 8 48 + 9 36 + 6 35 + 7 44 + 8 33 + 9 45 + 6 91 + 7 88 + 8 56 + 9 18 + 6 84 + 7 16 + 8 67 + 9 57 + 6 36 + 7 22 + 8 71 + 9 64 + 6 72 + 7 53 + 8 74 + 9 33 + 6 29 + 7 92 + 8 39 + 9 12 + 6 43 + 7 37 + 8 82 + 9 49 + 6 48 + 7 41 + 8 54 + 9 Add: 5. 67 24 36 50 28 6. 41 54 65 63 19 _8 6 9 7 _8 7 _6 8 9 _6 7. 37 45 92 69 11 8. 84 94 37 81 35 _7 _7 _8 9 J6 _8 6 _8 7 9 9. 49 15 62 92 35 10. 27 12 35 63 84 _6 7 9 _6 _8 _7 6 J_ 8 6 11. 75 37 46 73 52 12. 39 84 28 45 81 _8 _6 _9 _7 J_ _8 _6 _8 _6 _9 13. 36 44 85 23 92 14. 51 27 44 66 18 25 15 25 38 78 39 12 27 35 24 15. 81 37 25 48 92 16. 53 66 74 35 27 18 24 36 22 17 37 33 81 56 19 17. 92 18 50 73 44 18. 55 87 77 85 74 72 23 65 27 36 15 29 60 25 j)6 19. 58 27 33 81 28 20. 15 22 64 19 70 12 12 66 34 29 56 80 40 36 25 WHOLE NUMBERS ADDITION To add 9, add 10 and subtract 1. 15 2. 66 3. 34 ; 4. 24 23 44 45 36 67 33 • 56 48 84 22 27 52 19 32 + 9 35 78 ^ + 9 89 + 9 61 73 55 88 92 85 60 77 21 47 38 25 40 29 46, 30 13 70 + 9 24 plus 2 plus 5 13 plus 3 plus 9 42 plus 4 plus 7 50 plus 7 plus 8 12 plus 3 plus 6 37 plus 9 plus 4 64 plus 5 plus 2 6. 32 + 5+ 4 + 3 48 + 3+ 7 + 7 82 + 6+ 4 + 5 35 + 4+ 2 + 8 17 + 7+ 5 + 9 56 + 8+10 + 4 77 + 3 + 3 + 9 Note. The following method of adding is for higher grades only. Learn to recognize at a glance groups of figures which make 10. 7. 6 2 3 5 7 8. 3 2 6 3 3 5 81 1 6 8 4 6 9 3 2 6 1 4 3 8' 3 3 6 4, 3 3 1 7 2 2, 6 2 4. 2 7 1 7 6^ 5. 1 9 4 2 9 4^ 8 5 3 8 7 4 4, 8, 5^ 3 9 2" 4 5 8 3 : 6 1 3, 3 6 1 7 9 1 7 J 6 2 2, fr 6^ 4 3 4 9 3 3 5, 9 2 1 4 1 7 1 4 6 8 5 2 4 1 4 7 10 WHOLE NUMBERS ADDITION To add 11, add 10 arid 1 more. 15 23 67 84 19 32 55 60 38 46 2. + 11 •66 1 44 33 22 11 35 88 77 25 30 3, + 11 34 45 56 27 78 89 92 21 40 13 + 11 24 36 48 52 61 73 85 47 29 70 + 11 Add: 7. 11, 6, 5, and 9. 6. 13, 9, and 11. 8, 3, 4, 8, and 11. 27, 9, and 11. 5, 8, 3, 9, and 2. 54, 9, and 11. 6, 4, 4, 11, and 7. 62, 9, and 11. •3, 8, 9, 5, and 8. 39, 9, and 11. 4, 5, 5, 3, and 11. 45, 9, and 11. 2, 6, 8, 10, and 3. 76, 9, and 11. 5, 3, 7, 9, and 6. 28, 9, and 11. Groups of figures which equal 10 may be called 10 in adding. 5 4 5 2 7 6 8 3 4 3 6 2 8 7 2 9 1 3 5 7 1 9 1 1 2 7 8 4 9 3 6 1 5 3 5 3 7 1 5 7 3 3 4 3 4 3 2 1 4 9 5 8 2 6 2 2 4 5 5 1 9 7 4 7 3 5 4 1 2 8 6 7 7 2 5 3 2 8 7 4 3 3 5 5 6 6 5 5 2 8 7 4 3 5 6 8 1 6 4 5 7 8 2 5 6 3 WHOLE NUMBERS ADDITION 11 + 2 + 6 + 11 2. 22 3. 86 4. 85 59 21 62 63 32 49 91 90 37 87 44 ^Q 48 + 3 53 71 > + 4 20 25 84 33 30 67 58 76 35 64 38. 29. 46. 6. 29 7. 38^ 8. 69 35 76 28 67 25 47 84 44 26 53 48 \ 7 50 > + 7 87 ^ + 8 24 32 91 30 21 63 83 70 59 42 86. 22. 31. 0. 91 11. 55 12. 71 63 24 37 59 83 50 22 42 49 38 76 + U 31 — : 60 69 46 25 28 64 44 47 58 87. 26. 33. ^ + 5 12 WHOLE NUMBERS ADDITION Add: 1. 5 8 7 4 4 2. 3 5 2 9 6 3 2 3 8 3 2 4 6 1 2 4 1 3 6 3 7 1 4 7 3 3. 4 2 3 8 7 4. 6 3 9 5 7 3 9 7 8 1 7 5 8 5 2 6 5 8 2 2 3 2 4 4 4 5. 6 8 9 3 6 6. 2 1 5 7 4 6 3 4 2 2 7 6 4 6 2 4 2 5 9 2 7 3 6 5 8 ~~" and 5, 1, add 1( For 5 6 and 4, 7 and 3, 8 and 2, or 9 and J. 7. 3 9 4 3 8 8. 5 4 7 5 9 4^ 5 8 91 3 5j 3 2 \\ 6, 41 3 1J 91 1 21 3, 4 5 8 6j 5 1 7 U 7 8j 5 8" 2 3 5, 2 6^ 3 6 2 6, 2 7' 5 6 4 4 2^ 7 4 3 4 i 3 21 2 71 5 : 8] 61 3^ 2 6J 5 8J 8 3J 5 6 4j 7 1 3 Notice t b te n. he groups o f figures whi ch mak 9. 7 5 4 7 2 10. 2 3 6 4 4 3 5 9 6 4 6 7 4 4 4 3 3 8 5 7 3 6 5 2 2 1 5 3 5 2 2 6 5 6 7 3 4 5 8 1 5 2 3 7 1 5 6 5 8 5 9 3 6 2 8 9 1 4 9 8 8 1 6 6 7 7 3 9 8 6 2 6 6 4 4 3 3 1 2 1 7 4 5 1 8 2 7 6 2 WHOLE NUMBERS ADDITION 13 Add: 1. 3 2 8 4 6 2. 3 5 9 7 2 1 6 7 9 4 2 3 8 9 9 4 4 5 5 6 6 7 7 8 5 8 4 9 3 .2 7 8 1 4 3. 6 5 8 4 2 4. 3 6 8 7 5 7 1 3 2 4 5 6 8 4 6 8 5 6 7 8 5 2 3 2 9 5 6 7 4 3 7 2 3 2 5. 4 3] 2 7 6. 1 4^ 5 1 5 7' 7 J 3 6 4 6 1 1 1 31 6^ 5 4 3 5 11 41 8 7J 4, 1 5 9 8 9^ 6j 41 9 2 4^ 7 81 8] 3 8 81 6j 8 5 2j 3 71 2J 3 8 5 6, 6 2J 5 3, • 1] 9 7 5. 7 91 9 51 7 ! 2 9j 5 6 3 9 lj 5 5] 3j 4 . 3 7 ] 4 6 2 4 5 3 3 2 8 4 7 B 5 3 7. 5 2 5 8 8. 1 3 6 4 6 3 4 7 6 6 3 3 2 3 5 1 5 3 5 2 4 8 8 7 3 3 5 7 6 6 1 2 9 8 3 6 4 9 3 1 4 5 1 2 7 9 3 3 3 2 1 8 3 6 1 9 5 4 5 7 9 4 6 5 8 9 2 3 3 9 6 9 6 3 4 1 9 2 4 3 4 2 4 2 6 8 1 3 4 3 8 7 8 5 5 1 7 6 6 5 7 1 8 2 5 5 14 ADDITION DRILL FOR RAPIDITY Add l. 4 7 8 6 5 2. 6 8 3 9 9 7 9 • 5 4 6 7 7 5 6 3 3. 5 6 8 7' 9 4. 6 9 5 3 4 2 4 1 6 5 7 2 4 6 8 9 3 6 5 6 4 7 6 2 5 6. 5 2 8 4 7 6. 9 5 6 2 3 1 9 4 5 6 7 3 3 8 2 4 3 7 1 2 5 7 1 9 8 6 8 4 5 5 2 6 8 7 3 7. 8 4 2 7 5 8. 4 1 9 6 3 2 5 3 8 4 2 5 1 4 6 7 9 8 3 7 6 4 3 8 5 2 9 3 8 6 5 1 9 2 7 3 6 7 4 8 5 7 4 3 2 9. 8 5 9 4 3 10. 2 1 5 4 7 6 4 8 9 5 8 3 4 7 1 3 2 4 1 9 6 8 3 9 7 9 8 1 6 4 2 8 6 5 8 1 7 6 4 3 5 7 3 5 2 11. 6 5 3 4 8 12. 1 2 7 4 9 5 8 4 1 3 9 6 6 4 2 4 3 7 8 8 5 9 2 6 6 6 3 3 5 4 5 8 1 3 7 2 9 4 6 3 4 2 7 5 8 ADDITION DRILL FOR RAPIDITY 15 Add: 1. 3 7 3 8 3 2. 2 7 6 3 2 2 6 7 7 6 8 6 1 2 6 4 4 4 8 2 5 6 1 7 3 2 7 3 2 1 1 5 3 8 6 9 3 2 6 8 8 5 6 2 5 9 6 8 5 9 4 4 3 4 3 5 7 3 1 9 3 2 4 9 4 5 7 8 5 1 2 1 5 4 3 9 5 Add 10 for a group of figures equal to 10. 3. 2 3 2 7 4 4. 2 5 2 3 1 5 7 3 6 6 4 1 8 1 4 6 5 4 3 1 8 4 9 5 4 1 5 9 9 4 9 4 8 4 7 8 8 8 6 8 6 6 3 5 2 7 3 8 5 6 3 6 6 2 3 9 7 3 7 5 7 9 9 5 2 5 6 8 7 9 1 5 5 5 7 3 2 2 3 2 5 3 3 8 3 4 7 5 2 5. 6 7 5 4 6 6. 3 4 3 9 2 7 2 4 5 5 7 8 8 9 5 9 3 1 6 8 5 7 5 2 3 3 9 7 4 7 6 2 8 6 4 5 5 8 9 1 3 5 2 4 4 4 8 6 9 2 1 9 5 5 7 6 7 4 3 4 9 6 9 3 8 8 3 9 7 9 8 3 4 2 3 2 5 5 8 5 5 1 6 8 2 7 6 3 6 5 4 8 3 7 5 16 ADDITION DRILL FOR RAPIDITY Add: 1. 2 7 9 5 6 2. 3 2 9 4 7 3 9 2 5 5 3 3 5 5 8 4 2 4 4 4 7 1 8 7 2 3 2 1 4 8 3 9 4 4 6 8 7 7 4 8 3 6 5 9 7 6 5 8 4 5 6 1 5 2 9 3 6 4 2 4 6 7 2 5 5 3 6 7 1 3 1 4 1 8 7 7 1 8 7 3 7 9 8 8 2 9 5 3. 3 4 8 5 6 4. 1 9 3 4 7 2 7 4 6 8 3 3 7 5 9 3 8 6 4 7 2 8 8 1 3 7 4 2 9 6 7 5 4 8 9 9 6 5 5 4 3 2 5 7 2 1 8 6 5 6 7 9 1 5 5 2 9 4 3 8 3 7 4 6 5 7 3 8 2 9 6 1 8 4 4 2 9 3 3 7 2 2 5 8 4 6 5 1 5 8 5. 3 6 1 4 2 6. 8 7 9 5 3 1 8 7 6 5 4 4 3 7 2 1 9 3 7 2 9 4 7 7 6 1 9 8 3 7 1 5 8 8 7 1 5 4 1 6 6 5 5 2 9 4 5 7 2 5 8 4 2 5 6 3 8 9 6 2 3 9 4 1 8 6 5 7 2 1 5 3 4 4 7 2 1 2 7 5 4 8 6 2 2 7 5 8 4 2 3 1 ADDITION DRILL FOR RAPIDITY 17 id: 1. 2 4 6 5 8 2. 7 6 1 4 2 7 8 3 9 6 5 8 9 3 7 5 1 7 4 2 4 3 9 7 2 8 9 4 6 7 6 8 3 4 1 3 2 6 5 4 9 4 5 3 3 2 7 1 3 5 2 7 4 6 7 4 8 3 5 8 1 6 3 2 2 5 4 9 6 7 2 7 4 3. 5 6 4 2 9 4. 8 5. 5 3 . 1 2 8 5 7 4 7 5 3 2 8 6 1 9 8 5 4 2 7 9 4 8 7 6 2 3 1 9 8 4 6 6 8 4 9 6 3 8 5 5 1 3 2 1 4 6 8 1 4 6 3 7 8 5 6 2 3 5 6 2 4 6 4 3 1 8 2 3 2 8 6 2 3 9 8 5 4 7 3 1 5 3 6 4 3 2 6 2 7 4 1 5 7 8 6 9 6. 4 8 6 5 3 6 9 7 4 9 6 8 3 8 9 4 7 5 9 2 8 4 7 7 8 8 5 6 5 9 7- 4 3 6 5 7 5 3 8 5 9 6 8 4 3 2 7 5 9 3 8 7 6 9 7 6 4 8 5 7 2 5 6 5 9 9 2 3 5 8 6 8 4 6 4 5 8 5 7 5 9 6 3 8 5 2 7 2 9 3 6 9 8 4 6 1$ WHOLE NUMBERS SUBTRACTION 1. 4 less 2 2. 11 - 3 3. 12 - 4 4. 14 - 5 7 less 2 9-3 5-4 7-5 5 less 2 3-3 9-4 12-5 8 less 2 5-3 6-4 8-5 3 less 2 7-3 8-4 5-5 2 less 2 6-3 10-4. 6-5 9 less 2 4-3 4-4 9-5 6 less 2 8-3 7-4 10-5 10 less 2 10-3 11-4 11-5 11 less 2 12-3 13-4 13-5 Subtract : 5. 24 37 85 69 46 21 72 33 68 50 2 2 2 2 2 2 2 2 2 2 6. 54 67 55 49 76 31 92 83 58 70 3 3 3 3 3 3 3 3 3 3 7. 44 27 65 59 56 51 82 43 28 60 4 4 4 4 4 4 4 4 4 4 8. 94 87 25 89 36 41 62 53 78 80 5 5 5 5 5 5 5 5 5 _5 9. 80 87 82 85 88 83 89 86 81 84 12 12 12 12 12 12 12 12 12 12 10. 63 60 69 66 67 65 61 68 62 64 13 13 13 13 13 13 13 13 13 13 11. 55 58 51 54 59 57 53 56 50 52 14 14 14 14 14 14 14 14 14 14 12. 32 36 35 39 30 38 34 37 31 33 15 15 15 15 15 15 15 15 15 15 WHOLE NUMBERS SUBTRACTION 19 1. 14 less 6 2. 15 - 7 3. 17 minus 8 4. 9 - 9 9 less 6 10-7 11 minus 8 12-9 11 less 6 7-7 16 minus 8 18-9 10 less 6 14-7 12 minus 8 10-9 8 less 6 9-7 9 minus 8 15-9 7 less 6 11-7 13 minus 8 11-9 12 less 6 13-7 14 minus 8 14-9 6 less 6 16-7 10 minus 8 16-9 13 less 6 8-7 8 minus 8 13-9 15 less 6 12-7 15 minus 8 17-9 Subtract : 5. 24 37 85 69 46 21 72 33 68 50 6 6 6 _6 _6 6 6 6 6 6 6. 54 67 55 49 76 31 92 83 58 70 7 7 7 7 7 7 7 7 7 7 7. 44 27 65 59 56 51 82 43 28 60 8 8 8 8 _8 8 8 8 8 8 8. 94 87 25 89 36 41 62 53 78 80 9 9 9 9 9 9 9 _9 9 9 9. 46 44 49 43 40 42 47 45 41 48 16 16 16 16 16 16 16 16 16 16 10. 74 70 79 72 76 78 75 71 77 73 17 J7 17 17 17 17 17 17 17 17 11. 23 26 29 20 24 28 21 27 22 25 18 18 18 18 18 18 18 JL8 _18 18 12. 96 92 99 95 90 98 94 91 93 97 19 19 19 19 19 19 19 19 19 19 20 WHOLE NUMBERS SUBTRACTION 1. 8 9 11 17 10 15 12 9 14 7 2 3 4 8 6 5 3 5 3 2 2. 16 10 18 12 19 8 11 14 15 8 5 4 7 5 3 5 2 6 4 4 3. 14 12 13 10 16 15 14 11 13 18 7 7 6 5 9 6 _8 5 2 3 4. 11 15 19 10 12 18 16 13 17 14 10 10 10 10 10 10 10 10 10 JO Think of 9 as 10 less 1. Think of 1 1 as 10 plus 1 5. 32- -9 6. 55-9 7. 72- 1 8. 45- - 11 36- -9 51-9 76- 1 41 - - 11 33- -9 54-9 73- 1 44- - 11 39- -9 58-9 79- i: 48- - 11 35- -9 52-9 75 - i; 42- - 11 30- -9 50-9 70- 1] 47- 11 34- -9 57-9 74- 1] 40- - 11 37- -9 53-9 77- 1] 43- - 11 31 - -9 56-9 71 - 1] 46- 11 38- -9 59-9 78- 1] 49- 11 Subtract : 9. 45 38 86 72 55 77 94 65 89 54 31. 24 55 30 14 46 71 23 _?z 32 10. 29 37 48 56 65 74 89 98 66 57 22 16 27 34 42 51 75 26 35 46 11. 35 54 63 82 76 90 43 51 64 72 28 45 45 36 48 27 26 33 45 54 12. 70 40 30 80 90 60 50 70 80 60 35 24 16 52 67 38 21 49 33 _26 WHOLE NUMBERS SUBTRACTION 21 Drill for Rapidity. 1. 12-4 4. 87-9 7. 76-4 10. 33 - 5 33-2 13-7 88-7 61-3 26-3 72-2 15-2 95-6 40-7 63-4 32-5 56-9 58-9 41-5 94-8 20-3 62-6 36-7 78-3 83-4 19-5 98-6 25-6 74-6 64-2 27-3 47-4 36-2 96-8 95-9 81-3 71-5 71-4 57-7 48-8 92-9 2. 24-9 6. 65-4 8. 70-7 11. 63-2 55-8 17-8 93-9 40-4 89-5 30-2 54-3 35-5 35-6 66-8 11-7 68-7 73-3 72-5 38-5 17-8 29-7 31-9 74-2 96-4 60-5 45-5 21-6 52-3 44-4 97-6 43-7 34- 10 83-6 18-7 84-5 80-6 50-8 56-4 46-7 15-7 3. 16-6 6. 69-2 9. 91-8 12. 78-5 39-9 37-5 79-3 44-9 86-5 80-6 28-4 55-3 99-4 92-7 49-8 39-4 20-9 23-8 53-4 72- 10 61-2 68-2 77-2 41-5 52-8 42-7 51-5 54-6 67-3 34-3 85-3 93-9 22-5 82-4 59-6 65-6 90-3 75-7 14-9 24-7 22 WHOLE NUMBERS SUBTRACTION Practice first for accuracy, then for speed. 1. Starting at 24 subtract 2's until but 2 is left. 2. Starting at 36 subtract 3's until but 3 is left. 3. Starting at 48 subtract 4's until but 4 is left. 4. Starting at 60 subtract 5's until but 5 is left. 5. Starting at 72 subtract 6's until but 6 is left. 6. Starting at 84 subtract 7's until nothing is left. 7. Starting at 96 subtract 8's until nothing is left. 8. Starting at 108 subtract 9's until nothing is left. 9. Starting at 120 subtract 10's until nothing is left. 10. Starting at 132 subtract 11 's until nothing is left. 1. Starting at 50 subtract 2's until you reach zero. 2. Starting at 60 subtract 3's until you reach zero. 3. Starting at 80 subtract 4's until you reach zero. 4. Starting at 100 subtract 5's until you reach zero. 5. Starting at 102 subtract 6's until you reach zero. 6. Starting at 105 subtract 7's until you reach zero. 7. Starting at 104 subtract 8's until you reach zero. 8. Starting at 200 subtract 10's until you reach zero. 1. Starting at 100 subtract 3 as many times as you can. 2. Starting at 100 subtract 6 as many times as you can. 3. Starting at 100 subtract 7 as many times as you can. 4. Starting at 100 subtract 8 as many times as you can. 5. Starting at 100 subtract 9 as many times as you can. 6. Starting at 100 subtract 11 as many times as you can. 7. Starting at 100 subtract 12 as many times as you can. 8. Starting at 90 subtract 4 as many times as you can. 9. Starting at 99 subtract 5 as many times as you can. 1. 2. ADDITION AND SUBTRACTION 23 Drill for Rapidity. 5 + 2 4. 7-2 7. 3 + 4 10. 14-6 7 + 3 6-3 7 + 5 16-9 9 + 5 10-4 8 + 3 12-7 6 + 6 9-5 6 + 2 13-6 4 + 8 11-9 5 + 8 6-2 2 + 9 12-8 4 + 9 8-4 8 + 4 10-7 3 + 6 13-5 5 + 5 12-6 5 + 7 9-3 8 + 7 9-4 6 + 4 11-6 5 + 6 11-5 9 + 2 5-2 9 + 9 5. 11-8 8. 4 + 5 11. 14-7 2 + 4 15-9 3 + 3 8-3 6 + 3 7-6 9 + 8 17-8 7 + 8 8-5 6 + 7 7-4 3 + 9 9-2 5 + 9 14-9 8 + 6 7-3 7 + 6 7-5 3 + 2 12-9 4 + 2 8-6 5 + 3 14-8 5 + 4 13-8 9 + 4 11-7 8 + 5 18-9 2 + 7 10-6 4 + 3 15-7 6 + 9 6. 12-5 9. 8 + 8 12. 12-4 7 + 7 11-3 7 + 9 11-2 8 + 2 8-2 3 + 7 14-5 9 + 3 9-6 9 + 6 5-3 4 + 4 16-8 7 + 4 15-8 6 + 5 13-7 2 + 5 13-4 2 + 6 10-2 6 + 6 10-3 4 + 7 12-3 9 + 7 11-4 8 + 9 6-4 3 + 8 13-9 7 + 2 10-5 6 + 8 15-6 24 ADDITION AND SUBTRACTION Add, and subtract : 1. 40 60 80 70 90 20 30 50 30 20 10 50 60 10 20 20 2. 60 50 70 40 80 30 90 70 30 40 70 20 60 10 50 40 3. 90 80 60 50 70 40 80 60 30 50 10 30 20 10 30 40 4. 90 80 70 60 90 80 70 90 40 40 30 50 20 20 60 70 5. 110 90 120 80 170 70 150 60 140 50 180 40 160 30 190 20 6. 260 20 210 30 240 40 290 50 220 60 270 80 230 70 250 90 7. 350 20 320 70 390 40 360 80 330 60 380 50 340 90 370 30 8. 520 30 640 50 720 90 840 50 750 70 930 40 630 80 410 60 9. 260 540 360 750 420 350 300 600 110 420 240 500 120 220 150 250 10. 320 310 400 560 220 800 240 250 200 160 380 480 190 250 180 160 11. 280 200 300 400 500 600 700 800 140 130 210 280 340 480 150 ^20 12. 290 660 430 590 810 550 350 750 150 200 100 300 600 150 250 350 ADDITION AND SUBTRACTION 25 1. Count by 2's to 20, and back by 2's to 2. 2. Count by 3's to 30, and back by 3's to 3. 3. Count by 4's to 40, and back by 4's to 4. 4. Count by 5's to 50, and back by 5's to 5. 5. Count by 6's to 60, and back by 6's to 6. 6. Count by 7's to 70, and back by 7's to 7. 7. Count by 8's to 80, and back by 8's to 8. 8. Count by 9's to 90, and back by 9's to 9. 9. Count by 3's to 60. Count back to 3. 10. Count by 4's to 80. Count back to 4. 11. Count by 6's to 120. Count back to 6. 12. Count by 7's to 140. Count back to 7. 13. Count by 8's to 160. Count back to 8. 14. Count by 9's to 180. Count back to 9. 15. Count by ll's to 220. Count back to 11. 16. Count by 12's to 240. Count back to 12. 169? l 225? 17. Count by 13's to 169. How many 13's in 18. Count by 15's to 225. How many 15's in 225? 19. Count by 16's to 256. How many 16's in 256? 20. Count by 20's to 400. How many 20's in 400? 21. Count by 25's to 625. How many 25's in 625? 22. What is meant by the " square" of a number? 23. What is the square of 13? Of 15? Of 16? Of20?Of25? 26 WHOLE NUMBERS MULTIPLICATION 3. 5 times 2 = ? 9 times 2 .= ? 2 times 2 = ? How many 2's in 18? How many 2's in 10 ? How many 2's in 6? How many 2's in 24 ? How many 2's in 12 ? 10 20 30 X2 X2 X2 Count by 2's to 24, and back to 2 Recite the table of 2's. 7x2=? 10 times 2 1X2- ? 4X2= ? 40 X2 3 times 2 = ? 12 times 2 = ? How many 2's in 22? How many 2's in 8? How many 2's in 16? How many 2's in 4 ? How many 2's in 14? 50 60 70 X2 X2 X2 6X2 = 11 X2 = 8x2 = 80 X2 90 X2 )ly: Multii 4. 11 21 31 41 51 61 71 81 91 2 2 2 2 2 2 2 2 2 5. 12 22 32 42 52 62 72 82 92 2 2 2 2 2 2 2 2 2 6. 13 23 33 43 53 63 73 83 93 2 2 2 2 2 2 2 2 2 7. 14 24 34 44 54 64 74 84 94 2 2 2 2 2 2 _2^ 2 2 8. 15 25 35 45 55 65 75 85 95 2 2 2 2 2 2 . 2 2 2 9. 16 2 2 2 2 2 2 2 2 2 10. 17 27 37 47 57 67 77 87 97 2 2 2 2 2 2 2 2 2 11. 18 28 38 48 58 68 78 88 98 2 2 2 2 2 2 2 2 2 12. 19 29 39 49 59 69 79 89 99 2 2 2 2 2 2 2 2 2 WHOLE NUMBERS MULTIPLICATION 27 8x3=? 1 X3= ? 12 x 3 = ? Count by 3's to 36, and back to 3. Recite the table of 3's. 1. 3x3=? 8x3=? 7x3=? 10 X 3 = ? 5X3=? 2. How many 3's in 12? How many 3's in 21 ? How many 3's in 9? How many 3's in 24? How many 3's in 15? 3. 10 20 30 40 50 X3 X3 X3 X3 X3 6x3 = 4x3=? 2x3 11X3=? 9x3=? How many 3's in 6? How many 3's in 18? How many 3's in 36? How many 3's in 33? How many 3's in 27? 60 70 80 90 X3 X3 X3 X3 )ly: 11 81 iltii 4. 21 31 41 51 61 71 91 3 3 3 3 3 3 3 _3 3 5. 12 22 32 42 52 62 72 82 92 3 3 3 _3 3 3 3 _3 3 6. 13 23 33 43 53 63 73 83 93 3 3 3 3 3 3 3 3 _3 7. .14 24 34 44 54 64 74 84 94 3 3 3 3 3 3 3 3 _3 8. 15 25 35 45 55 65 75 85 95 3 3 3 3 3 3 3 3 _3 9. 16 26 36 46 56 66 76 86 96 3 3 3 _3 ^3 _3^ 3 3 3 10. 17 27 37 47 57 67 77 87 97 3 3 _3 3 3 3 3 3 3 11. 18 28 38 48 58 68 78 88 98 3 3 3 3 _3^ 3 3 ' _3^ 3 12. 19 29 39 49 59 69 79 89 99 3 3 3 3 3 3 3 _3 3 28 WHOLE NUMBERS MULTIPLICATION Count by 4's to 48, and back to 4. Recite the table of 4's. 1. 5x4=? 6x4=? 1x4=? 3x4=? 8X4=? 2x4=? 7X4=? 10x4=? 11X4=? 12x4=? 9x4=? 4x4=? 2. 36 is how many times 4? 16 is how many times 4? 12 is how many times 4? 8 is how many times 4? 28 is how many times 4? 24 is how many times 4? 20 is how many times 4 ? 48 is how many times 4 ? 44 is how many times 4 ? 32 is how many times 4 ? 3. 10 20 30 40 50 60 70 80 90 X4 X4 X4 X4 X4 X4 X4 X4 X4 Multiply : 4. 11 21 31 41 51 61 71 81 91 4 4 4 4 4 4 4 4 4 5. 12 22 32 42 52 62 72 82 92 4 4 4 4 4 4 4 4 4 6. 13 23 33 43 53 63 73 83 93 4 4 4 4 4 4 4 4 4 7. 14 24 34 44 54 64 74 84 94 4 4 4 4 _^ _4^ 4 4 _J 8. 15 25 35 45 55 65 75 85 95 4 4 4 4 4 4 4 4 4 9. 16 26 36 46 56 66 76 86 96 4 4 4 4 4 4 4 4 _J 10. 17 27 37 47 57 67 77 87 97 _^ 4 4 4 4 4 4 4 4 11. 18 28 38 48 58 68 • 78 88 98 4 4 4 4 4 4 4 4 4 12. 19 29 39 49 59 69 79 89 99 _^ 4 4 4 4 4 4 4 4 WHOLE NUMBERS MULTIPLICATION 29 Count by 5's to 60, and back to 5. Recite the table of 5's. 1. 12x5=? 9x5=? 4x5=? 2x5=? 3X5=? 11X5=? 6x5=? 5x5=? 8X5=? 7X5=? 10x5=? 1x5=? 2. 25 is how many times 5 ? 55 is how many times 5 ? 40 is how many times 5 ? 20 is how many times 5 ? 15 is how many times 5? 45 is how many times 5? 60 is how many times 5? 30 is how many times 5? 35 is how many times 5? 10 is how many times 5? 3. 10 20 30 40 50 60 70 80 90 X5 X5 X5 X5 X5 X_5 X_5 X5 X_5 Multiply : 4. 11 21 31 41 51 61 71 81 91 5 _J> 5 _5 _5 J> _5 _5 _5 5. 12 22 32 42 52 62 72 82 92 _5 5 _5 5 5 _5 5 5 5 6. 13 23 33 43 53 63 73 83 93 5 _5 5 J> _5 _5 _5 5 _5 7. 14 24 34 44 54 64 74 84 94 5 _5 5 _5 _5 _5 _5 _5 _5 8. 15 25 35 45 55 65 75 85 95 _5 _5 5 ^5 _5 _5 j5 _5 5 9. 16 26 36 46 56 66 76 86 96 _5 _5 J5 5 _5 _5 5 j5 5 10. 17 27 37 47 57 67 77 87 97 _5 _5 _5 _5 _^ _5 _5 5 5 11. 18 28 38 48 58 68 78 88 98 _5 _5 _5 5 _5 J5 _5^ _5^ _5 12. 19 29 39 49 59 69 79 89 99 ■_ft 5 5 Jy _5 _5 5 ^5 _5 30 WHOLE NUMBERS MULTIPLICATION Count by 6's to 72, and back to 6. Recite the table of 6's. Recite it backwards. 1. 6x6=? 5x6=? 1x6=? 3x6=? 10x6=? 12x6=? 4x6=? 9x6=? 2x6=? 8x6=? 11x6=? 7x6=? How many 6's 2. In 54? In 72? In 42? In 48? In 66? In 30? In 12? In 18? In 36? In 24? 3. 10 20 30 40 50 60 70 80 90 X6 X6 X6 X6 X6 x6 X6 x6 x6 4. 11 X 5 5. 12x5 6. 3X4 7. 2x2 5X4 10x2 8x2 4X3 12x3 5X5 9X5 8X5 6x2 11 X 3 10x4 6x4 11 X 4 7x2 9X3 7x3 5x3 9X4 11 X 2 9x2 4x2 10X3 12x4 2x4 8X3 7x4 3x3 10X5 7X5 3x5 4x4 12x2 6X3 8x4 6x5 2x3 2x5 3X2 5X2 4x5 Multiply : 8. 11 21 31 41 51 61 71 81 91 6 _6 6 6 6 6 6 6 6 9. 12 22 32 42 52 62 72 82 92 _6 _6 _6 6 _6 _6 6 6 6 10. 13 23 33 43 53 63 73 83 93 _6 6 6 6 6 6 6 6 6 11. 14 24 34 44 54 64 74 84 94 6 _6 _6 6 J> 6 6 6 _6 12. 15 25 35 45 55 65 75 85 95 _6 _6 _6 6 _6 6 6 6 6 WHOLE NUMBERS MULTIPLICATION 31 Count by 7's to 84, and back to 7. Recite the table of 7's. Recite it backwards. 1. 7X7=? 2x7=? 5X7=? 4x7=? 12x7=? 8x7=? 1x7=? 6x7=? 3x7=? 11x7=? 10x7=? 9x7=? How many 7's 2. In 14? In 84? In 49? In 42? In 35? In 28? In 21? In 77? In 63? In 56? 3. 10 20 30 40 50 60 70 80 90 X7 X7 X7 X7 X7 X7 X7 X7 X7 12x3 5. 11x5 6. 6x5 7. 6x6 9x4 10X3 12x4 5x5 2x5 8x4 9x3 3X4 8x6 5X6 4x6 8x3 5X3 4x5 3x5 9x5 10x6 11 X 3 3x3 12x6 12x5 6x3 6X4 5X4 11 X 4 10X5 7X6 4x3 7x3 11 X 6 2x4 9x6 4x4 8x5 2x6 10X4 2x3 7x4 7x5 3X6 Multiply : 8. 11 21 31 41 51 61 71 81 91 7 _7_ 7 7 7 7 7 7 _J_ 9. 12 22 32 42 52 62 72 82 92 7 7 _7_ 7 7 7 7 7 J7 10. 13 23 33 43 53 63 73 83 93 7 _7 _7 _7 _J7 J_ 7 7 _7 11. 14 24 34 44 54 64 74 " 84 94 7 _7 7 J_ _7 _7 J_ 7 ( 7 12. 15 25 35 45 55 65 75 85 95 7 7 7 7 7 7 Jl 7 7 32 WHOLE NUMBERS MULTIPLICATION Count by 8's to 96, and back to 8. Recite the table of 8's. Recite it backwards. 1. 6x8=? 2x8=? 4X8=? 8x8=? 3X8=? 10x8=? 12x8=? 11x8=? 9x8=? 7X8=? 5X8=? 1x8=? 2. 8 X ? = 16. 8 X ? = 24. 8 X ? = 32. 8 X ? = 48. 8 X ? = 40. 8 X ? = 80. 8 X ? = 64. 8 X ? = 72. 8 X ? = 96. 8 X ? = 56. 8 X ? = 88. 8 X ? = 8. 3. 10 20 30 40 50 60 70 80 90 X8 X8 X8 X8 X8 X8 X8 X8 X8 4. 5x4 5. 11 X 4 6. 2x6 7. 3x7 7X5 7x7 3x5 7X6 8X6 5x6 8x7 8x4 10x7 4x5 3x4 12x6 11 X 5 3X6 10X6 5X7 9x4 6X4 9X7 9x6 4X7 11 X 7 2x5 10X5 6x6 9x5 4X6 2x7 7x4 6x7 4x4 6x5 12x5 12x4 8X5 12x7 2x4 10x4 11 X 6 5X5 Multiply : 8. 11 21 31 41 51 61 71 81 91 _8 _8 8 8 8 8 8 _8 _8 9. 12 22 32 42 52 62 72 82 92 _8 _8 8 8 8 8 _8 8 _§• 10. 13 23 33 43 53 63 73 83 93 8 . _8 8 8 8 _8 8 8 _8 11. 14 24 34 44 54 64 74 84 94 _8 _8 8 8 8 _8 _8 8 8 12. 15 25 35 45 55 65 75 85 95 8 _8 __8 8 8 8 8 8 _8 WHOLE NUMBERS MULTIPLICATION 33 Count by 9's to 108, and back to 9. Recite the table of 9's. Recite it backwards. 1. 9X9=? 5X9=? 8X9=? 11x9=? 3x9=? 12x9=? 1x9=? 2x9=? 10x9=? 4x9=? 7x9=? 6x9=? 2. 9 X ? = 27 9 X ? = 81. 9 X ? = 18. 9 X ? = 90. 9 X ? = 45. 9 X ? = 108. 9 X ? = 36. 9 X ? = 9. 9 X ? = 63. 9 X ? = 72. 9 X ? = 54. 9 X ? = 99. 3. 10 20 30 40 50 60 70 80 90 X9 X9 X9 X9 X9 X9 x9 X9 X9 9X5 5. 12x8 6. 8X6 7. 12 x 7 10 X 6 9x6 7X8 11 X 5 9X7 10X5 2x7 8X7 5x8 5x6 3X5 4x8 7x7 .4X7 7x6 6X5 4x6 2x6 8x5 12x6 2x8 7x5 6x8 10x8 5X5 11 X8 3x7 5X7 11 X 6 6x6 4x5 10x7 6x7 12x5 3x6 2x5 11 X 7 8x8 9x8 3X8 Multiply : 8. 11 21 31 41 51 61 71 81 91 9 _9 9 9 9 _9 _9 9 _9 9. 12 22 32 42 52 62 72 82 92 9 9 9 9 _9 _9 9 9 9 10. 13 23 33 43 53 63 73 83 93 9 9 _9 __9 9 _9 _9 _9 _9 11. 14 24 34 44 54 64 74 84 94 _9 9 9 _9 9 _9 _9 _9 _9 12. 15 25 35 45 55 65 75 85 95 9 _9 _9 9 9 _9 _9 _9 9 34 WHOLE NUMBERS MULTIPLICATION Count by 12's to 144, and back to 12. Recite the table of 12's. Recite it backwards. 1. 5 X 12 = ? 6 X 12 = ? 2. 12 X ? = 120. 12 X ? = 60. 9X 12 = ? 3X 12 = ? 12 X ? o -48. 12 X ? = 24. 12 X 12 = ? 10 X 12 = ? 12 X ? . = 72. 12 X ? = 96. 4X 12 = ? 7X12 = ? 12 X ? = = 108. 12 X ? = 120. 8X 12 = ? 11 X 12 = ? 12 X ? m = 36. 12 X ? = 84. 2X12 m f 1X12 = ? 12 X f = 132. 12 X ? = 12. 3. 10 X 11 m ? 11 X 11 = ? 12 X 11 = , f 4. 2x6 5. 7X 12 6. 3x6 7. 2x8 8. 11 X 11 9x9 9X6 4x7 3x9 9X8 10X11 5x9 4x9 7X7 8x7 12x7 4x12 5X 12 4x6 3x8 6X6 12x11 8x9 12x8 2x9 5x8 9x7 11 X 7 11 X12 8X 12 11 X 9 8x6 5x6 7x9 10x9 3X 12 6x9 12 x 12 6X 12 6x8 2x7 2x 12 7x8 3x7 12x9 8x8 5X7 6x7 7x6 4x8 12x6 11 X 6 9X12 11 X 8 10 X 12 Multiply : 9. 16 26 36 46 56 66 76 86 96 6 6 6 6 6 6 _6 _6 6 10. 17 27 37 47 57 67 77 87 97 _6 6 6 _6 _6 __6 6 _6 J5 11. 18 28 38 48 58 68 78 88 98 _6 _6 6 6 _6 6 _6 _6 6 12. 19 29 39 49 59 69 79 89 99 6 _6 _6 j6 6 _6 _6 6 6 WHOLE NUMBERS MULTIPLICATION 35 1. 2x2x2 2. 4x5x3 3. 10x2x5 3x3x3 3x5x4 2x4x11 2x4x8 4x4x4 8x5x2 3x3x9 5x5x5 10x1x5 5x2x5 5x3x2 2x2x7 4x3x4 4x2x7 2x4x9 2x3x9 2x6x6 3x3x7 4x3x8 3x2x7 2x5x10 6x2x7 3x4x3 5x5x3 2x5x4 5x3x3 10x3x2 10 X20 5. 20 X 20 6. 200 x 3 11 X 20 25x20 500x6 12 X 20 30x20 300x4 13 X 20 30x30 400 x 5 14 X 20 40x20 800x2 15 X 20 40 x 30 600x8 16x20 50 x 20 150x5 17 x 20 50x40 250x4 18x20 40x40 125x3 19x20 50x50 450x2 7. 16 26 36 46 56 66 76 86 96 7 7 _7 7 7 _7_ 7 7 _7 8. 17 27 37 47 57 67 77 87 97 . 7 7 _1_ 7 7 _J_ 7 7 7 9. 18 28 38 48 58 68 78 88 98 7 7 _J_ 7 7 7 7 7 7 .0. 19 29 39 49 59 69 79 89 99 7 7 7 7 7 7 7 7 7 36 MULTIPLICATION TABLES REVERSED 1. 20 48 16 24 12 36 28 40 32 8 44 4. 10] 60 25 40 30 • 15 55 20 45 50 35 7. 42] 56 14 35 84 21 70 28 49 63 77 2. 56 3. 12' 32 20 72 4 16 22 How many 4's? 40 88 24 48 64 80 96, 5. 96 24 60 120 How | 8' many s? 18 8 10 6 14 24 16, 6. 15 36 6 21 How many 2'sf How many 36 72 How many 9 33 How many 5's? 108 48 144 84 132 ; 8. 99 ' 18 45 63 12 's? 18 27 12 24 30. 9. 24 60 12 36 3's? How many 7's? 108 36 90 27 72 54 81 How ' 9' many s? 66 30 72 54 42 18 48 How many 6's? THE FACTS OF THE MULTIPLICATION TABLES 37 Drill for Rapidity. 3. 2x9 4. 12 x 2 7. 3 x 12 10. 4x2 5x 10 5x4 10x9 3x9 9x4 6x6 5X11 11x3 11x5 11x8 6x 10 9x 10 10x3 2x 10 5x2 5x8 6x2 11 X 12 8x3 3x6 9x8 7x3 10x7 7x5 4x 12 8x5 4x8 10x4 3x 11 7x7 2x6 4x7 5x6 4x9 12x4 10 x 11 3x7 5. 2x11 8. 9x5 11. 9x12 8x 12 12 x 12 12x9 4x3 6x3 7x2 10x2 6x5 11x2 9x11 3x 10 12 x 11 7x4 3x3 12x3 9x9 6x9 4x 10 7x11 8x2 3x2 11x4 8x4 3x4 8x11 8x9 5x 12 11x6 2x8 2x5 10x5 12x7 5x5 7x8 6x7 6x8 10x6 6. 12 x 6 9. 4x6 12. 11 x 10 9x7 2x7 8x8 10 x 12 10 x 10 7x 12 2x 12 4x5 2x3 2x2 9x2 3x8 12x8 4x11 11 X 11 9x6 6x11 5x3 8X 10 11 X 9 4x4 7x6 9x3 8x7 7x 10 12 x 10 7x9 12X5 8x6 5x9 10x8 9x7 5x7 2x4 6x4 7x8 6x 12 11 X 7 3x5 6x7 38 MULTIPLICATION AND ADDITION Drill for Rapidity 1. Add 2 to 2. Add 3 to 3. Add 4 to 4. Add 5 to 3x4 3x9 9x 12 7x4 5x11 9x2 12x6 5x8 4x5 12x7 9x7 9x6 6x9 8x11 8x 12 8x7 7x 12 3x 12 12 x 11 9x8 12x5 6x4 8x5 7x6 11 X 11 4x9 8x9 4x 12 12 x 12 3x5 12 x 10 8x6 6x3 12x3 10 x 11 7x9 6. Add 6 to 6. Add 7 to 7. Add 8 to 8. Add 9 to 3x8 6x12 4x4 12 x 2 7x3 11x12 5x12 8x2 5x7 5x3 11x10 6x6 9x4 8x4 12x8 4x8 8x3 5x5 9x9 6x7 9x5 3x6 6x5 3x11 7x J 4x7 7x2 5x9 4x6 6X8 5x4 7x8 8x8 12x4 12x9 5x6 9. 16 26 36 46 56 66 76 86 96 _8 _8 8 _8 8 8 _8 8 8 10. 17 27 37 47 57 67 77 87 97 8 8 _8 8 8 8 8 8 8 11. 18 28 38 48 58 68 78 88 98 8 _8 _8 8 8 8 _8 _8 _8 12. 19 29 39 49 59 69 79 89 99 8 _8 _8 8 _8 8 8 8 _8 MULTIPLICATION AND SUBTRACTION 39 Drill for Rapidity 1. 2. 3. 4. Take 2 from Take 3 from Take 4 from Take 5 from 12 x 3 6x3 8x9 9x8 3x5 12 X 12 12 x 10 7x4 4x9 3x4 10x11 9x6 6x4 4x5 8x12 8x7 3x12 6x9 12x11 7x6 8x11 7 x 12 9x7 4 x 12 12 x 7 12 x 5 12 x 6 8x6 9x2 11x11 9x12 7x9 5. 6. 7. 8. Take 6 from Take 7 from Take 8 from Take 9 from 7x5 12 x 9 9x 11 5x6 8x8 12 x 4 5x4 7x8 4x 12 6x 8 7x2 5x9 7x7 4x 7 6x5 6x7 9x5 3x 6 9x9 4x8 8X3 8x4 12x8 6x6 9x4 5x 3 11 X 10 8x2 7x3 11 X 12 ► 5x 12 7x 11 3x8 26 6x 12 > 4x4 76 12x2 9. 16 36 46 56 66 86 96 9 9 9 9 9 9 9 _9 _9 10. 17 27 37 47 57 67 77 87 97 9 9 9 9 9 9 9 2 J. 11. 18 28 38 48 58 68 78 88 98 _9 9 9 9 9 9 J9 _9 9 12. 19 29 39 49 59 69 79 89 99 9 9 9 9 9 9 9 _9 _9 40 WHOLE : NUMBERS DIVISION 1. 18 divided by 2 2. 4 -f- 2 3. 16 H- 2 4. 6 + 2 21 divided by 3 27 + 3 15 + 3 9^3 24 divided by 4 8 ^4 32 ^4 28 + 4 40 divided by 5 25 + 5 10 + 5 20-5 36 divided by 6 24 + 6 18 + 6 42-6 21 divided by 7 63 ■* 7 49 + 7 28 * 7 40 divided by 8 48 + 8 72 + 8 56-8 18 divided by 9 45 + 9 72 ^9 54-9 33 divided by 11 77 4- 11 44 + 11 99 - 11 96 divided by 12 24 + 12 84 + 12 60- 12 5. 2)46 6. 3)84 7. 4)84 8. 5)95 9 . 6)120 10. 7)91 2)54 3)96 4)96 5)100 6)150 7)210 2)88 3)69 4)44 5)80 6)96 7)147 2)62 3)52 4)76 5)75 6)90 7)98 2)50 3)78 4)56 5)125 6)132 7)154 2)72 3)57 4)68 5)90 6)144 7)105 2)96 3)81 4)88 5)105 6)108 7)161 2)78 3)90 4)72 5)150 6)84 7)224 11. 2)264 12. 7)252 13. 3)654 : L4. 5)650 15. 2)270 3)357 4)252 4)340 6)372 3)270 6)624 6)192 7)714 4)372 4)900 4)516 2)508 6)240 3)810 6)450 5)720 5)375 2)500 7)350 7)364 WHOLE NUMBERS DIVISION 41 1. 10-5-2 2. 14-5-2 3. 12 - 2 4. 8-5-2 6^-3 24-5-3 12 -5- 3 18-5-3 36^-4 12-5-4 20 -4 16-4 15-5-5 30-5-5 35 + 5 45-5 30^-6 48+ 6 54 -5- 6 12-6 14-7 35 + 7 42 + 7 56-5- 7 24 + 8 64-8 32 + 8 16-s- 8 63-9 27-5-9 81 -5-9 36-5-9 55 + 11 88-5- 11 22 - 11 66 h- 11 48-s- 12 108 -5- U ► 72 - 12 36 + 12 5. 8)640 6. 9)198 7. 10)640 8. 11)341 9. 12)252 8)128 9)270 10)210 11)572 12)600 8)256 9)927 10)700 11)132 12)132 8)328 9)153 10)350 11)187 12)384 8)816 9)468 10)200 11)209 12)504 8)560 9)945 10)470 11)165 12)708 8)808 9)207 10)110 11)440 12)288 8)488 9)846 10)600 11)693 12)192 10. 7)3500 11. 8)6000 12. 11)2530 13. 8)8056 8)6480 11)4510 8)1616 12)1440 9)8109 7)1428 12)4800 11)3410 11)5533 12)6036 6)3606 9)2070 12)6012 9)4680 9)9045 6)6048 42 WHOLE NUMBERS DIVISION 1. 2. 3. 4. 5. 6. 9)36 4)60 12)36 8)64 12)132 8)72 12)72 3)45 4)48 12)96 7)28 4)28 7)35 5)40 11)11C I 7)21 8)32 7)84 11)66 11)132 6)24 3)15 12)120 9)45 12)60 12)48 8)24 5)60 3)18 12)108 9)27 8)56 12)24 12)84 5)30 11)44 6)42 7)63 5)45 6)36 7)42 4)24 4)32 9)72 3)27 4)20 6H8 10)120 7. 12 4- ? - 4 8. 28- - ? = 4 9. 72 - - ? = 6 27- - ? = 9 42- - ? = 7 56- - ? = 8 44- - ? = 4 L08- - ? = 12 132- - ?= 11 36- - ? = 6 84- - ? = 7 110- - ?= 10 81 - - ? = 9 54- - ? = 6 42- - ? = 7 72- - ?= 12 35- - ? = 7 54- - ? = 6 63- - ? = 9 42- - ? = 6 64- - ? = 8 56- r ?«7 63- - ? = 7 84- - ? = 12 10. Count by 25 's to 600. 11. Count by 75 j j 3 to 900. 12. 15)600 13. 50)600 1 L4. 1 5)450 15. 25)200 16 75)150 20)400 60)720 1 6)320 25)300 75)300 25)500 70)770 2 1)420 25)150 75)225 30)330 80)960 2 52)880 25)450 75)600 40): L60 90)270 2 4)720 25)600 75)750 DIVISION DRILL FOR RAPIDITY 43 Divide by 2 : 1. 20 42 36 44 26 60 32 28 2. 18 50 22 40 58 46 38 62 3. 34 52 24 30 48 64 56 66 4. 54 70 90 84 78 80 92 68 5. 86 94 82 74 96 72 88 76 Divide by 3 : 1. 12 21 42 15 36 24 30 18 2. 27 45 33 51 39 48 57 69 3. 54 81 60 84 75 66 72 93 4. 78 90 87 99 63 96 120 102 5. Ill 129 105 126 117 108 123 114 Divide by 4 : 1. 20 44 72 28 36 16 24 12 2. 40 56 68 52 76 60 48 64 3. 80 96 84 92 88 32 120 160 4. 104 144 116 136 168 124 108 132 5. 140 156 112 152 148 164 100 128 Divide by 5 1. 60 15 30 70 55 35 75 10 2. 50 95 20 90 65 40 85 25 3. 80 45 100 120 160 105 135 150 4. 110 140 180 115 165 190 125 155 5. 130 170 200 175 205 195 145 185 Divide by 10 : 1. 120 210 150 110 240 130 170 200 2. 190 300 140 160 220 180 250 230 44 DIVISION DRILL FOR RAPIDITY Divide by 6 1. 12 66 24 84 42 96 54 60 2. 18 72 30 90 36 48 78 102 3. 114 174 132 108 150 138 186 120 4. 156 126 144 192 162 198 168 180 5. 240 204 234 246 216 228 210 222 Divide by 7 * 1. 21 70 91 14 84 56 28 49 2. 63 77 35 98 42 105 140 126 3. 147 154 133 168 182 161 119 189 4. 112 175 196 210 280 203 245 266 5. 238 259 224 273 252 231 217 287 Divide by 8 : 1. 88 40 16 56 32 64 24 72 2. 96 48 80 104 160 144 112 136 3. 120 176 128 152 184 168 192 240 4. 200 280 232 208 256 216 264 224 5. 248 272 296 288 320 304 328 312 Divide by 9 : 1. 90 45 72 99 36 81 54 18 2. 27 63 108 135 180 117 153 198 3. 144 171 126 189 162 207 243 270 4. 216 252 288 234 225 261 279 297 6. 306 333 360 342 315 369 351 324 Divide by 11 1. 110 209 121 220 165 231 198 132 2. 264 187 143 176 154 253 275 242 DIVISION 45 How many times, and how many over? 1. 6)50 4)30 8)25 10)36 7)40 8)60 2. 4)21 3)18 8)42 5)19 12)63 8)75 3. 5)28 10)42 9)46 3)17 12)80 10)37 4. 4)45 3)22 6)67 7)56 8)70 5)18 6. 12)33 11)56 9)29 4)32 6)62 8)49 6. 9)88 11)76 5)54_ 7)55 4)37 6)52 7. 12)100 15)35 6 )130 5 )182 3 )205 8. 3 )100 25)54 8 )165 4 )330 6 )320 9. 8 )100 30)95 12)200 9 )640 7 )135 10. 6)100 20)83 9 )125 6 )254 4 )163 11. 7 )100 12 )150 7 )368 12 )302 8 )334 12. 9 )100 40)125 11 )452 8 )250 5 )481 13. 13)28 24)55 35)80 14)56 21)75 14. 50)112 16)48 75 )160 44)90 37)60 15. 15)75 28)60 33 )100 61 )125 7 0)300 16. 36)80 55)165 80 )250 45)53 22)100 17. 17)51 23)80 42)100 93)200 56)75 18. 30)160 18)90 36)45 19)62 66)80 46 WHOLE NUMBERS DIVISION How many 1. 3)16 times, and how many 2)21 5)18 over? 4)25 3)28 6)21 2. 4)19 3)25 2)15 6)39 5)23 3)14 3. 6)50 4)30 8)25 10)36 7)40 10)57 4. 4)21 3)32 8)42 5)19 12)63 8)60 5. 5)28 10)42 9)76 3)T7 . 12)80 8V75 6. 4)45 3)22 6)67 7)56 8)70 5)16 7. 12)33 11)56 9)29 4)35 6)62 8)49 8. 9)88 11)76 5)54 7)55 4)37 6)52 9. 5)48 2)T7 3)35 4)18 9)40 5)34 10. 8)36 6)40 5)58 3)10 7)44 11)40 11. 5)42 3)29 4)23 6)25 8)54 7)33 12. 3)23 3)11 3)19 3)23 3)31 3)38 13. 4)13 4)42 4)34 4)26 4)38 4)49 14. 5)12 5)56 5)41 5)36 5)27 5)52 15. 6)20 6)16 6)33 6)45 6)27 6)55 16. 7)17 7)50 7)25 7)38 7)62 7)75 17. 8)28 8)83 8)26 8)44 8)38 8)52 18. 9)35 9)70 9)50 9)67 9)31 9)22 19. 11)80 11)30 11)60 11)20 11)50 11)90 20. 12)50 12)65 12)44 12)27 12)18 12)99 DIVISION 47 Division is expressed in two ways. The division of 2 by 5 may be expressed "2 + 5" or "f." Read the following expressions as fractions. Tell whether each fraction is proper or improper. Change improper fractions to whole numbers, and proper fractions to lowest terms. 1. 12 - 4 2. 6 + 3 3. 3 - 6 4. 6 - 18 9-3 20-10 14 - 7 4-20 8-16 16-4 4-12 5-20 5-10 8-2 8-4 10-2 4-2 5-15 2-8 4-16 10-5 3-12 7-14 3-9 16-8 15-3 3-3 2-4 2-14 12-2 18-9 12-16 Read. Change to fractional form. Reduce. 5. 8 - 12 6. 7 - 49 7. 16 - 24 8. 45 - 60 4-16 8-56 24-36 15-21 6 + 48 15-25 30 - 40 14 - 77 7-21 6-28 9-15 54 - 60 9-63 4-18 32-40 16-72 8-40 12-18 27-36 5-30 3-18 9-9 40-64 12-20 4-32 21-35 36 - 42 40 - 50 Read as fractions. Reduce where possible to do so. 9. 2 - 3 10. 8 - 20 11. 100 - 8 12. 5 - 100 80-9 2-50 100-3 4-100 25 - 100 25-5 100-6 10 - 100 4-5 6-7 100-7 25-100 3 + 11 5+10 100 - 12 50 - 100 48 ALL THE FACTS OF THE DIVISION TABLES Drill for Rapidity. 1. 18-9 4. 24-2 7. 36 4- 12 10. 8v2 50- 10 20-4 90-9 27 ^9 36-4 36-6 55 - 11 33-3 55-5 88-8 60- 10 90- 10 30-3 20- 10 10-2 40-8 12-2 132 4- 12 24-3 18-6 72-8 21-3 70-7 35^-5 48- 12 40-5 32-8 40-4 33- 11 49-7 12-6 28-7 30-6 36-9 48-4 110 4- 11 2. 21-7 5. 22 + 11 8. 45 4- 5 11. 108 - 12 96- 12 14-2 108 h- 9 12-3 18-3 99 + 11 20-2 30-5 22-2 9-3 30- 10 132 4- 11 28-4 40- 10 36-3 81-9 54-9 44^-4 77 4- 11 . 16-2 6-2 72-9 32^4 12 -h 4 88 - 11 10-5 60 4- 12 .66-6 16-8 56^-8 50-5 84-7 25-5 72-6 42-7 48-8 3. 60-6 6. 14-7 9. 24-6 12. 110 - 10 63-7 24- 12 64-8 120 4- 12 100 - 10 4-2 84 - 12 20-5 6-3 44- 11 18-2 24^-8 96-8 15^3 121 - 11 54 -h 6 66 - 11 42 -h 6 80- 10 99 + 9 16^-4' 120 - 10 27-3 56-7 70- 10 45-9 63-9 60-5 48-6 8-4 80-8 63 + 7 35-7 144 - 12 24^-4 56 + 8 72^- 12 77 -'7 15^5 42 + 7 MULTIPLICATION AND DIVISION 49 1. Divide by 4 : 2. Divide by 6 : 3. Divide by 6x6 4x9 12x2 8X6 9x8 2X20 3x8 2x 12 6x 12 6x2 12x5 2x4 8x2 3x4 16X2 2x 10 2x30 4x 12 8X5 9x2 4x4 r ide: 4. 4 X 5 by 2 X 2. 5. 8 X 12 by 3 X 4. 6 X 6 by 3 X 2. 6 X 10 by 2 x 5. 8 X 6 by 4 X 3. 9x 2 by 3 X 2. 2 X 12 by 2 X 2. 7 X 4 by 2 X 2. 6. 10 X 4 by 5 x 2. 7. 10 x 10 by 5 X 5. 6 X 7 by 2 x 3. 8 X 9 by 3 x 4. 8 X 3 by 2 x 2. 6 X 11 by 2 X 3. 5 X 8 by 2 x 4. 12 x 6 by 3 X 3. 8. 3x4x5 divided by 2 X 2 = ? 9. 3x3x8 divided by 2 X 3 X 2 = ? 10. 4 x 10 X 3 divided by 2x2x5=? 11. 8x5x2 divided by 2 X 5 = ? 12. 9x5x2 divided by 3 X 3 = ? 13. 3x7x4 divided by 3x2x2=? 14. 5x7x2 divided by 2 X 5 = ? 15. 6x5x4 divided by 2x2x2=? 16. 10 X 10 X 2 divided by 5 X 5 = ? 17. 2 X 8 X 10 divided by 5 X 2 = ? 50 PRACTICE IN INTERPRETING SIGNS QUICKLY 1. 5-3 = 7 + 2 = 9-1-3 = 8-5 = 2x4 = 6 + 7 = 18-2 = 6x3 = 9-4 = 8+11 = 132 + 12 - 150 - 25 = 12 x 20 = 135 + 15 = 75 - 25 = 50 + 15 = 64x2 = 175 - 5 = 80 x 12 = 100 - 54 = 2. 3x3 = 16-7 = 8 + 5 = 20-4 = 14-2 = 3+ 11 = 15-7 = 7 + 8 = 4x5 = 12 + 8 = 3. 15-5 = 4x4 = 5+ 11 = 19-7 = 12-3 = 11 +4 = 8-2 = 16-9 = 3x5 = 7 + 11 = 10. 60x6 = 140 - 32 = 70 + 35 = 250 - 50 = 100 - 22 = 300 - 15 = 7x21 = 33 + 18 = 95 - 42 = 144 - 12 = 11. 55 X 2 = ? 108 - 36 = ? 43 + 62 = ? 88 - 27 = ? 39 + 26 = ? 165 - 15 = ? 16 x 6 = ? 80 - 48 = ( 48 - 16 = ? 50 X 12 = ? 4. 12-2 = 4+15 = 8-3 = 7 + 9 = 15-3 = 2x8 = 12-9 = 5x4 = 20 - 11 = 8 + 8 = 12. 13x3 = 225 - 25 = 105 - 40 = 18 + 54 = 72 - 36 = 100 - 14 = 96 - 16 = 50 + 75 = 5x25 = 75 - 15 - 5. 6. 7. 8. 24 + 8 = ? 12 x 5 = ? 88 + 11 = ? 48 + 6 = ? 49 - 7 = ? 96-8= ? 64-8 = ? 8x7=? 63 - 7 = ? 56 + 7 = ? 96 - 12 = ? 36 + 12 = ? 8x9= ? 7x8= ? 42- 7 = ? 60 - 12 = ? 14 + 14 = ? 45 - 9 = ? 32 + 8 = ? 35 - 7 = ? 56 - 7 = ? 8 X 12 = ? 27- 3 = ? 18 + 9 = ? 42 - 6 = ? 40 + 8 = ? 9x6 = ? 84 - 7 = ? 12 x 7 = ? 36 - 4 = ? 54-9 = ? 81 - 9 = ? 36 + 9 = ? 72 - 6 = ? 28- 7 = ? 40 - 4 = ? 84 - 12 = ? 40 - 5 = ? 42- 6 = ? 35 + 7 = ? PRACTICE IN INTERPRETING SIGNS QUICKLY 51 Tell whether your answer is product, quotient, sum, or re- mainder. 1. 3x4 2. 3x7 3. 2 X 11 4. 16 + 4 7 + 8 35-5 36-4 25-7 18-3 5 + 7 4 + 8 17 + 7 9-5 11-5 21-7 9x3 14 + 5 32-8 18-9 49-7 3x9 9 + 8 12 + 6 11 + 6 24-3 20-9 25-5 28-7 5x4 6x5 3x3 7x5 11-2 5 + 12 11-8 36-6 8 + 3 24-12 6 + 7 17-9 5 + 8 6. 2 X 15 7. 35-7 8. 9x9 8x7 45-5 18 + 7 14 + 5 42-7 18 + 5 56-7 25-9 17-8 15-7 6x 12 60-5 6x9 7x9 7 + 9 12x5 63-7 108-9 48-6 44- 11 .4+11 . 8 + 7 22-8 17-9 7x6 23-7 54-9 13 + 12 13-5 9x6 6x 11 8x8 40-4 60-2 34- 6 45-9 9. 125 - 5 10. 75 - 15 11. 102 - 12 12. 34 + 28 14 x 4 300-25 20 X 5 50 - 18 18 +18 80 - 16 150 - 3 75-62 600 - 12 18 X 5 . 250-2 120 - 40 20 x 8 17 + 17 12| x 8 40-15 75 + 50 33-8 6ix4 16x4 225 - 75 180 - 6 100-3 15 X 5 45-3 11 X 12 100 - 6 30-16 14 x 3 144 - 2 33| X 2 360 - 12 96 - 16 33 + 17 12| x 3 100 - 62 52 PRACTICE IN INTERPRETING SIGNS QUICKLY How many of these questions can you answer in one minute ? Answer in complete statements. 1. 7 12 6 15 28 8 48 18 16 25 -^-f^xJ+S -9 X7 +6 -_5 +_7 -_12 2. 12 27 11 34 15 14 12 40 18 9 X 7 -3 +_8 ^ -7 +8 X^3 - 11 + 7 x4 3. 17 25 15 40 50 ' 50 8 8 8 14 + 5 -6x2 -5 +25 -25 -8 X8+8 -9 5x2-3 = ? 1 5. 9x8h-6 = ? 6 . 30 + 15 + 2 = ? 6+2x7= ? 12 - 7 X 5 = ? 6 + 5- 11 = ? 7 - 4 + 12 = ? 18 - 9 + 1 = ? 25 - 20 x 7 = ? 16 + 8 X 10 = ? 3x7+5= ? 14 - 7 x 8 = ? 7x7-7 = ? 4+4x4= ? 6.6x6= ? 22 - 11 x 6 = ? 13 + 3 + 8 = ? 8 X 9 + 12 = ? 8x5-2= ? 10 - 10 + 3 = ? . 3 + 11 -s- 7 = ? 3+3x6= ? 9x1-8= ? 20 - 5 - 4 = ? Tell, as you answer the questions below, whether your answer is called sum, product, quotient, or remainder. 7. 132 - 11 = ? 8. 175 -r 25 = ? 9. 14 X 3 = ? 12 x 20 = ? 8 X 20 = ? 80 + 20 = ? 54 + 16 = ? 100 - 48 = ? 25 x 8 = ? 39 -r- 13 = ? 96 -^ 16 = ? 45 - 8 = ? 16 X 5 = ? 19 + 19 = ? 100 - 5 = ? 17 + 17 = ? 96 -^ 12 = ? 16 x 3 = ? 60 + 15 = ? 20 x 20 = ? 13 + 25 = ? 25 X 5 = ? 36 - 2 = ? 108 * 12 = ? RELATION OF NUMBERS 53 6 is what part 4 is what part 5 is what part 3 is what part 1 is what part 7 is what part 2 is what part 10 is what part 8 is what part 9 is what part of 12? of 16? of 15? of 9? of 5? of 14? of 10? of 60? of 24? of 36? 2. What part of 30 is 15? What part of 55 is 11? What part of 100 is 20? What part of 75 is 25? What part of 144 is 12? What part of 150 is 50? What part of 60 is 15? What part of 80 is 40? 5 is what part 8 is what part 2 is what part 9 is what part 10 is what part 6 is what part 3 is what part 7 is what part 1 is what part 4 is what part of 30? of 40? of 6? of 18? of 40? of 48? of 21? of 63? of 12? of 20? 4. What part of 150 is 75? What part of 300 is 75? What part of 45 is 15? What part of 88 is 11? What part of 44 is 22? What part of 200 is 25? What part of 48 is 16? What part of 96 is 12? Nine is what part of twelve ? Eight is what part of twelve ? Six is what part of nine? Four is what part of six? Eight is what part of ten ? Fifteen is what part of twenty ? Twelve is what part of sixteen ? Fourteen is what part of twenty- one? Twenty is what part of thirty ? Twelve is what part of eighteen ? Ten is what part of twenty-five ? Sixteen is what part of twenty ? Nine is what part of twenty- one? Twelve is what part of fifteen ? Thirty is what part of fifty ? Ten is what part of twelve ? For Ratio, and its use in solving simple problems, see Appendix. 54 CANCELLATION State results only : 1. 2. 3. 4. .12x5 8x 10 3x 14 9x4 6 5 7 " 3 24x9 40x3 2x25 49 x 10 8 10 5 7 5x 16 20x2 8x 36 33 x5 8 4 9 11 21 x 2 10x48 6^x 5 81 xU 7 12 9 9 28 x 12 6 x 35 10 x 42 50 x 5 6. 15x8 5 60 x 11 30 30x7 5 9x7 3 77x2 10 11 6. 7. 8. 9. 2x3x3 3x4x2 3x4x12 5x2x3 9 8 16 25 3 x 1 X 100 7x8x5 4x2x11 . 5 x 12 x 1 10 35 44 6 5 x 3 x 20 3 x 64 x 1 3x4x2 5 x 36 x 2 20 8 12 18 2 x 3 x 35 9 x 55 x 2 6 x 7 x 12 7x6x6 7 11 24 42 14 x 3 x 5 5 x 18 X 1 40 x 10 X 3 15 x 8 X 1 2 9 ' 20 "30 10. 11. 12. 13. 14. 48 x 12 60x7 65x5 75x8 200x3 16 5 13 15 25 96 x 7 140x8 132x6 7 x 54 35 x 5 16 20 11 18 7 120 x 5 200x9 200 x 11 132x4 34 x 5 30 50 88 44 17 25 x 3 80x7 72 x 3 60 x 12 100 x 1 25 16 24 24 5 CANCELLATION 55 State results: 1. 2. 3. 4. 5. 10 x 7 9x4 12x7 5x6 3x15 5 18 36 30 5 6x8 7x2 44x3 3x 17 4x5 32 14 11 15 25 3x8 15 x 7 10 x 13 5x2 35x4 27 28 26 8 7 10x7 8x7 7x5 5x 18 16 x 7 21 40 25 10 4 9x11 64 x 5 21 x 6 12x5 2x 16 99 8 3 30 4 6. 7. 8. 9. 2x3x3 5 X 4 X 2 3x 2 X8 5 X 2x 7 4 8 16 35 3 X 3 x 10 7x8x4 6x2 X 11 5 X 12 x 1 100 40 33 3 60 x 5 X 2 5x 6x 7 9x2 x 10 5 X4x 10 30 12 5 20 4x8x1 5 X 5 X 3 3x4 X2 2 X3x2 64 25 24 33 6x3x2 2x3x 18 9X 11 X2 2 X 1 X 7 60 6 55 6 10. 11. 12. 13. 14. 5x7 8x7 4x 18 9x9 6x7 4x 15 21x2 9x2 35x2 5x2 7x2 15x4 8x9 50 x 2 2X 11 20 x 3 2x3 3x24 5x25 44 X 12 27 x 50 16x25 4x7 13 x 2 11X4 9x 100 5x2 7x 12 8X5 3x33 80x5 56x7 5x45 12 X 12 7x90 1x20 7x8 10 x 9 3x3 45 x 2 56 CANCELLATION Give results 1. 3 2. 8 3. 11 7x 22 20 3x 15 32 11 X 8 11 44 x 5 21 3x4 4. 15 6x5 8 5x2 75 4x25 25 5x8 5 3 3 5 6 5. 36 7x6 10 32 x 5 4 7x 12 7 5x5 30 17x2 3 4x35 9 12x5 18 27x4 2 6x2 49 12x6 10 7x 10 35 14x5 7x3 6 5x 14 8X35 10 x 18 6. 21 7. 12 7 4 4 8. 56 9. 44 5x3x7 32 8x4x5 45 X 2x 1 6 X 11X5 15 5x8x3 11 9x2x5 8 x l: 16 X 12 X45x 2 50 2 x 33 X 5 20 2x8x5 60 x 3: 72 X5 X2x 7 36 7x5x3 8 15 X 1 X 4 7 9 x2: 18 <2 X 5x 2 25 3 X 24 X 5 35 x 3 x 3 l 2 x 7 : X9 3 X 100 X 2 10. 20x7 14x60 6x32 8x3 16x3 5x24 2x 18 11. 18 X 15 45x3 5x 12 48X3 4x7 9x8 27x3 12. 7x 23 10x21 6x2 4x9 5x 14 35 x 2 60 x 12 13. 50x4 3x 25 5x 11 88x8 56 X 3 6x8 2x21 14. 16x5 5x8 12 x 20 5x8 63 X 5 9x 10 48 X 2 24 X 2 9x2 4x15 5x7 20 x 6 CANCELLATION 57 Give results : 1. 7 x 12 2. 3 3. 3 X 5 4. 9x6x2 6 7x6 6x3 12 8x5 12 10x8 8x3x5 20 60x3 4x5 4 7x30 45 3x7 7x2x11 21 2x9 6x21 14 9x8 8 8x2 3x40 5 x 9 x 12 3 16x7 36 10 x 11 33 4x9 7 x 25 x 2 44 7x11 27 x 2 50 3x25 10 ' 5x 12 40 x 2 X 5 5 5x8 6x 10 20 6. 5x4 6. 4 7. 9 x 11 8. 10 x 11 X 8 36 12x7 8X33 90 6x7 20 15x4 2 x 3 x 28 42 15x4 8X3 7 2x9 7 10x25 5x2 6 x 15 x 2 27 6x35 75 50x4 48 6x5 36x3 12x4 15 40 3x4x2 28x5 18 18x4 48 7 9x 10 2x27 8x5x5 9. 4X 11 10. 63 11. 7x8 12. 8 20 4x7 24x3 3x5x24 10 X 18 30 8X 15 12 x 11 7x60 22 9 55 X 4 X 7 12x7 22x6 11 25x6 3x 50 6 60 9x4x5 8X7 26x4 13 8x9 5x 16 84 49 7 x 10 x 2 6x9 30 6x7 7x 15 45x49 56 45 9x5x5 58 Name two factors that make 1. 4 6 8 9 10 12 14 15 2. 16 18 20 21 22 24 25 27 FACTORS lake 28 4. 44 5. 60 30 45 63 32 48 64 33 49 66 35 50 70 36 54 72 40 55 75 42 56 77 Name two groups of factors making 1. 30 2. 36 3. 40 4. 20 18 16 48 42 60 12 72 24 80 28 Name the two equal factors of 1. 9 2. 25 3. 4 4. 64 81 49 90 32 16 100 Separate each of these numbers into 3 factors : 1. 27 2. 16 3. 66 4. 50 5. 56 12 24 20 28 32 63 60 48 72 18 40 45 30 80 70 Name two factors common to 6. 80 81 84 88 90 96 99 100 50 6. 150 100 200 160 180 120 240 36 6. 144 121 400 1. 12 and 18 24 and 36 15 and 30 14 and 42 18 and 36 50 and 30 64 and 80 21 and 63 22 and 132 35 and 70 3. 6. 36 90 44 75 28 and 56 54 and 66 40 and 64 45 and 30 75 and 90 FACTORS PRIME AND COMPOSITE NUMBERS 59 1, 2, 3, 5, 7, 11, 13, 17, 19, 4, 6, 8, 9, 10, ~ 12, 14, 15, 16, 18, 20. Can the numbers above the line be separated into factors? Can the numbers below the line be separated into factors? What name is given to numbers which cannot be factored? What name is given to all other numbers? Learn the prime numbers from 1 to 20. Learn the composite numbers from 1 to 20. All the composite numbers under 100 can be divided by some number less than 10. Tell whether each of the following numbers is prime or com- posite : 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 9 29 65 20 32 76 96 88 22 28 35 62 24 31 69 16 55 97 61 54 71 43 83 66 86 48 19 68 52 89 11 26 14 47 92 17 33 21 77 72 44 15 36 25 12 30 46 45 93 84 27 73 70 81 49 64 34 53 40 75 59 95 57 90 67 41 37 99 98 80 13 50 18 51 38 58 60 87 39 91 82 85 10 78 94 79 74 56 23 63 Separate the following numbers into their prime factors : 1. 21 2. 60 3. 27 4. 48 5. 64 6. 99 7. 49 8. 82 36 55 39 66 70 25 35 30 40 32 80 84 33 34 28 57 88 90 22 12 26 95 56 72 63 75 45 24 81 20 18 93 54 44 50 77 46 96 51 62 60 FACTORS AND MULTIPLES What prime numbers will exactly divide 1. 18? 2. 80? 3. 48? 4. 56? 1 J. 22? 6. 25? 84? 45? 90? 21? 35? 44? 50? 30? 63? 33? 40? 15? 20? 64? 36? 42? 72? 39? 66? 32? 54? 70? 49? 75? 24? 81? 60? 27? 28? 96? Name the greatest number that will exactly divide 7. 8. 9. 10. 9 and 12 20 and 40 12, 18, and 30 30, 60, and 75 10 and 12 15 and 30 10, 20, and 45 22, 33, and 77 10 and 15 30 and 50 9, 12, and 15 8, 12, and 20 16 and 24 14 and 28 15, 21, and 30 18, 27, and 63 18 and 30 21 and 35 8, 24, and 40 30, 36, and 60 24 and 36 32 and 56 21, 42, and 56 10, 11, and 12 30 and 45 40 and 64 2, 3, and 4 15, 18, and 33 20 and 25 12 and 36 14, 28, and 7 4, 12, and 20 Name the least number that will exactly contain 11. 12. 13. 14. 4 and 6. 7 and 8 2, 4, and 6 3,4, and 9 5 and 8 8 and 12 3, 2, and 4 12, 2, and 3 2 and 11 6 and 8 5, 10, and 12 2, 5, and 20 7 and 3 8 and 24 2, 4, and 5 4, 3, and 9 8 and 4 9 and 5 8, 4, and 16 6, 5, and 15 4 and 10 6 and 15 3, 5, and 10 12, 3, and 5 6 and 9 10 and 15 7, 2, and 4 3, 4, and 5 3 and 12 6 and 7 3, 6, and 18 6, 7, and 14 COMMON FRACTIONS REDUCTION 61 Change to whole or mixed numbers : 2. 3. 6. 8. 4 2" 9 15 25 5 40 TO 32 8 66 1 1 60 T5- 6 12 48 8 63 36 -3- 18 "9" 60 1 2 84 12 t 1 5 ~3~ 18 ~2~ 56 7 48 6 56 "8" 64 "8~ 80 "8 3 3 21 7 16 if 49 7 44 1 1 45 5 70 99 ~9 10 20 -5- 35 ~5~ 45 ~9~ 27 "3" 9 9 72 T2 63 "T~ 14 "7" 24 12 T2 - 42 6 28 "4* 42 7 75 2S 30 9. 10 11. 12. 13. 14. 15. 16. 5 10 12 27 -9" 15 48 ~6~ 39 -3" 40 7 16 nr 33 ~8~ 22 ~3~ 24 - 5~ 70 1 2 75 "8" 50 T¥ 9 14 _ 2~ 40 "7 50 1 7 ~S~ 42 ~8~ 80 -7- 60 1 1 12 -4~ 21 ~4- 54 45 1 1 25 60 T¥ 83 "9" 70 T¥ 1 1 36 nr 19 "3" 19 2 23 "7" 35 ~3 58 ~5~ 80 13 18 ~1~ 1 7 "3~ 20 -3~ 38 28 ~5~ 43 ~4~ 90 "3" Note. In actual business operations, improper fractions are rarely changed to mixed numbers. The fractions above are as large as are ordinarily met with in the business affairs of life. The work which fol- lows is, however, valuable for mental drill. 17. 150 T2 - 95 "3~ 132 18. 200 95 nr 105 "T5~ 19. w 125 TOT 87 "3" 20. 200 "25- 150 135 "10 21. 124 500 "25- 75 T5 22. 100 100 100 23. 132 65 T3 12 1 62 COMMON FRACTIONS REDUCTION Change 1. To halves : 3, 6, 2, 7, 5, 9, 12, 8, 10, 4 2. To sixths : 7, 4, 8, 2, 10, 3, 5, 9, 6, 7 3. To eighths : 8, 3, 5, 12, 7, 6, 9, 2, 4, 10 4. To fourths : 9, 6, 2, 10, 3, 5, 12, 7, 4, 8 5. To tenths : 5, 7, 9, 2, 4, 6, 3, 8, 10, 12 6. To thirds : 6, 4, 2, 7, 5, 3, 12, 8, 9, 10 7. To sevenths : 4, 3, 7, 6, 8, 5, 2, 10, 12, 9 8. To ninths : 2, 9, 3, 5, 6, 7, 4, 8, 11, 12 Ghi inge to improper fractions : 9. H, 2*, 8+, °2> 7+, 4+, 6ft, 9+ 10. Q2 12*, 8|, llf, 10-?, Q8 12*, 4f 11. 6#, 5ft> 8f, n, 12*, H+, 6 T 5 2, Q2 "3' 11* 12. 8A, 16*, 6ft, 20*, io+, 2ft i 2% Q 9 5f 13. Hi, 9ft, 1 1 9 9 30f, 50+, xu 8> 8-S. °9> 12+ 14. 15i, 12f, 4ft, 20*, 6+, 9*, 74 1 7? °To, 2 t 3 t 15. 6^- U 5> 8ft, 12*, 25*, 3f, &*, 7_5_ ' 1 2, 22+ 16. 1 1 2 13+, 20f, 33^-, 16|, 8-g-y 6+, 12+, 8f Note. See note on page 61, which applies also to the changing of mixed numbers to improper fractions, and to the work on this- page. 17. 25*, 15+, 75+, 60ft, 12ft, 40*, 50*, 30ft 18. 50f, 12ft, 18+, 20*, 26*, 30+, 75+, .60+ 19. 40*, 80+, 100+, 16*, 18ft, 21+, 40+, 26* 20. 37+, 62+, 90+, 80+, 70*, 60+, 100+, 45+ 21. 50ft, 40+, 30*, 20+, 42+, 15*, 30ft, 70+ 22. 10ft, 12ft, 35^, 100*, 10ft, 21*, 12ft, 90ft 23. 75+, 40*, 75*, 90+, 16+, 22+, 150+, 12++ 24. 55+, lift, 50*, 200+, 14f, 17+, 20*, Hft COMMON FRACTIONS REDUCTION 63 Express in lowest terms : 12 3 6 _5_ 2. _7_ 3. _2_ _9_ _3 _4_ 2_ _4_ _2_ _1_2 T? T2J 8? 105 6? 145 9? 10? 12? 21? 14? 16? 18? 20? 20 9 6. _6_ 4_ A 3. _4_ 10 _8_ _3_ _5_ _6_ _6_ _8_ _5_ .14. ■• 9? 12? 10? 8? 6? 16? 12? 24? 18? 25? 14? 16? 18? 20? 20 3 6 4 _9_ _8_ _8_ _6_ _2__ 12 _4_ _8_ 1.0. 10 10 _6_ _16 • TO"? 6? 18? 12? 10? 18? 12? 18? 20? 16? 14? 16? 18? 20? 2 A. _4_ JLQ. _6_ 16 _3_ 1.8. _5_ JLJ2 J_0. J_j6 JUL 19 Li. JL. JUL ■• 12? 30? 24? 20? 15? 24? 15? 24? 15? 24? 14? 16? 18? 20? 2 K 2. _2 IS JL _6_ JLO _4_ 15 _7_ 1.4. 9_ 14 16 1_0 6 u * 8? 11"? 15? 24? 15? 2 5? 24? 18? 21? 21? T5? 16? 18? 20? 2T 60? 45? 32? 45? 70? 75? 36? 72? 48? 36? 64? 30? 45? 63 7 JUL 3.2. jj. 0. JJL 2.0. 6.0. 4.5. 2.2. 2^4. 3.6. 48 20 42 56 ■• 40? 48? 75? 72? 45? 75? 55? 33? 48? 48? 64? 30? "45? 6"3" ft JL8_ 19, _2_ JL8_ 2 4 4_2 3_0 1_5 XA. ^_ 4_0 J. 4. 3_5 SI °* 27? 30? 48? 60? 64? 60? 50? 50? 28? 64? 64? 35? 50? 63 Q JLO .18. 3.6. 1.2. 1_6 2_5 XA 3.3. 16 5_0. 5_6 2.8. 5 18 ** 60? 45? 72? 84? 80? 40? 49? 88? 75? 75? 64? 35? 60? 81 in 2_0 JJL _9_ 3.5. 3_0 14 4_5. 7^2 IS. 3J 2 - 12 _25_ 4 A5 xv * 80? 96? 81? 56? 54? 63? 50? 80? 39? 40? 64? 35? 64? ¥T 1 1 25 IS 60 _5_0_ 1 6 _2_0_ _1_5_ _2_4_ 4 8 3_0 6 L - L * 100? 132? 180? 2 00? 160? 180? 18 0? "120? 108? 125? T5 1 9 _2_5_ 75 8 _9_0_ 36 _5_5_ _7_2_ _6_ _60_ _6_0 9 **• 125? 150? 120? 100? 144? 110? 144? 100? 108? 125? 150 1 Q 4 3 2 66 , , 2 5 30 _A2_ 18. _2 4 84 50 24 ±0 * 200? 120? 132? 175? 110? 126? 260? 144? 108? T25"? T"5"I) 1 A -J-J- 3 _2_5_ _4_5_ JJ 6 0_ 3_0_ 120 36 75 15 x ** 132? 100? 225? 135? 165? 240? 180? T80? 108? T25"? T5"0 IK 120 110 125 150 .1.20. 1.0_0 140 110 1 00 100 100 * v ' 150? 130? 200? 175? 360? 250? 210? 330? 108? 125? 150 Is it sensible to divide by the largest possible number? What reason can you give for your answer? 64 COMMON FRACTIONS REDUCTION Change to higher terms : 1. 2. 3. 4. 5. To twentieths : 1131234 1 3 7 2) 4> 4> 5) 5> 5) 5) TO) TO) TTT 1 2) 1 3;' 2 3> 1 4> 3 3? 2 4? 1 5) 3 4) 1 6> 3 1 2 2 4 5 4 2 2 1 3 7> 5> ■6> 4> f> 6> 8> 7> 8> 5 3 4 5 3 4 1 4 1 3 5 7> 5? "6> 8) 7? 10J 8? "9? 9> 9 6 7 2 3 7 6 5 5 6 7 7> 9> 9? 10? 8; 9> TU> 8) 8> TTT 6. To twenty-fourths : 1235357 1 5 7 21 3) 4 j 6) 8 J 8? 8? T2"> 121 T"2" 7. To thirtieths : 121415 3 9 2 11 2) 3) 5> 5> 6) 6> 10) TO) T5> TIT 8. To thirty-sixths : 1 2 3 _5 2. 5 7 11 1 5 2> 3) 4) 6) 9> 9) T2J T2) T"8> T8" 9. To fortieths: 1324171 9 1 7 2 f 4) 5) 5) 8) 8) 10) 10) "2~0> "2 0" 10. To forty-eighths : 1 2 3 _5 3 5 5 7 1 1 2) 3) 4? 6> 8) 8? T2> T2> T6> 2T Change to a like denominator : 11. 12. 13. 14. f and I -3% and f \ and ^ T 7 ^ and f ^ and ^ ^ and f f and ^ T 5 T and f T V and -fo ^ and f ^ and f ■& and % T \ and f ^ and J -^ and f & and «£r f and I T \ and T 5 ¥ i and ^ T % and H COMMON FRACTIONS REDUCTION 65 Change to their least common denominator : 1. J and \ 2. i and -f 3. J and | 4. J and ± | and J J and J £ and § £ and -f J and J | and | | and £ £ and £ J and § J and \ J and £ -J- and \ \ and J \ and J i and £ i and £ J and i i and J \ and J J and J J and £ J and \ \ and J \ and ^V i and f i and T V J and \ \ and £ |, i and i 6. §, i and J 7. i J, and T V i h and J J, i and \ \, \, and ^ i i and J §, ^ and i i, J, and iV |, |, and J |, i and \ #, }, and § h h and i i i and £ J, J, and ^ i i and i i |, and J J, T V, and i i i and T V J, J, and J i, J, and i i, i and J §, £, and T V T V, i and J f and J 9. Jandf 10. f and f 11. § and f | and | f and ± f and f f and § f and f ^ and 3 wiu 5 f aiiu 3 ¥ anu f -j^ ana f f and f f and f 1 and f f and T % f and | f and f I and f ^ and f f and f f and f f and f ft and J 68 COMMON FRACTIONS . ADDIT ION l. 21 + 1 2. 7i + If 3. 8f :.+ f 4. 3* + * H+H 21 + 1 f+3f 7f+l| ii+i 3f + i 7f+lf f + 5f 21 + 41 6 + 5f l* + 2* 4f+H I + 6| 3,11 5 T ±S *8 + 8 ^To + TV U + i <§'+* 5s + "8 To + 8ro 31 + 1 5f+U 2|+1| 'A + i-A 5 + 21 101 + 2| I + 6J io« +A 6. 6j + * 6. 8* + f 7- 3f + * 8, 41 + 21 61+1 41 + A 7| + | 71 + 1J 41 + 1 . 10i + i 9*+! 121 + 31 io*+t 5* + * 2i + f 91 + 41 41 + tV ^6 + 3 io| + A 61 + 7^ 2l + TS OS T 4 8 3 j_ 2 8 TTT X 5 101 + 31 6* + A 1tV + ! 6f + f 81 + 41 51 + tV 5* + ! 1A + 1 15A + 51 Add: 9. 10. 11. 12. 13. 14. 14f _3J 20| _5£ 15f 101 10* _6| 24f 8| 30* 45f m . 501 _5i 421 12j 64f 6f 18* 7| 75^ 251 35* _3| 60 T \ 17| 16* 7f 200* 37i 29 T V 6| 54^ HI COMMON FRACTIONS ADDITION 69 1. 5. 9. 13. lil 2jl 2,5 1 l 1 3 + 6 3-r"g" 3 + 6 2 + 3 111 2,1 2,4 I _l_ I 3+T2T 3+T3" 3 + ¥ 2 + 5 l_l_l 2__|1 2,7 i-Ll 3 + i 3 + 6 3 +T2- 2 + T l_l_] 2..1 2,4 i-L 1 3 + T8~ 3 + T8~ 3 + T3" 2 + 9" 2,1 1 | ii 1_|_1_ 3 "T T2 3 + T 8 2 + TT 1 _L 1 3 + XT 2. 6. 10. 14. ill 3 + 4 I J- 1 4 T 2? I + tV 3,3 4+8 III £-l-i 3,5_ 4-1-1 4 + T"2~ 4+8 4+1^ 3+5 111 3_,1 3,3 1 k» 1 4+2 4+21T 4+T6 3+T 111 3_,1 3 i 11 I _|_ 1 4 + T6~ 4+2 4+2TT 3+8 111 3,1 3.,5 Ij_l 4 + 8 4 + T2 4 + "2T 3 + TXT 3. 7. 11. 15. Ill Ail 5j_7 lil 6 + 2 6+2T ¥ + TO r 4+5 III 5,1 5_i_2 1 _L 1 6+T-8~ 6+T"2" ^-+3 4+6 III III 5 I 11 Ij_l 6+T~2~ 6+3 6" + T~2~ 4+T III 5_ , 1 5 i 15 l_Ll 6+3 6 + 2 "6+1*8* 4 + 9 6 + A" 6 + TS" f+A 4 + 9 1 Tcf 4. 8. 12. 16. Ill ^_1_1 5,9 Lil 8 + 4 8 + T¥ 8 + TO" 8 + 5 111 3,1 5,3. lj_l 8 + T~f 8 + 3"2" 8 + 4 ¥+6 I _1_I £ _l_ I 5,5 111 8 + 2 8 + 4 8+-3~2 S+T i_i_i ^.i-i 5,7 iii 8 + T2* 8 + 2 8+T6 5 + 6 i + ^ l + A i + ii "+* 68 COMMON FRACTIONS . ADDITION l. 2} + } 2. 7} + If 3. 81 + 1 4. 3} + | H+H 2} + i l + 3f 7* +11 11+ 1 3! + } 71+11 f + 5| 2} + 4} 6 + 5} 11 + 21 4f+l* f + 6| t + i* ^8+8 6A + A ii+i 4} + f 5"8 + 5g A + 8 A 3} + ! 5| + 1} 21+1} 7 5 I 1 7 5 + 2i 10} + 2} 1 + 6} io»+A 5. 5} + i 6. 81 + f 7. 3| + | 8. 4} + 2} 6*+} 4} + A 7! + ! 71+1} 4} + } 10} + i 9f + ! 12} + 3} m+t &i + t 2f + | 9} + 4} 4} + A °6 T 3 io! + A 6} + 7A 2s + A 81+1 8A + ! 10} + 3} 6} + A 1A+! 6f+f 8} + 4} 5} + A 5i + ! i* + * 15A + 5} Add: 9. 10. 11. 12. 13. 14. 14f 20! _5£ 15f 10} 10! _6} 24f 8} 301 45f 10} . 50} _6} 42} 12} 64f 6f 18| 7} 75A 25} 35* _3| 60fV 17} 16f 7! 200} 37} 29 T V 6} 54A iif COMMON FRACTIONS ADDITION 69 1. 5. 9. 13. lil 2,1 2,5 1 . 1 3 + 6 3 + ^ 3 + 6 2~|-3 2,1 2,4 1-1-1 3+H 3 T 9" 2T5 2j_l 2_,7 1-L-l + 6 3 +12 2 T f 1 _L 1 3 + 9 3 2_il 2,4 1-i-l 3+T8 3+T5" 2 + 9 _1_1 2,ii 1 * * + T 2 3 + T8 2 + TT 1 4- JL 3+18 1 _L 1 3 + TS 3 f TS 3 2. 6. 10. 14 3 I 1 3. , 3 4 + T^ 4+8 1 J- 1 4 T -2U ill ^4-1 3_1__5_ 4 + T"2" 4+8 4+12 lil 3,1 3,3 4 + 2 4 + '20' 4 + TB" 111 £ 4_ 1 3,11 4 + TB~ 4+2 4 + ^0~ 1.1 l_Ll 3.15 4+8 4+T^ 4+2T 3. 7. 11. i,i 6 + 2 5 + ? 3~CT 5 f + 2 3 5 f + H 5 6 + 15 TS 5 6 + A 111 £_!_! 5,7 l_l_i 8 + 3" "2 8 + 2 8+lHg" 5 + 6 8" + 2T 8+A 8 + if 5+4" 5 8 + 9 40" 5 8 + 3 4 5 8 + A 5 8 + 7 is 5 8 + 1 3 24 1 3 + 1 1 3 + i 1 3 + + 1 "3 + 1 1 3 + A 15. 1 4 + 1 1 4 + i 1 I + + 1 4 +i 1 4 + tV 1 4- -i- 6 + 2T iii s.i 6 + T¥ 6 + T2~ 1.1 5 , 1 6 + T"2~ 6+3 1.1 5 , 1 6+3 6 + 2 4 4- -JL- |j 1 6 + 2T 6 + TS 4. 8. 12. 16. Ill £_l_l 5,9 1_l1 8 + 4 8 + T 6" 8 + TO" 8 + 5 1_I_1 3j_l 5,3 1_1_1 8 + T6~ 8 + T2" 8 + 4 8" + 6 1.1 1_1_1 5,5 1.1 8 + 2 8 + 4 8 + 3"2 S+T 70 COMMON FRACTIONS SUBTRACTION 1. 2. 3. 4. 2-i 7-1 15-4| 2.wif 3 - f 5-| 12-2* 3- If 4-| 12 -A 4- If 7-5} 6-| 20 - | 10-3f 10-3f 9-| 10 -f 6-4tV 8-2* 8 - f 12 - | 7 - 5f 5 - If 7-i 25 -A 5 -If 11 - 4f 5-^ 6-f 9-3| 12-2^ 2-^ 8-f 4- If 2- If n- 1 8 2i- 1 4 7i _ 1 2 1 10 Q2 ^3 1 2 4|- 1 8 6f- 1 6 5f- 1 2 8f- 1 "3 6. 7. 5i- -3} 6f- -If 10} - -4f 12* - -2} 8f- -5f 71- -2f 20*- -M 11- -1} 811 ^2 2 3 ~ 4 ' 3 ~" 5 Q6 1 OH 9 1 °T — 2" zu To T 3 101 _ l n| _ i 6f-i 12} -J 11 3 1A2 3 4 e — 4 -10 3 — TOT Kl 1 C 8 1 °2~ 5 °T5 — 2 12} - } 40| - T \ 44 _ 1 OE1 _ 3 ^T 3 * D 2 TT Subtract : 9. 10. 11. , 12. 13. 14. 14 25J 50 *36f 40 28 O4 85 ""8 ^2 O3 7jg 42 37* 14f 44 6? T5 100 100 100 100 100 100 37J 12J 33| 66f 87J _62| COMMON FRACTIONS SUBTRACTION 71 12 5 3 _3 8 2 T5 ~ 5 2. 2 — 4 3. 3 1 11 3. _ 1 4 ~~ '4 2 — 6 42 13 I! 1 _ 1 8 — 8 3 — 6 63 9 4 1 1 2 _ 1 TO" ~ 10 312 36 4 2 11 5 1 5 — 5 2 "~ 8 82 6 5 I 1__ 1 _ 1 T 7 6 12 8 4 7 3_ 1 _ 1 _3 I TO 10 3 9 10 5 11 _ S I 1_ X _ i T2 12 2 10 9 3 5 4 3 G X 5 * 7 • 5 - 4 b « 8 - 6 •• T6 - - 8 3 7 2 If 8 T5 1 2 1 1 T ¥ 9 1 "0 7 T 6^ ~~ 1 3 7 2 7 9 10 7 8 6 7 1 6 7 T6" ~~ 5 T2 7 9 7 8 8 T3 1 2 5 7 2 1 1 9 10 5 6 T 2 ~ 6 8 9 ~~ 2 3 3 4 ~ 5 16 3 10 3 20 5 14 2 7 3 5 3 fi75* »742 ft 5! ~ - 3 O- T - 2 25 23 6_1 5_1 3 _ T 2 5" — TO T2 83 5.5 61 32 3._I 6 — T2^ T — 3 4 — 3 73 33 51 3_1 H 1 T — TO" "92 54 128 5 4 9 4 I _ 2. _7 2 6 — 5 TO "5 27 103 32 53. 22 74 4 — 5 6 — 4 3 — 5 8 — 5 72 85 31 52 8 ~ 3 ¥ — 6 4~6 8 — 5 112 71 71 12 T2 ~ 3 TT"~ 2 T0~2 2 — 9^ 9. e-f 10. T \-i 11. f- i 12. 5 T 2 ~ 1 5 1 6 1 3 7 9 7 10 2 1 30 4 1 5 7 1 2 3 8 1 4 1 5 5 6 9 20 - 1 s 72 COMMON FRACTIONS SUBTRACTION 1 1 2 — 4 5. 3 1 8 — TO* 1 1 2 12 3 1 8 — T 6 1 1 2 — 8 3 1 8 — 2T 1 1 2 - TU 3 1 8 — 4 1 1 2 — 6 3 1 8 - -3"2- 9. 13. 5 1 1 "2T TOT 3 ■3"2" 1 T i-A 1 1 3 — 6 6. 2 1 3 — -9 10. 2 4 3-9 1 1 3 — T3" 1 1 S - T8 2 7 3 — T5" I 1 3~9 2. 1 3 n 2 5 3 — T 2" 1 1 3 — T"8~ 2 1 3 — 6 2 11 3 — T8~ 1 1 2 1 3 - T^ 2 4 3 — 3T id i - i x 1 3 ~ ny 1 T 1-1 i _ l 3 - "g- I 1 *• 4 - Tl T"g- 7 3 1 '• 4 — T2 - 11. I- 15. i-i 1 1 4 — ^TT 3 1 4~2 1 l 4~8 3 1 4 - 21F I 1 4 — T2~ 3 1 4 — rg- 1 1 4 — 2T 3 1 4~8 2V 5 T6 A 7 1 Ta 1 T 4. i- 1 1 6 — T 8" 8. 5 1 6 — T "2 I 1 6 — "51T s 1 6 - -30- 1 1 6 — 2T 1 1 6 — T8" 1 1 6 — T"2" 5 1 6 - -g-g 1 1 6 — TST 1 1 6 - "ST 12. I 5 T2" TF 2 4 16. i-i 1 5 - l 8 1 2 - tV 1 6 - 1 9 l 5 - tV 1 T — 1 8 ADDITION AND SUBTRACTION 73 1. * plus * 2. \ + * 3. A and * 4. { + f 1 l occ 1 2 1 9 lpoa 1 7 _ 2 2 ieSS 2 3 — 2 Ta iebb 5 "5" 3 ! plus J I + i I and J A + i 2 l ot2t2 1 3 _ 1 7 1 p ™ 3 _5 1 3 iebb 6 4 2 8 1Utofe 4 12 4 } plus f | + * | and J T V + f * *— I t - I I less J A - I | plus f | + 1 A and I T 9 e + f 5 l oac 2 5 1 9 1 PQ Q 1 9 _ 1 6 ieSS 3 8 ~~ 2 TIT iebb 2 T6 8 I. 7j + l 6. 2 + If 7. 11 + ! 8. 18+1A 7*-* 2-1* If - f 18-l^r 10 + 3* 5| + i 15| + 1 9* + * 10 -3* 6f-| 15i-i 91-1 Oi I I 15,2 74 i 1 ^1_|_1 O5 T 2 J-G 1 3 *T T 2 °3 "T 6 841 152 74 1 Qll 5~"2 x 6 — 3 'T ~~ 2 °3 ~~ 6 3| + | 12* + f 4^ + | 5| + i Ql 1 lOl 3 A 3 1 K5 1 ^4 ~ 8 1Z 2 ~" 5 ^TO 5 °8 — 4 Add, and subtract : 20* _Zi 10. 50* 12| 11. 18* _8* 12. 37f 13. 44* 10* 14. 13* 75* 40| 20* 65| 10* 16* _2* 48* 19f _9* 37* 12i 12i 66| 33* 33* 16* 87* 12* 83* 16| 74 COMMON FRACTIONS MULTIPLICATION Give products : 1. 2 X | 2. 4 X i 3. 2 X T 5 T 4. 8xf 3 9xf 8xf 4x T V 4x 3xf 7x| 6xf 9x 4 X f 6 X | 9 X T 3 T 2 x | 7x| 2X| 7xf 3X| 5X6 « X i"o 0X4 0X4 8xf 9xf 8xj 6x| 6xf 5xf 5xf 7x^ 5. 10 X | 6. 7 X 4. 7. 2 X ft 8. 25 X i 12 x f 8 X H 8x| 32 x i 8XA 9xf 5xf 40 X f 7x| 10 xf 3xf 28 X I 10x| 11 Xf 6xi 45x* 9 X f 12 x I 9 x A 50 x tV 12 X f 20 X f 7 X f 36 X i 11 Xf 14xf 4X^ 44 Xi Solve by cancellation : 9. 28 X f 10. 84 X A "• 50 X ^ 12. 60 X U 18 X I 15 xi 24 x ^ 20 xf 44 x T 5 T 42 X f 45 X I 64 x f 75 x A 90 x i 36 X i 70 x T V 20 x A 27 Xf 80x T V 72 X A 21 xf 35x4 48 X A 40xf 30 x I 96 x H 32 x I 56 X f 66x T 8 T 49 Xf 81 X I 100x-2 8 5 COMMON FRACTIONS MULTIPLICATION 75 Multiply: 1. 2. 3. 4. H by 3 4 T 3 o by 2 2| by 3 61 by 8 4| by 5 7J by 5 3| by 4 121 by 4 61 by 4 21 by 7 5i by 8 9f by 10 2f by 2 5 T 2 T by 4 If by 5 3f by 8 8 t 2 t by 5 9i by 8 4| by 6 5| by 6 3| by 4 4f by 3 2f by 4 If by 12 7-| by 7 31 by 4 81 by 5 41 by 9 51 by 4 10A- by 2 lOf by 3 11 J by 6 5. 6. 7. 8. 41 by 5 31 by 10 2f by 4 81 by 7 3| by 6 7§ by 9 3f by 5 121 by 5 2} by 7 121 by 5 4f by 7 4| by 8 51 by 9 61 by 8 3| by 5 2f by 6 10| by 8 21 by 11 5f by 3 10J by 9 61 by 10 4 T V by 15 6J by 9 3f by 10 8A- by 11 81 by 7 4f by 9 81 by 11 91 by 12 91 by 9 3f by 7 5 T \ by 4 9. 10. 11. 12. 20 T V by 5 9 T 2 T by 20 10| by 9 11 by 12 4f by 12 4 T V by 11 18f by 5 51 by 16 16f by 5 8f by 40 40f by 4 21 by 18 4f by 20 6f by 15 21f by 4 6 T V by 20 6^ by 25 2| by 30 60f by 2 5 T \ by 15 8f by 12 3f by 25 . 25| by 6 4f by 21 4f by 16 51 by 20 221 by 3 131 by 3 15| by 5 7f by 14 50^ by 5 371 by 2 76 COMMON FRACTIONS MULTIPLICATION Find products, cancelling when possible : 1. i dt f 2. \ of f 3. i of | 4. § of f 1 y 8 ^ y 5- Av6 3wl 4 A ¥ 8 A 6 3 A 7 4 A 8 A y 8 2 y 3 5 V X 5 v 9 2 A TT T A 4 7 A T5" "9 A 2~a 4 y 3 1 y A 2 y 7 3 y 8 T A 8 2 A 2 ¥ A 8 8 A Y5 2w9 A y 1 *■ V 4 2 y 5 3 A TO 8 A 5 4 A 5 y A 2"^ A y 2_ 5 y 3 4 v 1 3 v 5 4 A 3 ¥ A 8 9 A T 2" TO A ¥ 2w3 3 y A iv 8 2 y 5 5*4 T A 6 2 A 9 lT A 8 5 y 3 A y 10 6y2 A y A ¥ X T¥ 5 X TT TT X 3 3X4 5. f AA 7 U1 3 5 6 JL nf - 7 - D - 11 U1 12 7. | of A 8. f of f 1 V - 1 - 5 A 11 5 y 3 TT A Ta 5 y 6 9 X 7 6 y 5 TT X 36 1 y 12 8 A 63 i V 1 2 6 X "2 5- 2 y 2 1 7 A TO" 4 v 6 5 A TT 1 1 y 7 TT A 33 2 A 8 7 y 8 "24 A TO 1 5 y 1 6 32 A 22 5 v 3 6 A 2T 6 y 7 7 A 1 5 10 y 3 TT A 5 1 Y 12 4 X 2T 4 y 7 1 ¥ A 16 8 y 1 TT A 4 9 y 5 10 A 7 10 y 7 11 A 20 4 y 8 T X 9 3 y 4 20 A 15 2 1 y 1 1 22 A 14 14 y 3 T 5" X y 8 y 5 10 A 32 5 y 6 1 2 A 7 3 y 10 40 A TT 1 2 y 9 TT A TTF Comparison of Fractions 9. Which of the following fractions equal one-half? ft _6_ 1 A JL 4. 2 _4_ 3. _5_ _7_ XJL 8> 12? 5? 9> 4? 7> 8J 10> 6> 10' 15? 20* Which are greater than \ ? Which are less ? How can you tell at a glance? 10. Which of the following fractions equal one-third? A. 3. Jl 3 3 _6_ 4_ IS 2. _6_ 2 _J_ 11 "9"? T2J 4> 8? -15? T2> 1"8~> 6> 18? 5> 20' Which are greater than § ? Which are less ? COMMON FRACTIONS MULTIPLICATION 77 Find products, cancelling when possible : i 1. H X f, or f X ! 21 X f , or i x f 4| X i or f X 1 If Xi or {Xf 3* X f , or J£ x | o^ X y> or -j- X y 2| X J, or f X I 6i X f, or V- X I 2. I X 2f, or I TT X 3y, or TT 4|, or I x- 1 / x-¥- 8. v 4-^ 9 A ^8; { x 2| , or f f X 6i or t X 5J, or i X 12f , or I X 10i or 22 7 V 35 x nr V 17 X " 6" V 49 X ~3~ V 25 V 8 1 If x 3f *fX If 8j X 1* Hx Oy X «->2 71 X 41 3* X 4* 64- X li 3. or V x J£ or - 3 / x -V- or %« X ii or fxV or -y- x J or -V- X f or -V- X « or - 2 / x f If X 10|, 5|X 11, 4AX If 2|X 21, 1 - 3 _ V ^ 3 x l l A o 10 , 91 x 6f iiixi T V, 61X1*, or -V- X I or||X ! or V X V 5 nr 14 v 33 0r TT X TO or - 2 / x - 4 / or V- X If 5 5 v 14 "9" x TT or % 5 - Multiply : 5. 45 6. 16 7. 24 8. 15 9. 21 10. 40 _2| _4| 9-5- ^T2 M 42 ^3 _5| 50 32 75 60 35 80 _8f Jf 42 ^3 95 93. _M 25 30 18 22 14 20 _M _M _2| Ji Jk 12} 78 COMMON FRACTIONS MULTIPLICATION Give products : 1. 2. 2X| 7x24 3| X 4 10X3| 1 of 5 « of A If X6 44x44 5. 6. f of 12 40X + 11x24 f of 10 2 X 4 4 of 45 2|x3 3X33J lV 4 of 3i X 4 f of 20 a t x ttf 10. 4 5" of 15 2| X 12 3 5 of 3 5 3. 124 x 2 4x64 84 X 3 4x24 6ix2 7. 2f X2| 20 xf 111 X 2 1 V 3 4 * 5^ 11. 3X 12| 3 A y 16f x3 4x24 4. A of f 14x14 8Xf 5x3| 8. 14 Xf 9x2tV I of 1 TO X 4 12. 61 1 2 81 X2 of 100 X6 50 X 13. 124x5 14 x 10 7xA fx24 17. 3X51 of 14. 5x94 7x121 -h of 100 ,6|X6 18. 4 of ioo 34x3 1 v 8 15. 50x2§ of 2 \ of 100 6i X 8 2x33| 9xf 19. f of 81 T V of 100 2|X5 6x 12i 16. I of 56 10 X A | of 100 13 Xf 20. 124 x 8 84x9 4x 121 4 of 45 FRACTIONAL PARTS OF NUMBERS 79 What is 1. 2. 3. 4. \ of 18? i 10 of 30? 2 3 of 12? i of 27? 1 11 of 55? 3 4 of 16? i of 40? 1 12 of 48? 2 5 of 20? i of 35? 1 T5 of 60? 3 5 of 15? i of 42? 1 2 of 80? 4 5 of 50? \ of 49? 1 25 of 100? 5 6 of 12? i of 32? 1 40 of 80? 2 7 of 14? 1 of 45? ■h of 100? 3 7 of 21? 5. 6. 7. f of 48? 3 5 of 55? 3 10 of 50? f of 64? 3 4 of 40? A of 84? i of 90? 5 8 of 96? 3 7 of 77? T 3 T of 44? 3 8 of 48? 4 9 of 45? T \ of 48? 5 6 of 72? 7 TO" of 40? | of 27? 7 8 of 56? 7 T2" of 36? •f- of 42? 4 5 of 35? 4 5 of 60? f of 33? 2 7 of 49? 2 TT of 55? 9. 10. 11. | of 140? A of 96? l 2 of 1240? 4 of 108? 9 20 of 100? 1 4 of 408? A of 132? A of 100? 1 ' 5 of 2000? T V of 144? 8 T5 of 90? 1 3 of 612? | of 180? A of 150? 1 7 of 721? A of 200? 5 8 of 160? 1 8 of 2400? T 7 T of 110? A of 130? 1 6 of 486? A of 75? 2 3 of 144? 1 9 of 405? 4 7 of 7? 5 7 of 28? 6 7 of 70? 3 8 of 24? 5 8 of 40? 7 8 of 16? 2 9 of 18? B 9 of 45? 8. f of 56? A of 80? •A- of 22? | of 72? f of 32? f of 63? | of 40? f of 42? 12. i of 45? i of 70? I of 50? i of 62? J of 31? £ of 80? | of 25? i of 40? 80 FRACTIONAL PARTS OF NUMBERS 1. 2 is J of what number? 10 is 2. ^q of what number ? 4 is i of what number? 6 is 4 of what number? 6 is J of what number ? 8 is J of what number? 8 is J of what number? 9 is -| of what number ? 5 is J of what number? 12 is | of what number ? 10 is \ of what number? 7 is ^ of what number ? 9 is \ of what number? 11 is J of what number? 3 is J of what number? 9 is iV of what number? 12 is \ of what number? 15 is | of what number ? 7 is \ of what number? 25 is J of what number? 3. 12 is f of what number? 40 is 4. f of what number ? 6 is § of what number? 36 is T % of what number? 8 is \ of what number ? 25 is | of what number? 15 is f of what number? 42 is f of what number? 10 is § of what number? 60 is T 5 2- of what number ? 20 is f of what number ? 35 is | of what number? 18 is f of what number ? 49 is ■£$ of what number? 9 is f of what number? 30 is f of what number? 14 is § of what number? 24 is f of what number ? 16 is \ of what number ? 21 is | of what number? 5. \ of 12 is f of how many? f of how many? f of how many ? f of how many ? f of how many ? | of how many ? 6. \ of 48 is \ of 30 is f of 60 is f of 16 is f of how many? § of 20 is f of how many? f of 35 is f of how many ? f of 36 is f of how many ? | of 80 is § of how many ? | of 27 is f of how many ? COMMON FRACTIONS DIVISION 81 2 + i 2. 2 + 1 3. 6 + J 4. 4 + | 4 + 1 5 + £ 3 + 1 5 + f 3+| 2+| 5+| 4+1 2 + 1 4+i 3+i 6 + i 4+i 3+| 2+1 4+| 3+| 5 + 1 4 + i 3 + | 6+i 3+ J 2++ 5 + 1 2 + 1 6+i 6+1 5+| 2 + f 6. 6 + | 7. 3 + | 8. 9 + i 4 + f 2 - 4 * + 6 5 + f 4+f 3 + ! 7 + 1 4 + f 7 + 1 3 + i 3 + J 6 + « 8 + f 5 + f 6 + f 2+f 3 + * 2 + J 5 + f 7 + i 4 + f 6 + i 8 + f 5 + f' 9^« 7+1 9 + i 8 + 1 8 + f 9. 6 + f 10. 6 + f 11. 8 + f 12. 8 + | 9 + | 7 + f 6 + | 10 ♦# 1 1 • 1 fi • 7 Q ^. II Q ^. II 11— 8 ° ~ T 0" ° • 12 y ' 12 8 + ^ 7 + f 10 + J 7 + | 6+f 7+f 8+f 9+f 7 + f 6 + 1 7 + A 8 8 + 1 9 + T % 6 + T V 6 10 + f 7 + A - 9 + i U 7 82 COMMON FRACTIONS DIVISION 3 — L 1 ^ A 4 — ^ -3 3 ~ ^ * + 2 i + 3 +•« i + 6 i + 3 4 + 5 4 + 2 4 + 3 8 — t) * + 4 f+3 4 + 5 4 + 6 ^2 4 + 6 4 + 5 4 + 2 1 + 4 4 + 5 + +6 4 + 4 6 ~ ^ 5. t + 2 6. A + 5 7. |*3 8. f + 6 f + 3 f + 9 4 + 6 * + 8 « + 4 f + 2 1 + 2 J7_ ^ Q 10 • y ! + 6 * + 3 1 + 7 5 _^ 4 6 ~ ^ 3 _,_ Z 8 — O f + 4 f + 5 f + 5 :& + 7 4 + 8 i + 9 4 + 2 i + s 1 + 7 i + 4 1 + 3 i+9 J + 6 1 + 8 f+7 9. 3 . TO ~ 12 5 . 8 * 12 7 12 5 . 1 2 * 12 9 . TT • 12 7 . 9 ~ 12 6 . 7 ' 12 7 TT ~ 12 10. 5 8 7 TIT 5 6 15 15 15 15 15 15 15 15 11. 4 + 20 12. ^ +25 I + 20 I + 25 4 + 20 1 + 25 $+20 § + 25 I + 20 f + 25 4 + 20 f + 25 | + 20 1 + 25 A + 20 f + 25 COMMON FRACTIONS DIVISION 83 3. 1 _^ A ro • o i . i t ~ ¥ 1 . 1 2 ~ 4 4. i TO 10 1 3 1 T l 3 TO ~ 5 8. 10 i i TO 9. 13. 10. i 12 17. 1 . i 2 — 9^ 1 . 1 TT ~ 2 1 6 1 10 14. 18. 1 "6 1 3 1 T ' l 9 1 1 1 11. 1 T 1 5 1 . 1 9 — T 1 . I 6 "' 2 15. 19. 1 . 7 "" 1 8 1 1 IS ~ 5 1 TT ~ 1 6 l . 1 8 l . 4 • 1 7 1 . 3 T 1 2 1 TO ~ 1 3 1 1 2 ' 1 9 1 1 1 * 1 4 1 . 7 ' 1 6 1 . 4 ~ 1 2 1 1 2 ' 1 6 1 . 8 ~ 1 3 1 . 3 ~ 1 1 1 . 4 ~ 1 11 12. 16. 20. TT l 1 TO 1 TO 1 TT l 6 1 1 1 4 — T2^ 84 SPECIAL ONE-MINUTE EXERCISES Practice first for accuracy, then for speed. 1. Start at 1. Count by threes. "1, 4, 7, 10, 13," etc. Record the number reached at the end cf one minute. Start at 2. Count by threes. Record as before. Start at 3. Count by threes. 2. In the same manner Start at 1. Count by fours. Count by fours, starting successively at 2, 3, and 4. 3. Start at 1. Count by fives. Count by fives, starting successively at 2, 3, 4, and 5. 4. Count by sixes, starting successively at 1, 2, 3, 4, 5, and 6. ] 5. Count by sevens, starting successively at 1 , 2, 3, 4, 5, 6, and 7. 6. Count by eights, starting successively at 1 , 2, 3, 4, 5, 6, 7, and 8- 7. Count by nines, starting successively at 1, 2, 3, 4, 5, 6, 7, 8, and 9. 8. Note. To follow the work in U. S. money. Starting at 12 j, count by 12$ 'a as far as you can in 1 minute. Starting at 16f , count by 16f 's as far as you can in 1 minute. Starting at 33j, count by 33|'s as far as you can in 1 minute. 9. How many of the following fractions can you name in their lowest terms in one minute? (a) 3 4 2 3 "6") 10) 8? 9) 6 T2^ 2 6") 5 10? 6 4 3 2 8) 6) 12) 4) 2 TO) 4 6 9 "§"? "9? T8" (*) 4 8 8 T2) To") 12? 6 TO? 3 T5? 9 14 4 9 2"T) TF) T"5") A, 5 15 5 T"5? 20"? 25? 2 0) 3 2T (c) 10 12 2 1 5 J 1 ^? 1 T5"? 10 "25") 12 T"5"> TO) 6 10 15 15) 20) 30) 20 2"5) 3 20 25 T8~? TO? 50) 10 40) 6 TIT (d) 2 15 6 TO"? "2"5~? T"8~? 9 27? 7 2"T? 9 6 12 11 2T) 18? 2 2) 5 TO? 2 10 12 18) 22) 24) 10 12) 14 T6 UNITED STATES MONEY 100 cents = $1. 1. What part of one hundred cents, or one dollar, is 50c 7 ? 10c7 20c 7 ? 80^? 25^? 5^? 40^? 75^ 4^? 60 c 7 ? 33^? 66^? 85 30^? 70c 7 ? 90c 7 ? 2. What coin equals 25 cents? 10 cents? 5 cents? 2 quarters? 5 nickels? 5 dimes? 10 dimes? 4 quarters? 10 quarters? How many nickels In a dime? In a quarter? In a half-dollar? In a dollar? How many dimes In a quarter? In a 50-cent piece? In a dollar? In a $2.50 gold piece? How many quarters in a $5 gold piece : How many dimes in a $5 gold piece ? How many nickels in a $5 gold piece ? How many half-dollars in a $5 gold piece ? 6. What part of a dollar is A cent? A nickel? A dime? A quarter? A 50-cent piece? What coins will make 7. 50c 7 ? 8. 40<£? 9. 20c 7 ? 25c 7 ? 75<£? SOc 7 "? 30^ 55^? 60^? 10. 70^? 11. 45^? 85c 7 ? 90^? 35^? $1? UNITED STATES MONEY Read : 1. 2. 3. 4. 5. 1.05 2.34 4.02 1.12 .90 .25 5.10 10.11 30.03 28.07 .01 .08 8.04 5.95 3.09 .75 202.45 103.03 20.40 25.19 6.84 8.00 20.27 226.63 .08 75.00 120.20 305.84 60.08 9.02 Add: 6. 7. 8. 9. 10. 11. $ .25 $.16 $ .50 $2.10 $5.15 $ .42 1.40 .90 1.50 .64 .40 1.08 $1.10 $.40 $ .33 $1.32 $ .75 $2.40 .65 .82 1.26 .27 1.75 .13 $2.01 $ .39 $2.84 $4.0 $2.20 $ .64 .67 1.30 .11 .76 .75 1.10 L.55 $8.25 $1.11 $1.64 $2.05 $3.30 .42 .13 2.00 1.12 2.56 1.25 12. 13. 14. 15. 16. 17. $.23 $.72 $.33| $.54 ' $ .08 $.46 .16 .20 .20 .12| .18 .24 .05 .09 .10 .03 1.25 .02 $.42 $.62| $.40 $ .95 $ .82 $.122 .37^ .18 .32 1.06 1.00 .09 .10 .50 .11 .03 .15 .871 &6.121 $20.30 $15.10 $1.50 $2,121 $1,331 4.10 8.75 3.331 2.871 1.621 l-16f UNITED STATES MONEY 87 Finding Amount of Purchases C8 06 1. 2. 3. 4. 5. $.05 $.06 $.25 $.12 $.15 .01 .09 .08 .07 .07 $.09 .05 $.14 .08 $.11 .12 $.17 .07 $.20 .06 $.16 .07 $.09 .08 $.22 .05 $.25 .12 $.18 .11 $.13 .10 $.21 .06 $.27 .05 $.19 .07 $.33 .08 $.38 .05 $1.12 .13 $1.15 .08 $1.10 .18 $1.14 .20 $1.31 .12 $1.17 .11 $1.15 .25 $1.25 A3 7. $.12 .05 What will the following purchases cost ? 8. $.15 .09 9. 10. 11. 12. 13. 14. 15. 16. $.25 $.12 $.08 $.20 $.38 $.30 $.13 $.24 .06 .07 .13 .10 .09 .18 .22 .04 .11 .08 .10 .06 .05 .04 .07 .11 $.50 $.42 $.36 $.54 $.22 $.40 $.62 $.14 .08 .12 .18 .09 .38 .17 .25 .30 .10 .03 .05 .05 .10 .09 .05 .03 $1.20 $1.00 $1.25 $1.50 $1.10 $1.05 $1.40 $1.60 .16 .30 .50 .12 .25 .15 .32 .25 .06 .07 .05 .10 .25 .20 .08 .15 17. 2\ doz. eggs @ 48<£. 18. 5J yd. ribbon @ 40jzf. 2\ doz. buttons @ 80^. 5 lb. coffee @ 37c 7 . 12 lb. sugar @ 8|c\ 4 jars fruit @ 62<£. 6 lemons @ 2 for 5ff. 3 doz. oranges @ 45^. 3J yd. lace @ 75cL 7 yd. scrim @ 12^. 2 yd. linen @ 62^. 20 spools thread % 60^ a dozen. 88 UNITED STATES MONEY Making Change Subtract : 1. 2. 3. 4. 5. 6. 7. 8. $.25 $.25 $.25 $.25 $.25 $.25 $.25 $.25 .07 .04 .10 .16 .08 .14 .06 .20 $.25 $.25 $.25 $.25 $.25 $.25 $.25 $.25 .09 .12 .15 .03 .13 .17 .19 .01 $.25 $.25 $.25 $.25 $.25 $.25 $.25 $.25 .18 .23 .21 .02 .05 .11 .22 .24 9. $.50 .38 10. $.50 .17 11. $.50 .26 12. $.50 .11 13. $.50 .28 $.50 .22 $.50 .13 $.50 .23 $.50 .16 $.50 ^18 $.50 .21 $.50 .35 $.50 .31 $.50 .24 $.50 .36 $.75 .62 $.75 .54 $.75 .58 $.75 .51 $.75 .66 17. $1.00 — 63^ = ? $1.00 -47*5 - ? $1.00 - 37^ = ? $1.00 - 85^ = ? $1.00 - 19^ = ? $1.00 - 54^ = ? $1.00 - 49^ m ? $1.00 - 72^ = ? 18. 14. 50 33 50 32_ 50 29 75 62 15. 16. .50 $.50 .14 .39 .50 .19 5.50 .34 1.75 .53 $.50 .37 $.50 .27 $.75 .59 $2.00 - $1.55 = ? $2.00 - .32 = 9 $2.00 - .75 = ? $2.00 - 1.10 = ? $2.00 - .88 = ? $2.00 - 1.20 = ? $2.00 - 1.85 = ? $2.00 - .62 = ? UNITED STATES MONEY" 89 Making Change 1. 2. 3. 4. 500 - 90 500 - 410 500 - 470 500 - 430 . 500 - 150 500 - 200 500 - 80 500 - 50 500 - 120 500 - 400 500 - 450 500 - 440 500 - 60 500 - 250 500 - 300 500 - 70 500 - 100 500 - 460 500 - 420 500 - Bi $1.00 - 100 $1.00 - 250 $1.00 - 200 $1.00 - 800 $1.00 - 400 $1.00 - 500 $1.00 - 90 $1.00 - 60 $1.00 - 70 $1.00 - 700 $1.00 - 600 $1.00 - 300 Subtract : 5. 6. 7. 8. 9. 10. 11. 12. $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 .15 .55 .12 .48 .27 .87 .38 .42 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 .68 .13 .72 .36 .28 .21 .43 .66 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 .45 .23 .58 .61 .57 .18 .65 .44 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 $1.00 .78 .64 .33 .26 .39 .84 .62 .14 13. $5.00 - $2.50 14. $10.00 - $3.75 15. $20.00 - $15.50 $5.00 - $1.75 $10.00 - $8.10 $20.00 - $12.00 $5.00 - $2.10 $10.00 - $6.50 $20.00 - $10.25 $5.00 - $3.25 $10.00 - $.67 $20.00 - $16.40 $5.00 - $4.15 $10.00 - $9.12 $20.00 - $8.75 $5.00 - $.85 $10.00 - $4.50 $20.00 - $9.50 $5.00 - $4.45 $10.00 - $2.25 $20.00 - $6.15 $5.00 - $2.20 $10.00 - $5.80 $20.00 - $19.10 See Subtraction of Decimals for further practice of this kind. 90 UNITED STATES MONEY Making Change Use business method in all cases. • What change should be given back to you at a store if you offer a quarter to pay for articles which amount to 1. 15 cents? 6. 70 and 100? 11. 100 and 100? 2. 17 cents? 7. 150 and 30? 12. 50 and 70? 3. 8 cents? 8. 40 and 50? 13. 120 and 20? 4. 6 cents? 9. 130 and 100? 14. 90 and 80? 5. 12 cents? 10. 60 and 100? 15. 70 and 80? w hat coins m ight you receive back, in each case ? What change should be given back to you if you offer a 50-cent piece in payment for articles which amount to 1. 37i cents? 6. 250 and 100? 11. 170 and 100? 2. 15 cents? 7. 200 and 150? 12. 250 and 70? 3. 25 cents? 8. 160 and 300? 13. 380 and 120? 4. 40 cents? 9. 120 and 240? 14. 180 and 50? 5. 12^ cents? 10. 90 and 400? 15. 100 and 330? What coin or coins would make the exact change? What change should you receive from a clerk to whom you hand a dollar, if your purchases amount to 1. 450? 6. 500 and 12^0? 11. 420 and 180? 2. 750? 7. 450 and 400? 12. 330 and 70? 3. 62(5? 8. 37J0and5O0? 13. 62^0 and 100? 4. 87|0? 9. 250 and 600? 14. 850 and 150? 5. 220? 10. 190 and 300? 15. 200 and 590? UNITED STATES MONEY 91 1. £ of $1 is 33£ cents, f of $1 is ? cents. Count by 33^s to 100. To 200. To 300, and back to 33f What is 2. Twice 33 J cents? 3. Three times 33 J cents? Nine times 33^ cents ? Four times 33 J cents? Five times 33 J cents? Seven times 33 J cents? Eight times 33 J cents? Ten times 33 J cents ? Eleven times 33 J cents? How many articles @ 33^ each can be bought for 4. 1 dollar? 1^ dollars? 2 dollars? 6f dollars? 10 dollars? 5 J dollars? 12 dollars? 9 dollars? $ 7-|? $15? $ 8£? $ 3f ? $ 8? $10§? $ 7? $20? $10? $ 1.33 J? $ 5.66f? $18? $25? , $20.33 J? $ 9.66|? $30? 7. 66|^ X 2 = ? mu X 3 = ? How many articles @ 66f i each can be bought for ! For $12? For $6? For $20? For $8? At 66f i each, what will be the cost of 8. 2 articles? 9. 5 articles? 10. 3 articles? 6 articles? 4 articles? 7 articles? J? For $4? 8 articles ? 9 articles? 10 articles? 92 UNITED STATES MONEY 1. of $1 is 16f cents. 50^ is ? sixths of 1 dollar. 16f ^ is ? sixths of 1 dollar. 66f i is ? sixths of 1 dollar. 331^ is ? sixths of 1 dollar. f (or 1) of 1 dollar is ? cents. -| (or 1) of 1 dollar is ? cents. £ (or § ) of 1 dollar is ? cents, f of 1 dollar is ? cents. 83-^ is ? sixths of 1 dollar. 3. Count by 16f 's from 16f to 100 and back to 16 Count by 16f 's to 200 and back to 16f . 4. Complete the table below and memorize it. 16f x 2 = . 16f x 4 = - 16f X 3 = 16f X 6 = 16| X 5 m How much is 5. Twice 16f cents? Four times 16f cents? Six times 16| cents? Eight times 16| cents? Ten times 16f cents? 6. Three times 16f cents? Five times 16| cents? Seven times 16f cents? Nine times 16f cents? Eighteen times 16f cents? At 16f i each, how many articles can be bought for 331 cents? 66f cents? 50 cents? 83 \ cents? 100 cents? 1 dollar? \\ dollars? 2 dollars? $11? $21? $f? $4J? $1?? $10? $31? $5? $1.50? $2.66f? $3.00? $1,331? $4.50? $ .831? $1.66f? $1,831? 10. What is 1 of 16f i ? What part of a dollar is this ? UNITED STATES MONEY 93 | of $1 is 12| cents. f (or J) of $1 is ? cents. f of $1 is ? cents. | (or !) of $1 is ? cents. f of $1 is ? cents. f (or f) of $1 is ? cents. J of $1 is ? cents. How much is 3. Twice 12| cents? Four times 12! cents? Six times 12! cents? Eight times 12! cents? Ten times 12! cents? Twelve times 12 \ cents? 50^ is ? eighths of 1 dollar. 87! j£ is ? eighths of 1 dollar. 25^ is ? eighths of 1 dollar. 62JC 7 is ? eighths of 1 dollar. 37! <£ is ? eighths of 1 dollar. 75^ is ? eighths of 1 dollar. 4. Three times 12 J cents? Five times 12! cents? Seven times 12! cents? Nine times 12 \ cents? • Eleven times 12! cents? Twenty times 12! cents? How many times is 12! c 7 contained in 5. 25 cents? 1 dollar? \\ dollars? 50 cents? 37| cents? 1! dollars? 62§ cents? . 2 dollars? 75 cents? 87! cents? Led in $5? 7. $ 1.50? $31? $ 2.121? $4i? $10.75? $lf? $ 9.37^? $10? $ 4.25? $6J? $ 7.871? $8? $ .371? $2f? $12.50? $9? $ m\i w % .87|? 94 UNITED STATES MONEY t. Count by 12!'s from 12| to 100 and back to 12J. Count by 12§'s to 200 and back to 12-|. 2. Complete the table below, and memorize it. 12* X 2 = . 12J X 5 -p 12j X 3 -m . 12| x 6 = 12| X 4 = . 13} x 7 12§ x 8 - . How many articles at 12|^ each can be bought for 3. $.87!? 4. $1.12| ? 5. $1,624? 6. $4.12!? $.50? $1.50? $2.00? $ 5.00? $.75? $1.37!? $2.50? $ 5.87!? $.37!? $1-75? $3.00? $ 6.00? $.25? $1.87!? $3.75? $ 6.25? $.62!? $1.25? $4.00? $10.00? 7. What is ! of 12|{£? What part of $1 is this? Find the cost of 8. 2 articles @ 37!j£ each ; © 62!^ each ; @ 87!^ each. 9. 3 articles @ $1.12! each; @ 37^ each ; @ 62!^ each. 10. 4 articles ® $1.37| each ; @ 62-J-fS each ; @ 87!j4 each. UNITED STATES MONEY 95 1. _i_ of $1.00 = ? -^ of $1.00 - ? 2V of $1.00 = ? I of $1.00 = ? iV of $1.00 = ? T V of $1.00 - ? Express as a fractional part of one dollar : 2. $.334 3. $.50 4. $.624 5. $.01 .12| .16f .40 .87i .10 .25 .06J .084 .05 .37| .30 .70 .04 .75 .661 .83* press as cents : J of a dollar. 7. f of a dollar. 8. ^5 of a dollar. 4 of a dollar. f of a dollar. ^ 3 5- of a dollar. | of a dollar. | of a dollar. f of a dollar. | of a dollar. | of a dollar. | of a dollar. i of a dollar. f of a dollar. i^ of a dollar. ■^q of a dollar. ■^ of a dollar. i^- of a dollar. J of a dollar. § of a dollar. f of a dollar. ^ of a dollar. ^ of a dollar. ^ of a dollar. Read the following amounts thus : "$1.40 is $1| 9. $1.40 10. $10.20 11. $12.75 12. $2.05 3.87| 1.334 9.40 10.04 2.10 15.60 8.16f 6.124 5.50 2.05 2.08J 5.834 1.121 3.37-1 25.121 7.624 6.66f 6.25 4.064 15.374 8.064 20.75 16.15 1.30 9.80 4.62| 5.084 8.70 96 THE NUMBER TWENTY-FIVE 1. 2 X 25 = ? 3 X 25 = ? 4 X 25 = ? 11 X 25 5 X 25 = ? 6X 25 = ? 7 X 25 = ? 8 X 25 = ? 9 x 25 = ? 10 x 25 = ? 12 x 25 = ? . 2. Count by 25's to 300. Count back to 25. Practice doing this until you can do it in 20 seconds or less. 3. How many 25's in 75? 125? 50? 25? 100? 150? 200? 175? 300? 275? 250? 225? 4. How much money will buy one thrift stamp? Two thrift stamps? Five? Eight? Three? Twelve? Four? Seven? Eleven? Six? Ten? How many quarters in • $1.? $4.? $10.? $6.? $7.? $1.25? $1.75? $5.? $3.? $ 8.? $9.? $2.? $2.50? $1.50? 6. How much is 256 256 and 50^? 506 25c 7 , and 75^? 25c 7 , 756 and 25^? 756 $1.00, and 25c 7 ? 7. What is the sum of 25 + 25 + 50 + 25? 75 + 25 + 25 + 25? 50+25 + 50 + 25? 25 + 75 + 50 + 50? 8. How many times 25% is 50%? 100%? 75%? 125%? 9. What is | of 25 cents? What is i of 25 cents? 256 $1.00, and 50c7 506 756 and $1.00? 506 506 and 75^? 756 756 and 25^? 50+ 25 + 75 + 25? 100+ 50+75 + 25? 75+ 125 + 50 + 50? 25+ 150 + 50 + 25? 200%? 150%? 175%? What is | of 25%? What is | of 25%? DECIMAL FRACTIONS ADDITION 97 .2 + .7 = ? .4 + .4 = ? •7 + .2 = ? .5 + .3 = ? .1 + .5 = ? .2 + .6 = ? .3 + .3 = ? .4 + .5 = ? Add 2. .3 + .? = ? .5 + .5 = ? .9 + .4 = ? .8 + .5 = ? .2 + .8 = ? .7 + .3 = ? .4 + .8 = ? .9 + .2 = ? 3. 8 + .6 = ? 3 + .8 = ? 9 + .6 = ? 7 + .5 - ? 8 + .7 = ? 6 + .6 = ? 7 + .7 = .? 8+ .8= ? .2 + .4 + .3 = ? .1 + .8 + .5 = ? 3 + .3 + .4 = ? .7 + .5 + .3 = ? .6 + .4 + .9 = ? .8 + .5 + .4 = ? .5 + .7 + .6 = ? .7 + .8 + .5 = ? i: 5. .2 .6 .5 .1 .4 6. .3 .6 .3 .5 .2 .6 .4 .5 .5 .3 .2 .3 .7 .1 .6 .6 .5 .6 .4 .7 .4 .5 .2 .2 .7 7. .4 .6 .3 .3 .4 8. .6 .4 .2 .7 .6 .3 .4 .7 .3 .8 .1 .5 .5 .3 .2 .5 .5 £ .3 .2 .3 .3 .5 .1 .8 9. .4 .1 .8 .7 .6 10. .8 .2 .2 .4 .4 .6 .3 .4 .1 .3 .1 .7 .8 .7 .1 .2 .4 .3 .9 .4 .5 .4 .5 .2 .1 5 .6 .3 .1 .4 .3 .1 .5 .6 .8 11. 3.6 5.8 7.5 2.5 4.3 .4 .7 .6 .5 .7 .5 .4 .7 .8 .6 12. 6.3 1.4 8.6 3.5 7.2 .6 .4 .2 .3 .9 .8 .2 .2 .6 .4 13. 4.1 7.6 .5 .4 .3 .5 3.8 .5 .5 5.5 .7 .2 14. 8.1 .8 .6 4.7 .7 .5 3.6 6.2 .9 .3 .1 .7 15. 1.5 6.8 5.7 3.3 4.7 6.9 3.8 5.7 16. 6.2 7.9 5.5 7.7 9.5 3.7 7.1 8.3 98 DECIMAL FRACTIONS ADDITION 1. 2. 3. 4. 5. .4+ .3 .2 + .5 .9 + .2 .8 + .2 .4 +.7 .6 +.5 .3 + .4 .7 + .3 .3 + .3 .8 + .8 .5 + .4 .9 + .1 .6 + .4 .7 + .5 .6+ .2 .9 + .8 .7 + .8 .2 +.7 .2 + .2 .9 + .0 .6 + .7 .9 + .7 .1 + .0 .8 + .3 .8 + .4 .9 + .3 .7 +.2 .5 + .5 .5 + .7 .9+ .5 .3 + .5 .8 + .7. .4 +.4 .6 + .8 .4 + .5 .2 +.9 .3 + .9 .6 +.3 .7 + .7 .3 + .6 .3 + .8 .5 + .3 .8 + .9 . .5 + .9 .7 +.9 .2 +.3 .7 + .4 .4 + .8 .2 + .4 .3 + .2 6. 7. 8. 9. 10. .9 + .4 .5 + .6 .5 + .2 .2 + .6 1.4 + .5 ' .4 + .6 .4 +.9 .9 + .6 1.1 + .3 1.0 + .4 .3 + .7 1.0 + .2 1.0 + .3 1.5 + .6 1.3 + .7 .5 + .8 .8 + .6 .7 + .6 1.2 + .7 1.1 + .8 .6 + .6 1,0 + .7 .4+ .2 1.3 + .2 1.2 + .5 .6 + .9 1.2 + .6 1.1 + .7 1.9 + .1 .8 +.2 .8 + .5 1.6 + .2 1.2 + .2 1.8 + .5 1.6 + .9 .9 + .9 1.9 + .4 1.6 + .6 1.4 + .7 1.0 + .5 1.2 + .1 1.0 + .8 1.5 + .3 1.9 + .3 1.9 + .2 1.7 + .2 1.5 + .7 1.8 + .6 1.6 + .5 1.1 + .5 11. 12. ' 13. 14. 15. 1.1 + .9 1.8 + .4 1.3 + .5 1.8 + .8 1.3 + .4 1.6 + .3 1.3 + .3 1.9 + .8 1.4 + .6 1.6 + .7 1.8 + .2 1.3 + .8 1.7 + .8 1.1 + .4 1.0 + .6 1.7 + .6 1.5 + .9 1.2 + .3 1.0 + .9 1.7 + .9 1.2 + .0 1.4 + .2 1.9 + .5 1.7 + .3 1.4 + .3 1.2 + .9 1.7 + .5 1.9 + .9 1.1 + .2 1.6 + .8 1.5 + .8 1.8 + .9 1.6 + .4 1.2 + .8 1.3 + .6 1.8 + .7 1.5 + .5 1.1 + .6 1.7 + .7 1.7 + .4 1.5 + .2 1.2 + .4 1.8 + .3 1.9 + .6 1.9 + .7 1.3 + .9 1.4 + .9 1.4 + . 4 1.5 + .4 1.4 + .8 DECIMAL FRACTIONS ADDITION 99 Add: 1. .05 .06 .04 .07 .02 .05 .04 .04 .05 .03 .05 .03 .08 .03 .06 .04 2. .06 .03 .05 .04 .08 .07 .09 .08 .07 .08 .09 .07 .08 .07 .04 J05 3. .16 .21 .15 .19 .25 .32 .44 .32 .07 .04 .08 .04 .06 .08 .06 .08 4. .38 .06 .35 .05 .61 .08 .28 .05 .33 .08 .57 .04 .68 .05 5.04 .18 .72 .08 5. 1.05 .13 2.17 .06 4.25 .12 3.34 .08 6.08 .15 7.18 .07 2.27 .11 10. 11. 6. 5.14 8.91 6.16 5.28 3.18 5.22 1.19 4.35 .02 .08 .08 .07 .09 .08 .15 .07 7. 1.02 5.24 3.05 4.10 8.11 2.20 5.05 3.25 6.14 1.33 2.20 6.35 1.80 3.17 1.60 2.20 8. 5.04 3.19 2.15 6.18 4.16 1.25 2.14 1.13 1.67 1.21 6.15 2.18 4.16 1.25 7.08 2.09 .75 .24 .55 .37 .87 .15 .45 .58 .68 .89 .66 .25 .34 .98 .79 .37 .02 .25 .13 4.18 6.22 .37 .19 .54 .16 2.51 3.12 .22 .15 5.52 2.11 .05 2.42 .18 .66 .05 .25 .03 .07 1.23 .05 .03 .02 3.11 .12 .42 2.05 5.22 1.20 .54 .25 .05 4.23 1.12 .11 .33 .10 1.02 2.62 .22 .04 .03 .52 .01 100 DECIMAL FRACTIONS SUBTRACTION 1. .9 - .4 2. .07 - .03 3. 1.7 - .5 4. 5.9 - ,6 .8 - .3 .09 - .06 1.8 - .7 3.7 - .3 .7 - .2 .08 - .05 2.4 - .3 2.6 - .5 .6 - .1 .05 - .01 3.6 - .6 4.8 - .3 .9 - .6 .06 - .03 4.8 - .5 3.9 - .5 .8 - .4 .09 - .07 1.9 - .8 2.5 - .4 .7 - .3 .08 - .03 2.7 - .4 3.7 - .2 .5 - .2 .07 - .02 5.B - .6 5.6 - .4 .9 -.5 .09 -.04 1.5 -.5 4.4 - .4 .8 - .2 .08 - .07 3.9 - .4 2.8 - .7 Subtract : 5. 1.7 1.8 2.4 3.6 4.8 1.9 2.7 5.8 .5 .1 .3 .6 .5 .4 .3 .6 6. 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 .7 .5 .2 .3 .8 .9 .6 .4 7. 2.0 5.0 3.0 6.0 9.0 4.0 7.0 8.0 .3 .7 .8 .2 .4 .9 .5 .6 8. 1.5 2.4 3.7 5.4 7.3 2.2 3.3 6.3 .8 .6 .8 _A _A _A __£ JL 9. .9 .8 .6 .5 .7 .4 .3 .8 .05 .02 .08 .04 .06 .07 M .5 .09 .7 .9 .4 .6 .4 .8 .7 .12 .54 .22 .35 .11 .33 .27 .46 10. 11. 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 .22 .36 .53 .61 .47 .28 .89 .74 12. .45 .64 .33 .41 .55 .84 .77 .62 ^ .18 45 .12 .36 .29 .18 .27 13. 1.09 3.25 2.16 1.17 5.22 3.06 4.32 9.11 .35 .16 .52 .48 .15 .25 .25 .04 DECIMAL FRACTIONS ^JJB^rRACTION \ \ 101 Subtract : 1. .4 .8 .9 1.2 1.3 2. 1.9 1.3 .9 .7 1.8 .2 .4 .9 .8 .4 .2 1.0 .6 .4 .9 3. 1.5 1.8 1.4 2.0 .8 4. 1.5 1.9 1.4 1.3 .8 1.3 1.0 .5 .6 .7 .8 .9 1.0 .5 ,3 5. 1.0 1.1 1.8 1.9 .5 6. 1.6 1.1 1.7 1.1 1.6 .2 .7 1.3 L6 .5 .9 1.0 .9 .8 1.3 7. 2.0 1.9 .5 1.2 1.5 8. 2.0 1.0 1.7 2.0 .5 1.5 1.2 .2 .4 _7 .7 .9 1.1 .2 .3 9. 1.7 1.8 1.3 .9 1.7 10. 1.2 1.7 1.6 2.0 1.2 1.2 1.5 .6 .5 _£ .6 1.4 1.0 .4 .9 11. .6 1.0 1.6 1.9 .3 12. .5 1.1 1.7 1.3 .9 .3 .6 1.5 .7 .3 .4 .5 1.0 .7 .3 13. .3 1.1 1.9 1.4 2.0 14. 1.3 1.9 1.6 .6 2.0 .2 .6 .5 1.1 .0 .8 1.4 .8 .2 1.3 15, 1.4 .7 1.9 1.3 1.5 16. 1.7 .8 1.0 .8 .7 .6 .2 .3 1.1 1.4 1.3 & .5 .2 .6 17. 1.3 1.6 1.8 2.0 1.0 18. 1.2 .6 1.5 .9 1.6 1.2 1.1 1.4 1.6 .7 1.1 .5 .9 J5 .7 19. .9 1.5 1.9 2.0 1.1 20. .7 1.4 1.8 1.9 1.2 .2 .6 1.1 1.4 .3 J .8 1.1 1.3 .7 21. .9 1.2 2.0 1.6 .2 22. 1.2 1.4 1.3 2.0 1.5 .4 .5 .5 1.2 .2 .3 .7 .9 1.2 1.2 23. .7 2.0 1.9 1.1 .9 24. .6 1.1 2.0 1.8 2.0 .5 .3 .4 .2* .7 .4 .9 .8 1.6 1.9 25. 1.8 .8 .8 .7 1.4 26. 10. 1.0 1.7 2.0 1.5 1.2 .6 .5 .3 1.3 .8 4 1.6 .9 1.0 102 : ^;(^MAL FRACTIONS SUBTRACTION 1. .14 - .09 2. .75 - .07 3. .61 - .02 4. .16 - .06 .24 - .07 .59 - .06 .20- .09 .50 - .08 .90 - .03 .22 - .05 .99 - .04 .83 - .06 .65 - .06 .67 - .03 .86 - .05 .44 - .04 .82 - .04 .52 - .08 .39 - .09 .60 - .05 5. .29 - .07 6. .24 - .09 7. .58 - .09 8. .34 - .03 .73 - .03 .71 - .04 .40 - .07 .42 - .07 .35 - .06 .96 - .08 .26 - .03 .68 - .02 .89 - .05 .64 - .02 .33 - .02 .23 - .08 .55 - .08 .19 - .05 .12 - .04 .92 - .07 9. .80 - .06 10. .97 - .06 11. .30 - .02 12. .27 - .03 .37 - .05 .45 - .05 .17 - .08 .98 - .06 .69 - .02 .31 - .09 .65 - .04 .36 - .07 .56 - .04 .72 - .05 .57 - .07 .41 - .05 .18 - .07 .66 - .08 .95 - .09 .63 - .04 13. .72 - .02 14. .15 - .02 15. .81 - .03 16. .11 - .07 .13 - .07 .32 - .05 .48 - .08 .38 - .05 .87 - .09 .94 - .08 .70 - .07 .74 - .02 .76 - .04 .78 - .03 .93 - .09 .21 - .06 .88 - .07 .25 - .06 .54 - .03 .43 - .07 17. .84 - .05 18. .49 - .08 19. .47 - .04 20. .20 - .03 .46 - .07 .53 - .04 .33 - .05 .83 - .04 .91 - .08 .77 - .02 .64 - .03 .74 - .06 .79 - .03 .51 - .05 .95 - .06 .36 - .02 .28 - .04 .85 - .03 .56 - .09 .71 - .05 21. .92 - .09 22. .17 - .08 23. .78 - .05 24. .54 - .06 .63 - .02 .96 - .04 .44 - .09 .93 - .09 .40 - .04 .52 - .03 .55 - .03 .18 - .05 .35 - .05 .80 - .06 .39 - .04 .31 - .07 .68 - .07 .15 - .07 .41 - .05 .62 - .08 DECIMAL FRACTIONS MULTIPLICATION 103 1. 2. 3. 4. 5. 2X .2 3X.3 4X .8 5x.2 6X.7 2X.5 3X .8 4X .4 5x.9 6X.3 2X .4 3X.4 4X.2 5x .6 6x .8 2X.9 3X.9 4x .6 5x .8 6X.9 2X.3 3X.5 4x .7 5x .5 6x .2 2X.6 3X .2 4X.5 5x .3 6x .5 2X .8 3X .6 4x .9 5x .7 6x .6 2X.7 3X.7 4X.3 5X.4 6X.4 6. 7. 8. 9. 10. 7x .08 8X .03 9 x .05 10 x .06 12 X .09 7x .02 8X .05 9x .02 10 x .02 12 x .02 7x .03 8X .09 9x .08 10 X .03 12 x .08 7x .06 8X .02 9x .06 10 X .05 12 x .06 7x .09 8X .06 9x .03 11 X .09 12 X .03 7x .04 8X .04 9x .07 11 X .07 12 X .07 7x .07 8x .07 9x .-04 11 X .04 12 x .04 7X.05 8x .08 9x .09 11 X .08 12 x .05 Multiply : 11. .9 .2 .4 .6 .7 3 .4 .9 .2 .8 .2 .6 .9 .5 .3 6 .7 .6 .3 .2 12. .5 .7 .4 .6 .7 .6 .4 .3 .5 .7 .5 .9 .4 & .5 .6 .5 .7 .8 .7 13. .05 .12 .04 .06 .11 .15 .03 .09 .01 .14 .5 .5 .4 .3 .7 .6 .9 _JS .9 .2 14. 1.2 1.1 8.4 7.5 2.1 1.5 7.0 4.2 1.3 1.8 • _7 .9 .2 .4 _£ .6 .5 .3 .7 .2 15. .06 .12 .15 .22 .07 .25 .11 .33 .16 .01 .04 .08 .05 .02 M .03 .12 .03 .05 .01 104 DECIMAL FRACTIONS MULTIPLICATION 1. 6X.7 2. 2X.3 3. 2X.2 4. 9X .3 3X.5 3X .9 4x .9 6X.4 11 X .7 11 X. 3 7x .7 7x .8 5X.9 4X.2 8X .5 9X.7 2X.4 5X.7 7X.3 10 X .8 5. 3x .2 6. 11 X .8 7. 8X.6 8. 8X .4 8X.8 6x .6 7X.9 12 X .3 4X.6 5x .4 12 X. 5 10 X. 2 6X.7 12 X .2 8X.7 12 x .4 10 x. 5 2X.9 11 X. 9 9X.5 9. 9X.4 10. 5X.6 il- 2x.6 12. 9x .6 11 X .5 3X.7 4x .8 3X .8 10 X. 3 6X.3 10 x .7 4x .5 6x .2 11 X. 2 8X.3 6x .8 9X.8 7x .4 5X.2 12 X. 7 13. 11 X .6 14. 10 X .9 ls. 6x.9 16. 4X.3 3X.4 7X.6 2x .8 4x7 8X.2 5X.3 5X.5 10 X. 4 9X.9 2X.7 10 X .6 7X .5 6X.5 12 X .6 9x.7 3X.6 17. 7X.2 18. 11 X .4 19. 7x 1.0 20. 8x 1.0 4X.4 3X.3 3x 1.1 2x 1.2 7x.8 9x .2 5x 1.2 7x1.1 2X.5 5X.8 3x 1.0 4x 1.0 8X.9 2x 1.0 2x1.1 3X 1.2 21. 4x1.1 22. 5x 1.1 23. 6X 1.0 24. 7x 1.2 9X 1.0 6x 1.2 8X 1.1 10 X 1.1 6x 1.1 11 X 1.0 12 X 1.2 12 X 1.1 4x 1.2 9x 1.1 11 X 1.0 8x 1.2 5x 1.0 12 X 1.0 9x 1.2 10 X 1.2 7x1.1 11 X 1.2 10 X 1.0 11 X 1.1 DECIMAL FRACTIONS MULTIPLICATION 105 Multiply : 1. .09 04 05 .03 02 08 .12 .11 2 9 11 10 6 9 4 3 2. .06 .07 .12 .03 .02 04 .09 .02 5 3 8 6 11 7 6 __3 3. .11 .08 .05 .06 .07 .03 .08 .11 8 2 5 10 9 2 12 _6 4. .04 .06 .07 .12 .02 .04 .06 .08 4 8 5 6 12 5 6 11 5. .12 .03 .05 .07 .09 .11 .12 .02 11 7 8 7 4 2 12 _7 6. .11 .03 .04 .09 .05 .08 .06 .07 9 3 11 8 2 7 12 2 7. .12 .07 .11 .03 .06 .09 .04 .07 2 6 4 5 7 5 2 11 8. .12 .09 .11 .02 .03 .07 .08 .06 3 10 5 5 _8 10 4 2 9. .04 .05 .09 .02 .03 .11 .04 .12 12 9 12 10 12 7 8 5 10. .05 .07 .06 .08 .12 .02 .11 .03 10 6 4 8 7 9 11 9 11. .09 .08 .04 .05 .02 .09 .03 .05 7 10 6 3 4 3 11 7 12. .08 .06 .04 .07 .11 .12 .03 .05 5 3 10 4 10 9 4 6 13. .11 .09 .02 .04 .06 .07 .08 .12 12 9 8 3 11 12 6 10 106 DECIMAL FRACTIONS DIVISION 1. .6* .3 1.2 + .6 2.0 4- .5 1.5 - .3 2.4 + .6 3.2 -r- .4 2.1 - .7 2.5 - .5 3.3 - .3 3.0 + .5 2. 1.2- .2 1.6 4- .4 1.8 - .9 2.1 - .3 1.6 4- .8 2.7 - .9 3.5 + .7 1.0 - .2 1.8 ^ .6 3.0 - .3 .9 1.4 3. * .2 .3 .2 1.0 - .5 2.0- 1.5 2.7 -^ .3 2.8 - .7 3.0 3.6 .6 .3 1.8 - .2 2.4 - .4 1.2 2.2 - .2 2.8 -v- .4 3.5 2.0 2.4- 3.6 2.4 .5 .2 .8 .9 .3 5. .8- .4 3.2 1.4 - .7 1.6 2.4 3.6 .2 1.2 3.0- 1.0 2.2 - 1.1 1.2 2.0 - 1.0 3.3 -r- 1.1 Divide : 6. 8)4.0 7. 12)4.8 8. 5)4.0 9. .6)36 10. .4)80 11. 1.1)55 7)5.6 11)7.7 9)4.5 .5)45 .6)60 1.2)108 5)6.0 10)7.0 2)6.6 .6)66 .8)96 1.5)30 8)4.8 21)4.2 8)8.0 .8)56 .4)100 2.5)100 5)7.5 25)5.0 6)7.2 .7)70 .2)40 1.5)75 7)4.2 12)6.0 5)5.5 .6)48 .3)66 1.6)32 9)5.4 25)7.5 7)4.9 .4)44 .2)32 2.1)42 7)8.4 40)8.0 4)4.0 .6)42 3)45 3.3)99 12. .7 ^-. 5 .9 -.2 .5 4- .4 .8 4- .3 .6 4- .5 13. 2.3- 3.2- 1.9- 4.5- 2.5 -=- .8 .4 .5 .6 .7 14. 2.8 - .9 3.7 4.8 5.5 + .6 1.4 .3 15. 3.5- 1.1 4.9 4- 1.2 5.2 - 2.5 3.4 - 1.5 2.5 4- 1.2 16. 4.5 - 2.2 6.8 - 1.1 3.8 - 1.2 1.7 - 1.4 6.3 -f- 1.5 DECIMAL FRACTIONS DIVISION 107 1. $.08 .18-5- .02 .12 -h .02 .06 * .03 .08 .16 .32 $.04 .02 .09 -f- .03 .12- .06 .04 24- .04 .08 ;.12 .18 .14 .15 .21 .24 .22 .27 .35 .18 $.03 .09 .02 .03 .03 .06 .02 .09 .07 .06 3 .14 - .25- .32- .21 - .33 - .15- .27- .28- .36- .35- $.07 .05 .04 .07 .03 .05 .03 .07 .03 *■ .05 .36 .16 .24 .22 .16 .18 .12 .24 .28 .36 $.09 .02 .12 .11 .08 .02 .04 .08 .04 .06 Divide : 5. 6. 7. 8. 9. 10. 7).42 .04)36. .7).84 .oi)a 1.2)1.44 .13)3.9 82,56 .08)72. .6)^66 .032,9 2.5)1.50 .04)4.4 7) .63 .03)21. .9).81 .02)^8 1.2) .96 .09)7^2 5).60 .09)54. .7^28 .03)^6 1.1)1.32 .15)7.5 1) .56 .06)48. .9) .27 .05^5 1.5).75 .03)8.1 9)^99 .12)72. .7).35 .01^3 1.2).84 .12)9.6 6).54 .07)49. .8). 64 .04^8 1.1)1.10 .07)7.0 8) .24 .04)32. .9). 63 m)A 1.7)1.70 .02)2.6 11. ,.25)$6.00 12. .07)$5.11 .18 ) 3.60 .12 ) 1.80 .07 ) 1.54 .09 ) 2.79 .35 ) 7.00 .08 ) 6.02 .02) 1.50 .11) 3.52 13. i.09)$189. .08 ) 256. .11 ) 451. .05) 100. 14. 6)$8.40 .07) 140. 4) 7.20 3 ) 1.26 5 ) 2.00 9) 6.03 15. S.04 )$18.4 .02 ) 66.6 .08 ) 17.6 .07 ) 23.1 .12) 37.2 .08 DECIMAL FRACTIONS DIVISION l 2 • 3. 4. 1.6- •- A 6.6- - .6 6.0- - .6 2.2- - .2 4.8- - .6 9.6- '- .8 8.8- =- 1.1 1.8- - .3 3.5- - .7 6.3- - .7 .6- - .2 9.6- - 1.2 1.2- - .2 2.5- - .5 5.4- - .9 2.1 - - .7 .6- - .3 1.6- - .8 2.8- - .4 3.0- - .6 5 6. 7. 8. 3.3- - 1.1 3.6- - .4 3.6- - .6 3.6- - .9 4.8- - 1.2 5.0- -1.0 8.8- - .8 2.2 - - 1.1 2.1 - - .3 1.8- - .9 2.0- - 1.0 1.4- - .2 3.0- - .3 2.4- - .2 4.0- - .5 .9- - .3 5.5- - .5 2.0- - .4 4.9- - .7 4.0- - 1.0 9 1C l. 11. 12 $.24- - $.03 $.45- - fo.05 $.60- -$.12 $.84- -$.12 .70- - .07 .20- - .02 .50- - .05 .18- - .02 .32- - .08 .30- - .10 .42- - .07 .80- - .10 .12- - .06 .36- - .03 .24- - .06 .27- - .03 .48- - .04 .32- - .04 .64- - .08 .63- - .09 13 14 15. 16 $.80- - $.08 $.33 - -$.03 $.40- - $.04 $.16- - $.02 .24- - .04 .90- - .10 .28- - .07 .12- - .04 .15- - .05 .40- - .08 .12- - .03 .66- - .06 .08- - .02 .18- - .06 .30- - .05 .84- - .07 .27- - .09 .35- - .05 .81 - - .09 .48- - .08 11 ? U I. 19. 2C >. ; .20- - $.05 $ .24- - $.08 $ .54- - $.06 $ .56- - $.07 .99- - .09 .60- - .05 .63- - .07 .42- - .07 .56- - .08 .72- - .12 1.10- - .11 1.32- - .12 1.08- - .12 1.20- - .12 1.20- - .12 .77- - .11 1.21 - h .11 1.44- i- .12 .72- - .12 1.00- - .10 DENOMINATE NUMBERS 109 What name is given to 1. J of a yard? 2. 12 times a unit? | of a quart? 100 times a cent? J of a pint ? 24 times an hour ? iV of a dollar ? 20 times a unit ? 4- of a week ? 36 times an inch ? i of a bushel ? 60 times a minute ? •^ of a year ? 9 times a square foot ? ^ of a pound ? 2000 times a pound ? | of a peck? 100 times a year? \ of a gallon? 320 times a rod? T X 2- of a foot ? 32 times a quart ? 8 times a pint? Give answers to the following questions in their lowest terms : 3. 4 quarts is what fractional part of a bushel? 8 units is what fractional part of a dozen? 10 months is what fractional part of a year ? 12 ounces is what fractional part of a pound? 24 minutes is what fractional part of an hour? 4. 4| inches is what fractional part of a yard? 200 pounds is what fractional part of a ton? 3 days is what fractional part of a week? 2 pints is what fractional part of a gallon? 16 hours is what fractional part of a day? Express 5. 2 quarts and 1 pint as the fraction of a gallon. 2 feet and 9 inches as the fraction of a yard. 1 peck and 4 quarts as the fraction of a bushel. 6. 3 gallons, 3 quarts, and 1 pint as gallons. 10 bushels, 3 pecks, and 4 quarts as bushels. 5 yards, 2 feet, and 9 inches as yards. 110 DENOMINATE NUMBERS 3 hr. is how many min. ? 2 lb. is how many oz.? 4 gal. is how many qt. ? 4 ft. is how many in. ? 3 wk. is how many da.? 5 yr. is how many mo. ? 4 bu. is how many pk. ? 10 min. is how many sec? 2. 6 sq. yd. is how many sq. ft.? 8 pk. is how many qt. ? 12 yd. is how many ft. ? 9 dol. is how many qr. ? 5 doz. is how many units? 2 rd. is how many ft. ? 16 qt. is how many pt.? 2 da. is how many hr.? Express 3£ bushels as pecks. 4^ feet as inches. 2.5 days as hours. 2\ (short) tons as pounds. 1^ feet as inches. 5J dozen as units. . 1.5 bushels as pecks. \ yard as inches. Express f of a yard as inches. \\ yards as inches. 4 rods as feet. 1\ years as months. , \\ dollars as cents. 8£ pecks as quarts. 2\ quires as sheets. 3$ sq. yards as sq. feet. 5. How many hr. in 5 da. ? How many sec. in 1 hr. ? How many pt. in 4 gal. ? How many gal. in 60 pt. ? How many qt. in If bu. ? How many bu. in 176 qt. ? How many yr. in 180 mo. ? How many hr. in If da.? 6. How many sq. rd. in f A. ? How many rd. in 2 mi.? How many in. in 2\ yd. ? How many ft. in \ mi. ? How many gi. in 2 gal. ? How many pt. in 2\ pk. ? How many oz. in 5£ lb.? How many rt. angles in 270° DENOMINATE NUMBERS 111 1. How many qt. in 16 pt.? How many wk. in 84 da. ? How many lb. in 48 oz. ? How many gal. in 40 qt. ? How many yd. in 72 in. ? How many da. in 48 hr. ? How many doz. in 96 units? How many yd. in 36 ft. ? si. How many hr. in 600 min. ? How many bu. in 24 pk. ? How many pk. in 56 qt.? How many min. in 120 sec? How many ft. in 84 in. ? How many rd. in 11 yd.? How many sq. yd. in 27 sq. ft. ? How many yr. in 120 mo. ? 3. 75 qt. is how many gal. ? 30 in. is how many ft. ? 15 pt. is how many qt. ? 66 mo. is how many yr. ? 20 oz. is how many lb. ? 25 ft. is how many yd. ? 30 units is how many doz.? 100 min. is how many hr. ? 4. 22 pk. is how many bu.? 20 qt. is how many pk. ? 15 da. is how many wk.? 72 sq. in. is how many sq. ft.? 60 sheets is how many quires? 5280 ft. is how many miles ? 5000 1b. is how many T.? 45 in. is how many yd. ? Express 4 rods as yards. £ mile as rods. 1^ rt. angles as degrees. 36 sq. inches as sq. feet. 2 cu. yards as cu. feet. 2 cords as cubic feet. \ cord as cubic feet. 1 ream as sheets. 6. Express 20 tons as pounds. \\ square feet as square inches. 100 quarts as bushels. \ bushel as pints. 75 units as dozens. 88 days as weeks. 2318 cents as dollars. 345 minutes as hours. 112 DENOMINATE NUMBERS 1. Express 1 ft. 4 in. as inches. 2 yd. 1 ft. as feet. 3 gal. 2 qt. as quarts. 1 lb. 6 oz. as ounces. 4 pt. 2 gi. as gills. 3 score and 10 yr. as years. 3 bu. 3 pk. as pecks. 4 pk. 7 qt/as quarts. 2. Express 31 qt. as gallons. 40 oz. as pounds. 17 ft. as yards. 50 in. as feet. 63 da. as weeks. 30 hr. as days. 75 mo. as years. 100 units as dozens. 3. Express 4 T. 8 cwt. as cwt. 3 da. 6 hr. as hours. 5 yr. 8 mo. as months. 5 hr. 30 min. as minutes. 2 mi. 18 rd. as rods. 10 min. 10 sec. as seconds. 8 lb. 2 oz. as ounces. 12 bu. 3 pk. as pecks. Express 4500 lb. as tons. 250 min. as hours. 117 qt. as gallons. 200 sq. rd. as acres. 150 in. as feet, f A. as sq. rods, f da. as hours, f lb. as ounces. Express 13 gal. 1 qt. 1 pt. as quarts. 2 T. 5 cwt. 5 lb. as pounds. 2 rd. 2 yd. 2 ft. as feet. 2 rd. 12 ft. 6 in. as feet. 1 bu. 3 pk. 4 qt. as quarts. 3 da. 8 hr. 10 min. as hours. 15° _ 45' _ 30" as minutes. RECKONING TIME 113 Pupils in elementary grades should go through these exercises first with the aid of the clock face, clearly visualizing each thought process. How long a time is it 1. From 9 a.m. to 7 p.m.? 2. From 7.30 p.m. to 6.30 a.m. ? From 8 a.m. to 5.30 p.m.? From 11.30 p.m. to 9 a.m.? From 7 a.m. to 6 p.m.? From 7.45 p.m. to 6 a.m.? From 8.30 a.m. to 4 p.m.? From 10 p.m. to 7.30 a.m.? From 10.30 a.m. to 8 p.m. ? From 9.30 p.m. to 7 a.m. ? At what time must you start in order to reach your destination at 7.45 a.m. if the walk requires 3. 20 minutes? 4. 5 minutes? 5. 10 minutes? Half an hour ? 25 minutes ? 35 minutes ? 15 minutes? 8 minutes? 3 minutes? 6. If your watch is 8 minutes fast, what time is it when your watch says 4.15? 12.30? 3.45? 6.18? Noon? 8.04? How many minutes of each school day should be given to a daily subject which is scheduled to have 7. 2| hours per week? 8. 4 hours per week? If hours per week? 1J hours per week? 6 hours per week? 3 J hours per week? Find the time that a train may be expected to arrive, if 9. 10. Due at 11.20 ; 40 minutes late. Due at 9.10 ; 1 hr. 20 min. late. Due at 6.45 ; 35 minutes late. Due at 4.35 ; 45 minutes late. Due at 10.12 ; 18 minutes late. Due at 8.54 ; 10 minutes late. Due at 3.22 ; 50 minutes late. Due at 7.37 ; 25 minutes late. Due at 5.48 ; 30 minutes late. Due at 1.15 ; 55 minutes late. 114 PERCENTAGE What per cent of a number is 1. 2. 1 J of it? $ of it? iof it? iof it? £ of it? ^of it? iof it? \ of it? r Of it? of it? 3. A of it? A of it? ^ of it? A of it? U of it? 4. A of it? A of it? A of it? A of it? What per cent of a number is 5. 6. 7. 8. | of it? f of it? A of it? A of it? f of it? f of it? A of it? A of it? f of it? | of it? T 3 ¥ of it? A of it? f of it? | of it? A of it? A of it? | of it? | of it? Profit? A of it? f of it? A of it? A of it? A of it? f of it? A of it? A of it? A of it? What per cent of a number is 9. Once the number? Twice the number? 4 times the number? H times the number? 5 times the number? 10. 2\ times the number? 8 times the number? \\ times the number ? 3 times the number? \\ times the number? What per cent 11. Of 50 is 150? Of 40 is 60? Of Yl\ is 50? Of 16 is 32? 12. Of 80 is 400? Of 75 is 100? Of 60 is 80? PERCENTAGE 115 What part of a number is 1. 2. 3. 50% of it ? 33|% of it ? 20% of it ? 25% of it ? 16f % of it ? 10% of it ? 12|% of it ? 8i% of it ? 5% of it ? 6i%ofit? 4% of it? 2i%ofit? 14f % of it ? 2% of it ? 3£% of it ? 3% of it ? 1% of it ? 100% of it ? What part of anything is 4. 5. 6. 75% of it ? 37^% of it ? 70% of it ? 66f% of it ? 87|% of it ? 15% of it ? 40% of it ? 30% of it ? 80% of it ? 60% of it ? 83^% of it ? 24% of it ? 80% of it ? 90% of it ? 18f % of it ? 28f % of it ? 62i% of it ? 45% of it ? What part of a number is 7. 8. 9. i% of it ? % % of it ? i% of it ? f%ofit? i%ofit? i%ofit? |%ofit? |%ofit? i%ofit? How many times a number is 10. 11. 12. 400% of it ? 125% of it ? 300% of it ? 200% of it ? 300% of it ? 275% of it ? 150% of it ? 450% of it? 100% of it? 116 PERCENTAGE The number sought is 100%. What is the number of which 1. 2. 3. 15 is 10%? 72 is 50%? 20 is 1%? 25 is 12|%? 10 is 16f%? 10 is 4% ? 16 is 20%? 11 is 25%? 18 is 50%? 12is8i%? 4is2i%? 9 is 33i%? 6is4%? 7is2%? 12 is 5% ? 3is6i%? 6 is 1%? 7isl2|%? 4 is 5%? 45 is 100%? 60 is 10%? 16 is 33!%? 15 is 20%? 5 is 2*%? Find the number of which 4. 5. 6. 24 is 37^%. 35 is 62i%. 63 is 874%. 60 is 75%. 72 is 90%. 18 is 45%. 9 is 30%. 16 is 80%. 6 is 15%. 50 is 66|%. 12is37i%. 40 is 8%. 45 is 83|-%. 4 is 40%. 54 is 6%. 90 is 60%. 33 is 75%. 48 is 1%. 49 is 87i%. 20 is 66|%. 7 is 3i%. 100 is 40%. 42 is 70%. 25 is 62i%. To find : The sum of which 7. 8. 9. $50 is 125%. $26 is 200%. $120 is 133^%. $75 is 150%. $42 is 105%. $100 is 166f %. $15 is 300%. $18 is 120%. $260 is 130%. $90 is 112i%. $36 is 300%. $150 is 125%. $84 is 175%. $50 is 250%. $240 is 160%. PERCENTAGE 117 What is 1. 25% of $50? 10% of $40? 12|%of$64? 33^% of $18? 6i%of $48? 16|%of $36? 5% of $20? 4% of $60? 50% of 32? 20% of 45? 8£%of 24? 11*% of 63? 5% of 80? 25% of 28? 14f%of 56? 33^% of 39? 3 l%of 3% of 6% of 8% of 4% of 5% of 7% of 9% of 200? 400? 500? 300? 100? 1000? 2000? 3000? nd 4. 5. 6. 75% of 200. 1% of $12. \\% of $400. 66f % of 450. 1% of $ 1.50 4^% of $200. 37i% of 160. . 1% of $ 3.00 2\% of $800. 40% of 250. 1% of $ 6.20 3^% of $600. 62i% of 320. 1% of $30. 5i% of $100. 87^% of 240. 1% of $25.50 Si% of $2000. 80% of 400. 1% of $ 7.90 6i% of $1000. 83^% of 300. l%of $ 1.25 \\% of $4000. What is 7. \% of $1600? i%of$400? i% of $1000? i%of $600? Tell how to express decimally 10. 11. ^ per cent. £ per cent. \ per cent. \ per cent. 8. i% of $2000? 1% of $1200? f% of $1500? f%of $800? 12. f per cent. § per cent. 9. |% of $2400? A% of $2000? %% of $2500? 13. f per cent, f per cent. 118 PERCENTAGE Increase the number 1. 12 by 50%. 15 by 20%. 20 by 10%. 8 by 25%. 6 by 33*%. 16 by 12*%. 18 by 16*%. 24 by 8*%. 40 by 20%. 36 by 33*%. 20 by 25%. 100 by 1%. 50 by 50%. 25 by 4%. 60 by 5%. 32 by 6*%. 35 by 80 by 45 by 28 by 70 by 27 by 30 by 64 by 14*%. 5%. 20%. 25%. 10%. 33*%. 16|%. 12*%. Decrease the numoer 4. 5. 6. 10 by 20%. 15 by 33*%. 9 by 66f %. 20 by 5%. 25 by 4%. 12 by 75%. 30 by 16f %. 36 by 25%. 16 by 12*%. 40 by 12*%. 48 by 6*%. 14 by 14f %. 50 by 50%. 56 by 12*%. 24 by 16|%. 60 by 8*%. 72 by 50%. 18 by 33*%. 70 by 14f %. 84 by 8*%. 28 by 25%. 80 by 6*%. 96 by 16|%. 32 by 6*%. Increase 7. i. $64 by 25 per cent. $48 by 16f per cent. $75 by 12 per cent. $36 by 66f per cent. $50 by 6 per cent. Decrease 8. $100 by 15 per cent. $120 by 50 per cent. $250 by 40 per cent. $320 by 37| per cent. $500 by 4 per cent. PERCENTAGE 119 What per cent is 1. 2. 3. 2 of 4? lof 5? $ 3 of $4? 5 of 10? 2 of 10? $ 8 of $12? 3 of 12? 8 of 4? $ 9 of $12? 2 of 6? 2 of 16? $ 5 of $25? lof 4? 3 of 21? $ 2 of $3? 9 of 3? 2 of 20? $10 of $4? 15 of 5? 30 of 10? $ 3 of $8? lof 2? 10 of 20? $15 of $10? What per cent is 4. 5. 6. 25 of 50? 33|-of 66f? 25 of62±? 12iof 25? 8Jof 50? 50 of 75? 6iof 12i? 12^ of 37^? 12| of 87i? 37iof 75? 16f of 33±? 6iof 50? 6£of 25? 25 of 75? 25 of87i? 12^ of 50? 50 of62|? 16| of 66f ? 37£of 50? 12$ of 62* ? 8Jof 25? 8j'of 33|? 8|of 16f? 3£ofl0? Compare 7. i of 5000 people with \% of them, f of a $1000 bond with f% of it. \ of a ton of coal with \% of it. f of your weight with f % of it. f of our national debt with f % of it. What ratio does the first answer bear to the second, in each case ? 120 PERCENTAGE AND DENOMINATE NUMBERS 1. A pint is what per cent of a quart? A foot is what per cent of a yard ? A nickel is what per cent of a quarter? A nickel is what per cent of a dime? A gill is what per cent of a pint? A quart is what per cent of a gallon? A cent is what per cent of a dime? A cent is what per cent of a nickel? A peck is what per cent of a bushel? A week is what per cent of a fortnight ? 2. What per cent of a gallon is a pint ? What per cent of a peck is a quart ? What per cent of a foot is an inch? What per cent of a pound is an ounce? What per cent of a week is a day? What per cent of a year is a month? What per cent of a quart is a gill? What per cent of a peck is a pint ? What per cent of a cord is a cord foot ? What per cent of a decade is a year? To the Pupil: Consult your dictionary or arithmetic if you need help. 3. A dozen is what per cent of a gross ? A foot is what per cent of a fathom? A quarter is what per cent of a year? A hundred weight is what per cent of a ton? A quire is what per cent of a ream? A cubic foot is what per cent of a cord foot ? PERCENTAGE AND DENOMINATE NUMBERS 121 1. What per cent of a gallon is lqt.? 2qt.? 3qt.? 4qt.? 1 pt.? 3 pt.? 5pt.? 2. What per cent of a pound is 8oz.? 4oz.? 12 oz.? loz.? 2oz.? 6 oz.? 16 oz.? 3. What per cent of a peck is 8qt.? 4qt.? 2qt.? 6q.? lqt.? 7 qt.? 1 pt.? 4. ' What per cent of a ton is 500 1b.? 200 1b.? 1000 1b.? 15001b.? 201b.? 1001b.? 5. What per cent of a day is 16 hr.? 12 hr.? 8hr.? 6hr.? 18 hr.? 3hr.? 9hr.? 6. What per cent of an hour is 15min.? 12min.? 6min.? 40min.? 45 min.? 20min.? 7. What per cent of a mile is 160 rd.? 40 rd.? 80 rd.? 240 rd.? 32 rd.? 120 rd.? 8. What per cent of a dozen is 10 units? 9 units? 8 units? 4 units? 3 units? 2 units? 9. What per cent of a right angle is 90°? 45°? 30°? 60°? 18°? 15°? 75°? 27°? 10. What per cent of a bushel is 16 qt.? 8qt.? 24 qt.? 1 pk.? 3pk.? 4pk.? § pk.? 11. What per cent of a month (30 days) is 10 da.? 6 da.? 15 da.? 20 da.? 3 da.? 5 da.? 24 da.? 122 PERCENTAGE AND DENOMINATE NUMBERS 1. 25% of a peck 50% of a year 50% of a day 25% of a quart 25% of a yard 75% of a yard 50% of a pound 75% of a foot i how many how many how many how many = how many how many how many » how many quarts ? months ? hours ? pints ? inches ? inches ? ounces ? inches ? 25% of an acre 50% of a circumference 75% of a mile 50% of a leap-year 25% of a ton 25% of a square foot 75% of an hour 75% of a dozen how many square rods? how many degrees? how many rods? ' how many days? how many pounds? how many square inches? how many minutes ? « how many things ? 3. 50% of a bushel 50% of a mile 25% of a cord 75% of an acre 50% of a rt. angle 75% of a gallon 25% of a square mile 75% of a ream = how many pints? = how many feet ? = how many cubic feet ? = how many square rods? = how many degrees? = how many gills? = how many acres ? = how many sheets of paper? PERCENTAGE AND DENOMINATE NUMBERS 123 1. 33 J % of a yard = how many inches? 10% of a minute = how many seconds? 20% of a quarter = how many cents ? 12 J% of a pound = how many ounces? 33 J % of a dozen = how many units? 12|% of a day = how many hours? 16 f% of a quire = how many sheets? 20% of a score = how many units ? 2. 66f % of a foot = how many inches? 37 J % of a peck = how many quarts? 60% of a dime = how many cents? 62|% of a pound = how many ounces? 84% of a dozen = how many units? 40% of an hour = how many minutes? 87|% of a day = how many hours? 6|% of a pound = how many ounces? How many inches in How many square inches in 3. 50% of a yard? 4. 50% of a square foot ? 25% of a yard ? 25% of a square foot ? 75% of a yard? 75% of a square foot? 33J% of a yard ? 33 \% of a square foot ? 66f % of a yard ? 66f % of a square foot ? 8f% of a yard ? 16f % of a square foot ? 12|% of a yard ? 8J% of a square foot ? 37J% of a yard? 12J% of a square foot? 62|% of a yard? 37-J% of a square foot? 16f % of a yard? 62|% of a square foot? 124 SPEED TESTS IN PERCENTAGE 1. 28 2. 100 3. 18 4. 150 5. 80 6. 30 7. 100 10 40 9 39 24 72 25 2 8 33 24 40 6 40 36 48 6 36 64 42 5 18 32 21 60 16 18 35 6 24 15 45 32 36 50 50 4 90 12 48 60 10 12 20 30 3 72 48 150 22 44 75 48 8 12 75 30 16 27 66 56 54 60 Name as rapidly as you can 1. 50% of each number in columns 1 and 2. 2. 25% of each number in column 2. 3. 75% of each number in column 2. 4. 33 J % of each number in columns 3 and 4. 5. 66f % of each number in column 3. 6. 66f % of each number in column 4. 7. 12J% of each number in column 5. 8. 37^% of each number in column 5. 9. 62|% of each number in column 5. 10. 87| % of each number in column 5. 11. 16f % of each number in column 6. 12. 83 J % of each number in column 6. 13. 20% of each number in column 7. 14. 40% of each number in column 7. 15. 60% of each number in column 7. 16. 80% of each number in column 7. 17. What common fractions are the same as these per cents? 10% 25% 12*% 8|% 33J% 75% 66f% 60% 16f% 61% 40% 37|% 50% 87*% 20% 83*% 30% 5% 80% 4% 70% 100% 14f% 90% AREAS AND PERIMETERS Find area and perimeter of 1. A 5-inch square. A 10-inch square. A 6-inch square. A 9-inch square. A 4-inch square. A 3-foot square. A 7-foot square. A 12-foot square. An 8-foot square. An 11-foot square. 3. What is the perimeter of A rectangle 6" X 4§"? A rectangle 2}" X 4"? A rectangle 8" X 1$"? A rectangle 9" x 2|"? A rectangle 10" X 5|"? An oblong 1' X i'? An oblong 12' x 15'? An oblong 15' x 20'? An oblong 20' x 5'? An oblong 30' x 2'? A rectangle A rectangle A rectangle A rectangle A rectangle A rectangle A rectangle A rectangle A rectangle A rectangle 125 5" by 2". 3" by 7". 4" by 10". 12" by 1". 8" by 2". T by 5'. 2' by 11'. 10' by 6'. 9' by 5'. 4' by 3'. A 5|" Al|" 4. What is the area of A 2J" square? A Z\" square? square ? square ? A 4^" square? A 20' square? A 30' square? A 2 ¥ square? A 10' square? A If square? 5. Find perimeter and area of A pasture 40 rods square. A garden 30 x 50 feet. A building lot 50 x 100 feet. A playground 100 X 200 feet. A park 25 x 30 rods. APPENDIX The few pages which follow are outside the plan of this book, but are inserted for the convenience of teachers who may have need of such material as they contain. These pages are nine in number : 1. Reading Exercise, Whole Numbers. 2. Reading Exercise, Whole Numbers. 3. Reading Exercise, U. S. Money. 4. Reading Exercise, Roman Numerals. 5. Months and Dates. 6. Ratio, and its Application to Simple Problems. 7. Questions for Leisure Moments. 8. Questions for Leisure Moments. 9. Questions for Leisure Moments. 126 READING OF WHOLE NUMBERS 1. 2,303 2. 5,012 3. 48,484 4. 31,527 9,091 2,270 30,103 90,318 8,808 8,008 67,380 66,123 6,590 5,060 23,489 40,831 7,227 9,876 41,707 28,506 2,772 2,100 20,120 75,009 5,099 4,404 11,006 40,040 3,303 5,055 84,090 10,001 8,017 6,600 10,005 56,950 5,110 1,011 70,020 88,020 207,840 6. 408,123 7. 4,000,000 8. 5,100,004 911,255 73,240 1,720,216 236,600 442,233 81,006 9,008,400 82,503 630,040 428,820 3,000,075 261,599 605,066 60,075 2,633,684 8,084,302 129,129 900,009 5,066,114 62,001 703,004 71,032 8,000,600 777,666 150,015 3,890 4,020,096 5,200,048 400,440 154,400 3,344,000 137,425 860,068 76,000 1,200,005 50,606 9. 23,640,125 10. 148,000,265 11. 13,605,400 8,347,720 804,012,000 724,100,098 91,100,042 160,006,060 5,000,225 58,000,004 432,593,687 417,069,008 3,374,810 220,000,220 24,403,100 28,136,000 864,102,300 6,000,550 1,012,012 521,000,336 920,109,111 6,700,000 101,612,000 5,005,500 25,025,009 254,369,845 612,018,000 10,100,100 912,814,711 115,230,003 127 128 READING OF WHOLE NUMBERS 1. 1,001 2. 25,000 3. 105,675 4. 75,204 7,240 10,204 920,043 3,319 9. 4,086 91,900 212,114 600,420 6,955 80,075 303,206 80,307 2,040 30,006 110,770 2,925 5,007 22,401 678,678 405,060 1,313 67,809 602,206 77,440 7,700 56,078 547,000 3,802 3,016 30,456 100,101 745,010 2,212 70,700 980,755 604,288 82,008 6, , 302,050 7. 2,750,933 8. 1,425,869 50,403 510,115 3,861,002 604,133 27,011 708,000 5,409,080 28,002 19,222 601,211 1,000,040 901,090 77,001 991,903 7,032,006 7,706,055 40,020 400,040 6,448,000 4,011 25,025 127,721 1,020,703 723,000 50,250 200,405 4,307,618 5,000,030 16,161 696,807 9,000,750 8,902,007 80,505 110,111 6,300,003 2,601 35,127,950 10. 734,100,200 11. 3,041,296 4,000,306 58,000,030 733,155 209,140,000 163,302,445 49,037,082 18,018,200 8,346,921 200,000,360 6,334,002 542,806,009 71,340,809 20,000,020 70,000,236 4,502,075 730,035,700 5,024,000 316,402 2,200,200 621,006 44,389,600 95,900,554 940,032,065 908,760,543 105,002,007 7,320,439 27,140 840,036 24,706 6,645,613 9,237,540 2,150,430 54,903,027 READING EXERCISE U. S. MONEY 129 1. $ 8.36 2. $ 50.00 3. $751.14 4. $863.20 51.25 250.00 45.50 20.25 270.04 6.39 332.28 71.00 7.20 40.88 88.40 301.12 80.08 931.27 190.87 5.74 44.21 804.05 345.68 36.95 670.03 22.02 91.12 310.00 , 9.27 150.16 171.80 65.05 60.20 570.04 6.55 414.80 488.34 39.00 18.42 50.50 5. ; 90.99 6. $ 426.80 7. $ 1,212.13 8. $51,502.36 213.67 5,019.05 45,008.50 7,243.68 55.04 100.84 171.12 44,000.00 580.92 2,971.70 8,063.09 2,063.24 6,008.00 4,222.04 75,012.00 751.25 12.50 68.25 2,184.75 2,002.40 345.07 6,120.00 7,007.10 40,321.21 924.36 466.00 640.02 6,780.09 7,000.20 7,280.15 50.09 818.58 66.06 3,000.95 833.27 11,010.04 9. $5,208,136.00 10. $ 543,287.10 11. $ 302,108.73 42,020.12 2,040,069.52 99,053.06 180,181.06 8,221.04 410,111.00 76,000.40 95,095.16 7,005.02 2,302,190.75 83,301.20 6,170,000.54 8,009, 10 260 953.88 33,598.11 78,403.00 5,000,275.00 4,080.08 590,000.95 705,003.05 7,600,540.20 3,000,625.70 1,009,008.60 50,050.50 1,100,000.00 42,000.10 2,800.00 55,209.38 317,700.25 5,000,439.80 600,020.08 8,000,025.42 625,012.15 130 READING EXERCISE ROMAN NUMERALS Note. Ability to read numbers expressed in the Roman no- tation is all that should be required of pupils, and but little time should be spent even in reading them. 1=1. V - 5. X = 10. L = 50. C = 100. D - 500. M = 1000. 1. 2. 3. 4. 5. 6. I II ccc XII LXXX XIV V III VI XIII IV XVI X XX VII XV IX XVII L XXX VIII LX XL XVIII C cc XI LXX XC XIX 7. 8. 9. 10. XXI XXIV LV LXXI XXXI XXXII LXVI XCIV XLI XLIII LXXVII LIII LI LVIII LXXXII XLVII LXI LXVII XXVIII XXXV LXXI LXXIX XXXIX LXVIII LXXXI LXXXVI XLIV XXVI XCI XCV XCIII LXXXIX 11. 12. 13. 14. D MDCC DLXIV MLXVI M MDCCC CDIV MCCXV CD MCM ecu MDLXIV DC DCX DLV MDCXVI DCC CDIV MM MDCXX DCCC DCLXV MDLXV MDCCCXII CM CCCX CDL MCDXCII MD CDX CDXLIV MDCCLXXVI MCD DXLV DCLXVI MCMXIV MDC DLXV ML MCMXXI MONTHS AND DATES 131 1. What is the first month of the year? The twelfth? The sixth? The eleventh ? The fifth? The fourth? The third? The tenth? The second? The seventh? The eighth? The ninth? 2. Which month of the year is October? June? December? February? March? April? November? August? January? 3. Memorize these two lines : May? July? September ? " Thirty days hath September, April, June, and November." 4. Name the month that has the fewest days. How many days has this month ? 5. All the months not named above have thirty-one days. Name them. 6. On business papers, the month is often expressed by a nu- meral, and the year abbreviated, thus : 2/24/05 5/15/12 8/26/09 4/17/11 1/5/18 10/26/14 7/12/15 3/30/16 7. Express in numerals, as above : Oct. 10, 1919 Feb. 22, 1920 July 4, 1915 March 23, 1900 Dec. 18, 1916 May 7, 1910 11/8/20 9/12/10 12/25/17 6/10/21 Aug. 6, 1920 Apr. 1, 1918 June 18, 1921 132 RELATION OF NUMBERS, OR RATIO The ratio of one number to another is the quotient of the first divided by the second. What is the ratio of 1. 20 dollars to 4 dollars? 40 quarts to 8 quarts? 30 inches to 6 inches ? 25 pounds to 75 pounds ? 12 ounces to 48 ounces? What is the ratio of 3. An inch to a foot ? A foot to a yard? A quart to a gallon? A day to a week? An ounce to a pound ? What is the ratio of 5. 4 ounces to 2 pounds? 3 pints to 3 quarts ? 5 months to 2\ years? 6 minutes to half an hour? 21 cents to 7 cents? 9 yards to 27 yards? 8 acres to 12 acres? 6 days to 8 days? 9 tons to 12 tons? A foot to 4 inches? A pound to 8 ounces A day to 6 hours? An hour to 15 minutes A year to 3 months? 6. 2 dozen units to 8 units ? 5 years to 10 months ? 4 pecks to 4 quarts ? 1 yard to 1J feet? Application of Ratio Pupils should be taught to solve by means of ratio all such problems as the following : If 5 quarts of milk cost 80 cents, how much will 10 quarts cost ? (It is not necessary to find the cost of 1 quart.) If a man's salary is $3600 a year, how much does he earn in 4 months? (Do not find salary for 1 month.) How much will a dozen apples cost at the rate of 3 for ten cents ? {What is the ratio of 12 to 3?) QUESTIONS FOR LEISURE MOMENTS 133 Questions for Leisure Moments To pupils : A study of the following questions, one or two at a time, will give you a small fund of useful information on everyday subjects. The information is to be found in your arithmetic or in the dictionary. 1. How long is a fortnight? A quarter? A decade? 2. What does bi-weekly mean ? Bi-monthly? 3. How many is three-score and ten? 4. Is a quart, liquid measure, just equal to a quart, dry measure ? Find out from the facts given here : The standard gallon contains 231 cubic inches. The standard bushel contains 2150.42 cubic inches. 5. What is the difference in pounds between the long ton and the short ton? Which one is commonly used in the United States? In England? 6. How many gallons does a barrel contain? A hogshead? 7. Give the dimensions of a cord of wood. Into what lengths is the wood sawed? 8. How is lumber sold? What does the abbreviation "M" stand for ? 9. How many acres in a square mile? 10. How deep is a fathom? 11. How long is a league? What is this unit of measure used for? 12. In measuring the earth removed in excavations, how much is called a load? 134 QUESTIONS FOR LEISURE MOMENTS 13. How large is a township? A section? Where are these terms chiefly used ? 14. How many quires of paper make a ream? 15. How many units make a gross ? A great gross? 16. How can the leap years be determined? 17. How much U S. money is equivalent to the English pound ? To the French franc? To the German mark? 18. Is the English penny equal in value to the United States cent? Find out from this table : 12 pence (pennies) make 1 shilling. 20 shillings make 1 pound. 19. Canada is a province of Great Britain. Do Canadians use English money? 20. What is a ten-dollar gold piece called? A twenty-dollar gold piece ? 21. Are our gold and silver coins made of the pure metal? 22. Name the coins of the United States, and the metal of which each is made. 23. 18-carat gold is what per cent pure gold? What per cent alloy ? 24. What does the word "perimeter" mean? 25. What is the perimeter of a circle called? 26. What relation has the radius of a circle to the diameter? What relation has the diameter to the circumference ? QUESTIONS FOR LEISURE MOMENTS 135 27. We measure distances on land by the English mile. What is the length of this mile in feet ? 28. The speed of a vessel is measured in knots, or nautical miles. A nautical mile is how many feet? 29. What is a lunar month? A calendar month? Which is the longer? 30. Explain local time, and standard time. Is it possible for local and standard time to correspond at any place? 31. Which unit of measure is longer, the meter or the yard? How much longer? 32. How was the length of the meter established? 33. In what countries is the Metric System of Weights and Measures commonly used? 34. What is the unit of weight by which diamonds and other precious stones are weighed ? 35. What are safe and proper ways of sending money to a person in another city or town ? 36. Should money ever be inclosed in a letter? 37. What does the abbreviation "Inc." after the name of a business firm mean? 38. Generally speaking, is it safer to invest money in stocks or in bonds? Why? J U> OvJU/CJ 075844 ' *?, UNIVERSITY OF CALIFORNIA LIBRARY 1 ;- : I I 3: 1 Iflppi I Si :j •"• ' ' ' 1