IN MEMORIAM 
 FLORIAN CAJOR1 
 
THE PRIMARY 
 PUBLIC SCHOOL ARITHMETIC 
 
THE PRIMARY 
 PUBLIC SCHOOL ARITHMETIC 
 
 BASED ON 
 McLELLAN AND DEWEY'S "PSYCHOLOGY OF NUMBER" 
 
 BY 
 J. A. McLELLAN, A.M., LL.D. 
 
 PRESIDENT ONTARIO NORMAL COLLEGE 
 AUTHOR (WITH DR. DEWEY) OF "TUB PSYCHOLOGY OF NUMBER," "APPLIED 
 
 PSYCHOLOGY," "ELEMENTS OF ALGEBRA," ETC. 
 AND 
 
 A. F. AMES, A.B. 
 
 HONOR GRADUATE IN MATHEMATICS J FORMERLY MATHEMATICAL 
 
 MASTER, ST. THOMAS COLLEGIATE INSTITUTE 
 SUPERINTENDENT OF SCHOOLS, RIVERSIDE, ILL. " 
 
 TEACHERS' EDITION 
 
 Nefo god* 
 THE MACMILLAN COMPANY 
 
 LONDON : MACMILLAN & CO., LTD. 
 1899 
 
 All rights reserved 
 
COPYBIOHT, 1898, 
 BY THE MACMILLAN COMPANY. 
 
 Set up and electrotyped May, 1898. Reprinted August, 
 1898 ; December, 1899. 
 
 Norfoooti 
 
 J. 8. Gushing & Co. - Berwick & Smith 
 Norwood Masi. U.S.A. 
 
/v 
 
 O 
 
 PKEFACE 
 
 THIS book is strictly introductory to "The Public 
 School Arithmetic," and forms with it a complete course. 
 In both, the method of treatment closely follows " The 
 Psychology of Number." A few special points in the 
 Primary may be noticed. 
 
 1. While number work in the first grade may be 
 largely incidental, it ought not to be accidental. The 
 teacher should have a clear conception of the work to be 
 done, and of the order and method by which the child 
 may step by step reach the desired end. When the child 
 enters school the number sense is alert; he is, roughly 
 speaking, in the counting stage of development. Upon 
 the principle " strike while the iron is hot," this counting 
 power should at once be used for further growth by 
 applying it to more definite measurements. Such appli- 
 cation arouses fresh interest in number, and is in a high 
 degree educative. On this point Dr. Dewey says, "Unless 
 there is to be arrested development when the child enters 
 school, some function must be found with reference, to 
 which he may utilize his ability to count the number 
 sense becomes vitalized and truly educative at this point by 
 being largely directed towards the definition of values in the 
 form of measurement" This book, therefore, while not 
 
 y 
 
yi PREFACE 
 
 giving first grade work in full, presents in systematic 
 form and in sufficient detail for any primary teacher the 
 amount of work to be done and the method of doing it. 
 
 2. Those to whom counting is the whole of number 
 hold that almost the sole object of number-work in 
 primary grades is quickness and accuracy in the figure- 
 work of the fundamental rules. They are inclined to 
 belittle the training of intelligence. Most teachers know, 
 however, that not accurate figure-work and rule-learning 
 is the crux, but rather what figure-work " what rule " 
 
 to apply in given cases. Accordingly, while not un- 
 mindful of the use of skill in figure-work, the authors of 
 this book have a wider purpose. Recognizing that num- 
 ber is the " tool of measurement," they have endeavored by 
 a careful grading and an unusual variety of concrete and 
 constructive exercises to develop true ideas of number 
 and numerical operations, as well as trained intelligence 
 and ability to apply what has been learned to the varying 
 problems of social life. 
 
 3. There are two extreme views regarding the nature 
 of number leading to two quite different pedagogical 
 methods: one of these, No ratio in number; the other, 
 No number in ratio. The one begins with the ratio idea, 
 and ignores or subordinates the " how many " (counting) 
 idea, letting it struggle into being incidentally in the 
 development of ratio. The other begins with the vague 
 "how many," and subordinates ratio or rather totally 
 ignores it as not involved in the number process. This 
 book, following as it does " The Psychology of Number," 
 avoids both extremes. It begins with the how many 
 (counting) as applied to some total ; and keeping together 
 
PREFACE vii 
 
 things which psychologically cannot be separated, viz. 
 number and quantity, proceeds from the vague how many 
 and the vague how much to the definite so many and the 
 definite so much. Thus there is gradually yet surely 
 evolved the concept of ratio a concept which is indis- 
 pensable in practical life, and without which there can 
 be no Science of Arithmetic. On this important point 
 Dr. Dewey whose views on the psychical nature of 
 number have never been questioned by a competent 
 critic says : " When counting is used by the child to 
 value some amount or other the ratio idea is implied. It 
 need not, therefore, be consciously or explicitly stated. 
 In fact, I should say that for a considerable period it 
 should not be. It is enough that the child gets a sense 
 for the use and application of number in measurement. 
 When number is so used, the transition to the conscious 
 ratio idea, whether in the form of ratio proper, or frac- 
 tions, or percentage, is natural and inevitable ; this is not 
 a mere doctrinaire statement ; it rests upon continuous 
 experimenting and observation in a school where the 
 child's number sense is developed in connection with 
 constructive operations in manual training, in which 
 number relations are introduced as instruments to prac- 
 tical valuation." 
 
 4. This has been verified during the preparation of 
 this book. Through the kindness of the publishers 
 printed sheets of the exercises and methods have been 
 placed in the hands of teachers in training (and public) 
 schools, and actually tested in the classes. The reports 
 have been unanimously favorable. The children got hold 
 of the idea of number as " The Tool of measurement," 
 
yiii PREFACE 
 
 as playing an important part in the affairs of life ; school 
 life was, in one respect at least, seen to be a part of social 
 life. It followed that interest, enthusiasm, self-activity 
 in connection with arithmetical work became the com- 
 mon experience in the schools. 
 
 For help in such experimenting our thanks are due to 
 a number of successful teachers, especially to Principal 
 Graham of the London Training School, to Principal 
 Elliott of the Hamilton Training School, to Mrs. Ran- 
 dolph (Los Angeles), and to Principal William Sparks 
 of Chatham. 
 
 Teachers are recommended to study with care Dewey 
 and McLellan's " Psychology of Number," and the " Pub- 
 lic School Arithmetic," which illustrates so many points 
 in the " Psychology of Number." 
 
 The "Teachers' Edition" of this book will contain all 
 needed answers to problems, suggestions for first grade 
 work, some illustrative lessons, and many suggestions as 
 to methods. 
 
CONTENTS 
 
 PAOB 
 
 SUGGESTIONS TO TEACHERS . . . . . xi 
 
 SUGGESTIVE LESSONS xxviii 
 
 SUGGESTIONS Ixiv 
 
 SECTION I 
 FIRST GRADE WORK REVIEWED 1 
 
 SECTION II 
 
 FUNDAMENTAL ADDITIONS EXTENDED SUBTRACTION DE- 
 NOMINATE NUMBERS QUANTITY UNIT OF MEASURE 
 NUMBER 20 
 
 SECTION III 
 
 MULTIPLICATION TABLES OF 2 AND 3 DIVISION DENOM- 
 INATE NUMBERS SQUARES AND OBLONGS FRACTIONS 
 
 RATIO 63 
 
 SECTION IV 
 
 MULTIPLICATION TABLES OF 4 AND 5 DIVISION DENOM- 
 INATE NUMBERS SQUARES AND OBLONGS FRACTIONS 
 
 RATIO 98 
 
 SECTION V 
 
 FUNDAMENTAL ADDITIONS EXTENDED SUBTRACTION MUL- 
 TIPLICATION TABLES OF 5 AND 6 DIVISION , , J21 
 
 is 
 
X CONTENTS 
 
 SECTION VI 
 
 PAGE 
 
 DOLLARS AND CENTS MISCELLANEOUS REVIEW QUESTIONS 137 
 
 SECTION VII 
 ADDITION SUBTRACTION MULTIPLICATION DIVISION 
 
 RATIO DENOMINATE NUMBERS VOLUME . . . 148 
 
 SECTION VIII 
 ROMAN NOTATION FRACTIONS 163 
 
 SECTION IX 
 
 TABLE OP DENOMINATE NUMBERS FUNDAMENTAL OPERA- 
 TIONS MULTIPLICATION TABLE ..... 178 
 
 SECTION X 
 
 NUMERATION AND NOTATION ADDITION TABLE MULTI- 
 PLICATION WITH Two FIGURES IN THE MULTIPLIER 
 LONG DIVISION . 194 
 
 SECTION XI 
 DECIMALS 210 
 
 SECTION XII 
 PERCENTAGE 224 
 
 SECTION XIII 
 MISCELLANEOUS REVIEW LESSONS 240 
 
 ANSWERS , , , , t t f , , 255 
 
SUGGESTIONS TO TEACHERS 
 
 Pages xi to xxvii of Suggestions to Teachers indicate 
 the kind of work that should be done by the class 
 previous to beginning Lesson 1 of this book. Les- 
 sons 1 to 8 review the work of this section. 
 
 I. Counting. Counting is of course the first thing 
 to look after : the child can probably count a little 
 when he enters school, but there is now to be count- 
 ing with a definite end in view the growth of the 
 relating process which gives rise to number ; there 
 is a whole to get an idea of, there are its parts ; 
 there is the how -many ; i.e. the child is counting 
 something. 
 
 1. (a) Start with a whole and count by single 
 things. For instance, count the number of girls in 
 the room. Of boys. Of children. Test how far the 
 number names are significant ; e.g. name the num- 
 ber and have corresponding objects selected, etc. 
 
 (6) It may be that the children cannot count 
 cannot give the consecutive number names and apply 
 them to corresponding groups of objects. In this case 
 the starting-point is the vague muchness (ideas of 
 more and less) and the vague how-many which must 
 
 xi 
 
xii SUGGESTIONS TO TEACHERS 
 
 be in the children's minds. Have them make com- 
 parisons involving ideas of more and less ; e.g. the 
 length of the desk is greater than the width, etc. 
 Also practice in the how-many idea ; e.g. compare 
 the how-many cubes (say 8) in this group with the 
 how-many (say 6) in that. They will be led to see 
 that the muchness of a quantity is determined by the 
 how-many parts in it, etc. Have constructive exer- 
 cises, bringing out relations of consecutively num- 
 bered objects (how five differs from six, etc.), and 
 arousing interest in number names ; e.g. have them 
 make a picket (two splints) ; try to make a triangle 
 with two splints ; they will need one splint more, and 
 will express the how-many as " two and one," or as 
 "one, and one, and one" Similarly, try to make a 
 square with three splints ; they will need one more 
 splint, and the how-many in the square will perhaps 
 be expressed as " three and one," or " two and one 
 and one," or (as we have often seen) " one and one' 
 and one' and one," with some rhythmic movement. 
 They will now fully appreciate the simple number 
 names which are substitutes for the round-about ex- 
 pressions. 
 
 The children will hence soon be ready to see that 
 we cannot find how much one quantity (as a line, 
 area, etc.) differs from another without finding the 
 how-many of some one thing (unit) in each. 
 
 2. Not to be confined to single things. Count this 
 IWQ rows of girls; of boys ; of all, how many 
 
SUGGESTIONS TO TEACHERS xiii 
 
 twos? Count pairs of hands, how many pairs? 
 Similarly, count groups of 3, how many threes, 
 etc. ? Also appeal to the ear : taps with stick, 
 strokes of bell, vocal sounds (as letters, etc.), this 
 both with single sounds, and groups of sounds (i.e. 
 sounds rhythmically marked off). 
 
 3. Test this relating process, e.g. start counting 
 with 4, i.e. 4, 5, 6 (units of any kind). Show by 
 fingers or marks or dots what preceded the 4. 
 
 4. Count the same quantity with different units 
 or groups, e.g. these 12 pupils : by 2's, how many? 
 (6). By 3's, by 4's, by 6's, how many in each case ? 
 This lot of 24, by 2's, by 3's, by 4's, etc., to deter- 
 mine the different numbers (how many) that measure 
 the same quantity. Also count different quantities 
 with the same unit of measure. This lot of 6 (pupils, 
 etc.) by 3's. This group of 12 by 3's, this group of 
 15 by 3's, etc. Use many familiar units. 
 
 5. Represent the various units by dots on the 
 blackboard; e.g. these rows of dots represent groups 
 of two (pupils, cents, etc.) each, J J how many ? 
 
 
 
 (4). This group of three each, how 
 many ? How many 4's ? etc. 
 
 6. Let all the foregoing be then extended to exact 
 measurements. Count the 2-inches in this foot-rule 
 (or line); the 3-inches, etc. Count the number of 
 3-inches in lines 12 in., 15 in., 18 in., etc., long, and 
 so on. 
 
xiv SUGGESTIONS TO TEACHERS 
 
 7. Cut out of cardboard strips, respectively, 1 in., 
 2 in., 3 in., ... 12 in. long. Ask the pupils to 
 select the 3 in. strip, the 5 in. strip, etc. 
 
 8. Have bags of sand or other material weighing 
 from 1 to 10 Ib. Let the pupils lift these and guess 
 their weights. 
 
 9. Make squares whose sides are respectively 2, 
 3, and 4 in. Cut them into parts each containing 
 1 sq. in. Count the parts and then put them 
 together again to form the original square. Count 
 the 2-sq. in., etc. 
 
 10. Similarly, make oblongs 2 in. by 3 in., or 3 in. 
 by 4 in., for example; divide into inch squares or 
 half-inch squares, count, and again reconstruct the 
 whole from the parts. Count as in 9 the 2-sq. in., etc. 
 
 11. Make simple measurements with the foot-rule 
 and tape measure ; for instance, measure the width 
 of the desk, the length of the table, the height of the 
 children, the number of inches around the head, the 
 distance around the chest when expanded or con- 
 tracted. 
 
 12. Take two points, say 2 or 3 or 4, etc., yards 
 apart, without the pupils knowing what distance 
 was measured. Let the pupils measure the distance 
 between the points with a yardstick. What num- 
 ber do you get ? How many yards ? Measure with 
 a foot-rule. How many feet ? Measure with a unit 
 one-half foot long. What number do you get ? How 
 many half-feet ? Write, 2 yd. = 6 ft. = 12 half -feet. 
 
SUGGESTIONS TO TEACHERS XV 
 
 Put (say) 2, 3, 4, etc., quarts of water into a pail. 
 Let the pupils measure it out with a quart measure. 
 What number do you get from the measurement? 
 With a pint measure what number do you get ? 
 With a gill measure what number do you get? 
 Write, 2 qt.=4 pt. = 16 gi. 
 
 13. Draw a line 12 in. long, without the pupils 
 knowing its length. Measure it with an inch unit. 
 What number do you get? How many inches? 
 Measured with a 2-inch unit what number ? How 
 many 2-inches ? With a 3-inch unit what number ? 
 How many 3-inches ? So also with 4-inch and 6- 
 inch units. Draw and measure other lengths with 
 other units. 
 
 II. Instantaneous recognition of the number pict- 
 ures. The work suggested in the above outline 
 should lead as directly as possible to the instanta- 
 neous recognition of the number pictures which 
 will aid in complete mastery, especially for the aggre- 
 gation idea of addition and subtraction, of the num- 
 bers from 110. 
 
 The picturing power should be used, in fact must 
 be used, for economy of energy. If this picturing is 
 rightly used, the whole analysis of ten will be given 
 (perceived at last) in the picture ** I ** no matter 
 what units are represented. 
 
 It must be understood that the symbolizing dots 
 stand for any units whatever ; e.g. ** stands for 
 
XVI SUGGESTIONS TO TEACHERS 
 
 not only 5 single cents, but five 2-ct., five 3-ct., five 
 5-ct., five dollars, five 2 boys, five 3 apples, etc., etc. 
 
 1. Let the children count a number of beans, say 
 eight, and separate them into two equal parts. How 
 many parts are there ? Separate each part into two 
 equal parts. How many of these parts are there 
 in each part? How many beans are there in each 
 part ? Or, arranging in perceptive forms, how many 
 ones in * ? How many twos in J * ? How many 
 pairs of twos in J | * * ? Similar exercises and 
 questions may be given with splints formed into 
 two squares, and into two groups of two pickets 
 each. Treat an oblong 4 in. by 2 in. similarly. 
 
 2. Put 1-in. units together to form the 2-in. unit, 
 2-in. units to form the 4-in. unit, 4-in. units to form 
 the 8-in. unit, and so on. Use also sq. in. units. 
 
 3. In the above arrangement of dots there are 
 how many single units ? How many 2-units or twos ? 
 How many 3-units or threes? Use this arrangement 
 to fix the place of 5 in the sequence between 4 and 6, 
 i.e. as 1 more than 4 and 1 less than 6. Make with 
 sq. in. a square, side 2 in., and an oblong 2 in. by 3 
 in. Give the pupils 5 sq. in. to work with. 
 
 4. Similarly, use this arrangement to show the 
 
SUGGESTIONS TO TEACHERS xvii 
 
 relation of 8 to 4, as two fours, and to fix the place 
 of 7 in the sequence between 6 and 8, i.e. as 1 more 
 than 6 and 1 less than 8. 
 
 5. Similarly, show the relation of 10 to 5, and fix 
 the position of 9 in the sequence between 8 and 10, 
 i.e. as 1 more than 8 and 1 less than 10. 
 
 6. In using these dot arrangements, the picturing 
 power should be definitely cultivated. Five dots 
 should be instantly recognized as 5, 6 as 6, 7 as 5 
 and 2 or 4 and 3, 8 as two 4's or four 2's, 9 as 5 and 
 4, 10 as two 5's or five 2's, and also other simple 
 relations within the groups. 
 
 7. After making the analysis of the visual forms, 
 for instance, 5 + 1 = 6, 4 + 2 = 6, etc., cover the 5 
 dots. How many are hidden ? How many are seen ? 
 Cover the 4. How many are hidden ? How many 
 seen ? So on, taking care that 6 is seen as 5 + 1 and 
 
 1 + 5, 4 + 2 and 2 + 4, and so on. 
 
 8. In every case practical examples should be 
 used as much as possible ; e.g. in the five. Cover 
 
 2 dots. What do you see? (3). How many are 
 unseen? (2). Then what must be done with the 
 
 3 to get 5 ? With 3 f to get 5 ^ ? With 3 eggs to 
 make up 6 eggs ? With 3 dollars to make up 7 
 dollars? With 3 dimes to make up 8 dimes? 
 With 3 2-dollar bills to make 5 2-dollar bills ? etc. 
 Count 8 by 2's : how many ? With 8 f how many 
 
xviii SUGGESTIONS TO TEACHERS 
 
 apples 2^ each can be bought? etc. Connecting 
 thus the practical work with the child's own experiences 
 as closely as possible. With 8 ten-dollar bills bought 
 cows at 2 ten-dollar bills each. How many? All the 
 combinations up to ten (including some of the factor 
 relations) can be mastered in a few weeks. The 
 practical element will make the work deeply interest- 
 ing to the child. 
 
 9. Arrange on separate pieces of cardboard dots 
 placed thus : 
 
 Show these cards separately to the class and have 
 the answer given instantly. Tell how many two's 
 in 6 ? in 8 ? in 10 ? Show the 10 picture an instant; 
 unseen, erase one dot, show for an instant what is 
 left. What number ? What was done with the 10 ? 
 Thus also erase two dots, etc. Similarly, change 6 
 to 8, 7, 9, etc. Make practical examples as in 8. 
 
 10. Cut out of cardboards units 1 in., 2 in., 3 in., 
 ... 10 in. long, respectively. Let the children 
 select the units which are together equal to the 3-in. 
 unit ; to the 4-in. unit ; to the 5-in. unit. Select 
 the units which will make triangles each of Avhose 
 sides is respectively 6 and 7 in. long. Select the 
 
SUGGESTIONS TO TEACHERS xix 
 
 units which will make squares whose sides are respec- 
 tively 8 and 9 in. long. Select the units which will 
 make a five-sided figure, each of whose sides is 10 
 in. long. 
 
 11. Simple work from dictation, for instance, 
 make a square each side of which is 4 in. Out of 
 each corner cut 1 sq. in. Fold, making a box. 
 Give similar constructive work. 
 
 12. Count by 2's the number of hands of the 
 children in the first row ; of the girls ; of the boys ; 
 of all the children in the class. Count thus : 2, 4, 
 6, 8, 10, etc. 
 
 13. Give exercises by dot arrangements and 
 measurements leading to and developing the idea 
 that for any given quantity any one measurement 
 gives a second measurement. 
 
 Thus * * signifies that the unit 2 measures 6 
 three times, and also that the unit 3 measures 6 
 twice. 12 by 3's implies 12 by 4's. 15 by 3's im- 
 plies 15 by 5's, and so on. Illustrate by dots. 12 in. 
 by 3 in. implies 12 in. by 4 in. Practical examples. 
 
 14. Cut a measure 1 ft. long out of . cardboard. 
 Cut this foot measure into parts each 6 in. long. 
 How many parts are there ? Place two 6-in. meas- 
 ures end to end. How long are they together? 
 Cut a foot measure into parts each 2 in. long. How 
 many parts are there ? Place six 2-in. measures end 
 to end. How long are they ? 
 
 15. Arrange constructive exercises similar to those 
 
XX SUGGESTIONS TO TEACHERS 
 
 in paragraph 14, dividing 1 ft. into 4-in. and 3-in. 
 units, respectively. Make also equilateral triangles 
 and squares and note the number in each case. 
 
 16. Cut out of cardboard units of measure respec- 
 tively 6 in., 4 in., 3 in., and 2 in. long. Find the 
 number of times that each unit measures 1 ft. 
 
 17. Divide 1 ft. into 2, 3, 4, and 6 equal parts, 
 respectively. How long are the equal parts? 
 
 18. Apply the foot measure to measure the yard. 
 What number do you get ? How many ft. ? 3 ft. in 
 what ? Apply the yard to measure the length of the 
 room and other quantities. How many yd. ? 6 yd. 
 in what ? Apply the pint to measure the quart, the 
 quart to measure the gallon, and the pint to measure 
 the gallon. What numbers do you get ? How many 
 pt. ? How many qt.? 4 qt. in what ? 8 pt. in what ? 
 
 19. Count off 12 objects into unit groups of 4 
 each. What is the number of groups? Similarly, 
 count off 15 objects, 18 objects, etc., into groups of 
 5, 6, etc., and count the number of groups. 
 
 20. Have each child form out of splints two 
 squares with their diagonals, thus: EJ. Arrange each 
 square into triangles. How many squares are there ? 
 How many triangles ? How many pairs of triangles ? 
 
 21. Measure a 12-in. length with a 6-in. unit, and 
 then again with a 3-in. unit. How many 6-in. units 
 in the whole? How many 3-in. units in the 6-in. 
 unit ? How many 3-in. units in the whole ? Simi- 
 larly, a 16-in. length with 8-in., 4-in., 2-in. units, etc. 
 
SUGGESTIONS TO TEACHERS XXI 
 
 III. Combination of the ten units. 1. While the 
 pupils were studying the number pictures in II they 
 were given many practical questions on the com- 
 binations of single units. While they study the 
 work outlined in III, give them many similar prac- 
 tical questions on the combinations of the 10-unit, 
 in fact, on all the combinations that have been 
 studied in the number pictures. Thus : 
 
 (1) I sold 3 cows for 6 ten-dollar bills. How 
 much for each ? How many dollars ? 
 
 (2) A tailor sold 4 suits of clothes, receiving 2 
 ten-dollar bills for each. How much did he get for 
 all ? How many dollars ? 
 
 (3) I gave $ 80 for a horse ; how many ten-dollar 
 bills will pay for it ? 
 
 (4) I bought a suit of clothes for $ 40 and an 
 overcoat for $30. What did both cost ? How many 
 ten-dollar bills would pay for both ? 
 
 (5) I bought a horse for $ 300 and 2 cows at $ 40 
 each. What did all cost ? 
 
 (6) I gave 4 dimes for a necktie and one-half as 
 many for a collar. What did both cost ? 
 
 (7) Write in figures : six, twenty-five, forty-four, 
 eighty, one hundred and thirty-six, seven hundred 
 and seventy-two, two hundred and four. 
 
 2. Teach combinations of the ten units in the fol- 
 lowing manner : Take a cubic centimeter (if a cubic 
 centimeter cannot be procured, take a half-inch or an 
 inch cube) for the primary unit of measure ; a rec- 
 
xxii SUGGESTIONS TO TEACHERS 
 
 tangular prism (a decimeter in length), equal to ten 
 of these units, will be the 10-unit and ten of these 
 the 100-unit. The units may be of different colors 
 and the units of the decimeter alternately white and 
 black. Let the notation accompany thus, one ten 
 and no units equals 10, two tens and no units equals 
 20, and so on up to ten tens which equals the new 
 unit one hundred, i.e. 100. Thus a rectangular 
 prism, whose surface is a square decimeter and 
 thickness one centimeter, will be equal to ten of 
 the 10-unit and will be the 100-unit. Ten of these 
 units will be the 1000-unit. Let the notation, as 
 before, accompany the recognition of the facts. 
 
 In case the cubes referred to above cannot con- 
 veniently be obtained, units, tens, and hundreds can 
 be cut out of cardboard, the square centimeter (about 
 f in. on each side) instead of the cubic, a strip 1 
 decimeter long and 1 centimeter wide for the 10-unit, 
 and a square decimeter, divided into ten strips, 
 colored alternately white and black, for the 100- 
 unit. Extend this as suggested in paragraphs 8 
 and 9. 
 
 3. Give the pupils the number names from one to 
 thirteen inclusive. Explain 13 as 3 and 10, teen 
 being ten. Ask them to suggest a name for 14, i.e. 
 4 and 10, which is fourteen, and so on up to 20. For 
 20 give the name twenty (twain-ty, twain being two 
 and ty ten). 
 
 Let the pupils suggest the names for 30 (three-ty 
 
SUGGESTIONS TO TEACHERS xxiii 
 
 or thirty), 40, and so on up to 90. Ten tens he will 
 probably call ten-ty, when he should be given the 
 new name one hundred and so on with the other 
 numbers he has been using. 
 
 4. Count by tens the number of fingers and 
 thumbs of the children in the first row ; of the 
 girls ; of the boys. Count thus : 1 ten, 2 tens, 3 
 tens, 4 tens, 5 tens, 6 tens or 60, i.e. 6 tens and no 
 units. 
 
 5. Give exercises in counting by tens from a clock 
 face. Count from XII to VI from right to left and 
 from left to right. Count from XII around to XII 
 again. 
 
 6. What is the temperature in the schoolroom at 
 10.30 A.M.? What is it outside? Answer thus: 
 6 tens and 8 and gradually change to 68, i.e. 6 tens 
 and 8 units. Continue this work from day to day. 
 
 7. Note the time on the clock face counting 
 by tens and minutes, for instance, 2 tens and 3 
 minutes after 9 o'clock. Change gradually to 23 
 minutes after 9 o'clock, i.e. 2 ten minutes and 3 
 minutes. 
 
 8. Measure certain distances with a metric stick ; 
 for instance, this distance is 2 meters, that is 4 
 meters, and so on. This distance is 1 meter 6 deci- 
 meters ; that, 2 meters 4 decimeters. Again, this 
 distance is 2 meters 1 decimeter 5 centimeters ; that, 
 3 meters 5 decimeters 8 centimeters, and so on. 
 
 9. Count the number of centimeters in a deci- 
 
xxiv SUGGESTIONS TO TEACHERS 
 
 meter. One decimeter is equal to 10 centimeters, 
 i.e. 1 decimeter and no centimeters. Two decime- 
 ters equal 20 centimeters, i.e. 2 decimeters and no 
 centimeters; and so on. Nine decimeters equal 90 
 centimeters, i.e. 9 decimeters and no centimeters. 
 
 10. One decimeter 1 centimeter is equal to 11 
 centimeters, i.e. 1 decimeter 1 centimeter. One 
 decimeter 2 centimeters is equal to 12 centimeters, 
 i.e. 1 decimeter 2 centimeters; and so on. One 
 decimeter 9 centimeters is equal to 19 centimeters, 
 i.e. one 1 decimeter 9 centimeters. 
 
 So with 2 decimeters 1 centimeter, 2 decimeters 
 2 centimeters, and so on, as continuously as necessary, 
 up to 9 decimeters 9 centimeters. 
 
 Test thus : 2 decimeters 4 centimeters = ? centime- 
 ters ? 65 centimeters = ? decimeters and centimeters ? 
 
 11.* Count the number of decimeters in a meter. 
 One meter is equal to 100 centimeters, i.e. 1 meter 
 no decimeters no centimeters. Two meters is equal 
 to 200 centimeters, i.e. 2 meters no decimeters no 
 centimeters, so on up to 9 meters. 
 
 One meter 1 decimeter is equal to 110 centimeters, 
 i.e. 1 meter 1 decimeter no meters. One meter 2 
 decimeters is equal to 120 centimeters, i.e. 1 meter 
 2 decimeters no centimeters, and so on up to 1 meter 
 9 decimeters, and so on as continuously as necessary 
 up to 9 meters 9 decimeters. 
 
 * This notation need not be extended beyond 99, unless thought 
 desirable, until after Lesson 14, 
 
SUGGESTIONS TO TEACHERS XXV 
 
 One meter 1 decimeter 1 centimeter is equal to 
 111 centimeters, i.e. to 1 meter 1 decimeter 2 centi- 
 meters. 
 
 Develop 112, 113, 114, etc., 121, 122, 123, etc., 
 as continuously as necessary up to 999. 
 
 Test thus : 5 meters 4 decimeters 8 centimeters is 
 equal to how many centimeters ? 2 meters 6 centi- 
 meters is equal to how many meters ? 
 
 516 or 607 centimeters is -equal to how many 
 meters, decimeters, and centimeters ? 
 
 In the above work use contractions, viz. m for 
 meter, dm for decimeter, and cm for centimeter. 
 
 12. Count ten pennies, using toy or, better, real 
 money. What coin is equal to ten pennies ? Write 
 the sum thus: 10^, i.e. 1 dime and no pennies. 
 Similarly, for 2 dimes write 20^, i.e. 2 dimes and no 
 pennies, and so on. 
 
 Count sums of money, using dimes and pennies. 
 Write the results thus: 12 i.e. 1 dime 2^; 46 
 i.e. 4 dimes 6^. Test the work as before in 10. 
 
 Count by tens from to 90 (using dimes as a 
 basis), from 1 to 91 (using 1 ^ and dimes), 2 to 92 
 (using 2 ^ and dimes) ; and so on. 
 
 Count ten dimes. What coin is equal to ten 
 dimes? Write the sum thus: 100^, i.e. $1, no 
 dimes, no pennies. Similarly, for $ 2 write 200 ^, 
 i.e. $2, no dimes, no pennies ; and so on. 
 
 Count by 100's from to 1000. Count by 100's 
 from 10 to 910; 11 to 911; 12 to 912 ; and so on. 
 
XXVI 
 
 SUGGESTIONS TO TEACHERS 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 11 
 
 21 
 
 31 
 
 41 
 
 51 
 
 61 
 
 71 
 
 81 
 
 91 
 
 12 
 
 22 
 
 32 
 
 42 
 
 52 
 
 62 
 
 72 
 
 82 
 
 92 
 
 13 
 
 23 
 
 33 
 
 43 
 
 53 
 
 63 
 
 73 
 
 83 
 
 93 
 
 14 
 
 24 
 
 34 
 
 44 
 
 54 
 
 64 
 
 74 
 
 84 
 
 94 
 
 15 
 
 25 
 
 35 
 
 45 
 
 55 
 
 65 
 
 75 
 
 85 
 
 95 
 
 16 
 
 26 
 
 36 
 
 46 
 
 56 
 
 66 
 
 76 
 
 86 
 
 96 
 
 17 
 
 27 
 
 37 
 
 47 
 
 57 
 
 67 
 
 77 
 
 87 
 
 97 
 
 18 
 
 28 
 
 38 
 
 48 
 
 58 
 
 68 
 
 78 
 
 88 
 
 98 
 
 19 
 
 29 
 
 39 
 
 49 
 
 59 
 
 69 
 
 79 
 
 89 
 
 99 
 
 Count by 10's from to 100 ; to 300 ; to 500 ; 
 500 to 1000. 
 
 13. Have the pupils name and write down all 
 numbers from 1 to 100 as indicated in the following 
 table : 
 
 Write the upper hori- 
 zontal row first and 
 then fill out each col- 
 umn. 
 
 Vary the exercise 
 by writing the first 
 column first and then 
 construct the horizon- 
 tal rows in succession. 
 Let the children simi- 
 larly construct the 200 table, the 300 table, and so on. 
 
 14. Review Lessons 1-8 are founded on the above 
 outline. The teacher is urged in this connection to 
 read the PSYCHOLOGY OF NUMBER and especially 
 Chapters VIII and IX on Primary Number Teaching. 
 
 IV. Related number work. Although all the 
 work suggested in the foregoing outlines is related 
 to the normal activities and experience of the child, 
 still there is another phase of related number work 
 that should be carefully thought out and systemati- 
 cally developed by the primary teacher, namely, that 
 in which number is distinctly related to the various 
 occupations of the schoolroom. Its purpose is the 
 development of the number sense rather than 
 
SUGGESTIONS TO TEACHERS xxvii 
 
 acquiring information or facility in number manipu- 
 lation. 
 
 It aids in laying a basis for future work, tends to 
 secure exactness, and holds the child's interest. 
 
 It may be grouped under four headings : 
 
 1. In connection with the school administration. 
 
 Thus a pupil who is selected to pass pencils to his 
 row of six pupils, counts out the number he needs, 
 or he is given four and finds that he is two short, 
 or eight and finds that he has two too many. 
 
 2.* In connection with the making of things, 
 involving length, surface, weight, size, bulk. An 
 instance of this is given, page xiii, 11. 
 
 3.* In connection with other subject matter, 
 especially science. 
 
 4. In connection with number games, involving 
 guessing, comparison, etc. 
 
 * " One Year's Outlines of Work in First Primary Grades " by 
 Flora J. Cooke of the Chicago Normal School is suggestive* 
 
SUGGESTIVE LESSONS 
 
 I. Counting 
 
 See Suggestion under Counting, p. xi. (b.) 
 
 CLASS. Six pupils, Willie, Charlie, Frank, Maud, 
 Edna, Edith. 
 
 TEACHER. Class, we shall have a talk to-day about 
 counting chairs, pencils, and other things. Charlie, 
 which is the tallest pupil in the class ? Edith is. 
 
 TEACHER. Which is the smallest boy, Edna? 
 Willie is. 
 
 TEACHER. Is this pointer equal to Willie's height, 
 Frank ? I can't tell. 
 
 TEACHER. How may we find out, Maud ? By 
 putting them together. 
 
 TEACHER. Do so, Maud, and tell me which is the 
 taller. The pointer. 
 
 TEACHER. Here are two piles of blocks ; which 
 has the most, Willie ? That one. 
 
 TEACHER. Class, how shall we find out how much 
 larger it is? Put the blocks of each pile on top 
 of one another, and see which is the higher pile. 
 
 TEACHER. Charlie, hold this apple for me. How 
 many apples has Charlie, Edith ? One. 
 
 xxv iii 
 
SUGGESTIVE LESSONS 
 
 TEACHER. Edna, hold this one. How many has 
 Edna, Frank? One. 
 
 TEACHER. Charlie, give yours to Edna. How 
 many has Edna now, Willie? One apple and one 
 apple. 
 
 TEACHER. How many pairs of shoes have Willie and 
 Charlie on their feet, Maud ? One pair and one pair. 
 
 TEACHER. We shall get some chairs now, and let 
 you sit down. Willie, get a chair and sit at this side 
 of the table. Charlie, get chairs for Frank and 
 yourself to sit at that end. How many chairs must 
 Charlie bring, Edith? One chair and one chair. 
 
 TEACHER. Frank will bring over one and one 
 chairs for all the girls to sit at the side ? That will 
 not be enough. 
 
 TEACHER. Why, Frank? There are more girls 
 than that. 
 
 TEACHER. Class, how many girls are there ? 
 One and one and one. 
 
 TEACHER. How many chairs shall Frank bring, 
 then, Maud ? One and one and one. 
 
 TEACHER. How many thumbs at this end of the 
 table, Willie ? One and one. 
 
 TEACHER. Wouldn't you like a shorter way of 
 naming the one and one, class ? Yes. 
 
 TEACHER. Well, we name the one and one, two. 
 Frank, how many eyes have you ? Two. 
 
 TEACHER. How many eyes have Charlie and 
 Frank, Maud ? Two eyes and two eyes. 
 
XXX SUGGESTIVE LESSONS 
 
 TEACHER. How many cents have I in this hand, 
 Edna ? Two. 
 
 TEACHER. In this one, Edith ? Two. 
 
 TEACHER. In both, Maud ? Two two-cents. 
 
 TEACHER. How many girls are there, Frank? 
 One and one and one. 
 
 TEACHER. Edith, you move your chair and sit 
 behind Edna and Maud. Willie, tell me in another 
 way how many girls there are ? Two and one. 
 
 TEACHER. Putting Edith first, how many girls 
 are there, Charlie ? One and two. 
 
 TEACHER. Willie, you sit at this end with Charlie 
 and Frank. How many pairs of shoes have the boys, 
 Edna ? Two pairs and one pair. 
 
 TEACHER. I will now tell you a shorter name for 
 the two and one. We call the two and one, three. 
 How many boys in our class, Edith ? Three. 
 
 TEACHER. How many boys and girls in our class, 
 Maud ? Three boys and three girls. 
 
 TEACHER. How many three-pupils in the class, 
 Charlie ? Two three-pupils. 
 
 TEACHER. Willie, count the girls, beginning with 
 Edith. One, two, three. 
 
 TEACHER. Beginning with Edna, Frank. One, 
 two, three. 
 
 TEACHER. I want a boy and a girl to sit on each 
 side of the desk. How many on all sides, Maud? 
 Three twos. 
 
 TEACHER. Charlie, count the pairs of shoes in 
 
SUGGESTIVE LESSONS Xxxi 
 
 the class. One two-pairs, two two-pairs, three two- 
 pairs. 
 
 TEACHER. Frank and Maud, please move, and sit 
 behind Willie and Edna. How many chairs at this 
 end of the table, Edith ? Two chairs and two chairs. 
 
 TEACHER. How many ears at this end, Charlie ? 
 Two two-ears and two two-ears. 
 
 TEACHER. Frank, move in front with Willie and 
 Edna. Tell me in another way, how many chairs at 
 this end, Edith. Three and one. 
 
 TEACHER. Another way, Maud. One and three. 
 
 TEACHER. A shorter way of saying this : two and 
 two is four. How many hands have Charlie and 
 Edith, Willie ? Four. 
 
 TEACHER. Count the slates at this end of the 
 table, Charlie, beginning with Edna's. One, two, 
 three, four. 
 
 TEACHER. Beginning with Maud's, count the 
 pencils, Frank. One, two, three, four. 
 
 TEACHER. How many pupils in our class, Charlie ? 
 Four and two. 
 
 TEACHER. How many dresses in our class, 
 Willie ? Three. 
 
 TEACHER. How many coats ? Three. 
 
 TEACHER. How many suits of clothes ? Three 
 and three, or two threes. 
 
 TEACHER. Class, count the fingers you have on 
 one hand, leaving out the thumb. One, two, three, 
 four. 
 
xxxii SUGGESTIVE LESSONS 
 
 TEACHER. Count them on the other hand, begin- 
 ning with the little finger. One, two, three, four. 
 
 TEACHER. Counting the thumb with the four 
 fingers, how many in all, Edna? Four and one. 
 
 TEACHER. Putting your hands together, finger to 
 finger and thumb to thumb, how many on both 
 hands, Maud ? Four twos and one two. 
 
 TEACHER. Four and one is called five. 
 
 (Give exercises on five, and then give the name 
 six, etc.). 
 
 II. Measuring 
 
 (Lesson in Number given to first grade pupils) 
 
 The children are rejoicing in the possession of 
 their new books, slates, and, above all, rulers. First 
 grade pupils always want rulers, probably because 
 they see them in use in the higher grades. The 
 children come with brand new foot rulers, joy in 
 their hearts and on their faces ; for the teacher has 
 told them that to-day they are to have their first les- 
 son in measuring, and therefore will have a chance to 
 use their treasures. The teacher has provided many 
 different colored slips of paper, varying in length 
 from one foot to six feet (no inches used to-day), 
 which the children are to measure ; also long slips 
 of paper, tape, or ribbon rolled up into a ball from 
 which different lengths can be cut. " Now, children, 
 we shall measure so many things to-day, all these 
 
SUGGESTIVE LESSONS xxxiii 
 
 bright pieces of paper, our aprons, and desks, and 
 we want to see how tall the littlest girl is. Who is 
 the littlest girl, do you think ? " (Class unanimous 
 in favor of Violet.) " Very well ; we will measure 
 Violet, and I think some one had better measure me. 
 I want to know how tall I am." (Hands wave fran- 
 tically in the air.) "But first we must know how 
 long our rulers are ; hold them up straight in front 
 of you to see if they are all the same length." (Cries 
 of Yes, yes.) ^ " Well, how long is that, Katie ? " 
 (Katie does not know.) " Charlie, do you know ? " 
 "Yes, it's one foot." "Right, Charlie. Now chil- 
 dren, how long is each ruler ? " " One foot." " Now 
 let us measure this pretty slip of blue paper first." 
 (Ethel measures and finds it to be one foot.) " This 
 piece." (Hazel measures and finds it to be one 
 foot.) " Surely we have some longer pieces. Who 
 is a good enough guesser to find me a piece about 
 two feet long, a piece twice as long as the ruler ? " 
 (Charlie holds up a piece.) " Well, Charlie, measure 
 it and let us see if you guessed right." (Children 
 anxiously watch the measuring.) " Was he right, 
 children? " (Cries of Yes, yes.) " How long is it ? " 
 "Two feet." "Now I shall give each one of you a 
 slip on your desk ; let me see who can measure the 
 most carefully." (During the few moments that this 
 measuring is going on, the teacher passes quickly 
 from child to child in order to see that each one 
 understands thoroughly what he is doing, questions 
 
XXxiv SUGGESTIVE LESSONS 
 
 here and there regarding the color of the paper, 
 comparing the piece on one desk in color and length 
 to that on another desk, etc., etc.) "I see you all 
 understand that very well indeed. 
 
 " Now I believe you can measure well enough to 
 see how tall I am." (Cries of Oh yes, we can, we 
 can.) " Well, I am going to choose a nice soft ruler 
 and have some quiet child measure me." (Children 
 try to look decorous.) " Well, George, you try." 
 (George carefully measures the teacher's height, 
 while class looks on in breathless interest.) "Well, 
 Katie, how tall am I ? " " Please, I counted four 
 feet." "Hazel?" "I counted five feet." (Most 
 of the class answer five feet.) "Well, George, try 
 again and then tell me." After another careful 
 measurement the class decide that the teacher is five 
 feet and a "little bit more." "Very well, we shall 
 not say anything about this little bit more to-day ; 
 some other day we shall talk about that ; we will say 
 that I am five feet. Now let us measure Violet ; 
 Mary, you try." Violet is measured and found to 
 be four feet. Similarly the tallest boy is measured, 
 Hazel's beautiful golden hair, the ribbon that ties it, 
 the teacher's apron, etc., etc. (All this measuring is 
 done by repeating the unit of measurement one foot; 
 it may be a foot of soft ribbon or a slip of paper 
 or the ruler, but it is the same unit all the way 
 through.) 
 
 "Now, children, we shall have some cutting and 
 
SUGGESTIVE LESSONS XXXV 
 
 measuring, too." (Holding up and unwinding the 
 ball of colored paper.) "I want some one to come 
 and cut off exactly a foot." (John measures a foot 
 very carefully and as carefully cuts it off.) " Give 
 that to Mary ; she wants it for a sash for her doll. 
 Is that enough, Mary ? " (Mary answers No, so John 
 cuts her two feet more.) " Now, children, how many 
 feet has Mary altogether ?" "She has three feet." 
 " How many did she have first ? And then how 
 many ? How many does that make ? Very well, I 
 want some one to make a picture on the blackboard 
 to show how many feet of ribbon or paper Mary 
 has." (Some child comes to the blackboard and 
 draws something like this: | | | .) "That is very 
 well, but sometimes we just make little dots like 
 this " (making three dots on the blackboard, thus \*). 
 " Now, Katie, come and show us with dots how many 
 feet of ribbon Mary has. Let us give Joe some 
 ribbon now for the tail of his kite ; cut him three 
 feet, Ethel." (Ethel cuts three feet, measuring with 
 ruler.) "He says that is not enough, Ethel; give 
 him two feet more. How much has he now, chil- 
 dren ? " Nearly every child will answer five ; those 
 who do not know may count. Teacher may drill 
 by getting Joe to hold the three pieces in one 
 hand, the two in the other, by making three colored 
 dots and two white ones, thus **, or by drawing a 
 line between them, thus ~i~. Many little devices 
 will present themselves to the mind of the teacher. 
 
XXXVI SUGGESTIVE LESSONS 
 
 She, too, will learn by doing. It is better not to con- 
 fine oneself to the combinations of any particular 
 number during the first lessons, and it may be well 
 not to have any addition at all, but simply the meas- 
 urements. At any rate, no effort should be made at 
 this early stage to memorize the combinations. In a 
 similar way may the yard and the inch unit of meas- 
 urement be introduced. This lesson is spoken of as 
 the first lesson. Much has been gained if during 
 this time the child has learned to measure with the 
 units of measurement the inch, the foot, and the 
 yard and got an idea of the use of Number. 
 
 III. Counting and Measuring 
 
 Suggestions for teaching the relation of 3 to 2 and 
 4, 5 to 4 and 6, 7 to 6 and 8, etc. 
 
 After the pupil has a good working idea of 2, and 
 has been drilled in constructive exercises in twos 
 and groups of twos, he will have a fair idea of four, 
 as two twos, but to reach a complete idea of four the 
 pupil must pass through the number three, i.e. he 
 must learn 3 as 1 more than 2, and 1 less than 4. 
 Similar remarks apply to 5, 7, and 9. 
 
 To teach 3, or 5, or 7, etc. 
 
 Give constructive exercises in which the numbers 
 2, or 4, or 6, as the case may be, are prominent, but 
 in which the ideas of 3, or 5, or 7, are present. E.g. 
 with these splints (6) construct two triangles, and 
 then, with the same number of splints, make as many 
 
SUGGESTIVE LESSONS XXXvii 
 
 pickets as possible. Having done so, question the 
 class as to the number of splints it requires to make 
 a triangle, viz. two and one. How many pickets 
 were made ? Two and one. Similarly treat 5 in its 
 relation to 4, etc. 
 
 Many such constructive exercises will show the 
 relation of three to two, viz. as one more than two, 
 or two and one ; now, to show its relation to 4, con- 
 struct a square with these splints (4). How many 
 splints did you use ? Two twos or two and two ? 
 Construct another with these (3). Pupils cannot 
 do it. It takes 2 twos to make a square. They 
 have 1 less than 2 twos, or two and 1, as before. 
 
 Having given many constructive exercises on three 
 in this way, with splints, blocks, measures, etc., the 
 name three may be given as a more convenient way 
 of saying two and one, and one less than two twos 
 (the expression two twos being used as the name 
 four has not yet been given). 
 
 The name three having been given, drill should 
 be given in constructive exercises in which threes 
 and groups of threes are prominent, and four should 
 now be taught as 3 and 1, and the name four given. 
 
 When the pupil knows 3 thoroughly, he really 
 knows 6 as 2 threes, and as he knows 4 also, the in- 
 termediate number 5 may be taught as 3 has been. 
 
 After plenty of drill with different units of meas- 
 ure and groups of units of measure, the number- 
 picture for 3 J may be given, in which the dots 
 
XXXVlii SUGGESTIVE LESSONS 
 
 may represent any unit of measure, and the symbol, 
 3, may now be introduced in association with its 
 number-picture, and this will serve to impress both 
 idea and symbol on the mind. 
 
 IV. The Tens 
 
 " Who was it came in late this morning, John, and 
 spoiled our nice clean record ? " John being the 
 culprit hangs his head and says nothing. " Can 
 any one tell me how late John was ? " (Various 
 answers are given ; the teacher, however, accepts the 
 " few minutes " answer, as the five minute is the unit 
 of measure desired for this lesson.) " Well, some of 
 you are almost right, but I will tell you exactly : he 
 was just five minutes late ; but how do you think 
 I knew, Katie?" "I saw you look at the clock." 
 "Let us all look at the clock." (Holding up clock 
 or paper clock face with hands that turn easily, see 
 how many marks it has to tell time by.) Let us 
 begin at one and count. The class counts from I to 
 XII, it being understood, of course, that the children 
 are not expected to learn these Roman numerals, ex- 
 cepting, perhaps, I, II, III, IIII, and possibly X ; 
 that is, no special effort should be made to learn 
 them. 
 
 " Very well ; I see you can count to twelve ; now 
 what do you call these little things that point to the 
 marks so that we may know which one to take ? 
 Well, this big hand is the one that told me about 
 
SUGGESTIVE LESSONS XXXIX 
 
 John's being five minutes late. Now you see it is just 
 nine o'clock " (moving hands to that time). " Who 
 can move this big hand so that it will be five minutes 
 later than nine ? " (Katie moves it a five-minute 
 space.) "Very well, move it five minutes more, 
 Ethel ; five minutes more, Charlie ; five more, John. 
 I see you all know that from one big mark to another 
 makes five minutes. Now I want you all to count 
 while I move the big hand, to see if you can tell how 
 many 5's I go over." (Moves hand slowly from XII 
 to I ; children count as one five from I to II ; chil- 
 dren count two 5's from II to IV ; children count 
 three 5's, etc., etc.) The teacher drills well on count- 
 ing the 5's before touching upon the hour or the 
 minute unit of measurement, and before counting the 
 10's. The counting (10's and by 10's) from a clock 
 face may be taken up somewhat as follows : 
 
 The teacher has a paper clock face ; the children 
 know that from one big mark (called big to dis- 
 tinguish it from the little minute mark which is to 
 be taken up later) to another there is one 5 ; e.g. 
 " If I move this minute hand from XII to I, how 
 many 5's, children?" "One five." "If I move it 
 from I to II?" "Two 5's." "Five minutes and 
 five minutes. Make a picture of that in dots, 
 Charlie." (These pictures have become familiar to 
 them in previous lessons, so Charlie at once makes 
 ** ** and the class at once recognizes it as 10.) 
 " Very well, indeed ; now I shall put a little red 
 
x l SUGGESTIVE LESSONS 
 
 mark at this ten-minute place " (making red stroke at 
 II on the paper clock face), " so as not to lose it, for 
 we want to count 10's now if we can. Dora, come 
 and move this big hand ten minutes more ; how 
 many 5's must you have, Dora ? " (Dora moves the 
 hand from II to III I, and the teacher puts another red 
 stroke to indicate 10 minutes more, and so on until 
 the six tens are each indicated by the red stroke. 
 The class then counts the 10's from the one first 
 marked to the one last marked, from the last to the 
 first, and in every conceivable way, understanding 
 all the time that any two five minute spaces, no mat- 
 ter what their position as regards the big marks, 
 make ten minutes. Then they count from the clock 
 face, from the paper face with the strokes erased, 
 etc., etc. In this counting by 10's, ten-cent pieces 
 may be used to good advantage.) 
 
 In introducing the minute unit of measurement, 
 some such plan as the following may be adopted : 
 "Now, children, here is our face again. We have 
 been talking all the time about these big marks" 
 (pointing to XII, I, II, III, etc.). "How many are 
 there ? " (" Twelve, twelve.") " Oh, I see you all 
 know that ; well, now I want you to put on your 
 spectacles and see if you can find me any little 
 marks. Well, Dora, show them to me. Now, count 
 how many there are from I to II." Dora counts 
 five. " Now, children, what does each of these little 
 marks show ? " " One minute," These minute marks 
 
SUGGESTIVE LESSONS xli 
 
 may have been introduced in the lesson on the five- 
 minute unit of measurement, but as it is better at 
 first to deal with but one unit of measurement at a 
 time, it is supposed that if there has been any men- 
 tion of these minute marks, it was merely a casual 
 mention ; the time has now come for giving atten- 
 tion to them. 
 
 " Now, children " (taking up the clock face with 
 the 10 minute spaces indicated by the red strokes), 
 " let us see if we were right when we marked these 
 ten minutes ; count the minute marks." Children 
 count the minute marks in each 10 minute space, 
 and agree that the strokes were correctly placed. 
 "Now, let us count 10's once all the way round." 
 (Class counts, " one ten, two tens, three tens, four 
 tens, five tens, six tens, or sixty") "Very well; 
 now the minute hand is going on a journey, but I 
 am going to make him run so fast that he will have 
 to rest quite often ; when he stops to rest, you call 
 out the name of the station " (turns hand quickly 
 from XII to II). (Class calls out, "One 10.") 
 " That is right ; now this station ? " (turning hand 
 from II to IIII). (Class calls Two 10's.) " Good ; ' 
 but can any one tell me what other name this station 
 has ; two tens are how many ? " Perhaps some child 
 can tell. If not, the teacher counts with them, two 
 10's or twenty minutes, three 10's or 30 minutes, 
 four 10's or 40 minutes, five 10's or 50 minutes, six 
 10's or 60 minutes. " And what do you think, chil- 
 
SUGGESTIVE LESSONS 
 
 dren, this last station has another name yet ; it has 
 three names. It has the same name as the little 
 hand ; now you know." (Some one in the class 
 will say hour.) " That is good ; now let us say 
 all together the three names of this station, "Six 
 tens or sixty minutes or one hour." 
 
 Of course, much drill will be necessary and much 
 variety in the modes of presentation. The dollar 
 may be taught in the same way with ten-cent pieces 
 as unit of measurement, e.g. one ten, two tens, or 20 
 cents, three tens or 30 cents . . . ten tens or 100 
 cents or one dollar. So also with metric units. After 
 a thorough drill in lessons of this kind, there will be 
 very little difficulty in such lessons as are indicated 
 in "Suggestion" III, 13. Practical questions are, of 
 course, given as soon as possible, e.g. If I am five 
 feet tall and Violet is four feet, how much taller am 
 I than Violet? Katie's ribbon is six feet, Violet's 
 piece is two feet. How many times can Violet's be 
 cut out of Katie's ? Mary has 20 cents ; how many 
 oranges can she buy if one cost 5 cents ? How many 
 minutes in one hour ? in one-half hour ? How 
 "many ten-cent pieces in fifty cents ? How many 
 dollars in 6 ten-dollar bills ? etc. 
 
 V. Constructive Exercises 
 
 The importance of constructive exercises in teach- 
 ing arithmetic will be evident if we keep in view 
 that number is the instrument of measurement, and 
 
SUGGESTIVE LESSONS xliii 
 
 as such contains three factors ; viz. the vague whole 
 of quantity to be measured, the unit of measure- 
 ment, and the times of its repetition to measure or 
 equal the whole quantity. 
 
 This necessitates from the very first exercises in 
 parting (breaking up or measuring off into units of 
 measure) and wholing (putting together or relating 
 these units to equal the whole). 
 
 Hence, for a short time the beginner may be exer- 
 cised in constructive acts without formal drill on the 
 how-many idea. For example : breaking up a large 
 cube, composed of, say, three small blocks, into its 
 parts, and putting them together again. Breaking 
 up and forming triangles, pickets, squares, lines, etc. 
 
 Having spent some time in such work, the num- 
 bers may be introduced gradually; thus, one and one 
 splint make one picket, one picket and one picket, 
 two pickets, two splints and one splint make a tri- 
 angle, two twos make a square, etc. Thus the need 
 for a certain number in each case is shown, and 
 children see the use and value of number. Such 
 exercises as, Construct a cube with 8 blocks, or rec- 
 tangular " bricks " of given dimensions, according 
 to the advancement of the child, also show the value 
 of number. 
 
 Then, in addition and subtraction, such exercises 
 as : The edge of a slate is measured by the parts 5 
 inches and 6 inches. How long is the slate ? 
 
 A pail is measured by a pint measure, a 2-pint 
 
xliv SUGGESTIVE LESSONS 
 
 measure, and an 8-pint measure. How many pints 
 does the pail hold? etc. Let the children take the 
 actual units and do the measuring, for a time at 
 least, until the operation is thoroughly familiar. 
 
 In multiplication and division : 
 
 How many square inches in a rectangle which is 
 9 in. long and 3 in. wide? Construct such a rec- 
 tangle, or rather let the class construct it, and, in 
 fact, whatever new idea you are introducing, do it 
 by use of constructive exercises, and thus let the 
 child actually see the meaning and use of the dif- 
 ferent operations. Now, let the inch stand for foot. 
 What is the problem ? The result ? 
 
 How many cords of wood in a pile 16 ft. long, 8 ft. 
 high, and 4 ft. wide? Construct such a pile, using 
 cubic inches to represent cubic feet. 
 
 How many yards of carpet, or how many rolls of 
 paper, will be required for a room ? Use strips of 
 colored paper or pasteboard to represent strips of car- 
 pet or paper, and place these side by side on a larger 
 piece of cardboard which represents the floor or wall 
 of the room. 
 
 VI. The Two Measurements 
 
 First by simple constructive exercises show that 
 one measurement carries with it a related one. 
 
 Measure a 6-inch line by a 2 -inch measure, then 
 by a 3-inch measure, and from the class get their 
 result in the form that 3 times 2 inches equals 6 
 
SUGGESTIVE LESSONS 
 
 inches, and 2 times 3 inches equals 6 inches, and then 
 in the form 3 times 2 in. = 2 times 3 in. = 6 in., or 
 2 x 3 in. = 3 x 2 in. = 6 in. Show with dots. 
 
 Then with blocks, cubic inches, 3x2 cu. in. = 
 2x3 cu. in. = 6 cu. in. Use many units of measure 
 until you lead the class to see that 3x2 units = 
 2x3 units = 6 units , whatever unit of measure 
 may be used. 
 
 Similarly with other sets of factors, as 4x8 = 
 8 x 4 = 32, etc. 
 
 Having thus shown that this " law of commutation " 
 is true, simple problems may be worked out, showing 
 how it is true, and the use of this essential principle. 
 Give such a problem as : 
 
 I. A rectangular piece of board (actually present 
 the board to the class) is 6 in. wide arid 8 in. long. 
 How many square inches does the surface measure ? 
 (Cover this board with square inches made of card- 
 board.) 
 
 Using horizontal row as 
 unit of measure, what is 
 the number ? 
 
 Using a vertical row as 
 unit of measure, what is 
 the number ? 
 
 It follows that 8 x 6 sq. in. 
 = 6 x 8 sq. in. 
 This is probably the simplest application of the 
 law of commutation. 
 
x lvi SUGGESTIVE LESSONS 
 
 II. Among 3 boys a number of pennies are divided, 
 giving 6 to each. How many pennies were there ? 
 first six. Let the dots on the board 
 
 second six. 
 
 represent the pennies. I may 
 
 third six. ,..,', 
 
 divide these pennies in one of 
 > | a * two ways, and it is immaterial 
 
 ^ 
 
 
 ' 
 
 which way I divide them. 
 
 / 
 
 I may give the first boy 
 
 A whole of 3 sixes or 6 threes. his wh()le 
 
 the second boy, etc. In that case I should have 6 
 cents taken 3 times = 3x6 cents = 18 cents. 
 
 (b) Again, I may give a cent to the first boy, an- 
 other to the second, and another to the third, making 
 a whole of 3 cents. This may be repeated 6 times, 
 making in all 6 times 3 cents = 18 cents. 
 
 The operations are identical, but viewed from two 
 standpoints. 
 
 VII. Fractions 
 
 1. Let pupils measure a foot line with a 6 in., 4 in., 
 3 in., 2 in., 1 in., and ^ in. measure. Hence, have 
 pupils draw 6 lines, each a foot long, and mark them 
 off with these units. How many equal parts in the 
 first line ? Two. One of these is one out of how 
 many ? How many equal parts in the second line ? 
 Three. One part is one out of how many ? Two 
 are two out of how many? etc., etc. This is how 
 we express one out of two : ^ ft. Ask class to show 
 how to express 1 out of 3, 4, 5, . . . 100, x. 
 
SUGGESTIVE LESSONS xlvii 
 
 2. How many equal parts in the third line ? 
 Four. Show how to express one of these. ^. Now, 
 we wish to express 2 out of 4, instead of 1 out of 4 ; 
 how shall we do so ? By putting 2 in place of the 1. 
 f . Express 3 out of 4, 4 out of 4, 7 out of 12, 8 out 
 of 24, etc. 
 
 3. From this, draw from the class that 1 part of 
 the first line is J of the whole, 2 parts, |, or the 
 whole line ; 1 part of the second line is J ; 2 parts, 
 |-; 3 parts, j, or the whole line ; etc., etc. Finally, 
 
 1 = T 4 2 = 2 8 ^ etc. From many other examples, lead 
 pupils to tell you that 
 
 12345 
 
 |=|= I 3 2=- 5 ^= . . . ad inf.; etc., etc. 
 
 4. The meaning of the numerator and denomi- 
 nator may now be impressed more strongly on the 
 pupils' minds. Thus: What is the name of each 
 part in the fourth line ? A sixth. Express 1 part, 3 
 parts, 6 parts. ^, f , f . Express 4 parts of the last 
 line. 2T' e ^ c - What does the denominator of each 
 fraction tell us ? The name of the part and the size 
 of it. Again, in the fifth line, what is the name of 
 each part ? A twelfth. What is the number of such 
 parts in the whole line ? 12. How many such parts 
 in l the line ? 6. Express the 6 parts ? -f%. What 
 does the 12 tell ? The name. What does the nu- 
 
xlyiii SUGGESTIVE LESSONS 
 
 merator tell? The number of parts that make up 
 the quantity. Give many other examples. 
 
 5. Give a pupil a strip of cardboard and ask him 
 to cut off a piece of it, equal to one of the parts in 
 the third line. How long is this strip of cardboard ? 
 ft. Use it to measure each of these lines that I 
 have drawn (9 in., 1 ft., 1^ ft., 2J ft., etc., any 
 length whatever). How many parts in each ? 3, 4, 
 5, 10, etc. What is the name of each part ? ^ ft. 
 How long, then, is the first line ? f ft. The second? 
 f ft. The third? | ft. The fourth? ^ ft., etc. 
 Use many other examples. 
 
 NOTE. The five points developed above have been, for 
 brevity, developed by means of lines only. Teacher should use 
 many other units, as T V of a dollar, T ^ of an hour, etc., etc. ; e.g. 
 show that 40 cents is 4 dimes or y 4 <y$; $1.30 is 13 dimes or |f $, 
 and so on. Fractions are thus simply another way of express- 
 ing numbers that pupils have handled from the first. 
 
 VIII. Number = The Tool of Measurement 
 
 TEACHER. To-day, boys and girls, let us have a 
 little talk on buying and selling, measuring and 
 counting, etc., with a view to finding out why such 
 processes are carried on. For example, why do peo- 
 ple in buying butter measure (weigh) it ? And why 
 is it dear at one season and cheap at another ? 
 
 PUPIL. Because butter is got only by hard work, 
 and because it is more plentiful at one time than 
 another. 
 
SUGGESTIVE LESSONS xlix 
 
 TEACHER. How is butter generally sold ? 
 
 PUPIL. By the pound. 
 
 TEACHER. Well, how do we generally buy butter ? 
 
 PUPIL. With money. 
 
 TEACHER. When people are selling butter, are 
 they very particular about weighing it (whether 
 they are giving more than a pound or not)? 
 
 PUPIL. Yes. 
 
 TEACHER. When people are buying butter do 
 they always like to get it as cheap as possible, or 
 will a few cents more make any difference ? 
 
 PUPIL. Yes. 
 
 TEACHER. Well, let us consider the question 
 from the buyers' and the sellers' standpoint, and dis- 
 cover what makes a transaction a fair one. First, 
 why is the farmer so particular in weighing his 
 butter ? 
 
 PUPIL. Because it is got only by hard work. 
 
 TEACHER. Now let us consider what it has cost 
 the farmer to produce butter. Name as many things 
 as you can that go to make up the cost. 
 
 PUPIL. He must buy the cows, pay for their feed 
 and attendance, churn the butter, bring it to market, 
 etc. 
 
 TEACHER. Well, then, do you think it right that 
 he should receive some remuneration for his labor 
 and expense by charging for the butter ? 
 
 PUPIL. Certainly. 
 
 TEACHER. Well, why is the one who buys the 
 
1 SUGGESTIVE LESSONS 
 
 butter so anxious to get his right weight and also 
 anxious to buy as cheaply as possible ? 
 
 PUPIL. Because he has to work hard for his money, 
 and desires therefore to make it go as far as possible. 
 
 TEACHER. Therefore, in fairness both to buyer 
 and seller we must measure (weigh), i.e. find out the 
 exact quantity of butter and of money. 
 
 TEACHER. Now, let us suppose that I am a buyer. 
 I wish to buy some eggs, and John Smith (one of 
 the pupils) has this basket of eggs to sell (teacher 
 hands John Smith a basket containing say a dozen 
 blocks, representing eggs). I look at the eggs and 
 I see that they are nice eggs, and I wish to have 
 them. What must I do ? 
 
 PUPIL. You will ask the price of them. 
 
 TEACHER. Well, John, what are you asking for 
 your eggs ? 
 
 JOHN. 16 ^ a dozen. 
 
 TEACHER. What shall I do now ? 
 
 PUPIL. If you think that is a reasonable price, 
 you will buy them. 
 
 TEACHER. Is it right for John to ask me anything 
 for them ? Why ? 
 
 PUPIL. Yes. Because John had to buy the hens, 
 pay for their feed, take care of them, collect the 
 eggs, etc. 
 
 TEACHER. Well then, is it right for me to be so 
 careful about getting nice eggs, and at the same 
 time cheap ones, when John has been put to so much 
 expense and trouble ? Why ? 
 
SUGGESTIVE LESSONS li 
 
 PUPIL. Yes. Because you had to work hard for 
 your money, and if you were not careful with it, you 
 would not have enough for all your needs. 
 
 TEACHER. Well, John, as long as it is a fair bar- 
 gain, here is your money for the eggs. (Teacher 
 lays a pile of pennies on John's desk and takes the 
 eggs.) 
 
 JOHN. Very well, there is just one dozen in the 
 basket. 
 
 TEACHER. Will John at once put the money in 
 his pocket, and will I take the eggs off home ? 
 
 PUPIL. No ; I think John will see if you gave him 
 enough money, and you will see if you have exactly 
 a dozen eggs. 
 
 TEACHER. Is this done because John may think 
 I am dishonest, or wish to cheat him if I could, and 
 because I think John is dishonest ? 
 
 PUPIL. No ; but because people sometimes make 
 mistakes unintentionally. 
 
 TEACHER. Well, let us consider this pile of 
 John's money first, and see how John is going to 
 find out whether he has the right money or not. 
 What is all he knows about it as it stands ? 
 
 PUPIL. He knows that it is a pile of coins ? 
 
 TEACHER. Does he or do any of you know exactly 
 how many there are ? 
 
 PUPIL. No. 
 
 TEACHER. How shall we find out ? 
 
 PUPIL. Count the pennies. 
 
Hi SUGGESTIVE LESSONS 
 
 TEACHER. Can we count them just as they lie in 
 a pile ? 
 
 PUPIL. No. 
 
 TEACHER. What must be done with them ? 
 
 PUPIL. They must be separated into parts. 
 
 TEACHER. (Separates them.) They are separated 
 now. (If pupils can count bj r twos, fours, etc., they 
 may be separated in different ways.) How many 
 parts are there ? 
 
 PUPIL. We cannot tell except by counting the 
 number of parts. 
 
 TEACHER. All of you see if John counts them 
 right. How many, John ? 
 
 .JOHN. Eight parts of 2 cents each (or 16 parts of 
 1^ each, 4 parts of 4^ each, as the case may be), or 
 16 cents. 
 
 TEACHER. Then, I made no mistake. Now, about 
 my eggs ; do any of you know for sure how many 
 eggs there are in this basket ? 
 
 PUPIL. No. 
 
 TEACHER. How can I make sure ? 
 
 PUPIL. By separating into parts and counting 
 the parts. 
 
 TEACHER. Do so for me (one pupil is asked to 
 find out) . How many ? 
 
 PUPIL. Six twos or 12 eggs. 
 
 TEACHER. Into what size parts was the basket 
 of eggs divided ? 
 
 PUPIL. Twos. 
 
SUGGESTIVE LESSONS liii 
 
 TEACHER. What was the number of twos ? 
 
 PtiPiL. Six. 
 
 TEACHER. Let us go back a little , in the case 
 of the eggs and the money, what did we start with ? 
 
 PUPIL. A pile (quantity) of money in one case 
 and a pile (or quantity) of eggs in the other. 
 
 TEACHER. What did we want to find ? 
 
 PUPIL. The exact value or size of the pile. 
 
 TEACHER. How did we do this ? 
 
 PUPIL. By separating into known parts and find- 
 ing the number of parts. 
 
 TEACHER. Couldn't we have found out without 
 separating into parts of some kind ? 
 
 PUPIL. No. 
 
 TEACHER. Well, after we had separated into parts 
 (ones, or twos, or threes), could we not tell, without 
 finding out the number of parts ? 
 
 PUPIL. No. 
 
 TEACHER. Let us now see if we do the same in 
 all cases. Suppose this stick that I have is a mould- 
 ing I bought for framing a small picture, and I wish 
 to know how much moulding I have ; can any of 
 you tell me exactly ? 
 
 PUPIL. No ; but 1 think I could guess pretty near 
 it. 
 
 TEACHER. Yes ; but mere guessing would not be 
 fair either to buyer or seller ; we found that out in 
 the case of butter and eggs. How can I find out 
 exactly ? 
 
liv SUGGESTIVE LESSONS 
 
 PUPIL. By measuring it. 
 
 TEACHER. What shall I use to measure it ? 
 
 PUPIL. One-inch, two-inch, six-inch, foot, or any 
 length-measure you wish. 
 
 TEACHER. Well, it would take too long with a 
 1-inch measure ; we shall use the 6-inch. How am 
 I to measure it, now that I have chosen what to 
 measure with ? 
 
 PUPIL. Apply the 6-inch measure, and mark off 
 as many as there are. 
 
 TEACHER. Well, Frank, you do so for me. What 
 have we done so far ? 
 
 PUPIL. We have separated it into parts. 
 
 TEACHER. Do we know the measure of the mould- 
 ing yet ? What is to be done yet ? 
 
 PUPIL. No, the number of parts must be found by 
 counting. There are six 6-inch parts, or the mould- 
 ing is 3 feet long. 
 
 TEACHER. Now tell me what we started with in 
 the case of the moulding and the successive steps we 
 went through ? 
 
 PUPIL. We started with an unknown length or 
 quantity, divided it into parts, and found the num- 
 ber of the parts. 
 
 TEACHER. Did we do exactly the same thing as 
 in each of the other cases ? 
 
 PUPIL. Yes. 
 
 TEACHER. Similarly, if we wish to find the num- 
 ber of cords in a pile of wood, or the number of 
 
SUGGESTIVE LESSONS l v 
 
 cattle in a field; in fact, if we wish to get a right 
 idea of any quantity, what do we always start with ? 
 
 PUPIL. We always start with the quantity and 
 try to get an exact idea of it. 
 
 TEACHER. In order to do this what must be done ? 
 
 PUPIL. We must choose some part or measure by 
 which to measure the whole, and break up the whole 
 into as many of these parts as it contains. 
 
 TEACHER. What still remains to be done before 
 the quantity becomes known definitely ? 
 
 PUPIL. The number of parts must be found by 
 counting. 
 
 TEACHER. I may now tell you that the part we 
 have used in each case to measure (to get a correct 
 idea of) the whole is called the unit of measure. 
 What unit of measure might we use to measure a 
 pail of milk ? A quantity of potatoes ? etc. . 
 
 PUPIL. Pint, 2-pint, or quart. Peck, bushel, etc. 
 
 TEACHER. But even after we had separated the 
 whole into minor parts by use of the unit of measure, 
 what in each case had to be done before we knew the 
 exact measurement of the quantity we desired to 
 measure ? 
 
 PUPIL. We had to find the number of parts. 
 
 TEACHER. Well, then, what might we say num- 
 ber is ? 
 
 PUPIL. It is that which tells us how many parts 
 or " units " make up the whole quantity. 
 
 TEACHER. Could we find exactly hoiv much a 
 
Ivi SUGGESTIVE LESSONS 
 
 quantity is without finding how many units (parts) 
 make it up ? 
 
 PUPIL. No. 
 
 TEACHER. What do we call this how many ? 
 
 PUPIL. Number. 
 
 TEACHER. For that reason we say briefly that 
 number is the instrument we use in order to measure 
 quantities or is "the tool of measurement." 
 
 IX. Multiplication. 
 
 A LESSON LEADING TO THE MULTIPLICATION 
 TABLE. 
 
 TEACHER. Count the number of hands there are 
 in this class. 
 
 PUPIL. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 
 
 TEACHER. Find out by adding by twos. 
 
 PUPIL. Two and two are four; four and two are 
 six, etc. 
 
 TEACHER. It may be done more quickly still by 
 counting by twos. 
 
 PUPIL. Two, four, six, etc. 
 
 TEACHER. Count the pupils by twos, and tell me 
 how many times there are two hands in the class. 
 
 PUPIL. Two, four, six. Six times two hands. 
 
 TEACHER. I am going to make a large square of 
 these small squares, and I want you to tell me how 
 many small ones there are. How many in each row ? 
 
SUGGESTIVE LESSONS Ivii 
 
 PUPIL. Nine squares. Three in each row. 
 
 TEACHER. Count them by thre 
 
 PUPIL. Three, six, nine. 
 
 TEACHER. How many times have we three small 
 squares to make one large square ? 
 
 PUPIL. Three times. 
 
 TEACHER. Here is a cardboard oblong and a 
 2-inch measure for each of you. I want you to 
 mark off the length and width in units of 2 inches, 
 and find how many times the unit is repeated for 
 each. 
 
 PUPIL. Length, 5 times 2 inches; width, 3 times 
 
 2 inches. 
 
 TEACHER. Add up the length and width, and find 
 out the dimensions of the oblong. 
 
 PUPIL. Length, 10 inches ; width, 6 inches. 
 
 TEACHER. Then what is 5 times 2 inches? What 
 is 6 inches equal to ? 
 
 PUPIL. 5 times 2 inches = 10 inches ; 6 inches = 
 
 3 times 2 inches. 
 
 TEACHER. With these blocks I want you all to 
 lay two rows of blocks from one end of your slate to 
 the other, and then tell me how many twos you had 
 to place to do so. 
 
 PUPIL. Eight twos. 
 
 TEACHER. Now find out how much eight times 
 two is. 
 
 PUPIL. Eight times two blocks is 16 blocks. 
 
 TEACHER. Now here is a stick 16 inches long. 
 
Iviii SUGGESTIVE LESSONS 
 
 What unit shall we use to find how many 2-inches in 
 the length of it ? 
 
 PUPIL. Two-inch measure. 
 
 TEACHER. Now measure it. and tell me how many 
 times 2 inches make 16 inches. 
 
 PUPIL. Eight times 2 inches make 16 inches. 
 
 TEACHER. How much would 8 times 2 blocks be ? 
 
 PUPIL. Eight times 2 blocks is 16 blocks. 
 
 TEACHER. Eight times $2? 2 apples? 2 any- 
 thing ? 
 
 PUPIL. Sixteen. 
 
 TEACHER. You found out what 3 times 2 inches 
 makes; what would 3 times 12 make ? 3 times 2 lb.? 
 3 times 2 anything? 
 
 PUPIL. Six dollars, six pounds, etc. 
 
 TEACHER. Here are some additions I would like 
 you all to do. What shall we say each 2 stands for 
 to-day ? 
 
 f2 2 2 2 
 2222 
 
 PUPIL. Pounds. 
 
 222 etc. 
 
 (to twelve 
 twos). 
 
 2 2 
 2 
 
 TEACHER. Now I would like to know your an- 
 swers. 
 
 PUPIL. 4, 6, 8, 10, etc;, pounds. 
 TEACHER. What do we call the numbers we add ? 
 PUPIL. Addends. 
 
 TEACHER: Can you tell me anything peculiar 
 about the addends in these questions? 
 
SUGGESTIVE LESSONS Hx 
 
 PUPIL. They are all twos. 
 
 TEACHER. How many twos in the first, second, 
 third, etc., questions? 
 
 PUPIL. 2, 3, 4, etc., twos. 
 
 TEACHER. When you were adding the twos did 
 you think of how many addends there were ? 
 
 PUPIL. No. 
 
 TEACHER. What made 4 in the first question ? 
 
 PUPIL. Two and two. 
 
 TEACHER. But tell me the same thing in another 
 way. 
 
 PUPIL. Two times two. 
 
 TEACHER. Now what do you learn from second 
 question? third? etc. 
 
 PUPIL. Three times 2 Ib. make 6 Ib., 4 times 
 2 Ib. make 8 Ib., etc. 
 
 TEACHER. How did you get the numbers 3, 4, 
 etc.? 
 
 PUPIL. By counting the addends. 
 
 TEACHER. Did you do that when adding ? 
 
 PUPIL. No. 
 
 TEACHER. Then you see we have started some- 
 thing different from adding. 
 
 Now write out on your slates what we learn from 
 each of the above questions. 
 
 2 times 2 makes 4, 
 
 p 3 times 2- makes 6, 
 
 4 times 2 makes 8, 
 etc. 
 
l x SUGGESTIVE LESSONS 
 
 TEACHER. How many times did you write the 
 words " times " and " makes " ? 
 
 PUPIL. Eleven. 
 
 TEACHER. Now I will show you a shorter way of 
 writing it, as that takes too long. For " times " we 
 use the sign " x ", and for "makes" the sign " = ," 
 which means equals. Then we have 
 
 2x2 = 4, 
 
 3x2 = 6, 
 
 4x2 = 8, 
 
 etc. 
 
 TEACHER. This is what we call the multiplication 
 table for two times, and I would like you all to learn 
 it for me, because you see how handy it is to say that 
 8 times 2 anything is 16, instead of adding up 8 twos. 
 I will show you how handy it is. We will build up 
 an oblong block of small cubic inch blocks, and I 
 would like you to find out, when it is built, how many 
 small blocks we have used, without counting or add- 
 ing. (Size 5" high, 2" wide, 2" thick.) How will 
 you do it ? 
 
 PUPIL. By finding how many twos in it, 
 
 TEACHER. How many layers have we ? 
 
 PUPIL. Five. 
 
 TEACHER. How many in each layer ? 
 
 PUPIL. Four. 
 
 TEACHER. Yes ; but how many twos is that ? 
 
 PUPIL. Two twos. 
 
SUGGESTIVE LESSONS Ixi 
 
 TEACHER. Well, how many two-twos shall we 
 have in five layers? 
 PUPIL. Five two-twos. 
 
 TEACHER. How many twos will that make ? 
 PUPIL. Ten twos. 
 TEACHER. Now, what is ten twos ? 
 PUPIL. Twenty blocks, 20 cu. in. 
 
 X. Reduction 
 
 The following lesson is suggested to precede Les- 
 son 23, questions 1, 2, 7, 8. Establish in the mind 
 of the children the relation between the pint and 
 the quart by actual measurement. Let the teacher 
 measure 3 qt. of water into a pail without the class 
 knowing how much is put in. Ask the class indi- 
 vidually to state how much water is in the pail. 
 Answers will vary, thus showing the necessity for 
 accurately measuring the quantity. Pupils will sug- 
 gest the quart as the unit of measure. On counting, 
 as the water is measured, they will get the number 
 3 ; i.e. there were 3 qt. in the pail. Write on the 
 board 3 qt. 
 
 What number will you get if you measure with 
 a pint? Measure; the pupils count 6, i.e. 6 pt. 
 Write on the board 3 qt. = 6 pt. In the same way, 
 without the class knowing how much water is put 
 in the pail, measure 2 qt., 4 qt., etc. Let the class 
 count the corresponding numbers and derive 2 qt. = 
 4 pt., 4 qt. =8 pt., and so on. 
 
Ixii SUGGESTIVE LESSONS 
 
 This by actual measurement. Now express these 
 relations without actual measurement. 
 
 5 qt. = ? pt. 6 qt. = ? pt. 8 qt. = ? pt. 
 ? qt. = 4 pt. ? qt. = 6 pt. ? qt. = 10 pt. 
 and so on. 
 
 Again : 
 
 If each dot represents 1 pt., what will 2 dots 
 represent (1 qt.)? 
 
 Count by pints (1, 2, 3, 4, 5, 6). Count by quarts 
 (1, 2, 3). 6pt.= 3 qt. 
 
 If these dots represent the quantity of water in 
 the pail, each dot representing 1 pt., how much water 
 is in the pail? (4 qt.) How many pints? (8 pt.) 
 4 qt. = 8 pt. 
 
 If these dots represent the quantity of water in a 
 pail, how many pints are in the pail? (10.) How 
 many quarts? (5.) 10 pt. = 5 qt. And so on. 
 
 Ask pupils to represent on the board the water in 
 a pail containing, say, 4 qt. 
 - What other measurement is indicated? (8 pt.) 
 
 What is assumed about the dots ? 
 
 Do the same kind of work, putting into the pail 
 3 qt. 1 pt., 2 qt. 1 pt., 4 qt. 1 pt., and so on. Use 
 
SUGGESTIVE LESSONS Ixiii 
 
 the dots to give facility in operation as soon as the 
 actual measurement has been done. 
 
 It will be seen that in the above work the children 
 start with a whole unmeasured quantity which they 
 have a motive for measuring. 
 
 In order to measure the quantity, they select a 
 unit, and while measuring count the number which 
 arises out of the measurement. The unit and the 
 number together (3 qt.) measure the quantity, which 
 is now definitely known. A second measurement 
 with a different unit gives rise, in a similar way, 
 to 6 pt., and establishes the relation 3 qt. = 6 pt. 
 After the process is once understood by actual 
 measurement, the symbolic representation by means 
 of dots enforces and gives facility in the operations. 
 Similarly, for the more complex reductions, 3 qt. 1 pt. 
 = 7 pt. and 7 pt. = 3 qt. 1 pt. 
 
SUGGESTIONS 
 
 Lessons 1-8 
 
 " Suggestions to Teachers," Sections I. -IV., have 
 special reference to these lessons. 
 
 Lesson 9 
 
 From the preceding work the children know that 
 2 and 3 are 5. Draw a line 15 in. long and measure 
 one part 12 in. long. How long is the other part ? 
 Test the answers by measuring. 
 
 Draw a line 25 in. long and measure one part 3 in. 
 long. How long is the other part ? Measure. 
 
 Similarly draw and divide a line 35 in. long. A 
 yard stick divided into inches can be used for meas- 
 uring. Express the results orally and in writing on 
 the board. Give many practical questions such as 
 question 2. 
 
 In question 3 let the class note where the 5-min. 
 mark is. Turn the hand through 2 minute spaces. 
 How many more to reach the 5-min. mark ? Simi- 
 larly for 15 min. Turn the hand through 3 minute 
 spaces. How many more ? Similarly for 25 min. 
 
 Ixiv 
 
SUGGESTIONS 
 
 Turn through 22 minute spaces. How many more ? 
 Continue this work until the sum equals 55 min., 
 constantly giving the children the opportunity to 
 make inferences. 
 
 The children will then infer that 
 
 62 + 3 = 65. 72 + 3 = 75. 
 
 This work at the board should precede Lesson 1, 
 and, in fact, all or nearly all of the succeeding 
 lessons should be preceded by oral work on the part 
 of the teacher with the class. Teach and use con- 
 tractions from the first, and constantly intersperse 
 the work with simple practical questions such as 
 questions 2, 4, 7, 13. 
 
 In adding and subtracting use many different units 
 as in questions 16, 17, and 18. 
 
 Lesson 10 
 
 Introduce this lesson by actual measurement as in 
 Lesson 9. In question 13 let it be understood that 
 each dot represents some unit of measure as 1 in., 
 1^, 2 lb., 3 yd., and repeat the question, using differ- 
 ent units. Thus, 5 3-yd. = 4 3-yd, + 1 3-yd., and 
 so on. 
 
 In question 15 let the class discover that there 
 are only four combinations that give 5. 
 
 Gradually develop the idea that the unit and the 
 number together measure quantity. Thus, let the 
 teacher draw on the board a line without the pupils 
 
SUGGESTIONS 
 
 knowing how long it is. Ask the pupils to judge 
 of its length. Answers will vary, showing the need 
 of a definite method of measurement. Measure 
 with a foot measure. How many times did you 
 measure? (4.) Thus the pupils had an unknown 
 quantity to be measured and a unit of measure. In 
 process of measurement they got by counting the 
 number 4. Thus the quantity, which is now known 
 to be 4 ft., is definitely measured in terms of the 
 number 4 and the unit 1 ft. Other quantities and 
 units may be chosen. See " Suggestions to Teachers," 
 L, 12 and 13. 
 
 Lesson 11 
 
 Questions 1, 2, 3, 10, are a preparation for sub- 
 traction. The pupils have already learned that 2 
 and 3 are 5 (Addition), which carries with it the 
 idea that 2 and 3 are 5 (Subtraction). In oral drill 
 put the questions also in the form of Lesson 1 2, ques- 
 tion 19. See " Public School Arithmetic," 42, 44. 
 
 In such questions as 12, 13, let the teacher place 
 the points without the pupils knowing how far they 
 are apart. Measure first with a yardstick, and 
 again with a foot rule. In question 17 apply the 
 same principle to the water put into the pail. As 
 soon as it can be done intelligently suggest the more 
 economical way of reducing without actually measur- 
 ing. The placing of dots as in question 18 will 
 assist in this. See " Suggestions," X. Reduction. 
 
SUGGESTIONS Ixvii 
 
 Lesson 14 
 
 Before this lesson is studied let the pupils measure 
 different lengths, as the length of the table, and 
 express their results thus, 1 yd. 2 ft. 6 in. Have 
 the children read these results. This will show the 
 necessity of the three units of length. Having done 
 this, measure such lengths as are given in the lesson; 
 add, and verify results by actual measurement. 
 
 Make such simple practical questions as 1321. 
 
 Lesson 15 
 
 In this lesson and also in subsequent lessons, when 
 necessary, use the foot ruler or clock face, and 
 illustrate the additions as in Lesson 1. 
 
 Give many questions in subtraction, here and else- 
 where, complementary to such questions as 2, 3, 4, 6, 
 8, 9, etc. 
 
 Thus: 
 
 Subtract: *7 *17 26 27 62626 
 4 14 24 3 2 21 4 
 
 Lesson 17 
 
 Read question 1, not 2 + 2 = 4, 4 + 2 = 6, but 2, 
 4, 6 ; 1, 3, 6, etc. 
 
 In adding such questions as 2, the lowest number 
 or 12 (see footnote, page 40) had better be omitted 
 after a little practice, the pupil simply saying 14, 16. 
 
 * Read 4 + 3 = 7; 14 + 3 = 17. 
 
Ixviii SUGGESTIONS 
 
 In adding 21 / to 13 think of the 2 in 21^ as 2 
 dimes, and the 1 in 13^ as 1 dime. 
 
 Lesson 18 
 
 In the operations in questions 7, 8, and 9, let the 
 pupil fancy that he is doing addition with the sum 
 at the top, and as he works set down the figures 
 3 and 1. 
 
 Lesson 19 
 
 Use such questions as 16, 17, 18, gradually to 
 develop the idea. (1) that the quantity is found by 
 multiplying the unit by the number, (2) that the 
 number is found by dividing the quantity by the unit, 
 (3) that the unit is found by dividing the quantity 
 by the number. 
 
 Lesson 30 
 
 Note that in question 1 the sums are found by 
 addition. In question 2 we find that the $ 2 in the 
 last column is repeated 6 times. 
 
 Thus we think of the unit $2 and the number 6, 
 giving as their product $ 12. 
 
 For this change from addition to multiplication 
 see the "Public School Arithmetic," 47. 
 
 Read the sign x as times, thus 3 x $ 2 = 3 times 
 
 Use the dots to develop the law of commutation, 
 viz. : 2x3 = 3x2; 4x6 = 6x4, etc. 
 
SUGGESTIONS Ixix 
 
 Lesson 31 
 
 Develop some parts of the multiplication tables by 
 actual measurement with units of different lengths. 
 Thus, cut out of cardboard 12 units of lengths, 
 respectively, 1 in., 2 in., 3 in., 12 in. long. Draw 
 a line on the board and measure along this line with 
 each unit, twice. Then, with a yardstick, measure 
 results, and we have the table of 2. Or, again, 
 repeat the unit 2 in. from 1 to 12 times, write the 
 corresponding results, and by the law of commuta- 
 tion we have the table of 2. 
 
 Extend the table as in questions 3, 4, 7, 8, 9. 
 
 Have the class make simple practical examples, 
 founding them on questions 11 and 12, or give them 
 such a price list as is found on page 75, question 23. 
 
 Lesson 33 
 
 Bring out the fact that in measuring distance we 
 have the units 1 in., 1 ft., 1 yd., and 1 mi. We 
 measure the value of things with the units 1^ and 
 $1. We measure milk with the unit 1 qt., kerosene 
 Avith the unit 1 gal., and so on. Hence to measure 
 area (a different kind of quantity), we need a new 
 unit, and this we naturally derive from the unit 
 1 in. Give plenty of work to precede this lesson, 
 and let the children draw and cut out and divide 
 simple areas. 
 
 Teach the area of an oblong somewhat after this 
 fashion. Have the pupils draw oblongs, say 4 in. 
 
Ixx SUGGESTIONS 
 
 by 3 in. Divide them into square inches. Count 
 the number of square inches. Count again by 
 4 sq. in. How many (3 4 sq. in. or 12 sq. in.)? 
 Count again by 3 sq. in. How many (4 3 sq. in. or 
 12 sq. in.)? Which of the three methods is most 
 economical? (Either of the last two, i.e. find tha 
 area by multiplication, not by addition.) What 
 would be the area if the oblong were 5 in. long 
 and 3 wide ? 6 in. long ? 8 in. long ? 5 in. long 
 and 4 in. wide, and so on ? Use other units of length 
 (2 in., 3 in., 1 ft., 1 yd., 1 mi.). 
 
 Lesson 34 
 
 The purpose of this lesson is to prepare the way 
 for division. Just as the preceding work in addition 
 and subtraction has made of the two substantially 
 one process, so the child should be led to think of 
 multiplication and division as substantially one pro- 
 cess. In multiplication 4 and 2 are factors of ? 
 In division 4 and ? are factors of 8. 
 
 See " Public School Arithmetic," preface, 2, and 
 also 60-63. 
 
 Lesson 35 
 
 Write the multiplication table of 2 on the board 
 in a column, thus : 
 
 2 x 1 in. = 2 in. 
 2 x 2 in. = 4 in. 
 
 2 x 12 in. = 24 in. 
 
SUGGESTIONS l xx i 
 
 Drill thus : 
 
 l of 2 in. = ? 1 of 4 in. = ? J of 6 in. = ? and 
 so on in any order. Also J of 20 in. = ? \ of 
 200 in. = ? and so on. Illustrate, if necessary, by 
 drawing lines 4 in., 6 in., 8 in., etc., and dividing 
 them into two equal parts. 
 
 Similarly, drill thus : 
 
 4 in. -5- 2 in. = ? 6 in. -s- 3 in. = ? 8 in. -=- 4 in. ='? 
 and so on in any order. Also 40 in. -v- 2 in. = ? 
 80 in. -j- 4 in. = ? 80 in. -r- 40 in. = ? and so on. 
 Illustrate, if necessary, by cutting from cardboard 
 strips 2 in., 3 in., 4 in., 5 in., etc., and using these 
 lines as units to measure the lines respectively 4 in., 
 6 in., 8 in., etc. Drill until this is mastered in any 
 order. Use other units instead of 1 in., as $1, 1^, 
 1 lb., 1 qt., etc. Throughout this work give many 
 practical examples. (See Lesson 34, questions 
 8-14.) Give also such examples as the following : 
 16 pt. -r- 2 pt. = ? How many quarts in 16 pt. ? 
 
 8 qt. -r- 4 qt. = ? How many gallons in 8 qt. ? 
 16 qt. -f- 8 qt. = ? How many pecks in 16 qt. ? 
 
 8 pk. -f- 4 pk. = ? How many bushels in 8 pk. ? 
 24 in. -j- 12 in. = ? How many feet in 24 in. ? 
 
 -|- of 4 pt. = ? What unit of measure ? \ of 8 qt. = ? 
 What unit ? J of 16 qt. = ? What unit ? \ of 
 8 pk. = ? What unit ? J of 24 in. = ? What unit ? 
 
 Name the odd numbers from 1 to 25. .What num- 
 ber must be subtracted from these odd numbers to 
 make them exactly divisible by 2 ? 
 
SUGGESTIONS 
 
 It is expected that with the price list furnished ir. 
 question 23, the pupils will make examples similar 
 to questions 14, 21, 22. 
 
 Lesson 36 
 
 Correlate the work in ratio with counting and 
 measurement. For instance, measure a 12-in. line 
 with a 2-in. unit, a 3-in. unit, a 4-in. unit, a 6-in. 
 unit. Count the number of measurements each 
 time. 6 is often called the ratio of 12 in. to 2 in., 
 4 that of 12 in. to 3 in., 3 that of 12 in. to 4 in., 
 and 2 that of 12 in. to 6 in. Again what part of 
 12 in. is equal to 6 in. ? (J) ^ is often called the 
 ratio of 6 in. to 12 in., and so on. 
 
 After the children have noted by drawings the 
 simple instances given in the lessons, write the mul- 
 tiplication table of 2 on the board, thus : 
 
 2 times 
 
 4*" 
 
 12 ^" 
 
 Then note from this table what 2 is the ratio of 
 and what J is the ratio of. Give such examples as 
 J- is the ratio of 4^ to ? 6^ to ? Of ? to 12*. Of? 
 to!8 Of 11^ to? 
 
SUGGKSTiONS Ixxiii 
 
 Give similar examples with 2 as the ratio. Use 
 other units. Give easy concrete examples similar 
 to the questions in Lesson 40. 
 
 Lesson 38 
 
 See suggestions, Lesson 36. 
 
 Lesson 39 
 
 Do as much actual measurement as is necessary to 
 illustrate this lesson. Measure the length and width 
 of the room, of tables, desks, books, height of pupils, 
 and so on. Note the size of books as measured 
 by the number of pages. Measure the quantity of 
 water in a pail or pitcher, the unit being 1 pt. or 
 1 qt. or 1 gal. Weigh different articles, and find 
 the weight of different pupils. Make it clear that in 
 order to measure any quantity we must use a suitable 
 unit of measure and we must find the number of units 
 that measures the quantity. 
 
 Lesson 42 
 
 Be sure that the pupils know by actual measure- 
 ment that 1 gal. = 4 qt., and similarly with other 
 tables referred to in this book. 
 
 Lesson 43 
 
 Make the method of finding the area of an oblong 
 clear by drawings on paper and on the board. 
 Emphasize the fact that the area is measured by 
 
Ixxiv SUGGESTIONS 
 
 the number and the unit. Develop the fact that the 
 number measuring the area is the product of the 
 numbers measuring the sides. Then use this fact 
 to find the measure of the areas and the areas of the 
 oblongs. Measure the dimensions of oblongs in the 
 room and calculate their areas. Let this work as 
 usual precede the study of the lesson by the children. 
 
 Lesson 45 
 
 See suggestions, Lesson 35. Use the table of 3. 
 
 Lesson 47 
 
 Let the oral work preceding this lesson be objec- 
 tive until it is clearly understood. In question 3, 
 for instance, draw lines 1 J ft. and 2 ft. long. Meas- 
 ure with a -J ft. unit, when the number of measure- 
 ments will be respectively 3 and 4, hence 1| ft. = f ft. 
 and 2 ft. = J ft. How can you reduce 2 ft. to half 
 feet without actually measuring ? Similarly, in ques- 
 tions 4 and 5, measure if necessary. In question 8, 
 take a string 6 in. long, cut off one part 4% in. long. 
 How long is the remainder ? Hence, 4^ in. + 1^ in. 
 = 6 in. Similarly with other parts of this question. 
 
 Lesson 48 
 
 In such questions as 16 let it be clearly under- 
 stood, not that 4 is contained in 16 4 times, but that 
 4 is contained in 16 tens 4 tens. Drill on such ques- 
 tions as 18 until the pupil can readily see in any 
 
SUGGESTIONS 
 
 number the next smaller number of which 4 is a 
 factor and can give the remainder. Such measure- 
 ments as are indicated in question 19 will give mean- 
 ing to the process. Let the pupils state simple 
 practical questions corresponding to 20 and 21. 
 
 Lesson 49 
 
 Practise reduction at first by actual measurement. 
 Where this is done it is better that the teacher or 
 some pupil should fix on some quantity without the 
 class knowing what it is. Measure this quantity 
 with two or more units, and let the result be, say, 
 
 2 ft. 4 in. Measure with the smaller unit, and the 
 result is found to be 28 in. This, stated as a relation 
 of equality, is 2 ft. 4 in. = 28 in. In this work the 
 children have the unknown quantity, the unit or units, 
 the number, then the measured quantity, and the 
 relation of equality growing out of two separate 
 measurements with different units. How do such 
 expressions as 2 ft. 6 in., 3 qt. 1 pt., and 1 hr. -30 
 min. arise in the measuring process ? 
 
 As soon as this measuring process gives signifi- 
 cance to the operation, let the pupils deduce the rule 
 and use it as the more economical method. You 
 reduce 3 gal. 2 qt. to quarts by multiplying 4 qt. by 
 
 3 and adding 2 qt. to the product. Practically it is 
 awkward to be constantly changing the multiplier. 
 Hence, by the law of commutation, we have : To 
 reduce gallons and quarts to quarts, multiply the 
 
SUGGESTIONS 
 
 number of gallons by 4 and add the number of 
 quarts. What is the multiplier in reducing yards 
 to feet? 
 
 Lesson 50 
 
 An oblong 4 in. long and 3 in. wide contains 12 
 ;(]_. in.; one 4 2-in. long and 3 2-in. wide contains 
 [2 2-in. squares or 12 4 sq. in., i.e. 48 sq. in. An 
 o')long 10 in. (5 2-in.) long and 8 in. (4 2-in.) wide 
 contains 5x4, or 20, 2-in. squares or 20 4 sq. in., 
 i.e. 80 sq. in. Here the unit that measures the 
 length is 2-in. and that which measures the area is 
 the 2-in. square or 4 sq. in. 
 
 Lesson 52 
 
 Teach the pupil to take ^ of a quantity by divid- 
 ing it by 3. This is much more economical practi- 
 cally than for him to think of one operation for 
 finding J of a quantity and another for dividing 
 it by 3. Teach him to take f of a quantity by 
 dividing it by 3 and multiplying by 2, or by multi- 
 plying the quantity by 2 and dividing the product 
 by 3. 
 
 Lesson 54 
 
 See suggestions, Lesson 36. 
 
 In order to make the oral lesson in ratio apply to 
 the solution of problems, it is not sufficient merely 
 to state the ratio of the given quantities. State also 
 the ratio of their cost, for instance. What is the 
 
SUGGESTIONS Ixxvii 
 
 ratio of 20 Ib. to 5 Ib. ? Of 5 Ib. to 20 Ib. ? Of 
 the cost of 20 Ib. of sugar to that of 5 Ib. ? Of the 
 cost of 5 Ib. of sugar to that of 20 Ib. ? If 5 Ib. of 
 sugar cost 25 what will 20 Ib. cost? If 20 Ib. 
 of sugar cost 104^, what will 5 Ib. cost? 
 
 Again, what is the ratio of 20 mi. to 4 mi. ? Of 
 the time a boy can ride 20 mi. to that which he will 
 need to ride 5 mi. ? If a boy rides on his bicycle 
 5 mi. in ^ hr., how long will it take him, at the 
 same rate, to ride 20 mi. ? Connect closely the ratio 
 and its reciprocal. What is the ratio of 20 mi. to 
 5 mi. ? What is the (reciprocal) ratio of 5 mi. 
 to 20 mi. ? So also with practical examples, as 
 follows : 
 
 (1) If a man drives 5 mi. in f hr., how long will 
 it take him, at the same rate, to drive 20 mi. ? 
 
 (2) If a train ran 20 mi. in 36 min., how long did 
 it take on the average for each 5 mi. ? 
 
 Questions (1) and (2) involve reciprocal ratios. 
 
 Lesson 57 
 
 Question 10, etc. Take points on the board 2 ft., 
 3 ft., and so on apart, without the pupils knowing 
 the distance. Measure with the 1-ft. unit. Measure 
 also with the units | ft., J ft., \ ft., and deduce the 
 relations 2 ft. = f ft. = f ft. = f ft, ; 3 ft. = f ft. 
 = f ft. = Jj 2 - ft. Develop the rule that to reduce 
 a number of feet to halves, thirds, or fourths, you 
 multiply the number of feet by 2, 3, or 4, as the case 
 
Ixxviii SUGGESTIONS 
 
 may be. Similarly develop the fact that 2J ft. = | ft., 
 and the corresponding rule. So also for thirds and 
 fourths. Apply your rules. 
 
 Lesson 59 
 
 This lesson is an exercise in numeration and nota- 
 tion, with special reference to Lesson 60, and should 
 be thoroughly mastered. Special drill should be 
 given in questions like 12, 13, 14, 15. 
 
 Lesson 60 
 
 As the pupils add and carry or subtract, be sure 
 that they understand the place value of the different 
 numbers. Question 6 is a preparation for the sub- 
 traction that follows in questions 7 and 8. 
 
 Lesson 61 
 
 When such questions as 5 and 10 occur in this 
 and the following lessons, frequently have the pupils 
 make out bills neatly and accurately. 
 
 Lesson 63 
 
 Note that any number ending in or 5 is divisible 
 by 5. As in question 6, find the common factor of 
 pairs of numbers and illustrate its meaning by meas- 
 urement. To bring out the meaning of common 
 factor more effectually, select a unit that is a factor 
 of only one of the numbers and measure the corre- 
 sponding qaantities with the given unit. 
 
SUGGESTIONS 
 
 Lessons 66-68 
 
 Lessons 66, 67, 68, are review lessons. If any 
 question is found to be too hard, make easier ques- 
 tions of the same kind leading up to the problem in 
 the book. 
 
 In question 17, page 141, the whole quantity is 
 850, the number is 5 and the unit is $10 (i.e. $50 
 -i- 5), which is the cost of the chain. In Lesson 68, 
 question 4, the pupil is given the unit 12^ and the 
 number 3J to find the quantity 3J x 12 or 42^. 
 The following are the two questions required : 
 
 (1) At 12^ a yd., how many yards of ribbon will 
 cost 42^? 
 
 (2) If 3| yd. of ribbon cost 42^, what is the cost 
 per yd. ? 
 
 Lesson 74 
 
 The method of finding the volume of a prism is 
 indicated in question 1. Count again first by 2's, 
 then by 6's (3 x 2). Count again first by 3's, then 
 by 12's (4 x 3), and so on. Let pupils measure the 
 dimensions of prisms in the room, such as boxes, 
 and calculate their volumes. What units of volume 
 have we? (1 cu. in., 1 cu. ft., 1 cu. yd., 1 cord.) 
 Why have we no larger unit of volume than 1 cord ? 
 
 Lesson 76 
 
 Develop clearly and apply in practice that to take 
 f of 128 you divide $28 by 7 and multiply the 
 
Ixxx SUGGESTIONS 
 
 quotient by 3 ; that to take f of a quantity, you 
 divide the quantity by 8 and multiply the quotient 
 by 5 ; that, in general, to take a fractional part of 
 a quantity, you divide by the denominator and 
 multiply by the numerator. Can you first multiply 
 by the numerator and then divide by the denomi- 
 nator ? Show instances where the latter method 
 is more economical, (f of $13, | of $3|.) See that 
 the pupils master this principle and are able to use 
 either method quickly and accurately. 
 
 Lesson 77 
 
 Develop addition and subtraction of fractions in 
 the order indicated in Lessons 77, 78, 79. Much 
 oral work will be needed. Have the pupils illus- 
 trate their work by placing dots and marking them 
 off as in questions 8, 15, 19. In some cases verify 
 by actual measurement. Let the pupils memorize 
 the simpler sums and differences. Let the work 
 gradually develop into the more generalized form 
 indicated by Lesson 78, questions 9, 10, 11. Finally, 
 have the children perform the simpler operations 
 mentally. Throughout the oral work preceding 
 these lessons give and let the pupils give many illus- 
 trative practical examples. 
 
 Lesson 80 
 
 Many interesting and practical questions may be 
 asked in connection with this lesson. Red rasp- 
 
SUGGESTIONS Ixxxi 
 
 berries are sold in pint boxes because they would 
 crush if put up in quart boxes. Black raspberries, 
 gooseberries, etc., being firmer, are sold in quart 
 boxes. Why are strawberries early in the season 
 frequently sold in pint boxes ? Which is the fairer 
 way to buy and sell eggs, by the pound or by the 
 dozen ? Why ? Illustrate questions 13 and 14 by 
 actual measurement. The principles r indicated in 
 question 22 are important and of frequent appli- 
 cation. 
 
 Lesson 81 
 
 Precede this lesson in sections by exercises with 
 the class, making questions similar to those in the 
 lesson, easier at first but gradually becoming more 
 difficult. Questions 5 and 6 illustrate this method. 
 
 The following examples relate to question 1 : 
 
 What quantity is measured by: 
 
 1. The number 4 and the unit 1 pt.? (2 qt.) 
 
 2. The number 4 and the unit 1 qt. 1 pt.? (6 qt.) 
 
 3. The number 4 and the unit 2 qt. Ipt.? (10 qt.) 
 
 4. The number 6 and the unit 2 qt. 1 pt.? (15 qt.) 
 
 5. The number 8 and the unit 2 qt.? (4 gal.) 
 
 6. The number 8 and the unit 2 gal. 1 qt.? 
 (18 gal.) 
 
 7. The number 6 and the unit 1 gal. 2 qt.? 
 (9 gal.) 
 
 8. Find the number of gallons of milk in 6 cans, 
 each of which contains 2 gal. 2 qt. 
 
Ixxxii SUGGESTIONS 
 
 Lesson 86 
 
 In question 8 the word "accurately" is emphasized, 
 because while it is important that pupils should work 
 rapidly, it is essential that their work should be accu- 
 rate. The question to the class should be not, " How 
 many questions did you work correctly ? " but " How^ 
 many of you worked correctly every question that you 
 did?" 
 
 Lesson 87 
 
 If pupils are to master long division so that they 
 will not lose time in guessing in a haphazard way at 
 the successive quotients, they must become expert in 
 the use of the trial divisor and the trial dividend. 
 
 Lesson 88 
 
 In questions 11 and 12 emphasize the place value 
 of the numbers. $ 29 divided by 4 gives $ 7 as quo- 
 tient and $ 1 as remainder. $16 dimes equals 
 16 dimes. 16 dimes divided by 4 equals 4 dimes. 
 4^ divided by 4 equals 1^. The quotient is 17.41. 
 Similarly with the long division. 
 
 Lessons 91-94 
 
 These lessons indicate the method of teaching 
 decimals. First make use of the pupil's knowledge 
 of the notation and numeration of dollars and cents. 
 
SUGGESTIONS Ixxxiii 
 
 Then use the metric stick, since a practical know- 
 ledge of it is useful in itself, and since it makes the 
 development of decimals objective. Pass on from 
 this to quantities expressed in terms of other units 
 of measurement. 
 
 Lesson 95 
 
 Percentage is simply a special case of fractions, 
 and should be so taught. A quantity divided into 
 fourths is measured by 4 units, and each part is ^ of 
 the quantity. Three parts are equal to f of the quan- 
 tity. Similarly with regard to quantities divided 
 into fifths, sixths, etc. A quantity, considered in 
 percentage, is divided into 100 parts, and is meas- 
 ured by 100 units. Each part is yro or 1 % f the 
 quantity, and 5 parts are YOQ- or 5 % of it. On the 
 other hand, 1 % of a quantity is one-hundredth of it, 
 and 5 % is five-hundredths of it. 
 
 Lesson 100 
 
 Section XIII. contains questions in review. They 
 will be found to be especially helpful in preparing 
 the pupils for the opening chapters of the " Public 
 School Arithmetic." 
 
ARITHMETIC 
 
 SECTION I 
 
 Lesson 1 
 
 1. Count the number of girls in your room. How 
 many ? How many boys ? How many boys and girls ? 
 
 2. Count the number of windows in the room. Of 
 window panes. Of windows in the school building. 
 
 3. Count the number of desks in your room. The 
 number that are not occupied. 
 
 4. Count the number of boards in the floor of 
 your room from one side to another. 
 
 5. Count the number of letters in this example. 
 
 6. Count the number of pieces of crayon in a box 
 of crayon. 
 
 7. Count the number of inches in a foot. Of 
 inches in a yard. Of feet in a yard. 
 
 8. Measure with a yardstick and count the num- 
 ber of yards in the width of the room. In the length. 
 
2 ARITHMETIC 
 
 9. Count the number of steps you take in going 
 from one side of the room to the other. From the 
 front to the back of the room. 
 
 10. Measure with a foot rule and count the num- 
 ber of feet in the width of the room. In the length. 
 
 11. How many yards long is the blackboard ? How 
 many feet? How many feet high? 
 
 12. How many inches long is this book? How 
 many wide ? How many pages does it contain ? 
 
 13. How tall are you? How old? How many 
 pounds do you weigh? 
 
 14. How many days of this week are gone ? How 
 many days of this month? Weeks of this month? 
 How many months of this year? 
 
 15. Fill a quart measure with a pint measure. 
 How many times do you empty the pint measure? 
 How many pints in a quart? 
 
 16. Fill a gallon measure with a quart measure. 
 How many quarts in a gallon ? 
 
 17. Fill a gallon measure with a pint measure. 
 How many pints in a gallon ? 
 
 18. How many pennies in a nickel? In a dime? 
 In a 25-cent piece ? 
 
 19. Count on a clock face the number of minutes 
 in a quarter of an hour. In half an hour. In three- 
 quarters of an hour. In one hour. 
 
LESSON 2 B 
 
 20. Ask your teacher to make raps with a stick, 
 strokes with a bell, or to pronounce the names of 
 letters. Count the number each time. 
 
 21. How can you get the expression 5 yd. by 
 measuring? What number will you obtain if you 
 measure the same distance with a foot rule? 
 
 22. How can you get the expression 3 qt. by meas- 
 uring? What number will you get if you measure 
 the same quantity with a pint ? 
 
 Lesson 2 
 
 1. Count the pupils in the first two rows by 2's. 
 How many 2's? Count all the pupils in the room 
 by 2's. How many 2's? 
 
 2. Count the number of pairs of hands in the 
 room. How many pairs? 
 
 3. Count the pupils in groups of 3. How many 
 groups? In groups of 4. How many groups ? 
 
 4. Count the number of fingers and thumbs in 
 the room by 10's. How many 10's? Count by 5's. 
 How many 5's? 
 
 5. Count the number of pieces of crayon in a box 
 of crayon by 12's. How many dozen in the box? 
 
 6. Count the number of 5-minute spaces in one 
 hour. Of 10-minute spaces. Of 15-minute spaces. 
 
 7. In counting, what numbers do you count before 
 the number 4? Before 6? Before 10? Before 15? 
 Before 25? 
 
4 ARITHMETIC 
 
 8. Ask your teacher to make taps with a stick, 
 strokes with a bell, or to pronounce the names of the 
 letters in groups of 2 or 3. Count the number of 
 groups. 
 
 9. Count 12 pupils by 2's. How many 2's? 
 Count by 6's. How many 6's? By 3's. How many? 
 By 4's. How many ? 
 
 10. Count 18 pupils by 3's. By 6's. By 2's. By 
 9's. How many in each case ? 
 
 11. Count by 2's. How many 2's in 8? How 
 many 2^ in 8^? How many 4's in 8? How many 
 4^ in 8^? 
 
 12. With 8^ how many lemons can you buy at 2^ 
 each ? How many oranges at 4 ^ each ? 
 
 13. A man gave 2^ to each of 4 children. How 
 much did he give away? How many pounds in 4 
 2-lb. cans of corn ? 
 
 14. How many 2's in 8? What is one-fourth of 
 8? What is ^ of 8 apples? If I have 8 apples and 
 give ^ of them away, how many do I give away? 
 How many are left? 
 
 15. How many 4's in 8? What is one-half of 8? 
 There are 8 trees on one side of the yard and \ as 
 many on the opposite side. How many are on the 
 opposite side? 
 
LESSON 3 5 
 
 16. Draw a line 2-in. long. Draw another line 2 
 2-in. long. 4 2-in. long. 6 2-in. long. How many 
 inches long is each line? 
 
 Lesson 3 
 
 l. Place ten dots. How many 2's in 10? How 
 many 5's in 10 ? What are 5 2's equal to ? What 
 are 2 5's equal to ? 
 
 2.' How many marbles can I get for 5 f at the rate 
 of 2 for a cent ? 
 
 3. How many lead pencils at 2^ each can you 
 buy for a dime? How many tablets at a nickel 
 apiece can you buy for a dime ? 
 
 4. A boy picked 10 pt. of raspberries. How 
 many quarts did he pick ? 
 
 5. A coat costs $ 10. How many $2 bills will pay 
 for it ? How many $ 5 bills ? 
 
 6. How many 2's in 10? What is one-fifth of 
 10? James paid 10^ for a ball and -J as much for an 
 apple. What did the apple cost him ? What did 
 both cost? 
 
 7. A boy earns half a dollar a day. How much 
 will he earn in 10 da. ? 
 
 8. If it takes 2 boys 5 hours to do a piece of work, 
 how long would it take one boy to do it ? Five boys ? 
 
 9. Place twelve dots. Let each dot represent 1 ^. 
 How many 2^ in 12^? How many 6^ in 12^? At 
 $2 a bbl. for apples, how many bbl. for 1 12? 
 
6 ARITHMETIC 
 
 10. Let each dot represent 1 pt. What unit of 
 measure do 2 dots represent ? 
 
 How many quarts in 12 pt.? How many pints in 
 6 qt. ? Out of a pail containing 12 pt. of water 
 2 qt. are taken. How many quarts are left ? 
 
 11. How many qt. in 2 pt. ? 4 pt. ? 6 pt. ? 8 pt. ? 
 10 pt. ? How many pt. in 1 qt. ? 2 qt. ? 3 qt. ? 
 4qt.? 5qt.? 
 
 12. How much will a man earn in 2 wk. at $ 1 a 
 day ? If he is paid in two-dollar bills, how many bills 
 does he get? 
 
 13. How many pounds of butter are there in 6 2-lb. 
 rolls ? In 2 5-lb. pails ? 
 
 14. How many 2's in 12? What is one-sixth of 
 12 ? How many inches in ^ of a foot rule ? If I 
 have $ 12 in my purse and spend J of it, how much 
 do I spend? How much have I left? 
 
 15. How many 6's in 12 ? What is one-half of 12 ? 
 What will half-a-dozen eggs cost at 2 f each ? 
 
 16. Count 12 dots by 4's. How many 4's in 12? 
 What is one-third of 12? What is one-fourth of 12? 
 
 If I pay $12 for 3 bbl. of flour, what is the cost 
 per barrel ? 
 
 17. Make simple practical questions illustrating 
 Jof 8^ = 4^, and 1 of 10 = 5. 
 
LESSON 4 7 
 
 Lesson 4 
 
 
 
 
 
 1. Count these dots by 3's. How many 3's in 15 ? 
 How many 5's in 15 ? 
 
 2. If each dot represents 1 ft., what unit do 3 
 dots represent ? 
 
 How many yards in 15 ft. ? 
 
 3. Draw lines dividing these 15 dots into 5 equal 
 parts. What is \ of 15 ? What is of 15 ? 
 
 Paid 15 dimes for 5 yd. of cloth, what was the 
 price per yard ? 
 
 4. An overcoat was paid for with 3 five-dollar 
 bills. How many dollars did it cost ? 
 
 5. Count the number of 2-in. lengths in a yard. 
 How many ? How many 3-in. in 36 in. ? How many 
 12-in. in 36 in.? How many 4-in. in 36 in.? How 
 many 9-in. ? How many 6-in. ? 
 
 6. What is the cost of 3 pt. of molasses, at 12^ 
 apt.? 
 
 In 36 eggs how many dozen ? 
 
 7. If I work 9 hr. a day, how many hours shall I 
 work in 4 da. ? 
 
 If 1 Ib. of raisins cost 9^, how many pounds can 
 you buy for 
 
8 ARITHMETIC 
 
 8. Measure two points 15 in. apart. Measure 
 this distance with 3-in. and 5-in. units. How many? 
 
 Measure two points 18 in. apart with 2-in., 9-in., 
 3-in., 6-in. units. How many? 
 
 9. Make simple, practical questions like questions 
 6 and 7. 
 
 10. Cut out of cardboard a unit 3 in. long; use 
 this unit to measure a line 9 in. long. How many 
 3 in. in 9 in. ? 
 
 How many 3 ^ in 9 ^ ? 3 dimes in 9 dimes ? 3 Ib. 
 in 9 Ib. ? At 3 # a yard, how many yards of tape can 
 you buy for 9 ^ ? 
 
 11. Use the 3-in. unit to measure lines respectively 
 12 in., 18 in., 24 in., 30 in., 36 in. long. How many 
 3-in. units in each case? How many 3 oranges in 12 
 oranges? In 18 oranges? How many cents in 8 
 3-ct. ? In 10 3-ct. ? 
 
 12. A boy divided 12 oranges among his play- 
 mates, giving 3 oranges to each. How many play- 
 mates were there? 
 
 13. What will 6 lemons cost, at 3^ apiece? At 
 3^ each, how many lemons can you buy for 24^? 
 
 14. Cut out of cardboard a unit 4 in. long ; use it 
 to measure a line 8 in. long. How many 4-in. in 8 
 in. ? How many 4-ct. in 8 ct. ? How many cents in 
 24-ct.? In42-ct.? 
 
 15. What will 2 hats cost at $4 each ? How many 
 apples at 2^ each can you buy for 
 
LESSON 5 9 
 
 16. Use the 4-in. unit to measure lines, respectively, 
 16 in., 24 in., 32 in. long. How many 4-in. units in 
 each case? How many 4^ in 24^? How many 
 cents in 4 4 f ? How many miles in 6 4-mi. ? 
 
 17. How many pounds of soap, at 4^ a pound, can 
 you buy for 24 $ ? How far will a man walk in 6 hr., 
 at the rate of 4 mi. an hour ? 
 
 18. Use the 5-in. unit to measure lines, respec- 
 tively, 15 in., 20 in., 30 in., 35 in. long. Use the 6-in. 
 unit to measure lines, respectively, 12 in., 24 in., 36 
 in. Into how many parts has each been divided ? 
 
 15 in. -5- 5 in. = ? 24 in. * 6 in. = ? 25 in. -f- 5 in. = ? 
 
 19. Divide a line 12 in. long into 2 equal parts. 
 How long is each part ? Into 3 equal parts. Into 4. 
 Into 6. How long is each part in each case ? What 
 is \ of 12 in.? \ of 12 in.? \ of 12 in.? \ of 12 in.? 
 
 20. What is the meaning of 18 in. -f- 3 in. = 6? 
 Of \ of 18 in. = 6 in.? Of 18 in. -5-3 = 6 in.? 
 
 21. Can you exactly measure a line 23 in. long 
 with a 2-in. unit? 3-in. unit? 4-in. unit? 5-in. 
 unit? 6-in. unit? 
 
 What remainder in each case ? 
 
 Lesson 5 
 
 1. With a piece of paper cover all of these dots 
 but one, How many do you see ? How many are 
 
10 AHI FHMETIC 
 
 covered? What must be done with 1 to get 4? 
 With 1^ to get 4^? With 1 dime to make 4 dimes? 
 With a line 2 in. long to get a line 4 2-in. long? 
 With 1 5-dollar bill to get 4 5-dollar bills? 
 
 2. Cover all the dots but 2. How many do you 
 see? How many are covered? What must be done 
 with 2 to get 4? 
 
 I have 2 doz. eggs. How many must I buy to 
 have 4 doz. ? 
 
 3. I have 4 dimes, and pay 10^ for a yard of cot- 
 ton. How many dimes have I left? 
 
 A gallon measure contains 3 qt. of water. How 
 much must I pour in to fill it? 
 
 4. Cover all these dots but 1 ; all but 2 ; all but 
 3 ; all but 4. In each case how many do you see ? 
 How many are covered? 
 
 5. I want to give an apple to each of 5 boys. If I 
 have 3 apples, how many more must I get ? 
 
 6. I buy a 2-ct. postage stamp. What change do 
 I get back from a nickel ? 
 
 Bought 2 yd. of cloth, at $ 2 a yard. What change 
 do I get out of a 5-dollar bill ? 
 
 7. Draw a line one part of which is 3 2-in. long 
 and the other 2 2-in. long. How many 2 in. in the 
 length ? How many inches ? 
 
LESSON 5 11 
 
 8. I paid $1 for a pair of gloves and 2 two-dollar 
 bills for a pair of shoes. What did both cost? 
 
 9. Mary was at school on Thursday, but was kept 
 at home the rest of the week on account of illness. 
 How many days was she absent? 
 
 10. Cover all the dots but 5 ; all but 4 ; all but 3 ; 
 all but 2; all but 1. In each case how mairy do you 
 see ? How many are covered ? Practise this until 
 you can do it correctly and quickly. 
 
 11. I spent 16 for a hat and a pair of shoes. If 
 the hat cost $2, what did the shoes cost? Three 
 rolls of butter weighed 6 Ibs. What was the average 
 weight per roll ? 
 
 12. A grocer has 6 50-lb. sacks of flour and sells 3 
 of them. How many sacks has he left ? 
 
 13. How many 3-lb. packages of wafers weigh 
 6 lb.? 6 10-dollar bills are changed for 20-dollar 
 bills ; how many 20's are received ? 
 
 14. How many dots all together ? Cover all but 
 6 ; all but 5 ; all but 4 ; all but 3 ; all but 2 ; all 
 but 1. In each case how many do you see ? How 
 many are covered ? Practise this until you can do it 
 quickly and accurately. 
 
12 AEITHMETIC 
 
 15. A boy has 7 mi. to go. If he rides 5 mi., how 
 far does he walk ? 
 
 16. The sum of what two numbers equals 7 ? 
 
 17. Henry had 7 marbles and lost 4 of them; how 
 many had he left ? 
 
 18. A boy has 7 dimes and buys 3 collars at 10^ 
 each. How many dimes has he left? 
 
 19. On Wednesday morning how many days of 
 the week are gone ? How many are still left. 
 
 20. How many nickels will pay for 5 2-cent 
 postage stamps? How many dimes will pay for 
 10 apples at 1 f each ? How many 25-ct. pieces will 
 pay for 25 lemons at 3^ each? 
 
 21. I have 7 25-ct. pieces and buy 25 one cent 
 stamps. How many handkerchiefs can I buy with 
 the remainder at 25 f each ? 
 
 22. I have 7 nickels and buy 5 apples at 2^ each. 
 How many nickels have I left ? 
 
 23. Seven 10-dollar bills are changed for 5-dollar 
 bills, how many 5's are received ? 
 
 Lesson 6 
 
 
 
 1. How many dots all together? Cover all but 
 7 ; all but 1 ; all but 6 ; all but 2 ; all but 5 ; all 
 but 3 ; all but 4. In each case how many do you 
 see? How many are covered? 
 
LESSON 6 13 
 
 2. A grocer has 8 6-lb. boxes of starch, and sells 
 3 of them. How many has he left? 
 
 3. How many pairs of two in eight? 
 
 4. If I carry home a parcel containing a 3-lb. can 
 of tomatoes and 5 Ib. of sugar, what is the weight 
 of my parcel ? 
 
 5. At 2 dimes a dozen, how many eggs for 8 
 dimes ? How many hours will it take a man walk- 
 ing 4 miles an hour, to go 8 miles? 
 
 6. What must be done with 8 dots to make 9 
 dots ? This did what with 4 of the 8 dots ? 
 
 7. Cover all these dots but 9; all but 8; all 
 but 7; all but 6; all but 5; all but 4; all but 3; 
 all but 2 ; all but 1. In each case how many do 
 you see ? How many are covered ? 
 
 8. A child is 4 yr. of age. In how many years 
 will it be 9? 
 
 9. 6 is one more than what number ? One less 
 than what number? 7 is one more than what num- 
 ber? One less than what number? 8 and 9 are 
 each one more than what number? One less than 
 what number ? 
 
 10. 9 boys were skating and 3 went home at 5 
 o'clock. How many remained ? 
 
14 ARITHMETIC 
 
 11. How many 3 in. in 9 in.? 3 ft. in 9 ft.? 3 
 dimes in 9 dimes ? 3 5-dollars in 9 5-dollars ? 3 tens 
 in 9 tens ? 
 
 12. If each dot represents 1 ^, what unit of money 
 do all represent ? How many nickels ? 
 
 13. Cover all these dots but 9 ; all but 1 ; all 
 but 8 ; all but 2 ; all but 7 ; all but 3 ; all but 6 ; all 
 but 4 ; all but 5. In each case how many do you 
 see? How many are covered? 
 
 14. How many 5's do you see in 10 ? How many 
 2's? How many oranges at 5^ apiece can you buy 
 for one dime ? How many eggs at 2 ^ each ? 
 
 15. If I pay 7 f for a cake of sapolio, what change 
 do I get back from a dime ? 
 
 16. What is the cost of 2 cakes of soap at 4^ 
 apiece and a yeast cake at 2^? 
 
 17. What is the weight of 2 3-lb. cans of corn and 
 3 1-lb. cans of peas ? 
 
 18. A line 10 in. long is divided into 5 equal parts. 
 How long is each part ? Draw the line. 
 
 19. With ten dimes how much butter can be bought 
 at two dimes a pound ? Bought flour at $5 a barrel 
 and paid for it with a ten-dollar bill. How many 
 barrels ? 
 
 20. How many f 2 in $10? 2ft. in 10 ft? Smiles 
 in 10 miles? 5 ten-dollar bills in 10 ten-dollar bills? 
 
LESSON 7 15 
 
 21. If I bought two lead pencils at 4^ each and an 
 eraser for 2 ^, what did all cost ? 
 
 22. How many 5-cent pieces make 50 X? 
 
 I gave James one dime and Robert ^ as much. 
 What did I give Robert? What did I give both? 
 
 23. I divided 10 quarter-dollars equally among 5 
 children. What did each receive ? How many cents ? 
 
 24. How many strips of wall paper, each 2 ft. wide, 
 will be needed for the side of a room 10 ft. in width ? 
 
 25. I have a dime and buy a tablet for 4 ^. How 
 many yards of ribbon at 3 ^ a yd. can I buy with the 
 change ? 
 
 Lesson 7 
 
 1. How many cents in 2 dimes? 4 dimes? 5 
 dimes ? . 8 dimes ? 
 
 What will 6 yd. of ribbon cost at one dime a yard? 
 
 2. How many cents in 3 dimes 2^ ? 6 dimes 4^? 
 7 dimes 1 nickel? 
 
 I gave 6 dimes and 3 ^ for a book. How many 
 cents did it cost? 
 
 3. I paid 3 ten-dollar bills and a five-dollar bill 
 for a cow. How many dollars did the cow cost me ? 
 
 4. How many dimes in 40^? 60 ? 90^? How 
 many dimes and cents in 24^? 56^? 89^? 
 
 I paid in dimes and cents 23^ for a comb. How 
 many of each did I pay, there being 5 coins in all? 
 
16 ABITHMETIC 
 
 5. I paid in dimes and nickels 75 ^ for a pair of 
 gloves. How many of each did I pay, there being 8 
 coins in all ? How many of each, there being 9 coins 
 in all? 
 
 6. What unit of money is equal in value to 2 dimes 
 and a nickel ? 5 dimes ? 10 dimes ? 20 dimes ? 
 
 7. I have 2 dimes. How many dimes must I put 
 with these to be able to exchange them for half-a- 
 dollar? 
 
 30 mi. + 6 mi. = ? mi. 20 mi. + 8 mi. = ? mi. 
 
 8. A man drove ten miles an hour for 4 hr. and 
 then walked 2 mi. How far did he go ? 
 
 9. A lady bought a rug for 4 ten-dollar bills, a 
 desk for 2 ten-dollar bills, and a chair for $8. What 
 did all cost her ? 
 
 10. A grocer had 9 10-lb. sacks of flour and sold 
 6 of them. How many had he left, and how many 
 pounds did they weigh ? 
 
 11. The minute hand of a clock moves through 5 
 10-min. spaces and 3 10-min. spaces in how many 
 minutes ? 
 
 12. The thermometer registers 4 ten degrees. 
 Through how many ten degrees must the temperature 
 rise to register 7 ten degrees? How many degrees 
 will it then register? 
 
 13. A boy has $1 and spends 4 dimes. How much 
 has he left? 
 
LESSON 8 17 
 
 14. From 85 Ib. of flour how many 10-lb. sacks can 
 be put up, and how many pounds will be left over ? 
 
 15. 64 gal. are equal to 6 ten-gallons and 4 gal. 
 Read the following in the same way : 32 yr. ; 27 da. ; 
 43 min. ; 58 mi. ; 64 Ib. ; 25 qt. 
 
 16. Write in figures and use contractions : Twenty- 
 five cents ; ninety-four dollars ; sixty-six gallons ; 
 eighty quarts ; sixteen years ; thirty-one days. 
 
 17. Write in figures : Fourteen ; fifty-five ; forty ; 
 ninety-one ; twenty-eight. 
 
 18. What number is equal to 
 
 2 + 10? 3 + 10? 4 + 10? 5 + 10? 
 8 + 10? 9 + 10? 20+ 2? 30+ 4? 
 5 + 40? 6 + 60? 7 + 80? 9 + 90? 
 
 19. Harriet is 3 yr. old and her sister Caryl 10. 
 What is the sum of their ages ? 
 
 20. How many cents in a nickel and a dime ? 
 
 21. A man bought 4 Ib. of lump sugar and 20 Ib. 
 of granulated. How many pounds of sugar did he 
 buy? 
 
 Lesson 8 
 
 1. What is the cost of 3 yd. of lace at 2 dimes a 
 yard ? How many cents ? 
 
 2. How many dimes in 20^? 
 
 How many yards of ribbon at 20^ a yd. can you 
 buy for 8 dimes ? 
 
 3. What is the cost of 2 gal. of syrup at 5 dimes 
 a gallon ? How many dollars ? 
 
18 ARITHMETIC 
 
 4. If 8 2-lb. cans of fruit cost 9 dimes, how many 
 dimes will one can cost? How many cents? 
 
 5. What will 10 Ib. of canary seed cost at J dime 
 per pound? 
 
 6. A lady bought 4 yd. of ribbon at 2 dimes a 
 yard, and two bunches of tape for 6^. How many 
 cents did both cost? 
 
 7. I paid 25 ^ for a handkerchief and a spool of 
 thread. If the handkerchief cost 2 dimes, what did 
 the thread cost? 
 
 8. A lady spent 5 ten-dollar bills for a sofa, a five- 
 dollar bill for a chair, 2 ten-dollar bills for a table. 
 How much did she spend in all ? 
 
 9. I bought a horse for $200 and 3 cows at 1 30 
 each. What did all cost? 
 
 10. A farmer sold horses for $600, cows for $80, 
 and a sheep for $ 6. How much did he receive for 
 all? 
 
 11. 645 gal. are equal to 6 one hundred-gal., 4 ten- 
 gal., and 5 gal. Read the following in the same way : 
 432 yr. ; 227 da. ; 543 min. ; 258 mi. ; 164 Ib. ; 325 qt. 
 
 12. Write in figures and use contractions: Three 
 hundred twenty-four dollars ; one hundred thirty-four 
 miles ; six hundred forty acres ; five hundred four 
 years ; nine hundred ninety-nine years ; seven hun- 
 dred three pounds ; one thousand dollars ; two 
 thousand dollars ; three thousand dollars. 
 
LESSON 8 19 
 
 13. Write in figures : Six hundred forty-nine ; 
 two hundred fifty; eight hundred fifty; three hun- 
 dred thirteen ; seven hundred fifty ; six hundred 
 five. 
 
 14. 100 + 62 = ? 200 + 45 = ? 300 + 17 = ? 
 
 200 + 50 + 4 = ? 6 + 40 + 100 = ? 
 
 300 + 40 + 5 = ? 2 + 10 + 200 = ? 
 
 15. A man weighs 200 Ib. and his son 64 Ib. What 
 is the sum of their weights ? 
 
 16. If I paid $3 for a hat, $20 fora suit of clothes, 
 and $100 for two rugs, what did all cost? 
 
 17. I paid |300 for a piano, 1 40 for a sofa, and $8 
 for a chair. What was the cost of all ? 
 
 18. How many cents in a dime ? Dimes in a dollar ? 
 How many single units in a ten-unit? Ten-units in 
 a hundred-unit? 
 
 19. A farmer sold a horse for one hundred dollars, 
 a cow for thirty dollars, and a sheep for six dollars. 
 What did he get for all? 
 
SECTION II 
 Lesson 9 
 
 Add: 
 
 1. 
 
 3 in. 
 
 3 in. 
 
 3 in. 
 
 3 in. 
 
 
 2 " 
 
 12 
 
 22 " 
 
 32 " 
 
 2. What is the sum of 32 in. and 3 in. ? 
 
 James can take a step 32 in. long and John 3 in. 
 farther. How far can John step? Draw a line on 
 the board and mark off the two steps. 
 
 3. 
 
 3 min. 
 
 3 min. 
 
 3 min. 
 
 3 min. 
 
 
 2 " 
 
 12 " 
 
 22 " 
 
 32 " 
 
 
 3 min. 
 
 3 min. 
 
 3 min. 
 
 3 min. 
 
 
 42 " 
 
 52 
 
 62 " 
 
 72 " 
 
 4. 22 min. -f 3 min. = ? min. 42 min. + 3 min. = 
 ? min. 
 
 Agnes takes 22 min. to learn her lesson, and Mary 
 3 min. longer. How long does Mary take ? 
 
 5. 3 ft. 
 2 " 
 
LESSON 9 21 
 
 6. 3^ 3^ 3^ 3<* 
 
 2^ 12^ 22^ 42^ 
 
 7. George paid 3^ for an orange and 12^ for a 
 pound of nuts. What did both cost ? 
 
 8. 2 in. 2 in. 2 in. 2 in. 
 3 " 13 " 23 " 32 " 
 
 9. 
 
 2 
 
 in. 
 
 2 
 
 in. 
 
 1 
 
 in. 
 
 2 
 
 in. 
 
 43 
 
 M 
 
 53 
 
 44 
 
 63 
 
 44 
 
 73 
 
 44 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 3 
 
 tt 
 
 13 
 
 44 
 
 23 
 
 44 
 
 32 
 
 44 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 2 
 
 min. 
 
 43 
 
 u 
 
 50 
 
 44 
 
 73 
 
 44 
 
 93 
 
 44 
 
 10. 333333333 
 212223142526072 82 
 
 11. 222222222 
 3 11 23 33 42 53 63 73 80 
 
 12. 323232322 
 2 3 12 13 22 23 32 33 42 
 
 13. Harry paid twenty -three cents for a book, and 
 two cents for an eraser. What did both cost ? 
 
 14. Add 3 to each of the following numbers, and 
 read their sums : 2, 12, 22, 32, 42, 52, 62, 72, 82, 92. 
 Memorize these results. 
 
22 ARITHMETIC 
 
 15. Add 2 to each of the following numbers, and 
 read their sums : 3, 13, 23, 33, 43, 53, 63, 73, 83, 93. 
 Memorize these results. 
 
 16. What is the sum of 3 1-cent pieces and 2 
 1-cent pieces? Of 3 5-cent pieces and 2 5-cent 
 pieces ? Of 3 10-cent pieces and 2 10-cent pieces ? 
 Of 3 units of any kind and 2 units of the same 
 kind ? 
 
 17. What is the sum of 2 half-dollars and 3 half- 
 dollars ? Of 2 quarter-dollars and 3 quarter-dollars ? 
 
 18. Draw two lines, end to end, one 3 2-in. long 
 and the other 2 2-in. long. How many 2-in. in the 
 sum of their lengths? How many inches? How 
 many 2-in. in 10-in. ? 
 
 19. Measure with a ruler the length of this book. 
 How many inches long is it ? One inch is called the 
 
 unit of measure. 
 
 20. How many cents did this book cost ? One 
 cent is the unit that measures the cost of this book. 
 
 21. Measure the blackboard with the pointer. 
 How many pointers long is it ? Measure it with a 
 twelve-inch rule. How many 12-in. in its length ? 
 
 22. What unit of measure did you use in each 
 case above ? 
 
 23. Harry, how would you proceed to measure the 
 height of Charlie ? What units of measure would 
 you use ? 
 
 24. What use do we make of these different units ? 
 
LESSON 10 
 
 Add: 
 l. 1 in. 
 
 2. 
 
 Lesson 10 
 
 lin. 
 14 
 
 1 min. 1 min. 
 4 " 14 " 
 
 lin. 
 24 " 
 
 lin, 
 33 " 
 
 1 in, 
 44 " 
 
 1 min. 1 min. 1 min. 
 
 22 " 34 " 44 " 
 
 1 min. 1 min. 2 min. 1 min. 1 min. 
 
 54 " 60 " 72 " 84 " 94 " 
 
 3. 1 ft. 
 
 1ft. 
 14 " 
 
 1 yd. 1 yd. 
 
 14 " 
 
 21 " 
 
 1 mi. 
 
 24 " 
 
 4. Two boys run a race ; the first runs 24 yd., and 
 the second comes in 1 yd. ahead. How many yards 
 does the second boy run ? 
 
 f It Zf II 81 
 
 ^ 24^ 41^ $44 154 
 
 5. 
 
 6. A man paid $34 for a suit of clothes and f 1 for 
 a necktie. What did both cost? What three bills 
 would pay for both ? 
 
 7. 
 
 4 in. 
 1 " 
 
 4 in. 
 11 " 
 
 4 in. 
 
 20 " 
 
 4 in. 
 31 " 
 
 2 in. 
 41 " 
 
 8. I took 11 min. to walk to the depot and then 
 had to wait 4 min. for the train. How many min- 
 utes before train time did I leave home ? 
 
24 ARITHMETIC 
 
 9. 4 min. 4 min. 4 min. 4 min. 4 min. 
 1 " 11 " 21 " 31 " 41 " 
 
 10. Add 1 to each of the following numbers, and 
 read their sums : 4, 14, 24, 34, 44, 54, 64, 74, 84, 94. 
 Memorize these results. 
 
 11. Add 4 to each of the following numbers, and 
 read their sums : 1, 11, 21, 31, 41, 51, 61, 71, 81, 91. 
 Memorize these results. 
 
 12. What is the sum of 4 half -hours and 1 half- 
 hour? Of 1 5-lb. pail of butter and 4 5-lb. pails of 
 butter? Of 4 2-lb. rolls of butter and 1 2-lb. roll of 
 butter ? Of 4 units of any kind and 1 unit of the 
 
 same kind? 
 
 c 
 
 A I 
 
 13. The distance from A to B is 25 miles; the 
 distance from B to C is 4 miles. How far is it from 
 A to C ? What unit was used to measure the dis- 
 tance from A to B ? From A to C ? 
 
 I 
 
 14. Read these dots from left to right, and also 
 from right to left. Thus, 5 = 4 + 1, or 1 + 4. 
 
 15. Make 5 dots and draw lines through them in 
 any direction. Read your results. 
 
 16. What two numbers give 5 when added? 15? 
 25? 35? 45? 
 
LESSON 11 25 
 
 17. A boy is 5 ft. high. What unit is used to 
 measure his height? 
 
 18. November 7 William was 12 mo. old, how old 
 will he be Feb. 7 of the next year ? 
 
 19. With a yardstick measure a piece of string 
 
 3 yd. long. Measure it again with a foot rule and 
 count the number of times you measure. What 
 number did you get? 3 yd. = ? ft. 
 
 20. Measure a piece of string 4 ft. long with a 
 unit half-a-foot long. What number did you get? 
 
 4 f t. = ? half-feet. 
 
 21. Draw two lines, end to end, one 4 3-in. long, 
 and the other 1 3-in. long. How many 3-in. in the 
 sum of their lengths? How many inches? How 
 many 3-in. in 12 in. ? 
 
 22. Measure the length of a table. What unit or 
 units did you use? 
 
 23. How long is your morning recess? What is 
 the unit that measures the length of your recess? 
 
 Lesson 11 
 
 1. 2 in. + 3 in. = ? in. 2 in. -f ? in. = 5 in. 
 3 in. + 2 in. = ? in. 3 in. -f ? in. = 5 in. 
 
 2. 4^ + 1^ = 5^ 4^+?^ = 5^ 
 1^ + 4^ = 5^ l^ + ?^ = 5 
 
 3. 3 -h? = 5 4+? = 5 
 l+? = 5 2+?=5 
 
26 ARITHMETIC 
 
 4. James had 2^, and his father gave him 
 How many cents did he then have ? 
 
 5. Harry had 12 marbles and found 3. How 
 many did he then have? 
 
 6. A man travelled 24 mi. by train and walked 
 
 1 mi. How far did he go ? 
 
 7. I paid |5 for a hat and a pair of gloves. The 
 hat cost $4. What did the gloves cost? 
 
 8. I bought a book for 22^ and a pencil for 3^. 
 What did I pay for both? 
 
 9. I gave a quarter of a dollar for a yard of 
 ribbon and received 2^ in change. What did the 
 ribbon cost me? 
 
 10. 12 + ? = 15 22 + ? = 25 ? + 3 = 25 
 32 + ? = 35 ? + 3 = 45 ? + 3 = 15 
 
 11. I paid $25 for a suib of clothes and a pair of 
 shoes. I paid 1 22 for the suit. What did the 
 shoes cost? 
 
 12. Take two points 2 yd., 3 yd., and again 4 yd. 
 apart. Measure each of these distances with a foot 
 rule. What numbers do you get? 1 yd. = ? ft. 
 
 2 yd. = ? ft. 3 yd. = ? ft. 4 yd. = ? ft. 5 yid, = ? ft. 
 
 13. Measure two points 1 yd. 2 ft. apart, 2 yd. 1 ft. 
 apart, and again 3 yd. 2 ft. Measure each of these 
 distances again with a foot rule. What numbers 
 do you get? 1 yd. 2 ft. = ? ft. 2 yd. 1 ft. = ? ft. 
 
 3 yd. 2 ft. = ? ft. 4 yd. 1 ft. = ? ft. 
 
LESSON 11 27 
 
 14. Measure the length of things in the room as 
 the table in yards and feet, and again in feet. 
 
 15. Find by measuring the number of yards and 
 feet in 8 ft. ; 14 ft. ; 16 ft. ; 20 ft. 
 
 16. What units does the milkman use to measure 
 milk? 
 
 17. Put 3 qt. of water into a pail. Measure this 
 again with a pint measure, and count as you do this. 
 What number do you get? Do the same with 4 qt. 
 of water. 1 qt. = ? pt. 2 qt. = ? pt. 3 qt. = ? pt. 
 4 qt. = ? pt. 5 qt. = ? pt. 
 
 18. How many dots ? Count by twos. How many 
 twos? If each dot represents 1 pt., what do 2 dots 
 represent ? How many pints are represented ? How 
 many quarts? 
 
 19. Place dots to represent 4 pt. of water in a pail. 
 6 pt., 8 pt., 10 pt., 12 pt. How many quarts are 
 represented each time? 
 
 20. 4 pt. = ? qt. 6 pt. = ? qt. 8 pt. = ? qt. 
 
 10 pt. = ? qt. 12 pt. = ? qt. 
 
 21. A line is measured by the unit 2 in. and the 
 number 6. How many inches long is the line ? Draw 
 it. With the unit 3 in., what number would measure 
 its length ? With the unit 4 in. ? 
 
28 ARITHMETIC 
 
 Lesson 12 
 
 . 
 
 Add: 
 
 
 
 
 
 
 1. 
 
 1 min. 
 
 1 min. 
 
 1 
 
 min. 1 
 
 min. 
 
 1 min. 
 
 
 5 " 
 
 15 " 
 
 25 
 
 35 
 
 u 
 
 45 " 
 
 2. 
 
 5^ 
 
 5^ 
 
 4^ 
 
 5* 
 
 5* 
 
 5^ 
 
 
 iy 
 
 11* 
 
 21* 
 
 31 
 
 40 J* 
 
 51* 
 
 3. 15 min. + ? min. = 16 min. 
 
 1 min. + ? min. = 16 min. 
 
 A boy takes 16 min. to walk to school. If he is 
 1 min. late, how many minutes before school time 
 did he leave home ? 
 
 4. Harry has 31 ^, and his brother 5 How much 
 have they together ? 
 
 5. 1 
 
 1 
 
 3 
 
 1 
 
 1 
 
 5 
 
 55 
 
 65 
 
 72 
 
 85 
 
 95 
 
 41 
 
 5 
 
 5 
 
 2 
 
 5 
 
 5 
 
 5 
 
 50 
 
 61 
 
 72 
 
 81 
 
 91 
 
 11 
 
 6. Five years ago a young man was twenty-one 
 years old. What is his age at present ? 
 
 
 
 7. Read these dots from left to right and also 
 from right to left. 
 
LESSON 12 29 
 
 8. Read your answer to question 6 again, letting 
 each dot represent one dime, one half-dollar, one 
 2-lb. package of oatmeal, one 3-qt. can of peas. 
 
 9. What is the meaning of 5 + 1 = 6 ? Of 
 4 + 2 = 6? Of 3 + 3 = 6? 
 
 10. Make 6 dots and draw lines through them in 
 any direction. Read your results. 
 
 11. Memorize : 
 
 15243 
 51423 
 
 666 66 
 
 12. What is the value of one nickel and 1 penny ? 
 Of one five-dollar bill and $1 ? 
 
 13. What is the weight of 3 2-lb. packages of cakes 
 and 3 2-lb. packages of wafers ? How many pounds ? 
 
 14. What is the sum of 4 2-qt. cans of berries and 
 2 2-qt. cans. How many quarts ? 
 
 15. Add 2 to each of these numbers: 
 
 3, 4, 14, 24, 23, 33, 44, 13, 54 
 
 16. Add 4 to each of these numbers: 
 
 1, 2, 12, 22, 31, 42, 51, 61, 82 
 
 17. Add 3 to each of these numbers: 
 
 1, 2, 3, 12, 21, 23, 31, 43, 52 
 
 18. 5 + 1=? 5+?= 6 l+?=6 
 4+ ? = 6 2+?= 6 3+?= 6 
 
30 ARITHMETIC 
 
 19. Subtract:* 
 
 6 6 6 6 6 16 26 
 
 5 1 4 2 3 12 22 
 
 20. A grocer has 6 10-lb. sacks of flour, and sells 3. 
 How many has he left ? How many Ib. ? 
 
 21. A family bought 6 2-lb. packages of oatmeal 
 for the month, and used 3. How many Ib. were left? 
 
 22. With a foot rule measure points on the board 
 1 ft. 6 in. apart. Measure the same distance with a 
 yardstick divided into inches. 1 ft. 6 in. = ? in. 
 
 23. Take two points on the blackboard not far 
 apart. Measure the distance between them with a 
 foot rule and then with a yardstick. Write your 
 result thus : 1 ft. 8 in. = 20 in. Select other points, 
 measure, and write your results in the same way. 
 
 24. Measure different things, as the width of the 
 table, of the desk, of the door, with a yardstick and 
 then with a foot rule. Write your results thus: 
 27 in. = 2 ft. 3 in. 
 
 25. 1 ft. = ? in. 1 ft. 2 in. = ? in. 1 ft. 4 in. = ? in. 
 
 Lesson 13 
 
 1. 5^ + 1^=? 
 
 2. John paid 5 $ for paper and 1 f for a pen. 
 How much did he pay for both ? 
 
 * Read 5 and 1 are 6, 1 and 5 are 6. Write down 1 under the 
 5, and 5 under the 1. 
 
LESSON 13 31 
 
 3. James paid 1 f for a slate pencil and 25 $ for 
 a book. How much did he pay for both ? . 
 
 4. If I paid 24 dimes for a hat and 2 dimes for a 
 collar, how much did I pay for both? 
 
 5. If I paid 5 half-dollars for a pair of shoes and 
 1 half-dollar for a hat, how much did I pay for both? 
 
 6. Represent this quantity on the blackboard by 
 dots, each 2 dots representing 1 half-dollar. What 
 will 1 dot represent? What quantity will be repre- 
 sented by 4 dots ? 
 
 7. A boy spent 13 1 for a top and 2 f for a string. 
 How much did he spend ? 
 
 8. 4^+2^=? 4^+?=6^ 22^+?=25^ 
 
 9. A boy has 6^ and spends 2^ for a postage 
 stamp. How much has he left ? 
 
 10. A boy has 6 nickels and buys 4 oranges at a 
 nickel apiece. How much has he left? 
 
 11. I buy a gallon of vinegar for 22^. What 
 change do I get back out of a 25 f piece ? 
 
 12. If in the purchase of a ball a boy receives 3 
 cents change from a 25 cent piece, what is the cost of 
 the ball? 
 
 13. A piece of ribbon 16 yd. long is cut into two 
 pieces ; one part is 12 yd. long. How long is the 
 other part ? 
 
 13 = ? 132 + $4 = ? $4 + ? = 136. 
 
32 ARITHMETIC 
 
 15. A man paid $ 12 for an overcoat and $3 for an 
 umbrella. What did both cost him ? 
 
 16. A man paid |4 for a calf and $32 for a cow. 
 What did he pay for both? 
 
 17. There were 16 marbles in a ring ; Arthur shot 
 away 3. How many were left in the ring ? 
 
 18. A man paid 5 five-dollar bills for a suit of 
 clothes and 1 five-dollar bill for a pair of shoes. 
 What did both cost him? 
 
 Lesson 14 
 Copy and add: 
 
 ft. in. ft. to. ft. in. 
 
 1. 1 2 11 12 
 
 13 14 14 
 
 How do you add ft. and in. to ft. and in.? 
 
 2. 
 
 3. 
 
 ft. 
 
 in. 
 
 
 ft. 
 
 in. 
 
 
 ft. 
 
 in. 
 
 2 
 
 1 
 
 
 2 
 
 3 
 
 
 1 
 
 3 
 
 1 
 
 5 
 
 
 3 
 
 3 
 
 
 5 
 
 2 
 
 yd. 
 
 ft. 
 
 in. 
 
 
 yd. 
 
 ft. 
 
 in. 
 
 
 1 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 2 
 
 
 1 
 
 1 
 
 4 
 
 
 1 
 
 1 
 
 3 
 
 
 How do you add yd., ft., and in. to yd., ft., and in. ? 
 
 yd. ft. in. yd. ft. in. 
 
 4. 1 1 213 
 
 224 213 
 
LESSON 14 33 
 
 5. A chain 3 ft. 4 in. long is joined to another 
 chain 2 ft. 2 in. long. How long is the chain formed 
 from the two ? 
 
 6. Represent these lengths by lines of the given 
 length. Measure the line formed by joining these. 
 How many feet and inches in this line ? 
 
 7. Add and memorize : 
 
 111 212 123 
 123 243 543 
 
 Subtract : 
 
 
 
 
 
 
 8. *2 3 3 
 
 4 
 
 5 
 
 5 
 
 5 
 
 5 
 
 121 
 
 2 
 
 4 
 
 1 
 
 3 
 
 2 
 
 9. 666 
 
 6 
 
 6 
 
 15 
 
 26 
 
 36 
 
 514 
 
 2 
 
 3 
 
 12 
 
 24 
 
 32 
 
 Copy and subtract: 
 
 
 
 
 
 
 ft. in. 
 
 10. 2 5 
 
 ft. 
 4 
 
 in. 
 6 
 
 
 ft. 
 5 
 
 in. 
 
 6 
 
 1 3 
 
 2 
 
 3 
 
 3 
 
 4 
 
 How do you subtract ft. 
 
 and 
 
 in. from 
 
 ft. 
 
 and in. 
 
 ? 
 
 ft. in. 
 
 11. 5 4 
 
 ft. 
 6 
 
 in. 
 6 
 
 
 ft. 
 4 
 
 in. 
 
 5 
 
 41 34 13 
 
 Find the difference in length between two ropes, 
 one 8 ft. 6 in. long, the other 3 ft. 4 in. 
 * Read 1 and 1 are 2, 1 and 2 are 3. 
 
34 ARITHMETIC 
 
 yd. ft. in. yd. ft. In. 
 
 12. 2 2 4 625 
 
 112 314 
 
 How do you subtract yd., ft., and in. from yd., ft., 
 and in.? 
 
 13. From a rope 5 yd. 2 ft. 6 in. long a piece 3 yd. 
 2 ft. 4 in. has been cut. How much is left? 
 
 14. Measure the length of the rope on the black- 
 board or floor. Measure the length cut off. Now 
 measure the remaining part. How much is left? 
 
 15. Measure in ft. and in. the length of the table, 
 and also the width. Find their difference. 
 
 16. Measure in ft. and in., and write down the 
 heights of different pupils in the room. 
 
 17. Find the difference in the heights of the tallest 
 and the shortest girl in the class. Of the tallest and 
 the shortest boy. 
 
 18. Find the difference in the heights of the tallest 
 boy and the tallest girl in the class. 
 
 19. Measure the heights of several pupils in yd., 
 ft., and in., and make questions about the sum or 
 difference of their heights. 
 
 20. James is 6 yr. 4 mo. old, and his sister Mary 
 2 yr. 3 mo. James is how much older than Mary ? 
 
 21. A milkman pours 3 gal. 2 qt. of milk from a 
 can, and has 2 gal. 1 qt. left in the can. How much 
 was in the can at first ? 
 
LESSON 15 35 
 
 Lesson 15 
 */ 
 
 1. What can each of these dots represent ? Read 
 these dots from left to right and from right to left. 
 
 Add: 
 
 2. 1 2 3 6 5 4 
 654123 
 
 3. 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 6 
 
 16 
 
 24 
 
 36 
 
 45 
 
 56 
 
 63 
 
 76 
 
 4. 
 
 6 
 
 6 
 
 6 
 
 4 
 
 6 
 
 6 
 
 3 
 
 6 
 
 
 1 
 
 11 
 
 31 
 
 51 
 
 71 
 
 91 
 
 22 
 
 41 
 
 5. What is the sum of 71 in. and 5 in. ? 
 Arthur can jump 71 in. and James 5 in. beyond 
 
 Arthur. How far can James jump ? 
 
 6. 2222222 
 5 25 45 64 85 33 55 
 
 7. How many dollars in 3 ten-dollar bills and a 
 two-dollar bill ? 
 
 I paid 3 ten-dollar bills and a two-dollar bill for a 
 desk, and a five-dollar bill for a chair. What did 
 both cost ? 
 
 8. 5555535 
 2 12 31 42 62 82 92 
 
36 ARITHMETIC 
 
 9. 3434343 
 4 3 14 13 24 23 34 
 
 10. A lady is 34 yr. of age, and her husband is 
 3 yr. older. What is his age ? 
 
 11. What numbers added give 7? 
 
 12. If in question 1 each dot represents 1 pt., 
 how many qt. and pt. are represented by the 7 dots ? 
 
 13. What is the weight of 4 10-lb. sacks of flour 
 and 3 10-lb. sacks ? 
 
 How many cents in 5 dimes and 2 dimes ? 
 
 14. If a boy is 16 yr. old to-day, when was he 
 13 yr. old ? 
 
 Add: 
 
 
 
 
 
 
 15. 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 13 
 
 113 
 
 3 
 
 23 
 
 223 
 
 16. 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 4 
 
 14 
 
 114 
 
 4 
 
 34 
 
 134 
 
 17. 134 mi. + 3 mi. = ? 3 mi. + 134 mi. = ? 
 134 mi. + ? = 137 mi. 3 mi. + ? = 137 mi. 
 
 A gentleman travels 134 mi. by train and drives 
 3 mi. from the station to his friend's house. How 
 far does he go all together ? 
 
 18. 2 2 222 2 
 5 25 125 5 44 145 
 
LESSON 16 37 
 
 19. 6 6 66 6 6 
 
 1 11 111 1 81 181 
 
 20. 5^+2^=?^ 5^ + 1^=?^ 5^+? = 7^ 
 
 21. ' 1 nickel = ? f 1 nickel 1 f = ? X 
 
 1 nickel 2 ^ = ? ^ 4 nickels = ? dimes 
 
 22. If I pay 2^ more than a nickel for a loaf of 
 bread, what does it cost ? 
 
 23. Draw two lines, end to end, one 5 3-in. long, 
 and the other 2 3-in. long. How many 3-in. in the 
 whole line ? How many inches ? How many 3-in. 
 in 21 in. ? 
 
 Lesson 16 
 
 1. 4 + 3 = ? 24 + 3 = ? 32 + ? = 36 
 
 2. A boy spends 4^ for an orange and 3^ for a 
 lemon. How much does he spend ? 
 
 3. A pound of butter costs 24^, and a pint of 
 milk 3 What do both cost? 
 
 4. I bought a bicycle for $36, and paid 132 cash. 
 How much did I then owe ? 
 
 5. Henry has a 25-cent piece and 2^. How 
 much money has he ? 
 
 6. A box is 33 in. long. It is how many inches 
 shorter than a yardstick ? 
 
 7. I gave a five-dollar bill for a pair of shoes and 
 2 orie-dollar bills for a hat, What did both cost ? 
 
38 ARITHMETIC 
 
 8. My milkman left me 3 qt. 1 pt. of milk, and I 
 paid him in pint tickets. How many did I give 
 him ? Represent by dots. 
 
 9. What unit does the grocer use to measure 
 kerosene ? To weigh butter ? 
 
 10. What other units might be used in each of 
 these cases? How does each of the latter units 
 compare in weight with each of the former ? 
 
 11. What is butter worth a pound ? What is 
 kerosene worth a gallon ? What unit measures the 
 value of a pound of butter, and also of a gallon of 
 kerosene ? 
 
 12. Measure a gallon of water with a quart meas- 
 ure. What number of quarts did you get ? 
 
 13. Put 1 gal. 3 qt. of water into a pail. Meas- 
 ure this with a quart measure. What number did 
 you get ? 1 gal. 3 qt. = ? qt. 
 
 14. Empty 5 qt. of water into a pail. Measure 
 this with gallon and quart measures. 5 qt. = ? gal. 
 ?qt. 
 
 15. If each dot represents 1 qt., what do 4 dots 
 represent? What do these dots represent? How 
 many qt. ? 
 
 16. Represent 2 gal. 2 qt. by dots. How many 
 qt. ? Represent 15 qt. by dots. How many gal. 
 and qt.? Make other questions. 
 
LESSON 17 39 
 
 17. 1 gal. = ? qt. 1 gal. 2 qt. = ? qt. 
 1 gal. 3 qt. = ? qt. 6 qt. = ? gal. ? qt. 
 
 18. 1 yr. = ? mo. 1 yr. 3 mo. = ? mo. 
 1 yr. 5 mo. = ? mo. 14 mo. = ? yr. ? mo. 
 16 mo. = ? yr. ? mo. 
 
 19. Harry is 1 yr. and 5 mo. old, Charlie is 3 yr. 
 and 7 mo. old. What is the sum of their ages ? 
 
 20. Charlie is how much older than Harry ? 
 
 21. Represent by dots on the board the age of 
 Charlie in months, each dot to represent 1 mo. 
 Mark off by a line the number of dots representing 
 Harry's age in months. 
 
 22. 1 da. = ? hr. 1 da. 2 hr. = ? hr. 
 
 25 hr. = ? da. ? hr. 27 hr. = ? da. ? hr. 
 
 23. If a cow gives a gallon of milk in the morn- 
 ing and 3 qt. at night, how many quarts does she 
 give in a day ? 
 
 24. A baby is 1 yr. 4 mo. old. How many months 
 old is he ? 
 
 Lesson 17 
 
 l. Read these dots in opposite directions, and 
 write your results thus : 2 + 2 + 2 = 6. 
 
40 
 
 ARITHMETIC 
 
 2. Add: 
 
 2 
 
 2* 
 
 1 
 
 1* 
 
 1 
 
 1 
 
 2 
 
 2 
 
 3 
 
 3 
 
 1 
 
 1 
 
 2 
 
 12 
 
 2 
 
 22 
 
 4 
 
 34 
 
 3. Count 6 dots by 2's. How many 2's ? If each 
 dot represents a pint, how many quarts are there ? 
 
 4. How many quarts in 3 2-qt. ? How many days 
 will 5 2-qt. jars of fruit last a family that eats 1 qt. a 
 day? 
 
 5. How many days will 3 2-lb. rolls of butter last 
 a family that eats J Ib. a day ? 
 
 6. Read these dots in opposite directions, and 
 write down your results. 
 
 Add: 
 
 
 
 
 
 
 7. 1 
 
 1 
 
 1 
 
 1 
 
 2 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 3 
 
 3 
 
 4 
 
 24 
 
 3 
 
 43 
 
 2 
 
 52 
 
 8. 1 
 
 1 
 
 3 
 
 1 
 
 2 
 
 3 
 
 2 
 
 4 
 
 1 
 
 2 
 
 1 
 
 2 
 
 13 
 
 12 
 
 23 
 
 34 
 
 62 
 
 71 
 
 9. What is the sum of 32^, l 3^? Of 23^, 2 
 Of 41/, 4^, 2^? James spent 22 f for a Reader, 
 
 * Add thus : 12, 14, 16 ; 22, 25, 26. 
 
LESSON 17 41 
 
 3 ^ for a lead pencil, and 2 $ for an eraser. What did 
 all cost? 
 
 10. A boy had 52^ in the Penny Savings on 
 Monday. Tuesday he put in 2 ^, and Wednesday 3^. 
 How much did he then have? 
 
 11. Copy and add : 
 
 21 ^ 22^ 32^ 26^ 30^ Uf 
 12 14 311 441 631 
 
 12. I paid 21^ for a Ib. of butter and 13^ for a 
 Ib. of cheese. What was the cost of both ? 
 
 13. Question 12 is founded on the first problem in 
 number 11. Make similar questions, using the quan- 
 tities given in number 11. 
 
 14. Copy and add : 
 
 11 15 21 20 20 22 
 
 14 30 11 30 25 21 
 
 22 32 33 25 31 14 
 
 15. Name two units each of which is used to 
 measure potatoes. 
 
 16. Make questions, using the following price-list: 
 
 Coffee at 31 f a Ib. 
 Baking powder at 22 a can 
 Gelatine at 13^ a package 
 Matches at 10 f a package 
 Nuts at 12^ alb. 
 Canctles at 15 f a Ib, 
 
42 ARITHMETIC 
 
 Lesson 18 
 Subtract : 
 
 1. 23344455555 
 12131241325 
 
 2. 66666777777 
 51423615243 
 
 3. 36457764276 
 02417210231 
 
 4. What is the meaning of 4-3 = 1? Of 
 5-2 = 3? Of6-2 = 4? Of7-4 = 3? 
 
 5. I paid 7^ for an apple and an orange. The 
 orange cost 5^ ; what did the apple cost ? 
 
 B 
 
 A | C 
 
 6. From A to C is 6 mi. If it is 4 mi. from A 
 to B, how far is it from B to C ? 
 
 Copy and subtract : 
 
 7. *35^ 46^ 75^ 66^ 57^ 
 
 22^ 24^ 31 26^ 14^ 
 
 8. 45 56 72 43 26 77 
 21 11 22 13 21 15 
 
 9. Write the second quantity under the first and 
 subtract: 65 mi. and 23 mi.; 174 and $33. 
 
 * Subtract thus : 2 and 3 are 6, 2 and 1 are 3, 
 
LESSON 19 48 
 
 10. From A to C is 35 mi. If it is 22 mi. from 
 A to B, how far is it from B to C ? 
 
 11. A man pays $42 on a bicycle that cost $ 65. 
 How much more will he have to pay ? 
 
 12. A man is 57 yr. of age, and his son 25 yr. 
 How much older is the father than the son ? 
 
 13. A yard is 36 in. How many inches are there 
 in a stick that is 11 in. shorter than a yard ? 
 
 14. From a box containing 72 pencils 30 have been 
 taken. How many are left in the box ? 
 
 15. Of a class of 46 pupils 34 are dismissed. How 
 many remain ? 
 
 16. A boy had 75^, and spent 32^ for an Arith- 
 metic. How much had he left? 
 
 17. There are seventy-seven pupils in the first two 
 grades of a school. If there are forty-three in the 
 first grade, how many are in the second? 
 
 Lesson 19 
 
 1. 4 + ? = 6 14 + ? = 16 2 + ? = 26 
 6 - 4 = ? 16-14 = ? 26-2 = ? 
 
 2. I buy 4 qt. of milk each morning and 2 qt. 
 each evening. How much milk do I buy a day ? 
 
44 ARITHMETIC 
 
 3. A man rides 14 mi. and walks 2 mi. How 
 far does he travel <? 
 
 4. If 22 pupils out of a class of 26 are present, 
 how many are absent ? 
 
 5. If 2 in. of snow fell on Monday and 5 in. on 
 Tuesday, how much fell on the two days ? 
 
 6. A boy spent 16^ in one day. In the morning 
 he spent 5^. What did he spend in the afternoon? 
 
 7. Two boys have 17 marbles. If the first has 
 13, how many has the second ? 
 
 8. Robert has a 25-cent piece, and Walter a 2-cent 
 piece. How much money have the two boys ? 
 
 9. John had 16^ and spent 4^ for an orange. 
 How much had he left ? 
 
 10. The schoolroom thermometer registered 63 
 and then rose 3. What did it then register ? 
 
 11. What is the unit that measures temperature ? 
 
 12. What is the sum of four and twelve ? 
 
 13. Find the cost of two rugs, one costing $25, 
 and the other $42. 
 
 14. How much more must I pay for a waste paper 
 basket costing 75^, than for one costing 55^? 
 
 15. Draw a line 4 2-in. long. How many inches 
 long is it ? If a line is measured by the number 5 
 a.ncl tlie unit 2-in. ? how long is it? Draw the line, 
 
LESSON 20 
 
 45 
 
 16. The weight of a parcel is measured by the 
 number 4 and the unit 3-lb. How many pounds does 
 it weigh ? 
 
 17. A line 12 in. long is measured by the unit 
 2-in. What number of 2-in. ? 6 is often called the 
 ratio of 12 in. to 2 in. 
 
 18. A line 10 in. long is measured by the num- 
 ber 5 and a certain unit. What is the unit ? Divide 
 the line into 5 equal parts, and measure each part. 
 
 19. Memorize : 
 
 12 12 123 123 
 32 43 543 654 
 44 55 666 767 
 
 Lesson 20 
 
 Add: 
 
 1. 
 
 2 dimes 
 
 2 dimes 
 
 3 dimes 
 
 1 dime 
 
 2. 
 3. 
 
 2 " 
 
 3 " 
 
 3 " 
 
 4 dimes 
 
 10^ 
 
 40^ 
 
 20? 
 20 1 
 
 20^ 
 30^ 
 
 30^ 
 30^ 
 
 1 dime 
 
 3 dimes 
 
 3 dimes 
 
 2 dimes 
 
 4. 
 5. 
 
 5 dimes 
 
 4 " 
 
 30^ 
 40 1 
 
 10 min. 
 
 2 " 
 
 5 " 
 
 20^ 
 
 50^ 
 
 30 min. 
 
 wy 
 
 50^ 
 
 30^ 
 
 201 
 
 20 min. 
 
 10 min. 
 
 ' 
 
 10 " 
 
 20 " 
 
 30 
 
 30 
 
46 ARITHMETIC 
 
 6. 10 in. 
 
 20 
 
 20ft. 
 20 " 
 
 20yd. 
 
 40 " 
 
 40 mi. 
 
 30 " 
 
 7. 20 min. 
 10 " 
 
 30 hr. 
 10 " 
 
 30 da. 
 30 " 
 
 20 da. 
 
 50 " 
 
 8. A boy takes 30 min. to go on an errand, and 
 20 min. to return. How long is he gone ? 
 
 9. There are 30 da. in April and the same number 
 in June. How many days in both months ? 
 
 10. What is the weight of two parcels, one weigh- 
 ing 10 lb., and the other 40 Ib. ? 
 
 11. 
 
 3 
 
 30 
 
 3 
 
 30 
 
 3 
 
 30 
 
 
 2 
 
 20 
 
 12 
 
 120 
 
 22 
 
 220 
 
 12. 
 
 4 
 
 40 
 
 4 
 
 40 
 
 4 
 
 40 
 
 
 2 
 
 20 
 
 12 
 
 120 
 
 22 
 
 210 
 
 13. 
 
 4 
 
 40 
 
 4 
 
 40 
 
 4 
 
 40 
 
 
 3 
 
 30 
 
 13 
 
 130 
 
 23 
 
 230 
 
 14. 
 
 1 
 
 10 
 
 100 
 
 1 
 
 10 
 
 100 
 
 
 1 
 
 10 
 
 100 
 
 2 
 
 20 
 
 200 
 
 15. 
 
 2 
 
 20 
 
 200 
 
 2 
 
 20 
 
 200 
 
 
 8 
 
 30 
 
 300 
 
 5 
 
 50 
 
 500 
 
LESSON 21 47 
 
 Subtract : 
 
 16. 40 40 50 50 60 70 
 30 20 10 20 30 40 
 
 17. 300 500 400 600 700 
 200 400 100 200 500 
 
 18. I paid 20^ for 1 Ib. of meat. What change 
 did I get back out of a fifty-cent piece ? 
 
 19. A farmer had 500 bu. of wheat and sold 300 ? 
 How many bushels had he left? 
 
 Lesson 21 
 
 1. Read these dots from left to right and from 
 right to left. 
 
 2. If each dot represent (a) a cent, (6) an inch, 
 (V) a year, (c?) $2, (e) 1 2-lb., read the result from 
 right to left and from left to right. Place these 
 readings in columns for addition, and add. 
 
 Add: 
 
 3. 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 6 
 
 5 
 
 4 
 
 3 
 
 2 
 
 4. 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 7 
 
 17 
 
 26 
 
 37 
 
 47 
 
 50 
 
48 ARITHMETIC 
 
 
 5. 2 
 
 2 
 
 
 2 
 
 
 6 
 
 46 
 
 
 56 
 
 
 6. 3 
 
 3 
 
 
 3 
 
 
 5 
 
 15 
 
 
 115 
 
 
 7. 4 
 
 4 
 
 
 4 
 
 
 4 
 
 14 
 
 
 114 
 
 
 8. Add 
 
 and memorize : 
 
 1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 2 
 
 3 
 
 2 
 
 4 
 
 
 
 1 2 
 
 3 
 
 1 
 
 
 
 6 5 
 
 4 
 
 7 
 
 222 
 64 76 86 
 
 333 
 25 125 135 
 
 444 
 124 134 144 
 
 21 123 
 
 35 543 
 
 234 
 644 
 
 9. A boy rode 15 mi. and walked 3 mi. How far 
 did he travel ? 
 
 10. Helen had 50 ^ and earned 30 t more. How 
 much did she then have ? 
 
 11. Find the cost of 2 Ib. of sugar at 5 ^ a lb., and 
 3 cakes of soap at 3 $ each. 
 
 12. A sack of flour cost 60 ^, and a pound of coffee 
 30 f. What did both cost ? 
 
 13. A young man is 20 yr. old, and his father is 
 50 yr. old. Find the sum of their ages. 
 
 14. I paid $87 for a horse and $ 55 less for a cow; 
 find the cost of the cow. 
 
LESSON 22 
 
 49 
 
 Lesson 22 
 
 
 
 
 
 y \ * * 
 
 i 
 
 > 
 
 
 
 / 
 
 i 
 
 4 
 
 
 
 1. Read these dots 
 and write your results 
 thus: 
 
 in opposite directions, 2 
 in columns for addition, 
 
 Ju 
 
 2 
 
 Add: 
 
 
 
 
 8 
 
 2. 
 
 2 2 
 
 3 3 
 
 2 
 
 2 
 
 
 3 3 
 
 3 3 
 
 2 
 
 2 
 
 
 3 23 
 
 2 12 
 
 4 
 
 44 
 
 3. 
 
 4 2 
 
 2 3 
 
 2 
 
 1 
 
 
 2 4 
 
 3 3 
 
 3 
 
 1 
 
 22 22 
 
 33 52 
 
 22 
 
 45 
 
 4. What is the meaning of 22 + 4 + 2 = 28? Of 
 33 + 2 + 3= 38? 
 
 5. Read these dots in opposite directions, and 
 write your results in columns for addition. 
 
 Add: 
 6. 2 
 5 
 
 23321 
 
 61154 
 
 21 2 42 32 53 
 
50 ARITHMETIC 
 
 7. 1 5 3 1 2 1 
 513243 
 
 22 22 41 65 72 84 
 
 8. Count 8 dots by twos. How many twos ? If 
 each dot represents a pint, how many quarts are 
 there ? 
 
 Count by fours. How many fours ? If each dot 
 represents a quart, how many gallons are there ? 
 
 9. If each of the 8 dots represent $ 1, how many 
 two-dollar bills are represented? If each dot repre- 
 sents half-a-dollar, how many dollars are there ? 
 
 10. Count 8 dots by twos. How many twos ? If 
 a family buys 2 qt. of milk a day, how many quarts 
 will it use in 4 days ? 
 
 Copy and add: 
 
 11. 43 
 
 23 
 
 25 
 
 42 
 
 66 
 
 16 
 
 41 
 
 51 
 
 43 
 
 25 
 
 21 
 
 71 
 
 12. 325 
 
 123 
 
 404 
 
 260 
 
 152 
 
 203 
 
 132 
 
 261 
 
 162 
 
 427 
 
 233 
 
 642 
 
 13. 10 23 31 22 31 11 
 22 21 14 10 30 21 
 13 22 23 35 17 36 
 
 14. Make groups of eight dots and draw lines as 
 in question 1. Write as many different columns for 
 addition as you can. 
 
LESSON 23 51 
 
 15. What two numbers give 8 when added ? 
 
 16. What three numbers give 8 when added ? 
 
 17. I carried home from the store a 2-lb. can of 
 corn, 4 Ib. of nuts, and a 2-lb. roll of butter. How 
 many pounds did my parcel weigh? How many 
 2-lb. ? How many 4-lb. ? 
 
 18. The cost of a chair is measured by the number 
 5 and the unit $ 2. What is its cost ? 
 
 19. A debt of |10 is measured by the unit $5 and 
 a certain number. What is the number ? 
 
 Lesson 23 
 
 1. How long is this oblong ? How wide ? 
 
 2. Draw a line as long as the four sides of this 
 oblong. How long is it? The perimeter of this 
 oblong is 8 in. 
 
 3. Draw an oblong 2 in. long and 1 in. wide. 
 What is the length of its perimeter ? 
 
 4. Draw a square each side of which is 2 in. 
 What is the length of its perimeter? 
 
ARITHMETIC 
 
 5. Draw a square each side of which is 1 inch. 
 This is called a square inch. Draw a square each 
 side of which is 4 inches. How many square inches 
 in this square ? How many 4-sq. in. ? What units 
 of measurement are used in the measurement of this 
 4-inch square ? 
 
 6. How long is this oblong? How wide? It 
 contains 3 square inches (3 sq. in.). One square 
 inch is the unit that measures the area of the oblong. 
 
 7. Draw an oblong 4 in. long and 1 in. wide. 
 Divide it into square inches. What is its area? 
 
 8. What is the area of an oblong 5 in. long and 
 1 in. wide ? 6 in. long and 1 in. wide ? 
 
 9. Draw an oblong containing 8 sq. in. How 
 many 2-sq. in. does it contain ? How many 4-sq. in.? 
 
 Add: 
 
 hr. 
 
 10. 3 
 
 2 
 
 min. 
 
 2 
 4 
 
 hr. min. 
 
 4 20 
 3 30 
 
 hr. 
 
 5 
 1 
 
 min. 
 
 4 
 
 22 
 
LESSON 24 
 
 53 
 
 da. 
 
 11. 2 
 5 
 
 hr. 
 
 5 
 3 
 
 da. 
 
 20 
 40 
 
 hr. 
 1 
 
 yr. 
 
 3 
 
 da. 
 30 
 
 30 
 
 12. A boy is 8 yr. 6 mo. old, and his sister 5 yr. 
 2 mo. What is the difference between their ages ? 
 
 13. A table is 3 ft. 6 in. long and 2 ft. 6 in. wide. 
 What is the sum of the length and width? What 
 is the perimeter of the table ? 
 
 Lesson 24 
 
 1. Read these dots from left to right and from 
 right to left. 
 
 2. Make two groups of 9 dots each. Draw lines 
 and show that 
 
 9 == 8 + 1, or 1 + 8 ; 7 + 2, or 2 + 7. 
 
 Add: 
 
 3. 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 3 
 
 1 1 
 
 1 
 
 
 8 
 
 18 
 
 26 
 
 38 
 
 48 
 
 53 
 
 68 70 
 
 88 
 
 4. 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 
 7 
 
 17 
 
 117 
 
 125 
 
 137 
 
 147 
 
 153 
 
 167 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 
 6 
 
 16 
 
 113 
 
 216 
 
 316 
 
 326 
 
 335 
 
 346 
 
54 ARITHMETIC 
 
 5. A man paid $ 65 for a bicycle, and spent $ 4 in 
 repairs during the year. What was the entire cost? 
 
 6. 454545 45 
 5415142524 35 34 
 
 7. Memorize : 
 
 9 = 8 + 1, or 1 + 8 ; 7 + 2, or 2 + 7 ; 
 6 + 3, or 3 + 6 ; 5 + 4, or 4 + 5. 
 
 8. Arrange 9 dots in groups of 3. How many 3 
 dots in 9 dots? If each dot represents a foot, what 
 unit of length do 3 dots represent ? 
 
 9. If each dot represents 1 Ib. of lard, how many 
 3-lb. pails of lard are represented by 9 dots ? 
 
 10. Add 3 to each of the following numbers : 
 6, 16, 26, 36, 46, 56, 66, 76, 86, 96. 
 
 11. I paid $ 35 for a sofa, the price of which had 
 been reduced $ 4. What was the original price ? 
 
 12. Subtract 4 from each of the following num- 
 bers: 
 
 9, 19, 29, 39, 49, 59, 69, 79, 89, 99. 
 
 13. I paid $ 49 for a rug, less $ 5 for cash. What 
 did the rug cost ? 
 
 14. Copy and add : 
 
 25 27 32 40 36 54 16 60 
 34 42 51 46 63 24 53 19 
 
LESSON 25 55 
 
 15. Copy and subtract : 
 
 76 92 48 78 63 76 59 99 
 23 81 34 37 12 26 41 64 
 
 16. A debt is measured by the number 5 and the 
 unit $2. What is the debt? With the unit 1 5, 
 what number would measure the debt? 
 
 Lesson 25 
 
 = ? 7 + ? = 9 
 = 9 4 + ? = 9 
 
 
 i. 
 
 8 
 
 + 
 
 1 = ? 
 
 
 8 
 
 + ? 
 
 = 9 
 
 
 7 
 
 + ^ 
 
 
 2. 
 
 6 
 
 + 
 
 ? = 9 
 
 
 3 
 
 + ? 
 
 = 9 
 
 
 5 
 
 + 1 
 
 
 3. 
 
 Subtract : 
 
 9 
 
 
 8 
 
 
 6 
 
 9 
 
 
 9 
 
 
 7 
 
 
 9 
 
 6 
 
 
 3 
 
 
 4 
 
 2 
 
 
 1 
 
 
 2 
 
 
 7 
 
 896 
 450 
 
 4. Bertha is 4 yr. old, and her sister 9. In how 
 many years will Bertha be as old as her sister is 
 now? 
 
 5. A post 9 ft. long is 3 ft. below ground. How 
 long is the part above ground ? Draw this post. 
 
 6. Write the following numbers under each 
 other, and add: 12 and 36 ; 25 and 51 ; 42 and 27 ; 
 33 and 53. 
 
 7. A boy is 12 yr. old, and his father 36. What 
 is the sum of their ages ? 
 
 8. It took me 26 min. to ride 4 mi. on a bicycle 
 against the wind, and 21 min. to return with the 
 wind. How long was I gone and how far did I ride ? 
 
56 AEITHMETIC 
 
 9. There are 28 da. in Feb. and 31 da. in March. 
 How many days are there in the two months ? 
 
 10. Write the following numbers under each other, 
 and subtract the smaller from the larger : 86 and 
 64 ; 78 and 31 ; 18 and 89 ; 95 and 34. 
 
 11. A boy has earned $ 32 toward buying a 1 55 
 bicycle. How much has he still to earn ? 
 
 12. Albert has 75 ^, and his sister Florence 50 ^. 
 Albert has how much more than Florence ? 
 
 Lesson 26 
 
 Subtract : 
 
 1. 
 
 5 
 
 15 
 
 25 
 
 6 
 
 16 
 
 26 
 
 6 
 
 26 
 
 
 3 
 
 3 
 
 3 
 
 2 
 
 2 
 
 2 
 
 3 
 
 3 
 
 2. 
 
 7 
 
 27 
 
 6 
 
 36 
 
 8 
 
 48 
 
 9 
 
 49 
 
 
 5 
 
 5 
 
 4 
 
 4 
 
 3 
 
 ~3 
 
 7 
 
 ~7 
 
 3. 
 
 8 
 
 58 
 
 7 
 
 37 ' 
 
 9 
 
 29 
 
 9 
 
 19 
 
 
 6 
 
 6 
 
 4 
 
 ~4 
 
 2 
 
 ~2 
 
 4 
 
 ~4 
 
 4. A person having a 25 ^ piece buys two 2 $ post- 
 age stamps. What change does he get in return ? 
 
 5. Out of 18 baskets of plums 3 baskets are 
 spoiled. How many are good? 
 
 6. It took me 19 min. to row a certain distance 
 up stream, and 6 min. less to return. How long did 
 it take to return ? 
 
LESSON 26 
 
 57 
 
 7. Read these dots from left to right and from 
 right to left, and write your results in columns for 
 addition. 
 
 8. If each dot represents $ 1, what unit of money 
 will 5 dots represent ? 2 dots ? How many dollars in 
 a five-dollar bill and 2 two-dollar bills ? 
 
 9. If each dot represents 1 ft., what unit does a 
 group of 3 dots represent ? What is the sum of 2 ft., 
 1 yd., and 4 ft. ? 
 
 10. Make 9 dots in groups of 3 dots. How many 
 3's in 9? Three yd. of tape at 3^ a yd., find the cost. 
 Paid $ 9 for 3 bbl. of apples. Find cost per bbl. 
 
 11. Arrange 9 dots in groups of 2's. Let each dot 
 represent 1 pt. Make two questions. Arrange in 
 groups of 4's. Let each dot represent 1 qt. Make 
 two questions. 
 
 12. Make groups of 9 dots and draw lines as in 
 question 7. Write as many different columns for 
 addition as you can. 
 
 Add: 
 13. 1 
 
 5 
 3 
 
 14. 
 
 3 
 3 
 
 63 
 
 1 
 
 5 
 
 13 
 
 2 
 
 2 
 
 42 
 
 2 
 3 
 
 22 
 
 2 
 
 5 
 
 31 
 
 5 
 
 3 
 
 31 
 
 4 
 
 3 
 
 12 
 
 1 
 6 
 
 72 
 
 2 
 3 
 
 83 
 
 1 2 
 
 3 5 
 
 64 72 
 
58 ARITHMETIC 
 
 15. Three years ago I was 32 years old. How old 
 shall I be 4 years from now? 
 
 16. I paid |61 for a bicycle, $2 for a lamp, and $6 
 for a bicycle suit. What was the entire cost ? 
 
 Lesson 27 
 
 1. Copy and add : 
 
 123 203 216 14 201 464 
 212 231 101 301 462 301 
 333 543 672 484 125 213 
 
 2. Copy and subtract : 
 
 762 968 650 934 687 989 
 421 265 120 323 534 232 
 
 3. Write the following numbers under each 
 other and add : 323 and 462 ; 236 and 423 ; 683 
 and 214 ; 337 and 542. 
 
 4. Write the following numbers under each 
 other and subtract the smaller from the larger : 
 697 and 182 ; 265 and 495 ; 108 and 279 ; 848 and 
 316. 
 
 5. I pay $250 for a span of horses and $220 for 
 a carriage. Find the cost of both. 
 
 6. There are 255 pupils in the grammar school 
 and 41 in the high school. How many pupils are 
 there in the entire school? 
 
LESSON 28 59 
 
 7. There are 35 pupils in the first grade, 32 in 
 the second, and 30 in the third. How many pupils 
 are there in the first three grades ? 
 
 8. There are 48 pupils in the Kindergarten, of 
 whom 26 are between 5 and 6 years old. How many 
 are between 4 and 5 ? 
 
 9. Of a school of 255 pupils, 231 were present 
 on Friday. How many were absent ? 
 
 10. If I read 122 pages of a book containing 346 
 pages, how many will I have still to read ? 
 
 Lesson 28 
 
 1. Read these dots from left to right and from 
 right to left. 
 
 2. Count 10 by 5's. How many 5's in 10 ? How 
 many nickels in a dime? Count 10 by 2's. How 
 many 2's in 10? How many 1 2 in $10? 
 
 3. If each dot represents a nickel, what unit of 
 money will 5 dots represent ? What unit, if each dot 
 represents 1 dime ? $1? 1 2? 
 
 4. Arrange 10 dots in groups of 2, 3, and 4, and- 
 let each dot represent 1 pt., 1 ft., or 1 qt. Make 
 questions similar to Lesson 16, questions 16 and 17. 
 
60 ARITHMETIC 
 
 5. If $10 is counted by a $2 unit, what is the 
 number? 5 is often called the ratio of 810 to 
 
 6. Make three groups of 10 dots each. Draw 
 lines and show that 
 
 10 = 9 + 1 or 1 + 9; 8 + 2 or 2 + 8 ; 6 + 4 or 4 +6. 
 
 7. Name the number which added to each of the 
 following numbers gives 10 : 
 
 8, 5, 3, 1, 7, 4, 9, 2, 0, 6, 10. 
 
 8. Fill the blanks : 
 
 6 + ? = 10 5 + ? = 10 2 + ? = 10 7 + ? = 10 
 
 9. Add: 22334455 
 
 818172726364555 
 
 10. What unit of money is equal to 10^? 5^? 
 100^? 
 
 11. If I buy two 2 ^ postage stamps, how much 
 change shall I get back out of a dime? 
 
 12. If I buy a postal card, how much change will 
 I get back out of a dime ? Out of a half-dollar ? 
 
 13. Some boys spent 45 ^ for melons and 5 $ for 
 peaches. How much did they spend ? What unit 
 of money would pay for both ? 
 
 14. A farmer sows 16 A. with wheat and 3 A. with 
 oats. How many acres did he sow ? 
 
 15. A man is 27 yr. old, and his son 3 yr. What 
 is the sum of their ages ? What is the difference ? 
 
LESSON 29 61 
 
 16. Two boys hire a boat one hour for 20 ^. If 
 the first pays 15 ^, what does the second pay ? 
 
 Lesson 29 
 
 1. Read these dots from left to right and from 
 right to left, and write your results in columns for 
 addition. 
 
 2. Make groups of 10 dots and draw lines as in 
 question 1. Write as many different columns for 
 addition as you can. 
 
 Add: 
 
 
 
 
 
 
 3. 2 
 
 4 
 
 4 
 
 5 
 
 1 
 
 3 
 
 3 
 
 2 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 4 
 
 24 
 
 42 
 
 66 
 
 83 
 
 4. 4 
 
 2 
 
 12 
 
 2 
 
 4 
 
 33 
 
 1 
 
 3 
 
 56 
 
 2 
 3 
 
 72 
 
 5 3 
 
 1 3 
 
 94 102 
 
 5. Copy and add: 
 
 231 222 212 102 202 
 
 321 134 303 214 471 
 
 215 541 584 683 416 
 
 6. Find the sum of 1142, $ 225, and 1 312. 
 
62 ARITHMETIC 
 
 7. Subtract: 
 
 10 9 10 8 10 9 10 10 
 ~62~51~24~1~3 
 
 8. Copy and subtract: 
 
 942 . 896 107 1085 1077 
 
 611 703 63 823 562 
 
 9. On a debt of $685 I pay $435. How much 
 do I still owe ? 
 
 10. Write the following numbers under each other 
 and add: 
 
 21, 60, and 15 ; 42, 27, and 30 ; 333, 324, and 511. 
 
 11. Write the following numbers under each 
 other and subtract the smaller from the larger: 
 
 899 and 473 ; 1064 and 521 ; 1056 and 823. 
 
 12. I bought three bicycles, paying for the first 
 $40, for the second $22, and for the third $16. 
 What did I pay for all three ? 
 
 13. James weighs 107 lb., and George 82 Ib. How 
 much more does James weigh than George ? 
 
 14. I paid 10 $ for bread, 32 ^ for coffee, and 56 ^ 
 for butter. What did I pay for all ? 
 
 15. A farmer planted 12 cherry trees, 24 apple 
 trees, and 13 plum trees. If eleven died, how many 
 trees were there in his orchard? 
 
1. Add: 
 
 SECTION III 
 Lesson 30 
 
 
 
 
 
 $2 
 
 
 
 
 $2 
 
 2 
 
 
 
 12 
 
 2 
 
 2 
 
 
 $2 
 
 2 
 
 2 
 
 2 
 
 $2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 2. What is the sum of the last column ? Count 
 the number of $ 2 in the last column. 6 x 1 2 = 1 12. 
 
 3. 2xf2 = ? 3x12 = ? 4xf2 = ? 5x$2=? 
 
 4. If 1 hat costs |2, what will 6 hats cost? 
 
 5. Count these dots by 2's. How many 2's in 6 ? 
 Count by 3's. How many 3's in 6 ? 
 
 6 = 3x2 or 2x3. 
 
 6. If each dot represents a pint, how many repre- 
 sent a quart? How many quarts in 6 pt. ? What 
 will 6 pt. of syrup cost at 2 dimes a quart? 
 
 7. If each dot represents 1^, how many represent 
 the value of a 2^ postage stamp ? What will 3 2-cent 
 postage stamps cost? 
 
4 ARITHMETIC 
 
 8. If each dot represents 1 ft., what unit will 3 
 dots represent? How many feet in 2 yd.? What 
 will 6 ft. of tape cost at 3^ a yd.? 
 
 9. 3x2dimes = ? 2 x 3 dimes = ? 
 3x2 tens = ? tens 2x3 tens = ? tens 
 3x2 5-lb. = ? 5-lb. 2x3 5-lb. = ? 5-lb. 
 
 10. What is the cost of 3 yd. of ribbon at 2 dimes 
 a yd. ? How many ten yard lengths of carpet in 3 
 times 2 ten yard lengths ? 
 
 11. Count 8 dots by 2 dots ; 8^ by 2^; 8 dimes by 
 2 dimes ; 8 3-lb. by 2 3-lb. ; 8 2-yd. by 2 2-yd. ; 8 6-sq. 
 in. by 2 6-sq. in. How many 2's in each case ? How 
 many 2-units in an 8-unit quantity? 
 
 12. Count again by 4's. How many 4 dots in 
 8 dots? 4^ in 8^? 4 dimes in 8 dimes? 4 3-lb. in 8 
 3-lb.? 4 2-yd. in 8 2-yd.? 4 6-sq. in. in 8 6-sq. in.? 
 How many 4-units in an 8-unit quantity ? 
 
 13. How many 2's in 8? How many 4's in 8? 
 
 8 = 4x2 or 2x4. 
 
 14. Place 10 dots, count by 2's and 5's, and show 
 
 that 
 
 10 = 5 x 2 or 2x5. 
 
 Count again as in questions 11 and 12. 
 
 15. Place 12 dots so as to show that 
 
 12 = 6 x 2 or 2 x 6. 
 
LESSON 30 65 
 
 16. Place 14, 16, 18, 20 dots, and make similar 
 questions. 
 
 17. Memorize : 
 
 6 = 2x3 or 3x2. 
 
 8 = 2x4 or 4x2. 
 
 10 = 2 x 5 or 5 x 2. 
 
 12 = 2 x 6 or 6 x 2. 
 
 18. 2 and 3 are called factors of 6. What are the 
 factors of 8? 10? 12714? 16? 18? 20? 
 
 19. 2 is one factor of 18. What is the other? 
 How many 2^ stamps can you buy for 18^? 
 
 20. How many 2-lb. bricks of codfish weigh 24 Ib. ? 
 
 21. A board 12 ft. long is cut into 4 pieces. Find 
 length of each piece. If cut into 4 ft. pieces, how 
 many pieces ? 
 
 22. What is the total weight of 5 2-lb. cans of 
 peas, 2 3-lb. cans of tomatoes, 2 6-lb. boxes of starch, 
 andl 10-lb. sack of flour? 
 
 23. Vegetables are put up in 1, 2, and 3-lb. cans, 
 and flour in 10-lb. sacks. Using this, make examples 
 like question 22. 
 
 24. Name the even numbers from 2 to 12. What 
 number is a factor of all these even numbers ? Name 
 all the odd numbers from 1 to 11. Is 2 a factor of 
 these ? How can you change an odd number to an 
 even number? 
 
ARITHMETIC 
 
 Lesson 31 
 
 1. 
 
 2 x 1 in. = ? 
 
 2 x 5 in. = ? 
 
 2 x 9 in. 
 
 = ? 
 
 
 2 x 2 in. = ? 
 
 2 x 6 in. = ? 
 
 2 x 10 in. 
 
 9 
 
 
 2 x 3 in. = ? 
 
 2 x 7 in. = ? 
 
 2 x 11 in. 
 
 = ? 
 
 
 2 x 4 in. = ? 
 
 2 x 8 in. = ? 
 
 2 x 12 in. 
 
 9 
 
 2. 
 
 3x2ft.= ? 
 
 3 x 2 yd. = ? 
 
 3x2 mi. 
 
 = ? 
 
 
 2x3ft. = ? 
 
 2x3yd. = ? 
 
 2x3 mi. 
 
 = ? 
 
 3. 
 
 3x $2 = ? 
 
 3x$20=? 
 
 3x$200 
 
 _ 9 
 
 
 2x $3 = ? 
 
 2x$30 = ? 
 
 2x$300 
 
 = ? 
 
 4. 
 
 4x $2 = ? 
 
 4x$20 = ? 
 
 4x$200 
 
 ? 
 
 
 2x $4 = ? 
 
 2x$40 = ? 
 
 2 x $400 
 
 = ? 
 
 5. A dealer sold 4 sets of furniture at $200 each, 
 and 2 bookcases at $30 each. What did all sell for? 
 
 6. A farmer received $200 for a span of horses, 
 $20 apiece for 3 cows, and $4 apiece for 2 sheep. 
 What did he receive all together? 
 
 7. 4x$20 = ? 5x820 = ? 6x $20 = ? 
 2x$40 = ? 2x$50=? 2x $60 = ? 
 
 8. 7x$20 = ? 8x$20 = ? 9x $20 = ? 
 2x$70 = ? 2x$80 = ? 2x 
 
 9. 10x$20 = ? llx$20 = ? 12 x $20 = ? 
 20x$10 = ? 20x$ll = ? 20 x $12 = ? 
 
LESSON 31 
 
 67 
 
 10. What is the cost of 3 2-lb. rolls of butter at 
 a lb., 2 Ib. of coffee at 30^ a lb., and 2 cakes of 
 
 soap at 4 ^ a cake ? 
 
 11. Find the cost of 2 lb. meat at 12 ^ a lb., 1 can 
 corn at 13^, 1 doz. lemons at 30^ a doz., and 1 lb. 
 bacon at 12^ a lb. 
 
 Copy and multiply : 
 
 12. 22^ 22^ 22^ 21^ 21^ 21^ 
 234567 
 
 13. 123 
 2 
 
 143 
 2 
 
 134 
 2 
 
 154 
 2 
 
 182 
 2 
 
 14. Place 2 under each of these quantities, and 
 multiply: 24 $42, 13 lb., 52 mi., 30 da., 64 yr. 
 
 15. There are 24 hr. in 1 da. How many hours in 
 2 da.? 
 
 16. If there are 21 hills of potatoes in a row, how 
 many hills are there in 6 rows ? 
 
 17. Multiply 23 lb. by 2, and 21 lb. by 3. Add 
 your results. 
 
 18. What is the cost of 5 doz. eggs at 21^ a dozen, 
 and 2 lb. of tea at 42^ a pound? 
 
 19. Memorize : 
 
 Two times 
 
 Iis2 
 
 5 is 10 
 
 9 is 18 
 
 2 is 4 
 
 6 is 12 
 
 10 is 20 
 
 3 is 6 
 
 7 is 14 
 
 11 is 22 
 
 4 is 8 
 
 8 is 16 
 
 12 is 24 
 
68 ARITHMETIC 
 
 20. What is the meaning of 2 x 3 = 6 ? Of 
 
 4x2 = 8? 
 
 21. Place dots so as to show that the factors of 14 
 are 2 and 7 or 7 and 2. How many pounds of rice 
 at 7^ a pound can you buy for 14^? 
 
 22. How many 8-lb. pails of butter can you get 
 from 16 lb.? From 160 lb.? 
 
 23. A length of 24 ft. is measured by the unit 
 4 ft., what is the number ? Draw this length, making 
 1 in. for 1 ft., and measure, counting the number. 
 If the number is 4, what is the unit of measure ? 
 
 24. What are the factors of 16 (16 = 2 x 8 or 8 
 
 x 2), 18, 20, 22, 24 ? 
 
 Lesson 32 
 
 1. 1 qt. = ? pt. 8 qt. = ? pt. 10 qt. = ? pt. 
 3 qt. = ? pt. 5 qt. = ? pt. 12 qt. = ? pt. 
 
 6 qt. = ? pt. 9 qt. = ? pt. 11 qt. = ? pt. 
 
 2. How many times must a pint measure full of 
 water be emptied into a quart measure to fill it? 
 By what number must you multiply to reduce quarts 
 to pints? A pint is what part of a quart? 
 
 3. A pitcher holds 3 qt. of milk. How many 
 pints will it hold? 
 
 4. 2 qt. 1 pt. = ? pt. 6 qt. 1 pt. = ? pt. 
 3 qt. 1 pt. = ? pt. 10 qt. 1 pt. = ? pt. 
 
 7 qt. 1 pt. = ? pt. 12 qt. 1 pt. = ? pt. 
 
LESSON 32 69 
 
 5. How do you reduce 8 qt. and 1 pt. to pints? 
 Multiply the number of quarts by 2, and add 1 to 
 get the number of pints. 
 
 6. lof 6in. = ?in. of 18 in. = ? in. 
 l of 10 in. = ? in. 1 of 24 in. = ? in. 
 J of 14 in. = ? in. J of 16 in. = ? in. 
 
 7. lof|4 = ? off 40 = ? lof |400 = ? 
 
 8. i of 6 pt. = ? pt. J of 16 pt. = ? pt. 
 l of 8 pt. = ? pt. i of 22 pt. = ? pt. 
 1 of 12 pt. = ? pt. 1 of 18 pt. = ? pt. 
 
 9. 2 pt. = 1 qt. 6 pt. = ? qt. 20 pt. = ? qt. 
 4 pt. = ? qt. 12 pt. = ? qt. 24 pt. = ? qt. 
 
 10. 5 pt. = ? qt. ? pt. 15 pt. = ? qt. ? pt. 
 9 pt. = ? qt. ? pt. 23 pt. = ? qt. ? pt. 
 
 11. What will 8 yd. of silk cost at 1 2 a yd.? 
 
 12. If a boy rides 9 mi. an hour, how far will he 
 ride in 2 hr.? 
 
 13. What will 5 qt. 1 pt. of milk cost at 2^ a pt. ? 
 
 14. What will 4 pt. of milk cost at 6/ a qt. ? 
 
 15. What is the price of 2 qt. 1 pt. of milk at 6^ a 
 quart ? 
 
 16. There are 29 fruit trees in an orchard, 5 are 
 cherry trees, 4 plum, and the rest apple ; how many 
 apple trees are there? 
 
TO 
 
 ARITHMETIC 
 
 Lesson 33 
 
 1. How long is this oblong ? How wide ? 
 
 2. How many square inches does it contain ? 
 
 3. The unit of length used to measure short dis- 
 tances is 1 in. The unit of area used to measure 
 small areas is 1 square inch (1 sq. in.). 
 
 4. Draw an oblong 4 in. long and 1 in. wide, and 
 divide it into sq. in. What is its area ? 
 
 5. Draw an oblong 6 in. long and 1 in. wide, and 
 divide it into sq. in. What is its area ? 
 
 6. What is the area of an oblong 8 in. long and 
 1 in. wide ? 10 in. long ? 12 in. long ? 
 
 7. Make an oblong 4 in. long and 2 in. wide. 
 Divide it into sq. in. How many sq. in.? Count 
 by 4's. How many 4 sq. in. ? Count by 2's. How 
 many 2 sq. in. ? 
 
 8. Make an oblong 8 in. long and 2 in. wide. 
 Divide it into sq. in. How many sq. in.? Count 
 by 8's. How many 8 sq. in. ? Count by 2's. How 
 many 2 sq. in. ? 
 
LESSON 33 71 
 
 9. Make other oblongs, divide them into sq. in., 
 and count their areas by sq. in., 2 sq. in., and so on. 
 
 10. How long is this oblong ? How wide ? 
 
 11. Into how many rows is it divided ? What is 
 the area of each row? What is the area of the 
 oblong ? 
 
 12. The area of this oblong is measured by the 
 number 6 (2 x 3) and the unit 1 sq. in. 
 
 13. Make an oblong 4 in. long and 2 in. wide. 
 Divide it as the oblong in question 7 is divided. 
 
 14. What number measures its area ? What is its 
 area? 
 
 15. What number measures the area of an oblong 
 5 in. long and 2 in. wide ? What is its area ? 
 
 16. What is the area of an oblong 6 in. long and 
 2 in. wide ? 
 
72 ARITHMETIC 
 
 17. How do you find the number of sq. in. in an 
 oblong 3 in. long and 2 in. wide? 4 in. long and 
 2 in. wide ? 6 in. long and 2 in. wide ? 8 in. long 
 and 2 in. wide? 10 in. long and 2 in. wide? Any 
 length and any width ? 
 
 18. Make problems like questions 15 and 16. 
 
 Lesson 34 
 
 1.2x3 = 6. 2 and 3 are called factors of 6. 6 
 is the product of 2 and 3. 
 
 2. 2 and 4 are the factors of what number ? 4 
 and 2 are the factors of what number ? 
 
 3. 2 and 6 are the factors of what number? 2 
 and 7? 9 and 2? 2 and 11 ? 12 and 2? 
 
 4. 2 is one factor of 8. What is the other factor ? 
 4 is one factor of 8. What is the other factor ? 
 
 5. 2 is one factor of each of the following num- 
 bers, what is the other factor ? 12, 18, 24, 16, 6, 14, 
 10, 22. 
 
 6. 7 is one factor of 14. What is the other factor ? 
 9 is one factor of 18. What is the other factor ? 
 
 7. What are the factors of each of the following 
 numbers : 6, 10, 12, 8, 20, 16, 24, 14, 22 ? 
 
 8. If 1 yd. of silk costs $3, what will 2 yd. cost ? 
 
 9. If 2 is one factor of 10, what is the other fac- 
 tor? If 2 loaves of bread cost 10^, what will 1 
 loaf cost? 
 
LESSON 35 73 
 
 10. If a man walks 1 mi. in 20 min., how long 
 will he take to walk 4 mi. ? 
 
 11. If 1 horse costs 1200, what will 4 such horses 
 cost? 
 
 12. What must 8^ be multiplied by to give 16^? 
 At 8^ a pound, how many pounds of rice will cost 
 16/2 
 
 13. What will 2 doz. lead pencils cost at 24 $ a 
 dozen? 
 
 14. What will 5 boxes of note paper cost at 20^ a 
 box? 
 
 Lesson 35 
 
 1. 2x 3^= 6 iof 6^ = ? 6^- 3^ = ? 
 2x 6^ = 
 
 2x 9^ = 
 2x12^ = 24^. 
 
 2. What is the meaning of J of 8 = 4? Of | of 
 12 = 6? 
 
 3. |-of|16 = ? l of |160 = ? iof24mi. = ? 
 l of 240 mi. =? l of 6 in. =? \ of 8 ft. = ? 
 
 4. 1 ft. = 12 in. 1 ft. = ? in. 2 ft. = ? in. 
 
 5. 1 dime = 10 ^ 1 dime = ? ^. 2 J- dimes = ? ^ 
 
 6. 11 = 100^. = ? I2i=?^. 
 
 7. 1 doz. = 12. 1 doz. = ? 21 doz. = ? 
 
 8. 1 hr, = 60 min. J hr. = ? min. 2J hr. = ? mill, 
 
74 ARITHMETIC 
 
 9. 1 da. = 24 hr. J- da. = ? hr. | yr. = ? mo. 
 
 10. 1 gal. = 4 qt. 1 gal. = ? qt. 2 J- gal. = ? qt. 
 
 11. 1 qt. = 2 pt. 6 J qt. = ? pt. 10 qt. = ? pt. 
 
 12. If 1 gal. of kerosene costs 1 dime, what part 
 of a dime will J gal. cost ? How many cents will 
 ^ gal. cost ? 
 
 13. If 1 Ib. of sugar costs 6^, how many cents 
 will 21 Ib. cost ? 
 
 14. What will half-a-dozen lemons cost at 24 $ a 
 doz.? Half-a-doz. silver spoons at $ 22 a doz. ? 1^ doz. ? 
 
 15. A pail contains 8 qt. of water. How many 
 quarts will be left in the pail after 10 pt. are taken 
 out? 
 
 16. If 1 qt. of molasses costs 40 ^, what will 1 pt. 
 cost? What will 2 qt. 1 pt. cost? 
 
 17. A dish holds 3 qt. of berries and 1 pint more. 
 How many pints did it hold, and what did they cost 
 at 10^ a qt.? 
 
 18. How many quarts in 2 gal. 2 qt. ? How many 
 pints in 2 gal. 2 qt. 1 pt. ? In 1 gal. 3 qt. 1 pt. ? 
 
 19. What is the cost of 2 gal. 2 qt. 1 pt. of milk 
 at 2 f a pt. ? 
 
 What does a milkman gain by buying 1 gal. 3 qt. 
 1 pt. of milk at 2 f a pt. and selling it at 3 ^ a pt. ? 
 
 20. Copy and multiply : 
 
 21^ 32^ 44^ 53^ 64^ 72^ 
 
 2 2 2-2 2 2 
 
LESSON 36 75 
 
 21. How much more will 2 yd. of cloth cost at 
 44? a yd. than 3 yd. at 22^ a yd. ? 
 
 22. A boy walks 2 mi. to the depot, rides on the 
 train for 2 hr. at the rate of 32 mi. an hour, and then 
 drives 4 mi. to his friend's house. What is the 
 whole distance ? 
 
 23. Make questions using the following price list : 
 Coffee at 30^ a Ib. Butter at 24^ a Ib. 
 Eggs at 14 ^ a doz. Fruit at 22 ^ a qt. 
 
 Lesson 36 
 
 1. How long is the line a ? How long is the 
 line b? 
 
 2. Compare b with a. The line b is measured 2 
 times by the line a. The ratio of b to a is 2. 
 
 3. Compare a with b. What part of b is needed 
 to make a ? a is of b. The ratio of a to b is . 
 
 4. How long is a ? How long is b ? 
 
 5. Compare b with a. b is measured how many 
 times by a ? The ratio of 5 to a is what ? 
 
 6. Compare a with 5. What part of b needed to 
 make a ? The ratio of a to is what ? 
 
76 ARITHMETIC 
 
 7. Compare 4 in. with 2 in. A 4-in. line is 
 measured how often by a 2-in. line ? The ratio of 
 4 in. to 2 in. is 2. 
 
 8. Compare 2 in. with 4 in. What part of 4 in. 
 is needed to make up 2 in. ? 2 in. is | of 4 in. The 
 ratio of 2 in. to 4 in. is J. 
 
 9. Draw a line 3 in. long. Draw a line 6 in, 
 long. Divide this line into parts each 3 in. long. 
 
 10 Compare 6 in. with 3 in. 3 in. measures 6 in, 
 how many times ? The ratio of 6 in. to 3 in. is 2. 
 
 11. Compare 3 in. with 6 in. What part of 6 in. 
 is needed to make up 3 in. ? 3 in. is what part of 6 
 in. ? The ratio of 3 in. to 6 in. is what? 
 
 12. Memorize : J is the ratio of 1 in. to 2 in. ; 
 of 2 in. to 4 in. ; of 3 in. to 6 in. 
 
 Lesson 37 
 
 Copy and add : 
 
 1. 
 
 2 
 
 1 
 
 2 
 
 3 
 
 2 
 
 2 
 
 4 
 
 6 
 
 
 3 
 
 3 
 
 2 
 
 3 
 
 1 
 
 6 
 
 4 
 
 1 
 
 
 2 
 
 4 
 
 4 
 
 3 
 
 5 
 
 2 
 
 1 
 
 3 
 
 2. 
 
 2 
 
 
 3 
 
 3 
 
 5 
 
 3 
 
 
 2 
 
 
 4 
 
 
 2 
 
 6 
 
 1 
 
 4 
 
 
 1 
 
 
 22 
 
 
 33 
 
 40 
 
 51 
 
 62 
 
 
 73 
 
 3. 
 
 4 
 
 
 6 
 
 3 
 
 1 
 
 4 
 
 
 3 
 
 
 1 
 
 
 2 
 
 3 
 
 3 
 
 3 
 
 
 3 
 
 
 10 
 
 
 81 
 
 43 
 
 61 
 
 12 
 
 
 92 
 
LESSON 37 77 
 
 21 
 
 12 
 
 54 
 
 
 66 
 
 73 
 
 24 
 
 11 
 
 30 
 
 21 
 
 
 10 
 
 14 
 
 30 
 
 51 
 
 46 
 
 34 
 
 
 22 
 
 12 
 
 25 
 
 231 
 
 111 
 
 
 121 
 
 
 545 
 
 32 1 
 
 222 
 
 304 
 
 
 502 
 
 
 123 
 
 130 
 
 314 
 
 182 
 
 
 375 
 
 
 331 
 
 533 
 
 6. There are 102 pages in the First Reader, 150 
 in the Second, and 245 in the Third. How many 
 pages are there in the three Readers ? 
 
 Copy and subtract : 
 
 32 45 64 96 85 69 
 
 ' 11 31 22 73 32 26 
 
 245 329 675 486 1065 
 
 123 115 254 232 253 
 
 9. A man's salary is $840, in addition to which 
 he has an income of $245. If his yearly expenses 
 are $ 625, how much can he save ? 
 
 896 678 795 888 999 
 
 ' 273 207 385 543 601 
 
 2345 3546 6547 9861 7209 
 
 1223 2314 4236 2341 2106 
 
 12. A span of horses weighs 2469 Ib. If one 
 weighs 1224 Ib., what does the other weigh ? 
 
78 ARITHMETIC 
 
 Copy and multiply : 
 
 13. 232 j* 423 j* 634^ 804 j* 806 <* 
 
 2 2 2 2.2 
 
 14. Make simple practical questions illustrating 
 
 $8 -=- 2 = |4, and $8 -i- $2 = 4. What is the mean- 
 ing of 6 H- 2 = 3 ? 
 
 Copy and divide : 
 
 15. 2)42 2)84 2)66 2)28 2)46 2)88 
 
 16. 2)246 2)128 2)642 2)804 2)188 
 
 17. |636 -3 = ? $488 -s- $4 = ? $168-*- 8 = ? 
 
 18. If a 2-lb roll of butter costs 64 what is the 
 price per Ib. ? 
 
 19. What is the price of cheese per Ib. when 4 Ib. 
 
 cost 84^? 
 
 20. Out of a bag containing 159 nuts 4 children 
 each took a handful and there were still left in the 
 bag 119 nuts. How many nuts did the children 
 take ? How many did each get on the average ? 
 
 Lesson 38 
 
 1. Draw a line 1 ft. long. Draw a line 2 ft. 
 long. Divide this line into parts each 1 ft. long. 
 
 2. Compare 2 ft. with 1 ft. The ratio of 2 ft. 
 to 1 ft. is what ? 
 
LESSON 38 79 
 
 3. Compare 1 ft. with 2 ft. What part of 2 it. 
 is needed to make up 1 ft. ? 1 ft. is what part of 2 
 ft.? The ratio of 1 ft. to 2 ft. is what ? 
 
 4. What is the ratio of 1 yd. to 2 yd.? Of 1^ 
 to 2^? Of $1 to $2? Of 1 da. to 2 da.? Of 
 1 hr. to 2 hr. ? 
 
 5. If 1 2 will buy 12 yd. of ribbon, what part of 
 12 yd. will $ 1 buy ? How many yards ? 
 
 6. If a train travels 60 mi. in 2 hr., what is the 
 rate per hour ? 
 
 7. Draw a line 4 in. long. Draw a line 8 in. 
 long. Divide this line into parts each 4 in. long. 
 
 8. Compare 8 in. with 4 in. 8 in. is measured 
 how many times by 4 in.? The ratio of 8 in. to 
 4 in. is what number ? 
 
 9. What is the ratio of 8 ft. to 4 ft. ? Of 8^ 
 to 4^? Of $8 to $4? Of 8 da. to 4 da.? Of 
 8 hr. to 4 hr. 
 
 10. A boy walks 10 mi. in 4 hr. At the same 
 rate, how many times 10 mi. will he walk in 8 hr. ? 
 How many miles ? 
 
 11. If $4 buys 3 yd. of cloth, how many yards 
 
 will 1 8 buy? 
 
 12. Compare 4 in. with 8 in. What part of 8 in. 
 is needed to make up 4 in. ? 4 in. is what part of 
 8 in. ? What is the ratio of 4 in. to 8 in. ? 
 
gO ARITHMETIC 
 
 13. What is the ratio of 4 ft. to 8 ft. ? Of $4 
 to 18? Of 4 yr. to 8 yr. ? Of 4 Ib. to 8 lb.? 
 
 14. At the rate of 18 a doz., what part of a dozen 
 pairs of stockings will cost $4? How many pairs? 
 What will 4 bars of soap cost, at the rate of 8 for 
 
 15. Draw lines 5 in. long and 10 in. long. Divide 
 the line 10 in. long into parts each 5 in. long. 
 
 16. What is the ratio of 10 in. to 5 in.? Of 
 5 in. to 10 in.? 
 
 17. What is the ratio of 2 to 4? 3 to 6? 4 to 8? 
 5 to 10? 
 
 18. Name other numbers that J is the ratio of. 
 
 19. 2 is the ratio of what numbers ? 
 
 20. What is the ratio of 12 to 6 ? Of 6 to 12 ? 
 Of 16 to 8 ? Of 8 to 16 ? 
 
 21. What will 8 lb. of sugar cost, when 16 lb. are 
 sold for 84^ ? What will 12 lb. cost ? 
 
 22. What is the ratio of 1 qt. to 1 pt.? Of 1 pt. 
 to 1 qt.? Of 1 dime to 1 nickel? Of 1 nickel to 1 
 dime ? Of one -quarter dollar to one-half dollar ? 
 
 Lesson 39 
 
 1. The length of a sheet of drawing-paper is 9 in. 
 Here the unit of measure is 1 in. The number that 
 measures the length is 9. 
 
LESSON 39 81 
 
 2. The width of a sheet of drawing-paper is 6 in. 
 What is the unit of measure? What is the number 
 that measures the width ? 
 
 3. The length of a table is 4 ft. What is the 
 unit of measure ? What is the number that measures 
 its length ? 4 is the ratio of the length to 1 ft. 
 
 4. The width of a room is 6 yd. What is the 
 unit of measure ? What is the number ? 
 
 5. The distance between two cities is 30 mi. 
 What is the unit of measure ? What is the number 
 of units ? 
 
 6. A pitcher holds 3 qt. of milk. What is the 
 unit of measure ? What number measures the quan- 
 tity of milk ? 
 
 7. A pail holds 6 2-qt. cans of milk. What is 
 the unit of measure ? What is the number of units ? 
 How many gallons will the pail hold ? 
 
 8. The quantity of kerosene in a can is measured 
 by the number 5 and the unit of measure 1 gal. How 
 much kerosene is there in the can ? 
 
 9. I buy 10 bu. of potatoes. What is the unit ? 
 What number measures the quantity of potatoes ? 
 
 10. A family eats 2 5-lb. pails of butter in 1 mo. 
 What is the unit ? How many units of 1 Ib. each. ? 
 How many 2-lb rolls of butter would the family eat 
 in one month ? 
 
82 ARITHMETIC 
 
 11. When a grocer sells sugar, why does he weigh 
 it ? What unit does he use ? 
 
 12. A book contains 250 pages. What number 
 measures the size of the book ? What is the unit ? 
 
 13. A room is 8 yd. 1 ft. 6 in. long. What three 
 units are used to measure the length of the room ? 
 
 14. The quantity of berries in a crate is measured 
 by the number 16 and the unit 1 qt. How many 
 quarts of berries are there in a crate ? 
 
 15. The cost of a yard of ribbon is measured by 
 the number 2 and the unit 1 dime. How many cents 
 did it cost ? What is the ratio of the cost to 1 nickel? 
 
 16. If the unit of money is a ten-dollar bill, how 
 many dollars are there in 2 units ? . If there are 2 
 units of money in 20 ^, what is the unit ? Paid an 
 account of 1 50 with 5 coins of equal value. How 
 many dollar units is each coin worth ? 
 
 17. Draw two oblongs each of which will contain 
 6 sq. in. 
 
 18. An oblong contains 6 sq. in. What is the 
 unit of measure ? What number measures the area ? 
 With a 2-sq. in. unit, what number ? With a 3-sq. 
 in. unit, what number ? 
 
 Lesson 40 
 
 1. What is the ratio of 1 in. to 2 in. ? Of 1 
 1 ft. to 2 ft. ? Of 1 yd. to 2 yd. ? - 
 
LESSON 40 83 
 
 2. If 2 yd. of cloth cost $1, what part of $1 
 will 1 yd. cost. ? How many cents ? 
 
 3. If 2 yd. of ribbon cost 12 what part of 12^ 
 will 1 yd. cost.? How many cents? 
 
 4. What is the ratio of 2 Ib. to 4 Ib. ? If 4 
 Ib. of sugar cost 20^, what part of 20^ will 2 Ib. 
 cost. ? What will 2 Ib. cost ? 
 
 5. If 4 loaves of bread cost 24^, what part of 
 24^ will 2 loaves cost ? What will 2 loaves cost ? 
 
 6. What is the ratio of 4 to 2 ? If 2 lead pen- 
 cils cost 5^, what will 4 lead pencils cost ? 
 
 7. What is the ratio of 3 to 6? If 6 spools 
 of thread cost 22^, what part of 22^ will 3 spools 
 cost ? What will 3 spools cost ? 
 
 8. What is the ratio of 8 to 4 ? If 4. lemons 
 costs 10^, how many times 10^ will 8 lemons costs? 
 What will 8 lemons cost ? 
 
 9. What is the ratio of a nickel to a dime ? 
 If a dime will buy 12 bananas, how many will a 
 nickel buy ? 
 
 10. What is the ratio of 4 Ib. to 2 Ib. ? If 
 2 Ib. of coffee cost 70^, how many times 70^ will 
 4 Ib. cost ? What will 4 Ib. cost ? 
 
 11. What is the ratio of a 50^ piece to a 
 piece? Of a 25^ piece to a 50^ piece? 
 
84 
 
 ARITHMETIC 
 
 12. If a 50^ piece will buy 16 Ib. of walnuts, how 
 many pounds will a 25 $ piece buy ? 
 
 13. What is the ratio of 1 unit of any kind (as 2 
 Ib., 3 yd., or $4) to two units of the same kind (as 4 
 Ib., 6 yd., or $8) ? If 2 units of ribbon (as 6 yd.) 
 cost 80^, what will 1 unit (or 3 yd.) cost? 
 
 14. Draw an oblong 3 in. long and 2 in. wide. 
 Draw an oblong 3 in. long and 1 in. wide. What 
 is the ratio of the first oblong to the second ? 
 
 Lesson 41 
 
 1. Memorize : 
 
 Three times 
 
 lis 3 
 
 5 is 15 
 
 9 is 27 
 
 2 is 6 
 
 6 is 18 
 
 10 is 30 
 
 3 is 9 
 
 7 is 21 
 
 11 is 33 
 
 4-is 12 
 
 8 is 24 
 
 12 is 36 
 
 2. Count by 3's from 3 to 36. 
 
 3. Count by 3's from 36 to 3. 
 
 4. Count the number of these dots by 4's ; by 3's. 
 There are how many counts of 4 dots ? 
 There are how many counts of 3 dots ? 
 12 = 3 x 4 or 4 x 3. 
 
LESSON 41 85 
 
 5. If each dot represents 1 ft., what do 3 dots 
 represent? How many yards in 12 ft.? How many 
 feet in 8 yd. 2 ft. ? 
 
 6. If each dot represents 1 qt., how many dots 
 represent 1 gal.? How many quarts in 3 gal.? 
 What is the price of 3 gal. 2 qt. of kerosene at 12^ 
 per gal. ? 
 
 7. If each dot represents 1 sq. in., draw the figure 
 represented by the 12 dots? How long is it? How 
 wide ? What is the area of an oblong 4 in. long and 
 3 in. wide? 4 yd. long and 3 yd. wide? Draw a 
 square yard on the blackboard. 
 
 8. Place 15 dots so as to show that 
 
 15 = 3 x 5 or 5 x 3. 
 
 How many feet in 5 yd.? The area of an oblong 
 5 in. long is 15 sq. in. How wide is it? 
 
 9. 3 is one factor of each of the following num- 
 bers, what is the other : 6, 18, 12, 21, 30, 24, 36, 27, 
 33? 
 
 10. 9 is one factor of 18. What is the other 
 factor ? 8 is one factor of 24 ? What is the other 
 factor ? 
 
 11. What are the two factors of each of the fol- 
 lowing numbers : 
 
 21 (3 x 7 or 7 x 3), 12, 27, 9, 33, 18, 36, 15, 30? 
 
 12. 12 is one factor of 36, what is the other? How 
 many feet in 36 in. ? A dozen yards of cloth cost 36 
 dimes, what is the cost of 1 yd. ? How many cents ? 
 
86 ARITHMETIC 
 
 Copy and multiply : 
 
 13. 
 
 21 
 
 33 
 
 42 
 
 63 
 
 52 
 
 13 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 r. 
 
 14. 
 
 72 
 
 53 
 
 81 
 
 92 
 
 60 
 
 82 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 
 
 15. 
 
 112 
 
 221 
 
 321 
 
 231 
 
 333 
 
 20;} 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 16. 
 
 7 
 
 3 5 
 
 3 
 
 3 
 
 3 3 
 
 3 
 
 
 3 
 
 7 3 
 
 5 
 
 9 
 
 6 8 
 
 12 
 
 17. 
 
 30 
 
 31 
 
 32 
 
 31 
 
 34 
 
 31 
 
 
 5 
 
 7 
 
 4 
 
 9 
 
 2 
 
 5 
 
 18. Find the total cost of : 
 
 3 Ib. crackers at 7 f a Ib. 
 
 2 Ib. wafers at 12^ a Ib. 
 7 Ib. oatmeal at 3 1 a Ib. 
 
 3 Ib. of raisins at 10^ a Ib. 
 
 19. A man walked east. 3 lir. at the rate of 3 mi. 
 an hr., and then walked west 5 mi. How far was he 
 then from his starting-point? Draw a line to repre- 
 sent the road, and mark the distances. 
 
 20. 3)39 3)63 3)96 3)246 3)336 3)696 
 
 21. 5)105 6)186 7)140 8)248 9)279 9)189 
 
 22. How many weeks are there in 210 da. ? How 
 many gallons in 128 qt. ? How many yd. in 150 ft.? 
 
LESSON 42 87 
 
 23. A man walks 12 mi. at the rate of 3 mi. an 
 hr., and returns at the rate of 4 mi. an hour. How 
 many hours is he gone ? 
 
 24. A farmer divides 336 A. equally among his 3 
 sons. What is the share of each? 
 
 Lesson 42 
 
 Multiply : 
 
 1. 
 
 4 
 
 40 
 
 50 
 
 200 
 
 30 
 
 30 
 
 110 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 6 
 
 8 
 
 3 
 
 2. 
 
 60 
 
 30 
 
 120 
 
 80 
 
 30 
 
 700 
 
 300 
 
 
 3 
 
 9 
 
 3 
 
 3 
 
 5 
 
 3 
 
 4 
 
 3. A milkman traded 3 horses worth $ 80 each for 
 7 cows worth $30 each. How much money should 
 he receive in addition ? 
 
 4. 2ft. = ?in. 2ft. 6in. = ?in. 3 ft. 2 in. = ?in. 
 
 5. 24 in. = ? ft. 28 in. = ? ft.? in. 
 
 39 in. = ?ft.?in. 
 
 6. 1 gal. = 4 qt. 3 gal. 2 qt. = ? qt. 
 
 3 gal. 3 qt. = ? qt. 
 
 7. 6yd. = ?ft. 6yd. 2ft. = ?ft. 8 yd. 1 ft. =?ft. 
 How do you reduce yards to feet? 
 
 8. 12 ft. =? yd. 8ft.=?yd.?ft. 28 ft. = ? yd.? ft. 
 How do you reduce feet to yards ? 
 
88 ARITHMETIC 
 
 9. 17 ft. = ? yd. ? ft. 23 ft. = ? yd. ? ft. 
 34ft. = ?yd. ?ft. 
 
 10. A jug contains 3 gal. 2 qt. of cider. How 
 many quarts of cider are there in the jug? 
 
 11. A room is 6 yd. 2 ft. long. How many feet 
 long is it ? 
 
 12. A rope is 15 ft. long. Into how many pieces 
 each 1 yd. long can it be cut ? 
 
 13. From a piece of cloth 4 yd. long a piece 2 ft. 
 long has been cut. How many feet of cloth are left? 
 
 14. If 1 qt. of milk costs 6 ^, find the cost of 1 qt. 
 and 1 pt. Of 2 qt. and 1 pt. 
 
 15. If 1 yd. of cambric costs 12^, find the cost of 
 2 yd. 1 ft. Of 3 yd. 1 ft. 
 
 16. What will a man earn in, 1 wk. 3 da. at $3 
 a day. 
 
 17. If a boy picks 8 pt. of berries in 1 hr., how 
 many quarts will he pick in 3 hr. ? 
 
 18. My chicken coop is 3 yd. 1 ft. long and 2 yd. 
 wide. How long must a rope be to go around it ? 
 
 19. If my hens lay 6 eggs a day, how many dozen 
 do they lay in one week ? What are they worth at 
 20 f a doz. ? 
 
 20. I divide ^ of 24 ^ equally among 3 boys. What 
 does each get? ^ of 24 is 3 times what number? 
 J of 16 is 4 times what number? J of 42 is 3 times 
 what number ? 
 
LESSON 43 
 
 Lesson 43 
 
 89 
 
 1. What is the length of this oblong? What is 
 its width? How many square inches are there in 
 the first row ? How many rows ? The area = 3 x 
 3 sq. in. = 9 sq. in. 
 
 2. Draw an oblong 4 in. long and 3 in. wide. 
 Divide it as the oblong in question 1. What is its 
 area? 
 
 3. Represent the area of the oblong in question 2 
 by dots, putting one dot for each square inch. 
 
90 ARITHMETIC 
 
 4. What is the area of an oblong 6 in. long and 
 3 in. wide ? 8 in. long and 3 in. wide ? 
 
 5. Make examples like question 3. 
 
 6. Draw on the board an oblong 3 ft. long and 
 
 2 ft. wide. What is its area ? Draw a square yard. 
 How many square feet in its area ? 
 
 7. What is the area of an oblong 4 ft. long and 
 
 3 ft. wide ? 6 ft. long and 3 ft. wide ? 6 yd. long 
 and 3 yd. wide ? 
 
 8. Draw the last oblong in question 6, making 
 1 in. for 1 yd. What doBS 1 sq. in. in your drawing 
 represent ? 
 
 9. An oblong contains 12 sq. in. The unit of 
 measure is 1 sq. in. The number 12 measures the 
 area. 
 
 10. What number and what unit measure the 
 area of an oblong containing 8 sq. in. ? 16 sq. in. ? 
 6 sq. ft. ? 10 sq. ft. ? 9 sq. yd. ? 14 sq. yd. ? 
 
 11. An oblong is 4 in. long and 3 in. wide. What 
 number measures its area ? What is its area ? 
 
 12. An oblong is 8 in. long and 3 in. wide. What 
 number measures its area ? 
 
 13. What numbers measure the areas of the fol- 
 lowing oblongs, and what are their areas ? 
 
 Length Width Length Width 
 
 4 in. 2 in. 10 in. 3 in. 
 
 6 in. 2 in. 7ft. 3ft. 
 
 9 in. 3 in. 8 yd. 3 yd. 
 
LESSON 44 91 
 
 14. A room is 12 ft. long and 9 ft. wide. How 
 many square yards of carpet are needed to cover it? 
 
 15. One oblong is 7 in. long and 2 in. wide. 
 Another is 5 in. long and 3 in. wide. Which is 
 larger, and how much ? 
 
 16. A rug is bought for a room 15 ft. by 12 ft. 
 If the edge of the rug is everywhere 1 ft. from the 
 wall, what are its length and breadth? Draw the 
 room and rug on the board, making 1 in. for 1 ft. 
 
 Lesson 44 
 
 1. What will 8 lemons cost at 3^ each? 
 
 2. What will 3J yd. of ribbon cost at 8^ a yd. ? 
 
 3. What is the cost of 12 yd. of tape at 2J^ a yd. ? 
 
 4. If 3 bbl. of flour cost $18, what will 1 bbl. 
 cost? 
 
 5. What is the cost of one dozen oranges at 3^ 
 apiece ? 
 
 6. A man walks 3 mi. an hour for 6 hr. How 
 far does he walk ? How long is he gone if he returns 
 at the rate of 9 mi. an hr. ? 
 
 7. A man travels 6 hr. at the rate of 30 mi. an 
 hour. How far does he travel ? 
 
 8. How many days are there in 3 wk. 2 da. ? 
 
 9. How many hours will it take to drive 24 nii., 
 at the rate of 8 mi. an hour ? 
 
92 ARITHMETIC 
 
 10. If a bag holds 3 bu. of potatoes, how many 
 bags will hold 36 bu. ? 
 
 11. Place 3 under each of these quantities and 
 multiply : $ 22, 31^, 42 qt., 52 Ib. 
 
 12. Find the cost of 3 bicycles at $ 32 apiece. 
 
 13. A milkman has 92 customers who take on the 
 average 3 qt. of milk a day. How many quarts of 
 milk does he sell a day? 
 
 14. Divide each of these quantities by 3 : $ 60, 
 39^, 66 qt., 93 Ib., 216 bu. 
 
 15. If 3 bu. contain 96 qt., how many quarts are 
 there in 1 bu. ? 
 
 16. In how many weeks will a person pay $156 
 for board at the rate of $ 3 a week ? 
 
 17. If 1 boy can do a piece of work in 6 da., how 
 long will it take 3 boys to do it? 
 
 Lesson 45 
 
 1. 1 of 6 in. = ? 1 of 18 in. =: ? of 24 in. = ? 
 of 33 in. = ? l of 150 in. = ? J of 210 in. = ? 
 
 2. 12 in. -*- 3 in. = ? 12 in. -=- 3 = ? 
 21 in. -=- 3 in. = ? 21 in. -f- 3 = ? 
 18 in. ^-6 in. = ? 18 in. ^ 6 = ? 
 
 3. 1ft. =?in. Jft. =?in. J ft. = ? in. 
 yd. = ? ft. 1 yd. = ? in. yd. = ? in. 
 
LESSON 45 93 
 
 4. 1 da. = ? hr. J- da. = ? hr. da. = ? hr. 
 
 1 hr. = ? min. J hr. = ? min. ^ hr. = ? rnin. 
 
 5. 1 min. = ? sec. ^ min. = ? sec. -J min. = ? sec. 
 j- doz. = ? doz. = ? J- doz. + 1 doz. = > 
 
 6. If 3 Ib. of sugar cost 15^, what will 1 Ib. 
 cost? What will 2 Ib. cost? 
 
 7. I paid $18 for coal at 16 a ton. How many 
 tons did I buy ? 
 
 8. If 3 gal. of kerosene cost 36^, what will 1 
 gal. cost ? What will 2 gal. cost ? 
 
 9. Mary spends 24 ^ for lace at 12 $ a yd. How 
 many yards does she buy ? 
 
 10. Divide 2 dozen roses equally among 3 persons. 
 
 11. A man buys 2 horses for $ 220. What is the 
 cost of each horse ? 
 
 12. An oblong is 4 in. long and 3 in. wide. How 
 many square inches does it contain ? 
 
 13. An oblong contains 15 sq. in. If it is 3 in. 
 wide, how long is it ? Draw the oblong. 
 
 14. I bought 1^ doz. bananas at the rate of 15^ a 
 doz. What did I pay for them ? 
 
 15. A mason earns 30 $ an hour. How much will 
 he earn in 1 da., if he works 9 hr. a day ? 
 
94 ARITHMETIC 
 
 Lesson 46 
 
 1. Draw a line 2 in. long. Draw a line 6 in. 
 long. 6 in. is measured how many times by 2 in. ? 
 The ratio of 6 in. to 2 in. is what ? The ratio of 
 2 in. to 6 in. is what ? 
 
 2. Draw lines 4 in. and 12 in. long. 12 in. is 
 measured how many times by 4 in. ? The ratio of 
 12 in. to 4 in. is what? 
 
 3. The ratio of 12 apples to 4 apples is what ? 
 If 4 apples cost 5^, how many times 5^ will 12 
 apples cost ? What will 12 apples cost ? 
 
 4. What is the ratio of 15 in. to 5 in.? What is 
 the ratio of 5 in. to 15 in.? 
 
 5. What is the ratio of 18 in. to 6 in.? What is 
 the ratio of 6 in. to 18 in.? 
 
 6. What is the ratio of 6 to 2 ? 2 to 6 ? 8 to 4? 
 4 to 8 ? 15 to 5 ? 5 to 15 ? 18 to 6 ? 6 to 18 ? 
 
 7. What is the ratio of 5 ft. to 15 ft.? 18 Ib. to 
 61b.? 18 doz. to 6 doz.? $8 to $24? 
 
 8. If 15 Ib. of butter cost 13, what will 5 Ib. 
 cost? 
 
 If 5 yd. of silk cost $ 8, how many yards will cost 
 $24? 
 
 9. l is the ratio of 4 to ? 5 to ? 6 to ? 7 to ? 
 8 to ? 9 to ? 10 to ? 11 to ? 12 to ? 
 
 10. 3 is the ratio of 12 to ? 15 to ? 18 to ? 21 
 to ? 24 to ? 27 to ? 30 to ? 33 to ? 36 to ? 
 
LESSON 47 95 
 
 11. ^ is the ratio of what numbers ? 3 is the ratio 
 of what numbers ? 
 
 12. What is the ratio of 6 doz. to 18 doz.? If 18 
 doz. eggs cost 1 3, what will 6 doz. cost ? 
 
 13. What is the ratio of 1 yd. to 1 ft.? If 1 ft. of 
 ribbon cost 5^, what will 1 yd. cost? 
 
 14. What is the ratio of 1 ft. to 1 yd.? If 1 yd. 
 of lace costs 30^, what will 1 ft. cost? 
 
 15. What is the ratio of 8 wk. to 24 wk.? If I 
 pay 8120 for board for 24 wk., what part of 1120 
 must I pay for 8 wk.? What must I pay for board 
 for 8 wk.? 
 
 16. What is J the ratio of ? What is 2 the ratio 
 of? 
 
 17. The ratio of the value of a purse to its con- 
 tents is |. If the purse is worth $3, how much 
 money does it contain ? 
 
 Lesson 47 
 
 1. Jof$60=? lof|48=? Jof$63=? 
 1 of 88 =? J of 39 =? -l of 99 =? 
 
 2. Draw a line 1 ft. long, and divide it into 
 halves. How many halves are there in 1 ft.? 
 
 1 ft. = | ft. (Read, 1 ft. = 2 halves of a foot.) 
 
 3. 11 ft. = | ft. 2 ft. = 2 ft. 21 ft. == 2 ft - 
 
 41 ft. = 2 ft ' 6 - ft - = 2 ft ' 7 i ft ' = 2 ft ' 
 
 How do you reduce 5J ft. to halves of a foot ? 
 
96 ARITHMETIC 
 
 4. | ft. = ? ft. | ft. = ? ft. | ft. = ? ft. 
 
 f ft. = ? ft. | ft. = ? ft. ^L ft. = ? ft. 
 
 5. 1 qt. = ? pt. qt. = ? pt. 41 qt. = ? pt. 
 6J qt. = ? pt. 8J qt. = ? pt. 121 qt. = ? pt. 
 
 How do you reduce 5 J qt. to pints ? 
 
 6. 1 pt. = ? qt. 4 pt. = ? qt. 5 pt. = ? qt. 
 9 pt. = ? qt. 15 pt. = ? qt. 21 pt. = ? qt. 
 
 How do you reduce 7 pt. to quarts ? 
 
 7. What is the cost of 5 pt. of milk at 6 ^ a qt. ? 
 
 8. 3 + 21 = ? 11 + 2 = ? 21 + l = ? 
 41 -f- 11 = ? 51 + 31 = ? 81 + 21 = ? 
 
 9. What is the weight of a parcel containing 1^- 
 Ib. of ham and 2 J Ib. of steak ? 
 
 Add: 
 
 10. $21 
 
 H 
 
 14 
 
 
 131 
 
 
 $41 
 6 
 
 $21 
 12 
 
 fioi 
 
 101 
 
 11. 21 
 ^ 
 
 % 
 12J 
 
 % 
 221 
 
 B| 
 
 ^ 
 
 H 
 
 24^ 
 
 4 
 
 44J 
 
 12. 211 
 
 14 
 
 13. 221 
 2321 
 
 32| 
 331 
 
 45 
 441 
 
 3151 
 4231 
 
 311 
 
 561 
 
 6041 
 314 
 
 181 
 M| 
 
 2301 
 4251 
 
 46| 
 5^ 
 
 3561 
 42l| 
 
 2431 
 5121 
 
 14. I paid $21 for a hat and $5 for a coat. What 
 change should I get back out of a ten-dollar bill? 
 
LESSON 47 97 
 
 15. What is the price of two rugs, one costing 
 $121 an d the other $161? 
 
 16. 3 + 11 = ? 3 + ? = 41 . J + ? = 1 
 
 31 + 2| = ? 3-1 + ? = 6 41 + ? = 8 
 
 17. James is 6 yr. old, and his brother 4J. What 
 is the difference in their ages ? 
 
 Subtract : 
 
 is i M Ii I. !L 1<L 
 
 " 4 5 21 21 41 61 
 
 19 37J 581 85i 43-1 64 58 
 
 ' 24 13 611 201 221 3(51 
 
 2Q 6261 3491 567 2161 475 7031 
 504 1291 4241 204 4441 6021 
 
 21. What is the difference in price between two 
 china closets, one of which costs $ 52J and the other 
 
 $32? 
 
 22. I select the cheaper of two bookcases, one of 
 which costs $77^ and the other $621. With the 
 difference in price how many chairs can I buy at $5 
 apiece ? 
 
SECTION IV 
 
 Lesson 48 
 
 1. Count by 4's from 4 to 48. 
 
 2. Count by 4's from 48 to 4. 
 
 3. Memorize : 
 
 Four times 
 
 lis 4 
 
 5 is 20 
 
 9 is 36 
 
 2 is 8 
 
 6 is 24 
 
 10 is 40 
 
 3 is 12 
 
 7 is 28 
 
 11 is 44 
 
 4 is 16 
 
 8 is 32 
 
 12 is 48 
 
 4. Give two factors of each of the following 
 numbers : 12, 28, 36, 8, 44, 32, 48, 24, 20, 16, 40. 
 
 5. 5 is one factor of 15, what is the other ? 5 apples 
 cost 15 ^, what will 3 cost ? 
 
 6. 5 is a factor of 15 tens, what is the other ? 3 is 
 a factor of 15 tens, what is the other ? 
 
 At 3 dimes a dozen, how many dozen oranges can 
 you buy for 12 dimes? How many oranges? 
 
 Multiply : 
 
 7. 21^ 32^ $52 $41 72 mi. 81 mi. 
 
 44444 4 
 
LESSON 48 99 
 
 8. 321 434 233 523 312 422 
 
 2 _2 _3 _3 _j _4 
 
 9. What is the cost of 4 doz. eggs at 21^ a 
 dozen, and 6 bunches of celery at the rate of 3 for 
 
 10. What is the cost of 4 Ib. of coffee at 32^ a lb., 
 and i lb. of tea at 60^ per lb. ? 
 
 11. An express train runs 42 mi. an hour. How 
 far does it go in 4 hr. ? How much farther than a 
 train that runs at half the rate ? 
 
 12. 
 
 6 
 
 4 
 
 4 
 
 4 
 
 4 
 
 
 4 
 
 
 4 
 
 4 
 
 
 4 
 
 6 
 
 8 
 
 7 
 
 9 
 
 
 11 
 
 12 
 
 10 
 
 13. 
 
 41 
 
 40 
 
 
 31 
 
 
 41 
 
 
 21 
 
 
 41 
 
 
 6 
 
 8 
 
 
 5 
 
 
 9 
 
 
 6 
 
 
 7 
 
 14. 
 
 Divide : 
 
 8)32 
 
 
 4)32 
 
 9)36 
 
 4)48 
 
 7)28 
 
 4)16 
 
 15. 4 is one factor of 16 tens, what is the other? 
 Of 20 tens, what is the other? How often is 6 con- 
 tained in 24 tens ? 8 in 32 tens? 4 in 8 hundreds? 
 
 16. Copy and divide : 
 
 4)164 4)208 6)246 8)328 4)804 
 
 17. 8 + 1 = ? 12 + 2 = ? 24 + ? = 27 
 4x2+1=? 4x 3+2=? 4x 6+?=27 
 
 18. What number smaller than 9 has 4 for a 
 factor? 8-*-4 = ? 9-5-4 = ? 
 
100 ARITHMETIC 
 
 19. What number smaller than 14 has 4 as a 
 factor? Smaller than 13? 15? 19? 21? 34? 35? 27? 
 
 38? 
 
 20. Draw on the board lines 13 in., 19 in., and 
 31 in. long. Measure each line with a 4-in. unit 
 and find out how many times the unit measures the 
 lines and note the remainder in each case. 
 
 Divide : 
 
 21. 4 in.)13 in. 4 in.)19 in. 
 
 4 yd.)34 yd. 4^)271 
 
 22. 4)18 4)25 4)22 4)29 4)36 4)39 
 
 Lesson 49 
 
 1. Take any two points less than a yard apart. 
 Measure the distance between them with a foot-rule 
 and also with a yardstick divided into inches. 
 
 Write your results thus : 
 
 1 ft. 8 in. =20 in. 2 ft. 3 in. =27 in. 
 
 Practise this measuring. 
 
 2. 1 ft. 6 in. = ? in. 1 ft. 4 in. = ? in. 
 2ft. 4in. = ?in. 2ft. 6in. = ?in. 
 3 ft. 3 in. = ? in. 4 ft. 2 in.=? in. 
 
 3. How can you change 2 ft. 4 in. to inches 
 without actually measuring? 
 
LESSON 49 101 
 
 4. Take any two points less than a yard apart. 
 Measure the distance between them with a yard- 
 stick and also with a foot-rule. Express your results 
 thus : 
 
 17 in. = 1 ft. 5 in. 34 in. =2 ft. 10 in. 
 
 Practise this measuring. 
 
 5. 15 in. =? ft. ? in. 18 in. =? ft. ? in. 
 26 in. =? ft. ? in. 29 in. =? ft. ? in. 
 39 in. =? ft. ? in. in. = ? ft. ? in. 
 
 6. How can you change 26 in. to feet and inches 
 without actually measuring? 
 
 7. Measure a gallon of water with a quart meas- 
 ure. What number do you get ? 1 gal. = ? qt. 
 
 Measure 2 gal. of water with a quart measure. 
 What number do you get ? 2 gal. = ? qt. 
 
 8. 3 gal. = ? qt. 5 gal. = ? qt. 4 gal. = ? qt. 
 7 gal. = ? qt. 6 gal. = ? qt. 8 gal. = ? qt. 
 
 How can you change gallons to quarts without 
 actually measuring ? 
 
 9. Measure 8 qt. of water into a pail. Measure 
 the same water with a gallon measure. What num- 
 ber do you get? 8 qt. = ? gal. 
 
 10. 12 qt. = ? gal. 20 qt. = ? gal. 36 qt. = ? gal. 
 24 qt. = ? gal. 16 qt. = ? gal. 48 qt. = ? gal. 
 
 How can you reduce quarts to gallons without 
 actually measuring? 
 
102 ARITHMETIC 
 
 11. Measure 1 gal. 3 qt. of water into a pail. 
 Measure this again with a quart measure. What 
 number do you get ? 1 gal. 3 qt. = ? qt. Measure 
 in a similar manner other quantities of water, and 
 write your results as before. 
 
 12. 3 gal. 3 qt. =? qt. 5 gal. 2 qt. = ? qt. 
 7 gal. 2 qt. = ? qt. 9 gal. 3 qt. = ? qt. 
 Ipt. 2gi.=?gi. 3pt. 2.gi.=?gi. 
 
 How do you reduce 3 gal. 2 qt. to quarts ? 
 
 13. 10 qt. = ? gal. ? qt. 27 qt. =? gal. ? qt. 
 
 9gi.=?pt. ?gi. 18gi.=?pt. ?gi. 
 
 14. 1 hr. = ? min. 2 hr. 30 min. = ? min. 
 
 3 hr. 10 min. = ? min. 4 hr. 25 min. = ? min. 
 
 15. 2 wk. 4 da. =? da. 3 wk. 3 da. = ? da. 
 
 4 wk. 2 da. = ? da. 26 da. = ? wk. ? da. 
 
 16. 4 yd. 3 ft. = ? ft. 6 yd. 2 ft. = ? ft. 
 How do you reduce 5 yd. 2 ft. to feet ? 
 
 16 ft. = ? yd. ? ft. 23 ft. = ? yd. ? ft. 
 
 How do you reduce 25 ft. to yards and feet ? 
 
 17. A road is 6 yd. 2 ft. wide. What is the width 
 in feet ? In inches ? 
 
 18. A room is 8 yd. 2 ft. long. How many steps 
 will a boy take in walking the length of the room if 
 he steps 2 ft. each time ? 
 
 19. A man steps 30 in. at each step. How many 
 feet and inches does he step ? 
 
LESSON 50 103 
 
 20. How many times will a pail containing 2 gal. 
 2 qt. of water fill a quart measure ? 
 
 21. How many 2-qt. jars will hold 8 gal. 2 qt. 
 of fruit ? 
 
 22. What will 1 gal. of cream cost at 30^ a qt.? 
 
 23. What will 2 gal. 2 qt. of milk cost at 2^ a pt.? 
 
 24. A milkman sold 1 qt. of milk to each of 48 
 customers. How many gallons did he sell ? 
 
 Lesson 50 
 
 1. Draw an oblong 4 in. long and 3 in. wide. 
 Divide it into square inches. What is its area ? 
 
 2. If each dot represents 1 sq. in., how many 
 sq. in. are represented by all the dots? What figure 
 is represented? (An oblong 4 in. long and 3 in. 
 wide.) 
 
 3. If each dot represents 1 sq. ft., what figure is 
 represented? What is its area? 1 sq. yd.? 1 sq. mi.? 
 
 4. Draw an oblong 6 in. long and 4 in. wide. 
 Represent its area by dots. What does each dot 
 represent? What is its area? 
 
 5. What is the area of an oblong 6 ft. long and 
 4 ft. wide? 6 yd. long and 4 yd. wide? 6 mi. long 
 and 4 mi. wide ? 
 
104 ARITHMETIC 
 
 6. Draw an oblong 5 yd. long and 4 yd. wide, 
 making 1 in. stand for 1 yd. What is its area? 
 Could the same drawing represent an oblong 5 mi. 
 long and 4 mi. wide? What would 1 in. then stand 
 for ? What area would it then represent ? 
 
 7. What is the area of each of these oblongs? 
 
 Length Width Length Width 
 
 5 in. 4 in. 8 yd. 4 yd. 
 
 7 ft. 3 ft. 10 mi. 4 mi. 
 
 9 ft. 3 ft. 12 mi. 3 mi. 
 
 8. Draw an oblong 3 in. long and 3 in. wide. 
 What is its area? 
 
 An oblong whose length is equal to its breadth 
 is a square. 
 
 9. Draw a square whose side is 4 in. What is its 
 area? Could the same drawing represent a square 
 whose side is 4 mi.? What area would it then 
 represent ? 
 
 10. What is the area of a 2-in. square? a 3-in. 
 square ? a 4- in. square ? 
 
 11. How many square inches in an oblong 4 in. 
 long and 3 in. wide? 
 
 12. Draw an oblong 4 2-in. long and 3 2-in. wide 
 and divide it into 2-in. squares. How many ? 
 
 13. How many 2-in. squares in an oblong 10 in. 
 long and 8 in. wide ? Draw the oblong. 
 
LESSON 51 105 
 
 14. How many 3-in. squares in an oblong 4 3-in. 
 long and 3 3-in. wide ? Draw the oblong. 
 
 15. How many 4-in. squares in an oblong 4 4-in. 
 long and 3 4-in. wide ? Draw the oblong. 
 
 16. How many 4-in. squares in an oblong 12 in. 
 long and 8 in. wide ? 
 
 17. If 6 is one factor of 24, what is the other ? 
 An oblong is 6 in. long and contains 24 sq. in. 
 
 How wide is it? What is its perimeter ? 
 
 18. An oblong is 5 mi. long and contains 20 sq. mi. 
 What is its perimeter ? How many hours would it 
 take a person to walk around it at the rate of 3 mi. 
 an hour. How wide is it ? Draw the oblong. 
 
 19. What is the side of a square which contains 
 4sq. in.? 9 sq. ft.? 16 sq. yd.? 1 sq. yd.? 16 sq.mi.? 
 
 20. A blackboard is 12 ft. long and 4 ft. wide. 
 How many square feet of surface has the board ? 
 
 21. A strip of carpet is 9 ft. long and 3 ft. wide. 
 How many square yards does it contain ? 
 
 22. A strip of carpet containing 24 sq. ft. is 2 ft. 
 wide. How long is it ? How many yards ? 
 
 Lesson 51 
 
 1. At 4^ a pt., what will 5 qt. of raspberries 
 cost? 
 
 2. At 6^ a pt., how many quarts of raspberries 
 will cost 
 
106 ARITHMETIC 
 
 3. If 4 men can do a piece of work in 7 da., how 
 long will it take 1 man to do it ? 2 men ? 
 
 4. If a mail earns $4 a day, how much will he 
 earn in 9 da.? In how many days would he earn 
 this at 13 a day? 
 
 5. If a man earns $3 a day and spends $2, in 
 how many days will he save $ 36 ? 
 
 6. A farmer bought 4 cows at $30 a head, and 3 
 sheep at $ 6 each. How much did they cost him ? 
 
 7. A farmer sold 30 sheep at $4 a head and 6 
 lambs at $ 3 each. How much did he sell them for ? 
 
 8. An express train ran 5 hr. at the rate of 40 
 mi. an hour. How far did it go ? 
 
 9. If 4 A. of land cost $320, what did 1 A. cost ? 
 
 10. A dealer bought 4 bicycles at $40 apiece and 
 sold them at $ 62 apiece. What was his gain ? 
 
 11. Write 4 under each of. these quantities and 
 multiply: $32, $61, $72, $208, $322, $421. 
 
 12. A man saves $32 a month. How much will 
 he save in 3 mo.? 
 
 13. What is the value of 24 yd. of cloth at $2 a 
 y ard ? At f J a yard ? At $ 2 a yard ? 
 
 14. If a man pays $4 a week for board, how much 
 does he pay for board in one year of 52 wk.? 
 
 15. If 4 doz. eggs cost 84^, what is the price per 
 dozen ? 
 
LESSON 52 107 
 
 Lesson 52 
 
 1. Divide 2 4 6 8 10 12 14 16 
 
 18 20 22 24 by 2. 
 
 Take l of 2 4 6 8 10 12 14 16 18 
 20 < 22 24 
 
 How do you find one-half of a quantity ? 
 
 2. Divide 3 6^, 9^, 12 15 18 21 24 
 
 27 30^, 33 36 by 3. 
 
 Take l of 3 6^, 9^, 12^, 15^, 18^, 2l 24^, 
 27^, 30^, 33^, 36^. 
 
 How do you find one -third of a quantity ? 
 
 3. Divide $8, $20, $12, $32, $4, $16, $36, $28, 
 $48, $24, $44, $40, by 4. 
 
 Take \ of $20, $32, $40, $36, $48, $24, $8, $16, 
 $4, $44, $12, $28. 
 
 How do you find one-fourth of a number? 
 
 4. If a yard of cloth cost 24^, what will ^ yd. 
 cost? \ yd.? 
 
 5. Divide 5 ft., 10 ft., 15 ft., 20 ft., by 5. Take 
 ^ of 5 ft., 10 ft., 15 ft., 20 ft. 
 
 How do you find one-fifth of a quantity? 
 
 6. Divide 6 yd., 18 yd., 12 yd., 24 yd., by 6. 
 Take of 6 yd., 18 yd., 12 yd., 24 yd. 
 
 How do you find one-sixth of a quantity ? 
 
 7. Divide 7 mi., 14 mi., 21 mi., 28 mi., by 7. 
 Take \ of 7 mi., 14 mi., 21 mi., 28 mi. 
 
 How do you find one-seventh of a quantity? 
 
108 ARITHMETIC 
 
 8. Divide 8 A., 24 A., 16 A., 32 A., by 8. Take 
 | of 8 A., 24 A., 16 A., 32 A. 
 
 How do you find one-eighth of a quantity? 
 
 9. Divide 9, 18, 27, 36, of any unit by 9. Take 
 
 1 of 9, 18, 27, 36, of any unit. 
 
 How do you find one-ninth of a quantity? 
 
 10. If I cut a piece of ribbon 36 in. long into 
 fourths, what will be the length of each piece ? If 
 into sixths? If into ninths? 
 
 11. Divide 20 lb., 10 lb., 40 lb., 30 lb., by 10. 
 Take T V of 20 lb., 10 lb., 40 lb., 30 lb. 
 
 How do you find one-tenth of a quantity? 
 
 12. Divide 11 qt., 33 qt., 44 qt., 22 qt., by 11. 
 Take -. O f 22 qt., 11 qt., 44 qt., 33 qt. 
 
 How do you find one-eleventh of a quantity? 
 
 13. Divide 12 gal., 24 gal., 36 gal., 48 gal., by 12. 
 Take ^ o f 12 gal., 24 gal., 36 gal., 48 gal. 
 
 How do you find one-twelfth of a quantity? 
 
 14. In 5 hr. a man walked 20 mi. How far did 
 he walk in 1 hr.? In 3 hr.? 
 
 15. If 6 times Helen's age is 24 yr., how many 
 years younger is she than her sister who is 9 yr. old ? 
 
 16. How much will 6 bananas cost when 4 doz. 
 cost 48^? 
 
 17. If 8 oranges cost 32^, what is the price of 
 
 2 doz. oranges ? 
 
LESSON 53 109 
 
 18. Divide 36^ equally among 12 children. "What 
 does each child get? 
 
 19. If 1 yd. of ribbon costs 40^, what will ^ yd. 
 cost ? If 2 yd. cost 24^, what will J yd. cost ? 
 
 20. If 4 cows cost $ 120, what is the cost of each 
 cow? What is the gain on selling them for 1 36 
 apiece ? 
 
 21. If a 3-lb. pail of lard costs 24^, what is the 
 price per lb.? What is saved through buying a 5-lb. 
 pail for 39^? 
 
 22. If 12 bars of soap cost 48 /, what will 1 bar 
 cost ? What will 6 bars cost ? 
 
 23. If one 2-lb. can of fruit costs 22^, what will 
 4 cans cost? 
 
 24. If 2 5-lb. boxes of biscuits cost 64^, what will 
 20 lb. of biscuits cost? 
 
 25. Make questions using the following table of 
 prices : 
 
 Butter 22^ per lb. Olives 40** per pt. 
 
 Corn 12 f per 2-lb. can. Salt 7 f per 10-lb. sack. 
 
 Fish 9^per-lb. can. Soap 4^ per bar. 
 
 Lesson 53 
 
 1. In this arrangement of dots what can each dot 
 represent ? 
 
HO ARITHMETIC 
 
 ? | of 12^ = ? f of 12^=? 
 
 | of 12^=? of!2^ = ? fof!2^=? 
 
 2. Draw a line 12 in. long and divide it into 4 
 equal parts. 
 
 Jofl2in. = ? | of 12 in. =? fof!2in. = ? 
 | of 12 in. =? of!2in.=? fof!2in. = ? 
 
 3. How do you find J of a quantity ? f of it ? f ? 
 ? How do you find J of a quantity ? -| of it ? 
 
 4. A boy had 24 words in his spelling lesson and 
 spelled correctly -| of them. How many did he spell 
 correctly ? Represent by dots. 
 
 5. Make 6 dots and divide them into 3 equal 
 groups. Name units that each dot can represent. 
 
 4 of 6 units = ? * of 6 units = ? f of 6 units = ? 
 
 O O .0 
 
 6. Draw. a line 12 in. long and divide it into 3 
 equal parts. 
 
 of!2in. = ? fofl2in. = ? Jo15in. = ? 
 fof!5in. = ? lof!8in.=? |ofl8in.=? 
 
 7. How do you find ^ of a quantity ? ? 
 
 8. Juliette is 6 yr. old and her brother Albert | 
 as old. How old is Albert ? 
 
 9. Jofl6 = ? | of 16 = ? of20 = ? 
 I of 20 = ? of24 = ? | of 24 = ? 
 
 10. Jft. = ?in. |ft.=?in. Jyd. = ?in. 
 
 . = ? in. ft. = ? in. f ft. = ? in. 
 ?in. | yd. = ? in. |yd.=?in. 
 
LESSON 53 HI 
 
 11. J hr. = ? min. |- hr. = ? min. | hr. =? min. 
 Jda.=?hr. fda.=?hr. fda.=?hr. 
 da.=?hr. fda. = ?hr. da.=?hr. 
 
 12. If a baby sleeps one-half of the time, how 
 many hours a day does he sleep ? How many hours 
 a day does a man sleep who sleeps one-third of the 
 time ? 
 
 13. | of 15 = ? | of 18 = ? f of 24 = ? 
 f of 21 = ? | of 30 = ? | of 36 = ? 
 | of 6 = ? fof 9 = ? -I of 5 = ? 
 
 o o o 
 
 14. If I cut a yard of ribbon into halves, how 
 many pieces will I have ? How many halves in a 
 whole ? 
 
 15. If I cut a yard of silk into thirds, how many 
 pieces will I have ? How many thirds in a whole ? 
 
 16. How many fourths in a whole ? What is one- 
 fourth of a gallon ? How many quarts in a gallon ? 
 
 17. How many fifths in a whole ? What is one- 
 fifth of a nickel ? How many cents in a nickel ? 
 What is one-fifth of a dime ? How many 2-cents in 
 a dime ? 
 
 18. How many sixths in a whole? Sevenths? 
 Eighths? Ninths? Tenths? Elevenths? Twelfths? 
 
 19. What is one-seventh of a week ? How many 
 days in a week? What is one-tenth of a dime? 
 How many cents in a dime? What is one-twelfth 
 
112 ARITHMETIC 
 
 of a foot? How many inches in a foot? What is 
 one-twelfth of a yard? How many 3-inches in a 
 yard? 
 
 20. What will | of a yard of cloth cost at 24 ^ a 
 yard? yd.? f yd.? f yd.? yd.? If yd.? 
 
 21. fof8 = ? fof!6 = ? | of 12 = ? How do 
 you find | of 8? Would it be correct to multiply 8 
 by 3 and divide by 4? f of 12 = ? f of 32 = ? f of 
 24=? |of8 = ? | of 20=? of6 = ? 
 
 22. l da. +1 da. = ? hr. 1 da. - ^ da. = ? hr. 
 f doz. - doz. = ? | doz. - | doz. = ? 
 
 23. A boy bought ^ doz. oranges and ate J doz. 
 How many were left ? If these were divided equally 
 among 3 boys, how many did each boy get ? 
 
 24. If 1 ton of coal lasts 30 da., how long will J 
 ton last? How long will f ton last? If ^ ton of 
 coal lasts 8 da., how long will 1 ton last? 
 
 25. If 1 yd. of ribbon is worth 40^, what is ^ yd. 
 worth? What is -| yd. worth? If ^ yd. of ribbon is 
 worth 6^, what is 1 yd. worth ? 
 
 26. A melon worth 40^ was cut into 4 equal 
 pieces. What was 1 piece worth ? 3 pieces ? 
 
 27. A man had $24 and spent f of it for a watch. 
 What did the watch cost him? 
 
 28. Monday, James rode 36 miles on his bicycle, 
 and Tuesday he rode -| as far. How far did he ride 
 on Tuesday ? 
 
LESSON 54 
 
 Lesson 54 
 
 1. $8 is the quantity, $2 the unit, what is the 
 number? 4 is often called the ratio of $ 8 to $2. 
 
 2. How often is the unit 8 Ib. contained in 
 32 Ib. ? What is the ratio of 32 Ib. to 8 Ib.? 
 
 3. What will 32 Ib. of flour cost, if 8 Ib. cost 
 22^? 
 
 4. 4 gal. is one of the 3 equal parts of 12 gal. 
 We say the ratio of 4 gal. to 12 gal. is J. What is 
 the ratio of 5 gal. to 10 gal. ? Of 6 doz. to 18 doz. ? 
 
 5. What is the ratio of 4 A. to 16 A.? Of the 
 cost of 4 A. to that of 16 A.? If 16 A. cost $800, 
 what will 4 A. cost ? 
 
 6. What is the ratio of 9^ to 27^? 9 dimes to 
 27 dimes? 9 25-ct. pieces to 27 25-ct. pieces? 9 50- 
 ct. pieces to 27 50-ct. pieces ? 9 of any unit to 27 of 
 the same unit ? 
 
 7. What is the ratio of the price of 6 bu. of 
 wheat to that of 24 bu.? If 24 bu. of wheat cost 
 120, what will 6 bu. cost? 
 
 8. The ratio of the value of a purse to the money 
 in it is ^. If there is $ 8 in the purse, what is the 
 value of the purse ? 
 
 9. Name as many quantities as you can of which 
 
 2 is the ratio. Of which 1 is the ratio. 
 
 10. Name as many quantities as you can of which 
 
 3 is the ratio ; ^ the ratio ; 4 the ratio ; J the ratio. 
 
 x 
 
114 ARITHMETIC 
 
 11. What is the ratio of 3 bu. to 12 bu.? 24 Ib. 
 to 8 Ib.? 1 pt. to 1 qt.? 3 pt. to 3 qt.? 1 qt. to 
 1 gal.? 3 qt. to 3 gal.? 6 to 18 ? 12 to 3 ? 
 
 12. If 12 bu. of potatoes cost 1 8, what will 3 bu. 
 cost? 
 
 13. If 8 boxes of candy weigh 4 Ib., what will 24 
 boxes of candy weigh ? 
 
 14. What is the cost of 18 bunches of firecrackers 
 when 6 bunches cost 30^? 
 
 15. If 3 boxes of berries cost 30^, what will 18 
 boxes cost ? 
 
 16. What is the ratio of 1 gal. to 1 qt. ? Of 1 qt. 
 to 1 gal. ? Of 4 qt. to 4 gal. ? Of 3 gal. to 3 qt. ? 
 
 17. If 1 gal. of maple syrup is worth 80^, what is 
 the value of 1 qt. ? 
 
 18. When butter is worth 24^ a Ib., how much 
 can I buy for 12^? 
 
 19. If cheese is worth 16^ a Ib., how much can I 
 buy for 4^ ? How much for 12^? 
 
 20. When eggs are 12^ a dozen, how many can I 
 buy for 36^? For 6^? 
 
 21. If 1 qt. of milk is worth 6 ^, what must I pay 
 for 1 gal. 2 qt. 1 pt. ? If 3 qt. of kerosene are worth 
 10 ^, what are 3 gal. worth ? 
 
 22. John has 2 dimes and James 7 times as much. 
 How much have they together ? James has how 
 much more than John ? 
 
LESSON 55 115 
 
 Lesson 55 
 
 1. I sold a cow for 4 ten-dollar bills ; how much 
 did I get for the cow ? If I had been paid in live- 
 dollar bills, how many would I have got ? 
 
 2. I paid 3 five-dollar bills and a two-dollar bill 
 for an overcoat. What did it cost me? 
 
 3. I paid 12 two-dollar bills and 2 one-dollar bills 
 for a suit of clothes. What did it cost me ? 
 
 4. I paid in dimes 30^ for a book. How many 
 dimes did I pay ? 
 
 5. I paid in nickels 20^ for a handkerchief. 
 How many nickels did I pay ? If I had paid in 
 dimes, how many ? 
 
 6. The 1 cent piece, the 5 cent piece (nickel), the 
 ten cent piece (dime), the quarter dollar (25^), the 
 half dollar (50f), and the dollar (100^) are called 
 coins of the United States. 
 
 7. I bought a yard of ribbon for 15^, giving 3 
 coins in payment. What was the value of the coin ? 
 
 8. I bought a yard of cloth for 60^, giving 6 coins 
 in payment. What was the value of the coin ? 
 
 9. I paid 50^ for a bushel of potatoes, giving 2 
 coins in payment. What was the value of the coin ? 
 
 10. I bought a loaf of bread for 6^, giving two 
 coins in payment. What were the coins ? 
 
 11. I paid 15^ for a dozen bananas, giving two 
 coins in payment. What were the coins ? 
 
116 ARITHMETIC 
 
 12. If I buy a pound of butter for 25^, with 
 what coins can I pay for it ? 
 
 13. I bought a pound of meat for 16^. What 
 three coins would pay for it ? 
 
 14. I bought a dozen eggs for 22^. What coins 
 would pay for the eggs ? 
 
 15. These coins are called units of measure because 
 they measure the value of things. 
 
 16. Name all the units of measure you can, that 
 measure the value of things. 
 
 17. If I paid 4 five-dollar bills, a two-dollar bill, 
 and a one-dollar bill for an overcoat, how much did 
 I pay in all ? 
 
 18. Jf I paid 3 ten-dollar bills and a five-dollar 
 bill for a suit of clothes, and received in change a 
 two-dollar bill, how much did the suit cost me ? 
 
 Lesson 56 
 
 1. | doz. % doz. = ? Your answer is what part 
 of a doz. ? 4 doz. + 4- doz. = ? Your answer is 
 
 o o 
 
 what part of a dozen ? -| doz. | doz. = ? Your 
 answer is what part of a dozen ? 
 
 2. 1 ft. -^ ft.= ? in. | ft. -1 ft. = ? in. 
 | ft. ^ ft. = ? in. Your answer is in each case 
 what part of a foot ? 
 
LESSON 56 117 
 
 3. 1 day J day = ? hr. J day J day = ? hr. 
 | day + ^ day = ? hr. Your answer is in each case 
 what part of a day ? 
 
 4 . 1 hr. + hr. = ? min. J hr. - J hr. = ? 
 min. J hr. ^ hr. = ? min. Your last two 
 answers are in each case what part of an hour? 
 
 5. J Ib. + $ Ib. = ? oz. \ Ib. + | Ib. = ? oz. 
 | Ib. ^ Ib. = ? oz. Your last answer is what part 
 of a pound? 
 
 6. f gal. - 1 gal. = ? qt. f gal. - 1 gal. = ? 
 qt. J gal. + f gal. = ? qt. Your first two an- 
 swers are in each case what part of a gallon ? 
 
 7. From a pail containing | doz. eggs, ^ doz. are 
 taken. How many are left in the pail ? What part 
 of a dozen ? 
 
 8. From a pitcher containing | gal. of milk, J 
 gal. is poured. How many quarts are left in the 
 pitcher? What part of a gallon? 
 
 9. What is the cost of | gal. of milk at 6 ^ a qt. ? 
 
 10. Draw a line 1 ft. long and divide it into four 
 equal parts. 
 
 What part of a foot is each of these parts ? J ft. 
 =,*ft. 
 
 11. l ft. + i ft. = ft. l ft. - ft. = ? ft. 
 ft. +f ft. =*= ?ft. 
 
 12. lyd. = yd. lyd. +lyd. = ?yd. \ yd. + 
 | yd. = ? yd. f yd. + \ yd. = ? yd. 
 
118 
 
 ARITHMETIC 
 
 13. Add: 
 
 $21 
 
 How do you add these quantities ? 
 14. Add : 
 
 8 20 6 4 
 
 15. Subtract : 
 8} T} 
 
 9} 
 
 5} 
 
 41 
 
 10} 
 
 How do you subtract these numbers ? 
 
 16. Copy and add : 
 
 12J 82J 531 25 
 23J 16 14 14 
 
 33} 
 
 Lesson 57 
 
 1. Edward is 31 yr. old and John 4. What is 
 the sum of their ages ? 
 
 2. James has 1 21 and Harry $ 5^. How much 
 have they together ? 
 
 3. John has |6f and Albert $21. How much 
 more has John than Albert ? 
 
 4. A table is 4 ft. long and 21 ft. wide. What 
 is the difference between its length and width ? 
 
LESSON 57 119 
 
 5. A farmer planted f of a field with corn and 
 the rest with potatoes. What part of the field did 
 he plant with potatoes ? If there were 2 A. of pota- 
 toes, how many acres were planted with corn ? 
 
 6. What is .the sum of f and ? Of { and f ? 
 Of l and ? Of and f> Of | and J? Of J 
 andl? 
 
 7. What is the difference between 1 and f ? 1 
 andj? landj? and J? fandj? J and J? 
 
 8. Draw a line 1 ft. long, and divide it into 
 fourths. How many fourths in 1 ft. ? How many 
 fourths in 1 J ft. ? 1 ft. = ^ ft. 1 ft. = ft. 
 
 9. Draw a line 3 ft. long and measure it with a 
 unit one-fourth of a foot long. What number do 
 you get ? 3 ft. = ? fourths of a foot ? 3 ft. = ft. 
 
 10. How many fourths of a foot are there in 2 ft. ? 
 3 f t. ? 4 ft. ? 5 ft. ? 6 ft. ? How do you reduce 
 a number of feet to fourths of a foot ? 
 
 11. Draw a line 4^ ft. long, and measure it with a 
 unit one-fourth of a foot long. What number of 
 units do you get ? 4J ft. = ? fourths of a foot ? 
 
 12. 2 ft. = ft. 3 ft. = ft. 3f ft. = ft. 
 l f t. = ft. 6f ft. = T ft. 8f ft. = ft. 
 
 How do you reduce 5^ ft. to fourths of a foot? 
 
 13. f ft. = ? ft. | ft. = ? ft. * ft. = ? ft. 
 f ft. = ? ft. ? in. \ 5 - ft. = ? ft. ? in. 
 
120 ARITHMETIC 
 
 14. 1 gal. = ? qt. gal. = ? qt. f gal. = ? qt. 
 7-1 gal. = ? qt. lOf gal. = ? qt. 12J gal. = ? qt. 
 
 15. What is the cost of 2^ gal. of milk at 20^ a 
 
 gal.? 
 
 16. 8 qt. == ? gal. 12 qt. = ? gal." 5 qt. = ? gal. 
 17 qt. = ? gal. 34 qt. = ? gal. 27 qt. = ? gal. 
 
 How do you reduce quarts to gallons ? 
 
 17. f qt. = ? qt. ? pt. -y- qt. = ? qt. ? pt. 
 \ 5 - gal. = ? gal. ? qt. -^ S al - = ? S al - ? ^k 
 
 18. Multiply: 
 
 52f 71J 81f 
 
 19. What is the cost of 2 rugs at $22 apiece ? 
 
 20. Divide : 
 
 2)261 2)65 2)43 4)81 4)47 4)89 
 
 21. If 4 boys divide 1 21, which they earn, equally 
 among them, what does each get ? 
 
 22. Julian rides 4 mi. in half-an-hour. At this rate 
 how far will he ride in 2^- hr.? 
 
 23. A lady paid 12^ a yard for ribbon. If she had 
 paid 16^ a yard, it would have cost her 20^ more. 
 How many yards did she buy? 
 
SECTION V 
 
 Lesson 58 
 
 1. Cut out of cardboard units 1 in., 2 in., 3 in., , 
 11 in. long. 
 
 2. Select five pairs of units which put end to end 
 are as long as the 11-in. unit. 
 
 3. With these five pairs of units and the 11-in. 
 unit make two triangles, each of whose sides is 
 11 in. long. 
 
 4. As in question three, make a square; a five- 
 sided figure ; a six-sided figure, each of whose sides 
 is 11 in. long. 
 
 5. Memorize the sum of : 
 
 2345 9876 
 
 9876 2345 
 
 6. The 1 to the right in 11 in. means one unit of 
 
 1 in. The 1 to the left means 1 unit of 10 in. 
 What does the 1 mean in 12 in.? What does the 
 
 2 mean? 
 
 7. Select as often as you can three units which 
 placed end to end are as long as the 11-in. unit. 
 Write your results in columns for addition. 
 
 121 
 
122 ARITHMETIC 
 
 w w w w 
 
 8. Draw lines through the above arrangement of 
 dots to show that the sums found in question 5 are 
 correct. 
 
 9. Draw lines through the above arrangement of 
 dots to show that 11 is the sum of each of the follow- 
 ing columns for addition. 
 
 3246222724 
 5443513073 
 3532486424 
 
 10. A grocer buys pineapples at 8^ apiece, and 
 retails them for 11 ^ each. How much does he gain 
 on every dozen he sells ? 
 
 12. Find the cost of : 
 
 -| doz. peaches at 9^ a doz. 
 ^ doz. apples at 6^ a doz. 
 doz. figs at 8^ alb. 
 
 13. Add: 222334455 
 
 919298287372666 
 
 14. Add; *3 4423154 
 
 32326224 
 2515343742485463 
 
 * Add thus : 25, 28, 31. 
 
LESSON 59 123 
 
 15. Write these questions under each other and 
 add: |12,|4,$3; $26, $3, $2; 3^,44^,3^; 5 
 
 16. I paid 23^ for a book, 5^ for a block of paper, 
 and 3^ for a lead pencil. How much did I pay 
 in all? 
 
 17. If in question 14 I gave the clerk 3 dimes and 
 a nickel, what change did I get back? 
 
 Lesson 59 
 
 1. 2 dimes = ? 4 dimes = ?X 6 dimes= ? 
 
 2 dimes 4^= ? f 5 dimes 6^ = ? t 
 8 dimes 9^= ? f 7 dimes 20 = ? ^ 
 
 2. 14^ = 1 dime 4 64^=? dimes and cents. 
 25^ = ? dimes and cents. 88^ = ? dimes and cents. 
 .32^ = ? dimes and cents. 90^ = ? dimes and cents. 
 
 3. 25 Ib. is equal to 2 10-lb. (read 2 ten Ib.) and 
 5 Ib. Read in the same way each of the following: 
 28 Ib., 34 mi., 23 sq. mi., 16 A., 52 sq. mi., 2T yr., 
 49 da., 15 hr., 32 min., 65 gal., 65 qt., 40 bu. 
 
 4. 23 units are equal to 2 tens arid 3 units. State 
 how many tens and units are in each of the following 
 number of units: 18, 50, 44, 72, 97, 9, 36. 
 
 5. 2 tens = ? 4 tens = ? 8 tens = ? 
 
 3 tens 5 units = ? 7 tens 4 units = ? 
 2 tens 8 units = ? 6 tens units = ? 
 6 tens 6 units = ? 9 tens 5 units = ? 
 
124 ARITHMETIC 
 
 6. 64 = 6 tens 4 units. 91 = ? tens and units. 
 24 = ? tens and units. 40 = ? tens and units. 
 82 = ? tens and units. 19 = ? tens and units. 
 57 = ? tens and units. 77 = ? tens and units. 
 
 7. 64 in. =6 units of ten inches and 4 units of one 
 inch. 
 
 24 in. = ? 82 ft. = ? 57 yd. = ? 91 da. = ? 
 15 hr. = ? 44 min. = ? 18 sec. = ? 85 Ib. = ? 
 
 8. Read: 11.25, $2.50, 16.42, 87.08, $4.44, $9.25. 
 
 9. $256 is equal to 2 units of one hundred dol- 
 lars, 5 units of ten dollars, and 6 units of one dollar. 
 
 256 yd. is equal to 2 units of one hundred yards, 
 5 units of ten yards, and 6 units of one yard. 
 
 10. Read as in question 9 each of the following : 
 $625, 342 mi., 705 A., 432 sq. mi., 250 yd., 999 yr., 
 1099 yr., 365 da., 894 hr. 
 
 11. 736 = 7 hundreds, 3 tens, and 6 units. 
 325 = ? hundreds, tens, and units. 
 
 415, 608, 840, 927, 1027, 265, 1265, are each equal 
 to how many hundreds, tens, and units f 
 
 12. How many units in ten ? In 20 units how 
 many tens? In 40 units? In 60 units? In 80 
 units ? 
 
 13. In 18 units how many tens and units? In 
 37 units how many tens and units ? In 65 units ? 
 In 88 units? In 96 units? 
 
LESSON 60 125 
 
 14. How many tens in one hundred ? In 10 tens 
 how many hundreds ? In 20 tens ? In 40 tens ? 
 In 60 tens? In 80 tens? 
 
 15. In 18 tens how many hundreds and tens? 
 In 25 tens how many hundreds and tens? In 48 
 tens? In 67 tens? In 84 tens? 
 
 16. 4 hundreds 5 tens 2 units = ? number. 
 
 6 hundreds 4 tens units = ? number. 
 
 7 hundreds tens 8 units = ? number. 
 5 hundreds 3 tens 9 units = ? number. 
 
 8 hundreds 8 tens 8 units = ? number. 
 
 17. Count by 10's from to 100; from 100 to 
 200; from 200 to 300. 
 
 18. Count by 100's from to 1000; from 1000 
 to 2000; from 2000 to 3000. 
 
 Lesson 60 
 
 %f Add thus: 8^ and 3^ are 11^, or 1 
 
 1. 28_^ dime and 1^. Write down 1 and add 
 
 31^ the 1 dime to the 2 dimes, making 3 
 
 dimes. Write down 3. The sum is 
 
 2. Add as in question 1 : 
 
 3^ 5^ 6^ 2^ 8 8 2 6 
 
 48^ 66^ 54^ 49^ 83 42 99 105 
 
 In all these questions you carry 1 to the tens' 
 column. 1 what ? 
 
126 
 
 AEITHMETIC 
 
 Add: 
 
 3. 
 
 43 
 
 38 
 
 25 64 
 
 35 27 
 
 62 
 58 
 
 44 
 
 77 
 
 56 89 
 45 30 
 
 73 
 
 39 
 
 4. 
 5. 
 
 223 
 474 
 
 234 
 
 635 
 
 226 
 
 342 
 
 308 
 443 
 
 420 
 
 427 
 384 
 
 279 
 641 
 
 396 
 
 825 
 
 314 
 
 314 
 
 392 
 
 
 523 
 
 203 
 
 135 
 
 182 
 
 204 
 
 225 
 
 
 212 
 
 174 
 
 316 
 
 421 
 
 215 
 
 642 
 
 6. Add, placing the sum above the line : 
 
 68 
 
 23 
 
 
 33 
 
 13 
 
 62 
 
 25 
 
 16 
 
 32 
 
 35 
 
 45 
 
 
 62 
 
 28 
 
 28 
 
 46 
 
 34 
 
 19 
 
 66 
 
 Subtract : 
 
 
 7. 
 
 68 
 
 95 
 
 *41 
 
 60 
 
 71 90 
 
 81 
 
 51 
 
 
 
 45 
 
 62 
 
 28 
 
 28 
 
 35 42 
 
 33 
 
 16 
 
 
 
 999 
 
 816 
 
 
 808 
 
 741 
 
 601 
 
 1051 
 
 
 
 
 367 
 
 254 
 
 
 728 
 
 503 
 
 257 
 
 342 
 
 9. A man paid $165 for a horse and $225 for a 
 carriage ? How much did he pay for both ? 
 
 10. An arithmetic costs 45^, a reader 36^, and a 
 grammar 30 $. How much did they all cost ? 
 
 * Subtract thus : 8 and 3 are 11 ; carry 1 to 2 as in addition, 
 making it 3 ; 3 and 1 are 4. Write 3 under 8 and 1 under 41 
 2 thus, 28 
 
 That is, fancy you are doing addition with the sum at the top. 13 
 
LESSON 61 127 
 
 11. A man bought a lot for $ 975 and sold it for 
 1 850. How much did he lose? 
 
 12. I paid 11.25 for a roast of beef and 11.10 for 
 potatoes. What did I pay for both? 
 
 13. A farmer sold his wheat for $854 and hay for 
 1237. How much did he get for both? 
 
 14. A merchant took in 1 332 on Monday, $204 
 on Tuesday, and $455 on Wednesday. How much 
 did he take in on these three days ? 
 
 Lesson 61 
 
 i. 
 
 Memorize the sum of : 
 
 3 
 
 4 
 
 5 
 
 6 
 
 
 
 9 
 
 8 
 
 7 
 
 6 
 
 2. 
 
 Find the sum of : 
 
 9 
 
 8 
 
 7 
 
 6 
 
 
 
 3 
 
 4 
 
 5 
 
 6 
 
 Add: 
 
 3. 39565473 
 19 13 26 36 77 48 65 38 
 
 4. 44553323 
 44263933 
 
 22 34 44 51 63 70 85 96 
 
 5. What is the cost of : 
 
 4 Ib. raisins at 8^ a Ib.? 
 lib. dates at 6^ a Ib.? 
 Jib. nuts at 12^ a Ib.? 
 
128 ARITHMETIC 
 
 6. *5 
 
 *2 
 
 3 
 
 4 
 
 1 
 
 4 
 
 2 
 
 4 
 
 4 
 
 5 
 
 3 
 
 8 
 
 3 
 
 4 
 
 2 
 
 4 
 
 2 
 
 1 
 
 3 
 
 4 
 
 5 
 
 5 
 
 5 
 
 4 
 
 14 
 
 56 
 
 33 
 
 70 
 
 65 
 
 43 
 
 26 
 
 84 
 
 7. 18 
 
 26 
 
 33 
 
 53 
 
 34 
 
 28 
 
 57 
 
 23 
 
 42 
 
 36 
 
 62 
 
 74 
 
 48 
 
 92 
 
 65 
 
 88 
 
 8. 748 
 
 121 
 
 643 
 
 232 
 
 
 495 
 
 355 
 
 161 
 
 234 
 
 879 
 
 586 
 
 497 
 
 
 307 
 
 565 
 
 768 
 
 In each 
 
 of these questions you 
 
 carry 
 
 1. This 1 
 
 is 1 what? 
 
 
 
 
 
 
 
 
 9. 426 
 
 284 
 
 294 
 
 325 
 
 
 272 
 
 444 
 
 111 
 
 343 
 
 303 
 
 125 
 
 254 
 
 
 416 
 
 333 
 
 444 
 
 212 
 
 241 
 
 702 
 
 411 
 
 
 412 
 
 222 
 
 555 
 
 10. What is the cost of : 
 
 J bu. apples at 60^ a bu.? 
 21 Ib. biscuits at 8^ a Ib.? 
 4 Ib. sugar at 5-J^ a Ib.? 
 Subtract : 
 
 989 t521 625 930 641 989 862 
 752 263 283 615 228 457 129 
 
 11. 
 
 * Add thus : 14, 16, 20, 25 ; 56, 57, 62, 64. 
 
 t Subtract thus : 3 and 8 are 11 ; carry 1 to 6, as in addition, 
 making it 7 ; 7 and 5 are 12 ; carry 1 to 2 making it 3 ; 3 and 2 
 are 5. That is, fancy you are doing addition with the sum at 
 the top. 
 
12. 
 
 13. 
 
 LESSON 62 129 
 
 4564 7498 7594 8989 9387 7845 
 
 2342 4288 6571 6363 8326 6043 
 
 7982 9322 5745 4102 7629 1521 
 
 2646 4218 2730 2052 1038 1432 
 
 14. A farmer has 638 sheep in one flock and 234 
 in another. How many has he all together ? 
 
 15. I bought a house -for $4825 and sold it for 
 $ 3460. How much did I lose ? 
 
 16. A man spent $124 on Monday, $423 on Tues- 
 day, and $673 on Wednesday. How much did he 
 spend all together ? 
 
 17. How many days are there in April, May, and 
 June ? How many days are there in July, August, 
 and September ? 
 
 Lesson 62 
 
 4 
 987456 
 
 l. Memorize the sum of : 
 
 Add: 
 
 2. 58495538 
 18 15 39 34 47 68 78 85 
 
 3. 46359644 
 54534343 
 
 31 23 44 65 60 72 82 96 
 
130 ARITHMETIC 
 
 4. 
 
 1 
 
 3 
 
 4 
 
 2 
 
 4 
 
 8 
 
 2 
 
 4 
 
 
 3 
 
 2 
 
 2 
 
 3 
 
 2 
 
 1 
 
 3 
 
 4 
 
 
 3 
 
 4 
 
 2 
 
 5 
 
 1 
 
 6 
 
 3 
 
 4 
 
 
 12 
 
 21 
 
 34 
 
 41 
 
 56 
 
 63 
 
 73 
 
 71 
 
 5. What is the cost of : 
 
 4 yd. of elastic at 6^ a yd.? 
 10yd. of tape at 2^ a yd.? 
 2J yd. lining at 10^ a yd.? 
 J yd. ribbon at 4^ a yd.? 
 
 6. 28 38 27 39 25 33 56 40 
 33 45 54 63 78 99 82 98 
 
 7. 235 248 427 655 568 909 263 566 
 548 671 496 714 815 204 574 546 
 
 8. Find the cost of 2 bu. of potatoes at 40^ & bu., 
 and 3J Ib. of meat at 12 X a Ib. 
 
 9. 212 141 504 141 333 333 634 232 
 154 320 412 453 444 111 307 260 
 702 168 183 138 555 666 241 318 
 
 Subtract : 
 
 10. 674 954 439 715 609 938 310 609 
 231823275438546444154352 
 
 11. 6739 4903 6048 7354 3429 6336 7273 5128 
 
 2435 2701 2035 1321 2316 2332 3123 4128 
 
LESSON 63 181 
 
 12. 8653 9125 3522 4175 4967 2364 6001 5385 
 
 7439 4135 2140 3514 3643 1423 3453 2962 
 
 13. A farmer received $ 235 for his corn and $ 470 
 for his wheat. How much did he receive for both ? 
 
 14. A cattle dealer had 3245 cattle and sold 1340. 
 How many had he left ? 
 
 15. A man bought a farm for $8225 and sold it 
 for $ 9415. How much did he gain ? 
 
 16. If a man earns 12500 a year, and his expenses 
 are $1500, how much does he save? 
 
 17. Find the sum of 121, 121, 121, 121. Multiply 
 121 by 4. 
 
 18. Mr. Brown owed Mr. Smith $225. He paid 
 the debt by giving him $160 and a horse. What 
 was the horse worth? 
 
 Lesson 63 
 
 1. Count by 5's from 5 to 200. 
 
 2. Memorize : 
 
 Five times 
 
 lis 5 
 
 5 is 25 
 
 9 is 45 
 
 2 is 10 
 
 6 is 30 
 
 10 is 50 
 
 3 is 15 
 
 7 is 35 
 
 11 is 55 
 
 4 is 20 
 
 8 is 40 
 
 12 is 60 
 
132 ARITHMETIC 
 
 3. Give two i actors of each of the following 
 numbers: 28, 45 r 44, 32, 55, 27, 60, 48, 40, 35. 
 
 4. Give the two equal factors of each of the 
 following numbers : 4, 9, 16, 25. 
 
 5. Give as many pairs of factors as you can for 
 each of the following numbers : 
 
 24<2 x 12, 3 x 8, 4 x 6), 12, 18, 20, 28, 30, 36, 40. 
 
 6. 4 is a factor of 12. What is the other factor? 
 4 is a factor of 20. What is the other factor ? 
 
 4 in a common factor of 12 and 20. 
 Draw lines 12 in. and 20 in. long and measure 
 them with a 4-in. unit. How many units in each ? 
 
 7. What number is a common factor of 20 and 
 25 ? Of 9 and 12 ? Of 25 and 30 ? Of 10 and 14 ? 
 Of 12 and 15 ? 
 
 8. How long is the unit that will exactly measure 
 two pieces of ribbon one 12 in. long and the other 
 15 in. With what coin can you pay a debt of 
 and also of 
 
 Multiply : 
 
 9. 21 *23 33 51 63 42 
 
 555555 
 
 * Multiply thus : 5 times 3 is 15 ; write down 5 and carry 1 ; 
 5 times 2 is 10 ; 10 and 1 are 11 ; write down 11. The product is 
 115. 
 
LESSON 63 133 
 
 In multiplying 23 by 5 you carry 1. This 1 is 
 1 what ? 
 
 10. 
 
 262 
 
 341 424 
 
 521 203 
 
 313 
 
 
 2 
 
 3 4 
 
 5 5 
 
 5 
 
 11. 
 
 6 
 
 5 5 4 
 
 555 
 
 5 
 
 
 5 
 
 687 
 
 7 9 12 
 
 10 
 
 12. 
 
 41 
 
 52 42 
 
 50 53 
 
 52 
 
 
 6 
 
 6 7 
 
 7 8 
 
 9 
 
 13. James rode 33 mi. on his bicycle in one week, 
 and Henry 4 times as far all but 12 mi. How far 
 did Henry ride ? 
 
 14. Divide : 
 
 5)45 5)450 8)40 7)350 9)45 6)300 
 
 15. What number smaller than 12 has 5 for a 
 factor? smaller than 16? 18? 22? 28? 33? 36? 
 39? 42? 47? 49? 
 
 Divide : 
 
 16. *5)215 5)315 5)325 5)280 5)365 5)390 
 
 On dividing 325 by 5 you have a remainder 2 on 
 the first division. This 2 is 2 what ? 
 
 * Divide thus : 5 is contained in 21 4 times with remainder 1 ; 
 write down 4 ; 5 is contained in 15 3 times ; write down 3. The 
 quotient is 43. 
 
134 
 
 ARITHMETIC 
 
 17. 4)212 3)252 5)375 4)304 2)572 3)291 
 
 There is a remainder on the first division each 
 time. Is this remainder units, tens, or hundreds ? 
 
 18. 6)312 7)294 8)416 5)340 9)369 9)468 
 
 19. At $ 5 a bbl. how many barrels of flour will 
 cost 1325? 
 
 20. How many miles an hour must a train travel 
 to go 272 mi. in 8 hr. ? In 6 hr. ? 
 
 21. If a train travels 26 mi. an hour, how far dis- 
 tant is a city which it will reach in 4J hr. ? 
 
 22. A farmer received $128 for a cow and some 
 lambs. He received $32 for the cow and $3 for 
 each lamb. How many lambs did he sell ? 
 
 Lesson 64 
 
 1. 1x6= 6 6xl=? 4x6=24 6x4=? 
 2x6=12 6x2=? 5x6 = 30 6x5=? 
 3x6 = 18 6x3=? 6x6=? 6x6=? 
 
 2. Count by 6's from 6 to 72. 
 
 3. Memorize : 
 
 Six times 
 
 lis 6 
 
 5 is 30 
 
 9 is 54 
 
 2 is 12 
 
 6 is 36 
 
 10 is 60 
 
 3 is 18 
 
 7 is 42 
 
 11 is 66 
 
 4 is 24 
 
 8 is 48 
 
 12 is 72 
 
LESSON 64 135 
 
 4. Give two factors of each of the following num- 
 bers : 30, 21, 48, 54, 55, 72, 27, 66, 42, 60. 
 
 5. Give as many pairs of factors as you can of 
 each of the following numbers : 18(2 x 9, 3 x 6), 
 16, 36, 48, 24, 54, 60, 44. 
 
 6. What number is a common factor of 12 and 
 15? 15 and 25? 22 and 33 ? 30 and 42? 28 and 
 32? 
 
 7. Two logs, one 15 ft. and the other 25 ft. in 
 length, were cut into the longest possible pieces of 
 equal length. What is the length of each piece ? 
 
 Multiply : 
 
 8. *49 24 35 47 58 66 
 
 J5 _6 _6 _6 _6 _6 
 
 In multiplying 49 by 6 you carry 5. This 5 is 
 5 what ? 
 
 9. A dealer bought 84 sheep at $ 6 apiece, and 
 sold them for $600. Find his gain. 
 
 10. 396 396 396 396 396 506 
 _2 _3 _j* _5 _j6 6 
 
 In multiplying 396 by 3 you carry 1. This 1 is 
 1 what ? You also carry 2. This 2 is 2 what ? 
 
 11. 86566655 
 68 9 7 9 12 12 11 
 
 * Multiply thus : 6 times 9 is 54 ; write down 4 and carry 5 ; 6 
 times 4 is 24 ; 24 and 5 are 29 j write down 29, The product is 294, 
 
136 ARITHMETIC 
 
 12. 22 34 83 75 36 66 
 
 978698 
 
 13. A farmer's barn cost him $225, and his house 
 9 times as much. Find the cost of both. 
 
 14. Divide: 
 
 6)426 8)400 6)546 9)549 5)505 9)369 
 
 15. What number smaller than 20 has 6 for a 
 factor? Smaller than 15? 17? 26? 29? 34? 
 38? 47? 49? 52? 58? 
 
 Divide : 
 
 16.* 6)150 6)324 6)456 6)294 6)402 6)732 
 
 17. 2)576 3)576 4)576 5)650 6)864 6)834 
 
 18. 4)704 6)702 5)735 7)448 8)448 9)459 
 
 19. 6)594 9)594 8)520 7)364 8)504 9)504 
 
 20. Divide the contents of 240 bags of oats equally 
 among three bins. How much in each ? 
 
 " 21. How many bushels of wheat in 24 bags each 
 containing 2 bu., and 18 bags each containing 3 bu.? 
 
 22. I paid i 240 for a horse and bicycle. If the 
 horse cost 5 times as much as the bicycle, find the 
 cost of each. 
 
 * Divide thus : 6 is contained in 15 2 times with remainder 3 ; 
 write down 2 ; 6 is contained in 30 5 times ; write down 5. The 
 quotient is 25. 
 
SECTION VI 
 
 Lesson 65 
 
 l. 82.75 is read, two dollars and seventy-five 
 cents. The decimal point (.) separates dollars from 
 cents. All the figures to the left of the decimal 
 point denote dollars, and the first two figures to the 
 right denote cents. 
 
 2. Read the following : 
 $2.43 136.10 162.24 
 $4.29 164.76 143.60 
 
 3. Read the following : 
 
 1169.65 
 $691.80 
 
 $1864.86 
 $1759.45 
 
 $.15, $.05, $.08 
 
 4. Read the following : 
 
 $.05 $ .07 $ 15.17 $ 204.04 
 
 $.09 $ .30 $ 77.60 $ 300.06 
 
 $.01 $ .75 $ 20.05 $ 300.60 
 
 $.12 $2.16 $291.98 $1732.25 
 
 $.18 $3.04 $201.64 $5300.20 
 
 $.69 $5.20 $311.20 $6040.06 
 
 5. Write in figures as in question 4 : Three dol- 
 lars and twenty-five cents ; thirty-seven dollars and 
 
 137 
 
138 ARITHMETIC 
 
 fifty cents ; sixteen cents ; eighty-three cents ; four 
 cents ; nine cents ; twenty dollars and six cents. 
 
 6. Write in figures : One hundred nineteen dol- 
 lars and twenty-five cents ; two hundred forty -three 
 dollars and ninety-one cents ; six hundred eight 
 dollars and eight cents ; nine hundred ninety-nine 
 dollars and ninety-nine cents. 
 
 7. How many cents in $ 2 ? In $.25? In $2. 25? 
 
 8. How many cents in ? 
 
 $3.75 $8.19 $4.06 $25.64 $10.06 
 $6.07 $3.10 $6.43 $34.08 $20.20 
 
 9. Write and read as dollars and cents : 
 
 16 6 300 f, 210 625 409 2463 1250 
 2400 1650 1825 
 
 10. How many cents in $, $ J, $|, $1, $JL? 
 
 11. Write as dollars and cents : 
 
 $5J, $6J, $8f, $12, $24f, $43 T L, $64^. 
 
 12. How many dollars, dimes, and cents in ? 
 $2.45, $6.40, $3.08, $4.00, $.90. 
 
 13. How many ten-dollars, dollars, dimes, and 
 cents in $36.25, $40.16, $62.01, $3.04, $11.11? 
 How many cents in 1 dime? Dimes in 1 dollar? 
 Dollars in 1 ten-dollar ? 
 
 14. Add: 
 
 <2.14 $13.21 $215.42 $1212.33 
 
 3.20 22.16 211.00 2104.12 
 
 4.53 24.00 420.06 3013.41 
 
LESSON 65 139 
 
 15. Find the sum of 124.33, 121.14, and 117.22. 
 Find the sum of 1134.25, $243.40, and $510.53. 
 
 16. What will it cost to settle a grocery bill of 
 $22.33, a meat bill of $14.12, and a drug bill of 
 $2.14? 
 
 17. Subtract : 
 
 $8.75 $53.92 $369.43 $2146.56 
 
 3.42 12.60 328.12 1013.45 
 
 18. What is the difference in cost between two 
 rocking-chairs, one costing $27.75 and the other 
 $16.50? 
 
 19. I buy a chair for $2.65 ; what change should 
 I get back from a five-dollar bill ? 
 
 20. Multiply : 
 
 $5.23 $22.15 $31.51 $213.42 
 3 4 5 6 
 
 21. What is the cost of 5 T. of coal at $ 6.25 a ton, 
 and 2 cords of wood at $4.25 a cord ? 
 
 22. Find the value of: $48.26-2; $82.50-5-3; 
 $.92-4; $.06-2; $628.75-j-5; $483.90-=-6. 
 
 23. If an agent makes $ 994.60 in 4 mo., what are 
 his average monthly earnings ? 
 
 24. Find the cost of : 
 
 6 cups at $ .20 apiece. 
 
 4 knives at $1.25 apiece. 
 
 5 plates at $ .25 apiece. 
 
 2 spoons at $1.50 apiece. 
 
 3 salt dishes at $ .25 apiece, 
 
140 ARITHMETIC 
 
 Lesson 66 
 
 1. A pitcher holds 3 pt. How many quarts and 
 pints does it hold? How many quarts and pints in 
 5 pt. ? 9 pt. ? 7 pt. ? 11 pt. ? 
 
 2. In adding pints, what unit can you always put 
 in place of every 2 pt.? 
 
 3. In one pail there are 2 qt. 1 pt. of water ; in a 
 second pail 3 qt. 1 pt. ; in a third 1 gal. 1 pt. How 
 much water in the three pails ? 
 
 4. Measure, and prove your answer to question 
 3 correct. 
 
 5. Make problems like question 3. 
 
 6. How many gallons and quarts are there in 
 6qt.? 9qt. ? 5 qt. ? 7 qt.? 
 
 7. What unit of measure can you put instead of 
 every 4 qt. in a quantity of liquid ? 
 
 8. How many quarts and pints in 3 cans, each of 
 which holds 5 pt. ? How many gallons, quarts, and 
 pints in 3 cans, each of which holds 7 pt. ? 
 
 9. If 3 pieces of ribbon of the same length cost 
 $.15, what will 1 piece cost? 
 
 10. Draw a line three-quarters of a yard long, 
 and divide it into pieces each one-quarter of a yard 
 long. How many pieces? What is the cost of each 
 piece if all costs 18^? Of 4 such pieces? How 
 long will 4 such pieces be ? 
 
LESSON 66 141 
 
 11. If three-quarters of a yard of ribbon costs 
 what will one-quarter of a yard cost? Four- 
 quarters of a yard ? One yard ? One yard and one- 
 quarter ? 
 
 12. If | yd. of cloth costs 21 what is the cost of 
 1 yd. ? How do you find the cost of 1 yd. of cloth 
 when you know the cost of | yd. ? 
 
 13. If ^ Ib. of butter cost 24 ^, what is the price 
 per Ib. ? When you know the cost of | Ib. of butter, 
 how do you find the cost of 1 Ib. ? Of 1J Ib. ? 
 
 14. A boy sold 6 qt. of berries at 6^ a qt. How 
 many oranges at 3^ each could he buy with the 
 money he got for the berries ? What unit measures 
 the value of an orange ? 
 
 15. When milk costs 24^ a gallon, what is the 
 cost of 1 qt. ? What is the cost of 1 pt. ? Of 1 gal. 
 3 qt. 1 pt. ? What is the cost of 2 gal. 3 qt. 1 pt. 
 at 2 f a pt. ? 
 
 16. A man spent f of his salary. What part of 
 it did he save ? If he had spent f of his salary, what 
 part would he have saved? If this was $120, what 
 was his salary? 
 
 17. A watch cost $50, which was five times the 
 value of the chain. What was the cost of the 
 chain? Of both? What is the whole quantity 
 here ? What is the number ? What is the unit ? 
 
142 ARITHMETIC 
 
 18. Draw a square whose side is 4 in. Divide it 
 into 2-in. squares. How many? Name the whole 
 quantity, the unit, and the number. How did you 
 find the number ? 
 
 19. How many 2-in. squares in a square whose 
 side is 6 in. ? 8 in.? 10 in. ? 1 ft. ? 
 
 20. How many more 3-in. squares can be cut from 
 a square whose side is 12 in. than from one whose 
 side is 9 in. ? 
 
 21. How many 4-in. squares in an oblong 12 in. 
 by 20 in. ? 1 ft. 8 in. by 3 ft. ? How many tiles, 
 each 4 in. square, are needed for a piece of tiling 
 4 ft. long and 1 ft. 4 in. wide ? 
 
 Lesson 67 
 
 1. A milkman has 4 gal. 1 qt. of milk in one 
 can ; in another 3 gal. 1 qt. 1 pt. ; in a third 
 2 qt. 1 pt. How much milk has he ? 
 
 2. A milkman sold 3 cans of milk, each contain- 
 ing 2 gal. 3 qt. How much did he sell ? 
 
 3. How many quarts in 5 gal. 2 qt. ? To how 
 many customers can a milkman sell 5 gal. 2 qt. if 
 he sells 2 qt. to each customer? Name the quan- 
 tity, the unit, and the number. 
 
 4. If I divide 8 gal. 3 qt. of syrup equally 
 among 5 persons, how much does each get? In this 
 
LESSON 143 
 
 question you are given the quantity and the number 
 and are required to find the unit. State the ques- 
 tion in which you are given the quantity and unit to 
 find the number. 
 
 5. A man buys milk at 4^ a qt., and sells it at 
 3^ a pt. How much does he gain on each gal. ? 
 How much on 6 gal. ? 
 
 6. If three-quarters of a yard of cloth cost 18 ^, 
 what will one-quarter of a yard cost ? Four-quarters 
 of a yard ? One yard ? One yard and one-half ? 
 
 7. If | yd. of ribbon costs 27 ^, what will 1 yd. 
 cost? 1J yd.? If -| Ib. of raisins cost 15^, what 
 will 1 Ib. cost ? 21 Ib. ? 
 
 8. The desks in a schoolroom cost 172 at $2 a 
 desk ; how many desks are there in the room ? How 
 many rows of desks with 6 in a row ? 
 
 9. If | of the number of desks in a room are 33, 
 how many desks are in the room ? How do you find 
 a number when you are given | of it? 
 
 10. A milkman sold milk at $.03 a pint. What 
 was the price per gallon ? What will 5 gal. sell for ? 
 
 11. James paid $-| for a book and $ J for a slate. 
 How much more did the book cost than the slate ? 
 How much did both cost ? 
 
 12. A milkman having 25 gal. 2 qt., sold -J of it. 
 How much did he sell? If he had sold |- of it, how 
 much would lie have sold ? 
 
144 ARITHMETIC 
 
 13. A farmer sold 6 doz. eggs to a grocer at $.12 
 a doz., 5 Ib. of butter at $.18 a Ib. He took his 
 pay in sugar at 6^ a Ib. How many pounds of sugar 
 did he receive ? 
 
 14. Florence paid $.64 for an arithmetic and ^ as 
 much for a reader. What did both cost ? What 
 change should she get back from a dollar bill ? 
 
 15. My hens lay 5 eggs a day. In how many 
 weeks will they lay 140 eggs ? 
 
 16. What will 2 doz. apples cost at the rate of 
 2 apples for 3^ ? What is the unit here ? 
 
 17. How many feet long is your schoolroom? 
 How many feet wide ? Now find, without measur- 
 ing, the number of yards it is half-way around the 
 room. Test your answer by measuring. 
 
 18. A boy earns $.09 an hour, and works 8 hr. a 
 day. How much more does he earn in 1 wk. than a 
 boy who earns $ . 10 an hour, and works 7 hr. a day ? 
 
 19. In question 20, place one dot for each dollar 
 left. How many ? How many dots should you 
 place for the money spent for groceries ? How 
 many for what was in my purse at first ? 
 
 20. I spent f of the money in my purse for gro- 
 ceries, and had $5 left. What part of my money 
 did I have left ? How much had I at first ? 
 
 21. What three different coins make $ .16 ? 
 
LESSON 68 145 
 
 Lesson 68 
 
 1. Monday a boy picked 5 qt. 1 pt. of berries, 
 Tuesday 4 qt. 1 pt., and Wednesday 6 qt. 1 pt. 
 How much did he pick on these three days ? 
 
 2. The boy in question 1 sold his berries at 6^ a 
 quart, and bought a ball and bat with the money. 
 What did he pay for the ball and bat ? 
 
 3. What is the cost of 6 qt. 1 pt. of milk at f .24 
 a gallon ? 
 
 4. What will 3J yd. of ribbon cost at 12^ a yard ? 
 Of the three terms, quantity, unit, number, which 
 are you given and which must you find ? Using the 
 same numbers, state a question in which you are 
 given the quantity and unit to find the number. 
 State a question in which you are given the quantity 
 and number to find the unit. 
 
 5. School is in session from nine to twelve o'clock, 
 and from a quarter after one to half -past three. This 
 is how many hours a day? Count on the clock. 
 How many hours a week ? 
 
 6. If it takes 1 man 6 hours to cut a cord of 
 wood, how long will it take 2 men to do it ? How 
 long will it take 3 men ? 
 
 7. A man takes 6 hours to cut a cord of wood, 
 cutting each stick into two pieces. How long will 
 it take him if he cuts each stick into three pieces-? 
 In each case draw a stick, and mark where it is cut ? 
 
146 ARITHMETIC 
 
 8. What number of cents can you divide into 
 thirds and have 6^ in each third ? Test your answer 
 by making 6 dots for each third, and then counting 
 all your dots by 6's. How many 6's ? How many 
 dots? 
 
 9. What number can you divide into fourths 
 and have 25 in each part? Into fifths? Into sixths? 
 
 10. If one-sixth of the distance between Chicago 
 and Springfield is 29 mi., how far is it between these 
 two cities ? 
 
 11. How many weeks in 1 yr ? | yr. ? ^ yr. ? 
 fyr.? 
 
 12. If a boy earns 16 a week, how much will he 
 earn in J yr. ? 
 
 13. If a boy earns $ 7 a week and it costs him $ 5 
 a week to live, how much can he save in ^ yr. ? 
 
 14. What five different coins make 91 ^ ? 
 
 15. A lady made 6 gal. of preserves and put them 
 up in pint cans. How many cans did she use ? 
 
 16. A 5-lb. pail of butter costs 90 ^. At this rate 
 what must I pay for 21 Ib. ? 
 
 17. How many pennies will be required to form 
 a square if there are 5 pennies on each side of the 
 square? Place pennies so as to show how many are 
 needed. 
 
 18. A grocer has 8 gal. 2 qt. 1 pt. of cider which 
 he divides equally among 3 customers. What does 
 
LESSON 68 147 
 
 each receive ? Name the quantity and the number. 
 What is the unit ? How did you find it ? 
 
 19. To how many customers can a milkman sell 
 8 gal. 3 qt. of milk, if he sells 5 pt. to each cus- 
 tomer? Name the quantity and the unit. What is 
 the number ? How did you find it ? 
 
 20.' A pole is ^ in the ground and J in the air. 
 Draw the pole. If it is 4 ft. in the ground, how 
 long is the part in the air ? How long is the pole ? 
 
 21. A pole is -| in the air and -J in the ground. 
 If the height above ground is 6 ft., how long is 
 the pole? 
 
 22. Two boys walk, one east at the rate of 3 mi. 
 an hour, and the other west, at | that r;ite. How 
 far apart will they be 4 hr. after they part ? 
 
SECTION VII 
 
 Lesson 69 
 
 i. 
 
 Memorize the sum of : 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 9 
 
 8 
 
 7 
 
 6 
 
 5 
 
 Add: 
 
 2. 59687796 
 1916282647 -37 6687 
 
 3. 53569675 
 44944358 
 
 22 37 30 44 51 63 72 81 
 
 2 
 
 4 
 
 1 
 
 6 
 
 , 9 
 
 7 
 
 8 
 
 4 
 
 2 
 
 1 
 
 3 
 
 4 
 
 1 
 
 6 
 
 4 
 
 3 
 
 4 
 
 3 
 
 4 
 
 6 
 
 2 
 
 2 
 
 3 
 
 8 
 
 12 
 
 25 
 
 32 
 
 14 
 
 42 
 
 58 
 
 41 
 
 60 
 
 5. I bought a coat for $12, and had left a five- 
 dollar bill and 2 two-dollar bills. How much money 
 had I at first ? 
 
 6. I bought a carriage for $61, paid $5 for re- 
 pairs, and sold it so as to gain $8. What did I sell 
 
 148 
 
LESSON 69 149 
 
 7. 35 15 48 94 69 46 55 49 
 
 24 77 86 39 72 38 77 80 
 
 8. 234 639 149 475 298 329 758 829 
 181 70 673 328 443 872 686 555 
 
 9. 275 654 283 333 206 542 257 426 
 453 513 708 325 304 129 509 328 
 221 331 544 516 692 783 134 156 
 
 10. 25 years ago a young man entered the <ti'my 
 at the age of 19. How old is he now ? 
 
 11. In an orchard there are 96 apple trees and 
 J as many cherry trees. How many trees are there 
 in the orchard? 
 
 12. A farmer has 435 sheep in one flock, 322 in 
 a second, and 239 in a third. How many has he all 
 together ? 
 
 Subtract : 
 
 784 638 743 801 417 846 931 432 
 352 234 561 271 234 395 888 189 
 
 14. 
 
 15. Mrs. Ellis was 24 yr. old on Feb. 19, and 
 Caryl 8. What is the difference in their ages? 
 
 6465 
 
 9039 
 
 4398 
 3489 
 8429 
 
 6000 
 2009 
 
 7172 
 
 3040 
 
 2361 
 
 1847 
 
 2127 
 8666 
 
 1945 
 5329 
 
 1321 
 
 4888 
 
 3516 
 
 6354 
 
 1678 
 
150 ARITHMETIC 
 
 16. There are 25 pupils in the second grade, and 
 16 more in the first. How many are there in both 
 grades ? 
 
 17. A boy rode 75 mi. on a bicycle in two days. 
 If he rode 49 mi. the first day, how far did he ride 
 the second day ? How many miles less than on the 
 first day ? 
 
 18. A farmer has 165 A. in oats, 124 A. in barley, 
 and 225 A. in wheat. How many acres of grain 
 has he? 
 
 19. A farmer sold 2 cows at $ 23 each and 3 sheep 
 at 16.25 apiece. What did he receive altogether ? 
 
 20. A farmer sold a grocer 6 T. of hay at 1 12 a 
 
 ton and bought $25.50 worth of groceries. How 
 much cash did he receive ? 
 
 21. My salary is $ 84 a month. I spend J of this 
 for board, 1 for clothing, and ^ for other expenses. 
 How much do I spend altogether? How much do 
 I save ? 
 
 22. Alder had 24 marbles. In the morning he 
 lost ^ of them and in the afternoon he won | as many 
 as he had at noon. How many marbles had he at 
 night ? 
 
 Lesson 70 
 
 1. Memorize the sum of : 6789 
 
 9876 
 
LESSON 70 151 
 
 Add: 
 
 
 
 
 
 
 
 
 
 2. 
 
 6 
 
 6 
 
 9 
 
 9 
 
 7 
 
 7 
 
 8 
 
 8 
 
 
 29 
 
 49 
 
 66 
 
 86 
 
 18 
 
 38 
 
 57 
 
 77 
 
 3. 
 
 9 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 3 
 
 8 
 
 
 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 7 
 
 7 
 
 
 22 
 
 34 
 
 45 
 
 66 
 
 77 
 
 88 
 
 92 
 
 16 
 
 4. 
 
 1 
 
 5 
 
 9 
 
 5 
 
 6 
 
 7 
 
 5 
 
 2 
 
 
 2 
 
 4 
 
 2 
 
 1 
 
 7 
 
 3 
 
 6 
 
 9 
 
 
 3 
 
 2 
 
 2 
 
 3 
 
 8 
 
 4 
 
 6 
 
 5 
 
 
 13 
 
 24 
 
 32 
 
 44 
 
 56 
 
 68 
 
 77 
 
 84 
 
 5. A man had his life insured 7 years ago when 
 he was 48 yr. of age. How old is he ? 
 
 6. A man earns $22.50 a week, his oldest son 
 \ as much, and the youngest J as much. What is 
 the sum of their weekly earnings ? 
 
 7. A box weighing 5 Ib. contains 48 Ib. of sugar, 
 6 Ib. of coffee, and 3 Ib. of tea. Find its entire 
 weight. 
 
 8. 29 65 65 86 86 54 43 67 
 4674573849369088 
 
 9. 458 29 284 777 506 364 285 789 
 203 843 369 666 909 859 367 412. 
 
 10. 34 702 266 280 423 638 215 242 
 
 23 516 315 398 27 399 328 381 
 
 919 370 864 246 392 541 785 899 
 
152 ARITHMETIC 
 
 11. Two men travel, one 68 mi. east of Chicago 
 and the other 47 mi. west. How far apart will they 
 be when they reach their destination ? Draw a line 
 and represent the three places on this line. 
 
 12. Two men travel, one east and the other west 
 of Chicago, the first at the rate of 36 mi. an hour 
 and the other at the rate of 24 mi. an hour. How 
 far apart will they be in 2 hr. ? 
 
 Subtract : 
 
 684 647 811 502 824 721 554 921 
 13 ' 253 385 468 341 527 315 379 763 
 
 6724 5289 6903 8000 
 
 14 ' 3103 4503 4278 3574 
 
 6105 3060 8140 3435 
 
 4239 1432 2352 1547 
 
 15. One of two farms contains 384 A. and the 
 other is ^ as large. The first contains how many 
 more acres than the second ? 
 
 16. A man bought 6 doz. oranges at 22^ a dozen. 
 One dozen were spoiled, and he sold the rest at 30^ a 
 dozen. How much did he gain ? 
 
 17. I sold a lot for $650, losing $275; what 
 should I have sold it for to gain $125? 
 
 18. James had $.42. He spent f of it for a ball, 
 and 5/ for an orange. How much had he left ? 
 
LESSON 71 
 
 153 
 
 19. I bought a house and lot for $ 4250 and spent 
 11000 on it in repairs. I then sold it for 15925. 
 What was my gain ? 
 
 20. A laborer worked 248 days during the year. 
 He worked how many days more than he was idle ? 
 
 Lesson 71 
 
 i. 1x7= 7 7xl = ? 5x7 = 35 7x5 = ? 
 
 2x7 = 14 7x2 = ? 6x7 = 42 7x6 = ? 
 
 3x7 = 21 7x3 = ? 42 + 7= ? 7x7 = ? 
 
 4x7 = 28 7x4 = ? 49 + 7= ? 8x7 = ? 
 
 2. Count by 7's from 7 to 84. Count by 7's from 
 
 84 to 7. 
 
 3. Memorize : 
 
 Seven times 
 
 lis 7 
 
 5 is 35 
 
 9 is 63 
 
 2 is 14 
 
 6 is 42 
 
 10 is 70 
 
 3 is 21 
 
 7 is 49 
 
 11 is 77 
 
 4 is 28 
 
 8 is 56 
 
 12 is 84 
 
 4. Give two factors of each of the following num- 
 bers : 32, 56, 66, 63, 35, 48, 84, 44, 27, 77. 
 
 5. What number is the greatest common factor of 
 24 and 32 ; 35 and 55 ; 42 and 28 ; 48 and 56 ; 72 
 
 and 84. 
 
154 ARITHMETIC 
 
 6. Draw two lines, one 18 in. and the other 
 30 in. long. What is the longest line that can be 
 used to measure both lines? Test by measuring. 
 
 7. Find the largest can that can be used to 
 measure the oil in each of two barrels, one of which 
 has 20 gal. and the other 25 gal. 
 
 8. Multiply : 
 
 54 32 63 89 77 99 48 
 
 7 7 JT 7 7 7 7 
 
 In multiplying 54 by 7 you carry 2. This 2 is 2 
 what? In multiplying 5 by 7 you get 35. This 5 
 is 5 what ? 35 is 35 what ? 35 tens + 2 tens = ? 
 
 9. 456 581 695 945 998 672 
 
 4 5 6 7 7 7 
 
 10. At the rate of 36 mi. an hour, how far will a 
 rain run in 4 hr. ? Name the unit, the number, 
 and the quantity. How did you find the quantity ? 
 With the same numbers state the question in which 
 you have to find the unit. Another in which you 
 have to find the number. 
 
 11. A lawyer employs in his office 7 clerks, and 
 pays them on the average $456 a year. What is the 
 total amount of their yearly salaries ? 
 
 12. What number smaller than 20 has 7 for a 
 factor? Smaller than 39? 52? 31? 60? 41? 43? 
 34? 64? 58? 55? 
 
LESSON 
 
 155 
 
 13. Find the value of : 
 294 -*- 7 182-7 
 
 511-7 
 
 245-7 
 
 14. How many weeks and days are there in a 
 year of 366 da. ? 
 
 15. A merchant buys gloves at 85^ per pair, and 
 sells' them at 99^ a pair. How much does he gain 
 on 8 pairs if one pair is damaged and is sold for 50 ^ ? 
 
 16. How many barrels of flour at $5 a barrel will 
 cost as much as 40 bbl. of apples at $ 3 a bbl. ? 
 Name the quantity and the unit. How did you find 
 the number? 
 
 17. Harry bought 7 chickens at $ .25 apiece, 
 much had he left out of 1 2 ? 
 
 How 
 
 18. Find the cost of the following articles : 3 2-lb. 
 packages cracked wheat at $.12 each, 7 Ib. graham 
 flour at 1.03 a Ib., and 1 Ib. coffee at 1.35 a Ib. 
 
 Lesson 72 
 
 1. Count by 8's from 8 to 96. 
 from 96 to 8. 
 
 Count by 8's 
 
 2. Memorize : 
 
 Eight times 
 
 1 is 8 
 
 5 is 40 
 
 9 is 72 
 
 2 is 16 
 
 6 is 48 
 
 10 is 8.0 
 
 3 is 24 
 
 7 is 56 
 
 11 is 88 
 
 4 is 32 
 
 8 is 64 
 
 12 is 96 
 
156 ARITHMETIC 
 
 x 
 
 3. Find the value of each of the following: 
 8 x 13.05, 8 x35 A., 8 x 57 lb., S x 88 bu., 8 x 96 T. 
 
 4. What is the weight of 8 25-lb. sacks of .flour 
 and 4 50 -lb. sacks ? 
 
 5. Last year my coal cost $61.50. This year I 
 bought 8 T. at $6J a ton. How much less did my 
 coal cost this year than last? 
 
 6. A lady bought 8 yd. of cloth at $ 3|- a yard, 
 a hat for $8, and had $16 left in her purse. How 
 much had she at first ? 
 
 7. Find the value of: 4x13.15, 5x$8.09, 
 6x$2.19, 7x$2.56, 8 x $3.96. 
 
 8. How many pages are there in 8 arithmetics, 
 each of which contains 218 pages? 
 
 9. A drover bought 356 sheep at $8 apiece. 
 What did they cost him? If he sold them for $9 
 apiece, what did he gain ? 
 
 10. What is the value of $1968 ^ 8, $2440 -5- $8, 
 2848 bu. -j-Sbu., 6984 bu. + 8? 
 
 11. If 1408 A. is divided into 8 farms of equal 
 size, how many acres are there in each farm ? Name 
 the quantity, number, and unit. 
 
 12. An employer distributes $2192 among his 
 workmen, giving $8 to each. Find the number of 
 workmen. Wha t is the unit here ? 
 
 13. If 3 lb. of sugar cost 16 what will 24 lb. 
 cost ? What is the number here ? 
 
LESSON 72 157 
 
 14. How long are the lines a and b? What part 
 of b is equal to a ? a is equal to % of b. The ratio 
 of a to b is . The ratio of b to a is I-. 
 
 o .4 
 
 15. Draw lines 2 2-in. long and 3 2-in. long. 
 What part of the line 3 2-in. is equal to the line 
 2 2-in. ? 2 2-in. is what part of 3 2-in. ? What is 
 the ratio of 2 2-in. to 3 2-in. ? Of 3 2-in. to 2 2-in. ? 
 
 16. What is the ratio of 2 2-dots to 3 2-dots? 
 Of 3 2-dots to 2 2-dots? What is the ratio of the 
 weight of 2 2-lb. rolls of butter to that of 3 2-lb. 
 rolls? Of the cost? 
 
 17. If 3 2-lb. rolls of butter cost 90 ^, what will 
 2 2-lb. rolls cost? 
 
 18. What is the ratio of the cost of 3 2-lb. of 
 butter to that of 2 2-lb. ? If 2 2-lb. rolls of butter 
 cost 48^, what will 3 2-lb. rolls cost? 
 
 19. What is the largest unit that measures 4 in. 
 and 6 in. ? How often in each case ? What is the 
 ratio of 4 in. to 6 in. ? Of 6 in. to 4 in. ? 
 
 20. What is the ratio of 4 yd. to 6 yd. ? Of 6 yd. 
 to 4 yd. ? Of the cost of 4 yd. of ribbon to the cost 
 
158 ARITHMETIC 
 
 of 6 yd.? If 6 yd. of ribbon cost $.63, what will 
 
 4 yd. cost? 
 
 21. What is the ratio of 4 f to 6 f ? Of $4 to 1 6 ? 
 Of 6^ to 4^? Of $6 to 14? Of the amount $4 
 will buy to that which $6 will buy? If $4 will buy 
 
 5 gal. of maple syrup, how many quarts will $6 buy? 
 
 22. What is the largest unit that measures 6 in. 
 and 8 in. ? 6 in. = ? 2-in. 8 in. = ? 2-in. What 
 is the ratio of 6 in. to 8 in. ? Of 8 in. to 6 in. ? Of 
 
 6 ft. to 8 ft.? Of 8 yd. to 6 yd.? Of 4 to 8^? 
 Of 8 dimes to 6 dimes ? 
 
 23. At 6 boxes for 33^, what will 8 boxes of ber- 
 ries cost? At 8^ for |- pk. of apples, how many 
 quarts of apples can you buy for 6^? 
 
 24. James caught a ball 6 times out of 8. How 
 many times did he miss it in 96 chances? 
 
 Lesson 73 
 
 1. Fill a peck measure with a quart measure. 
 How many quarts in one peck ? 1 pk. = ? qt. 
 
 2. Fill a bushel measure with a peck measure. 
 How many pecks in one bushel? How many quarts 
 in one bushel? ? pt. =1 qt. ? qt. =1 pk. ? pk. = 
 1 bu. 1 bu. = ? qt. 
 
 ' 3. 3 pk. = ? qt. 6 pk. = ? qt. 4 pk. = ? qt. 
 5 pk. = ? qt. 8 pk. = ? qt. 9" pk. = ? qt. 
 How can you reduce pecks to quarts without actu- 
 ally measuring ? 
 
LESSON n 
 
 4. Reduce to quarts : 2 pk. 3 qt. ; 5 pk. 6 qt. ; 
 7 pk. 4 qt. ; 1 bu. ; 3 bu. ; 5 bu. 4 qt. 
 
 How do you reduce bushels to quarts ? 
 
 5. 11 bu. = ? qt. 3J- bu. = ? qt. 2J bu. = ? qt. 
 21 pk. = ? qt. 3f pk. = ? qt. 
 
 6. 2 bu. 3 pk. = ? pk. 2 bu. 3 pk. 4 qt. = ? qt. 
 3 bu. 2 pk. 4 qt = ? qt. 4 bu. 3 qt. = ? qt. 
 
 7. A bushel of oats weighs 32 Ib. What does 
 1 qt. of oats weigh? 1 pk. ? 
 
 What is the weight of 2 bu. 3 pk. 6 qt. of oats? 
 
 8. What part of a bushel is 2 pk. ? 
 
 A bushel of beans weighs 60 Ib. What is the 
 weight of 3 bu. 2 pk. ? 
 
 9. 15 pk. = ? bu. pk. 25 pk. = ? bu. pk. 
 30 qt. = ? pk. qt. 18 qt. = ? pk. qt. 
 
 10. 36 qt. = ? bu. 18 pk. = ? bu. 48 qt. = ? bu. 
 What is the cost of 48 qt. of potatoes at 60 f a bu. ? 
 
 11. What is the weight of 40 qt. of wheat if 1 bu, 
 weighs 60 Ib. ? 
 
 12. How many ounces are there in 1 Ib. of butter 9 
 Name other articles, one pound of which contains 16 
 oz. How could such an expression as 2 Ib. 6 oz. 
 arise ? 
 
 13. 1 J Ib. = ? oz. 2f Ib. = ? oz. 3f Ib. = ? oz 
 4 oz. = ? Ib. 8 oz. = ? Ib. 12 oz. = ? Ib 
 1 oz. = ? Ib. 2 oz. = ? Ib. 5 oz. = ? Ib. 
 
160 ARITHMETIC 
 
 14. What is the price of pepper per oz. when 
 |lb. costs 8^? 
 
 15. What is the weight in ounces of 5 J-lb. cans 
 of mustard, 3 J-lb. cans, and 2 1-lb. cans ? 
 
 16. 3 Ib. 4 oz. = ? oz. 4 Ib. 6 oz. = ? oz. At 
 $ .16 a Ib. what is the cost of 5 Ib. 8 oz. of butter? 
 
 Lesson 74 
 
 1. Place cubic inches, making a pile 4 in. long, 
 3 in. wide, 2 in. thick. Count their number thus : 
 One 3-cu. in, two 3-cu. in., i.e. 6 cu. in. (2x3 = 6). 
 One 6-cu. in., two 6-cu. in., three 6-cu. in., four 
 6-cu. in., i.e. 24 cu. in. (4x6 = 24). The volume = 
 24 cu. in. 
 
 2. How can you get the number 24 in question 1 
 without counting? What is the unit? 
 
 3. How many cubic inches in a prism 2 in. long, 
 1 in. wide, and 1 in. thick ? Make this prism. 
 
 4. Find the number of cubic inches in each of 
 the following prisms, the dimensions being given in 
 inches : 
 
 Length Width Thickness Length Width Thickness 
 
 311 642 
 
 321 633 
 
 432 843 
 
 653 864 
 
LESSON 74 161 
 
 How do you find the number of cubic inches in a 
 prism ? 
 
 5. What is the volume of a 1-in. cube? 2-in. 
 cube? 3-iu. cube? 4-in. cube? 5-in. cube? 6-in. 
 cube? 7-in. cube? 8-in. cube? 
 
 6. A 2-in. cube can be cut into how many 1-in. 
 cubes? A 4-in. cube can be cut into how many 
 2-in. cubes? What is the unit of length here? 
 The unit of volume? 
 
 7. An 8-in. cube can be cut into how many 4-in. 
 cubes ? How many 2-in. cubes ? What is the unit 
 of volume here ? 
 
 8. A 6-in. cube can be cut into how many 3-in. 
 cubes? How many 2-in. cubes? 
 
 9. Measure and find the volume of as many 
 prisms as you can find. 
 
 10. Mark off and build up in the corner of the 
 room one cubic foot. 
 
 11. What is the volume of a prism 8 in. long, 
 4 in. wide, and 4 in. high? 
 
 12. What is the volume of a pile of wood 8 ft. long, 
 4 ft. wide, and 4 ft. high? How do you find the 
 number of units of volume in any prism? 
 
 13. A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. 
 high is called a cord. Mark off a cord in the corner 
 of the room ? What is sold by the cord ? 
 
 M 
 
ARITHMETIC ' 
 
 14. How many cubic feet are there in a box 3 ft. 
 long, 1 ft. wide, and 1 ft. deep? 
 
 15. How many cubic feet are there in a box 3 ft. 
 long, 3 ft. wide, and 2 ft. deep? 4 ft. long, 3 ft. 
 wide, and 2 J ft. deep ? 
 
 16. How many 3-in. cubes could be placed in a 
 box 3 ft. long, 2 ft. 6 in. wide, and 1 ft. 6 in. deep? 
 
 17. How many cubic inches in a tin box 11 in. 
 long, 7 in. wide, and 3 in. deep? Such a box will 
 hold exactly a gallon. Pour a gallon of water into 
 such a box and prove this. 1 gal. = ? cu. in. 
 
 18. A cubic foot of water weighs 1000 oz. A tank 
 4 ft. long, 2 ft. wide, and 1 ft. deep is full of water. 
 How many ounces does it weigh? 
 
 19. What is the weight of a block of stone 6 in. 
 long, 4 in. wide, and 2 in. thick, if 8 cu. in. weigh 
 1 Ib. ? 
 
 20. How many square inches are there on the 
 surface of a cube whose edge is 4 in. ? 
 
 21. Measure the dimensions of several boxes and 
 find their volumes. 
 
SECTION VIII 
 
 Lesson 75 
 
 1. In the Roman notation numbers are expressed 
 by means of seven capital letters. These letters are 
 used to denote numbers, and their values are written 
 in question 2. This is called the Roman notation 
 because the Romans were the first to use these letters 
 for this purpose. 
 
 2. I. V. X. L. C. D. M. 
 
 1. 5. 10. 50. 100. 500. 1000. 
 
 3. VI (V + 1) = 6 VIII (V + HI) = 8 
 XV (X + V) = 15 XX (X + X) = 20. 
 
 4. Write in Roman notation 6, 7, 8 ; 15, 16, 17, 18. 
 
 5. Write in Roman notation 20, 21, 22, 23 ; 25, 
 
 26, 27, 28. 
 
 6. Write in Roman notation 30, 31, 32, 33; 35, 
 
 36, 37, 38. 
 
 7. Write in Roman notation 50, 51, 52, 53 ; 55, 
 
 56, 57, 58. 
 
 8 . IV (V - I) = 4 IX (X - I) = 9 
 XL (L - X) = 40 XC (C - X) = 90. 
 
 163 
 
164 ARITHMETIC 
 
 9. Write in Roman notation 4, 14 ; 20, 24 ; 30, 
 34; 40,44; 50, 54. 
 
 10. Write in Roman notation 9, 19, 29, 39, 49, 59, 
 
 69, 79, 89. 
 
 11. Write in Roman notation 90, 91, 94, 95, 97, 
 99, 100. 
 
 12. Look at the clock face, in the prefaces of 
 books, at the beginning of chapters or sections of 
 books, and find out where Roman numerals are used. 
 
 Study the following carefully : 
 
 13. 1= 1 
 
 XI = 11 
 
 ? = 21 
 
 11= 2 
 
 XII = 12 
 
 ? = 22 
 
 111= 3 
 
 XIII = 13 
 
 ? = 23 
 
 IV = 4 
 
 XIV = 14 
 
 ? = 24 
 
 V= 5 
 
 XV = 15 
 
 ? = 25 
 
 VI = 6 
 
 XVI = 16 
 
 ? = 26 
 
 VII = 7 
 
 XVII = 17 
 
 ? = 27 
 
 VIII = 8 
 
 XVIII = 18 
 
 ? = 28 
 
 IX = 9 
 
 XIX = 19 
 
 ? = 29 
 
 X = 10 
 
 XX = 20 
 
 ? = 30 
 
 14. XL = 40 
 
 XC= 90 
 
 D= 500 
 
 L = 50 
 
 = 100 
 
 DC= 600 
 
 LX = 60 
 
 CXXX = 130 
 
 DCC= 700 
 
 LXX = 70 
 
 CCC = 300 
 
 M = 1000 
 
 15. Write in Roman numerals the numbers from 
 30 to 100. 
 
LESSON 76 165 
 
 16. Write in Roman numerals 110, 140, 149, 150, 
 154, 182, 190, 194. 
 
 17. Write in Roman numerals 300, 15, 315 ; 200, 
 84, 284 ; 500, 99, 599 ; 614, 739, 827, 934. 
 
 18. Write in Roman numerals 1000, 250, 1250; 
 344, 1344, 1898, 1492. 
 
 19. Read, and write the numbers in figures : 
 
 (a) Henry Hudson discovered the Hudson River 
 in MDCIX. 
 
 (6) The Pilgrims landed in MDCXX. 
 
 (c) Georgia was settled in MDCCXXXIL 
 
 (cT) The battle of Bunker Hill was fought in 
 MDCCLXXV. 
 
 (e) The World's Fair was held in Chicago in 
 MDCCCXCIII. 
 
 Lesson 76 
 
 1. Review the multiplication tables of 7 and 8. 
 
 2. Write down one-seventh of $14, $28, $35, 
 $56, $70. Write down three-sevenths of $14, $28, 
 $ 35, $ 56, $ 70. How do you find one-seventh of a 
 quantity ? Three-sevenths ? 
 
 3. A man's salary was $42 a week, and his ex- 
 penses of his salary. How much did he save each 
 week? 
 
 4. Write down one-eighth of $ 16, $ 24, $ 32, $ 64, 
 Write down five-eighths of $16, $24, $32, 
 
166 ARITHMETIC 
 
 $64, $ 96. How do you find one-eighth of a quantity ? 
 Five-eighths ? 
 
 5. A lady had $40, and .spent | of it for groceries. 
 With the remainder she bought a wrap. What did 
 the wrap cost ? 
 
 6. My expenses in one month were $ 56; I spent | 
 of it for board, ^ of it for a suit of clothes, and the 
 remainder for an overcoat. What did I spend for 
 each item ? 
 
 7. A grocer paid $ .60 a bu. for potatoes, and sold 
 them for 20^ a pk. What did he gain per bu.? 
 
 8. Which will cost more, J pk. of apples at 24 $ a 
 pk. or | pk. of potatoes at 15^ a pk. ? How much? 
 
 9. A man saved ^ of his salary. What part of 
 his salary did he spend? If he had spent | of his 
 salary, what part of it would he have saved ? 
 
 10. A watch cost 7 times as much as the chain. 
 The cost of both was how many times the cost of the 
 chain ? What do you take as the unit of measure ? 
 
 11. If the watch and chain in question 10 together 
 cost $ 80, what was the cost of the chain ? Of the 
 watch ? 
 
 12. | of $24 =? |of$20 =? fof$32 =? 
 f of 20 Ib. = ? | of 10 Ib. = ? | of 30 Ib. = ? 
 
 13. f of 18 gal. = ? fof28gal.=? fof21gal.=? 
 
 40yd.=? |of56yd. =? of24yd. =? 
 
LESSON 76 167 
 
 14. A lady bought a piece of cloth containing 
 18 yd. She required J of it for a dress for herself 
 and J as much for her daughter. How many yards 
 were in each dress ? How much was left over ? 
 
 15. What is the ratio of 4 ft. to 8 ft. ? Of 8 ft. 
 to 4 ft. ? 1 yd. 1 f t. = ? ft. 2 yd. 2 ft. = ? ft. 
 What is the ratio of 1 yd. 1 ft. to 2 yd. 2 ft-? Of 
 2 yd. 2 ft. to 1 yd. 1 ft. ? Draw lines 1 yd. 1 ft. 
 long and 2 yd. 2 ft. long and prove your result 
 correct. 
 
 16. If 2 yd. 2 ft. of cloth cost 96^, what part of 
 96 ^ will a piece 1 yd. 1 ft. long cost ? How much ? 
 
 17. How many ft. in 2 yd. 1 ft.? In 7 yd.? What 
 is the ratio of 2 yd. 1 ft. to 7 yd. ? Of the cost of 
 2 yd. 1 ft. to that of 7 yd. ? 
 
 18. If 7 yd. of ribbon cost 84 what will 2 yd. 
 1 ft. cost ? 
 
 19. How many pints in 2 qt. 1 pt. ? In 7 qt. 1 pt. ? 
 What is the ratio of 2 qt. 1 pt. to 7 qt. 1 pt. ? Of 
 7 qt. 1 pt. to 2 qt. 1 pt. ? 
 
 20. If 2 qt. 1 pt. of milk cost f .15, what will 
 7 qt. 1 pt. cost? 
 
 A milkman sells 2 qt. 1 pt. of milk to each of 
 three customers. How much do they all buy ? 
 
 21. How many quarts in 2 gal. 1 qt. ? If 2 gal. 
 1 qt. of oil cost 18 f, what will 9 gal. cost ? If 6 gal, 
 
168 ARITHMETIC 
 
 3 qt. of maple syrup cost f 6, what will 2 gal. 1 qt. 
 cost? 
 
 22. What is the ratio of 2 bu. 1 pk. to 11 bu. 
 1 pk. ? Of 11 bu. 1 pk. to 2 bu. 1 pk.? If 2 bu. 
 
 I pk. of barley weigh 108 lb., what will 11 bu. 1 pk. 
 -reigh? 
 
 23. If 2 bu. 1 pk. of oats weigh 72 lb., what will 
 
 II bu. 1 pk. cost at 1 f a lb. ? 
 
 24. If an express train runs 45 mi. in 1 hr. 30 min., 
 far will it run in 3 hr. at the same rate ? 
 
 Lesson 77 
 
 
 
 1. Let each dot represent 1 ^. 1 f is what part 
 of 6^? 2^ is what part? 3^? 4^? 5^? 
 
 2. Let each dot represent 1 lb. 2 lb. is what 
 part of 8 lb.? 4 lb. ? 6 lb. ? 7 lb. ? 8 lb. ? 
 
 3. 1 lb. + 3 lb. = ? lb. The sum of 1 lb. and 
 
 3 lb. is what part of 8 lb. ? The sum of 2 lb. and 
 
 4 lb. is what part of 8 lb. ? 
 
 4. From a piece of ribbon 8 yd. long were sold 
 2 yd. to each of 2 customers. The part sold was 
 what part of the original piece ? 
 
LESSON 77 169 
 
 5. ft. + I ft. = ? 1 ft, + | ft. = ? f ft. + f ft. = ? 
 lft.+fft. = ? fft.+flt.=? fft.+ft.=? 
 
 6. Find the sum of ^ ft. and J ft. Why can you 
 not find the sum of ^ ft. and J ft. as you found the 
 sum of J ft. and | ft. ? How can you find their sum ? 
 
 7. Draw a line 1 ft. long, and divide it into 6 
 equal parts. Mark off on this line parts ^ ft. and 
 ^ ft. long. Their sum is what part of 1 ft. ? Their 
 difference is what part? Into how many units was 
 1 ft. divided? 
 
 8. If these 6 dots represent 1 ft., what part of a 
 foot is represented by 2 dots, by 3 dots, by 4 dots, by 
 5 dots, by 6 dots ? 
 
 9. If these 6 dots represent 1 ft., how many dots 
 represent 1 ft? 1 ft.? Their sum? This is what 
 part of a foot? How many dots represent their 
 difference ? This is what part of a foot ? |- f t. + ^ ft. 
 = fft. ft.+ft. = ? 1ft. -lft.=lft. 
 
 10. What is the sum of | yd. and 1 yd. ? What 
 is their difference? Draw a line 1 yd. long, mark it 
 off into parts as in question 7, and prove your answers 
 correct. Into how many units was 1 yd. divided? 
 
 11. i da. - i da. = ? l da. + 1 da. = ? 
 | hr. - | hr. = ? 1 hr. + hr. = ? 
 1 bu. + 1 bu. = ? \ bu. - l bu. = ? 
 
 f yr. + yr. = ? 
 
170 AKITHMETIC 
 
 12. What is the sum of one-half of a quantity and 
 one-third of it? Of one-third of a quantity and one- 
 
 lalf of it? What is the difference between one-half 
 of a quantity and one-third of it ? 
 
 13. A young man spent J of his weekly salary for 
 board, J of it for clothing, and the rest he saved. 
 What part of his salary did he spend? What part 
 did he save ? If he saved $ 2, what was his weekly 
 salary ? 
 
 14. A man left J his money to his wife, and J to 
 his oldest son. What was the difference between 
 their shares? If this was 3000, how much money 
 was left? 
 
 15. If these 8 dots represent 1 gal., mark off by 
 a line the number of dots that represent f gal. and 
 ^ gal. How many represent their sum? This is 
 what part of a gallon? Their difference? This is 
 what part of a gallon? 
 
 f gal- - i gal. = ? gal. f gal. + J gal. = ? gal. 
 
 16. How many pints in 1 gal. ? In | gal. ? In- 
 ^ gal. ? In the difference between f gal. and J gal. ? 
 This is what part of a gallon ? How many pints in 
 their sum? This is what part of a gallon? 
 
 17. Into a pitcher containing | gal. of water there 
 is poured ^ gal. How many pints are there in the 
 pitcher ? There is what part of a gallon ? 
 
LESSON 77 171 
 
 18. What is the sum of f of a man's salary and 
 J of it? The difference? 
 
 What part of a year is gone when J and |- of it 
 are gone? What is the sum of one-fourth and 
 three-eighths of a quantity? What is the differ- 
 ence? 
 
 19. Using the 8 dots in question 15 to represent 
 $1, find the sum of $1, f , ||. 
 
 Place 8 dots in each case, and mark off the dots 
 that represent the fractions in each question. 
 
 20. By how many dots or units will you represent 
 one dollar in the following questions ? 
 
 21. What is the weight of a parcel containing 
 J Ib. of candy and | Ib. of figs? 
 
 22. James is and his brother Arthur ^ of their 
 father's age. If the difference in their ages is 5 yr., 
 how old is their father? 
 
 23. When you found in question 9 the sum of 
 J ft. and J ft., by how many dots or units did you 
 represent 1 ft. ? How is 6 related to 2 and 3 ? If 
 you were adding ft. and ^ ft., into how many parts 
 or units would you represent 1 ft. as being divided ? 
 How is this number related to 3 and 4?. 
 
172 ARITHMETIC 
 
 24. Place 12 dots to represent 1 ft., and mark off 
 the number representing | ft. and ^ ft. -J- ft. = 
 ? dots. -J ft. = ? dots. J ft. + J ft. = ? dots. This 
 is what part of a foot ? 
 
 Lesson 78 
 
 1. In each of the following cases, into how many 
 parts do you think of $1, 1 lb., etc., as being 
 divided ? 
 
 When you add $J and $|; J lb. and f lb. ; $ J 
 and 9& ; f lb. and & lb. ; yd. and yd. ; f yd. 
 and | yd. ; f gal. and gal. ; A. and 1 A. ? 
 
 2. In each of the following questions represent 
 1 lb. by dots, and mark off the number of dots that 
 represent the parts of 1 lb. : 
 
 1 lb. + % lb. = ? j- lb. - | lb. = ? i- lb. + f lb. = ? 
 Jlb.-flb. = ? flb.-|lb. = ? flb.-ilb.=? 
 
 3. If Caryl had ^ lb. of candy, and gave % lb. 
 away, how much did she keep for herself? What 
 did her candy cost at 25^ a lb.? 
 
 4- i gal. + t gal. = ? J gal. - 1 gal. =? 
 fgal.+igal.=? i + i +A = ? A _i + i = ? 
 
 5. What is the cost of 1 lb. of baking powder at 
 If a lb., and 2 lb. butter at f a lb.? How many 
 cents? What change should be given back out of 
 a dollar bill ? 
 
LESSON 78 173 
 
 6. In terms of what unit do you express 3 nickels 
 and 2 dimes before you can add them? 1 yd. and 
 1 ft. ? 2 ft. 4 in. and J ft. ? 3 gal. and 2 qt. ? 
 One-quarter dollar and 3 dimes? 
 
 7. In terms of what unit do you express ^ ft. 
 and ^ ft. before you can add them? 
 
 (This unit is one-sixth of a foot.) 
 ^ f t. = ? sixths of a foot. J = how many sixths of 
 a foot? 1 ft. + 1 ft. =? i ft. - 1 ft. = ? 
 
 8. In terms of what unit do you express ^ yd. and 
 \ yd. before you can add them ? J yd. = ? twelfths 
 of a yard. ^ yd. = ? twelfths of a yard. 
 
 f yd. + J yd. = ? yd. - \ yd. = ? 
 
 9. Why can you not add two fractions without 
 changing them to the same unit ? Reduce J, ^, and 
 J to sixths ? 
 
 10. Reduce these fractions to 12ths : J, , f , -^, f , 
 J, f . How did you reduce J to 12ths ? f ? f ? 
 
 11. Reduce these fractions to lOths : %, -J, f , f , -f, 
 f . How did you reduce l to lOths ? | ? |? | ? 
 
 12. A piece of land containing % A. is divided 
 into lots each containing ^ A. Find the number of 
 lots. 
 
 13. Reduce these fractions to 8ths : J, ^, -|, . 
 
 14. A piece of ribbon | yd. long is divided into 
 pieces each ^ yd. long. How many pieces? 
 
174 ARITHMETIC 
 
 15. What is meant by the sum of \ and J? Find 
 the sum of : 
 
 ^ and ^ 
 
 f and f 
 
 f and f 
 
 |and 
 ^ and f 
 f and J 
 
 21 and l 
 1 and If 
 2 and 3f 
 
 f and f 
 31 and 4 
 If and T 7 
 
 16. What is meant by the difference between | 
 and J ? Find the difference between : 
 
 | and 1 - and f 3 and If 
 
 | and | i and ^ 5 T ^ and 21 
 
 | and I | and f 4^ and 2^ 
 
 f and f 2f and ^ 3^ and 1 
 
 17. How do you find the sum of two fractions ? 
 The difference? 
 
 18. From a piece of land containing 3 A., the 
 owner sells 2J A. How much has he left? 
 
 19. Mr. Ellis gave Alder a five-dollar bill with 
 which to buy a hat that cost $2. How much 
 change should Alder return to his father ? 
 
 20. Daisy gave f 5J for a pair of shoes, and f 16 J 
 for a jacket. How much had she left from 1 25? 
 
 21. Draw three lines each 1 ft. long. Divide the 
 first into 2 equal parts, the second into 4 equal parts, 
 and the third into 6 equal parts. 
 
 ft. = ? in. f ft. = ? in. f ft. = ? in. 
 
 Which is greater, \ ft., ft., or f ft. ? 
 
LESSON 79 175 
 
 22. Find the number of inches in J yd., % yd., 
 and | yd. Which is greater, J yd., % yd., or f yd. 
 
 Find the number of hours in ^ da., % da., | da., 
 and | da. Which is greater, % da., f da., f da., or 
 |da. 
 
 23. What is meant by saying that J, -|, |, and -| 
 are equal ? 
 
 24. Is J also equal to T 5 or -^? Test by finding 
 the number of minutes in J hr., -fa hr., and -^ hr. 
 
 25. Show that bu. of oats is equal to f or f or 
 T% or if ^ it. (1 bu. oats weighs 32 Ib.) 
 
 i = f = t = T 8 6=M' i = t = T 5 0=A- 
 
 26. Show that J=f = f and that i=| = ^L. 
 
 Lesson 79 
 
 1. A young man spent \ of his weekly salary for 
 board and \ of it to meet other expenses. What part 
 of his salary did he spend? What part did he save? 
 If this was f 1.50, what was his salary? 
 
 2. What is the difference between ^ of a quantity 
 and \ of it ? If the difference between J of my age 
 and \ of it is 2 years, how old am I ? 
 
 3. If three-fourths of a yard of ribbon cost 15^, 
 what will one-fourth of a yard cost? What will a 
 yard cost? 
 
 If f yd. of cloth cost 24^, what will \ yd. cost? 
 
 lyd.? 
 
176 ARITHMETIC 
 
 4. l a field is planted with potatoes and ^ of it 
 with carrots. What part of the field is planted with 
 these two vegetables ? Draw the field. 
 
 5. I invest ^ of my money in a house and lot and 
 |- of it in business. This is what part of my money ? 
 What part is left? If I have $600 left, how much 
 had I at first? 
 
 6. Draw the farm in question 7 ; divide it into 15 
 equal parts ; mark off the parts sold to each, and also 
 the remainder. Then mark the number of acres in 
 each part sold. 
 
 7. The owner of a farm sells f of it to one man 
 and ^ of it to another. What part of it does he sell ? 
 What part does he keep ? If this is 10 A., how large 
 was his farm ? 
 
 8. What is the difference between of a school 
 
 o 
 
 term and J of it? If the difference is 10 da., how 
 many days are there in the school term ? 
 
 9. If 5 of these dots represent 40^, what will 1 
 dot represent? What will 6 dots represent? If 
 these 6 dots represent the cost of 1 yd. of cloth, what 
 will 5 dots represent ? 1 dot ? 6 dots ? 
 
 10. f yd. of cloth costs 40 
 
 J yd. of cloth costs ? 
 & yd. of cloth costs ? 
 1 yd. of cloth costs ? 
 
LESSON 79 177 
 
 11. A. of land costs 
 
 ^ A. of land costs ? 
 -| A. of land costs ? 
 1 A. costs ? 
 
 12. If | of my weekly salary is $20, what is my 
 salary ? 
 
 13. A cask that is f full contains 24 gal.; find the 
 number of gallons it holds. Draw the cask, and 
 mark off the parts. 
 
 14. A man divided his farm among his three sons. 
 The oldest got -| of it, and the second \. What 
 part of the farm did these two get ? What was 
 the share of the youngest? 
 
 15. If the youngest son got 90 A., what was the 
 size of the farm? How many acres did each son get? 
 
 16. A gallon measure is half full. If I pour out 
 ^ gal., what part of a gallon is left in the measure ? 
 
 17. A boy gave \ of his marbles to one boy and \ 
 to another. What part of them did he give away? 
 What part did he keep? 
 
 18. A man spent f of his money for clothes and ^ 
 for a hat. What part of it did he spend? What 
 part did he have left? If this is $9, how much had 
 he at first ? 
 
SECTION IX 
 
 Lesson 80 
 
 UNITS OF VALUE 
 United States Money 
 
 10 cents (ct. or ^) = 1 dime (d.) 
 10 dimes 
 
 Gill 
 
 Pint 
 
 Quart Gallon 
 
 UNITS OF CAPACITY 
 Liquid Measure 
 
 4 gills (gi.)=l pint (pt.) 
 2 pints = 1 quart (qt.) 
 4 quarts = 1 gallon (gal.) 
 
 Pint Quart peck 
 
 Dry Measure 
 
 2 pints (pt.) = 1 quart (qt.) 
 
 8 quarts = 1 peck (pk.) 
 
 4 pecks, or 32 quarts = 1 bushel (bu.) 
 178 
 
LESSON 80 ' 179 
 
 UNITS OF WEIGHT 
 
 Avoirdupois Weight 
 
 16 ounces (oz.) = 1 pound (lb.) 
 
 100 pounds = 1 hundredweight (cwt.) 
 
 2000 pounds, or 20 hundredweight = 1 ton (T.) 
 
 UNITS OF LENGTH 
 
 Long Measure 
 
 12 inches (in.) = 1 foot (ft.) 
 
 3 feet = 1 yard (yd.) 
 
 5 yards, or 16^ feet = 1 rod (rd.) 
 320 rods > 
 
 1760 yards > =1 mile (mi.) 
 
 5280 feet ) 
 
 Measure in the schoolroom two points one rod apart. 
 Name two places one mile apart. 
 
 UNITS OF SURFACE 
 
 Surface, or Square Measure 
 
 144 square inches (sq. in.) 1 square foot (sq. ft.) 
 9 square feet = 1 square yard (sq. yd.) 
 
 30 square yards = 1 square rod (sq. rd.) 
 
 160 square rods = 1 acre (A.) 
 
 640 acres = 1 square mile (sq. mi.) 
 
 A township is 6 mi. square and contains 36 sq. ini. 
 
180 ARITHMETIC 
 
 UNITS OF TIME 
 
 Measure of Time 
 
 60 seconds (sec.) = 1 minute (min.) 
 60 minutes = 1 hour (hr.) 
 
 24 hours = 1 day (da.) 
 
 7 days = 1 week (wk.) 
 
 12 months (mo.) = 1 year (yr.) 
 
 365 days = 1 common year 
 
 366 days = 1 leap year 
 
 MISCELLANEOUS UNITS 
 
 12 units = 1 dozen (doz.) 
 20 units = 1 score 
 24 sheets = 1 quire 
 20 quires = 1 ream 
 
 1. Commit these tables to memory. 
 
 2. A man ran 100 yd. in 10 sec. What is the 
 unit of length ? Of time ? Give instances in which 
 1 min. is the unit of time. 1 hr. 1 da. 1 wk. 
 1 mo. 1 yr. 
 
 3. Name things that are bought and sold by the 
 quart, liquid measure ; by the gallon ; by the pint ; 
 by the gill. Of what use is the gill ? 
 
LESSON 80 181 
 
 4. Red raspberries are sold in boxes of what size ? 
 Why? Strawberries are measured by units of what 
 size ? Why ? 
 
 5. Name articles that are sold by the peck; by 
 the bushel. 
 
 6. Why is the quart measure generally used by 
 milkmen to measure their milk ? Why is the quart 
 measure not a convenient measure to use in selling 
 kerosene ? 
 
 7. Why is pepper put up in -lb. or J-lb. bottles 
 instead of in larger quantities ? 
 
 8. Why is the price of eggs quoted at so much a 
 dozen instead of at so much each ? Name other arti- 
 cles, the price of which is quoted by the dozen. 
 
 9. Flour is sold in sacks containing -J- bbl. (24J lb.), 
 J bbl. (49 lb.), and by the barrel (196 lb.). Why 
 are these convenient quantities ? 
 
 10. Butter is put up for sale in 1-lb., 2-lb. rolls and 
 in 5-lb. pails. Why are these convenient quantities ? 
 
 11. Name things sold by the ton ; measured by the 
 acre ; by the square mile. 
 
 12. Why are spices sold by the ounce ? Give in- 
 stances in which one dozen, one score, one quire, and 
 one ream are used as units of measure. 
 
 13. How might such expressions as the following 
 arise by acts of measurement : 2 yd. 1 ft. 6 in. ; 1 gal. 
 2 qt. 1 pt. ; 8 bu. 2 pk. ; 2 lb. 8 oz. ; 4 T. 500 lb. ; 
 6 yr. 4 mo. ; 2 hr. 20 min.? 
 
182 ARITHMETIC 
 
 14. How might such statements as the following 
 arise by acts of measurement : 
 
 24in. = 12x2in. 24 in. = 8x3 in. 24 in. = 6x4 in. 
 24in.= 4x6in. 24 in. = 3 x 8 in. 24 in. = 2x!2 in. 
 
 What is the ratio of 24 in. to 2 in.? Of 24 in. to 
 3 in. ? To 4 in. ? To 6 in. ? To 8 in. ? To 12 in. ? 
 
 15. In question 14, name the different units that 
 have been used to measure the quantity, 24 in. Name 
 the numbers. 
 
 As the unit becomes larger, what change takes 
 place in the number? What is their product? 
 
 16. What two things are necessary to express the 
 measurement of a quantity? How can you obtain 
 the quantity from the number and the unit? 
 
 17. In the following examples what are the quan- 
 tities measured by the given numbers and units ? 
 
 Number Unit Number Unit 
 
 4 2 qt. 37 da. 
 
 3 2 in. 63 doz. 
 
 4 f 5 55 sq. in. 
 3 $10 8 10 A. 
 
 18. If the quantity 36 in. is measured by a 4-in. 
 unit, what number expresses the measurement ? 
 
 19. In the following examples what numbers ex- 
 press the measurements? 
 
Quantity 
 
 Unit 
 
 Quantity 
 
 24 hr. 
 
 8hr. 
 
 3bu. 
 
 30^ 
 
 6* 
 
 6bu. 
 
 2 da. 
 
 6hr. 
 
 48 
 
 120 
 
 $5 
 
 4-in. sq. 
 
 $1 
 
 1 dime 
 
 1 qt. 
 
 4 gal. 
 
 2qt. 
 
 1ft. 
 
 LESSON 81 183 
 
 Unit 
 
 Ipk. 
 4pk. 
 
 1 doz. 
 
 2 sq. in. 
 Igal. 
 lyd. 
 
 20. If the number 8 expresses the measurement of 
 the quantity 40 in., what is the unit? How can you 
 obtain the unit from the number and the quantity? 
 
 21. In the following examples what units have 
 been used to measure the quantities? 
 
 Quantity Number Quantity Number 
 
 112 6 $200 10 
 
 30 da. 5 $200 20 
 
 2 bu. 4 6 gal. 12 
 
 15 doz. 5 35^ 5 
 
 22. How do you obtain the quantity from the 
 number and unit? The unit from the quantity and 
 number ? The number from the quantity and unit ? 
 
 Lesson 81 
 
 1. What is the quantity measured by the number 
 6 when the unit is 3 gal. 2 qt. of milk ? 
 
 2. Find the weight of the unit that measures the 
 quantity 9 Ib. 8 oz. 4 times. 
 
 3. To what unit must 2 yd. 1 ft. 6 in. be reduced 
 in order to find the number of times it is measured 
 
184 ARITHMETIC 
 
 by the unit 3 in. ? Find this number. This number 
 is often called the ratio of 2 yd. 1 ft. 6 in. to 3 in. 
 If you actually measured a line 2 yd. 1 ft. 6 in. long 
 by the unit 3 in. to find this number, would it be 
 necessary to reduce 2 yd. 1 ft. 6 in. to inches ? 
 
 4. Find the ratio of 5 bu. 1 pk. to 3 pk. Find the 
 cost of 5 bu. 1 pk. of potatoes at the rate of 3 pk. 
 for 
 
 5. Make a drawing to represent a field 120 yd. 
 long and 80 yd. wide. How long must a wire be to 
 go around it ? What would be its cost at 6 ^ a yard ? 
 What would 4 rows of wire fencing cost? 
 
 6. What would 4 rows of wire fencing cost for a 
 chicken coop 6 yd. long and 4 yd. wide at 6 ^ a yd.? 
 
 7. If a yard measure is ^ in. too long, what is the 
 actual distance between two points which are found 
 by this measure to be 6 yd. apart? 
 
 8. A 200-acre farm is sown with grain as follows : 
 barley 25 A., oats 46 A., wheat 75 A. The buildings, 
 garden, and orchard occupy 12 A., and the rest is 
 pasture. How many acres of pasture are there ? 
 
 9. A map is drawn so that half an inch represents 
 1 mi. What will 1 in. represent? How many square 
 miles will 1 sq. in. represent? 
 
 10. Find the weight of an iron bar 1 ft. long if 
 1 yd. weighs 18 Ib. 
 
LESSON 81 185 
 
 Find the weight of an iron bar 4 yd. 2 ft. long, of 
 which 1 yd. weighs 15 Ib. 
 
 11. Find the cost of fencing a piece of railway 
 (both sides), 7 rd. long, at $5.50 a rod? 
 
 12. A block of stone is 8 in. long, 6 in. wide, and 
 4 in. thick. Find its weight if 6 cu. in. weigh 1 Ib. 
 
 13. A merchant buys 28 yd. of cheese cloth at 6 $ a 
 yd. He uses a certain number of yards in his store 
 and sells the remainder for the total cost price at 7 ^ a 
 yard. How many yards does he sell? How many 
 does he use ? 
 
 14. What does a bushel of wheat weigh ? If 3 Ib. 
 of wheat makes 2 Ib. of flour, how many pounds of 
 flour will 1 bu. of wheat make ? 
 
 15. Find the cost of cementing the floor of a cellar 
 6 yd. long and 5 yd. wide at 12^ per sq. yd. 
 
 16. Find the cost of digging a cellar 4 yd. long, 
 3 yd. wide, and 2 yd. deep, at 20^ per cu. yd. 
 
 17. A certain map is drawn so that 2 mi. is repre- 
 sented by 1 in. On this map the township of Scott 
 is a square whose side is 3 in. What is the length 
 of the township ? What is its area ? 
 
 18. Find the number of strips of paper in the wall 
 of a room 24 ft. long and 20 ft. wide, the paper being 
 2 ft. wide. What is the unit here ? 
 
186 
 
 ARITHMETIC 
 
 19. A farmer sowed 3 pk. of wheat in a small field 
 and raised 14 bu. 1 pk. of seed. What is the average 
 yield per peck of seed ? 
 
 20. An express train takes 8 hr. 20 min. to travel 
 320 mi. If stops of 5 min. each are made at 4 dif- 
 ferent places, find the average rate at which the train 
 is travelling. 
 
 21. A railway train travels at the rate of 1 mi. in 
 2 min. What is its speed per hour? 
 
 Lesson 82 
 
 1. What is the sum of : 
 788 
 989 
 
 Add: 
 
 8 
 39 
 
 48 
 
 9 
 59 
 
 9 
 10 
 
 9 
 30 
 
 10 
 
 8 
 
 9 
 
 28 
 
 8 
 
 7 
 
 60 
 
 9 
 
 3 
 
 45 
 
 9 
 
 9 
 
 80 
 
 6 7 
 
 2 8 
 
 98 90 
 
 4 
 
 3 
 
 91 
 
 4. 
 
 4 
 
 1 
 
 2 
 
 3 
 
 4 
 
 8 
 
 7 
 
 9 
 
 
 2 
 
 4 
 
 8 
 
 9 
 
 8 
 
 4 
 
 5 
 
 6 
 
 
 9 
 
 8 
 
 5 
 
 5 
 
 5 
 
 3 
 
 2 
 
 3 
 
 
 19 
 
 27 
 
 22 
 
 45 
 
 63 
 
 71 
 
 83 
 
 90 
 
LESSON 82 187 
 
 Add: 
 5. $39.46 
 
 86.74 
 
 $45.49 
 23.87 
 
 $38.94 
 59.36 
 
 $97.56 
 36.79 
 
 $352.69 $ 
 176.29 
 
 388.14 
 279.56 
 
 $6243.80 
 2597.80 
 
 $1873.45 
 2794.63 
 
 6. $165.95 
 
 258.71 
 147.58 
 
 $229.69 
 141.65 
 299.57 
 
 $370.80 
 156.93 
 881.79 
 
 $179.79 
 324.67 
 250.60 
 
 7. A merchant sold goods on Monday to the 
 value of $187.91, Tuesday $254.82, and Wednesday 
 $181.79. What were the total sales on these three 
 days? 
 
 8. A farmer sold 23 bu. wheat for $24.84, 34 bu. 
 for $33.31, and 15 bu. barley for $14.70. How many 
 bushels of grain did he sell and for how much ? 
 
 Subtract : 
 
 9. $37.33 $28.77 $427.97 $626.78 
 
 29.38 19.89 368.48 349,79 
 
 10. $356.71 $3026.69 $2281.79 $6006.25 
 
 248.24 1456.84 1584.82 3750.82 
 
 11. A real estate agent bought a lot for $1880 and 
 sold it for $ 2375. Find his gain. 
 
 12. A man paid $137 for one horse and $89 for 
 another. They cost him for feed $24.75. He sold 
 them for $275. Find his gain. 
 
188 
 
 ARITHMETIC 
 
 13. Find the amount of the following bill : 
 
 6 pairs of stockings at 3 for $ 1.00. 
 24 handkerchiefs at $1.75 per doz. 
 6 yd. cloth at $.48 a yd. 
 3 yd. muslin at $.15 a yd. 
 
 14. A farmer's wife sold 20 Ib. of butter at 15 $ a 
 pound. She then bought 16 Ib. of sugar at 5|^ a 
 pound, and 2 Ib. of tea at 60 a pound. How many 
 pounds of raisins at 8 ^ a pound can she buy with the 
 rest of her money ? 
 
 Lesson 83 
 
 1. Count by 9's from 9 to 108. 
 Count by 9's from 108 to 9. 
 
 2. Memorize : 
 
 Nine times 
 
 1 is 9 
 
 5 is 45 
 
 9 is 81 
 
 2 is 18 
 
 6 is 54 
 
 10 is 90 
 
 3 is 27 
 
 7 is 63 
 
 11 is 99 
 
 4 is 36 
 
 8 is 72 
 
 12 is 108 
 
 3. In the table of 9's what is the sum of the two 
 digits in each product? 
 
 4. Name the numbers less than 100 of which 9 
 is a factor. What number is the greatest common 
 factor of 18 and 24 ; 18 and 45 ; 35 and 56 ; 63 and 
 81; 40 and 55; 99 and 72? 
 
LESSON 83 180 
 
 5. What is the largest unit that will divide 45 A. 
 and 63 A. ? Two farms contain, respectively, 45 A. 
 and 63 A. If these two farms are divided into fields 
 of equal size, containing as many acres as possible, 
 how many acres will there be in each field? How 
 many fields ? 
 
 Multiply: 
 
 6. 1514.02 11180.66 $26.55 $97.22 
 7 8 9 9 
 
 7. $851.02 $738.75 $243.44 $1097.47 
 9 9 9 9 
 
 8. What number smaller than 20 has 9 for a 
 factor? Smaller than 25? 61? 33? 70? 80? 
 82? 74? 26? 44? 
 
 9. Give the quotient and remainder on dividing 
 $231 by 9; $868 by $9; 798 mi. by 9; 676 of any 
 unit by 9 -, 319 of any unit by 9 of the same unit. 
 
 10. A speculator gave his check for the price of 
 9 city lots at $ 2450 apiece, and after this was cashed 
 he still had $1250 in the bank. How much had he 
 at first? 
 
 11. A farmer got 315 bu. of oats off a nine-acre 
 field. How many bushels to the acre ? 
 
 State the corresponding question in which you are 
 required to find the number. The quantity. 
 
 12. In how many days would a man walk 216 mi., 
 at the rate of 3 mi. an hour for 9 hr. a day ? 
 
190 ARITHMETIC 
 
 13. What is the ratio of 3 dots to 4 dots ? Of 4 
 dots to 3 dots ? If each dot represents 6 ?, what will 
 3 dots represent ? 4 dots ? What is the ratio of 1 8 4 
 to 24?? Of 24? to 
 
 14. If 24? will buy a peck of peas, what part of a 
 peck will 18? buy? How many quarts? 
 
 15. What is the ratio of 4 dots to 6 dots? If each 
 dot represents 9 yd., what will 4 dots represent? 6 
 dots ? What is the ratio of 36 yd. to 54 yd. ? Of 
 54 yd. to 36 yd. ? 
 
 16. If 54 yd. of cloth cost $ 67.50, what will 36 yd. 
 of the same kind cost? 
 
 If 54 men can do a piece of work in 6 da., how 
 long will it take 36 men to do it? 
 
 17. Refer to the dots in question 15 and give the 
 value of 1 dot, 2 dots, 3 dots, 4 dots, 5 dots, and 
 6 dots, when each dot represents 9 Ib. 
 
 18. What is the ratio of 9 Ib. to 36 Ib. ? Of 36 Ib. 
 to 9 Ib.? Of 18 Ib. to 45 Ib.? Of 45 Ib. to 18 Ib.? 
 Of 27 Ib. to 54 Ib. ? Of 54 Ib. to 27 Ib. ? 
 
 19. If 18 Ib. of coffee cost 1 5.40, what will 45 Ib. 
 cost at the same rate ? 
 
 20. 54 T. of coal cost $310.50. What will 27 T. 
 cost at the same rate ? 
 
LESSON 84 
 
 191 
 
 21. What is the ratio of 4 5-cd. of wood to 9 5-cd. 
 of wood ? Of 20 cd. to 45 cd. ? Of 45 cd. to 20 cd. ? 
 If 45 'cd. of wood cost $144, what will 20 cd. cost? 
 
 22. If 36 T. of hay cost 1 320, what will 27 T. 
 cost? 
 
 23. The value of a purse and the money within it 
 is $12. If the ratio of the money to the value of the 
 purse is 3, find the value of each. 
 
 Lesson 84 
 
 1. Memorize : 
 
 Ten times 
 
 lislO 
 
 5 is 50 
 
 9 is 90 
 
 2 is 20 
 
 6 is 60 
 
 10 is 100 
 
 3 is 30 
 
 7 is 70 
 
 11 is 110 
 
 4 is 40 
 
 Sis 80 
 
 12 is 120 
 
 2. In what figure do all these products of 10 end ? 
 
 3. Multiply: 
 
 35 62 288 164 2164 3256 
 10 10 10 10 10 10 
 
 In what figure do all these products of 10 end? 
 
 4. What is the easiest way of multiplying a num- 
 ber by 10? Write the product of these numbers 
 multiplied by 10: 
 
 16, 21, 24, 43, 72, 245, 631, 725. 
 
ARITHMETIC 
 
 5. Multiply 16 by 10 and the product by 10. How 
 can you multiply a number by 10 twice in succession 
 without actually multiplying ? How can you multi- 
 ply a number by 100 without actually multiplying ? 
 
 6. Write the product of these numbers when 
 multiplied by 100: 
 
 5, 8, 12, 
 
 24, 35, 68, 215, 625. 
 
 1 
 
 x 
 
 11=11 
 
 11 
 
 x 
 
 1=? 
 
 8.1 
 
 x 12 = 12 
 
 12 x 1=? 
 
 2 
 
 x 
 
 11 = 22 
 
 11 
 
 x 
 
 2=? 
 
 2 
 
 x 12 = 24 
 
 12 
 
 x 
 
 2 = ? 
 
 3 
 
 X 
 
 11 = 33 
 
 11 
 
 X 
 
 3=? 
 
 3 
 
 x!2 = 36 
 
 12 
 
 x 
 
 3=? 
 
 4 
 
 X 
 
 11 = 44 
 
 11 
 
 X 
 
 4 = ? 
 
 4 
 
 x!2 = 48 
 
 12 x 
 
 4=? 
 
 5 
 
 X 
 
 11 = 55 
 
 11 
 
 X 
 
 5=? 
 
 5 
 
 x 12 = 60 
 
 12 
 
 X 
 
 5=? 
 
 6 
 
 x 
 
 11 = 66 
 
 11 
 
 X 
 
 6=? 
 
 6 
 
 x 12 = 72 
 
 12 
 
 x 
 
 6=? 
 
 7 
 
 X 
 
 11 = 77 
 
 11 
 
 X 
 
 7=? 
 
 7 
 
 x 12 = 84 
 
 12 
 
 X 
 
 7=? 
 
 8 
 
 X 
 
 11 = 88 
 
 11 
 
 X 
 
 8=? 
 
 8 
 
 x 12 = 96 
 
 12 
 
 X 
 
 8=? 
 
 9 
 
 X 
 
 11 = 99 
 
 11 
 
 X 
 
 9 = ? 
 
 9x12 = 108 
 
 12 
 
 X 
 
 9 = ? 
 
 10 
 
 X 
 
 11 = 110 
 
 11 
 
 X 
 
 10 = ? 
 
 10 
 
 x 12 = 120 
 
 12 
 
 X 
 
 10 = ? 
 
 11 
 
 X 
 
 11= ? 
 
 11 
 
 X 
 
 11 = ? 
 
 11 
 
 x 12=132 
 
 12 
 
 X 
 
 11 = ? 
 
 12 
 
 X 
 
 11= ? 
 
 11 
 
 X 
 
 12=? 
 
 12 
 
 x 12=144 
 
 12 
 
 X 
 
 12 = ? 
 
 9. Write out and memorize the multiplication 
 tables of 11 and 12. 
 
 10. What is the area of a square whose side is 
 12 in. ? How many square inches in a square foot? 
 
 11. In a garden there are 12 rows of potatoes with 
 11 hills in a row; how many hills of potatoes are 
 there in the garden? Name the number, unit, and 
 quantity. State the corresponding question in which 
 you are required to find the number. The unit.. 
 
LESSON 84 
 
 193 
 
 12. If 1 pk. of potatoes is obtained from each hill 
 on the average, what is the yield in bushels ? 
 
 13. Review the Multiplication Table : 
 
 Two- times 
 
 Three times 
 
 Four times 
 
 Five times 
 
 Six times 
 
 Seven times 
 
 1 is 2 
 
 lis 3 
 
 1 is 4 
 
 1 is 5 
 
 1 is 6 
 
 lis 7 
 
 2 " 4 
 
 2 " 6 
 
 2 " 8 
 
 2 " 10 
 
 2 " 12 
 
 2 " 14 
 
 3 " 6 
 
 3 " 9 
 
 3 " 12 
 
 3 " 15 
 
 3 " 18 
 
 3 "21 
 
 4 " 8 
 
 4 " 12 
 
 4 " 16 
 
 4 "20 
 
 4 "24 
 
 4 "28 
 
 5 " 10 
 
 5 " 15 
 
 5 " 20 
 
 5 "25 
 
 5 " 30 
 
 5 "35 
 
 6 " 12 
 
 6 " 18 
 
 6 "24 
 
 6 " 30 
 
 6 " 36 
 
 6 "42 
 
 7 " 14 
 
 7 "21 
 
 7 "28 
 
 7 "35 
 
 7 "42 
 
 7 "49 
 
 8 " 16 
 
 8 "24 
 
 8 "32 
 
 8 "40 
 
 8 "48 
 
 8 "56 
 
 9 " 18 
 
 9 "27 
 
 9 "36 
 
 9 "45 
 
 9 " 54 
 
 9 "63 
 
 10 " 20 
 
 10 " 30 
 
 10 " 40 
 
 10 " 50 
 
 10 " 60 
 
 10 " 70 
 
 11 " 22 
 
 11 " 33 
 
 11 " 44 
 
 11 " 55 
 
 11 " 66 
 
 11 " 77 
 
 12 " 24 
 
 12 " 36 
 
 12 " 48 
 
 12 " 60 
 
 12 " 72 
 
 12 " 84 
 
 Eight times 
 
 Nine times 
 
 Ten times 
 
 Eleven times 
 
 Twelve times 
 
 lis 8 
 
 lis 9 
 
 1 is 10 
 
 1 is 11 
 
 lis 12 
 
 2 " 16 
 
 2 " 18 
 
 2 " 20 
 
 2 " 22 
 
 2 " 24 
 
 3 " 24 
 
 3 " 27 
 
 3 " 30 
 
 3 " 33 
 
 3 " 36 
 
 4 " 32 
 
 4 " 36 
 
 4 " 40 
 
 4 " 44 
 
 4 " 48 
 
 5 "40 
 
 5 " 45 
 
 5 " 50 
 
 5 " 55 
 
 6 " 60 
 
 6 "48 
 
 6 " 54 
 
 6 " 60 
 
 6 " 66 
 
 6 " 72 
 
 7 " .56 
 
 7" 63 
 
 7 " 70 
 
 7 " 77 
 
 7 " 84 
 
 8 "64 
 
 8 " 72 
 
 8 " 80 
 
 8" 88 
 
 8 " 96 
 
 9 " 72 
 
 9 " 81 
 
 9 " 90 
 
 9 " 99 
 
 9 " 108 
 
 10 " 80 
 
 10 " 90 
 
 10 " 100 
 
 10 "110 
 
 10 " 120 
 
 11 "88 
 
 11 99 
 
 11 " 110 
 
 11 "121 
 
 11 " 132 
 
 12 " 96 
 
 12 " 108 
 
 12 " 120 
 
 12 " 132 
 
 12 " 144 
 
SECTION X 
 
 Lesson 85 
 
 Read the following quantities : 
 
 1. $1000 $2000 $6000 $8000 $625 
 $1625 $4625 $6615 $8314 $9276 
 
 2. $12,000 $18,000 $46,000 $90,000 
 
 $423 $12,423 $25,428 $36,250 
 
 $58,736 $60,235 $60,035 $80,005 
 
 3. $438 $438,000 $649,000 
 $625,346 $549,763 $245,084 
 1333,333 $325,040 $520,006 
 
 4. $1,000,000 $4,000,000 $6,000,000 
 $1,250,000 $4,645,000 $6,236,124 
 
 $2,825,127 $2,478,042 $4,048,026 
 
 5. $312.83 $2678.28 $1052.47 
 $45,624.25 $17,322.50 $30,420.08 
 $70,055.04 $841,762.50 $123,750.65 
 
 Write in figures : 
 
 6. Six hundred twenty-five ; eight hundred sixtj; 
 five hundred seventy-six ; one thousand two hundred 
 forty-six; two thousand sixty; three thousand eighty; 
 six thousand eight ; nine thousand nine. 
 
 194 
 
LESSON 85 195 
 
 7. Fifteen thousand three hundred fifty-four ; 
 seventy-five thousand two hundred forty-nine ; ten 
 thousand two hundred fifty ; twenty thousand four 
 hundred five ; sixty-four thousand twenty-six ; eighty 
 thousand seven. 
 
 8. Three hundred twentj^-four dollars and twenty- 
 five cents ; two thousand six hundred fifty dollars 
 and four cents; forty-five thousand nine hundred 
 ninety-eight dollars and twenty-three cents ; two 
 hundred seventy-six thousand five hundred four dol- 
 lars and seventeen cents. 
 
 9. Review these addition tables : 
 
 12 123 123 
 43 543 654 
 
 1234 1234 
 
 1 i i il 65 
 
 12345 2345 
 
 98765 9876 
 
 3456 456 567 
 
 9_ 8 7^ 6 9 8_ 7 987 
 
 67 78 8 9 9 
 98 98 9 9 10 
 
196 ARITHMETIC 
 
 Add: 
 
 10. 
 
 1811.04 
 
 1360.00 
 
 1 26.55 
 
 $851.02 
 
 
 650.12 
 
 215.17 
 
 418.60 
 
 312.60 
 
 
 19.25 
 
 12.50 
 
 20.63 
 
 147.22 
 
 
 32.50 
 
 311.20 
 
 105.24 
 
 568.35 
 
 
 113.56 
 
 235.32 
 
 222.42 
 
 116.02 
 
 11. 
 
 $ 636.99 
 
 $ 859.69 
 
 $ 97.22 
 
 $1180.66 
 
 
 1850.14 
 
 2223.42 
 
 8148.60 
 
 342.65 
 
 
 311.20 
 
 1097.47 
 
 3839.25 
 
 1237.50 
 
 
 1201.64 
 
 1214.03 
 
 694.62 
 
 2678.28 
 
 12. New Hampshire contains 9305 sq. mi., Ver- 
 mont 9565, Massachusetts 8315, Rhode Island 1256, 
 Connecticut 4990. What is the total area of these 
 five states? 
 
 13. This total area is how many square miles 
 greater than that of Maine, the area of which is 
 33,040 sq. mi.? 
 
 Subtract : 
 
 $403.59 $875.13 $6168.37 $1035.42 
 94.63 694.73 467.89 559.83 
 
 $3839.25 $5300.20 $7357.51 $36,501.28 
 15< 3661.09 1214.03 1777.60 21,420.64 
 
 16. Vermont contains 9565 sq. mi. and Massachu- 
 setts 8315 ; what is the difference in their areas ? 
 
 17. Lake Erie contains 7750 sq. mi., Ontario 
 6950, and Michigan 22,000. How much larger is 
 
 14. 
 
LESSON 86 197 
 
 Lake Michigan than the united area of Lake Erie 
 and Lake Huron ? 
 
 18. A, B, and C engaged in trade; A put in 
 82450, B, 13275, and C as much as A and B together. 
 How much money did C put into the business ? 
 What was the total capital? 
 
 Multiply : 
 19. 134.71 
 8 
 
 $28.79 
 6 
 
 $33.72 
 9 
 
 $24.95 
 5 
 
 20. $134.36 
 4 
 
 1364.76 
 
 7 
 
 $1763.29 
 8 
 
 $2678.28 
 9 
 
 21. A is worth $3275, and B 4 times as much. 
 What is B worth ? 
 
 22. Divide : 
 
 6)15876.40 7)$ 4956. 35 8)13008.96 9)15842.35 
 
 23. A dealer bought sheep at the average rate of 
 $ 6 each ; how many did he buy for $ 3816 ? What 
 are you given ? What are you required to find ? 
 
 24. A furniture dealer gains $ 1296 buying sofas 
 for $18.75 each and selling them for $27.75. How 
 many did he sell ? What is the unit here ? 
 
 Lesson 86 
 
 l. 64,395 is equal to 5 units, 9 tens, 3 hundreds, 
 4 thousands, 6 ten-thousands. 
 
198 ARITHMETIC 
 
 2. Give, as in question 1, the place value of each 
 figure: 25; 37; -272; 582; 6548; 2094; 42,965; 
 37,048. 
 
 3. What is the units' place, the tens' place, the 
 hundreds', the thousands', the ten-thousands' ? 
 
 4. Multiply 2 tens by 3, how many tens? Mul- 
 tiply 2 by 3 tens, how many tens ? Multiply 4 tens 
 by 5, by 6, by 7, by 8 ; how many tens in each case ? 
 Multiply 4 by 5 tens, by 6 tens, by 7 tens, by 8 tens ? 
 How many tens in each case ? 
 
 5. 25 units = ? units tens. 
 
 24 tens = ? tens hundreds. 
 58 tens = ? tens hundreds. 
 32 units = ? units tens. 
 64 tens = ? tens hundreds. 
 16 tens = ? tens hundreds. 
 
 6. 3 tens multiplied by 2 equals 6 tens. 
 
 3 tens multiplied by 2 tens equals 6 what? 
 6 tens multiplied by 4 tens equals what ? 
 6 tens multiplied by 2 tens equals what ? 
 
 7. 68 Multiply 68 by 4, and the product is 272. 
 24 The 7 is 7 what? The 2 in 24 is 2 what ? 
 
 272 Multiply 8 by 2 tens and the product is 
 186 16 tens or 1 hundred 6 tens. Place 6 tens 
 3 under 7 tens, and carry the 1 to the hun- 
 dreds' place. Multiply 6 tens by 2 tens, and the 
 product is 12 hundreds. To this add 1 hundred, 
 
LESSON 86 199 
 
 and the sum is 13 hundreds. Add, and the complete 
 product is 1632. 
 
 8. Study question 7, then place 24 under 68 and 
 multiply without looking at the book. Do this until 
 you can work quickly and accurately. 
 
 9. Multiply : 
 
 38 58 36 76 $64 $47 
 
 24 24 24 32 25 16 
 
 10. A bushel of oats weighs 32 Ib. ; how many 
 pounds in 48 bu.? 
 
 11. A page of a book contains 39 lines, averaging 
 13 words to a line. Find the number of words on 
 the page. 
 
 12. A speculator buys 25 A. of land at $65 an 
 acre and sells it for $ 88 an acre. Find his gain. 
 
 13. Multiply : 
 
 00 (ft) 00 00 00 CO 
 
 $35 $17 32 Ib. 27 mi. 19 mi. $48 
 _28 __13 68_ 38 16 24 
 
 14. Question 13 shows the multiplications that 
 must be done for simple practical examples like 
 questions 10, 11, 12. 
 
 Write out these examples : 
 
 (a) About the cost of 28 cows at $35 each. 
 
 (b) About the gain on selling 13 horses. 
 
 (c) About the number of pounds in 68 bu. of oats. 
 
42 
 
 79 
 
 89 
 
 93 
 
 75 
 
 86 
 
 39 
 
 67 
 
 99 
 
 58 
 
 94 
 
 86 
 
 231 
 
 176 
 
 224 
 
 168 
 
 365 
 
 893 
 
 24 
 
 32 
 
 13 
 
 43 
 
 64 
 
 75 
 
 200 ARITHMETIC 
 
 (ct) About the distance a boy rides on his bicycle 
 in 38 days. 
 
 (e) About the distance apart two boats will be, 
 one going down stream at 11 mi. an hr., the other 
 up stream at 8 mi. an hr. 
 
 (/) About a man's savings in 2 yr. 
 
 Multiply : 
 15. 
 
 16. 
 
 17. $22.13 $43.07 $29.04 $34.45 $54.39 $47.81 
 24 27 16 82 18 29 
 
 18. $39.17 $94.26 $87.91 $60.86 $68.77 $74.93 
 45 66 89 19 95 68 
 
 19. A business man pays in wages $96.75 each 
 week ; what wages does he pay in 1 yr. (1 yr. = 
 52 wk.)? 
 
 20. How far will a bicyclist travel in 36 da., if he 
 travels 8 hr. a day at the rate of 9 mi. an hour? 
 
 Lesson 87 
 
 l. Divide 714 by 21. 21)714(34 
 2 is called the trial divisor. 63 
 
 2 is contained in 7 3 times. Multiply ~^ 
 21 by 3. The product is 63. Place 63 84 
 
 under 71, subtract, and bring down 4. 
 
LESSON 87 201 
 
 2 is contained in 8 4 times. Multiply 21 by 4, and 
 write the product 84 under 84. 
 
 The quotient is 34. How would you prove 34 the 
 correct answer? 
 
 2. What is the trial divisor when the divisor is 
 21? 31? 41? 51? 
 
 Find the quotients : 
 
 903-5-21 992 -r- 31 2542 -*- 41 3162-^-51 
 11344-^-21 $1488-5- $31 
 
 3. What is the trial divisor when the divisor is 
 22? 42? 62? 72? 
 
 Find the quotients : 
 
 726 -i- 22 2352 -v- 42 4650 -f- 62 5188 -r- 72 
 $726-^-22 = ? $2352-s-|42 = ? $4650 H- 62 = ? 
 
 4. A cattle dealer paid $682 for 22 head of cat- 
 tle. What was the average price? Name the quan- 
 tity, number, and unit. 
 
 5. If a train travels 32 mi. an hour, how long 
 will it take to travel 1152 mi., there being stops 
 amounting to one hour? 
 
 6. How many cows at $ 31 apiece can a man buy 
 with the money he receives for 9 horses sold at an 
 average price of $ 124 ? 
 
 7. What is the cost of 1472 Ib. of oats at 9} 
 a bu. ? (1 bu. oats weighs 32 Ib.) 
 
 8. What is the trial divisor when the divisor is 
 23,24,33,44,54,63,84? 
 
202 ARITHMETIC 
 
 Divisor Dividend Quotient Divisor Dividend Quotient 
 
 9. (a) 23)6285(273 (6) 24)3877(161 
 
 46 24 
 
 168 147 
 
 161 144 
 
 ~T5 ~37 
 
 69 24 
 
 6 Remainder 13 Remainder 
 
 (a) The trial divisor 2 is contained in the trial 
 dividend 6 3 times. On multiplying 23 by 3, the 
 product 69 is seen to be too large. Why ? Try 2 
 in the quotient. Again, 2 is contained in 16 8 times. 
 On multiplying 23 by 8, the product 184 is seen to 
 be too large. Why? Try 7 in the quotient. 2 is 
 contained in 7 3 times. The remainder is 6. 
 
 (6) On the second division 2 is contained in 14 7 
 times. Why is 7 too large? 
 
 (<?) When 23, 24; 33, 34; 43, 44 ; and so on, are 
 the divisors, the quotient obtained by using the trial 
 divisor is frequently too large. If so, try in the 
 quotient the number next smaller. 
 
 10. Study question 9 carefully, then copy the 
 examples, and divide. Do this until you can divide 
 accurately and quickly without looking at the book. 
 
 11. Find the quotients : 
 
 3197 -v- 23 5940 --44 5355 -r 68 12,936 + 84 
 
LESSON 88 203 
 
 12. Find the quotients and remainders : 
 
 1527 -v- 34 2632 -f- 54 46,798-^64 2954-5-14 
 7549 -=- 13 u 6493 -5- 84 26,495 + 94 3823 -r- 44 
 
 13. How many days are there in 1728 hr. ? 
 4008 hr.? 21,768 hr.? 
 
 14. How many sheets of paper in 1 quire ? If a 
 business man uses 7488 sheets of paper in a year, 
 how many quires does he use? 
 
 15. A man whose salary is $40 a week spends 
 $ 26 a week. In how many weeks can he save $686 ? 
 What is the unit that measures his savings ? 
 
 16. A speculator paid $6654 for 64 horses and 85 
 sheep. If the sheep cost $6 apiece, what was the 
 average cost of each horse ? 
 
 Lesson 88 
 
 Divisor Dividend Quotient Divisor Dividend Quotient 
 
 1. (a) 29)7948(274 (6) 57)8898(156 
 58 57 
 
 214 118 
 203 87 
 
 319 
 
 285 
 
 118 31 
 116 
 
 2 Remainder 
 
 348 
 342 
 
 Remainder 
 
 (a) As 29 is nearly equal to 30, the trial divisor is 
 3. 3 is contained in 7, 2 times, in 21, 7 times, and in 
 
204 ARITHMETIC 
 
 11, 3 times. On multiplying 29 by 3 the product is 
 87. On placing 87 under 118 and subtracting, the 
 remainder is 31. This is larger than 29, and therefore 
 the quotient is 1 larger than 3, or 4. 
 
 () On the last division the trial divisor 6 is con- 
 tained in 34 5 times. Why is 5 too small? 
 
 0) When 27, 28, 29 are the divisors, the trial 
 divisor is 3. What is the trial divisor when the 
 divisors are 37, 38, or 39? 47, 48, or 49? 57, 58, or 
 59? 67? 88? 99? 
 
 2. Name the trial divisors. Find the quotients 
 and remainders : 
 
 5842 - 29 
 9546 -4- 59 
 8113-*- 67 
 
 8572 -r- 98 
 
 9843 -j- 25 
 4554 ^ 36 
 3580 - 64 
 3679 -v- 47 
 
 3134 + 44 
 8967 ^ 79 
 17,988 -j- 34 
 97,445 -*- 67 
 
 Prove your answers correct by multiplying and 
 adding in the remainder. If correct, this sum will 
 equal the dividend. 
 
 3. How many pounds of sugar are there in 3600 oz.? 
 (1 Ib. = ? oz.) What would it cost at 5^ a Ib. ? 
 
 4. A farmer sells 2160 Ib. of wheat at 80 1 a bushel. 
 Find the number of bushels and the total selling price. 
 (1 bu. of wheat weighs 60 Ib.) 
 
 5. Find the value of 12,288 Ib. barley at $.50 a bu. 
 (1 bu. barley weighs 48 Ib.) 
 
LESSON 68 205 
 
 6. A farm of 85 A. cost $6375 ; what is the price 
 per acre ? If the owner of this farm wishes to increase 
 it to 100 A., how many acres must he buy, and what 
 will they cost at the same rate ? 
 
 7. If 25 wagons cost $1375, what will 1 cost? 
 What will 45 cost at $ 3 apiece less ? 
 
 8. A bicycle dealer bought 3 doz. bicycles for 
 $1620; how many could he have bought for $2160? 
 
 9. Find the quotients and remainders : 
 23,487 +- 31 58,049 -r- 28 44,555 -+ 63 
 84,287 -f- 59 13,947 *- 16 65,287 -f- 17 
 86,777 -5- 92 30,049 ^ 19 99,498 -5- 43 
 38,695 -5- 67 78,243 H- 99 84,827 -5- 15 
 
 10. A wholesale merchant paid $13,625 to a manu- 
 facturer for rugs at $25 apiece. How many did he 
 buy? 
 
 Divide : 
 
 5)$ 37.50 6)$17.64 8)$ 2.64 
 
 4)$. 24 7)$. 98 2)$. 08 
 
 12. Find the quotients : 
 
 U3-31 $22.68-i-42 $743.50-25 
 
 $64.68-^22 $84.42-5-63 $369.84-67 
 
 $42.68-=-22 $13.50-5-18 $854.37-5-99 
 
 13. If 25 T. of coal cost $121.25, find the price 
 per ton. 
 
 14. If a dozen and a half boxes of soap cost $56.70, 
 what is the price of one box ? 
 
206 ARITHMETIC 
 
 Lesson 89 
 
 1. Divide $.72 by $.06. 
 
 1.06)1.72 Change $.06 to 6^ and $.72 
 6 , 72 j to 72^ and divide 6^ into 72^. 
 
 12 
 
 2. Divide $36.25 by $.25. 
 
 $.25)$36.25( Change $.25 to 25^ 
 
 25^)3625^(145 and $ 86 ; 25 to 3625 ^ 
 
 25 and divide 25^ into 
 
 100 
 125 
 125 
 
 $l.SO-j-$.30=? $3.25-*- 25^=? $3.60-*- $.90=? 
 
 4. At $.06 a quart, how many quarts of milk can 
 you buy for $ .48 ? How many gallons ? 
 
 5. At 7 ^ a cake, how many cakes of soap can you 
 buy for $.63 ? How many boxes, there being 3 in a 
 box? 
 
 6. At $.30 a dozen, how many dozen lemons will 
 cost $1.80? 
 
 7. How many pecks of potatoes can you buy for 
 $.45 at 15^ a peck? What part of a bushel ? 
 
 8. At $.24 a lb., how many pounds of butter will 
 cost $1.92? 
 
LESSON 89 207 
 
 9. At 8^ a lb., how many 2-lb. boxes of biscuits 
 
 can you buy for $ . 64 ? 
 
 10. At $.10 a gal., how many 5-gal. cans of oil 
 can you have filled for $1.50? 
 
 11. A lady pays $.96 for dimity at $.12 a yard. 
 How many dresses can she make from it for her 
 little girl, if each dress takes 4 yd. ? 
 
 12. How many collars can you buy for $2.00 at 
 the rate of 3 for 50^? 
 
 13. A merchant bought cloth at $.36 a yard and 
 sold it for $.45 a yard. His gain was $22.50 ; how 
 many yards did he sell? 
 
 14. $8.32-1.16= ? $ 9.45-i-$.35 = ? 
 
 $2.52-1.18= ? $15.84-$. 44= ? 
 
 $3.60-j-$.24= ? $14.25-f-$. 57= ? 
 
 15. At $ .35 a basket, how many baskets of peaches 
 can you buy for $ 25.20 ? How many dozen baskets ? 
 
 16. At 28^ each, how many hammers can you buy 
 for $4.48? 
 
 17. How many bushels of potatoes, at $.65 a 
 bushel, can you buy for $11.05? 
 
 18. At $.54 a bushel, how many bushels of corn 
 can you buy for $176.04? If you sell the corn at 
 58^ a bushel, what is your gain? 
 
 19. A grocer bought potatoes in the fall at $.45 
 a bu., and sold them in the spring for $.68 a bu. 
 
208 ARITHMETIC 
 
 His gain was 157.50; how many bushels did he buy ? 
 What is the unit that measures his gain ? 
 
 20. Bought apples at 55^ a bu. and sold them at 
 20 ^ a pk. If my gain was $ 37.50, how many bushels 
 did I buy ? 
 
 Lesson 90 
 
 1. Write in figures : Two hundred twenty-five 
 dollars and seventy-five cents ; one thousand forty dol- 
 lars and six cents ; six thousand three hundred dol- 
 lars sixty-seven cents. 
 
 2. Reduce to dollars and cents: 341^; 2159^; 
 7804**; 25425^; 25039^. 
 
 3. Reduce to cents : $4; 16.25; 127.03; $30.14; 
 150.20; $254.27; $360.02. 
 
 4. A farmer receives $29.25 for wheat, $19.02 
 for corn, $7.25 for vegetables, and $8.46 for turkeys. 
 What does he receive in all ? 
 
 5. A lady bought a bookcase for $9.98, a chair 
 for $5.35, a hat-rack for $11.50, and a lounge for 
 $12.88. Find the amount of her bill. 
 
 6. Find the amount of these bills : meat $12.63, 
 daily paper 65^, laundry $2.36, gas $3.25, and 
 plumber $1.70. 
 
 7. Ice cream salt is sold at ll a Ib., or for 85^ 
 per 100 Ib. sack. Find what is saved by buying 
 100 Ib. at a time. 
 
LESSON 90 209 
 
 8. A man had $5000 in the bank. He withdrew 
 $3496.75; how much remained in the bank? 
 
 9. I bought a horse for $150 and a cow for 
 $32.75, and paid cash $126.49. How much is still 
 due? 
 
 10. A lady paid 64^ for cotton, 75^ for ribbon, 
 $4.25 for a pair of shoes, and $3.73 for cloth. What 
 change should she have left from a ten-dollar bill? 
 
 11. Find the amount of this bill : 
 
 3 cans peaches at 32^ each 
 
 2 packages gelatine at 17^ each 
 57 Ib. sugar at 19 Ib. for $1 
 
 3 packages cracked wheat at 11 $ each. 
 
 12. Find the amount of this bill : 
 
 2 Ib. cheese at $.16 alb. 
 51b. butter at $.22 alb. 
 10 Ib. ham at 12^ alb. 
 2 bottles pickles at 29 ^ each 
 J doz. glasses jelly at $4.40 a doz. 
 
 13. If 25 Ib. coffee cost $8.25, what is the cost 
 of 1 Ib. ? 
 
 14. A merchant received $86.70 for cloth sold at 
 $.34 a yard. How many yards were sold? 
 
 15. Paid $317.52 for wheat at $.98 a bushel. 
 Find the number of bushels bought. 
 
 16. A merchant bought cloth at 36^ a yard, and 
 sold it for $56.25 at a profit of 9^ a yard. How 
 many yards did he buy? 
 
SECTION XI 
 
 Lesson 91 
 
 1. In the expression $2.34 the 3 is 3 what? 
 What part of a dollar? The 4 is 4 what? What 
 part of a dollar? The 34 is 34 what? What part 
 of a dollar ? 
 
 2. In the expression $4.73 what part of a dollar 
 is the 7? The 3? The 73? 
 
 3. Read as dollars and hundredths of a dollar: 
 
 $2.31, $4.65, $7.60, $6.05, $6.46, $6.09, $.35, $.06, 
 $.43, $.09. 
 
 4. Measure with a metric stick and count the 
 number of meters (m.) in the length of the room. 
 In the width. 
 
 5. Measure different lengths with the metric 
 stick. 
 
 6. Guess at two points on the blackboard one 
 meter apart. Test by measuring with a metric stick. 
 
 7. Count the number of decimeters (dm.) in a 
 meter. How many ? 
 
 210 
 
LESSON 91 211 
 
 8. One decimeter is what part of a meter? 2 
 decimeters is what part of a meter ? 3 dm. ? 6 dm. ? 
 
 9. Measure the width of the door and state its 
 width in decimeters. 
 
 10. Similarly measure the width of your desk ; its 
 length ; the height of the blackboard above the floor, 
 etc. 
 
 11. Cut a strip of cardboard 1 decimeter long. 
 Use it to measure the metric stick. How many deci- 
 meters in a meter ? 
 
 12. 1 meter 1 decimeter is written 1.1 meters, 
 meaning by that one meter and one-tenth of a meter. 
 1 meter 2 decimeters is written 1.2 meters, meaning 
 one meter and two-tenths of a meter. 
 
 1 m. 1 dm. = 1.1 m. 1 m. 2 dm. = 1.2 m. 
 The dot between the 1 and 1, and between the 1 and 
 2, is called the decimal point. It separates units from 
 tenths. 
 
 13. 2.5 m. is read two and five-tenths meters. 
 Read similarly : 
 
 1.3 m., 2.4 m., 3.6 m., 4.2 m., 6.8 m., .8 m., .2 m., 
 .1 m. 
 
 14. Measure the length of the room and express 
 your result in meters. (Thus, 8.4 m.) 
 
 15. Measure and express the results in meters : 
 The width of the room ; points taken at random on 
 the blackboard ; the heights of different pupils, etc. 
 
212 ARITHMETIC 
 
 16. Draw an oblong .2 m. long and .1 m. wide. 
 Take points 1.4 m. apart; 3.4 m. apart; 4.6 m. apart. 
 
 17. 2.5 Ib. is read two and five-tenths pounds. 
 Read similarly : 2.5 da., 2.7 hr., 1.6 mi., 4.8 yd., .8 yd., 
 8.4 gal., .6 qt. 
 
 18. Write in figures, using contractions: Three 
 and four-tenths meters, five and six-tenths pounds, 
 four and seven-tenths dollars, two-tenths of a mile. 
 
 19. Count the number of centimeters (cm.) in a 
 decimeter ; of centimeters in a meter. 
 
 20. Find the number of centimeters in the height 
 of this book ; in the width. 
 
 21. Measure the number of centimeters in the 
 length of a line of this book; in the length and 
 width of a sheet of paper, length of a lead pencil, 
 and of other things. 
 
 22. Draw an oblong 12 cm. long and 8 cm. wide. 
 
 23. ? cm. = 1 dm. ? dm. = 1 m. ? cm. = 1 m. 
 
 1 cm. is what part of 1 dm. ? 1 dm. is what part of 
 1m.? 1 cm. is what part of 1 m. ? 
 
 24. What part of 1 m. is 2 cm.? 4 cm.? 8 cm.? 
 15cm.? 25cm.? 36cm.? 
 
 25. 1 dm. 2 cm. = ? cm. What part of a meter? 
 
 2 dm. 4 cm. = ? cm. What part of a meter? 
 
 26. 1 m. 1 dm. 1 cm. is written 1.11 m., meaning 
 by that one meter, one-tenth of a meter, one-hun- 
 
LESSON 92 213 
 
 dredth of a meter, or one and eleven-hundredths 
 meters. 
 
 27. 4.68 m. is read four and sixty-eight hundredths 
 meters. Read similarly : 
 
 2.56 m., 4.29 m., 3.64 m., .45 m., .06 m., 3.0T m., 
 5.60 m. 
 
 28. 4.65 Ib. is read four and sixty-five hundredths 
 pounds. Read similarly : 
 
 2.25 Ib., 3.17 mi., 6.43 A., 5.89 yr., .23 da., .64 hr., 
 .04 hr., .06 gal., 2.09 gal., 4.06 bu., 4.60 bu., 3.49, .75, 
 2.09, .06. 
 
 29. Take two points 4.62 m. apart; 3.12 m. apart ; 
 2.40 m. ; 3.07 m. 
 
 30. In the expression 4.62 m. the place value of 
 each figure is given thus : 4 is four meters, 6 is six- 
 tenths of a meter, and 2 is two-hundredths of a meter. 
 
 Give the place value of each figure in the follow- 
 ing: 2.31 m., 4.59 m., 7.35 m., 2.09 m., 4.30 m., 2.07 m. 
 
 31. Give the place value of each figure in the fol- 
 lowing: 2.15 Ib., 3.74 mi., 3.66 A., 2.09 yr., .32 da., 
 .64 hr., .06 yr., 2.60 gal., 4.65, 7.23, .41, 2.04, .04. 
 
 Lesson 92 
 
 1. Count the number of millimeters (mm.) in a 
 centimeter ; of centimeters in a decimeter ; of deci- 
 meters in a meter ; of millimeters in a meter. 
 
214 ARITHMETIC 
 
 2. Find the number of millimeters in the width 
 of the margins of this book ; in the thickness of this 
 book ; in the length of the printed word millimeter; 
 in the distance between the lines on ruled paper ; and 
 in other short distances. 
 
 3. Draw and cut a slit 2 mm. wide and 3 cm. lonq- 
 
 O 
 
 in a sheet of paper. 
 
 4. ? mm. = 1 cm. ? cm. = 1 dm. ? dm = 1 m. 
 ? mm. = 1 m. 1 mm. is what part of 1 cm. ? 1 cm. 
 is what part of 1 dm. ? 1 dm. is what part of 1 m. ? 
 1 mm. is what part of 1 m. ? 
 
 5. What part of 1 m. is 2 mm. ? 8 mm. ? 25 mm. ? 
 84 mm. ? 264 mm. ? 625 mm. ? 
 
 6. 1 dm. 2 cm. 5 mm. = ? mm. What part of a 
 meter? 3 dm. 4 cm. 6 mm. = ? mm. What part of 
 a meter ? 
 
 7. 1 m. 1 dm. 1 cm. 1 mm. is written 1.111 m., 
 meaning one meter, one-tenth of a meter, one-hun- 
 dredth of a meter, one-thousandth of a meter, or one 
 and one hundred eleven thousandths meters. 
 
 8. 4.685 m. is read four and six hundred eighty- 
 five thousandths meters. Read similarly : 
 
 2.346 m., 6.275 m., 3.204 m., 4.250 m., 4.016 m., 
 4.006 m., 7.005 m., .214 m., .015 m., .006 m., .004 m., 
 3.146 m. 
 
 9. 4.625 Ib. is read four and six hundred twenty- 
 five thousandths pounds. Read similarly : 
 
LESSON 92 215 
 
 2.245 lb., 2.145 T., T.543 A., 5.019 A., 7.016 yr., 
 2.005 da., .243 da., .075 hr., .009 bu., .004 gal., 
 3.468 mi., 4.248, .329, .024, .082, .002, .005. 
 
 10. Write in figures, using contractions : 
 
 One and three hundred sixty-eight thousandths 
 pounds ; nine and six hundred four thousandths 
 tons; three hundred thirty -five thousandths of a 
 mile ; forty-nine thousandths of a day ; six thou- 
 sandths of a year ; seventeen thousandths of a year. 
 
 11. Take two points 1.245 m. apart; 2.436 m. 
 apart; 3.104 m.; 2.005m. 
 
 12. What is the place value of each figure in 
 question 11 ? 
 
 13. Give the place value of each figure in the 
 following : 
 
 3.764 m., 8.157 lb., 2.829 T., 4.666 mi., 8.095 A., 
 1.906 A., 3.008 yr., .247 yr., .016 yr., .009 mi., 
 3.980 mi., 5.823, 7.048, .042, .248, .009. 
 
 14. Read the following : 
 
 2.15 2.356 80.004 666.016 
 
 9.08 32.356 311.25 850.14 
 
 73.25 432.356 636.09 189.1 
 
 , 96.03 80.4 357.512 914.019 
 
 245.2 80.04 201.001 10.011 
 
 15. What is the place value of each figure in 
 the last column of question 14? 
 
216 ARITHMETIC 
 
 16. Show on a metric stick the following, and 
 note carefully, by comparing the part cut off with 
 the meter, what part of a meter each quantity seems 
 to be : 
 
 .25 m., .15 m., .356 m., .4 m., .246 m., .14 m. 
 
 Lesson 93 
 
 Copy and add : 
 
 1. 
 
 2345 
 
 234 
 
 .5 
 
 
 23. 
 
 45 
 
 
 2.345 
 
 
 3482 
 
 348 
 
 .2 
 
 
 34. 
 
 82 
 
 
 3.482 
 
 
 6134 
 
 613 
 
 .4 
 
 
 61. 
 
 34 
 
 
 6.134 
 
 
 8753 
 
 875 
 
 .3 
 
 
 87. 
 
 53 
 
 
 8.753 
 
 2. 
 
 64.215 
 
 
 16. 
 
 43 
 
 
 
 222 
 
 .342 
 
 
 28.528 
 
 
 24. 
 
 213 
 
 
 
 530 
 
 .030 
 
 
 21.835 
 
 
 5. 
 
 342 
 
 
 
 112 
 
 .458 
 
 
 17.652 
 
 
 44. 
 
 653 
 
 
 
 738 
 
 .754 
 
 3. Write in columns and add : 
 2.174 + 5.073 + 4.256 + 3.543. 
 
 .214 bu. + .876 bu. + .371 bu. + .444 bu. 
 
 4. Show on a metric stick .214 m., .876 m., 
 .371 m., .444 m. 
 
 5. Find the number of acres in a farm that is 
 divided into four fields, containing, respectively, 
 23.875 A., 15.18 A., 12.316 A., and 16.245 A. 
 
 6. In the following question draw the road and 
 mark the distances ; 
 
LESSON 93 217 
 
 Four towns, A, B, C, D, lie on a road running 
 north and south. The distance from A to B is 
 4.186 mi., from B to C 6.56 mi., and from C to D 
 8.514 mi. Find the distance from A to D. 
 
 Copy and subtract : 
 
 7. 3.426 
 1.312 
 
 8. 3.42 
 
 6.539 
 
 38.492 
 
 62.073 
 
 2.153 
 
 25.861 
 
 44.444 
 
 8.4 
 
 6. 
 
 796.873 
 
 3.156 
 
 4.251 
 
 636.134 
 
 1.204 
 
 9. From a piece of cloth containing 16.5 yd. I cut 
 12.375 yd. How much was left in the piece ? 
 
 10. From a farm containing 100 A. the owner sold 
 32.875 A. How much did he still own ? 
 
 11. A man bought a house and lot with .125 of 
 his money and invested the remainder in business. 
 What part of his money went into business ? 
 
 12. Draw a line and mark off on it 7 parts, each 
 .5 ft. long. Measure the whole part cut off. What 
 is its length ? 7 x .5 ft. = ? ft. 
 
 13. Add: 
 
 .2yd. 
 
 .3bu. 
 
 .32 gal. 
 
 2.64 A. 
 
 .428 da. 
 
 .2 
 
 .3 
 
 .32 " 
 
 2.64 " 
 
 .428 " 
 
 .2 " 
 
 .3 
 
 .32 " 
 
 2.64 
 
 .428 " 
 
 .2 
 
 .3 " 
 
 .32 
 
 2.64 " 
 
 .428 " 
 
218 ARITHMETIC 
 
 Copy and multiply: 
 
 14. .2 yd. .3 bu. .32 gal. 2.64 A. .428 da. 
 _4 _4 _4 _J _jt 
 
 How many figures are there to the right of the 
 decimal point in the multiplicands ? In the products ? 
 
 15. .141 1.98 3.452 8.234 26.019 
 
 __6 _3 7 8 7 
 
 As you multiply give the place value of each 
 partial product. 
 
 16. 
 
 17. 
 
 18. Look at the metric stick and find out the 
 number of inches in one meter. If 1 meter is equal 
 to 39.371 in., how many inches long is a line that 
 measures 3 meters ? 
 
 19. Measure a line 3 meters long on the black- 
 board, find the number of inches in it by measuring, 
 and test the correctness of the answer to question 18. 
 
 20. What will 25 loads of wheat weigh, the aver- 
 age weight being 1.135 T. ? 
 
 21. A merchant sold 45 yd. of cloth a day at a 
 gain of $ .125 a yd. Find his gain on a week's sales. 
 
 2.13 
 
 4.25 
 
 87.1 
 
 .642 
 
 .057 
 
 16 
 
 24 
 
 36 
 
 44 
 
 64 
 
 1.75 
 
 99 
 
 2.034 
 
 27 
 
 3.506 
 
 81 
 
 23.5 
 69 
 
 3.006 
 
 72 
 
LESSON 94 219 
 
 22. Find the cost of 48 thousand feet of lumber 
 at $43.875 per thousand. 
 
 23. Multiply .36 by 24 ; 24 by .36 ; .256 by 6 ; 
 6 by .256 ; 8 by .53. Find .53 of 1 8 ; .64 of 96 yd.; 
 2.54 of 26 ; .26 of 254 ; 3.18 of 42 ; .42 of 350 sheep. 
 
 24. A drover sold .24 of his flock of 250 sheep. 
 How many did he sell ? 
 
 25. Monday a merchant sold .924 of a piece of 
 cloth containing 36 yd. How many did he sell ? If 
 the rest went to the remnant counter, how many 
 yards went to the remnant counter ? 
 
 Lesson 94 
 
 1. Divide 34.458 by 6. 
 
 6 is contained in 34 5 times, 
 6)34.458 in 44 tenths 7 tenths, in 25 hun- 
 
 5.743 dredths 4 hundredths, and in 
 
 18 thousandths 3 thousandths. 
 
 2. Find the value of : 
 
 8. 652 -=-4 
 
 23.191 -=- 7 
 
 8.992-5-4 
 
 17.664-6 
 
 4.996 + 2 
 
 8.253 + 9 
 
 84.708 + 9 
 
 6.336-5-8 
 
 4.995 + 5 
 
 .897 + 3 
 
 2.457 -r- 7 
 
 25.938 + 3 
 
 98.475 + 5 
 
 .544 -r- 8 
 
 86.824-8 
 
 3. If a vessel travels 64,688 mi. in 4 hr., what is 
 the rate per hr.? 
 
220 ARITHMETIC 
 
 4. I paid $4.375 for 5 yd. of cloth. What was 
 the price per yd.? 
 
 5. If 1 bu. contains 2150.42 cu. in., how many 
 cubic inches will 1 qt. dry measure hold ? 
 
 6. If 1 gal. holds 231 cu. in., how many cubic 
 inches will 1 qt. liquid measure hold? 
 
 7. Divide 357.84 by 42. 
 
 42)357.84(8.52 
 
 336 42 is contained in 357 8 
 
 218 times, in 218 tenths 5 tenths, 
 
 210 in 84 hundredths 2 hun- 
 
 84 dredths. 
 84 
 
 8. Find the value of : 
 
 35.289^27 120.93-1-29 
 
 106.08-^34 66.317 -r- 47 
 
 3.266-^-23 2629.8 --54 
 
 6.544 -=- 16 124.5 -*- 75 
 
 As you divide give the place value of each figure 
 in the quotient. 
 
 9. I paid $ 2031.75 for 63 A. of farm land. Find 
 the cost per acre. 
 
 10. A merchant paid $65.625 for a chest of tea 
 containing 75 Ibs. Find the cost per pound. What 
 would be the total gain on selling it at $1 a lb.? 
 
LESSON 94 
 
 221 
 
 11. Divide 2.574 by .6. 
 
 Place the decimal point one 
 place to the right in both di- 
 visor and dividend and divide 
 as in the example. Why can 
 you do this ? 
 
 12. Copy and divide : 
 ,3)3.45 .4Y196 
 
 .4)3.508 
 .8)289.2 
 .5). 3625 
 
 .4)24 .6)15 .8)960 .9)10.8 
 
 Give the place value of each figure in the quotient. 
 
 13. Find the number of steps in a stairs between 
 two floors, one of which is 14.5 ft. higher than the 
 other, if each step is .5 ft. high. Name the unit of 
 measure and the quantity. How do you find the 
 number when the unit and quantity are known ? 
 
 14. A drover sold .6 of his flock of sheep and had 
 240 left. Find the number of sheep in the flock at 
 first. 
 
 15. A merchant sold cloth so as to gain .3 of the 
 cost. If the gain on each yard was 27 X find the 
 cost price. Find the selling price. 
 
222 ARITHMETIC 
 
 16. Divide .435 by .06 and 9.112 by 3.4. 
 
 (a) (ft) 
 
 .06). 435 3.4)9.112( 
 
 6)43.50 34)91.12(2.68 
 
 7.25 68_ 
 
 231 
 204 
 
 272 
 
 (a) Since in this division 6 is contained in 15 
 twice with remainder 3, annex a zero. 6 is con- 
 tained in 30 5 times. 
 
 (&) 34 is contained in 91 units two times. Write 
 down two and continue the division. 
 
 17. Divide 15.288 by .42. 
 .42)15.288( 
 
 42)1528.8(36.4 
 
 126 Move the decimal point two 
 
 268 places to the right in both divisor 
 
 252 anc l dividend before dividing. 
 
 168 Why can you do this ? 
 168 
 
 18. Find the value of : 
 
 .264 -=-.04 
 
 88.76 HH 1:8 
 
 8-H.4 
 
 3.78 -j-. 03 
 
 29.97 + .37 
 
 12-*- .06 
 
 14.35 -f- .05 
 
 2.808 -r-. 45 
 
 3 -;-.25 
 
 4.062 -j-. 06 
 
 59.636 -5- 1.7 
 
 18 -s- .45 
 
 3.4 -f-. 05 
 
 37.625 -s- 43 
 
 450-^.75 
 
 12.6-5-6 
 
 29.664 H- .24 
 
 36 -i- .09 
 
LESSON 94 
 
 19. When do you move the decimal point one 
 place to the right before dividing ? When two 
 places ? When do you put the decimal point in 
 your quotient? When do you annex zeros to the 
 dividend ? 
 
 20. If 39 bu. of wheat cost $34.125, what is the 
 price per bushel ? 
 
 21. At 1.12 a gallon, how many gallons of kero- 
 sene can you buy for $ 2.76? 
 
 22. A merchant pays $240 for cloth at $.75 a 
 yard. How many yards does he buy ? 
 
 23. A drover lost .045 of his flock of sheep by 
 wolves, .125 by disease, and .16 by theft. What 
 part of his flock did he lose ? If he sold the re- 
 mainder, what part of his flock did he sell ? 
 
 24. If in question 23 there were sold 201 sheep, 
 how many were in the flock at first ? 
 
 25. If a man earns $4.75 a day, and his average 
 daily expenses are $3.40, in how many days will he 
 save $ 81 ? What is the unit here ? 
 
SECTION XII 
 
 Lesson 95 
 
 1. The term per cent (%) is used constantly in 
 business. The merchant gains 20% on selling 
 cloth, meaning by this that he gains 1 20 on every 
 $ 100 that the cloth cost him. The insurance com- 
 pany charges 2% for insuring furniture, meaning 
 that $ 2 is charged for every $ 100 worth of furniture 
 insured. A man pays 5% for the use of money, 
 meaning that he pays $5 a year on every $ 100 
 borrowed. Per cent means hundredths. 50% of a 
 quantity is 50 hundredths of it. 
 
 2. A quantity divided into fourths is measured by 
 4 units ; a quantity divided into fifths is measured 
 by 5 units. 
 
 3. By how many units is a quantity measured 
 that is divided into sixths ? Into eighths ? Tenths ? 
 Twentieths? Fiftieths? Hundredths? 
 
 4. Quantities considered in percentage are meas- 
 ured by 100 units. 
 
 By how many units is \ of a quantity, considered 
 in percentage, measured ? J ? j- ? % ? 
 
 224 
 
LESSON 95 225 
 
 5. -J of a quantity equals what per cent of it ? ^ ? 
 
 50% 
 
 50% 
 
 6. What part of 1 sq. in. is 50% of it? 
 
 7. Draw lines 1 in., 2 in., 4 in., 6 in., 7 in. long, 
 and so on. Mark off 50% of each line. This is 
 what part of each line ? How many inches ? What 
 is 50% of 6 in. ? 9 in. ? 12 in. ? 6 ft. ? 18 yd. ? 
 80 yd. ? 60 mi. ? 120 mi. ? 
 
 8. What part of a quantity is 50% of it? How 
 many yards of carpet in 50% of 120 yd. ? What is 
 the cost at 50 ^ a yd. ? 
 
 9. Draw a 2-in. square and mark off 50% of it. 
 Draw an oblong 4 in. by 2 in. and mark off 50% of 
 it. How many square inches in 50% of the square ? 
 Of the oblong? 
 
 10. A farmer gave his son 50% of his farm of 
 160 A. How many acres did he receive? 
 
 11. How many inches in 50% of 1 ft.? In 50% 
 of 1 yd.? How many quarts in 50% of 1 gal.? 
 Pints in 50% of 1 qt.? Quarts in 50% of 1 bu. ? 
 Quarts in 50% of 1 pk.? Ounces in 50% of 1 lb.? 
 
226 
 
 ARITHMETIC 
 
 Months in 50% of 1 yr. 
 Minutes in 50% of 1 hr.? 
 Units in 50% of 1 score? 
 
 ? Hours in 50% of 1 da.? 
 Sheets in 50% of 1 quire ? 
 
 25% 
 
 25% 
 
 25% 
 
 25% 
 
 12. 25% of 2 sq. in. is what part of it? 
 is what part? 75%? 100%? How many square 
 inches in each case ? 
 
 13. A quantity considered in percentage is meas- 
 ured by how many units ? ^ of the quantity ? By 
 what per cent? 75% is what part of the quantity ? 
 
 14. Draw a line 1 ft. long and divide it into parts 
 each of which is 25% of 1 ft. Show 75% of 1 ft. 
 What part of 1 ft. is 25% of it? 75% of it? How 
 many inches ? 
 
 15. Draw a square inch and divide it into parts 
 each of which is 25% of it. What part of 1 sq. in. 
 is 25% of it? 50% of it? 75% of it? 100% of it? 
 What part of a quantity is 25% of it? 75% of it? 
 100% of it? 
 
 16. A farmer sold 25% of his flock of 240 sheep. 
 How many sheep did he sell ? What per cent of his 
 flock did he keep ? How many sheep ? 
 
LESSON 95 227 
 
 17. A man paid 75% of $160 for a horse. What 
 did the horse cost ? 
 
 18. How many inches in 25% of 1 ft.? Inches in 
 25% of 1 yd.? Quarts in 25% of 1 gal.? Gills in 
 25% of 1 qt? Quarts in 25% of 1 bu.? Quarts 
 in 25% of 1 pk.? Ounces in 25% of 1 lb.? Months 
 in 25% of 1 yr.? Hours in 25% of 1 da.? Cents in 
 25% of $1? Units in 25% of 1 score? Sheets in 
 25% of 1 quire? 
 
 How do you find 25% of a quantity? 
 
 19. Find 75% of each quantity in question 18. 
 How do you find 75% of a quantity? 
 
 20. What per cent of a quantity is J of it? -J-? 
 |? 5 f is what part of 10 ^? What per cent? 
 
 21. A grocer paid 60 ^ a lb. for tea and sold it so 
 as to gain 25% ; find the gain. Find the selling 
 'price. 
 
 22. I paid 36 f a yd. for cloth and sold it at a gain 
 of 9 ^ a yd. What part of the cost do I gain ? What 
 per cent ? 
 
 23. If 25% of the cost of a cow is $8, what did it 
 cost? 
 
 24. Land was bought at f 20 an acre and sold so 
 as to gain 25%. Find the selling price. 
 
 25. A horse that cost $ 80 was sold at a gain of 
 25%. Find the selling price. 
 
228 ARITHMETIC 
 
 26. If I take off ^ of the marked price on selling 
 a book, what per cent of the marked price is left ? 
 
 27. Cecil had 80^. He spent 50% of it to have 
 his bicycle mended, and 25% of the remainder for 
 oranges. How much had he left? 
 
 28. What per cent of 20 f is 5 fl Of 16 f is 8^? 
 Of 1 ft. is 6 in.? Of 1 da. is 6 hr.? Of 1 gal. is 
 Iqt.? 
 
 29. A merchant sold an overcoat at a gain of $ 3, 
 which was 25% of the cost. What was the cost 
 price ? The selling price ? 
 
 so. Roy's age is 25% of his father's. If Roy is 
 9 yr. of age, how old is his father ? 
 
 31. A man who earns $240 a month spends 75% 
 of it. How much does he save a month? How 
 much a year ? 
 
 Lesson 96 
 
 1. J of 100 units = ? | of 100 units = ? J of a 
 quantity is what per cent of it ? |- of a quantity is 
 what per cent of it ? 
 
 2. What part of a line is 331% of it? Draw 
 lines 3 in., 6 in., 9 in., and 12 in. long. Divide each 
 line into parts each of which is 3#l% of the whole 
 line. How many inches in 33^% of each line ? 
 Show 66|% of each line. How many inches in 
 66|% of each line? 
 
LESSON 96 229 
 
 3. What part of a quantity is 33|-% of it? 
 66f% of it? What is 33% of 6 ft.? 18 yd.? 
 45 mi. ? $75? 90 T. ? What is 66f % of each of 
 these quantities? 100% of each? 
 
 4. How many months in 33J-% of 1 yr. ? Hours 
 in 33J% of 1 da. ? Minutes in 331% O f 1 hr. ? Seconds 
 in 33J% of 1 min. ? Find 66f % of each of these 
 quantities. 100% of each. 
 
 5. 331% of 1 ft. = ? 331% of 1 yd. = ? 33J% of 
 1 doz. = ? 331% of 1 quire = ? Find 66f % of each 
 of these quantities. 100% of each. 
 
 6. Draw a 3-in. square and a 6-in. square. Show 
 33J% and also 66f % of each. 33|% of 1 sq. yd. =? 
 sq. ft. 66f % of 1 sq. yd. = ? sq. ft. 
 
 7. What part of a quantity is equal to 25% of it ? 
 66|%? 75%? 33J%? 100%? 50%? 
 
 8. What per cent of a quantity is equal to f of 
 
 it? j? f? i? |? |? |? 
 
 9. Cloth which cost $.75 a yard was sold at a 
 loss of 33 J%. Find the selling price. 
 
 10. If 33^% of a cargo of flour consisting of 
 6300 bbl. was damaged, how many barrels -were 
 damaged ? 
 
 11. A grain dealer invested $4500 in wheat, and 
 66|% of that amount in oats. How much did he 
 invest in oats ? In both ? 
 
230 ARITHMETIC 
 
 12. A merchant bought apples at 60^ a bushel, 
 and sold them at a gain of 33|%. Find the selling 
 price per bushel. Per peck. 
 
 13. A person gave $ 80 for one horse and $ 75 for 
 another. He sold the first at a gain of 25% and the 
 second at a gain of 33 J%. Find his gain on both. 
 
 14. A merchant bought goods for 1 120. He sold 
 half of them at a gain of 33^% and the remainder at 
 a gain of 25%. Find his total gain. 
 
 15. One village has a population of 2000 and 
 another 75% of that number. Find the population 
 of the second village. 
 
 16. What part of $6 is $2? What per cent? 
 What per cent of $24 is $6? Of $24 is $18? 
 Of 16 bu. is 8 bu. ? Of 16 bu. is 12 bu. ? Of $15 
 is $10? Of $36 is $24? 
 
 17. What per cent of 1 ft. is 4 in. ? Of 1 yd. is 
 2 ft. ? Of 1 sq. yd. is 6 sq. ft. ? Of 1 gal. is 1 qt. ? 
 Of 1 qt. is 1 pt. ? Of 1 bu. is 3 pk. ? Of 1 pk. is 
 6 qt. ? Of 1 Ib. is 4 oz. ? Of 1 yr. is 8 mo. ? Of 
 1 da. is 12 hr. ? Of 1 dime is 2 nickels ? Of 1 quire 
 is 18 sheets ? 
 
 18. I bought a rug for $24, and sold it at an 
 advance of $8. Find the gain per cent. To find 
 the gain per cent, you always compare the gain with 
 what? 
 
LESSON 97 231 
 
 19. I bought a cow for $28 and sold her for $35. 
 Find the gain per cent. 
 
 20. A dealer bought a bicycle for $ 60, and sold it 
 for $40. Find his loss per cent. 
 
 21. A merchant gains 33^% by selling cloth at 
 an advance of 25 ^ a yard. Find the cost price per 
 yard. 
 
 22. A speculator lost $800 by selling a house at 
 25% below cost. Find what he paid for it. 
 
 23. If 66 J% of the population of a certain town is 
 1800, find the population. 
 
 24. If 75% of the cost of a farm is $ 3600, find the 
 cost. 
 
 Lesson 97 
 
 1. of 100 units = ? | of 100 units = ? f of 
 100 units = ? | of 100 units = ? f of 100 units = ? 
 
 What per cent of a quantity is of it ? f ? f ? 
 
 v v 
 
 2. Draw an oblong 5 in. long and 1 in. wide, and 
 divide it into five equal parts. What per cent of 
 the oblong is each part ? Mark this per cent in each 
 part. What per cent of the oblong is 2 parts ? 
 3 parts ? 4 parts ? 5 parts ? 
 
 3. What part of a quantity is 20% of it? 40%? 
 33l%? 60%? 75%? 80%? 100%? 
 
 What per cent of a quantity is of it ? | ? f ? f ? 
 
 I? *? F f? 
 
232 ARITHMETIC 
 
 4. How many cents in 20% of 1 dime? In 40% 
 of 1 nickel? In 80% of half a dollar? In 60% of 
 a 25-ct. piece ? How many minutes in 40% of 1 hr.? 
 Seconds in 00% of 1 min.? Sheets in 75% of 1 quire? 
 Units in 40% of 1 score ? 
 
 5. If I have 5 5-ct. pieces and buy a lead pencil 
 for 5 ^, what per cent of my money do I spend ? If 
 I spend 15 ^, what per cent do I spend ? 
 
 6. A lady has a piece of cloth containing 16 yd. 
 She cuts off 12 yd. to make a dress. What per cent 
 of the entire piece is required for the dress ? 
 
 7. Romney lost 33^% of his marbles and then had 
 16 left. How many had he at first ? 
 
 8. Blanche is 18 yr. old, and Violet 10. The 
 difference between their ages is what per cent of 
 Violet's age? 
 
 9. A grocer bought tea at 75 ^ a lb., and sold it 
 for 90 $ a lb. Find his gain per cent. What would 
 have been the selling price to lose 20%? 
 
 10. A man sold a horse for f of the cost price. 
 Find his loss per cent. 
 
 11. A merchant put 2 yd. of cloth, which sold at 
 $2.50 a yd., on the remnant counter, and reduced 
 the price 40%. Find the selling price. 
 
 12. Pencils bought at 48 ^ a doz. were sold at a 
 gain of 25%. Find the selling price of each pencil. 
 
LESSON 97 233 
 
 13. A grocer bought coffee so that he could sell it 
 for 36^ a Ib. and make a profit of 331%. Find the 
 cost per Ib. 
 
 14. A drover bought 40 sheep at 1 6 apiece, and 
 sold them at a gain of 20%. Find his gain. 
 
 15. I paid $60 for one bicycle and $75 for an- 
 other. I sold the first at a gain of 33^% and the 
 second at a loss of 20%. Find my gain on the 
 whole transaction. 
 
 16. What is the gain per cent when the selling 
 price is 1^ times the cost ? 
 
 17. What is the loss per cent when the selling 
 price is f of the cost ? 
 
 18. A merchant bought 12 overcoats for $ 180 and 
 sold them at a gain of 20%. Find the selling price 
 of each coat. 
 
 19. Bought pencils at 24^ a dozen and sold them 
 at 3 ^ each. Find the gain per cent. 
 
 20. A wholesale dealer marks bicycles at $60, 
 subject to a discount of 33^%. Find the actual 
 selling price. 
 
 21. If I buy 600 sheep at $5 apiece, and pay 
 66|% of the cost price, how much do I still owe ? 
 
 22. A library has 800 volumes, of which 25% are 
 history. If 50% of the remainder are fiction, how 
 many volumes of fiction are there in the library ? 
 
234 
 
 AKITHMETIC 
 
 23. A man spent ^ of his money for a suit of 
 clothes and ^ of it for an overcoat. What per cent 
 of his money did he spend ? 
 
 Lesson 98 
 
 1. T V of 100 units = ? ^ of 100 units = ? 
 T \ of 100 units = ? ^ of 100 units = ? T 8 7 of 100 
 units = ? $ of 100 units = ? What per cent of a 
 quantity is T % of it? ^? T V? T V? ft? 
 
 10% 
 
 10% 
 
 10% 
 
 io,% 
 
 10% 
 
 10% 
 
 10% 
 
 10% 
 
 10% 
 
 10% 
 
 2. What part of this oblong is 10% of it? 20% ? 
 ? 40%.? 50%? 60%? 70%? 80%? 90%? 
 
 *7 
 
 3. What per cent of this oblong is J of it ? ^ of 
 
 ^ iW t? iV? T 9 o"? f? 
 
 4. How many cents in 10% of 1 dime? In 30% 
 of $1 ? In 30% of half a dollar? How many days 
 in 10% of the month of June? Seconds in 30% of 
 1 min. ? Units in 90% of 1 score? 
 
 5. A farmer raised 360 bu. of wheat, and kept 
 10% of this for flour for his own family. How many 
 did he sell ? 
 
LESSON 98 
 
 235 
 
 6. A man saves each month 10% of his salary. 
 If this is 1 22, what is his salary ? 
 
 7. If 10% of a boy's rate of walking is ^ mi. per 
 hr., what is his rate per hr. ? 
 
 8. A boy saved $40 in one year, and the next 
 year he saved 10% more than that. How much did 
 he save in 2 yr. ? 
 
 9. A house rents at $300 a year, which is 10% of 
 its value. What is the house worth ? 
 
 10. 1 of 100 units = ? J of 100 units = ? f of 
 100 units = ? What per cent of a quantity is -^ of 
 
 it? ? 
 
 121% 
 
 12} % 
 
 12*% 
 
 121% 
 
 12}% 
 
 12* % 
 
 12} % 
 
 12} % 
 
 11. What part of this oblong is 12J% of it? 
 What per cent of this oblong is J- of it? ? %? 
 
 t? t? 
 
 12. What part of any quantity is 12J% of it? 
 What per cent of any quantity is -|- of it ? 
 
 13. How many inches in 12|% of 1 ft. ? Square 
 inches in 121% o f l sq . ft.? Pints in 12J% of 
 1 gal.? Quarts in 12J% of 1 bu. ? Ounces in 
 
236 
 
 ARITHMETIC 
 
 12|% of 1 Ib. ? Hours in 12J% of 1 da. ? Sheets 
 in 12- O f 
 
 14. Four pupils of the first grade were absent 
 Monday. If this was 12 J% of the whole number, 
 how many are in the first grade ? 
 
 15. One-eighth of a box of oranges was found to 
 be decayed on opening the box. What per cent of 
 the oranges was good ? 
 
 16. A laboring man is idle 2 da. out of 8. What 
 per cent of the time is he idle ? 
 
 17. A fruit dealer buys pineapples at 8^ apiece, 
 and sells them at 9 ^ apiece. Find his gain per cent. 
 
 18. What is of 100%? f of 100 ? 
 
 19. What part of this oblong is 16 J% of it? 
 What per cent of this oblong is of it ? ? f ? f ? 
 
 20. How many inches in 16|% of 1 ft. ? Inches 
 in 16f % of 1 yd. ? Square inches in 16f % of 1 sq. 
 ft. ? Hours in 16f % of 1 da. ? Minutes in 16|% 
 of 1 hr. ? Months in 16|% of 1 yr. ? Sheets in 
 16|% of 1 quire? 
 
LESSON 99 237 
 
 21. What is the difference in hours between 
 16f % and 12J% of one day? 
 
 22. What per cent of 1 gal. is 1 pt. ? Of 1 qt. is 
 1 pt. ? Of 1 da. is 4 hr. ? Of 1 yr. is 8 mo. ? Of 
 1 quire is 18 sheets ? Of 1 score is 8 units ? 
 
 23. Mrs. Hume spent $ 4 for a chair and $ 28 for 
 a rug. What per cent of the whole sum did the 
 chair cost ? 
 
 24. If the price of flour advances from $5 to 
 $5.50 a bbl., what is the per cent of increase? 
 
 25. A fruit dealer buys oranges at 8^ a doz., and 
 sells them at 1 ^ apiece. Find his gain per cent. 
 
 Lesson 99 
 
 1. Find the quantity of which $2 is 12J%. 
 $.08 is 50%. 12.50 is 16f %. p t. i s 25%. 6 bu. 
 is 66f %. 12 mi. is 75%. 12 mi. is 60%. 
 
 2. What is meant by saying that 12J%=|-? 
 16J#=*? i = 33i%? 66f%=f? |=75%? 
 100% =1? 
 
 3. What per cent of 1 Ib. Avoir, is 12 oz. ? Of 
 1 quire is 18 sheets ? Of 1 da. is 8 hr. ? Of 1 yr. 
 is 6 mo.? Of $1 is 20^? 
 
 4. What is the ratio of 25% of a quantity to 
 75% of it? Of 75% to 25 ? Of 33J% to 66f% ? 
 Of 80% to 20%? Of 20% to 80%? Of 16|% to 
 
238 ARITHMETIC 
 
 % 
 
 331% ? Of 33^% to 16f % ? Of 60% to 40% ? Of 
 40% to 60%? 
 
 5. In a certain school 33^% of the pupils are 
 boys, and there are 28 girls. Find the number of 
 boys. 
 
 6. A young man spends 40% of his salary; what 
 per cent does he save ? If he spends $ 24 a month, 
 what does he save? 
 
 7. A kitchen range burns 50% of 1 T. of coal a 
 month. How many tons does it burn in one year ? 
 
 8. A man sold a cow that cost $ 36 at a loss of 
 25%. Find the selling price. 
 
 9. A young man put 1 64 in a savings bank and 
 soon after drew out 12^% of it. How much still 
 remained in the bank? 
 
 10. From a 5-gal. can of oil 2 gal. are drawn out. 
 What per cent still remains in the can? 
 
 11. What per cent is lost by selling goods at | of 
 the cost ? At | of the cost ? 
 
 12. What per cent is gained by selling goods at | 
 of the cost? At | of the cost? 
 
 13. 25% of the number of bushels of grain raised 
 by a farmer are oats and 50% wheat. If he raises 
 320 bu. of oats, how many bushels of wheat does he 
 raise ? 
 
LESSON 99 239 
 
 14. A young man in the High School studies 
 at home 12 \% of the entire day. How many hours 
 does he study at home each day ? 
 
 15. A merchant buys 60 yd. of silk for $ 180 and 
 sells it at an advance of 20%. Find the selling price 
 per yd. 
 
 16. A man paid $ 150 for a horse and 50% more 
 for a carriage. Find the cost of both. 
 
 17. What per cent is gained if cloth costing 30 ^ a 
 yard is sold for 40^? 36^? 42/? 35^? 50^? 
 
 18. What per cent is lost if cloth bought at 36 1 is 
 sold for 27^? 30^? 
 
 19. If hats are bought at $2.50 and sold for $3 
 apiece, find the gain per cent. 
 
 20. Eggs bought at $ 3 a crate of 30 doz. are sold 
 at 12 ^ a dozen. Find the gain per cent. 
 
SECTION XIII 
 
 Lesson 100 
 
 1. Name five different units of length that will 
 exactly measure a line 12 in. long. What is the 
 ratio of the line to the 6-in. unit? 
 
 2. I owe a debt measured by the number 8 and 
 the unit $5. How many ten-dollar bills will pay 
 the debt? What is the ratio of the debt to $ 10? 
 
 3. A fruit dealer arranges- his apples in piles of 
 4 for 5 $. If he sells 1 pile to each of 6 customers, 
 how many apples does he sell ? For how much ? 
 
 4. If the measuring unit is a line 3 in. long, draw 
 the line made up of three parts, the first being 3 
 times, the second 4 times, and the third 5 times the 
 measuring unit ? How many inches in the line ? 
 
 5. What is the quantity which is equal to the 
 sum of 5, 3, and 6 times the measuring unit ? 
 
 6. A fruit dealer sells his apples at the rate of 
 6 for 5 f. He sold five cents' worth to each of 9 
 customers. How many apples did he sell ? 
 
 240 
 
LESS,*' 100 241 
 
 7. A horse which travels at the rate of 6 mi. 
 an hour goes from A to B in 2 hr., and from B to C 
 in 3 hr. How long is the road from A to C ? 
 
 8. Find the number of times that a clock strikes 
 from 8.30 A.M. until 2.30 P.M., if the clock strikes 
 every hour. 
 
 9. A man left to his widow 8350, to his son 
 1 6425, and to his daughter $ 5725. Find the value 
 of his property. 
 
 10. Find the capacity of four bins, the first of 
 which will contain 65.223 bu., the second 34.542 bu., 
 the third 20.112 bu., and the fourth 19.123 bu. If 
 these four bins are full of wheat, what is it worth at 
 $ 1 a bushel ? 
 
 11. A merchant sold 122 yd. of cloth from a piece 
 containing 150 yd. What is the remainder worth 
 at ft. 50 a yd.? 
 
 12. What quantity is the difference between the 
 numbers 6 and 2, the unit being $ 5 ? 8 10? 1 20? 
 
 13. How much greater are 6 units of $ 9 than 5 
 units of $ 10 ? What is the ratio of this difference 
 to the unit $ 2 ? 
 
 14. A car containing 24 T. of coal was divided 
 between two families. If the first got 11.25 T., how 
 many did the second get ? 
 
 15. Find the number of square feet in an oblong 
 garden 12 yd. long and 9 yd. wide. 
 
242 ARITHMETIC 
 
 16. Two vessels start from the same point and 
 travel down stream, the first at the rate of 12 mi. an 
 hr. and the second at the rate of 8 mi. an hr. How 
 far apart will they be in 6 hr. ? 
 
 17. If these two vessels travel in opposite direc- 
 tions at the same rate, how far apart will they be in 
 6 hr. ? Mark off a line to represent this distance ? 
 
 18. A speculator bought 5 lots at $600 each, and 
 4 lots at $ 500 each. He sold them for $ 575 apiece. 
 Find his gain. 
 
 19. Find the weight of a block of wood 3 ft. long, 
 2 ft. wide, and 1 ft. thick, weighing 32.5 Ib. per 
 cu. ft. 
 
 20. A drover bought 8 sheep at $5.35 per head, 
 and 17 at $4.25. Find the total cost. Find his gain 
 on selling them for $ 150. 
 
 Lesson 101 
 
 1. A string 36 in. long has a piece 4 in. long cut 
 off, and then another piece of the same length, and 
 so on. How often can this be done ? What is the 
 unit here ? 
 
 2. In question 1, what is the ratio of the length of 
 the string to that of the unit ? Of the length of the 
 unit to that of the string ? 
 
 3. Divide $ 24 between A and B, giving B 3 times 
 as much as A. What is the unit here? 
 
LESSON 101 243 
 
 4. Divide 1 30 between A, B, and C, giving B 
 twice as much as C, and A 1J times as much as B. 
 What is the unit here ? 
 
 5. A merchant sold cloth at $1 a yd., and an 
 equal quantity at 1 2 a yd. What did 1 yd. of 
 each sell for? If all the cloth sold for $24, how 
 many yards of each did he sell ? What is the unit 
 here? 
 
 6. A merchant sold silk at $ 2 a yd., and an equal 
 quantity at 13 a yd. If all the silk sold for $80, 
 how many yards of each did he sell ? What is the 
 unit here ? 
 
 7. A township is 6 mi. square. Draw a town- 
 ship, making 1 in. for 1 mi. What is its area ? 
 
 8. A township is divided into 36 sections, each 
 1 mi. square. Divide the township you have drawn 
 into 36 sections. How many square inches in your 
 drawing represent one section ? 
 
 9. Each section of one square mile contains 640 A. 
 Divide one section into 4 farms of 160 A. 
 
 10. What is the difference in area between a 6 in. 
 square and an oblong containing 6 sq. in.? 
 
 11. Into how many townships can a tract of land 
 12 mi. square be divided ? 
 
 12. What is the ratio of 20 min. to 1 hr.? A 
 train runs 15 mi. in 20 min. At the same rate how 
 far would it go in 1 hr.? 
 
244 ARITHMETIC 
 
 13. Soap that cost 4 f a cake is sold for 5 ^. The 
 gain is what part of the cost? What per cent of 
 the cost? 
 
 14. If 3 ft. is the unit of length, what is the unit 
 of area ? 
 
 15. Divide $ 48 between Julian and Alder so that 
 Julian may get $ 3 for every $ 1 Alder gets. What is 
 the unit here ? 
 
 16. Roy has 24 marbles, and Cecil 6. They play 
 together, and Roy loses \ of his. How many has 
 Cecil now? 
 
 17. Draw a line 10 in. long. Measure it with a 
 unit J ft. long. How many times did you measure ? 
 10. in. is equal to f ft. What is the unit here? 
 What is the number? 
 
 18. Draw a line 9 in. long. Measure it with a 
 unit \ ft. long. How many times did you measure ? 
 9 in. is equal to f ft. What is the unit here ? What 
 is the number ? 
 
 19. Name the units that measure the following 
 quantities and give the number of units : f ft., 
 | yd., | yd., f f, | lb., 1 da., f hr., | bu., f wk., 
 ^ quire, and -^ score. 
 
 20. What part of a dollar is needed to give \ of a 
 dollar to each of 4 persons ? What is the number 
 here ? The unit ? The quantity ? 
 
LESSON 102 245 
 
 21. What quantity is measured by the number 12 
 and the unit | ft. ? 
 
 22. What quantity is measured 4 times by the 
 unit \ wk. ? 
 
 23. How often does the unit bu. measure the 
 quantity | bu.? 
 
 24. What is the unit that measures the quantity 
 f Ib. 3 times ? 
 
 Lesson 102 
 
 1. George gives away J of his marbles and has 
 16 left. How many had he at first ? 
 
 2. A paid $40 an acre for a farm. This was ^ of 
 what B paid an acre for his farm. What did B pay 
 for his farm of 60 A.? 
 
 3. A man earns $ 3| a day, and his daily expenses 
 are $ 1 J. In how many days will he save enough to 
 buy a bicycle costing $ 60 ? 
 
 4. Bought tea at 75 ^ a Ib. and sold it at a gain 
 of 331%. Find the selling price. 
 
 5. James received a present of $ 24. He gave ^ 
 of it to his sister, and J of the remainder to his 
 brother, and kept the rest himself. How much did 
 each receive ? 
 
 6. How many pounds of butter, worth $ .21 a Ib., 
 will cost 120.58? 
 
246 ARITHMETIC 
 
 7. If a man eats 32 oz. of bread in one day, how 
 many pounds will he eat in one week ? 
 
 8. Two farmers go to market. The first has 36 
 bu. of wheat weighing 60 Ib. a bu., and the second 
 48 bu. of oats weighing 32 Ib. a bu. Which load is 
 heavier and how much ? 
 
 9. What will 12 bu. 30 Ib. of wheat cost at $ .84 
 a bu. ? What will 15 bu. 8 Ib. of oats cost at $ .36 
 abu.? 
 
 10. A farmer sold 6 loads of wheat, each contain- 
 ing 32 bu., at 8.94 a bu. Find the total selling 
 price. 
 
 11. Find the cost of laying a cement sidewalk 
 30 yd. long and 4 ft. wide, at 16 f a square foot. 
 
 12. A house worth $4800 is insured for 75% of 
 its value. For what is it insured ? 
 
 13. A manufacturer employed 25 men, paying on 
 the average $1.50. What will it cost him a day to 
 increase their wages 10%? 
 
 14. Of 30 pupils in a grade 3 were not promoted. 
 What per cent of the class failed to be promoted ? 
 
 15. A lady is 27 years of age. If her age is 75% 
 of her husband's, how old is he ? 
 
 16. A lady spent 66|% of the money in her purse 
 for furniture, 16 -|% for carpet, and the rest for a 
 Jacket. What per cent did she spend for a jacket ? 
 If this, was $ 25, how much had she at first ? 
 
LESSON 103 
 
 24T 
 
 17. A dressmaker has 12 dresses to make. If she 
 makes 33 J% of them in 12 da., how many days will 
 she take to make them all ? 
 
 18. I bought 6 doz. lemons at $.20 a doz., and 
 sold them for 2 f each. What was my gain per cent ? 
 
 19. A man had $ 6000 in the bank. He drew out 
 50% of it and bought a house with 75% of the sum 
 drawn out. Find the cost of the house. 
 
 20. In a school there are 42 pupils , the ratio of 
 the number of boys to the number of girls is 3 to 4. 
 How many of each ? 
 
 Lesson 103 
 
 l. Write down neatly the following statement of 
 six weeks' cash receipts ; add the amounts vertically 
 and find the sum of the totals : 
 
 
 MON. 
 
 TUBS. 
 
 WED. 
 
 THUR. 
 
 FKI. 
 
 SAT. 
 
 1st 
 
 $26.53 
 
 $32.15 
 
 $36.21 
 
 $28.06 
 
 $25.84 
 
 $45.63 
 
 2d 
 
 21.78 
 
 28.28 
 
 31.43 
 
 32.60 
 
 27.97 
 
 44.55 
 
 3d 
 
 18.66 
 
 24.12 
 
 26.55 
 
 27.13 
 
 24.95 
 
 41.16 
 
 4th 
 
 26.94 
 
 35.92 
 
 32.19 
 
 36.08 
 
 22.31 
 
 48.29 
 
 5th 
 
 16.23 
 
 31.14 
 
 35.56 
 
 32.23 
 
 29.99 
 
 54.93 
 
 6th 
 
 19.20 
 
 25.05 
 
 24.97 
 
 29.67 
 
 24.15 
 
 60.03 
 
 TOTAL 
 
 
 
 
 
 
 
248 ARITHMETIC 
 
 2. Add as in question 1 : 
 
 
 Mox. 
 
 TUBS. 
 
 WED. 
 
 THUR. 
 
 FRI. 
 
 SAT. 
 
 1st 
 
 $54.73 
 
 $35.71 
 
 $68.68 
 
 $37.69 
 
 $ 53.44 
 
 $67.41 
 
 2d 
 
 46.17 
 
 65.41 
 
 34.76 
 
 62.07 
 
 61.16 
 
 52.61 
 
 3d 
 
 45.80 
 
 57.29 
 
 42.63 
 
 71.28 
 
 68.72 
 
 67.43 
 
 4th 
 
 47.47 
 
 60.50 
 
 78.25 
 
 63.36 
 
 45.76 
 
 43.80 
 
 5th 
 
 64.52 
 
 39.65 
 
 45.38 
 
 15.75 
 
 32.74 
 
 74.45 
 
 6th 
 
 52.41 
 
 43.77 
 
 58.97 
 
 42.57 
 
 41.78 
 
 65.28 
 
 TOTA L 
 
 
 
 
 
 
 
 3. Add as in question 1 : 
 
 
 MON. 
 
 TUBS. 
 
 WED. 
 
 THUR. 
 
 FRI. 
 
 SAT. 
 
 1st 
 
 $86.93 
 
 $76.19 
 
 $67.60 
 
 $74.61 
 
 $69.65 
 
 $68.29 
 
 2d 
 
 93.47 
 
 68.37 
 
 86.43 
 
 64.62 
 
 57.42 
 
 74.95 
 
 3d 
 
 64.55 
 
 76.04 
 
 53.86 
 
 65.02 
 
 69.38 
 
 78.54 
 
 4th 
 
 97.98 
 
 93.57 
 
 64.36 
 
 59.41 
 
 23.45 
 
 96.71 
 
 5th 
 
 62.67 
 
 86.21 
 
 68.15 
 
 62.39 
 
 46.29 
 
 76.58 
 
 6th 
 
 49.78 
 
 46.53 
 
 76.28 
 
 78.35 
 
 95.43 
 
 93.75 
 
 TOTAL 
 
 
 
 
 
 
 
 Add: 
 
 4. 
 
 6134 
 
 9268 
 
 3257 
 
 2168 
 
 
 8497 
 
 5769 
 
 7931 
 
 8394 
 
 
 4758 
 
 3275 
 
 4528 
 
 5486 
 
 
 2738 
 
 4623 
 
 2832 
 
 9034 
 
 
 4243 
 
 2752 
 
 4654 
 
 9657 
 
LESSON 103 
 
 249 
 
 5. 25146 
 
 
 67125 
 
 92745 
 
 9829 
 
 
 878 
 
 35924 
 
 58797 
 
 
 4572 
 
 57436 
 
 6543 
 
 
 27639 
 
 25372 
 
 462 
 
 
 44444 
 
 31819 
 
 6. 34 
 
 58 
 
 52 78 
 
 39 69 
 
 15 
 
 47 
 
 93 73 
 
 86 93 
 
 75 
 
 29 
 
 35 28 
 
 64 82 
 
 ; 62 
 
 97 
 
 67 89 
 
 26 45 
 
 28 
 
 32 
 
 63 83 
 
 97 37 
 
 99 
 
 49 
 
 68 44 
 
 36 66 
 
 95 
 
 78 
 
 81 60 
 
 99 58 
 
 32 
 
 52 
 
 39 33 
 
 78 87 
 
 57 
 
 91 
 
 42 56 
 
 64 62 
 
 43 
 
 47 
 
 55 78 
 
 76 63 
 
 7. 
 
 6958.994 
 
 7936.042 
 
 6683.145 
 
 
 8772.343 
 
 7721.358 
 
 948.03 
 
 
 5822.962 
 
 2546.563 
 
 7364.207 
 
 
 7319.526 
 
 7864.289 
 
 4563.09 
 
 
 8393.751 
 
 7325.004 
 
 7825.4 
 
 Subtract : 
 
 8. 
 
 $3862.93 
 
 $6760.68 
 
 $1696.65 
 
 1391.76 
 
 $3976.98 
 1678.63 
 
 1098.91 
 
 $2035.68 
 364.76 
 
 43.68 
 
 $1948.39 
 1754.46 
 
250 
 
 ARITHMETIC 
 
 10. 
 
 11. 
 
 12. 
 
 13. 
 
 14. 
 
 15. 
 
 16. 
 
 17. 
 
 18. 
 
 19. 
 
 20. 
 
 21. 
 
 22. 
 
 83559.83 
 
 $4264.15 
 
 1763.29 
 
 1932.57 
 15436.29 
 
 1268.34 
 
 $2678.28 
 
 685.38 
 
 $1180.66 
 
 4963.19 
 12016.72 
 
 312.83 
 
 $8416.60 
 
 119.25 
 $5300.20 
 
 1215.17 
 $1732.25 
 
 1542.24 
 $4656.20 
 
 2223.42 
 
 $1097.47 
 
 1214.03 
 $3661.00 
 
 738.75 
 $1201.60 
 
 1024.74 
 $1850.14 
 
 1139.67 
 24375 
 
 311.20 
 
 95657 
 6478 
 
 49328 
 1760 
 
 205639 
 
 196.17 
 16125 
 
 14692 
 
 84329 
 59761 
 
 819634 
 
 5765 
 
 29845 
 14008 
 
 726998 
 
 497256 
 
 337.877 
 199.601 
 
 56.979 
 
 174593 
 
 698.206 
 587.964 
 
 34.702 
 
 395432 
 279.345 
 
 158.709 
 632.194 
 
 28.034 
 84.67 
 
 15.96 
 49.107 
 
 576.4 
 56.5 
 
 19.483 
 
 158. 
 
 28.315 
 223. 
 
 26.548 
 
 599.78 
 64.532 
 
 77.065 
 
 36.427 
 382.635 
 
 1.89 
 
 32.808 
 
 13.284 
 
 12.08 
 
 49.17 
 

 LESSON 104 
 
 251 
 
 -3 392 
 
 45.652 
 
 445.2 
 
 1.473 18.654 
 
 159.304 
 
 < 171.8' 
 
 672.39 
 
 239.76 
 
 25.631 43.1 
 
 173.291 
 
 
 Lesson 104 
 
 
 Multiply : 
 
 
 
 l. 456 
 32 
 
 439 862 
 _25 85 
 
 676 864 
 68 96 
 
 2. 155.76 
 28 
 
 162.24 134.36 
 48 43 
 
 $76.82 $46.29 
 15 75 
 
 3. 157.06 
 13 
 
 167.82 $43.85 
 26 58 
 
 $60.09 $39.95 
 
 88 63 
 
 4. 57261 
 
 38 
 
 89437 65435 
 ^5 48 
 
 23826 16436 
 73 84 
 
 5. 653 
 231 
 
 429 384 
 324 256 
 
 629 439 
 125 121 
 
 6. 307 
 
 268 
 
 255 460 
 199 121 
 
 720 840 
 340 350 
 
 7. 907 
 
 359 
 
 707 796 
 
 660 263 
 
 129 930 
 
 888 725 
 
 8. 1495 
 236 
 
 1598 2716 
 426 287 
 
 3948 5048 
 635 650 
 
252 ARITHMETIC 
 
 9. 
 10. 
 11. 
 12. 
 13. 
 14. 
 15. 
 16. 
 
 3526 
 
 819 
 
 1521 
 
 637 
 
 6432 
 
 568 
 
 $18.64 
 253 
 
 9780 
 876 
 
 1946 
 
 621 
 
 $64.32 
 321 
 
 $32.34 
 125 
 
 $84.50 
 212 
 
 $13.67 
 631 
 
 $63.51 
 
 208 
 
 $17.01 
 
 784 
 
 $83.95 
 214 
 
 $22.35 
 523 
 
 $38.26 
 350 
 
 $26.57 
 801 
 
 $68.91 
 141 
 
 $11.51 
 
 189 
 
 $14.93 
 276 
 
 $39.03 
 
 168 
 
 $90.75 
 324 
 
 $34.26 
 
 275 
 
 $64.29 
 343 
 
 $35.28 
 653 
 
 $42.86 
 797 
 
 42.57 
 375 
 
 6.293 
 435 
 
 8.764 
 423 
 
 1.534 
 264 
 
 9.12 
 
 258 
 
 .295 
 147 
 
 .375 
 294 
 
 .826 
 131 
 
 6.293 
 219 
 
 2.03 
 145 
 
 115.5 
 
 818 
 
 3.064 
 513 
 
 48.18 
 155 
 
 585.3 
 306 
 
 4.659 
 314 
 
 In the following questions name the trial divisors 
 and find the quotients and remainders : 
 
 17. 32)4985 52)2735 61)6751 43)8668 
 
 18. 49)3548 66)5675 54)2085 19)5921 
 
 19. 36)6772 87)5439 73)9106 99)6487 
 
 20. 212)2524 314)7768 425)3467 512)5394 
 
LESSON 104 253 
 
 21. 108)5695 219)9488 706)9983 822)7786 
 
 22. 198)9897 299)3428 384)7534 795)2857 
 
 23. 346)67894 578)17639 289)33333 684)46999 
 
 24. 563)26407 662)40640 147)68952 365)41707 
 
 25. 839)17788 777)18810 556)79964 319)68795 
 
ANSWERS 
 
 Lesson 58 
 12. 11 15. $19, $31, 50^, 68 16. 31 17. 4^ 
 
 Lesson 60 
 
 3. 81, 60, 91, 110, 121, 101, 119, 112. 4. 697, 861, 
 751, 811, 920, 1221. 5. 969, 719, 871, 917, 811, 1181. 
 
 6. 68, 95, 41, 90, 71, 50, 51, 101. 7. 23, 33, 13, 32, 36, 
 48, 48, 35. 8. 632, 562, 80, 238, 344, 709. 9. $ 390. 
 10. $1.11. 11. $125. 12. $2.35. 13. $1091. 
 
 14. $991. 
 
 Lesson 61 
 
 5. 41 7. 60, 62, 95, 127, 82, 120, 122, 111. 8. 982, 
 1000, 1229, 729, 802, 920, 929. 9. 981, 828, 1121, 990, 
 1100,999,1110. 10. 71 11. 237,258,342,315, 
 413, 532, 733. 12. 2222, 3210, 1023, 2626, 1061, 1802. 
 13. 5336, 5104, 3015, 2050, 6591, 89. 14. 872. 
 
 15. $1365. 16. $1220. 17. 91 da., 92 da. 
 
 Lesson 62 
 
 5. 72 6. 61, 83, 81, 102, 103, 132, 138, 138. 
 
 7. 783, 919, 923, 1369, 1383, 1113, 837, 1112. 8. $1.22. 
 9. 1068, 629, 1099, 732, 1332, 1110, 1182, 810. 10. 443, 
 131, 164, 282, 63, 494, 156, 257. 11. 4304, 2202, 4013, 
 
 255 
 
256 ANSWERS 
 
 6033, 1113, 4004, 4150, 1000. 12. 1214, 4990, 1382, 
 661, 1324, 941, 2548, 2423. 13. $ 705. 14. 1905^ 
 
 15. $1190. 16. $1000. 18. $65. 
 
 Lesson 63 
 
 10. 524, 1023, 1696, 2605, 1015, 1565. 13. 120 mi. 
 22. 32. 
 
 Lesson 64 
 
 10. 792, 1188, 1584, 1980, 2376, 3036. 13. $ 2250. 
 
 16. 25, 54, 76, 49, 67, 122. 17. 288, 192, 144, 130, 144, 
 139. 18. 176, 117, 147, 64, 56, 51. 19. 99, 66, 65, 52, 
 63,56. 21. 102 bu. 22. $200, $40. 
 
 Lesson 65 
 
 14. $ 9.87, $ 59.37, $ 846.48, $ 6329.86. 15. $ 62.69, 
 $888.18. 16. $38.59. 17. $ 5.33, $41.32, $ 41.31, 
 $ 1133.11. 18. $ 11.25. 19. $ 2.35. 20. $ 15.69, $ 88.60, 
 $ 157.55, $ 1280.52. 21. $ 39.75. 22. $ 24.13, $ 27.50, 
 $ .23, $ .03, $ 125.75, $ 80.65. 23. $ 248.65. 24. $ 11.20. 
 
 Lesson 66 
 3. 2 gal. 2 qt. 1 pt. 15. 6/, 3/, 45/, 69/. 
 
 Lesson 67 
 
 1. 8 gal. 1 qt. 4. 1 gal. 3 qt. 5. Sf, 48^. 12. 8 gal. 
 2qt, 17 gal. 13. 27 Ib. 14. 96?, 4 15. 4 wk. 
 16. 36 ^. 18. 12 /. 20. $ 15. 21. Dime, nickel, and 
 penny. 
 
ANSWERS 257 
 
 Lesson 68 
 
 1. 16 qt. 1 pt. 2. 99 3. 39 5. 5J hr., 26 \ hr. 
 10. 174 mi. 12. $234. 13. $52. 16. 45^. 18. 2 gal. 
 3 qt. 1 pt. 19. 14. 22. 20 mi. 
 
 Lesson 69 
 
 5. $21. 6. $74. 7. 59,92,134,133,141,84,132, 
 129. 8. 415, 709, 822, 803, 741, 1201, 1444, 1384. 
 
 9. 949, 1498, 1535, 1174, 1202, 1454, 900, 910. 11. 144. 
 12. 996. 13. 432, 404, 182, 530, 183, 451, 43, 243. 
 14. 4104, 6912, 909, 3991, 1095, 526, 3778, 4913, 818, 3651. 
 16. 66. 17. 26 mi. ; 23 mi. ia 514 A. 19. $ 64.75. 
 20. $ 46.50. 21. $ 63, $ 21. 22. 24. 
 
 Lesson 70 
 
 6. $ 41.25. 7. 62 Ib. 8. 75, 139, 122, 124, 135, 90, 
 133, 155. 9. 661, 872, 653, 1443, 1415, 1223, 652, 1201. 
 
 10. 976, 1588, 1445, 924, 842, 1578, 1328, 1522. 11. 115 mi. 
 12. 120 mi. 13. 431, 262, 343, 161, 297, 406, 175, 158. 
 
 14. 3621, 786, 2625, 4426, 1866, 1628, 5788, 1888. 
 
 15. 256 A. 16. 18 17. $1050. 18. 9 19. $675. 
 20. 131 days. 
 
 Lesson 71 
 
 5. 8 ; 5 ; 14 ; 8 ; 12. 6. 6 in. 7 5 gal. 9. 1824, 
 2905, 4170, 6615, 6986, 4704. 11. $ 3192. 13. 42, 26, 
 73,35. 15. 63^. 16. 24bbl. 17. 25?. 18. 92^. 
 
 Lesson 72 
 
 5. $9.50. 6. $50. 7. $ 12.60, $ 40.45, $ 13.14, 
 $17.92, $31.68. 8. 1744. 9. $2848, $356. 
 
258 ANSWERS 
 
 10. $ 246, 305, 356, 873 bu. 11. 176 A. 12. 274. 
 13. $1.28. 17. 60 23. 44^, 3qt. 24. 24 times. 
 
 Lesson 73 
 
 4. 19 qt., 46 qt., 60 qt., 32 qt., 96 qt., 164 qt. 5. 48 qt., 
 112 qt., 72 qt., 20 qt., 30 qt. 6. 11 pk., 92 qt, 116 qt., 
 131 qt. 7. 1 lb., 8 lb., 94 Ib. 8. 1 bu., 210 lb. 
 10. 11 bu., 41 bu., libu., 90^. 11. 75 lb. 13. 24 oz., 
 44 oz., 58 oz., \ lb., i lb., f lb., T V lb., $ lb., T 5 lb. 14. 4 
 15. 76 oz. 16. 52 oz., 70 oz., 
 
 Lesson 74 
 16. 720. 17. 231 cu. in. 18. 8000 oz. 19. 6 lb. 
 
 20. 96 sq. in. 
 
 Lesson 75 
 
 16. CX, CXL, CXLIX, CL, CLIV, CLXXXII, CXC, 
 CXCIV. 17. CCC, XV, CCCXV; CC, LXXXIV, 
 
 CCLXXXIV; D, XCIX, DXCIX; DCXIV, DCCXXXIX, 
 DCCCXXVII, DCCCCXXXIV. 18. M, CCL, MCCL; 
 CCCXLIV, MCCCXLIV; MDCCCXCVIII, MCCCCXC1I. 
 
 Lesson 76 
 
 3. $18. 5. $15. 6. $21, $24, $11. 7. 20^. 
 8. The latter, l 11. $10, $70. 12. $16, $15, 
 $ 24, 8 lb., 6 lb., 24 lb. 13. 15 gal., 16 gal., 18 gal., 
 
 15 yd., 35 yd., 21 yd. 14. 12 yd., 6 yd., none. 16. i, 
 48 18. 28^. 19. i, 3. 22. ; 5; 540 lb. 
 
 23. $ 3.60. 24. 90 mi. 
 
 Lesson 77 
 
 16. 64 pt., 24 pt., 16 pt, 8 pt., \ gal., 40 pt., | gal. 
 17. 40 pt., f gal. 22. 40 yr. 
 
ANSWERS 259 
 
 Lesson 78 
 
 2. A, T 8 7T> A> A T 3 o> A lb - 3 - T 3 o ib., 20 f. 5. $ T <v, 
 
 90 ^ 10 6. 1 cent, 1 nickel, or 1 dime. 15. f , |, 
 
 2A, 5, 1A> H> 7 H> 2^. 16. i, i, 
 
 19. $2|. 20. $3J. 
 
 Lesson 79 
 
 1. $ 9. 5. T \, A, $ 6000. 7. if, A, 15 A - 
 8. 60 da. 14. |, {. 15. 240 A., 90 A., 60 A., 90 A. 
 18. T V, T 3 o, $30. 
 
 Lesson 81 
 
 1. 21 gal. 2. 2 lb. 6 oz. 3. 1 in., 30, No. 4. 7, 
 f 3.50. 5. 400 yd., $ 24, $ 96. 6. $ 4.80. 7. 6 yd. 
 3 in. 8. 42 A. 9. 2 mi., 4 sq. mi. 10. 6 lb., 70 lb. 
 
 11. $77. 12. 32 lb. 13. 24yd., 4yd. 14. 60 lb., 
 40 lb. 15. $ 3.60. 16. $ 4.80. 17. 6 mi., 36 sq. mi. 
 18. 44 strips, 2 ft. 19. 4 bu. 3 pk. 20. 40 mi. an hr. 
 21. 30 mi. 
 
 Lesson 82 
 
 4. 34, 40, 37, 62, 80, 86, 97, 108. 5. $ 126.20, $ 69.36, 
 $ 98.30, $ 134.35, $ 528.98, $ 667.70, $ 8841.60, $ 4668.08. 
 6. $ 572.24, $ 670.91, $ 1409.52, $ 755.06. 7. $ 624.52. 
 8. 72 bu., $ 72.85. 9. $ 7.95, $ 8.88, | 59.49, $ 276.99. 
 10. $ 108.47, $ 1569.85, $ 696.97, $ 2255.43. 11. $ 495. 
 
 12. $24.25. 13. $8.83. 14. 12 lb. 
 
 Lesson 83 
 
 5. 9 A., 12 fields of 9 A. each. 6. $ 3598.14, $ 9445.28, 
 $ 238.95, $ 874.98. 7. $ 7659.18, $ 6648.75, $ 2190.96, 
 
260 ANSWERS 
 
 $ 9877.23. 9. $25, $ 6 ; $ 96, $ 4 ; 88 mi., 6 mi. ; 75 
 of the unit, 1 of the unit ; 35 of the unit, 4 of the unit. 
 10. $ 23,300. 11. 35 bu. 12. 8 da. 16. $ 45, 9 da. 
 19. $ 13.50. 20. $ 155.25. 22. $ 240. 23. $ 3, $ 9. 
 
 Lesson 84 
 4. Add zero. 5. Add two zeros. 12. 16 bu. 2 pk. 
 
 Lesson 85 
 
 10. $1626.47, $1134.19, $793.44, $1995.21. 
 
 11. $3999.97, $5394.61, $12,779.69, $5439.09. 
 
 12. 33,431 sq. mi. 13. 391 sq. mi. 14. $308.96, 
 $ 180.40, $ 5700.48, $ 475.59. 15. $ 178.16, $ 4086.17, 
 $ 5579.91, $ 15,080.64. 16. 1250 sq. mi. 17. 7300 
 sq. mi. 18. $ 5725, $ 11,450. 19. $ 277.68, $ 172.74, 
 $ 303.48, $ 124.75. 20. $ 537.44, $ 2553.32, $ 14,106.32, 
 $ 24,104.52. 21. $ 13,100. 22. $ 979.40, $ 708.05, 
 $ 376.12, $ 649.15. 23. 636 sheep. The quantity and 
 the unit. The number. 24. 144. 
 
 Lesson 86 
 
 9. 912, 1392, 864, 2432, $ 1600, $ 752. 10. 1536 Ib. 
 11. 507. 12. $575. 13. $980, $221, 2176 Ib., 
 1026 mi., 304 mi., $ 1152. 15. 1638, 5293, 8811, 5394, 
 7050, 7396. 16. 5544, 5632, 2912, 7224, 23,360, 66,975. 
 17. $531.12, $1162.89, $464.64, $2824.90, $979.02, 
 $ 1386.49. 18. $ 1762.65, $ 6221.16, $ 7823.99, $ 1156.34, 
 $ 6533.15, $ 5095.24. 19. $ 5031. 20. 2592 mi. 
 
ANSWERS 261 
 
 Lesson 87 
 
 2. 43, 32, 62, 62, $ 64, 48. 3. 33, 56, 75, 72-4, 33, $ 56, 
 $ 75. 4. $ 31, 5. 37 hr. 6. 36 cows. 7. $ 23. 
 
 11. 139, 135, 85, 154. 12. 44, 31; 48, 40; 731, 14; 
 211; 580, 9; 77, 25; 281, 81; 86, 39. 13. 72 da., 
 167 da., 907 da. 14. 312 q. 15. 49 wk., $ 14. 16. $ 96. 
 
 Lesson 88 
 
 2. 201, 13 ; 161, 47 ; 121, 6 ; 87, 46 ; 393, 18 ; 126, 18 ; 
 55, 60; 78, 13; 71, 10; 113, 40; 529, 2; 1454, 27. 
 3. 225 lb., $ 12.25. 4. 36 bu., $ 28.80. 5. $ 128. 
 6. $75, 15 A., $1125. 7. $55, $2340. 8. 4 doz. 
 
 9. 757, 20 ; 1428, 35 ; 943, 21 ; 577, 36 ; 2073, 5 ; 871, 11 ; 
 1581, 10 ; 790, 33 ; 707, 14 ; 3840, 7 ; 2313, 39 ; 5655, 2. 
 
 10. 545 rugs. 11. $ 7.41, $ 7.50, $ 2.94, $ .33, $ .22, 
 $.06, $.14, $.04. 12. $1.23, $2.94, $1.94, $.54, 
 $1.34, $.75, $29.74, $5.52, $8.63. ' 13. $4.85. 
 14. $3.15. 
 
 Lesson 89 
 
 8. 8 lb. 9. 4. 10. 3. 11. 2. 12. 12. 13. 250. 
 14. 52, 14, 15, 27, 36, 25. 15. 72, 6 doz. 16. 16. 17. 17. 
 18. 326, $13.04. 19. 250 bu., 23^. 20. 150 bu. 
 
 Lesson 90 
 
 4. $63.98. 5. $39.71. 6. $20.59. 7. 15^ per 
 100 lb. 8. $1503.25. 9. $56.26. 10.63^. 11. $4.63. 
 
 12. $5.45. 13. 33^. 14. 226. 15. 324. 16. 125. 
 
262 ANSWERS 
 
 Lesson 93 
 
 1. 20,714, 2071.4, 207.14, 20.714. 2. 132.23, 90.638, 
 1603.584. a 15.046, 1.905 bu. 5. 67.616 A. 6. 19.26 mi. 
 7. 2.114, 4.386, 12.631, 17.629. 8. 2.216, 5.244, 1.740, 
 160.739. 9. 4.125yd. 10. 67.125 A. 11. .875. 
 13. 10.56 A., 1.712 da. 14. 10.56 A., 1.712 da. 15. .840, 
 5.94, 24.164, 65.872, 182.133. 16. 34.08, 102, 3135.6, 
 28.248, 3.648. 17. 173.25, 54.918, 283.986, 1621.5. 
 216.432. 18. 196.855. 20. 28.375. 21. $33.75. 
 22. $2106. 23. 8.64; 8.64; 1.536; 1.536; 4.24; $4.24; 
 $61.44; 66.04; 66.04; 133.56; 133.56. 24. 60. 
 25. 33.264 yd., 2.736 yd. 
 
 Lesson 94 
 
 2. 2.163, 2.944, 9.412, .299, 19.695, 3.313, 2.498, .792, 
 .351, .068, 2.248, .917, .999, 8.646, 10.853. 3. 16.172 mi. 
 4. $ .875. 5. 67.2 cu. in. 6. 57.75 cu. in. 8. 1.307, 
 3.12, .142, .409, 4.17, 1.411, 48.7, 1.66. 9. $32.25. 
 10. $.875; $9.375. 12. 11.5, 8.77, 361.5, .725, 60, 
 .049, 9.5, 11.15, .203, 25, 4.5, 42, 8.41, 5.24, 1200, 52, 
 12.52, .387, 5.63, 12. 13. 29. 14. 600. 15. 90^; 
 $ 1.17. 18. 6.6, 126, 287, '67.7, 68, 2.1, 25.96+, 81, 6.24, 
 35.08, .875, 123.6, 20, 200, 12, 40, 600, 400. 20. .875. 
 21. 23. 22. 320. 23. .33 ; .67. 24. 300. 25. 60 da. 
 
 Lesson 95 
 
 23. $32. 24. $25. 25. $100. 27.30^. 29. $12, 
 $15. 30. 36 yr. 31. $60, $720. 
 
ANSWERS 263 
 
 Lesson 96 
 
 9. 50 f. 10. 2100. 11. $3000, $7500. 12. 
 20^. 13. $45. 14. $35. 15. 1500. 18. 331%. 
 
 19. 25%. 20. 33|-%. 21. 75^. 22. $3200. 23. 2700. 
 24. $4800. 
 
 Lesson 97 
 
 5. 20%, 60%. 6. 75%. 7. 24. 8. 80%. 9. 20%, 
 60^. 10. 25%. 11. $3. 12. 5 13. 27^. 14. $48. 
 15. $5. 16. 25%. 17. 33|%. 18. $18. 19. 50%. 
 
 20. $40. 21. $1000. 22.' 300. 23. 58J%. 
 
 Lesson 98 
 
 6. $220. 7. 2 mi. 8. $ 84. 9. $3000. 23.12%%. 
 24. 10%. 25. 50%. 
 
 Lesson 99 
 
 5. 14. 6. 60%, $36. 7. 6T. 8. $27. 9. $56. 
 10.60%. 11. 25%, 331%. 12. 25%, 33$%. 13. 640 bu. 
 14. 3hr. 15. $3.60. 16. $375. 17. 33^%, 20%, 40%, 
 16f%,66f%. 18. 25%,16|%,33i%. 19.20%. 20.20%. 
 
 Lesson 100 
 
 1. 1, 2, 3, 4, and 6 in. ; 2. 2. 4 ; 4. 3. 24 apples ; 
 30 4. 36 in. 5. 14 times the unit. 6. 54 apples. 
 7. 30 mi. 8. 45 times. 9. $ 20,500. 10. 139 bu. ; 
 $139. 11. $14. 12. $20; $40; $80. 13. $4; 2. 
 14. 12.75 T. 15. 972 sq. ft. 16. 24 mi. 17. 120 mi. 
 18. $ 175. 19. 195 Ib. 20. $ 115.05 ; $ 34.95. 
 
264 ANSWERS 
 
 Lesson 101 
 
 1. 9 times, 4 in. 2. 9, . 3. $6, $18; A's share. 
 4. A $15, B $10, C $5; C's share. 3. $3; 8 yd.; $3, 
 i.e. the selling price of 1 yd. of each. 10. 30 sq. in. 
 11. 4. 12. i; 45 mi. 13. 1,25%. 14. 9 sq.ft. 
 15. $ 36 ; $ 12 ; $ 4. 16. 12. 17. 5 times ; f t. ; 5. 
 18. 3 times, ft. ; 3. 19. 1 ft., 2 ; \ yd., 3, etc. 20. $ f , 
 4, $ |, $ f 21. 3 ft. 22. \ wk. or 4 da. 23. 5 times. 
 
 Lesson 102 
 
 1. 24. 2. $ 4800. 3. 30 da. 4. $ 1. 5. $ 8 each. 
 6. 98 Ib. 7. 14 Ib. a Load of wheat ; 624 Ib. 9. $ 10.50 ; 
 $5.49. 10. $180.48. 11. $57.60. 12. $3600. 
 
 13. $3.75. 14. 10%. 15. 36 yr. 16. 16f%; $150. 
 17. 36 da. 18. 20%. 19. $2250. 20. 18,24. 
 
 Lesson 103 
 
 1. $129.34, $176.66, $186.91, $185.77, $155.21, 
 $294.59; $1128.48. 2. $311.10, $302.33, $328.67, 
 $292.72, $303.60, $370.98; $1909.40. 3. $455.38, 
 $ 446.91, $ 416.68, $ 404.40, $ 361.62, $ 488.82 ; $ 2573.81. 
 4. 26,370 ; 25,687; 23,202 ; 34,739. 5. 100,777 ; $ 144,658; 
 243,296. 6. 540, 580, 595, 622, 665, 662. 7. 37267.576 ; 
 33393.256; 27383.872. 8. $2471.17; $5661.77; 
 
 $1652.97. 9. $2298.35; $1670.92; $193.93. 
 
 10. $1627.26; $2995.81; $1077.91. 11. $473.10; 
 $2365.45; $1061.41. 12. $801.55; $6874.36; 
 
 $3076.78. 13. $518.22; $3917.45; $72.73. 
 
 14. $2521.33; $890.40; $1653.97. 15. 9683; 89,169; 
 10,360. 16, 24,568; 47,568; 15,837, 17. 322,378; 
 
ANSWERS 265 
 
 31,046; 331,566. 18. 138.276; 110.242; 120.636. 
 
 19. 28.945; 18.742; 55.794. 20. 65.187; 20.792; 
 
 29.952. 21. 121.573 ; 221.11 ; 535.248. 22. 369.351 ; 
 20.728; 27.895. 23. 390.527; 26.998; 285.896. 
 
 24. 146.169; 629.29; 66.469. 
 
 Lesson 104 
 
 1. 14,592; 10,975; 73,270; 45,968; 82,944. 
 2. $1561.28; $2987.52; $1477.48; $1152.30; 
 $3471.75. 3. $741.78; $1763.32; $2543.30; $5287.92; 
 $2516.85. 4. 2,175,918; 1,341,555; 3,140,880; 
 1,739,298; 1,380,624. 5. 150,843; 138,996; 98,304; 
 78,625; 53,119. 6. 82,276; 50,745; 55,660; 244,800; 
 294,000. 7. 325,613; 466,620; 209,348; 114,552; 
 674,250. 8. 352,820; 680,748; 779,492; 2,506,980; 
 3,281,200. 9. 2,887,794; 968,877; 3,653,376; 8,567,280; 
 1,208,466. 10. $20,646.72; $4042.50; $4715.92; 
 $17,914; $8625.77. 11. $13,335.84; $17,965.30; 
 $11,689.05; $13,391; $13,210.08. 12. $9716.31; 
 $ 2175.39 ; $ 4120.68 ; $ 21,282.57 ; $ 6557.04. 
 13. $29,403; $9421.50; $22,051.47; $23,037.84; 
 $34,159.42. 14. 15,963.75; 3707.172; 404.976; 
 43.365; 110.25. 15. 2737.455; 108.206; 2352.96; 
 1378.167; 294.35. 16. 94,479; 1571.832; 7467.9; 
 179,101.8; 1462.926. 17. 155, 25; 52, 31; 110, 41; 
 201, 25. 18. 72, 20 ; 85, 65 ; 38, 33 ; 311, 12. 19. 188, 
 4 ; 62, 45 ; 124, 54 ; 65, 52. 20. 11, 192 ; 24, 232 ; 8, 
 67 ; 10, 274. 21. 52, 79 ; 43, 71 ; 14, 99 ; 9, 388. 22. 49, 
 195; 11, 139; 19, 238; 3, 472. 23. 196, 78; 30, 299; 
 115, 98; 68, 487. 24. 46, 509; 61, 258; 469, 9; 114, 
 97. 25. 21, 169; 24, 1C.2; 143, 456; 215, 210. 
 
Public School Arithmetic 
 
 BASED ON 
 McLELLAN AND DEWEY'S 
 
 "PSYCHOLOGY OF NUMBER" 
 
 BY 
 
 J. A. McLELLAN, A.M., LL.D., 
 
 AND 
 
 A. F. AMES, A.B. 
 
 I2mo. Strong Buckram. Price, 60 cents, net. 
 
 This book, based upon sound psychological principles, stands for a 
 needed reform in the methods of teaching Arithmetic. 
 
 SPECIAL FEATURES. 
 
 The treatment of the subject is in strict line with the idea of num- 
 ber as measurement. 
 
 This true idea of number running through the whole work estab- 
 lishes the unity of the whole. 
 
 Fractions are divested of their traditional difficulty by being placed 
 in their true relation to integers. 
 
 Great care has been taken in selecting and grading the examples. 
 
 This treatment of the subject will prove a good preparation for 
 algebra. 
 
 THE MACMTLLAN COMPANY, 
 
 66 FIFTH AVENUE, NEW YORK. 
 
COMMENTS. 
 
 " I can see that it is an important contribution to the art of teaching numbers." 
 W. T. HARRIS, U.S. Commissioner, Bureau of Education. 
 
 " From a careful examination it seems to me to have many advantages over the 
 books on the subject now in use. Its wise omission of topics of no practical use, the 
 clearness of its methods and problems, and its neat typography appeal to every 
 teacher who has occasion to deplore the bulky and involved arithmetics in so many 
 of our schools." GEORGE GILBERT, Principal Chester Academy, Chester, Pa. 
 
 "I heartily approve of the method of this book." W. B. SMITH, McDonogh 
 School, McDonogh, Md. 
 
 " The processes are explained logically and the subjects are arranged in their 
 proper order in the course. The examples given are such as require thought and at 
 the same time are not such as can be considered unfairly puzzling, nor are they too 
 simple, but are all such as might be learned from some of the preceding parts of the 
 book." FREDERICK DOOLITTLE, Acting School Visitor and Clerk of Committee 
 on Education, of Connecticut. 
 
 " This volume is a very successful attempt to give expression to the better teach- 
 ing of psychology as to the growth and development of the idea of number. The 
 plan of the work is thoroughly scientific, the methods are well presented and the ex- 
 amples well chosen. This little book should assist greatly in the reform in teaching 
 arithmetic, now in progress." PROF. ALFRED I. DE LURY, University of Toronto. 
 
 " This book contains many admirable features. I like especially the early intro- 
 duction of decimal operations." CYRUS BOGER, A.M., Superintendent Schools, 
 Lebanon, Pa. 
 
 " Naturally I am pleased with the extent to which the bpok bases the treatment 
 of fundamental operations of fractions and ratio upon the dea of measure and of 
 numbers as units of measurement. I am particularly struck with the fact that the 
 pupil's attention is definitely called to some special quantity or whole which furnishes 
 the object of attention, and within which, so to speak, the numerical processes take 
 place; also with the clearness and conciseness of the method of treatment; the logi- 
 cal order of the selection of topics; and the exclusion of useless and irrelevant mat- 
 ter. The simplification of treatment due to sticking close to fundamental principles, 
 must recommend the book to teachers and pupils who have been bewildered by the 
 great number of topics treated in the ordinary aiithmetic topics which do not 
 differ at all in their logical or arithmetical basis, but are simply different practical 
 expressions of the same principle. I wish the book the success it deserves." PRO- 
 FESSOR DEWEY, University of Chicago. 
 
 " ' The Psychology of Number,' by Professors McLellan and Dewey, placed on a 
 rational basis the methods to be pursued in the elementary treatment of number. 
 This has now been followed by ' The Public School Arithmetic,' by Professors 
 McLellan and A. F. Ames, in which these rational methods, set forth in the former 
 work, are systematically and successfully presented. The special feature of this 
 book consists in its treatment of number as the result of measurement. The authors 
 have brought out very clearly the proper methods of dealing with the fundamental 
 operations, with fractions, and with the commercial rules. The definitions are con- 
 sistent and accurate a feature not common in elementary texts of arithmetic. 
 There is an excellent collection of well-graded examples. Few of the tricky prob- 
 lems which have done so much to discredit arithmetic are to be found. The book 
 consequently deserves speedily to win a place among recognized text-books." 
 PROFESSOR McKAY, McMaster University. 
 
 " One of those wise books that make school study more pleasant and effective 
 than in the old days when routine study was the rule. . . . Both teachers and pupils 
 will welcome this very valuable book." Saturday Evening Gazette, Boston. 
 
 THE MACMTLLAN COMPANY, 
 
 66 FIFTH AVENUE, NEW YORK. 
 
FOURTEEN DAY USE 
 
 RETURN TO DESK FROM WHICH BORROWED 
 
 This book is due on the last date stamped below, or 
 
 on the date to which renewed. 
 Renewed books are subject to immediate recall. 
 
 u 
 
 General Library 
 
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 THE UNIVERSITY OF CALIFORNIA LIBRARY