jMWiWHHitWWHHHW^ 
 
 
LIBRARY 
 
 OF THK 
 
 UNIVERSITY OF CALIFORNIA. 
 
 OF" 
 
 V 
 Accession 85969 Class 
 
HEATH'S 
 PRIMARY ARITHMETIC 
 
s 
 
 3 
 
 o 
 
 e 
 
 t 
 
HEATH'S 
 
 PRIMARY ARITHMETIC 
 
 BY 
 
 CHARLES E. WHITE 
 
 \\ 
 AND 
 
 BRUCE M. WATSON 
 
 SYRACUSE, N.Y. 
 
 BOSTON, U.S.A. 
 
 D. C. HEATH & CO., PUBLISHERS 
 1901 
 
COPYRIGHT, 1901, 
 BY D. C. HEATH & Co. 
 
PREFACE 
 
 IN education, as in other affairs of life, there is a tendency, on the part 
 of many, to pursue good ideas to unreasonable extremes, and ofttimes to the 
 exclusion of other ideas quite as good. 
 
 This book has been prepared with the design of bringing together the 
 manifest advantages of the topically arranged text-book and the equally 
 manifest advantages of the so-called " spiral " plan. 
 
 Each subject is treated by itself as exhaustively as the scope and purpose 
 of tl$ book will warrant. At the same time each new subject introduced is 
 considered in all its relations with and bearing upon preceding subjects. 
 
 By the great abundance and variety of the drill work and problems 
 throughout the book, all subjects are kept in constant review, every principle 
 is applied in as many ways as possible, and the unity of the 'book is 
 preserved. 
 
 The order of subjects is determined by the law of dependence, the degree 
 of simplicity of the matter to be taught, and the relative importance of the 
 respective subjects in the business of life. 
 
 The development of the various principles and processes has been written 
 with great care and considerably in detail, with a view both to furnish the 
 teacher a definite plan for presenting the work and to help the student in 
 his efforts toward independent achievement. 
 
 Both the method and the matter of the book have been tested by actual 
 use in the schoolroom ; they are not in any sense an experiment. 
 
 Part I is a strictly primary arithmetic. The first few lessons are extremely 
 simple, yet they furnish an illustration of the logical steps in the develop- 
 ment of ideas of number. If any child begins the use of the book with 
 elementary notions of number already developed in his mind to a certain 
 point, the judicious teacher will be wise enough to begin where the child's 
 previously acquired knowledge stops. 
 
 The development work preceding each table is designed to give the child 
 a concrete understanding of the processes by which the table is made instead 
 of forcing him to memorize abstract results obtained by making arbitrary 
 combinations. But after a table has been thoroughly developed, the pupil 
 
 85969 
 
VI PREFACE 
 
 should be drilled in all its combinations until he can give results instantly 
 without reference to the mental processes by which they may be obtained. 
 To this end the drill charts should be used daily until all results can be given 
 correctly without an instant's hesitation. 
 
 The problems following the tables were selected from lessons given by 
 scores of successful primary teachers, and it is believed that they are far 
 richer in variety of work and forms of statement than any list prepared by 
 a single individual. 
 
 Part II is an introduction to written arithmetic proper. The color work, 
 both here and in Part I, is introduced not merely to embellish the pages, 
 but rather to furnish the best means of illustration and practice in certain 
 arithmetical operations. 
 
 Much of the mental work in Part II may be used as supplementary to the 
 questions in Part I. 
 
 Definitions are given only when and where they are needed. 
 
 In the treatment of fractions the fact that a fraction is an expression of 
 division is kept prominent. 
 
 Throughout the book the authors have endeavored to insert whatever may 
 help the pupil to an understanding of principles ; to omit whatever is super- 
 fluous or may tend to confusion. 
 
 B. M. W. 
 
 SYRACUSE, February 8, 1901. 
 
TABLE OF CONTENTS 
 
 PART I 
 
 PAGE 
 
 NOTATION AND NUMERATION 1 
 
 ADDITION 7 
 
 SUBTRACTION ............ 20 
 
 MULTIPLICATION ........... 31 
 
 DIVISION 42 
 
 PAET II 
 
 NOTATION AND NUMERATION ......... 75 
 
 Arabic . 77 
 
 Roman 80 
 
 Federal Money .82 
 
 ADDITION 83 
 
 SUBTRACTION 94 
 
 REVIEW PROBLEMS .......... 102 
 
 MULTIPLICATION ........... 104 
 
 DIVISION 113 
 
 REVIEW EXERCISES 124 
 
 REVIEW PROBLEMS 125 
 
 FACTORING 130 
 
 CANCELLATION 132 
 
 GREATEST COMMON DIVISOR ......... 134 
 
 LEAST COMMON MULTIPLE ......... 135 
 
 INDICATED OPERATIONS .......... 137 
 
 FRACTIONS 140 
 
 REDUCTION OF FRACTIONS . . . . * 143 
 
 ADDITION OF FRACTIONS . . . 152 ' 
 
 SUBTRACTION OF FRACTIONS 154 
 
 SUBTRACTION OF MIXED NUMBERS 155 
 
 MULTIPLICATION OF FRACTIONS . . . . . . . .156 
 
 DIVISION OF FRACTIONS . . . . . . . . . . 161 
 
 COMPLEX FRACTIONS . . . . . . . . ... 166 
 
 THE THREE QUESTIONS OF RELATION ....... 167 
 
 ALIQUOT PARTS ........... 170 
 
 REVIEW OF FRACTIONS 172 
 
 DECIMAL FRACTIONS 176 
 
 To read Decimals . . . 179 
 
 To write Decimals .......... 180 
 
 REDUCTION OF DECIMALS ......... 182 
 
 vii 
 
viii TABLE OF CONTENTS 
 
 PAGE 
 
 ADDITION OF DECIMALS ......... 184 
 
 SUBTRACTION OF DECIMALS 185 
 
 MULTIPLICATION OF DECIMALS 186 
 
 DIVISION OF DECIMALS 188 
 
 REVIEW OF DECIMALS 191 
 
 BILLS AND ACCOUNTS .......... 192 
 
 DENOMINATE NUMBERS .......... 194 
 
 Linear Measures 194 
 
 Surface Measures 196 
 
 Cubic Measures 199 
 
 Liquid Measures 200 
 
 Dry Measures 202 
 
 Avoirdupois Weight 203 
 
 Troy Weight 205 
 
 Apothecaries' Weight 205 
 
 Federal Money 206 
 
 Time 207 
 
 Miscellaneous Tables 208 
 
 REDUCTION OF DENOMINATE NUMBERS ....... 209 
 
 Descending 211 
 
 Ascending 212 
 
 REVIEW OF REDUCTION . 215 
 
 ADDITION OF COMPOUND NUMBERS 216 
 
 SUBTRACTION OF COMPOUND NUMBERS . . . . . . . 217 
 
 DIFFERENCE BETWEEN DATES . . . . . . . . 218 
 
 MULTIPLICATION OF COMPOUND NUMBERS . . . . ... 219 
 
 DIVISION OF COMPOUND NUMBERS 220 
 
 SURFACE MEASUREMENTS ......... 221 
 
 Plastering and Painting . . 223 
 
 Carpeting Rooms 224 
 
 Papering Walls . . . . . . . . . .227 
 
 Board Measure 227 
 
 VOLUME MEASUREMENTS . . . . . . . . . 228 
 
 Wood Measure . . . 231 
 
 Capacity of Cisterns 232 
 
 Capacity of Bins 232 
 
 PERCENTAGE 233 
 
 SIMPLE INTEREST ........... 238 
 
 TOPICAL REVIEW . . . . 241 
 
 Notation and Numeration 241 
 
 Common Fractions 241 
 
 Decimal Fractions .......... 242 
 
 Denominate Numbers 244 
 
 ANSWERS ............ 247 
 
PRIMARY ARITHMETIC 
 
 PART FIRST 
 
 To THE TEACHER. For early work with numbers, a " counting 
 table" is almost a necessity, whatever text-book may be used. 
 It should be about two feet high, thirty inches wide, and six 
 feet to fourteen feet in length, according to the size of the class. 
 It should be surrounded by a slightly raised casing to prevent the 
 counters from falling off. 
 
 Toothpicks and shoepegs are very good to use as counters, on 
 account of their cheapness and convenience of handling. 
 
 1. Counters are in a pile in front of the pupils. 
 
 Take one counter. 
 
 Put another one with it. How many? 
 
 Put another with it. How many ? 
 
 So on until ten have been taken. 
 
 Take three counters ; seven counters ; five ; nine ; 
 six ; four ; ten ; eight. 
 
 Count the girls in the class. 
 
 Count the boys in the class. 
 
 How many fingers have you on your right hand? 
 On your left hand ? 
 
 i 
 
PRIMARY ARITHMETIC 
 
 How many fingers have you on both hands ? 
 How many fingers and thumbs have you ? 
 Count ten with your eyes shut. 
 
 Give much drill on these numbers, using counters and other 
 objects. 
 
 2. Make the figures 1 , 2, 3, 4, 5, lo, ^ 8, C|. 
 
 Teacher place figure 1 on blackboard, and pupils take as many 
 counters. Teacher place figure 2 on the blackboard and children 
 take as many counters. So on with all the figures, one at a 
 time, the pupils each time taking as many sticks as the figure 
 means. 
 
 Teacher count out three, five, nine, seven, eight sticks, etc., 
 and pupils make figures to represent them. 
 
 Make the figure to tell how many years old you are. 
 Make the figure to tell how many fingers you have. 
 Make the figure to tell how many hands and feet 
 you have. 
 
 Make the figure to tell the hour for coming to school. 
 Much drill should be given in this kind of work. 
 
 How many leaves on this 
 cherry branch ? 
 
 How many cherries ? 
 
 Make the figure that tells 
 how many leaves. 
 
 Make the figure that tells 
 how many cherries. 
 
 Make a stem holding 5 cher- 
 ries; 8 cherries; 10 cherries. 
 
PRIMARY ARITHMETIC 
 
 How many roses in the 
 picture ? 
 
 How many rosebuds ? 
 
 What figure tells how 
 many roses ? 
 
 What figure tells how 
 many buds ? 
 
 Count the roses and buds 
 together. 
 
 How many parts has a wood- 
 
 bine leaf? 
 
 Make the figure. 
 
 How many leaves are there 
 
 on a c l ver stem ? 
 Make the figure. 
 Make two woodbine leaves. 
 Count the parts in the two leaves. 
 
 Count the red stripes in the flag. 
 
 Count the white stripes. 
 
 Make the figure that tells how 
 many red stripes. 
 
 Make the figure that tells 
 how many white stripes. 
 
 Count all the stripes. 
 
 Count the stars in the bot- 
 tom row. 
 
 How many colors in the flag ? 
 
 How many stripes below the blue field ? 
 
 How many red stripes below the blue field? 
 
PRIMARY ARITHMETIC 
 
 Count the daisies in the 
 picture. 
 
 How many? 
 
 What figure tells how 
 many ? 
 
 Count the tall daisies. 
 Make the figure that tells 
 how many are not tall. 
 How many apples are in this picture ? 
 Make the figure that tells how many apples. 
 Count the red 
 apples. 
 
 Count the other 
 apples. 
 
 Make the figure 
 that tells how many 
 red apples. 
 
 How many pears are there in the picture ? 
 Make the figure that tells how many. 
 
 
 One, 1. Two, 2. Three, 3. Four, 4. 
 Five, 5. Six, 6. Seven, 7. 
 Eight, 8. Nine, 9. Ten, 10. 
 
PRIMARY ARITHMETIC 5 
 
 3. Take ten sticks. m 
 Tie them in a bunch, thus, it 
 
 Count out ten such bunches and tie them up. 
 
 Call each bunch "a ten." 
 
 Put one bunch on the table. fj n 
 
 Put one stick beside it, thus, ml 
 
 How many sticks are there ? | | 
 
 Put another stick with it, thus, if If 
 
 How many sticks are there ? I J2 
 Take another ten and put three with it, iijjj 
 thus, if UHII 
 
 How many are there ? I 3 
 
 Go on in this way to nineteen. 
 
 What does the figure 1 stand for in the number 12? 
 In the number 13 ? 
 
 In 14, 15, 16, 17, 18, 19 ? 
 
 How many tens in 11 ? How many over ? 
 
 In 12, 13, 14, 15, 16, 17, 18, 19 ? ' 
 
 4. Suppose we wish to write the number ten. We 
 will use 1 to stand for ten the same as in the other 
 numbers. 
 
 How many will there be over? 
 
 What shall we use to show that jj 
 there is none over ? * 
 
 We will use this figure, 0. Thus, I 
 
 The figure, 0, is called naught, and is used where 
 nothing belongs. 
 
6 
 
 PRIMARY ARITHMETIC 
 
 Take two tens. How many sticks in all ? 
 To write twenty we use 2 to stand for two tens, 
 and to show that there is none over, thus, 
 
 Take two tens and one, thus, 
 
 How many ? Write it thus, 
 
 m 
 Make the figures for: jj 
 
 
 
 5. In the same manner as in the preceding lesson, develop 
 numbers to one hundred. 
 
 Write fifteen ; twenty ; eighteen ; fourteen. 
 Write twenty-five ; thirty-seven ; forty. 
 Write eighty-tw r o ; ninety-six ; seventy. 
 Write sixty-one ; forty-seven ; fifty. 
 Write seventy-nine ; twenty-one ; ninety. 
 Write forty-eight ; nineteen ; thirty-three. 
 Lay counters to make forty-two, thus, 
 Lay counters to make sixty-three. 
 Lay counters to make seventeen. 
 Count the desks in your room. 
 
 What number will the counters on the table make ? 
 
PRIMARY ARITHMETIC 7 
 
 Count the hands in your schoolroom. 
 Write the number of books on the teacher's desk. 
 Count fifty forward and backward. 
 Read these numbers : 25, 21, 38, 45, 36, 28, 72, 64. 
 Write them in a column, so that the tens will be in a 
 vertical line. 
 
 Write them in words. 
 
 ADDITION 
 
 '6. Take one counter. 
 
 Take one more counter. 
 
 How many counters have you ? 
 
 How did you get two counters ? 
 
 One counter and one counter are how many counters ? 
 
 One stick and one stick are how many sticks ? 
 
 One book and one book are how many books ? 
 
 One boy and one boy are how many boys ? 
 
 One and one are how many ? 
 
 and are ? 
 
 One and one are ? 
 
 1 and 1 are ? 
 
 Write, 1 and 1 are 2. 
 
 Take two counters. 
 
 Put one more with them. 
 
 How many counters are there ? 
 
 How did you get three counters ? 
 
 Two counters and one counter are how many counters ? 
 
PRIMARY ARITHMETIC 
 
 If the apples in the boy's hand be put with the apple 
 on the table, how many will there be on the table ? If 
 the one book be put on the three books, how many 
 books will there be in the pile ? 
 
 Make a number story about the two books and one 
 book. 
 
 Make a number story about the apples in the basket 
 and the apple on the table. About one marble and one 
 marble. 
 
 Two chairs and one chair are how many chairs ? 
 
 Two and one are how many ? 
 
 and * are ? 
 
 Two and one are ? 
 
 2 and 1 are ? 
 
PRIMARY ARITHMETIC 
 
 9 
 
 In the same way teach three and one, four and one, and so on 
 to ten and one. 
 
 Have children write : 
 
 1 
 
 and 
 
 1 
 
 are 
 
 2 
 
 1 
 
 + 1 
 
 = 2 
 
 2 
 
 and 
 
 1 
 
 are 
 
 3 
 
 2 
 
 + 1 
 
 = 3 
 
 3 
 
 and 
 
 1 
 
 are 
 
 4 
 
 3 
 
 + 1 
 
 = 4 
 
 4 
 
 and 
 
 1 
 
 are 
 
 5 
 
 4 
 
 + 1 
 
 = 5 
 
 5 
 
 and 
 
 1 
 
 are 
 
 6 
 
 5 
 
 + 1 
 
 = 6 
 
 6 
 
 and 
 
 1 
 
 are 
 
 7 
 
 6 
 
 + 1 
 
 = 7 
 
 7 
 
 and 
 
 1 
 
 are 
 
 8 
 
 7 
 
 4-1 
 
 * 8 
 
 8 
 
 and 
 
 1 
 
 are 
 
 9 
 
 8 
 
 4-1 
 
 = 9 
 
 9 
 
 and 
 
 1 
 
 are 
 
 10 
 
 9 
 
 + 1 
 
 = 10 
 
 10 
 
 and 
 
 1 
 
 are 
 
 11 
 
 10 
 
 + 1 
 
 = 11 
 
 BLACKBOARD DRILL 
 
 Add the 1 to each of the other 
 numbers around the circle. 
 
 7. Take 1 counter. Take two more counters. 
 
 How many counters have you ? 
 
 How did you get three counters ? 
 
 One counter and two counters are how many counters ? 
 
 One apple and two apples are how many apples ? 
 
 One and two are how many ? 
 
 Take two counters. Take two more counters. 
 
 How many counters have you? 
 
10 
 
 PRIMARY ARITHMETIC 
 
 How did you get four counters ? 
 
 Two counters and two counters are how many 
 counters ? 
 
 Two boards and two boards are how many boards ? 
 
 Two sheep and two sheep are how many sheep ? 
 
 Two and two are how many ? 
 
 Take three counters. Take two more counters. 
 
 How many counters have you ? 
 
 How did you get five counters ? 
 
 Three counters and two counters are how many 
 counters ? 
 
 Three books and two books are how many books ? 
 
 Three trees and two trees are how many trees ? 
 
 Three and two are how many ? 
 
 In a similar way teach the entire table of twos. 
 Have children write : 
 
 1 
 
 and 
 
 2 
 
 are 
 
 3 
 
 1 
 
 + 2 
 
 = 3 
 
 2 
 
 and 
 
 2 
 
 are 
 
 4 
 
 2 
 
 + 2 
 
 = 4 
 
 3 
 
 and 
 
 2 
 
 are 
 
 5 
 
 3 
 
 _l_ 2 
 
 = 5 
 
 4 
 
 and 
 
 2 
 
 are 
 
 6 
 
 4 
 
 _l_ 2 
 
 = 6 
 
 5 
 
 and 
 
 2 
 
 are 
 
 7 
 
 5 
 
 + 2 
 
 = 7 
 
 6 
 
 and 
 
 2 
 
 are 
 
 8 
 
 6 
 
 i 2 
 
 = 8 
 
 7 
 
 and 
 
 2 
 
 are 
 
 9 
 
 7 
 
 i 2 
 
 Q 
 
 8 
 
 and 
 
 2 
 
 are 
 
 10 
 
 8 
 
 _j_ 2 
 
 = 10 
 
 9 
 
 and 
 
 2 
 
 are 
 
 11 
 
 9 
 
 + 2 
 
 = 11 
 
 10 
 
 and 
 
 2 
 
 are 
 
 12 
 
 10 
 
 _j_ 2 
 
 = 12 
 
PRIMARY ARITHMETIC 11 
 
 Make a number story about 3 dolls and 2 dolls. 
 Another child give the answer. 
 
 Make a number story about 7 red roses and 2 white 
 roses. Give the answer. 
 
 Make a story about 6 and 2, 7 and 2, etc. 
 
 and are ? 
 
 Six and two are ? 
 
 6 + 2 = ? 
 
 c^ ^ ^ 
 
 V^^ ^V BLACKBOARD DRILL 
 
 b( C\ \ 
 ) LL Add the 2 to each of the other num- 
 ^ ^ T 4 
 
 T 
 
 \ / bers quickly. 
 
 / ^- ^o 
 
 I 
 
 8. Take 1 counter. Take 3 more counters. 
 
 How many counters have you ? 
 
 How did you get 4 counters ? 
 
 One counter and three counters are how many 
 counters? 
 
 One stick and three sticks are how many sticks ? 
 
 One marble and three marbles are how many mar- 
 bles? 
 
 One cat and three cats are how many cats ? 
 
 One and three are how many ? 
 
 Take two counters. Take three more counters. 
 
 How many counters have you ? 
 
 How did you get five counters ? 
 
12 
 
 PRIMARY ARITHMETIC 
 
 Two counters and three counters are how many 
 counters ? 
 
 and are how many dots ? 
 
 Two cows and three cows are how many cows ? 
 
 Two and three are how many ? 
 
 In a similar ,way, teach all the table of threes. 
 
 Make a number story about 2 red cherries and 3 red 
 cherries. Another child give the answer. 
 
 Make a story about 8 green leaves and 2 green leaves. 
 
 Make a number story about 2 boys and 5 boys. 
 
 Make a number story about 7 dollars and 3 dollars. 
 About 9 and 3. 
 
 Have children write : 
 
 1 
 
 and 
 
 3 
 
 are 
 
 4 
 
 1 
 
 + 3 = 
 
 4 
 
 2 
 
 and 
 
 3 
 
 are 
 
 5 
 
 2 
 
 1 O 
 
 -f- o 
 
 5 
 
 3 
 
 and 
 
 3 
 
 are 
 
 6 
 
 3 
 
 + 3 = 
 
 6 
 
 4 
 
 and 
 
 3 
 
 are 
 
 7 
 
 4 
 
 4-3 = 
 
 7 
 
 5 
 
 and 
 
 3 
 
 are 
 
 8 
 
 5 
 
 + 3 = 
 
 8 
 
 6 
 
 and 
 
 3 
 
 are 
 
 9 
 
 6 
 
 + 3 = 
 
 9 
 
 7 
 
 and 
 
 3 
 
 are 
 
 10 
 
 7 
 
 + 3 = 
 
 10 
 
 8 
 
 and 
 
 3 
 
 are 
 
 11 
 
 8 
 
 + 3 = 
 
 11 
 
 9 
 
 and 
 
 3 
 
 are 
 
 12 
 
 9 
 
 + 3 = 
 
 12 
 
 10 
 
 and 
 
 3 
 
 are 
 
 13 
 
 10 
 
 4-3 = 
 
 13 
 
 In a similar manner teach the entire table of Addition, giving 
 much drill with both concrete and abstract work, as you proceed, 
 to fix the tables in the minds of the children. 
 
 Vary the work, sometimes the teacher doing the work and 
 pupil telling what she did, and the result. 
 
 Have children make questions. 
 
PRIMARY ARITHMETIC 
 
 13 
 
 9. 
 
 BLACKBOARD DRILL 
 
 Add the 3 to each of the other num- 
 bers quickly. 
 
 TABLE OF ADDITION 
 
 1+1= 2 
 
 1+2= 3 
 
 1+3= 4 
 
 1+4= 5 
 
 1+ 5= 6 
 
 2 + 1= 3 
 
 2+2= 4 
 
 2+3= 5 
 
 2+4= 6 
 
 2+ 5= 7 
 
 3 + 1= 4 
 
 3+2= 5 
 
 3+3= 6 
 
 3+4= 7 
 
 3+ 5= 8 
 
 4 + 1= 5 
 
 4+2= 6 
 
 4+3= 7 
 
 4+4= 8 
 
 4+ 5= 9 
 
 5 + 1= 6 
 
 5 + 2= 7 
 
 5 + 3= 8 
 
 5 + 4= 9 
 
 5+ 5=10 
 
 6+1= 7 
 
 6+2= 8 
 
 6+3= 9 
 
 6+4=10 
 
 6+ 5 = 11 
 
 7 + 1= 8 
 
 7 + 2= 9 
 
 7+3=10 
 
 7+4 = 11 
 
 7+ 5 = 12 
 
 8 + 1= 9 
 
 8+2=10 
 
 8+3 = 11 
 
 8+4 = 12 
 
 8+ 5=13 
 
 9 + 1 = 10 
 
 9+2=11 
 
 9+3 = 12 
 
 9 + 4=13 
 
 9+ 5=14 
 
 io + i=n 
 
 10+2 = 12 
 
 10+3 = 13 
 
 10+4=14 
 
 10+ 5=15 
 
 1 + 6= 7 
 
 1 + 7= 8 
 
 1+8= 9 
 
 1 + 9 = 10 
 
 1+10=11 
 
 2+6= 8 
 
 2+7= 9 
 
 2+8=10 
 
 2+9 = 11 
 
 2+10=12 
 
 3+6= 9 
 
 3+7 = 10 
 
 3+8 = 11 
 
 3 + 9 = 12 
 
 3 + 10=13 
 
 4+6=10 
 
 4 + 7=11 
 
 4+8=12 
 
 4 + 9 = 13 
 
 4+10=14 
 
 5 + 6 = 11 
 
 5+7=12 
 
 5+8 = 13 
 
 5+9 = 14 
 
 5+10=15 
 
 6+6 = 12 
 
 6 + 7 = 13 
 
 6+8 = 14 
 
 6+9 = 15 
 
 6+10=16 
 
 7 + 6 = 13 
 
 7 + 7 = 14 
 
 7 + 8 = 15 
 
 7 + 9 = 16 
 
 7 + 10=17 
 
 8 + 6 = 14 
 
 8+7 = 15 
 
 8+8=16 
 
 8 + 9 = 17 
 
 8 + 10 = 18 
 
 9 + 6 = 15 
 
 9 + 7 = 16 
 
 9 + 8 = 17 
 
 9+9=18 
 
 9+10=19 
 
 10 + 6 = 16 
 
 10 + 7 = 17 
 
 10 + 8 = 18 
 
 10+9 = 19 
 
 10 + 10=20 
 
14 PRIMARY ARITHMETIC 
 
 Give three answers to each question below : 
 
 1. ?- 
 
 h? 
 
 = 10 
 
 9. 
 
 9 _ 
 
 f-? 
 
 = 12 
 
 2. ?H 
 
 h? 
 
 = 17 
 
 10. 
 
 9 _ 
 
 h? 
 
 = 15 
 
 3. ?H 
 
 h ? 
 
 = 9 
 
 11. 
 
 9 _ 
 
 h? 
 
 = 21 
 
 4. ?- 
 
 h? 
 
 = 20 
 
 12. 
 
 9 _ 
 
 h? 
 
 = 11 
 
 5. ?H 
 
 -? 
 
 = 14 
 
 13. 
 
 9 _ 
 
 h? 
 
 = 8 
 
 6. ?H 
 
 _ 9 
 
 rr 
 
 14. 
 
 ?- 
 
 h? 
 
 = 6 
 
 7. ?H 
 
 _ 9 
 
 = 16 
 
 15. 
 
 ?- 
 
 h? 
 
 = 18 
 
 8. ?H 
 
 _ 9 
 
 = 13 
 
 16. 
 
 ?H 
 
 h? 
 
 = 19 
 
 ADDITION DRILL CHART 
 
 This chart contains all additions which result in sums no 
 larger than 20. It should be copied on the blackboard, and 
 
 6 
 
 5 
 
 6 
 
 10 
 
 2 
 
 8 
 
 3 
 
 3 
 
 2 
 
 '7 
 
 7 
 
 7 
 
 1 
 
 5 
 
 4 
 
 2 
 
 4 
 
 1 
 
 9 
 
 1 
 
 5 
 
 7 
 
 2 
 
 4 
 
 5 
 
 10 
 
 4 
 
 3 
 
 6 
 
 7 
 
 10 
 
 5 
 
 2 
 
 5 
 
 7 
 
 3 
 
 2 
 
 4 
 
 4 
 
 4 
 
 3 
 
 1 
 
 5 
 
 6 
 
 8 
 
 6 
 
 2 
 
 3 
 
 2 
 
 1 
 
 10 
 
 4 
 
 6 
 
 7 
 
 8 
 
 3 
 
 1 
 
 9 
 
 3 
 
 8 
 
 1 
 
 3 
 
 1 
 
 6 
 
 1 
 
 9 
 
 9 
 
 4 
 
 6 
 
 9 
 
 2 
 
 10 
 
 8 
 
 6 
 
 9 
 
 10 
 
 3 
 
 1 
 
 5 
 
 3 
 
 5 
 
 7 
 
 8 
 
 1 
 
 8 
 
 6 
 
 5 
 
 2 
 
 10 
 
 2 
 
 10 
 
 8 
 
 9 
 
 4 
 
 10 
 
 7 
 
 8 
 
 7 
 
 10 
 
 9 
 
 4 
 
 10 
 
 5 
 
 9 
 
 9 
 
 6 
 
 9 
 
 8 
 
 8 
 
 7 
 
 children should recite the sums every day until they can do so 
 without making an error. Vary the drill. Begin at different 
 
PRIMARY ARITHMETIC 
 
 15 
 
 places and go through the entire chart to the place of beginning. 
 Change the order, going sometimes to right, and to left, and some- 
 times up -or down. Vary concert and individual recitation with 
 and without the pointer. Sometimes pupils use the pointer. 
 Use the chart persistently. 
 
 10. To THE TEACHER. Pupils need drill on this kind of work 
 till they can give results instantly. 
 
 1 . How many boys are 5 boys and 3 boys ? 
 
 2. Three eggs and 4 eggs are how many eggs ? 
 
16 PRIMARY ARITHMETIC 
 
 3. How many are six tops and 3 tops ? 
 
 4. How many are 8 hens and 7 hens ? 
 
 5. Two cats and four cats are how many cats ? 
 
 6. Five books and two books are how many 
 books ? 
 
 7. Four hats and six hats are how many hats ? 
 
 8. Eight slates and nine slates are how many? 
 
 9. 3 chairs and 5 chairs are how many chairs ? 
 
 10. Six balls and three balls are how many balls ? 
 
 11. Five and two are how many ? 
 
 12. Nine and three are how many ? 
 
 13. How many are four and four? 
 
 14. May had three cents, and I gave her 8 cents ; 
 how many cents did she have then ? 
 
 15. John found 4 eggs in one nest and six in another ; 
 how many eggs did he find ? 
 
 16. James had 7 cents and found 4 more ; how many 
 cents did he then have ? 
 
 17. Make a number story about 3 birds and 6 birds. 
 4 men and 6 men. 5 and 2. 
 
 11. 1. A boy saw 6 squirrels in one tree and 4 in 
 another. How many squirrels did he see ? 
 
 2. 5 oranges + 3 oranges = ? 7 pins + 9 pins = ? 
 6 + 7 = ? 
 
 3. Henry had 5 cents, John 4, and George 8. How 
 many cents did they all have ? 
 
 4. A wagon carried 7 women, 5 men, and 3 chil- 
 dren. How many persons did it carry? 
 
PRIMARY ARITHMETIC 
 
 17 
 
 5. 
 
 3+2+4=? 
 
 22. 
 
 8 + 5 = ? 
 
 6. 
 
 2+7+5=? 
 
 23. 
 
 3+8+1+1=? 
 
 7. 
 
 4 + 8+2=? 
 
 24. 
 
 4+6+9=? 
 
 8. 
 
 6+5+3=? 
 
 25. 
 
 2+3+6+4=? 
 
 9. 
 
 9+2+5=? 
 
 26. 
 
 8+2+2+6=? 
 
 10. 
 
 6+1+4=? 
 
 27. 
 
 18 + 3 = ? 
 
 11. 
 
 6+1+5=? 
 
 28. 
 
 28 + 3 = ? 
 
 12. 
 
 5+6+1=? 
 
 29. 
 
 48 4- 3 = ? 
 
 13. 
 
 7 + 24-8 = ? 
 
 30. 
 
 69 + 5 = ? 
 
 14. 
 
 l4_2 + 3 + 9 = ? 
 
 31. 
 
 49 4. 10 + 1 = ? 
 
 15. 
 
 6+3+1+8=? 
 
 32. 
 
 95 + 5 = ? 
 
 16. 
 
 1+2+4+8=? 
 
 33. 
 
 7 4. 8 + 5 = ? 
 
 17. 
 18. 
 19. 
 20. 
 
 l4_9 + 2 + l = ? 
 54-2 + 3 + 9 = ? 
 6+4+8=? 
 6+3+4=? 
 
 34. 
 35. 
 
 Add by fives from 
 to 20. 
 Add by threes 
 from to 30. 
 
 21. 
 
 6+1+6+2=? 
 
 
 
 36. Count by 2's from to 40. 
 
 37. Count by 4's from to 40. 
 
 38. Count by 6's from to 48. 
 
 39. Count by 7's from to 35. 
 
 40. Count by 8's from to 48. 
 
 From 1 to 21. 
 From 2 to 30. 
 From 5 to 42. 
 From 5 to 47. 
 From 6 to 54. 
 5 
 
 41. Make a number story about 5 swallows, 9 
 swallows, and 3 swallows. 
 
 . 
 
 42. Make a number story about 5, 3, and 8. 
 
 12. 1. Eight boys and 5 boys are how many boys? 
 2. Seven eggs and three eggs are how many eggs? 
 
18 
 
 PRIMARY ARITHMETIC 
 
 3. 9 tops and three tops are how many tops? 
 
 4. 6 cats and 2 cats are how many cats ? 
 
 5. 7 books and 5 books are how many books ? 
 
 6. 10 hats and 4 hats are how many hats ? 
 
 7. 10 slates and 1 slate are how many slates ? 
 
 8. How many chairs are 8 chairs and 3 chairs? 
 
 9. How many balls are 10 balls and 6 balls? 
 
 10. How many dogs are 6 dogs and 5 dogs? 
 
 11. 11 days and 4 days are how many days? 
 
 12. Seven apples and 4 apples are how many apples? 
 
 13. 11 balls and 5 balls are how many balls? 
 
 14. 8 cows and 3 cows are how many cows ? 
 
 15. 11 and 5 are how many? 
 
 16. 10 and four are how many? 
 
 17. How many are 11 and 6 ? 
 
 18. John spent 3 cents for candy, 5 cents for a top, 
 and 6 cents for marbles. How much did he spend in all ? 
 
 19. A man had three cows in one field, four in an- 
 other, and seven in another. How many did he have in 
 all ? Make a picture of the fields using dots for cows. 
 
 20. 9 -f 4 = ? 
 
 28. 5+ 7 = ? 
 
 36. 7 + 9 = ? 
 
 21. 8 + 5 = ? 
 
 29. 4+ 8 = ? 
 
 37. 8 + 10 = ? 
 
 22. 6 + 2 = ? 
 
 30. 4+ 9 = ? 
 
 38. 2 + 5 + 3 = ? 
 
 23. 9 + 2 = ? 
 
 31. 5 + 10 = ? 
 
 39. 4 + 6 + 7 = ? 
 
 24. 6 + 2 = ? 
 
 32. 8+ 5 = ? 
 
 40. 9 + 1 + 5 = ? 
 
 25. 6 + 3 = ? 
 
 33. 9+ 6 = ? 
 
 41. 8 + 2 + 3 = ? 
 
 26. 9 + 4 = ? 
 
 34. 8+ 7 = ? 
 
 42. 9 + 9 + 2 + 1 = ? 
 
 27. 5 + 5 = ? 
 
 35. 8+ 8 = ? 
 
 43. 1+2+3+4 + 5 = ? 
 
PRIMARY ARITHMETIC 19 
 
 13. 1. George picked O O Q ^ rom on ^ tree > 
 O C O O O from another tree, and Q Q Q 
 O O O fr m an ther tree. How many did he pick 
 in all? 
 
 2. There were 
 
 one row, 4 in another, and 9 in another. How many 
 trees were there in all ? 
 
 3. A girl earned 8 cents, found 5 cents, and had 
 
 3 cents given to her. How many cents had she ? 
 
 4. A cat caught X^X^fe V^Xjf*' in the 
 
 and %^%/%/%/%/^%/<%/ in 
 
 the field. How many did she catch in all ? 
 
 5. A gardener gave Ned ^ ^ ^ }, Nell K K 
 
 [X) ^), and Will as many as the other two. How 
 many fVs did he give all ? 
 
 6. Frank ate three plums, gave Charles nine, and 
 had four left. How many plums had he at first ? 
 
 7. I saw on the lawn 10 sparrows, 6 robins, and 
 
 4 orioles. How many birds did I see in all ? 
 
 8. A boy paid 2 dollars for shoes, 1 dollar for a 
 hat, 5 dollars for a coat, and 9 dollars for books. How 
 much did he pay for all ? 
 
 9. A boy caught 10 fish, and his sister 9. How 
 many fish did both catch? 
 
20 PRIMARY ARITHMETIC 
 
 10. Nancy walked 2 miles on Monday, 3 miles on 
 Wednesday, 4 miles on Thursday, and 9 miles on Sat- 
 urday. How far did she walk ? 
 
 11. 1 + 2 + 3 + 4 + 5 = ? 16. 7 + 7 + 6 = ? 
 
 12. 2 + 1 + 9 = ? 17. 12 + 8 = ? 
 
 13. 10 + 10 = ? 18. 5 + 1 + 6 + 3 = ? 
 
 14. 4 + 8 + 2 = ? 19. 3 + 4 + 5 = ? 
 
 15. 9 + 1 + 6 = ? 20. 6 + 9 = ? 
 
 SUBTRACTION 
 
 14. Teacher take two counters, and children tell 
 how many. Teacher take one away, and children tell 
 what she has done, and how many are left. 
 
 Children take two counters, take one away, and tell 
 how many are left. 
 
 Two counters less one counter are how many 
 counters ? 
 
 Two boxes less one box are how many boxes ? 
 
 Two knives less one knife ? 
 
 Two flowers less one flower ? 
 
 Two less one are how many ? 
 
 Teacher take three counters, and children tell how 
 many. Teacher take one away, and children tell what 
 she did, and number left. 
 
 Three counters less one counter are how many 
 counters ? 
 
 Three books less one book are how many books ? 
 
 Three less one are how many ? 
 
PRIMARY ARITHMETIC 
 
 21 
 
 O O less O 
 
 Three less one are 
 3 less 1 are 
 
 So on till all the ones are taught. 
 Children write : 
 
 2 
 
 less 
 
 1 
 
 are 
 
 1 
 
 2- 
 
 1 = 
 
 1 
 
 3 
 
 less 
 
 1 
 
 are 
 
 2 
 
 3- 
 
 1 = 
 
 2 
 
 4 
 
 less 
 
 1 
 
 are 
 
 3 
 
 4- 
 
 1 = 
 
 3 
 
 5 
 
 less 
 
 1 
 
 are 
 
 4 
 
 5- 
 
 1 = 
 
 4 
 
 6 
 
 less 
 
 1 
 
 are 
 
 5 
 
 6- 
 
 1 = 
 
 5 
 
 7 
 
 less 
 
 1 
 
 are 
 
 6 
 
 7 
 
 1 = 
 
 6 
 
 8 
 
 less 
 
 1 
 
 are 
 
 7 
 
 8- 
 
 1 = 
 
 7 
 
 9 
 
 less 
 
 1 
 
 are 
 
 8 
 
 9- 
 
 -j 
 
 8 
 
 10 
 
 less 
 
 1 
 
 are 
 
 9 
 
 10- 
 
 1 = 
 
 9 
 
 11 
 
 less 
 
 1 
 
 are 
 
 10 
 
 11- 
 
 1 = 
 
 10 
 
 
 
 
 
 I 
 
 
 
 Make a number story 
 about the holly leaves. 
 Give the answer. 
 
 Make an adding story 
 about the holly buds. 
 Give the answer. 
 
 Make a number story 
 about a tree, 9 blackbirds, 
 and 1 blackbird. 
 Make a number story about 8 and 1. 
 
PRIMARY ARITHMETIC 
 
 BLACKBOARD WORK 
 
 Take one from each of the other 
 
 numbers, 
 o 
 
 15. Teacher take three counters, and children tell 
 how many. 
 
 Take away two counters. Children tell what has 
 been done and how many are left. 
 
 Children take three counters. Take away two 
 counters. Tell what has been done, and how many 
 are left. 
 
 Three counters less two counters are how many 
 counters ? 
 
 Three peaches less two peaches are how many 
 peaches ? 
 
 Three less two are how many ? 
 
 Teacher take four counters. Take away two counters. 
 How many are left ? Children tell what has been done, 
 and the result. 
 
 Teacher take five counters ; take away two. Chil- 
 dren watch carefully and tell the whole story what 
 has been done and the result. 
 
 OOOOO less CO are ? 
 Five less two are ? 
 
 5 - 2 = ? 
 
PRIMARY ARITHMETIC 
 
 23 
 
 How many oranges on the plate in the picture ? 
 If the girl takes away 2 oranges, how many will 
 be left? 
 
 Five less two are how many ? 
 
 So on through the remainder of table of twos. 
 Children write : 
 
 3 
 
 less 
 
 2 
 
 are 
 
 1 
 
 3 
 
 _ 2 
 
 1 
 
 4 
 
 less 
 
 2 
 
 are 
 
 2 
 
 4 
 
 2 = 
 
 2 
 
 5 
 
 less 
 
 2 
 
 are 
 
 3 
 
 5 
 
 _ 
 
 3 
 
 6 
 
 less 
 
 2 
 
 are 
 
 4 
 
 6 
 
 2 = 
 
 4 
 
 7 
 
 less 
 
 2 
 
 are 
 
 5 
 
 7 
 
 -2 = 
 
 5 
 
 8 
 
 less 
 
 2 
 
 are 
 
 6 
 
 8 
 
 2 
 
 6 
 
 9 
 
 less 
 
 2 
 
 are 
 
 7 
 
 9 
 
 -2 = 
 
 7 
 
 10 
 
 less 
 
 2 
 
 are 
 
 8 
 
 10 
 
 2 = 
 
 8 
 
 11 
 
 less 
 
 2 
 
 are 
 
 9 
 
 11 
 
 -2 = 
 
 9 
 
 12 
 
 less 
 
 2 
 
 are 
 
 10 
 
 12 
 
 o 
 
 10 
 
24 PRIMARY ARITHMETIC 
 
 Make a number story about a pond, a bank, 9 ducks, 
 and 2 ducks. Give the answer. 
 
 Make a number story about 8 less 2. 
 
 BLACKBOARD WORK 
 
 Take 2 from each of the other num- 
 bers. 
 
 16. Children watch. 
 
 Teacher take four counters, and take away three. 
 
 Children tell what is done, and the result. 
 
 Four counters less three counters are how many 
 counters ? 
 
 Four roses less three roses ? 
 
 Four hats less three hats ? 
 
 Four less three ? 
 
 Children watch. 
 
 Teacher take five counters, and take away three. 
 
 Children do just what teacher has done, tell what 
 they have done, and the result. 
 
 Five less three are how many ? 
 
 So on until all the threes have been taught. 
 
 Make a number story about 9 eggs, a nest, and 3 
 eggs. Give the answer. 
 
 Make a story about 12 less 3. 
 
 Children write the table of threes as in previous lessons. 
 
PRIMARY ARITHMETIC 25 
 
 ' 
 
 1. Mary had 9 roses, and gave Helen 3. How many 
 roses had she left ? 
 
 NOTE. If a child fails, let him take 9 counters, call them roses; 
 take away three " roses," and see how many roses are left. 
 
 2. George earned 5 cents, and spent 3 cents. How 
 many cents had he left ? 
 
 3. Seven quarts of water were in a pail. Three 
 quarts leaked out. How many were left ? 
 
 4. Henry has 7 cents. How much must he earn to 
 buy a ball for 10 cents ? 
 
 5. Make a question that has 3 for an answer. 
 
 II 
 
 BLACKBOARD DRILL 
 
 Subtract 3 from each of the other 
 numbers around the circle. 
 
 In a similar way teach all the table of subtraction. Show 
 with counters that 2-2 = 0, ^-3 = 0, 4-4 = 0, 5-5 = 0. 
 
 17. TABLE OF SUBTRACTION 
 
 1-1= 
 
 2-2= 
 
 3-3= 
 
 4-4= 
 
 5-5= 
 
 2-1 = 1 
 
 3-2= 1 
 
 4-3= 1 
 
 5-4= 1 
 
 6-5= 1 
 
 3-1= 2 
 
 4-2= 2 
 
 5-3= 2 
 
 6-4= 2 
 
 7-5= 2 
 
 4-1= 3 
 
 5-2 = . 3 
 
 6-3= 3 
 
 7-4= 3 
 
 8-5= 3 
 
 5-1= 4 
 
 6-2= 4 
 
 7-3= 4 
 
 8-4= 4 
 
 9-5= '4 
 
 6-1= 5 
 
 7-2= 5 
 
 8-3= 5 
 
 9-4= 5 
 
 10-5= 5 
 
 7-1= 6 
 
 8-2= 6 
 
 9-3= 6 
 
 10-4= 6 
 
 11-5= 6 
 
 8-1= 7 
 
 9-2= 7 
 
 10-3= 7 
 
 11-4= 7 
 
 12-5= 7 
 
 9-1= 8 
 
 10-2= 8 
 
 11-3= 8 
 
 12-4= 8 
 
 13-5= 8 
 
 10-1= 9 
 
 11-2= 9 
 
 12-3= 9 
 
 13-4= 9 
 
 14-5= 9 
 
 11-1 = 10 
 
 12-2 = 10 
 
 13-3=10 
 
 14-4 = 10 
 
 15-5 = 10 
 
26 
 
 PRIMARY ARITHMETIC 
 
 TABLE OF SUBTRACTION (Continued) 
 
 6-6= 
 
 7-7 = 
 
 8-8= 
 
 9-9= 
 
 10-10= 
 
 7-6= 1 
 
 8-7= 1 
 
 9-8= 1 
 
 10-9= 1 
 
 11-10= 1 
 
 8-6= 2 
 
 9-7= 2 
 
 10-8= 2 
 
 11-9= 2 
 
 12-10= 2 
 
 9-6= 3 
 
 10-7= 3 
 
 11-8= 3 
 
 12-9= 3 
 
 13-10= 3 
 
 10-6= 4 
 
 11-7= 4 
 
 12-8= 4 
 
 13-9= 4 
 
 14-10= 4 
 
 11-6= 5 
 
 12-7= 5 
 
 13-8= 5 
 
 14-9= 5 
 
 15-10= 5 
 
 12-6= 6 
 
 13-7= 6 
 
 14-8= 6 
 
 15-9= 6 
 
 16-10= 6 
 
 13-6= 7 
 
 14-7= 7 
 
 15-8= 7 
 
 16-9= 7 
 
 17-10= 7 
 
 14-6= 8 
 
 15-7= 8 
 
 16-8= 8 
 
 17-9= 8 
 
 18-10= 8 
 
 15-6= 9 
 
 16-7= 9 
 
 17-8= 9 
 
 18-9= 9 
 
 19-10= 9 
 
 16-6=10 
 
 17-7 = 10 
 
 18-8=10 
 
 19-9=10 
 
 20-10=10 
 
 Give three answers to each of these questions : 
 
 1. 20-? = ? 
 
 7. 14-? = ? 
 
 13. 8-? = ? 
 
 2. 19-? = ? 
 
 8. 13-? = ? 
 
 14. 7-? = ? 
 
 3. 18-? = ? 
 
 9. 12-? = ? 
 
 15. 6-? = ? 
 
 4. 17-? = ? 
 
 10. 11-?*=? 
 
 16. 5-? = ? 
 
 5. 16_? = ? 
 
 11. 10-? = ? 
 
 17. 4-? = ? 
 
 6. 15-? = ? 
 
 12. 9-? = ? 
 
 18. 3-? = ? 
 
 SUBTRACTION DRILL CHART 
 
 This chart contains all the subtraction table. It should be 
 copied on the blackboard, and remainders recited by the class 
 every day till mastered. Vary the drill. Begin sometimes at 
 the upper left-hand corner, sometimes at the lower right-hand 
 corner. Go up and down, to the right and the left. Recite 
 sometimes in concert and sometimes individually, teacher or 
 pupil using the pointer, and sometimes without the pointer. 
 
PRIMARY ARITHMETIC 
 
 27 
 
 11 
 
 4 
 
 15 
 
 9 
 
 13 
 
 12 
 
 6 
 
 15 
 
 11 
 
 16 
 
 -10 
 
 -2 
 
 -7 
 
 -9 
 
 -8 
 
 -9 
 
 -5 
 
 -6 
 
 -2 
 
 -8 
 
 9 
 
 12 
 
 13 
 
 6 
 
 11 
 
 10 
 
 19 
 
 7 
 
 6 
 
 8 
 
 -6 
 
 -5 
 
 -9 
 
 -1 
 
 -6 
 
 -8 
 
 -10 
 
 -4 
 
 -2 
 
 -3 
 
 8 
 
 11 
 
 7 
 
 8 
 
 9 
 
 6 
 
 11 
 
 3 
 
 3 
 
 15 
 
 -5 
 
 g 
 
 -3 
 
 -6 
 
 -3 
 
 -3 
 
 -5 
 
 -2 
 
 -1 
 
 -8 
 
 10 
 
 13 
 
 9 
 
 14 
 
 13 
 
 9 
 
 11 
 
 10 
 
 9 
 
 5 
 
 -6 
 
 -5 
 
 -7 
 
 -6 
 
 -7 
 
 -1 
 
 -8 
 
 -7 
 
 -8 
 
 3 
 
 14 
 
 12 
 
 11 
 
 17 
 
 6 
 
 7 
 
 2 
 
 14 
 
 8 
 
 17 
 
 -10 
 
 -6 
 
 -3 
 
 -9 
 
 -4 
 
 -6 
 
 2 
 
 -8 
 
 -5 
 
 -10 
 
 12 
 
 10 
 
 12 
 
 12 
 
 11 
 
 7 
 
 9 
 
 5 
 
 8 
 
 17 
 
 -3 
 
 -1 
 
 _ j 
 
 -8 
 
 -9 
 
 -1 
 
 -5 
 
 -4 
 
 -8 
 
 -8 
 
 9 
 
 7 
 
 8 
 
 8 
 
 4 
 
 16 
 
 18 
 
 9 
 
 4 
 
 8 
 
 -5 
 
 -2 
 
 -2 
 
 7 
 
 -3 
 
 -10 
 
 -10 
 
 -2 
 
 -1 
 
 -1 
 
 13 
 
 15 
 
 5 
 
 10 
 
 11 
 
 i 
 
 3 
 
 13 
 
 5 
 
 16 
 
 -6 
 
 -9 
 
 2 
 
 -9 
 
 -1 
 
 -5 
 
 -3 
 
 -5 
 
 _1 
 
 9 
 
 14 
 
 5 
 
 7 
 
 14 
 
 12 
 
 10 
 
 12 
 
 11 
 
 16 
 
 10 
 
 -5 
 
 5 
 
 -7 
 
 -9 
 
 5 
 
 -5 
 
 -10 
 
 7 
 
 -7 
 
 -5 
 
 10 
 
 4 
 
 10 
 
 6 
 
 14 
 
 18 
 
 15 
 
 2 
 
 13 
 
 1 
 
 -10 
 
 -4 
 
 -3 
 
 -6 
 
 7 
 
 -9 
 
 -10 
 
 -1 
 
 -10 
 
 -1 
 
 FOR THE TEACHER : After a table has once been developed, 
 the pupil should be thoroughly drilled upon it. 
 
 Give much concrete work. In drill work, do not allow the 
 child to use counters in finding the answers, but require him to 
 rely upon his memory. If he gives a wrong answer, he should 
 find and correct his error by means of the counters. 
 
28 
 
 PRIMARY ARITHMETIC 
 
 BLACKBOARD DRILL 
 
 15 
 
 
 
 18. 1. May had 4 pictures and gave away 2 of them. 
 How many had she left ? 
 
 2. In a field were 11 sheep. The dogs killed 5 of 
 them. How many were left ? 
 
 3. In a class were 9 scholars. Four of them were 
 boys. How many were girls? 
 
 4. Henry had 13 marbles. He lost 3 and gave away 
 1. How many had he left ? 
 
 5. In a class were 12 scholars. Six of them were 
 girls. How many were boys ? 
 
 6. The number of boys in a class was ten. The 
 number of girls was 3 less. How many girls were 
 there ? 
 
 7. William is 14 years old. James is nine. Wil- 
 liam is how much older than James ? 
 
PRIMARY ARITHMETIC 
 
 29 
 
 8. Celia is 12 years old. Sarah is 5 years younger. 
 How old is Sarah ? 
 
 9. A farmer planted 18 trees. Ten of them died. 
 How many lived ? 
 
 10. A hen hatched 11 chickens. Two of them were 
 white and the rest speckled. How many of them were 
 speckled ? 
 
 11. 
 
 13 
 
 less 
 
 6 
 
 are 
 
 9 
 
 24. 
 
 19 
 
 9 = 
 
 9 
 
 12. 
 
 12 
 
 less 
 
 5 
 
 are 
 
 9 
 
 25. 
 
 17 
 
 - 8 = 
 
 9 
 
 13. 
 
 9 
 
 less 
 
 5 
 
 are 
 
 9 
 
 26. 
 
 12 
 
 rr 
 
 9 
 
 14. 
 
 8 
 
 less 
 
 6 
 
 are 
 
 9 
 
 27. 
 
 12 
 
 - 6 = 
 
 9 
 
 15. 
 
 5 
 
 less 
 
 2 
 
 are 
 
 9 
 
 28. 
 
 14 
 
 7 = 
 
 9 
 
 16. 
 
 10 
 
 less 
 
 9 
 
 are 
 
 9 
 
 29. 
 
 18 
 
 - 8 = 
 
 9 
 
 17. 
 
 11 
 
 less 
 
 4 
 
 are 
 
 9 
 
 30. 
 
 17 
 
 - 8 = 
 
 ? 
 
 18. 
 
 13 
 
 less 
 
 4 
 
 are 
 
 9 
 
 31. 
 
 18 
 
 - 9 = 
 
 9 
 
 19. 
 
 15 
 
 less 
 
 5 
 
 are 
 
 9 
 
 32. 
 
 11 
 
 - 5 = 
 
 9 
 
 20. 
 
 14 
 
 less 
 
 7 
 
 are 
 
 9 
 
 33. 
 
 12 
 
 - 4 = 
 
 9 
 
 21. 
 
 9 
 
 less 
 
 5 
 
 are 
 
 9 
 
 34. 
 
 15 
 
 - 8 = 
 
 9 
 
 22. 
 
 8 
 
 less 
 
 6 
 
 are 
 
 9 
 
 35. 
 
 20 
 
 -10 = 
 
 9 
 
 23. 
 
 9 
 
 less 
 
 5 
 
 are 
 
 9 
 
 36. 
 
 19 
 
 9 _ 
 
 9 
 
 19. 1. A boy had 5 cents and earned 7 cents more. 
 How many cents did he then have ? 
 
 2. A boy had 15 cents and spent 10 cents. How 
 many cents had he left ? 
 
 3. A lady had 7 pies on a shelf and 3 on a table. 
 How many pies had she ? 
 
 4. A man had 8 horses and bought 6 more. How 
 many had he then ? 
 
30 PRIMARY ARITHMETIC 
 
 5. There were 17 apples in a dish. A boy took out 
 9 of them. How many were left ? 
 
 6. I had 9 dollars. I paid 5 dollars for a chair 
 and the rest of my money for a table. What did the 
 table cost ? 
 
 7. There were 8 boys in a chestnut tree and 7 on 
 the ground. How many in all? 
 
 8. Henry had 5 books. His aunt gave him 3 and 
 his sister 4. How many had he then? 
 
 9. Mary is 15 years old and John is 5 years younger. 
 How old is John ? 
 
 10. Make a number story about 6 and 5. 
 
 11. Make a number story about 13 and 4. 
 
 12. Make a number story about 2 and 7. 
 
 13. Make a subtracting story about hens. 
 
 14. Make an adding story about birds. 
 
 20. 1. A clerk cut 10 yards of cloth from a piece 
 containing 19 yards. How many yards were left ? 
 
 2. Seven ducks came to a pond; then 8 more came; 
 then 6 flew away. How many were left ? 
 
 3. Robert earned 6 cents on Monday, 4 cents on 
 Tuesday, and 7 cents on Wednesday. He spent 9 cents 
 on Thursday. How much had he left ? 
 
 4. There were 15 words in the spelling lesson. 
 Richard missed 4. How many did he spell right? 
 
 5. A carpenter cut 7 feet from a 16-foot board. 
 How long a piece was left ? 
 
 6. In a basket were 5 red plums, 5 green ones, and 
 9 blue ones. How many were there ? 
 
PRIMARY ARITHMETIC 31 
 
 7. A boy had a nickel and a dime. He bought a 
 top for 3 cents and some buns for 4 cents. How much 
 money had he left ? 
 
 8. A farmer sold some wheat for 10 dollars and 
 some potatoes for 7 dollars. He wanted to buy some 
 clothing for 20 dollars. How much more money did he 
 need ? 
 
 9. A boy had 13 cents. He spent 6 cents and 
 earned 9 cents. How much had he then ? 
 
 10. Count by threes from 2 to 23. 
 
 11. 8 + 7 = ? 18. 14-5 = ? 
 
 12. 15-8 = ? 19. 14-9 = ? 
 
 13. 7 = 15-? 20. 9 + ?= 14 
 
 14. 18 = 9 + ? 21. 2 + 4 + 7-8 + 3 = ? 
 
 15. 9 + ?=18 22. 13-4-6 + 3 + 8 = ? 
 
 16. 9 + 9 = ? 23. 1 + 2 + 3-3 + 7 + 9 = ? 
 
 17. 14 = 5 + ? 24. 12 + 1 + 1 + 1-10 + 4 = ? 
 Count by 2's backward from 28 to 0. From 39 to 1. 
 Count by 5's from to 50, and back again. 
 
 Add by 6's from to 54, and subtract by 6's back 
 to 0. 
 
 MULTIPLICATION 
 
 21. Take one counter. 
 
 Take one more counter. 
 
 What have you done ? 
 
 How many times did you take one counter ? 
 
 Two times 1 counter are how many counters ? 
 
 Two times 1 stick are how many sticks ? 
 
32 
 
 PRIMARY ARITHMETIC 
 
 Two times 1 boy are how many boys ? 
 
 Two times 1 chair are how many chairs ? 
 
 Two times 1 are how many ? 
 
 Take one counter. Take one more counter. Take 
 one more counter. How many counters have you ? 
 
 What did you do to get 3 counters ? 
 
 Three times 1 counter are how many counters? 
 
 Three times 1 pencil are how many pencils ? 
 
 Three times 1 day are how many days ? 
 
 Take 1 counter. Take 1 more counter. Take 1 more 
 counter. Take 1 more counter. What did you do ? 
 How many counters have you ? 
 
 Four times 1 counter are how many counters ? 
 
 Four times 1 star are how many stars ? 
 
 Four times 1 leaf are how many leaves ? 
 
 Four times 1 are how many ? 
 
 Similarly teach to " 10 times 1 are 10." 
 Have children write : 
 
 2 
 
 times 
 
 1 
 
 are 
 
 2 
 
 1 
 
 X 
 
 2 = 
 
 2 
 
 3 
 
 times 
 
 1 
 
 are 
 
 3 
 
 1 
 
 X 
 
 o 
 
 3 
 
 4 
 
 times 
 
 1 
 
 are 
 
 4 
 
 1 
 
 X 
 
 4 = 
 
 4 
 
 5 
 
 times 
 
 1 
 
 are 
 
 5 
 
 1 
 
 X 
 
 5 = 
 
 5 
 
 6 
 
 times 
 
 1 
 
 are 
 
 6 
 
 1 
 
 X 
 
 6 = 
 
 6 
 
 7 
 
 times 
 
 1 
 
 are 
 
 7 
 
 1 
 
 X 
 
 7 = 
 
 7 
 
 8 
 
 times 
 
 1 
 
 are 
 
 8 
 
 1 
 
 X 
 
 o 
 
 8 
 
 9 
 
 times 
 
 1 
 
 are 
 
 9 
 
 1 
 
 X 
 
 9 = 
 
 9 
 
 10 
 
 times 
 
 1 
 
 are 
 
 10 
 
 1 
 
 X 
 
 10 = 
 
 10 
 
PRIMARY ARITHMETIC 33 
 
 22. Lay 2 counters. Lay 2 more counters. Thus, 
 
 How many counters have you ? 
 
 What did you do to get four counters ? 
 
 How many times did you take 2 counters ? 
 
 Two times two counters are how many counters ? 
 
 Two times 2 dots are how many dots ? 
 
 Two times 2 balls are how many balls ? 
 
 Two times 2 are how many ? 
 
 Lay 2 counters. Lay 2 more. Lay 2 more. Thus, 
 
 How many counters have you ? 
 
 How did you get six counters ? 
 
 Three times 2 counters are how many counters ? 
 
 Three times 2 pegs are how many pegs ? 
 
 Three times 2 knives are how many knives ? 
 
 Three times 2 are how many ? 
 
 Lay 2 counters, 2 more, 2 more, 2 more. Thus, 
 
 How many counters have you? 
 
 How did you get eight counters ? 
 
 Four times 2 counters are how many counters? 
 
 Four times 2 bats are how many bats ? 
 
 Four times 2 rabbits are how many rabbits ? 
 
 Four times 2 are how many ? 
 
 Similarly teach the rest of this table. 
 
34 
 
 PRIMARY ARITHMETIC 
 
 Children write : 
 
 2 
 
 times 
 
 2 
 
 are 
 
 4 
 
 2 
 
 X 
 
 2 
 
 = 4 
 
 3 
 
 times 
 
 2 
 
 are 
 
 6 
 
 2 
 
 X 
 
 3 
 
 = 6 
 
 4 
 
 times 
 
 2 
 
 are 
 
 8 
 
 2 
 
 X 
 
 4 
 
 - 8 
 
 5 
 
 times 
 
 2 
 
 are 
 
 10 
 
 2 
 
 X 
 
 5 
 
 -10 
 
 6 
 
 times 
 
 2 
 
 are 
 
 12 
 
 2 
 
 X 
 
 6 
 
 = 12 
 
 7 
 
 times 
 
 2 
 
 are 
 
 14 
 
 2 
 
 X 
 
 7 
 
 -14 
 
 8 
 
 times 
 
 2 
 
 are 
 
 16 
 
 2 
 
 X 
 
 8 
 
 = 16 
 
 9 
 
 times 
 
 2 
 
 are 
 
 18 
 
 2 
 
 X 
 
 9 
 
 -18 
 
 10 
 
 times 
 
 2 
 
 are 
 
 20 
 
 2 
 
 X 
 
 10 
 
 -20 
 
 23. 1. In our yard are 3 trees, and 2 birds live in 
 each tree. How many birds live in all the trees ? 
 
 2. How many hands have 4 boys ? 
 
 3. How many thumbs have 5 girls ? 
 
 4. How many shoes in 10 pair? 
 
 5. How many sleeves are there in 7 coats ? 
 
 6. How many noses have 6 dogs ? 
 
 7. How many eyes have 6 sheep ? 
 
 8. Make a story about 3 pockets and 2 cents. 
 
 9. Make a story about 6 times 2 feet. 
 
 10. Make a story about 8 times 2 gloves. 
 
 11. Make a story about 9 windows and 2 panes of glass. 
 
 BLACKBOARD DRILL 
 
 Take 2 times each number around 
 the circle. 
 
PRIMARY ARITHMETIC 
 
 35 
 
 How many peaches do you see in the picture ? If 
 the boy puts all of the peaches into the dish, taking 
 two at a time, how many times will it take him ? 
 
 Make a number story about the books on the table. 
 
 24. Teacher lay 3 counters, and 3 more counters. Children 
 watch and tell the teacher what she did and how many counters 
 she has. 
 
 Two times 3 counters are how many counters ? 
 Two times 3 pegs are how many pegs ? 
 Two times 3 sticks are how many sticks ? 
 Two times 3 trees are how many trees ? 
 Two times 3 are how many ? 
 
 In the same way teach the rest of this table to " 10 times 3." 
 Children write the table as in preceding lesson. 
 
36 PRIMARY ARITHMETIC 
 
 v5 
 
 BLACKBOARD DRILL 
 
 '"H O }*^ Find 3 times each of the numbers 
 V / around the circle. 
 
 \r\ 
 
 1. Two girls had 3 cents apiece. How many cents 
 had both ? 
 
 2. Six men earn three dollars a day apiece. How 
 many dollars do all earn in a day ? 
 
 3. Fred has 9 three-cent pieces. How much money 
 has he ? 
 
 4. There are 3 feet in 1 yard. How many feet in 
 7 yards ? 
 
 5. If a cord of wood costs 3 dollars, what will 8 
 cords cost ? 
 
 6. What is the cost of 4 pencils at 3 cents apiece ? 
 
 7. How far can you walk in 8 hours, if you walk 
 3 miles every hour ? 
 
 8. If it takes 3 horses to draw a van, how many 
 horses can draw 8 vans ? 
 
 9. If lemons cost 4 cents apiece, what will 3 lemons 
 cost? 
 
 10. In an orchard there are 3 rows of trees with 10 
 trees in a row. How many trees are in the orchard ? 
 
 In the same way teach the remainder of the multiplication 
 table. Give much concrete work after each part of the table. 
 Call attention to 1 x = 0, 2 x = 0, 3 x = 0, etc. 
 Also, 1x1 = 1, 1x2-2, 1x3 = 3, etc. 
 
PRIMARY ARITHMETIC 
 
 37 
 
 25. 
 
 TABLE OF MULTIPLICATION 
 
 lx 1= 1 
 
 2x 1= 2 
 
 3x 1= 3 
 
 4x 1= 4 
 
 5x 1= 5 
 
 Ix 2= 2 
 
 2x 2= 4 
 
 3x 2= 6 
 
 4x 2= 8 
 
 5x 2= 10 
 
 lx 3= 3 
 
 2x 3= 6 
 
 3x 3= 9 
 
 4x 3 = 12 
 
 5x 3= 15 
 
 lx 4 = 4 
 
 2x 4= 8 
 
 3x 4=12 
 
 4x 4 = 16 
 
 5x 4= 20 
 
 lx 5= 5 
 
 2x 5=10 
 
 3x 5=15 
 
 4x 5=20 
 
 5x 5= 25 
 
 lx 6= 6 
 
 2x 6=12 
 
 3x 6 = 18 
 
 4x 6 = 24 
 
 5x 6= 30 
 
 lx 1= 1 
 
 2x 7=14 
 
 3x 7=21 
 
 4x 7 = 28 
 
 5x 7= 35 
 
 lx 8= 8 
 
 2x 8=16 
 
 3x 8=24 
 
 4x 8=32 
 
 5x 8= 40 
 
 lx 9= 9 
 
 2x 9=18 
 
 3x 9 = 27 
 
 4x 9 = 36 
 
 5x 9= 45 
 
 1x10=10 
 
 2x10 = 20 
 
 3x10=30 
 
 4x10 = 40 
 
 5x10= 50 
 
 6x 1= 6 
 
 7x 1= 7 
 
 8x 1= 8 
 
 9x 1= 9 
 
 10 x 1= 10 
 
 6x 2-12 
 
 7x 2 = 14 
 
 8x 2 = 16 
 
 9x 2=18 
 
 10 x 2= 20 
 
 6x 3-18 
 
 7x 3=21 
 
 8x 3=24 
 
 9x 3 = 27 
 
 10 x 3= 30 
 
 6x 4=24 
 
 7x 4=28 
 
 8x 4=32 
 
 9x 4=36 
 
 10 x 4= 40 
 
 6x 5=30 
 
 7x 5=35 
 
 8x 5=40 
 
 9x 5=45 
 
 10 x 5= 50 
 
 6x 6=36 
 
 7x 6=42 
 
 8x 6=48 
 
 9x 6=54 
 
 10 x 6= 60 
 
 6x 7=42 
 
 7x 7=49 
 
 8x 7=56 
 
 9x 7=63 
 
 10 x 7= 70 
 
 6x 8=48 
 
 7x 8 = 56 
 
 8x 8 = 64 
 
 9x 8 = 72 
 
 iOx 8= 80 
 
 6x 9 = 54 
 
 7x 9=63 
 
 8x 9=72 
 
 9x 9=81 
 
 10 x 9= 90 
 
 6x10=60 
 
 7x10=70 
 
 8x10=80 
 
 9x10=90 
 
 10x10=100 
 
 1. 
 
 ?x 
 
 ? = 81 
 
 
 2. 
 
 ? x 
 
 ?=12 
 
 (Two answers) 
 
 3, 
 
 ?x 
 
 ? = 24 
 
 (Two answers) 
 
 4. 
 
 ?x 
 
 ? = 32 
 
 
 5. 
 
 ?x 
 
 ? = 20 
 
 (Two answers) 
 
 6. 
 
 ?x 
 
 ? = 16 
 
 (Two answers) 
 
 7. 
 
 ?x 
 
 ?=18 
 
 (Two answers) 
 
 8. 
 
 ?x 
 
 ? = 25 
 
 
 9. 
 
 ?x 
 
 ?=45 
 
 
 10. 
 
 ? X 
 
 ? = 56 
 
 
 11. 
 
 ?x 
 
 ?=63 
 
 12. 
 
 ? X 
 
 ? = 90 
 
 13. 
 
 ?x 
 
 ?=72 
 
 14. 
 
 ? X 
 
 ? = 50 
 
 15. 
 
 ?x 
 
 ? = 21 
 
 16. 
 
 ?x 
 
 ? = 14 
 
 17. 
 
 ?x 
 
 ?=35 
 
 18. 
 
 ?x 
 
 ? = 64 
 
 19. 
 
 ?x 
 
 ? = 40 
 
 20. ?x? = 28 
 
38 
 
 PRIMARY ARITHMETIC 
 MULTIPLICATION DRILL CHART 
 
 This chart contains all combinations of two factors from 1 to 
 10. It should be copied on the blackboard, and the products 
 should be recited daily till mastered. Vary the drill as in Sub- 
 traction and Addition. Persist in the use of the chart. 
 
 9 
 
 5 
 
 9 
 
 3 
 
 6 
 
 rr 
 i 
 
 2 
 
 7 
 
 8 
 
 9 
 
 10 
 
 3 
 
 4 
 
 7 
 
 3 
 
 4 
 
 6 
 
 2 
 
 5 
 
 1 
 
 5 
 
 2 
 
 10 
 
 7 
 
 6 
 
 3 
 
 2 
 
 4 
 
 10 
 
 3 
 
 10 
 
 8 
 
 8 
 
 7 
 
 1 
 
 5 
 
 2 
 
 1 
 
 3 
 
 5 
 
 1 
 
 8 
 
 2 
 
 8 
 
 8 
 
 8 
 
 1 
 
 5 
 
 7 
 
 10 
 
 6 
 
 10 
 
 6 
 
 4 
 
 9 
 
 3 
 
 6 
 
 1 
 
 5 
 
 2 
 
 3 
 
 2 
 
 4 
 
 3 
 
 1 
 
 2 
 
 9 
 
 6 
 
 9 
 
 9 
 
 8 
 
 5 
 
 8 
 
 7 
 
 10 
 
 9 
 
 10 
 
 8 
 
 1 
 
 9 
 
 1 
 
 7 
 
 1 
 
 5 
 
 3 
 
 6 
 
 4 
 
 9 
 
 9 
 
 8 
 
 5 
 
 6 
 
 10 
 
 7 
 
 7 
 
 4 
 
 10 
 
 5 
 
 4 
 
 6 
 
 4 
 
 2 
 
 6 
 
 1 
 
 7 
 
 4 
 
 2 
 
 10 
 
 3 
 
 4 
 
 Occasionally let one pupil read the chart aloud from the book, 
 using the upper number for a multiplier, the other pupils of the 
 class giving the products. 
 
 26. Drill on the table of multiplication. 
 
 If a pupil gives a wrong answer, let him find and correct his 
 mistake by means of counters. 
 
 1. What will 10 oranges cost at 5 cents apiece? 7 
 lemons at 3 cents? 6 tops at 8 cents? 9 sleds at 4 
 dollars ? 
 
 2. Six boys each picked 7 quarts of berries. How 
 many quarts did all pick ? 
 
 3. A newsboy made 5 cents a day for 9 days. How 
 much did he make ? 
 
PRIMARY ARITHMETIC * i 39 
 
 ^sL* u F o tyiiJX^ 
 
 ' ^^^^BBHMBHI^^'^^ 
 
 4. How much could a newsboy make in 5 days, at 
 9 cents a day ? In 8 days, at 1 cents a day ? In 3 
 days, at 7 cents a day ? 
 
 5. A dime is 10 cents. How many cents in 2 
 dimes ? In 4 dimes ? In 5 dimes ? In 7 dimes ? In 
 9 dimes ? 
 
 6. Which is greater, 9 times 8, or 8 times 9 ? 
 
 7. A man has 4 fields of corn, and 4 men work in 
 each field. How many men in all the fields ? 
 
 8. A lady has 5 boxes, with 6 spoons in each box. 
 How many spoons has she ? 
 
 9. Write the table of 8's, 9's, 7's, 5's, 6's, 4's. 
 
 10. At 10 cents a dozen, what will 8 dozen bananas 
 cost? 
 
 11. How many wings have 5 birds ? 
 
 12. Rose has 8 marbles, and her brother 7 times as 
 many. How many has her brother ? 
 
 13. If there are 9 plants each in 5 rows, how many 
 plants in all ? 
 
 14. If a dozen eggs cost 12 cents, what will 10 dozen 
 cost? 
 
 15. Harry can pick 4 quarts of berries in one day. 
 At the same rate, how many can he pick in 10 days ? 
 
 Make stories about this picture. 
 
 Make a picture of 5 squares in 6 rows, and tell a 
 number story about it. 
 
40 
 
 PRIMARY .ARITHMETIC 
 BLACKBOARD DRILL 
 
 Multiply the figure in the centre of each circle by the different 
 numbers around it. Answers should be instantaneous. 
 
 10 
 
 3 
 
 27. Addition, Subtraction, and Multiplication. 
 
 1. A man saw 4 ducks in one pond, 5 in another, 
 and 7 in another. How many ducks did he see ? Make 
 a picture. 
 
 2. A man picked six pears from one tree, six from 
 another, and five from another. How many pears did 
 he pick ? 
 
 3. Suppose each of these dots is a tree. How 
 many rows of trees are there ? How 
 
 many trees in a row ? How many 
 
 trees in the orchard ? How do you 
 
 find it ? ' 
 
 
PRIMARY ARITHMETIC 41 
 
 4. Make an orchard of 3 rows, with 9 trees in a 
 row. How r many trees in the orchard ? 
 
 5. Make an orchard of 4 rows, with 7 trees in a 
 row. How many trees in the orchard? 
 
 6. Nelly had 11 apples arid gave away 5. How 
 many had she left ? 
 
 7. Make a story about 3 apples, 4 apples, and 7 
 apples. 
 
 8. Will's father gave him 20 cents. He paid five 
 cents for a tablet and 5 cents for a pencil. How much 
 had he left ? 
 
 9. A man had 8 rows of corn, with 10 hills in a 
 row. The cows ate 50 hills. How many were left ? 
 Make a picture. 
 
 10. A man had 8 sheep in one pen and 6 in another. 
 Five of them got away. How many were left ? 
 
 11. 5 + 3-4 + 9 + 3^-5-4 + 9=? 
 
 12. 5x7 + 7-2-? 
 
 13. Add, subtract, and multiply the numbers in each 
 of these .pairs : 
 
 4, 7 5, 8 10, 6 17, 2 5, 9 11, 4 6, 6 9, 4 
 
 14. What will 7 tables cost at 8 dollars each? 
 
 15. How many days in 8 school weeks ? 
 
 16. There are 8 quarts in a peck. How many quarts 
 in 7 pecks ? 
 
 17. A boy gave 6 cents for an orange, 8 cents for 
 pencils, and 10 cents for a ball. How many cents did 
 he pay for all ? 
 
 18. Add 9 ? 7, and 8, and then subtract 5. 
 
42 PRIMARY ARITHMETIC 
 
 DIVISION 
 
 28. Children watch. Teacher take 4 counters. Lay down 
 two counters, and two more. Thus, II II. Children do the 
 same. 
 
 What did you do ? 
 
 How many times did you lay down two counters ? 
 
 How many counters did you take ? 
 
 Take 4 crayons. Give me two crayons. Give me 
 two more. How many times did you give me two 
 crayons ? 
 
 How many 2's in 4 ? 
 
 Take 6 sticks. Lay 2 of them. Lay 2 more. Lay 
 2 more. Thus, II II II. How many times did you lay 
 down 2 sticks ? 
 
 Make 6 marks. Point them off in twos. Thus, II, II, II. 
 
 How many groups are there ? 
 
 How many times must you make 2 marks to have 
 6 marks ? 
 
 How many 2 7 s in 6 ? 
 
 So on till you have taught " there are ten 2's in 20." 
 Children write the table thus : 
 
 2-*-2 = l 
 
 12-2= 6 
 
 4-2 = 2 
 
 14-2= 7 
 
 6-2 = 3 
 
 16-2= 8 
 
 8-2 = 4 
 
 18-2= 9 
 
 10 - 2 = 5 
 
 20 - 2 = 10 
 
PRIMARY ARITHMETIC 
 
 43 
 
 How many pears on the table in the picture ? 
 
 To how many children can the girl give the six pears, 
 if she gives 2 pears to each child ? 
 
 To how many sick people can she give the 6 roses, 
 if she gives 3 roses to each ? 
 
 1. A boy has 4 cents. How many pencils can he 
 buy at 2 cents apiece ? 
 
 2. A boy can earn 2 cents in an hour. In how many 
 hours can he earn 10 cents? 14 cents? 18 cents? 6 
 cents? 8 cents? 16 cents? 20 cents? 
 
 3. How many 2's in 10 ? In 18 ? In 12 ? In 20 ? 
 
 b 
 
 BLACKBOARD DRILL 
 
 Divide each of the numbers around 
 the circle by 2. Answer quickly. 
 
44 PRIMARY ARITHMETIC 
 
 29. Teacher and children each take 6 counters. 
 
 Lay 3 of them. Lay 3 more. Thus, III III. 
 Children tell what has been done. 
 
 How many counters in each group ? 
 
 How many groups ? 
 
 How many groups of three-counters in six counters ? 
 
 How many groups of 3-crayons in 6 crayons ? 
 
 How many 3-cents in 6 cents ? 
 
 OO CO 
 
 00 
 
 O O O O O 
 
 How many apples are in the first row ? How manj 
 in the second row ? 
 
 Tell two ways of making 6. 
 How many 3's in 6 ? 
 
 Similarly with 9, 12, etc., counters. 
 Children write the table thus : 
 
 3 
 
 -8-3 = 1 
 
 18 
 
 . 
 
 6 
 
 6 
 
 Q O 
 
 T- O 
 
 21 
 
 -1-3. a 
 
 7 
 
 9 
 
 -3 = 3 
 
 24 
 
 . O 
 
 8 
 
 12 
 
 -3 = 4 
 
 27 
 
 -3 = 
 
 9 
 
 15 
 
 -3 = 5 
 
 30 
 
 . O 
 
 10 
 
PRIMARY ARITHMETIC 
 
 45 
 
 BLACKBOARD DRILL 
 
 1 5 Divide each of the numbers around 
 the circle by 3. 
 
 1. How many pencils at 3 cents each will 12 cents 
 buy? 
 
 2. How many suits can be made from 18 yards of 
 cloth if it takes 3 yards for one suit ? 
 
 3. How many yards in 30 feet ? 
 
 4. Twenty-one boys stood in three equal lines for ex- 
 ercises. How many boys were in each line ? 
 
 5. If a man ploughs 3 acres in one day, in how many 
 days can he plough 24 acres ? 
 
 In a similar manner, teach the entire table of division. 
 
 30. 
 
 TABLE OF DIVISION 
 
 1-1= 1 
 
 2-2= 1 
 
 3-3= 1 
 
 4-4= 1 
 
 5- 5= 1 
 
 2-1 = 2 
 
 4-2= 2 
 
 6-3= 2 
 
 8-4= 2 
 
 10- 5= 2 
 
 3-1 = 3 
 
 6-2= 3 
 
 9-3= 3 
 
 12-4= 3 
 
 15- 5= 3 
 
 4-1= 4 
 
 8-r-2= 4 
 
 12-3= 4 
 
 16-4 = 4 
 
 20- 5= 4 
 
 5-1= 5 
 
 10-2= 5 
 
 15-3= 5 
 
 20-4= 5 
 
 25-i- 5= 5 
 
 6-*-! = 6 
 
 12-2= 6 
 
 18-3= 6 
 
 24-4= 6 
 
 30- 5= 6 
 
 7-1 = 7 
 
 14-2= 7 
 
 21-3= 7 
 
 28-4= 7 
 
 35-f- 5= 7 
 
 8-s-l= 8 
 
 16-2= 8 
 
 24-3= 8 
 
 32-4= 8 
 
 40- 5= 8 
 
 9-5-1= 9 
 
 18-2= 9 
 
 27-3= 9 
 
 36-4= 9 
 
 45-j- 5= 9 
 
 10-1 = 10 
 
 20-2=10 
 
 30-3 = 10 
 
 40-4 = 10 
 
 50-j- 5=10 
 
46 
 
 PRIMARY ARITHMETIC 
 
 TABLE OF DIVISION (Continued) 
 
 6-6= 1 
 
 7-7 = 1 
 
 8-8= 1 
 
 9-9= 1 
 
 10-10= 1 
 
 12-s-6= 2 
 
 14-7= 2 
 
 16-8= 2 
 
 18-9= 2 
 
 20-10= 2 
 
 18-6= 3 
 
 21-7= 3 
 
 24-8= 3 
 
 27-9= 3 
 
 30-10= 3 
 
 24-6= 4 
 
 28-7= 4 
 
 32-8= 4 
 
 36-9= 4 
 
 40-10 = 4 
 
 30-6= 5 
 
 35-7= 5 
 
 40-8= 5 
 
 45-9= 5 
 
 50-10= 5 
 
 36-6= 6 
 
 42-7 = 6 
 
 48-,-8= 6 
 
 54-9= 6 
 
 60-10= 6 
 
 42-6= 7 
 
 49-7= 7 
 
 56-8= 7 
 
 63-9= 7 
 
 70-10 = 7 
 
 48-6= 8 
 
 56-7 = 8 
 
 64-8 = 8 
 
 72-9= 8 
 
 80-10= 8 
 
 54-6= 9 
 
 63-7= 9 
 
 72-8= 9 
 
 81-9= 9 
 
 90-10 = 9 
 
 60-6=10 
 
 70-7=10 
 
 80-8=10 
 
 90-^-9=10 
 
 100-10=10 
 
 1. 15-3 = ? 
 
 2. 15-5 = ? 
 
 3. 15 = 5 x ? 
 
 4. 15 = 3 x ? 
 
 5. 56 = 8 x ? 
 
 6. 56 = 7 x ? 
 
 7. 56^-7 = ? 
 
 8. 56-8 = ? 
 
 9. 54-9 = ? 
 
 10. 54-6 = ? 
 
 11. 54 = 9 x ? 
 
 12. 54 = 6 x ? 
 
 13. 40-4 = ? 
 
 14. 40-10= ? 
 
 15. 40 = 10 x ? 
 
 16. 40 = 4 x ? 
 
 17. 27 = 9 x ? 
 
 18. 27 = 3 x ? 
 
 19. 27- 3= ? 
 
 20. 27- 9= ? 
 
 21. 72- 9= ? 
 
 22. 72- 8= ? 
 
 23. 72 =? x 8 
 
 24. 72 = 9 x ? 
 
 25. 70 x ? = 70 
 
 DIVISION DRILL CHART 
 
 This chart contains all divisions in which the dividend does 
 not exceed 100 and the divisor and quotient do not exceed 10. 
 
PRIMARY ARITHMETIC 
 
 47 
 
 It should be used daily till mastered. Vary the work, as sug- 
 gested with the previous drill charts. Drill persistently. 
 
 10)100 
 
 6)30 
 
 9)90 
 
 1)1 
 
 6)18 
 
 9)9 
 
 1)4 
 
 6)60 
 
 6)54 
 
 7)28 
 
 7)42 
 
 1)5 
 
 6)24 
 
 9)81 
 
 3)9 
 
 6)12 
 
 5)15 
 
 10)20 
 
 4)24 
 
 8)40 
 
 2)18 
 
 9)27 
 
 6)36 
 
 10)90 
 
 2)14 
 
 10)10 
 
 4)20 
 
 9)36 
 
 2)2 
 
 6)48 
 
 7)35 
 
 3)30 
 
 8)56 
 
 2)16 
 
 9)18 
 
 3)6 
 
 9)72 
 
 3)3 
 
 10)60 
 
 5)10 
 
 1)6 
 
 10)30 
 
 5)40 
 3)12 
 
 6)6 
 
 5)20 
 
 8)48 
 
 7)70 
 
 7)21 
 
 8)64 
 
 2)4 
 
 6)42 
 
 7)28 
 
 9)63 
 
 1)2 
 
 10)40 
 
 3)15 
 
 9)45 
 
 3)18 
 
 10)80 
 
 7)49 
 
 8)16 
 
 1)10 
 
 3)27 
 
 7)63 
 
 2)6 
 
 8)24 
 
 4)8 
 
 7)14 
 
 4)4 
 
 11? 
 
 4)16 
 
 10)50 
 
 2)12 
 
 4)12 
 
 9)54 
 
 2)10 
 
 5)45 
 
 3)21 
 
 8)32 
 
 7)56 
 
 8)8 
 
 5)35 
 
 5)25 
 
 3)24 
 
 8)72 
 
 1)8 
 
 10)70 
 
 1)7 
 
 5)5 
 
 4)40 
 
 4)36 
 
 5)30 
 
 II 9 
 
 8)80 
 
 2)8 
 
 5)50 
 
 2)20 
 
 4)32 
 
 7)7 
 
 31. 1. Take 24 counters. Divide them into 4 equal 
 groups. How many are there in each group ? How 
 many 4's are there in 24 ? How many 6 ? s are there 
 in 24? 
 
 2. Take 15 counters. Divide them into 3 equal 
 parts. How many are there in each part ? How many 
 3's in 15 ? How many 5 ? s in 15 ? 
 
 3. Two pints will fill a quart measure. How many 
 
48 PRIMARY ARITHMETIC 
 
 quart measures will 8 pints fill? 12 pints? 6 pints? 
 18 pints? 20 pints? 16 pints? 14 pints? 24 pints? 
 
 4. An orchard of 28 trees has 7 trees in each row. 
 How many rows are there ? Make a picture of the 
 orchard. 
 
 5. Make a picture of an orchard having 30 trees with 
 10 trees in each row. How many rows are there ? 
 
 6. A man has 72 peaches in 9 baskets, the same 
 number in each basket. How many peaches in each 
 basket ? 
 
 7. If a man puts 4 plums in a row in a basket, 
 how many rows would hold 24 plums? Make a pic- 
 ture, thus, 
 
 8. Make a picture of 48 birds with 8 in each flock. 
 How many flocks ? 
 
 9. A man had 81 cents. He divided them among 
 some boys, giving each boy 9 cents. How many boys 
 were there ? 
 
 10. A man's wages are 18 dollars per week. How. 
 much a day does he get ? 
 
 11. Divide 63 sheep into 7 equal flocks. How many 
 in each flock ? Make a picture. 
 
 12. If you can buy 5 sheets of paper for a cent, how 
 many cents will pay for 50 sheets ? 
 
PRIMARY ARITHMETIC 
 
 BLACKBOARD DRILL 
 
 49 
 
 oooooooo 
 
 32. How many apples do you see here ? 
 If these 8 apples are divided equally between two 
 boys, how many apples will each boy receive? 
 How many apples are one half of 8 apples ? 
 
 1. 10 dollars -*- 2 are how many dollars ? 
 
 2. i of 10 dollars are how many dollars? 
 
 3. How do you find \ of 10 dollars ? 
 
 4. 8-^2 are how many ? 
 
 5. l of 8 are how many ? 
 
 6. How do you find \ of 8 ? 
 
 7. 16 quarts divided by 2 are how many quarts? 
 
 8. \ of 16 quarts are how many quarts? 
 
50 PRIMARY ARITHMETIC 
 
 9. How do you find ^ of a number ? 
 
 10. Find 1 of 12. 12. Find 1 of 18 cents. 
 
 11. Find i of 6 pencils. 13. Find 1 of 4. 
 
 ooooooooo 
 
 14. If these 9 apples are divided equally among 3 
 boys, how many will each receive ? 
 
 15. ^ of 9 apples are how many apples ? 
 
 16. 9 bushels -*- 3 are how many bushels? 
 
 17. ^ of 9 bushels are how many bushels ? 
 
 18. How do you find J of a number ? 
 
 19. Find l of 21. 23. Find l of 24. 
 
 20. Find l of 30. 24. Find of 27. 
 
 21. Find! of 12. 25. Find 1 of 15 days. 
 
 22. Find i of 6. 26. Find 1 of. 3. 
 
 33. 1. 8 quarts -5- 4 are how many quarts? 
 
 2. 1 of 8 quarts are how many quarts ? 
 
 3. 12 -i- 4 are how many ? 
 
 4. ^ of 12 are how many ? 
 
 5. 20 cents -s- 4 are how many cents ? 
 
 6. 1 of 20 cents are how many cents ? 
 
 7. ^ of 24 are how many ? 
 
 8. How do you find l of a number ? 
 
 9. Find J of 16. 12. Find J of 28 pounds. 
 
 10. Find 1 of 40 pounds. 13. Find | of 36 pounds. 
 
 11. Find l of 32 apples. 14. Find J of 4. 
 
 15. Divide 15 by 5. 
 
 16. |- of 15 are how many ? 
 
PRIMARY ARITHMETIC 51 
 
 17. 30 -s- 5 are how many ? 
 
 18. Find 1 of 30 marbles. 
 
 o 
 
 19. How do you find ^ of a number ? 
 
 20. Find of 40 feet. 
 
 21. Find of 10 toes. 
 
 22. Find of 35 houses. 
 
 23. Find l of 45. 
 
 34. 1. How can you find ^ of a number? \ of a 
 number? ? ? T ^? 
 
 2. Find l of 40. 5. Find of 54. 
 
 3. Find l of 49. 6. Find ^ of 100. 
 
 4. Find of 36. 7. Find of 45. 
 
 8. Hugh has 20 rabbits and Ralph has 1 as many. 
 How many has Ralph ? 
 
 9. Edna has 4 dolls and Susan has \ as many. 
 How many dolls has Susan ? 
 
 10. Mr. Smith walked 48 miles and Mr. Fox walked 
 \ as far. How many miles did Mr. Fox walk ? 
 
 11. William had 40 marbles and Frank had ^ as 
 many. How many had both ? 
 
 12. There were 50 men in a factory. |- of them were 
 black. How many were white ? 
 
 13. Kate solved 42 problems ; Ruth solved \ as many. 
 How many did Ruth solve ? 
 
 35. 1. How many twos in eight? 
 
 2. How many threes in ten, and how many over? 
 
 3. \ of 10 men are how many men ? 
 
10. 3x3 
 
 8-5 
 
 4 + 4 
 
 11. 8-6 
 
 11-4 
 
 3x2 
 
 12. 5 + 3 
 
 6 + 5 
 
 5x2 
 
 13. 7 + 2 
 
 11-5 
 
 6 + 4 
 
 52 PRIMARY ARITHMETIC 
 
 4. Two mice have 8 feet. How many feet has one 
 mouse ? 
 
 5. If 4 oranges cost 8 cents, how many cents does 
 one orange cost ? 
 
 6. If 3 balls cost 9 cents, what is the cost of 1 ball ? 
 
 7. How many nickels in a dime ? 
 
 8. How many two-cent pieces in ten cents? In 8 
 cents ? 
 
 9. 2)10 4)8 3)9 5)10 2)8 3)6 
 
 W-n-2 
 
 lof 6 
 iof 8 
 
 14. If 5 pencils cost 10 cents, what does one pencil 
 cost? 
 
 15o Put 8 sheep in 4 pens. How many sheep in each 
 pen ? (Picture.) 
 
 16. How many two-cent stamps can I buy for 8 
 cents ? 
 
 17. Make problems for the numbers in Ex. 10. 
 Ex. 11. Ex. 12. 
 
 18. Make a problem for -| of 6. 
 
 19. Make a problem for J of 8. 
 
 36. 1. Eight boys and one boy are how many boys? 
 
 2. One ox and 5 oxen are how many oxen ? 
 
 3. If 1 sheep costs $ 3, what will 3 sheep cost ? 
 
 NOTE. Teach the use of the dollar mark. 
 
PRIMARY ARITHMETIC 53 
 
 4. How many knives can I buy for $ 10, if one 
 knife costs $2? 
 
 5. If 4 geese cost $ 8, what does 1 goose cost ? 
 
 6. 
 
 Add 
 
 3 
 
 5 
 
 6 
 
 
 5 
 
 7 
 
 3 
 
 
 5 
 
 
 
 
 2 
 
 3 
 
 4 
 
 
 5 
 
 3 
 
 
 
 
 4 
 
 
 7. 
 
 Subtract 
 
 8 
 
 9 
 
 10 
 
 10 
 
 9 
 
 
 6 
 
 8 
 
 
 
 
 -3 
 
 -5 
 
 
 
 6 
 
 -10 
 
 -6 
 
 
 
 3 
 
 -2 
 
 8. 
 
 4x2 
 
 
 8x 
 
 1 
 
 2 
 
 X 
 
 4 
 
 lOx 
 
 
 
 
 2x3 
 
 9. 
 
 6x1 
 
 
 3x 
 
 3 
 
 5 
 
 X 
 
 2 
 
 10 x 
 
 1 
 
 
 8^4 
 
 10. 
 
 5)10 
 
 
 4)8 
 
 3' 
 
 2 
 
 )6 
 
 
 2)10 
 
 
 4)4 
 
 
 2)8 
 
 11. Mary has two dolls, and Annie has nine: How 
 many have both ? 
 
 12. There are 5 chairs in one row and 6 in another. 
 How many chairs in all ? 
 
 13. John had 10 balls and lost three. How many 
 had he left? 
 
 14. How many cents are 2 cents, 3 cents, and 5 
 cents ? 
 
 15. How many boys are 2 boys, 4 boys, and 5 boys? 
 
 37. 1. A window had 10 panes of glass and a boy 
 broke 3 panes. How many were left ? 
 
 2. If a pail holds 6 quarts, and there are 5 quarts 
 of milk in it, how many quarts more will it hold ? 
 
 3. Four teams of goats are how many goats ? 
 
 4. How many pair will 10 shoes make? 
 
54 PRIMARY ARITHMETIC 
 
 5. There were 10 white mice in a box and 7 ran 
 out. How many were left in the box ? 
 
 6. What 3 pieces of money make 5 cents ? 
 
 7. How many three-cent cakes can you buy for 10 
 cents, and how much will you have left ? 
 
 8. If a six-quart pail is half full, how many quarts 
 are in the pail ? 
 
 9. How much less than a dime is 3 cents ? 
 
 10. 3 books cost $6. What will one book cost? 
 What will 5 books cost? 
 
 11. I bought an orange for 3 cents and candy for 
 5 cents. How much money did I spend ? 
 
 12. I- of 6 is what ? of 8 is what? 
 
 13. i of 10 is what ? \ of 10 is what ? 
 
 14. 3x?=9. 9-3 = ? 10-4 = ? 6 + 3 = ? 
 
 15. ? + 4 = 8. 8-4 = ? 9-? = 4. 10-? = 8. 
 
 16. How do you find \ of a number? ^? ^? 
 
 38. 1. Add 3 (2) 6 (3) 2 (4) 5 (5) 1 (6) 4 (7) 3 
 433 2753 
 3 1 3_ 2 1 3 
 
 8. 5 + 3-1 = ? 3 + 3-2 = ? 2 + 2 + 2 = ? 
 
 9. 6-4 + 2 = ? 8-4-2 = ? 3 + 3 + 3 = ? 
 
 10. \ of 10, i of 6, 3x3, 5x2. 
 
 11. \ of 8, \ of 9, 4x2, S-s-4. 
 
 12. Ned lives 6 blocks east of the school, and Fred 4 
 blocks east. How far from Ned's to Fred's ? (Picture.) 
 
PRIMARY ARITHMETIC 55 
 
 13. John lives 4 blocks west of the school. How 
 far from John's to Ned's ? From Ned's to John's ? 
 (Picture.) 
 
 14. One week and 5 days are how many days ? 
 
 15. Nellie had 5 two-cent pieces. She bought a book 
 for 4 cents, and a pencil for 3 cents. How much money 
 did she spend ? How much was left ? 
 
 16. May had ten cents and spent one-fifth of it for a 
 pencil. How much did the pencil cost, and how much 
 has she left? 
 
 17. From three 3's take two 4's. 
 
 18. One book costs $4. How much will 2 books 
 cost? 
 
 39. 1. A farmer had 11 turkeys and sold 6 of them. 
 How many had he left ? 
 
 2. If there are two nests, with 5 eggs in each nest, 
 how many eggs in both nests ? (Picture.) 
 
 3. If George had 10 cents and gave ^ to his sister, 
 how much will she have ? How much will he have 
 left? 
 
 4. Rose had 3 apples; her brother had twice as 
 many. How many had her brother ? How many had 
 both? 
 
 5. A hen had 11 chickens; 2 were black, 4 were 
 brown, and the rest were white. How many were 
 white ? 
 
 6. A lady bought 11 yards of cloth, and used 6 
 yards. How many has she left ? 
 
56 PRIMARY ARITHMETIC 
 
 7. May is 11 years old. Maud is 4 years younger. 
 How old is Maud ? 
 
 8. 3 + 4 + 2 8-3-2 5x2 + 1 
 
 9. 2 + 7 + 2 7 + 4-6 3x3 + 2 
 
 10. 2 + 2 + 7 6 + 5-8 4 + 4 + 3 
 
 11. Add 3 (12)1 (13)2 (14)3 (15) 2 (16) 3 (17)4 
 
 4 32 34 1 2 
 2523333 
 2252112 
 
 40. 1. One tooth and 11 teeth are how many teeth? 
 
 2. A dime and a two-cent piece make how much ? 
 
 3. Six two-cent pieces are how much money? 
 
 4. How many cents in 4 three-cent pieces ? 
 
 5. How many 2-cent stamps can you buy for 12 
 cents ? 
 
 6. In 12 pencils how many dozen ? 
 
 7. Find the cost of 4 oranges at 3 cents apiece. 
 
 8. If one hat costs $ 6,, what will 10 hats cost ? 
 
 9. Mary has 9 cents, Lillie has 6 times as much. 
 How much has Lillie ? 
 
 10. A pint of milk costs 2 cents. How many pints 
 will 12 cents buy? 
 
 11. 4 triangles have how many angles? (Picture.) 
 
 12. Four men and 18 men are how many men ? 
 
 13. Twelve eggs less 7 eggs are how many eggs ? 
 
 14. Three times four balls are how many balls ? 
 
 15. Three squares have how many sides ? (Picture.) 
 
PRIMARY ARITHMETIC 57 
 
 16. Twelve feet less one foot are how many feet ? 
 
 17. If there are 12 plants in four rows, how many 
 plants in each row ? (Picture.) 
 
 18. Fred had 12 marbles. He gave 3 to Henry and 
 2 to Tom. How many had Fred left ? 
 
 19. Six boys can wear how many shoes? 
 
 41. 1. 7 boys can wear how many shoes ? 
 
 2. How many 2-cent pieces in 14 cents ? 
 
 3. If one dress costs $ 7, what will 2 dresses cost ? 
 
 4. In 14 days how many weeks ? 
 
 5. From 14 cents take 9 cents. How many cents 
 are left ? 
 
 6. If you can buy 1 peach for 2 cents, what will 7 
 peaches cost ? 
 
 7. Mary has 4 three-cent pieces and a 2-cent piece. 
 How much money has she ? 
 
 8. There were 14 children in a class; 9 were girls. 
 How many were boys ? 
 
 9. If it takes 7 yards of cloth for one dress, how 
 many dresses can be made from 14 yards ? 
 
 10. Mrs. Smith had $ 14 and spent $ 8 for a dress. 
 How many dollars were left? 
 
 11. 1x15 of 15 15- 4 
 
 12. 15-*- 15 lof 15 9+ 6 
 
 13. 15 x 1 13+ 2 15-9 
 
 14. 3x5 3 + 13 15-15 
 
 15. Make problems for : 
 
 3x5 iof!5 13 + 2 
 
58 PRIMARY ARITHMETIC 
 
 42. 1. There are 7 red apples and 10 green ones in 
 a basket. How many apples are in the basket ? 
 
 2. Frank had 9 balls and bought 8 more. How 
 many had he then ? 
 
 3. Three five-cent pieces and a two-cent piece are 
 how many cents ? 
 
 4. If Henry finds 9 eggs in one nest and 8 eggs in 
 another, how many eggs does he find in all ? (Picture.) 
 
 5. A farmer has 6 cows in one yard and 11 in 
 another. How many cows in both yards ? (Picture.) 
 
 6. In a flock of 17 sheep 6 sheep are black. How 
 many are white ? 
 
 7. Frank paid 17 cents for a top and sold it for 
 8 cents. How much did he lose ? 
 
 8. A lady bought a book for $17 and paid $9. 
 How much did she still owe ? 
 
 9. 16- 1 15+ 1 lof 16 
 
 10. 1x16 16-15 iof!6 
 
 11. 16-f- 8 16- 1 lof 15 
 
 12. 16 x 1 14+2 lof 15 
 
 13. 4x4 16-14 11+ 5 
 
 14. 16- 4 2 + 14 10+ 6 
 
 15. 2x 8 13+3 16-9 
 
 16. 16-2 13-13 16-0 
 
 17. 8x2 12+ 4 4 + 12 
 
 18. Count to 16 by 2's; by 4's. 
 
 19. Make problems for 16 - 4, 1 of 16, 16 * 8. 
 
PRIMARY ARITHMETIC 59 
 
 43. 1. May is 10 years old ; John is 9 years older. 
 How old is John ? 
 
 2. May had 6 cents, Lucy had 8 cents, Ella had 
 5 cents. How much had they all ? 
 
 3. A pole was 19 feet long. I cut off 6 ft. at one 
 time and 10 ft. at another time. How many feet were 
 cut off and how many were left ? (Picture.) 
 
 4. From nineteen take nine. 
 
 5. I spent $4 for books, $ 10 for a case, and had 
 $ 5 left. How much had I at first ? 
 
 6. 19 children were at school and 7 of them went 
 home. How many are left ? 
 
 7. Jane had 9 roses ; her sister had 4 more. How 
 many must they pick to have 19 roses in all? 
 
 8. 
 
 5+ ? = 14 
 
 ?x6 = 
 
 18 
 
 | of 18 = ? 
 
 9. 
 
 16-8= ? 
 
 ?-9 = 
 
 6 
 
 1 of 16 = ? 
 
 10. 
 
 14-5= ? 
 
 12- ? = 
 
 5 
 
 1 of 18 = ? 
 
 11. 
 
 7+ ? = 13 
 
 17- ? = 
 
 8 
 
 6 is 1 of ? 
 
 12. 
 
 16 + 2= ? 
 
 ? + 2 = 
 
 8 
 
 4 is i of ? 
 
 13. 
 
 5x4 
 
 20-3 
 
 
 lof 20 
 
 14. 
 
 20-e-5 
 
 16 + 4 
 
 
 fofl5 
 
 15. 
 
 Add 16 18 
 
 17 15 
 
 8 
 
 452 
 
 
 4 2 
 
 3 5 
 
 12 
 
 14 12 13 
 
 16. 5)20 4)20 2)16 9)18 3)15 4)12 
 
 44. 1. Take 3x4 from 2x9. 
 
 2. If my newspaper comes twice a week, how many 
 papers will I get in 8 weeks ? 
 
60 PRIMARY ARITHMETIC 
 
 3. A boy had 18 apples. He gave away l of them 
 and lost 3. How many had he left? 
 
 4. 7 is J of ? 12 is twice what ? 
 
 5. 4 is J of ? 18 is three times what ? 
 
 6. A hen had a dozen chickens. Six were black 
 and the rest were white. How many were white ? 
 
 7. How many thumbs have four pair of mittens ? 
 
 8. Count to 18 by 3'a. 
 
 9. A ten-cent piece and a two-cent piece will buy 
 how many marbles at 4 cents each ? 
 
 10. 13 birds were on a tree and 7 flew away. How 
 many remained ? 
 
 11. Nellie had 19 apples and gave away 4 of them 
 and ate 1. How many had she left ? 
 
 12. How many twos in 20 ? 
 
 13. 2x8- ? = 4 16. i of 20 = 5x? 
 
 14. 18 = 3x5 + ? 17. 7x2 + 3 = ? 
 
 15. 4x2x2= ? 
 
 45. DRILL EXERCISE 
 
 1. iof 20= ? 3 x 4 = ? 
 
 z 
 
 2. i of ? = 3 7 + 11 = ? 
 
 o 
 
 3. 5x 3 + 2 = ? |of!8 = ?' 
 
 4. iof 14= ? |ofl8 = ? 
 
 5. iof ? = 8 19- 7 = ? 
 
 6 . 20- iof 14 = ? 20*10 = ? 
 
PRIMARY ARITHMETIC 61 
 
 7. 
 
 Add 8 (8) 7 (9) 6 (10) 2 (11) 7 (12) 9 
 3454 2 9 
 5576 5 1 
 
 
 4 4 
 
 1862 
 
 13. 
 
 From 20 take 11, 
 
 4, 6, 12, 9, 8. 
 
 
 14. 
 
 1 of 16 = ? t 
 
 L of 18 = ? 1 
 
 of 18 = ? 
 
 15. 
 
 Iofl2 = ? j 
 
 Lofl2 = ? 1 
 
 of 15 = ? 
 
 16. 
 
 To 7 add 4, 12, 8, 
 
 9, 3, 5. 
 
 
 17. 
 
 2)20 9)18 
 
 2)16 3)15 
 
 4)16 
 
 18. 
 
 Divide 50, 60, 70, 
 
 80, 90 each by 
 
 10. 
 
 19. 
 
 5 in 15, 20, 10, 5, 
 
 0. 
 
 
 20. 
 
 20- 1 
 
 19+ 1 
 
 16+4 
 
 21. 
 
 1x20 
 
 20- 1 
 
 20-16 
 
 22. 
 
 20-20 
 
 1 + 19 
 
 4 + 16 
 
 23. 
 
 20 x 1 
 
 20-19 
 
 20-4 
 
 24. 
 
 2x10 
 
 18+ 2 
 
 15+ 5 
 
 25. 
 
 20- 2 
 
 20-18 
 
 20-15 
 
 26. 
 
 29-10 
 
 20-2 
 
 5 + 15 
 
 46. 1. Find the cost of 8 pair of shoes at $3 a pair. 
 
 2. If a man earns $12 a week, how much can he 
 earn in 2 weeks ? 
 
 3. How many eggs in 2 dozen? 
 
 4. How many two-quart pitchers will 24 quarts of 
 water fill ? 
 
 5. How many threes in 2 dozen ? 
 
62 
 
 PRIMARY ARITHMETIC 
 
 6. What number is J of 24 ? 
 
 7. Find the cost of 6 books at $4 each. 
 
 8. A lady bought a dozen eggs, l of them were 
 bad. How many were good ? 
 
 9. My square table is 6 feet on a side. How many 
 feet of fringe will it take to go around it ? (Picture.) 
 
 10. Bought 6 lemons for 24 cents. What did one 
 lemon cost ? 
 
 11. Two weeks and 10 days are how many days? 
 
 12. How many feet have 3 cats and 3 rats ? 
 
 13. What four numbers added together make 21 ? 
 
 14. iof!2ct. = ? lof $12 = ? ^of 18 = ? 
 15.^7)21 6)18 3)15 4)16 ' 3)21 8)16 
 
 16. 
 
 8 
 
 7 
 
 62487 
 
 9 8 
 
 
 x2 
 
 x3 
 
 x3 x9 x4 +5 x3 
 
 + 7 +6 
 
 17. 
 
 17 
 
 18 
 
 14 17 15 
 
 7 9 
 
 
 -6 
 
 -9 
 
 -2 -6 -2 
 
 x3 +4 
 
 18. 
 
 i<* 
 
 20 = ? 
 
 lof 15 = ? 
 
 lof 15 = ? 
 
 19. 
 
 i of 
 
 18 = ? 
 
 lof 20 = ? 
 
 lof 21 = ? 
 
 20. What three equal numbers in 21 ? 
 
 21. What seven equal numbers in 21 ? 
 
 47. 1. 5x5 = ? 
 
 2. 25 + 5 = 
 
 3. of25 
 
 Add 4, 5, 3, 5, 5. 
 6+4+5+6+1=? 
 
99 TM* 
 
 UNIVERSITY 
 
 PRIMARY 
 5 6 
 
 5. 18 + ? = 25 3x8 = ? 5x3 = ? 
 
 6. 25^-5 = ? 24-^8 = ? 
 
 7. Harry bought a knife for 15 cents and sold it for 
 25 cents. What did he gain? 
 
 8. There are 25 apples in a basket. I take | of 
 them. How many do I take ? How* many are left ? 
 
 9. How many 3-cent pieces in 27 cents ? 
 
 10. How many nickels in a quarter ? 
 
 11. How many cents in-nine nickels? 
 
 12. Give 3 cents to each of nine children. How 
 much do all get ? 
 
 13. John bought 3 dozen buttons at 9 cents a dozen. 
 How much did they cost ? 
 
 14. If 9 books cost $27, what does one book cost? 
 
 15. How many 9's in 27 ? 
 
 16. There are 3 feet in a yard. How many yards in 
 27 feet ? (Picture.) 
 
 48. 1. A table has four sides; each side is 7 feet 
 long. How many feet around the table ? (Picture.) 
 
 2. 7 oranges cost 28 cents. What is the cost of 
 one orange ? 
 
 3. What will 4 books cost at 7 cents each ? 
 
 4. 7 pair of oxen have how many horns ? 
 
 5. If there are 4 trees in a row, how many trees in 
 7 rows ? (Picture.) 
 
 6. What three equal numbers make twenty-four? 
 
64 PRIMARY ARITHMETIC 
 
 7. What month, has 28 days ? When does it have 
 29 days ? 
 
 8. If I make $ 4 in selling a stove, how many stoves 
 must I sell to make $ 28 ? 
 
 9. How many school days in 6 weeks ? 
 
 10. Into what three equal numbers can 30 be 
 divided ? 
 
 11. A milkman had five six-quart cans of milk. How 
 much milk had he ? 
 
 12. How many 5's in 3 x 10 ? 
 
 13. $10 is ^ of how much money ? 
 
 14. How many two-cent stamps can I buy for 30 
 cents ? 
 
 15. What piece of money is l of 30 cents ? 
 
 16. John has 30 cents, and Mary has |- as much. 
 How much has Mary? 
 
 17. If 8 pencils cost 32 cents, what does 1 pencil 
 cost ? What will 7 pencils cost ? 
 
 18. If 32 cents are divided equally among 8 chil- 
 dren, how many cents will each receive ? 
 
 19. What will 8 pounds of rice cost at 4 cents a 
 pound ? 
 
 
 
 49. 1. How many 8's in 35, and how many over? 
 
 2. In 36 feet how many yards ? (Picture.) 
 
 3. How many boys will it take for 4 baseball 
 nines ? (Picture ball ground.) 
 
 4. How many months in 3 years ? 
 
 5. What cost 9 lemons at 36 cents a dozen? 
 
PRIMARY ARITHMETIC 65 
 
 6. A man earns $9 a week. How much does he 
 earn in 4 weeks ? 
 
 7. How many 4-dollar chairs can be bought for $ 36 ? 
 
 8. How many eggs in 3 dozen ? 
 
 9. Three boys earned 36 cents. How much was that 
 for each one ? 
 
 10. What two equal pieces of money make - of 36 
 cents ? 
 
 11. 5x 7 = ? of 35 7x ? = 35 
 
 12. 35- 5 = ? | of 28 6x ? = 30 
 
 13. 35-*- 7 = ? J-of24 8+ ? = 30 
 
 14. 4 + 6 + 9 + 6 + 3 = ? 17. 6 + 8 + 9 + 7 + 5 = ? 
 
 15. 7 + 4 + 3 + 7 + 2 = ? 18. 2 + 7 + 6 + 4 + 6 = ? 
 
 16. 9 + 3 + 6 + 2 + 9 = ? 19. 7 + 7 + 7 + 7 + 7 = ? 
 
 20. Make seven rows of squares with five squares in 
 a row. How many squares ? How many angles have 
 ^ of these squares ? 
 
 21. lofl6 Jof39 16 -s- 8 
 
 22. Jof32 Jof40 14-s- 2 
 
 23. iof27 Iof36 28-14 38-18 
 
 24. iof32 T 1 oof40 36-18 
 
 25. | of 21 | of 25 27^- 9 36-20 
 
 50. 1. In 16 dimes how many cents, and how many 
 over? 
 
 2. A father gave to one of his sons 30 cents, to 
 another 14 cents, and to his daughter 2 cents. How 
 much did he give them in all ? 
 
 
66 PRIMARY ARITHMETIC 
 
 3. I bought a stove for $ 40 and a table for 1 as 
 much. How much did both cost ? 
 
 4. Count from 3 to 45 and back by sixes. 
 
 5. Find the sum of 7 times 4 and 4 times 2. 
 
 6. Add 3 (7) 9 (8) 9 (9) 6 (10) 4 (11) 6 
 
 5 
 
 4 
 
 8 
 
 11 
 
 6 
 
 5 
 
 10 
 
 6 
 
 7 
 
 9 
 
 9 
 
 11 
 
 11 
 
 3 
 
 6 
 
 3 
 
 6 
 
 5 
 
 5 
 
 2 
 
 5 
 
 8 
 
 4 
 
 9 
 
 7 
 
 1 
 
 4 
 
 7 
 
 5 
 
 9 
 
 12. Multiply 578694756 
 
 9647387 10 6 
 
 13. 36 is how many times 6 ? 
 
 14. 45 is 9 times what number ? 
 
 15. 45-9 + 3 = ? 
 
 16. 45-15 + 10 = ? 49-7 = ? 
 
 17. of45 5x8 20. * of 42 
 
 18. i of 45 7 x 6 21. 1 of 48 
 
 19. .Jof44 
 
 51. 1. How many cents in 6 dimes ? 
 
 2. How many school days in 8 weeks ? 
 
 3. How many working days in 5 weeks ? 
 
 4. In 48 eggs how many dozen ? 
 
 5. A lady bought a shawl for $30 and a dress for 
 as much. What did both cost ? 
 
PRIMARY ARITHMETIC 67 
 
 6. If I buy some cloth for $44 and sell it at a loss 
 of $13, what do I get for it ? 
 
 7. If a pound of candy costs 12 cents, what will 
 4 pounds cost ? 
 
 8. How many nickels in $ .45 ? 
 
 NOTE. Teach how to indicate cents by means of the decimal 
 point and dollar sign. 
 
 9. If 4 quarts of vinegar can be bought for 28 
 cents, how many quarts can be bought for 49 cents ? 
 
 10. Mr. Smith gave $50 to his five boys. How 
 much did each get ? 
 
 11. lof $.40 3x$.09 
 
 12. i-of$.42 4x$.ll 
 
 13. i of $ .49 8 x $ .06 
 
 14. 1 of $ .48 4 x $ .12 
 
 15. of$.45 
 
 16. 1 of $.48 5x$.ll 4x8 + 6 
 
 17. 45- ? = 9 ?x 6 = 48 
 
 18. 49-f-7=? ? + 15 = 45 
 
 19. From 9x5 take 7x6. 
 
 20. How many days does a man work in nine weeks ? 
 
 21. A load of potatoes had 54 bushels. I bought ^ 
 of the load. How many bushels have I ? 
 
 22. How many hats can a man buy for $54 if 4 hats 
 cost $ 24 ? 
 
 52. 1. If 8 bars of soap cost $.56, what is the cost 
 of one bar ? 
 
68 PRIMARY ARITHMETIC 
 
 2. What is the cost of 9 Ib. of sugar at 6 ct. a 
 pound ? 
 
 3. Willie has 20 marbles, James 20, and John 10. 
 How many have all ? 
 
 4. May had $.59. She spent 10 cents for paper. 
 How much had she left ? 
 
 5. Into how many lots of 7 acres each can a 56-acre 
 lot be divided ? 
 
 6. How many days in 6 weeks ? 
 
 7. How many eggs in 4 dozen ? 
 
 8. If I owe $.58 and pay all but 10 cents, how 
 much have I paid ? 
 
 9. Max bought a knife for 41 cents and sold it so 
 as to gain 10 cents. What did he sell it for ? 
 
 10. 
 
 11. 
 
 10 + 1 
 
 10 + 2 
 
 10 + 3 
 
 10 + 4 
 
 20 + 1 
 
 20 + 2 
 
 20 + 3 
 
 20 + 4 
 
 30 + 1 
 
 30 + 2 
 
 30 + 3 
 
 30 + 4 
 
 40 + 1 
 
 40 + 2 
 
 40 + 3 
 
 40 + 4 
 
 50 + 1 
 
 50 + 2 
 
 50 + 3 
 
 50 + 4' 
 
 10-2 
 
 10-3 
 
 10-4 
 
 HMtf 
 
 20-2 
 
 20-3 
 
 20-4 
 
 20-5 
 
 30-2 
 
 30-3 
 
 30-4 
 
 30 T. 5 
 
 40-2 
 
 40-3 
 
 40-4 
 
 40-5 
 
 50-2 
 
 50-3 
 
 50-4 
 
 50-5 
 
 12. Count to 55 by fives. 
 
 53. 1. In a garden are 48 plants in 6 equal rows. 
 How many plants in each row? 
 
PRIMARY ARITHMETIC 69 
 
 2. How many weeks must a man work to earn 
 if he earns $ 12 a week ? 
 
 3. A boy paid $ .40 for a knife and $ .15 for a slate. 
 What was the cost of both ? 
 
 4. From a piece of calico containing 58 yards I cut 
 18 yards. How many yards were left ? 
 
 5. If I earn $ .09 a day for a week, how much have 
 I earned ? 
 
 6. At 8 cents each, what will 7 cocoanuts cost? 
 
 7. John lives 10 blocks east of the school, and 
 William 15 blocks west. How far does John live from 
 William ? (Illustrate.) 
 
 8. If a ship sails 63 miles in 9 hours, how far will 
 she sail in 1 hour? 
 
 9. 
 
 11- 
 
 K4 
 
 11 
 
 -4 
 
 12 
 
 -5 
 
 12 H 
 
 h5 
 
 10. 
 
 21- 
 
 h4 
 
 21 
 
 -4 
 
 22 
 
 -5 
 
 22 H 
 
 h5 
 
 11. 
 
 31- 
 
 \-4: 
 
 31 
 
 -4 
 
 32 
 
 -5 
 
 32 H 
 
 h5 
 
 12. 
 -"13. 
 
 41- 
 51- 
 
 1-4 
 h4 
 
 41 
 51 
 
 -4 
 -4 
 
 42 
 52 
 
 -5 
 
 -5 
 
 42 H 
 52 H 
 
 h5 
 -5 
 
 /i4. Count to 60 by 5's ; by 3's ; by 2's. 
 
 15. 9x5 8x4 7x5 9x7 
 
 ]. 9x4 8x6 6x7 7x7 
 
 17. 9x6 8x5 7x8 6x6 
 
 18. 9x3 8x8 7x4 11 x 4 
 
 54. 1. How many dimes in 60 cents ? 
 
 2. Bought 9 lamps at 4 dollars apiece, and sold 
 them at 7 dollars apiece. How much did I gain ? 
 
70 PRIMARY ARITHMETIC 
 
 3. What cost 2 oranges at 60 cents a dozen ? 
 
 4. In one field there were 20 cows ; in another 
 twice as many. How many in the second field ? How 
 many in both fields ? 
 
 5. If 4 apples cost 12 cents, how much will 9 apples 
 cost? 
 
 6. What 7 equal numbers make 56 ? 
 
 7. If 8 bars of soap cost $.56, what is the cost 
 of one bar? 
 
 &. What is the cost of 9 pounds of sugar. at 6 cents 
 a pound ? 
 
 9. Willie has 20 marbles, James 20, and John 10. 
 How many have all ? 
 
 16. 
 
 13 
 
 + 5 
 
 13- 
 
 6 
 
 
 14 
 
 + 
 
 7 
 
 
 14- 
 
 -7 
 
 li. 
 
 23 
 
 + 5 
 
 23- 
 
 6 
 
 
 24 
 
 + 
 
 7 
 
 
 24- 
 
 -7 
 
 12. 
 
 33 
 
 + 5 
 
 33- 
 
 6 
 
 
 34 
 
 + 
 
 7 
 
 
 34- 
 
 -7 
 
 13. 
 
 43 
 
 + 5 
 
 43- 
 
 6 
 
 
 44 
 
 + 
 
 7 
 
 
 44- 
 
 -7 
 
 14. 
 
 53 
 
 + 5 
 
 53- 
 
 6 
 
 
 54 
 
 + 
 
 7 
 
 
 54- 
 
 -7 
 
 15. 
 
 Add 6, 
 
 9, 8, 7, 3, 4 
 
 , 2, 15, 4. 
 
 16. 
 
 Add 8 
 
 (17) 6 
 
 (18) 
 
 12 
 
 (19) 
 
 10 
 
 (20) 
 
 4 
 
 
 
 12 
 
 8 
 
 
 2 
 
 
 
 
 5 
 
 
 6 
 
 
 
 10 
 
 4 
 
 
 8 
 
 
 
 
 4 
 
 
 10 
 
 
 
 8 
 
 9 
 
 
 11 
 
 
 
 
 6 
 
 
 
 5 
 
 
 
 9 
 
 12 
 
 
 9 
 
 
 
 
 1 
 
 
 5 
 
 55. 1. How many spools of thread at 4 cents a spool 
 can you buy for 36 cents ? 
 
 2. In an orchard are 8 rows of trees with 9 trees in 
 each row. How many trees in the orchard ? 
 
PRIMARY ARITHMETIC 71 
 
 3. I have five 10-pound jars of butter, and sell it 
 all at a profit of 6 cents a pound. What do I make ? 
 
 4. How many pounds of steak at 8 cents a pound 
 can I buy for 32 cents ? 
 
 5! If 60 cents be paid for thread at 4 cents a spool, 
 how many spools are bought ? 
 
 6. Count from 6 to 61 and back by fives. 
 
 7. Count from 8 to 62 and back by 6's. 
 
 . How many suits of clothes can be made from 63 
 yards of cloth, if one suit takes 7 yards ? 
 
 9, A wagon cost $ 64, a harness ^ as much. What 
 did both cost ? 
 
 1ft. At $ 12 a week, how much will a man earn in 5 
 weeks ? 
 
 11* If a pair of boots cost $ 6, what will be the cost 
 of 5 pair ? 7 pair ? 9 pair ? 
 
 12. If a boy can ride a bicycle 6 miles in 6 hours, 
 how far can he go in an hour ? 
 
 18. At 7 cents a pound, how many pounds of sugar 
 can I buy for 63 cents ? 
 
 14. Count from 5 to 69 and back by fours. 
 
 15. Count from 28 to 72 and back by 4's. 
 
 16. 9 times .4; 6 ; 3 ; 2 ; 9 ; 8 ; 7; 10 ; 11 ; 12. 
 IT^Count by nines to 108. 
 
 ir^J + 7 
 
 11-7 
 
 12 + 7 
 
 12-7 
 
 le. 21 + 7 
 
 21-7 
 
 22 + 7 
 
 22-7 
 
 0. 31 + 7 
 21. 41 + 7 
 
 31-7 
 41-7 
 
 32 + 7 
 42 + 7 
 
 32-7 
 
 42-7 
 
72 PRIMARY ARITHMETIC 
 
 56. 1: How many 5-cent pieces in 50 cents? 
 2. How many eggs in 6 dozen ? 
 3>. What must I pay for 7 pencils at 4 cents each? 
 
 4. If 3 girls can do a piece of work in 6 days, in 
 how many days can one girl do it ? 
 
 5. If 5 cents is J of my money, how much money 
 have I ? 
 
 6. How many months in 6 years ? 
 
 7. How many boots in 1 dozen pair ? 
 
 8. How many are 6 dozen oranges less 8 oranges ? 
 
 9. What four pieces of money make 75 cents ? 
 
 10. In 72 books how many dozen ? 
 
 11. If it takes 9 yards of calico for one dress, what 
 will it take for 8 dresses ? 
 
 12". 9x 8 
 
 12x6 
 
 63+ 7 
 
 70-40 
 
 13. 4x5 
 
 72 + 9 
 
 15 + 15 
 
 75 -,25 
 
 14. 3x12 
 
 64 + 8 
 
 12 + 20 
 
 36-20 
 
 15. 8x 8 
 
 7x9 
 
 18 + 10 
 
 50-25 
 
 16-. Count from 7 to 73 and back by sixes. 
 17. Count from 8 to 78 and back by sevens. 
 
 18. 
 
 11 + 9 ' 
 
 11 
 
 -9 
 
 13 
 
 + 8 
 
 13 
 
 -8 
 
 
 
 
 
 
 
 
 i 
 
 
 19. 
 
 21 H 
 
 h9 
 
 21 
 
 -9 
 
 23 
 
 + 8 
 
 23 
 
 -8 
 
 20. 
 
 31 H 
 
 h9 
 
 31 
 
 -9 
 
 33 
 
 + 8 
 
 33 
 
 -8 
 
 2J-. 
 
 41 H 
 
 h9 
 
 41 
 
 -9 
 
 43 
 
 + 8 
 
 43 
 
 -8 
 
 22. 
 
 51- 
 
 h9 
 
 51 
 
 -9 
 
 53 
 
 + 8 
 
 53 
 
 -8 
 
 l 
 
 
 
 
 
 
 
 
 
 23. 
 
 i 
 
 61- 
 
 h9 
 
 61 
 
 -9 
 
 63 
 
 + 8 
 
 63 
 
 -8 
 
PRIMARY ARITHMETIC 73 
 
 57. 1. How many dimes in 70 cents? 
 
 2. Twenty-eight horseshoes will shoe how many 
 
 horses ? 
 
 i 
 
 3. In our class there are seven children in each 
 row. How many children in 8 rows ? 
 
 4. Will had 35 papers, and Harry had twice as 
 many. How many had Harry ? 
 
 5. At 4 dollars a day, how much does a man. .earn 
 in 2 weeks ? 
 
 d. If I have $ 8 in quarters, how many quarters 
 have I ? * 
 
 fi t 7. How many legs have a dozen flies ? 
 
 $. At 7 cents each, how many tablets can I buy for 
 84 cents? 
 
 9. John had eighty-four apples. How many dozen 
 did he have ? 
 
 10. If 1 dozen oranges cost 48 cents, what does 1 
 orange cost? 
 
 1}. 12 + 8 + 6+9 + 4 + 5 + 3 + 2-? 
 12. 8 + 9 + 10 + 6 + 5 + 6+4 + 3 = ? 
 1^. 3x3x3x3 = ? 2x2x2x2x2x2 = ? 
 
 14. 
 
 2H 
 
 h9 
 
 52 
 
 + 9 
 
 52 
 
 -9 
 
 6H 
 
 -5 
 
 1. 
 
 12 H 
 
 h9 
 
 62 
 
 + 9 
 
 42 
 
 -9 
 
 16 H 
 
 -5 
 
 
 
 
 
 
 
 
 
 I 
 
 l. 
 
 22- 
 
 h9 
 
 72 
 
 + 9 
 
 ' 32 
 
 -9 
 
 26 H 
 
 ^5 
 
 iV. 
 
 32- 
 
 h9 
 
 72 
 
 -9 
 
 22 
 
 _ 9 
 
 36 H 
 
 -5' 
 
 18. 
 
 42- 
 
 (-9 
 
 62 
 
 -9 
 
 12 
 
 -9 
 
 46 H 
 
 (-5 
 
74 PRIMARY ARITHMETIC 
 
 58. 1. How many school weeks in 40 days? 
 
 2. How much sugar at $ .08 a pound can I buy for 
 $.72? 
 
 3. Emma is 9 years old ; her father is five times as 
 old. What is her father's age ? 
 
 4. If you earn 12 cents in a week, how much do 
 you earn in a month ? 
 
 5. How many quarts of oil do we use in 12 weeks 
 if we use 1 quart each day ? 
 
 6. There are 7 days in a week. How many days 
 in 3 weeks and 5 days ? 
 
 7. Ned has J of 27 cents. George has ^ of 28 cents. 
 How many cents have both ? 
 
 8. Eight chairs cost $32. How much apiece do 
 they cost ? 
 
 9. There are 12 things in a dozen. 4x9 are how 
 many dozen ? 
 
 10. Seven apples cut into quarters make how many 
 quarters ? 
 
 11. A lady had 32 apples. She gave 5 boys 6 apples 
 apiece. How many had she left ? 
 
 12. 
 
 72 
 
 + 
 
 6+1 
 
 ' = 20 
 
 100 + 
 
 10- 
 
 ?= 1 
 
 
 
 13. 
 
 7 
 
 X 
 
 9 
 
 100- 
 
 4 
 
 19 + 
 
 8 
 
 19- 
 
 8 
 
 14. 
 
 100 
 
 X 
 
 5 
 
 96 + 
 
 12 
 
 29 + 
 
 8 
 
 29- 
 
 8 
 
 15. 
 
 18 
 
 X 
 
 4 
 
 72 + 
 
 12 
 
 39 + 
 
 8 
 
 39- 
 
 8 
 
 16. 
 
 16 
 
 X 
 
 5 
 
 88 + 
 
 11 
 
 49 + 
 
 8 
 
 49- 
 
 8 
 
 17. 
 
 14 
 
 X 
 
 5 
 
 72 + 
 
 9 
 
 59 + 
 
 8 
 
 59- 
 
 8 
 
2 
 
 CQ 
 
 Pu 
 
 
 
 s, 
 
PART SECOND 
 
 NOTATION AND NUMERATION 
 
 1. That which tells how many is Number. As, 11, 12 
 books, 15 cents. 
 
 2. One is a Unit. As, 1, 1 dollar, 1 horse. 
 
 3. Every number is made up of units. Three contains 3 
 units. Twenty contains 20 units. Fifty trees contains 50 
 units. 
 
 4. Writing numbers is Notation. As, 7, VII, seven. 
 
 5. Writing numbers in figures is Arabic Notation. As, 13. 
 
 6. In Arabic notation, ten figures are used in writing num- 
 bers. They are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. They are called 
 naught, one, two, three, four, five, six, seven, eight, nine. 
 The first figure is also sometimes called a cipher or zero. 
 
 One is written 1 
 
 Ten is written 10 
 
 One hundred is written 100 
 
 One thousand is written 1000 
 
 Ten thousand is written 10000 
 
 One hundred thousand is written . . . 100000 
 
 One million is written 1000000 
 
 Ten million is written 10000000 
 
 One hundred million is written .... 100000000 
 
 7. Read the above numbers. What would the numbers 
 be if 5 were used where 1 is ? 
 
 If 7 were used where 1 is ? If 3 were used where 1 is ? 
 
 75 
 
76 PRIMARY ARITHMETIC 
 
 How many ones are there in 10 ? 
 
 How many tens are there in 100 ? 
 
 How many hundreds are there in 1000 ? 
 
 How many thousands are there in 10,000 ? 
 
 How many ten-thousands are there in 100,000 ? 
 
 How many hundred-thousands are there in 1,000,000 ? 
 
 How many millions are there in 10,000,000 ? 
 
 How many ten-millions are there in 100,000,000? 
 
 What is the value of ? 
 
 Since has no value, what is it that has value in these 
 numbers ? 
 
 How does the value of the figure 1 in the second number 
 compare with the value of the figure 1 in the first number ? 
 
 The 1 in the third number with the 1 in the second num- 
 ber ? 
 
 The 1 in the fourth number with the 1 in the third number? 
 
 The 1 in any of these numbers with the 1 in the number 
 before it ? 
 
 The place of the 1 in any of these numbers compares how 
 with the place of the 1 in the number before it ? Answer 
 all these questions about the numbers, using 2, 3, 5, or 7 in 
 place of 1. 
 
 What must you do with the 1, 2, 3, 5, or 7 in any of these 
 numbers to get the number after it ? That would affect the 
 value of the figure how ? 
 
 What would you have to do with the 1, 2, 3, 5, or 7 in 
 any of these numbers to get the number before it ? How 
 would that affect the value of the figure ? 
 
 On what, then, does the value of a figure depend ? 
 
 For what are the ciphers used ? 
 
 8. The answers to the foregoing questions show the fol- 
 lowing : 
 
NOTATION AND NUMERATION 
 
 77 
 
 Principles of Arabic Notation 
 
 1. Each removal of a figure one place to the left 
 increases its value tenfold. 
 
 2. Each removal of a figure one place to the right 
 decreases its value tenfold. 
 
 3. The value of a figure depends upon its place in 
 the number. 
 
 4. Ciphers are used to give the other figures their 
 proper places. 
 
 1OO,OOO,OOO = ONE HUNDRED MILLION 
 
 . 10,OOO,OOO = TEN MILLION = 111 MILLION 
 
 . . 1,OOO,OOO = ONE MILLION 
 . . . 10O,OOO = ONE HUNDRED THOUSAND 
 .... 1O,OOO = TEN THOUSAND = THOUSAND 
 
 1,000 = ONE THOUSAND 
 
 100 = ONE HUNDRED 
 
 10 = TEN = HI (UNITS) 
 
 1 = ONE 
 
 111,111,111 = 111 MILLION, HI THOUSAND, HI 
 
 o 
 
 m z 
 D 
 
 3g5 
 
78 PRIMARY ARITHMETIC 
 
 Q 
 
 Q 
 
 E o 
 
 UJ CC CC Q. Q 
 
 a g 
 
 j u x 
 
 i i 1 I 
 
 h 2 Z j- 
 
 O 
 
 51 UJ 
 
 
 UJ 
 
 
 5 
 
 
 
 PLACE 
 
 
 
 < 
 
 51 u 
 
 w q 
 
 
 
 
 DRED-TRILLIONS' 
 TRILLIONS' PLAC 
 
 .LIONS' PLACE 
 
 DRED-BILLIONS' 1 
 
 BILLIONS' PLACE 
 
 IONS' PLACE 
 
 DRED-MILLIONS' 
 
 MILLIONS' PLACE 
 
 UJ 
 
 
 
 2 
 
 CO 
 
 z 
 
 
 
 DRED-THOUSAND 
 THOUSANDS' PL/! 
 
 USANDS' PLACE 
 
 DREDS' PLACE 
 
 5 
 
 5l ? 
 
 z 
 
 _i 
 
 z 
 
 Z 
 
 _i 
 
 Z 
 
 Z 
 
 _j 
 
 Z Z 
 
 
 
 Z 
 
 2 t 
 
 D UJ 
 
 E 
 
 D 
 
 
 
 
 UJ 
 
 
 D Id 
 
 I 
 
 D 
 
 
 I h 
 
 h 
 
 I 
 
 h 
 
 CO 
 
 I 
 
 h 
 
 !E 
 
 I h 
 
 h 
 
 I 
 
 h 3 
 
 695,432,741,897,654 = six hundred ninety-five 
 trillion, four hundred thirty-two billion, seven hundred 
 forty-one million, eight hundred ninety-seven thousand, 
 six hundred fifty-four. 
 
 320,105 = three hundred twenty thousand, one hundred 
 five. 
 
 907,035,700 = nine hundred seven million, thirty-five 
 thousand, seven hundred. 
 
 5,001,006 = five million, one thousand, six. 
 
 70,000,025 = seventy million, twenty-five. 
 
 13,000,000,500,000 = thirteen trillion, five hundred thou- 
 sand. 
 
 11. 1. Each figure occupies a place. How many places 
 are there in a period ? 
 
 2. Beginning at the right, name in order five periods. 
 
 3. How many figures are there in five periods ? 
 
 4. How many places are there in five periods ? 
 
 5. Name fifteen places in order, beginning at the right. 
 
NUMERATION 79 
 
 6. In reading numbers, when you come to a period com- 
 posed of three ciphers, what do you read for that period ? 
 
 7. Why is it necessary to use three ciphers in writing 
 the number ? 
 
 8. How does the name of each period compare with the 
 name of its right-hand place ? 
 
 9. Write a number containing one period. 
 
 10. Write a number containing three periods. 
 
 11. Write a number containing 12 places. How many 
 periods are there in such a number ? 
 
 NUMERATION 
 
 12. Naming the places of figures and reading numbers is 
 Numeration. Thus, to numerate 43,008,160, you should say, 
 " Units, tens, hundreds, thousands, ten-thousands, hundred- 
 thousands, millions, ten-millions forty-three million, eight 
 thousand, one hundred sixty." 
 
 13. Numerate the numbers below : 
 
 1. 385 6. 35,000,730 
 
 2. 1,421 7. 8,460,000 
 
 3. 25,678 8. 423,000,501 
 
 4. 315,129 9. 8,003,040,631 
 
 5. 6,785,342 10. 8,900,760 
 
 i 
 
 14. Write in figures : 
 
 1. Two hundred thousand, sixteen. 
 
 2. Eleven thousand, two. 
 
 3. Four million, six hundred eight thousand, three hun- 
 dred seventy-five. 
 
80 PRIMARY ARITHMETIC 
 
 4. Twenty-five thousand, three hundred eighty-seven. 
 
 5. Nineteen thousand, seventeen. 
 
 6. Twenty-seven million, six hundred fifty-two. 
 
 7. Eighty million, six hundred nine thousand, four hun- 
 dred twenty -eight. 
 
 8. Four hundred thirty -six thousand, forty-one. 
 
 9. Six hundred twenty million, seventeen thousand, four 
 hundred seventy-seven. 
 
 10. One hundred fifty-seven million, six hundred eight 
 thousand, four hundred seventy-seven. 
 
 11. Three billion, fifty-seven million, four hundred seven- 
 teen thousand sixty. 
 
 ROMAN NOTATION 
 
 15. The Roman notation, instead of using figures to 
 represent numbers, uses seven capital letters, as follows : 
 I, V, X, L, C, D, M. 
 
 Repeat the letters in the above order until you can say 
 them very rapidly. 
 
 The values of these letters are as follows : 
 
 1= i (ii = 2, 111 = 3). 
 
 V = 5 (IV = 4, VI = 6, VII = 7, VIII = 8). 
 
 X = 10 (IX = 9, XI = 11, XII = 12, XXX = 30). 
 
 L = 50 (XL = 40, LX = 60, LXXXVIII = 88). 
 
 C = 100 (XC = 90, CCC = 300, XCIX = 99). 
 
 D = 500 (CD = 400, DCCIX = 709). 
 
 M = 1000 (M ~ 1000000, MDC = 600, MXVI = 1018> 
 
ROMAN NOTATION 81 
 
 To express other numbers these same letters are combined 
 according to the following 
 
 Principles of Roman Notation 
 
 16. 1. Placing a letter after one of greater value adds 
 its value to that of the greater. 
 
 2. Placing a letter before one of greater value sub- 
 tracts its value from that of the greater. 
 
 3. Placing a letter between two letters of greater 
 value subtracts its value from their sum. 
 
 4. Repeating a letter repeats its value. 
 
 5. Placing a bar over a letter multiplies the value of 
 the letter by 1000. 
 
 ILLUSTRATIONS 
 
 17. l. X = 10, V = 5, X V = 10 + 5 = 15. Which prin- 
 ciple does this illustrate ? 
 
 2. V = 5, I = 1, I V = 5 1 = 4. Which principle does 
 this illustrate ? 
 
 3. C - 100, L = 50, X = 10, CXL = 100 + 50 - 10 = 140. 
 Which principle does this illustrate? 
 
 4. X = 10, XXX = 10 + 10 + 10 = 30. Which principle 
 does this illustrate ? 
 
 5. D = 500. D = 500000. Which principle does this 
 illustrate ? 
 
 6. CCCLX = 360. Which principle ? 
 
 7. MOM = 1900. Which principle ? 
 
 8. MDCLXVI = 1666. Which principle ? 
 
 9. Write numbers to illustrate all the principles of 
 Roman notation. 
 
 10. Express in Roman notation all numbers from 1 to 100. 
 
82 
 
 PRIMARY ARITHMETIC 
 
 18. Read : 
 
 1. XLV. 6. MCIV. 
 
 2. CDII. 7. DCCVI. 
 
 3. MI. 8. MXIX. 
 
 4. XIX. 9. DCX. 
 
 5. LXXXVI. 10. CDLI. 
 
 Write in Roman notation : 
 
 1. 284 5. 319 
 
 2. 98 6. 1,515 
 
 3. 1,013 7. 745 
 
 4. 56 8. 47 
 
 11. DCXCIV. 
 
 12. MCCV. 
 is. CCXI. 
 14. MMV. 
 is. DLXVI. 
 
 9. 2,870 
 
 10. 837 
 
 11. 1,400 
 
 12. 245 
 
 NOTATION OF FEDERAL MONEY 
 
 19. Federal Money is the money used in the United States. 
 10 mills = 1 cent. Mills are not coined. The smallest 
 coin used is the cent. Cents are written ct. or tf. 
 
 100 cents = 1 dollar, written $1. When dollars and cents 
 are written together, a period, called the decimal point, is 
 placed between them. Thus, four dollars and sixty-seven 
 cents is written $4.67. 
 
 The first two places at the right of the point are occupied 
 by cents, the third place by mills. 
 
 Nine cents four mills is written $.094. 
 Four dollars sixty-five cents three mills is written $4.653. 
 Copy and read : 
 
 1. $ 8.40 2. $16.30 3. $ 92.003 
 
 $ 17.03 $ 9. $ .105 
 
 $ 2.842 $ .087 $256.428 
 
 $200.504 $4007.91 $ 94.02 
 
 Write in figures : 
 
 1. Seventy dollars twenty-six cents. 
 
ADDITION 
 
 20. Addition is the process of uniting two or more like 
 numbers into one number. Thus, 2 and 5 are 7. 
 
 21. The numbers added are Addends. Thus, 3 and 10 are 
 13 ; 3 and 10 are the addends. 
 
 22. The result of addition is the Sum. Thus, 8 books 
 and 7 books are 15 books ; 15 is the sum. 
 
 The addends and sum are called the terms of Addition. 
 
 23. The Sign of Addition is a vertical cross placed between 
 the addends. Thus, 5 + 9 are 14. 
 
 The sign = means are or equals. Thus, 8 + 3 = 11. 
 What kind of numbers can be added ? 
 
 45599 
 2 :L ^ 5 
 
 67899 
 I i S. 5 
 67891 
 1 1 1 * J 
 67689 
 1 1 1 J[ 
 
 83 
 
 24. 
 
 Add 
 
 at sight : 
 
 
 2 
 
 6 
 
 7 
 
 3 
 
 5 
 
 3 
 
 1 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 1 
 
 3 
 
 4 
 
 4 
 
 2 
 
 3 
 
 4 
 
 5 
 
 2 
 
 3 
 
 8 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7 
 
 9 
 
 8 
 
 7 
 
84 PRIMARY ARITHMETIC 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 3 
 
 4 
 
 5 
 
 5 
 
 2 
 
 5 
 
 4 
 
 4 
 
 2 
 
 3 
 
 4 
 
 9 
 
 6 
 
 7 
 
 7 
 
 8 
 
 4 
 
 5 
 
 6 
 
 5 
 
 6 
 
 6 
 
 5 
 
 7 
 
 25. Oral. 
 
 1. Ruth had 7 cents and earned 8 cents more. How 
 many cents had she then ? 
 
 2. We had 8 books in our library and bought 10 more. 
 How many have we now ? 
 
 3. Five pupils are absent from a class and 12 are present. 
 How many pupils are there in the class ? 
 
 4. Edward had 10 cents in his bank and put in 6 more. 
 How much money has he now ? 
 
 5. There are 12 pears in one box and 10 in another. 
 How many in both boxes ? 
 
 6. Albert spent 8 cents for a ball, 4 cents for a pencil, 
 and 12 cents for a writing-book. How much did he pay 
 for all ? 
 
 7. Willard had 7 marbles in one bag and 12 in another. 
 How many had he in both bags ? 
 
 8. A boy sold a pair of skates for 20 cents, which was 
 10 cents less than they cost. What did they cost ? 
 
 9. John paid 5 cents for paper, 2 cents for pens, and 4 
 cents for pencils. How many cents did he pay? 
 
 10. Will has six marbles and Frank 11. How many have 
 both? 
 
 11. Mary bought a nine-cent ball and a twelve-cent pine- 
 apple. How much did she pay for both ? 
 
 12. Susie had 12 violets and picked 9 more. How many 
 had she then ? 
 
ADDITION 85 
 
 13. Three boys went fishing. One caught 15 fish, another 
 11, and the other 16. How many fish were caught ? 
 
 14. A boy spent 8 cents for a slate and 21 cents for a book. 
 How much did both cost ? 
 
 15. A boy had a nickel. He found a dime, and his mother 
 gave him 8 cents. How many cents did he then have ? 
 
 26. Oral. Add: 
 i. 3 2. 5 3. 4 4. 5 5. 6 6. 7 7. 3 8. 7 9. 7 
 
 268785054 
 6^82938923 
 
 10. 6+5 + 4=? 8 + 5 + 3 = ? 7 + 6+8 = ? 
 
 11. 4+6 + 3 = ? 7 + 9 + 8 = ? 5 + 5+5 = ? 
 
 12. 6+3 + 8 = ? 5 + 4 + 3 = ? 7 + 7+9 = ? 
 is, 6+6 + 8 = ? 9 + 8 + 9 = ? 6 + 5+4 = ? 
 
 14. 10+ 5 + = ? 8 + 9 + 7 = ? 7 + 1+8 = ? 
 
 15. 2 + 10 + 9 = ? 4 + 8 + 7 = ? 5 + 1 + 11 = ? 
 
 
 
 16. A grocer sold a melon for 25 cents and a basket of 
 
 grapes for 15 cents. How much did he receive for both ? 
 
 17. A boy is 7 years old. His sister is 4 years older, and 
 his father 25 years older than his sister. How old is his 
 father ? 
 
 18. Mr. A lives 10 miles east of a village, and Mr. B 17 
 miles west. How many miles from Mr. A's to Mr. B's ? 
 
 19. Mary had 15 cents, and John 25 cents. How many 
 had both ? 
 
 20. A drover bought 8 cows, 5 horses, and 10 sheep. How 
 many animals did he buy ? 
 
 21. Fred paid 10 dollars for a goat and 12 dollars for a 
 cart. How much did both cost him ? 
 
86 PRIMARY ARITHMETIC 
 
 27. 
 
 Written. 
 
 Add: 
 
 i. 3 
 
 2. 
 
 7 
 
 3. 
 
 8 4. 
 
 7 
 
 5. 
 
 6 
 
 6 
 
 . 7 
 
 7. 8 8. 
 
 3 
 
 4 
 
 
 6 
 
 
 9 
 
 4 
 
 
 
 
 
 5 
 
 5 
 
 9 
 
 5 
 
 
 4 
 
 
 2 
 
 3 
 
 
 9 
 
 
 4 
 
 7 
 
 8 
 
 9 
 
 
 3 
 
 
 5 
 
 8 
 
 
 5 
 
 
 6 
 
 6 
 
 7 
 
 In 
 
 adding 
 
 f columns like 
 
 the 
 
 1st, 
 
 say 91418 21, not 
 
 9 and 
 
 5 are 14 and 
 
 4 are 18, etc. 
 
 9. 7 
 
 10. 6 
 
 11. 
 
 4 
 
 12. 5 
 
 13. 
 
 4 
 
 14. 
 
 7 
 
 15. 8 
 
 16. 9 17. 
 
 5 
 
 5 
 
 5 
 
 
 5 
 
 9 
 
 
 3 
 
 
 5 
 
 7 
 
 7 
 
 4 
 
 3 
 
 4 
 
 
 6 
 
 8 
 
 
 9 
 
 
 6 
 
 5 
 
 6 
 
 3 
 
 
 
 9 
 
 
 
 
 6 
 
 
 2 
 
 
 2 
 
 
 
 4 
 
 9 
 
 6 
 
 3 
 
 
 8 
 
 5 
 
 
 7 
 
 
 3 
 
 7 
 
 2 
 
 8 
 
 18. 3 
 
 19. 9 
 
 20. 
 
 2 
 
 21. 8 
 
 22. 
 
 2 
 
 23. 
 
 6 
 
 24. 2 
 
 25. 3 26. 
 
 5 
 
 9 
 
 7 
 
 
 8 
 
 5 
 
 
 9 
 
 
 9 
 
 9 
 
 5 
 
 5 
 
 8 
 
 5 
 
 
 7 
 
 
 
 
 6 
 
 
 5 
 
 7 
 
 7 
 
 8 
 
 5 
 
 3 
 
 
 9 
 
 7 
 
 
 5 
 
 
 8 
 
 6 
 
 
 
 r- 
 < 
 
 7 
 
 2 
 
 
 5 
 
 4 
 
 
 8 
 
 
 7 
 
 8 
 
 8 
 
 7 
 
 4 
 
 
 
 
 7 
 
 3 
 
 
 4 
 
 
 6 
 
 4 
 
 7 
 
 6 
 
 2 
 
 4 
 
 
 2 
 
 2 
 
 
 rr 
 
 
 2 
 
 9 
 
 6 
 
 3 
 
 28. 
 
 i. 13 
 
 + 5 
 
 
 6. 13 
 
 + 6 
 
 
 11. 
 
 14 
 
 + 7 
 
 16. 14 + 
 
 8 
 
 
 2. 23 
 
 + 5 
 
 
 7. 23 
 
 + 6 
 
 
 12. 
 
 24 
 
 + 7 
 
 17. 24 + 
 
 8 
 
 
 3. 33 
 
 + 5 
 
 
 8. 33 
 
 + 6 
 
 
 13. 
 
 34 
 
 + 7 
 
 18. 34 + 
 
 8 
 
 
 4. 43 
 
 + 5 
 
 
 9. 43 
 
 + 6 
 
 
 14. 
 
 44 
 
 + 7 
 
 19. 44 + 
 
 8 
 
 
 5. 53 
 
 + 5 
 
 
 10. 53 
 
 + 6 
 
 
 15. 
 
 54 
 
 + 7 
 
 20. 54 + 
 
 8 
 
 21. A boy rode his wheel 23 miles on Monday, 10 miles on 
 Tuesday, and 5 miles on Wednesday. How many miles did 
 he ride in the three days ? 
 
 22. A farmer purchased a cow for 35 dollars, and a pig for 
 8 dollars. What was the cost of both ? 
 
ADDITION 87 
 
 23. Iii a certain school 28 pupils were present, 5 were 
 absent on account of sickness, and 4 were absent for other 
 reasons. How many pupils belonged to the school ? 
 
 24. A farmer sold 25 bushels of apples to one man, 10 to 
 another, and 8 to another. How many bushels did he sell? 
 
 25. John had 40 cents in his bank. He added 8 cents on 
 Monday, and 10 cents on Wednesday. How much money 
 had he then in his bank ? 
 
 26. A man paid for paint 56 dollars, and for labor 10 dol- 
 lars. How much did he pay for both ? 
 
 27. Bought sheep for 50 dollars, turkeys for 12 dollars, 
 and chickens for 8 dollars. How much did they cost ? 
 
 28. A man in repairing his house paid 35 dollars for lum- 
 ber, 8 dollars for paint, 2 dollars for nails, and 10 dollars for 
 labor. What was the cost of his repairs ? 
 
 29. How many fish did Mr. A catch in 4 days if he caught 
 12 the first day, 8 the second, 9 the third, and 7 the fourth ? 
 
 30. A girl spent for car fare 5 cents, for pencils 4 cents, 
 for paper 8 cents, for ribbon 10 cents, for lunch 15 cents, 
 and had 9 cents left. How much money had she at first ? 
 
 31. John has 20 marbles, Henry 4 more than John, and 
 Fred 5 more than Henry. How many marbles has Fred? 
 
 Add: 
 
 32. 
 
 42 
 
 33. 
 
 52 
 
 34. 62 
 
 35. 72 
 
 36. 
 
 82 
 
 37. 92 
 
 
 9 
 
 
 9 
 
 9 
 
 9 
 
 
 9 
 
 9 
 
 38. 34 39. 54 40. 74 41. 94 42. 44 43. 64 
 
 888888 
 
 44. 28 45. 48 46. 68 47. 38 48. 58 49. 78 
 
 777777 
 
88 PRIMARY ARITHMETIC 
 
 50. 24 51. 34 52. 54 53. 74 54. 44 55. 64 
 
 888888 
 888888 
 
 29. Written. i. Add 4150 
 
 and 5827 
 
 7 units and units are how many units ? 
 2 tens and 5 tens are how many tens ? 
 
 8 hundreds and 1 hundred are how many hundreds ? 
 
 5 thousands and 4 thousands are how many thousands ? 
 All the above work might be expressed thus : 
 
 4150 
 
 = 9977 Sum. 
 
 2. Three or more numbers may be added in the same way, 
 
 thus : 
 
 543,122 ] 
 
 12,367 
 10,200 
 
 1,100 J 
 566,789 Sum. 
 
 3. Add: 
 
 763 How should we write the addends so that 
 
 528 we may easily add units and units, tens and 
 
 659 tens, etc. ? 
 435 
 
 5 units + 9 units + 8 units -f 3 units are how many units ? 
 
 25 units make how many tens and how many units over ? 
 Put the 5 units under units' column, and add 2 to tens' 
 column. 
 
ADDITION 89 
 
 2 tens + 3 tens 4- 5 tens + 2 tens + 6 tens are how many 
 tens ? 18 tens make how many hundreds and how many 
 tens over ? 
 
 Put the 8 tens under tens' column, and add 1 to hundreds' 
 column. 1 hundred -f- 4 hundreds -f- 6 hundreds + 5 hun- 
 dreds + 7 hundreds are how many hundreds ? 23 hundreds 
 make how many thousand and how many hundreds over ? 
 
 Put 3 hundreds under hundreds' column and 2 thousands in 
 thousands' column in the sum. What would you do with 2 
 thousands if there were thousands in the addends ? 
 
 30. From the foregoing examples we may make the fol- 
 lowing 
 
 Rule for Addition 
 
 1. Write the addends so that the figures in units' 
 place in all the addends shall stand in the same column. 
 
 2. Add the figures in the right-hand column. If 
 the sum is less than ten, write it under units' column. 
 If it is ten or more, divide it by ten, write the remain- 
 der under units' column, and add the quotient with the 
 figures in tens' column. Proceed in this way till all 
 the columns have been added. 
 
 3. Whenever the sum of any column is 10 or more, 
 divide it by 10, put the remainder under the column 
 added, and add the quotient with the next column to 
 the left. 
 
 4. To add Federal Money, write the addends so that 
 all the decimal points shall stand in the same column. 
 Add the same as other numbers, and place the deci- 
 mal point in the sum under the decimal points in the 
 addends. 
 
90 PRIMARY ARITHMETIC 
 
 Proof of Addition 
 
 1. Add the numbers in a different order. If the re- 
 sults agree, the work is generally correct. Or, 
 2. Subtract the addends, one at a time, from the sum. 
 If the last result is zero, the addition is correct. 
 
 31. Add: 
 
 
 
 
 
 4. 36 5. 
 
 25 
 
 6. 96 
 
 7. 25 8. 
 
 87 9. 38 
 
 70 
 
 98 
 
 39 
 
 75 
 
 96 49 
 
 21 
 
 76 
 
 78 
 
 84 
 
 48 96 
 
 84 
 
 29 
 
 54 
 
 26 
 
 93 44 
 
 10. 28 11. 
 
 639 
 
 12. 1050 
 
 is. 126 
 
 14. 1115.85 
 
 39 
 
 874 
 
 394 
 
 149 
 
 327.15 
 
 76 
 
 596 
 
 769 
 
 1260 
 
 495.27 
 
 42 
 
 421 
 
 564 
 
 1004 
 
 160.03 
 
 89 
 
 397 
 
 285 
 
 986 
 
 598.09 
 
 73 
 
 269 
 
 784 
 
 24 
 
 784.06 
 
 15. 97 16. 
 
 857 
 
 17. 283 
 
 18. $208.40 
 
 19. $356.24 
 
 98 
 
 943 
 
 2075 
 
 32.03 
 
 35.09 
 
 79 
 
 268 
 
 298 
 
 26.. 07 
 
 2.15 
 
 68 
 
 207 
 
 963 
 
 18.94 
 
 30.05 
 
 40 
 
 976 
 
 859 
 
 236.29 
 
 5.16 
 
 87 
 
 888 
 
 876 
 
 28.15 
 
 304.29 
 
 20. 2673 
 
 21. 
 
 837 
 
 22. 628 
 
 23. 8063 
 
 846 
 
 
 2964 
 
 4307 
 
 259 
 
 1025 
 
 
 418 
 
 526 
 
 8264 
 
 92 
 
 
 3825 
 
 8279 
 
 1287 
 
 837 
 
 
 842 
 
 428 
 
 428 
 
 642 
 
 
 29. 
 
 4273 
 
 3064 
 
ADDITION 91 
 
 Add: 
 24 
 
 $26.43 
 
 25. $715.30 
 
 26. $165.00 
 
 27. $ 20.863 
 
 18.75 
 
 21.86 
 
 8.429 
 
 129.40 
 
 2.93 
 
 9.246 
 
 113.82 
 
 5208.00 
 
 4.10 
 
 10.163 
 
 6.804 
 
 .926 
 
 128.06 
 
 7.208 
 
 39.625 
 
 128.753 
 
 563.13 
 
 516.00 
 
 11.31 
 
 37.15 
 
 28.00 
 
 8.096 
 
 476.203 
 
 192.097 
 
 28. Add seventeen thousand, nine hundred six ; four 
 thousand, two hundred eighty-nine; eight hundred twelve 
 thousand, seven hundred eight ; six hundred two ; forty-two 
 thousand, nine hundred two ; twelve thousand. 
 
 29. Find the sum of eleven thousand, six hundred seven- 
 teen ; sixty-eight ; four thousand, twenty-five ; two thousand, 
 three hundred nine ; eighty-five thousand. 
 
 30. A merchant's sales were $2963.84 in January, $1463.27 
 in February, $3846.25 in March, and $2016.92 in April. 
 What did his sales amount to in the four months? 
 
 31. Find the sum of all the numbers between and includ- 
 ing 167 and 174. 
 
 32. A man had $170 in his pocket, which was $70.75 less 
 than he had in his safe. How much money had he in the 
 safe? 
 
 33. Add nine dollars six cents; fifteen dollars seventy- 
 two cents; sixty dollars eighty-seven cents; fifty-nine cents; 
 four dollars five cents ; two hundred dollars thirteen cents. 
 
 34. Add 3160, 4980, 7592, 8324, 6958. 
 
 35. Add 21563, 74321, 58026, 79532, 43984. 
 
 36. Add 32162, 19073, 76352, 698725, 49623. 
 
 37. Add 36, 512, 7198, 41960, 75, 34, 812, 916. 
 
92 PRIMARY ARITHMETIC 
 
 38. Add $5.28, $13.936, $17.84, $16.05, $28.006. 
 
 39. Add $28.75, $19.87, $16.97, $14.82, $17.64, $18.26, 
 $19.78. 
 
 40. Add 28, 97, 386, 9428, 359601, 4289, 86. 
 
 41. 69872, 594760, 653051, 21876, 394321. 
 
 42. Add 8 thousand 312 ; 25 thousand 906 ; 215 thou- 
 sand 7 hundred 8 ; 15 thousand 9 hundred 15 ; 56 thousand 
 2 hundred 74 ; 328 thousand 906. 
 
 43. Add 5 dollars 18 cents 5 mills; 28 dollars 1 cent; 
 19 dollars 24 cents 5 mills; 17 dollars 18 cents; 84 dollars 
 2 cents 9 mills ; 29 dollars 8 cents ; 328 dollars 50 cents 4 
 mills. 
 
 PROBLEMS IN ADDITION 
 
 32. l. Georgie has 18 peaches, and Donald 23 peaches. 
 How many have both? 
 
 2. In a schoolroom are 24 boys and 17 girls. How 
 many children are there in all ? 
 
 3. A farmer has 21 sheep in one pasture, 32 in another, 
 and 45 in a third. How many sheep has he in all? 
 
 4. A boy picked up 26 bushels of potatoes on Monday, 
 29 bushels on Tuesday, and 32 bushels on Wednesday. 
 How many bushels did he pick up in all ? 
 
 5. Frank paid 35 cents for a knife, 45 cents for a ham- 
 mer, and 50 cents for a saw. How much did he pay for all ? 
 
 6. Mr. Smith has 42 apple trees, 24 pear trees, 16 plum 
 trees, and 19 cherry trees. How many fruit trees has he ? 
 
 7. John picked 23 quarts of berries, Henry 19 quarts, 
 Sarah 26 quarts, and Mildred 12 quarts. How many quarts 
 did they all pick? 
 
PROBLEMS IN ADDITION 93 
 
 8. Charles lives 84 miles west of Chicago, arid William 
 49 miles east. How far apart do they live ? 
 
 9. In a yard are 56 hens, 24 ducks, 28 turkeys, and 18 
 geese. How many fowls in the yard ? 
 
 10. A lady bought eggs for 45 cents, sugar for 75 cents, 
 tea for 68 cents, and meat for 32 cents. How much did she 
 pay for all ? 
 
 11. Mary is 10 years old, Clara is 5 years older than Mary, 
 and their brother is as old as both of them together. What 
 is the sum of their ages ? 
 
 12. On one side of a street are 62 houses, and on the other 
 59 houses. How many houses are on the street? 
 
 13. If a boy is 10 minutes late at school on Monday, 8 
 minutes on Tuesday, 15 minutes on Wednesday, 7 minutes 
 on Thursday, and 12 minutes on Friday, how many minutes 
 does he lose in the week? 
 
 14. Three boys went fishing, and caught 16 perch, 19 
 pickerel, and 8 black bass. How many fish did they catch 
 in all? 
 
 15. Two trains starting from the same place run two days 
 in opposite directions. One runs 530 miles the first day and 
 525 miles the second, while the other runs 492 miles the first 
 day and 510 miles the second. How far apart are they at 
 the end of the two days ? 
 
 16. A man bought coal for $5.60, wood for $3.45, and a 
 stove for $45. What was the whole cost? 
 
 17. There are 112 bushels of wheat in one bin, 175 in 
 another, and 234 in the third. How many bushels in all? 
 
 18. There are 218 pages in my reader, 245 pages in my 
 arithmetic, and 195 pages in my geography. How many 
 pages in the three books ? 
 
 
SUBTRACTION 
 
 33. Subtraction is the process of finding the difference be- 
 tween two like numbers. Thus, 21 less 7 = 14 ; 13 ct. less 
 5 ct. = 8 ct. 
 
 34. The number from which we subtract is the Minuend. 
 Thus, 15 less 9=6; 15 is the minuend. The number sub- 
 tracted is the Subtrahend. Thus, 12 cents less 5 cents = 7 
 cents ; 5 cents is the subtrahend. 
 
 35. The result of subtraction is called the Difference or 
 Remainder. Thus, 25 miles less 15 miles = 10 miles; 10 
 miles is the difference or remainder. The minuend, subtra- 
 hend, and remainder are called the Terms of Subtraction. 
 
 The Sign of Subtraction is a short horizontal line placed 
 before the subtrahend ; thus, 12 birds 4 birds = 6 birds. 
 
 What kind of numbers can be subtracted ? How does the 
 minuend compare with the subtrahend ? With the remainder? 
 
 36. 
 
 Subtract at sight : 
 
 i. 
 
 14- 
 
 4 
 
 11. 
 
 12 
 
 -5 
 
 21. 
 
 16- 
 
 10 
 
 31. 
 
 8- 
 
 6 
 
 2. 
 
 12- 
 
 7 
 
 12. 
 
 16 
 
 -8 
 
 22. 
 
 18- 
 
 8 
 
 32. 
 
 7- 
 
 1 
 
 3. 
 
 15- 
 
 9 
 
 13. 
 
 13 
 
 -6 
 
 23. 
 
 19- 
 
 5 
 
 33. 
 
 9- 
 
 
 
 4. 
 
 17- 
 
 8 
 
 14. 
 
 11 
 
 -8 
 
 24. 
 
 7 
 
 6 
 
 34. 
 
 11- 
 
 3 
 
 5. 
 
 9- 
 
 5 
 
 15. 
 
 16 
 
 -5 
 
 25. 
 
 10- 
 
 2 
 
 35. 
 
 10- 
 
 6 
 
 6. 
 
 11- 
 
 4 
 
 16. 
 
 7 
 
 -4 
 
 26. 
 
 11- 
 
 10 
 
 36. 
 
 15- 
 
 9 
 
 7. 
 
 13- 
 
 3 
 
 17. 
 
 11 
 
 -6 
 
 27. 
 
 15- 
 
 15 
 
 37. 
 
 20- 
 
 10 
 
 8. 
 
 7- 
 
 7 
 
 18. 
 
 9 
 
 -2 
 
 28. 
 
 13- 
 
 2 
 
 38. 
 
 13- 
 
 7 
 
 9. 
 
 15- 
 
 5 
 
 19. 
 
 8 
 
 -5 
 
 29. 
 
 14- 
 
 7 
 
 39. 
 
 15- 
 
 3 
 
 10. 
 
 17- 
 
 10 
 
 20. 
 
 7 
 
 -3 
 
 30 
 
 16- 
 
 2 
 
 40. 
 
 14- 
 
 3 
 
 94 
 
 
SUBTRACTION 95 
 
 41. 
 
 7 
 
 + ? = 
 
 14 
 
 51. 
 
 15 + 
 
 ? = 20 
 
 61. 
 
 18 
 
 - 9 = 
 
 ? 
 
 42. 
 
 8 
 
 + ? = 
 
 11 
 
 52. 
 
 11 + 
 
 ? = 15 
 
 62. 
 
 13 
 
 -11 = 
 
 ? 
 
 43. 
 
 6 
 
 + ? = 
 
 15 
 
 53. 
 
 9 + 
 
 ? = 14 
 
 63. 
 
 15 
 
 -10 = 
 
 ? 
 
 44. 
 
 5 
 
 + ? = 
 
 11 
 
 54. 
 
 8 + 
 
 ? = 15 
 
 64. 
 
 17 
 
 -10 = 
 
 ? 
 
 45. 
 
 7 
 
 + ? = 
 
 16 
 
 55. 
 
 7 + 
 
 ? = 12 
 
 65. 
 
 ? 
 
 + 5 = 
 
 11 
 
 46. 
 
 8 
 
 + ? = 
 
 16 
 
 56. 
 
 8 + 
 
 ? = 11 
 
 66. 
 
 ? 
 
 + 7 = 
 
 16 
 
 47. 
 
 6 
 
 + ? = 
 
 9 
 
 57. 
 
 17- 
 
 8 = ? 
 
 67. 
 
 ? 
 
 + 5 = 
 
 16 
 
 48. 
 
 7 
 
 + ? = 
 
 15 
 
 58. 
 
 14- 
 
 5 = ? 
 
 68. 
 
 ? 
 
 + 6 = 
 
 19 
 
 49. 
 
 11 
 
 4- ? = 
 
 14 
 
 59. 
 
 17- 
 
 5 = ? 
 
 69. 
 
 ? 
 
 + 4 = 
 
 13 
 
 50. 
 
 13 
 
 + ? = 
 
 16 
 
 60. 
 
 20- 
 
 9 = ? 
 
 70. 
 
 ? 
 
 + 6 = 
 
 11 
 
 37. Oral. 
 
 1. Frank had 15 cents in his bank and took out 5 cents. 
 How many cents remained ? 
 
 2. There were 13 sparrows upon a limb, and 5 flew away. 
 How many sparrows remained on the limb ? 
 
 3. A farmer planted potatoes and corn in a field contain- 
 ing 12 acres. He planted potatoes in 7 acres. In how many 
 acres was corn planted ? 
 
 4. John had 14 marbles and gave away 6 of them. How 
 many had he left ? 
 
 5. Frank lives 12 blocks east of the schoolhouse, and 
 Henry 5 blocks east. How many blocks between Frank's 
 home and Henry's home ? 
 
 6. In a garden there are 20 rose bushes. Only 10 of 
 them bear red roses. How many bushes do not bear red 
 roses ? 
 
 7. Mary added two numbers, and her answer was 18. 
 The smaller number was 8. What was the larger ? 
 
 8. A farmer having 17 cows sold 6 of them. How many 
 remained ? 
 
 9. A clerk earns 14 dollars a week and spends 6 dollars. 
 How much does he save each week ? 
 
96 PRIMARY ARITHMETIC 
 
 10. Mary bought ribbon for 10 cents and paper for 5 cents. 
 How much had she remaining from 20 cents ? 
 
 11. From a basket containing 16 oranges, 7 were taken. 
 How many were left ? 
 
 12. James is 7 years younger than his brother, who is 15 
 years old. How old is James ? 
 
 13. If you have 19 cents and spend 10 cents, how much 
 have you left ? 
 
 14. A boy sold for 12 cents a ball that cost him 20 cents. 
 How much did he lose ? 
 
 15. How much more is 20 than 11 ? 
 
 16. Tom has 20 marbles, and Edward 11. How many has 
 Tom more than Edward ? 
 
 17. If you give 15 cents in payment for a slate worth 20 
 cents, how much do you still owe ? 
 
 18. Nell had 21 chickens, but a dog killed 10 of them. 
 How many were left ? 
 
 19. Lucy is 20 years old, and her sister 6 years younger. 
 How old is her sister ? 
 
 20. John'had $20. He spent $10 for a coat and $3 for a 
 hat. How much had he left ? 
 
 21. A pole is 19 feet long. I cut off 4 feet at one time 
 and 6 feet at another. How many feet were left ? 
 
 38. Oral. Subtract : 
 i. 38 2. 48 3. 58 4. 88 5. 68 6. 78 7. 98 
 
 7 7 JT _T_ _1_ _T_ _7 
 
 8. 13 9. 23 10. 53 11. 73 12. 83 13. 63 14. 43 
 _5 _5 _5 _5 _5 _5 _5 
 
 15. 26 16. 36 17. 56 18. 66 19. 46 20. 76 21. 96 
 
SUBTRACTION 97 
 
 22. 21 23. 31 24. 41 25. 71 26. 91 27. 51 28. 81 
 
 9999999 
 
 29. 
 
 15- 
 
 3 
 
 33. 
 
 55- 
 
 3 
 
 37. 
 
 14- 
 
 7 
 
 41. 
 
 54- 
 
 7 
 
 30. 
 
 25- 
 
 3 
 
 34. 
 
 65- 
 
 3 
 
 38< 
 
 24- 
 
 7 
 
 42. 
 
 64- 
 
 7 
 
 31. 
 
 35- 
 
 3 
 
 35. 
 
 75- 
 
 3 
 
 39. 
 
 34- 
 
 7 
 
 43. 
 
 74- 
 
 7 
 
 32. 
 
 45- 
 
 3 
 
 36. 
 
 85- 
 
 3 
 
 40. 
 
 44- 
 
 7 
 
 44. 
 
 84- 
 
 7 
 
 45. Subtract 6 from each of these numbers : 
 
 15, 25, 35, 45, 55, 65, 75, 85, 95. 
 
 46. 3 + 6 + 5 + 8-10-? 8 + 6 + 5 + 5-8-? 
 
 47. There are 45 pupils in our class. 8 are absent. How 
 man} 7 ' are present ? 
 
 48. A man earns $ 56 a month. He pays $ 7 a month for 
 rent. How much is left ? 
 
 49. 51 birds were on a tree. 7 flew away. How many 
 remained ? 
 
 50. A lady had 54 pounds of butter in a tub, and used 7 
 pounds. How many pounds remained in the tub ? 
 
 51. Mr. R. had 42 animals in a field. 5 of them were 
 horses, and the rest cows. How many were cows ? 
 
 52. Ella had 48 cents. She gave 5 to Mary and 4 to Lucy. 
 How many had she left ? 
 
 NOTE. Subtract 5 from 48, then 4 from the result. 
 
 53. Will had 53 marbles and gave 9 to Max and 8 to Fred. 
 How many had he left ? 
 
 39. 1. From 9867 
 take 4263 
 
 7 units less 3 units are how many units ? Write 4 units 
 under units' column. 
 
 6 tens 6 tens = how many tens ? Write under tens' 
 column. 
 
98 PRIMARY ARITHMETIC 
 
 8 hundreds 2 hundreds = how many hundreds ? Write 
 
 6 hundreds under hundreds' column. 
 
 9 thousands 4 thousands = how many thousands ? Write 
 5 thousands under thousands' column. 
 
 All this work may be expressed thus : 
 
 9867 Minuend. 
 -4263 Subtrahend. 
 = 5604 Remainder. 
 2. From 4285 
 take 597 
 
 From 5 units take 7 units. Can it be done ? From 8 
 tens take 1 ten and change the 1 ten to units. It equals 
 how many units? Add 10 units to 5 units- How many 
 units does it make ? From 15 units take 7 units. How 
 many units are left ? Write 8 units under units' column. 
 
 Since you have taken 1 ten from 8 tens in the minuend, 
 how many tens are left ? From 7 tens take 9 tens. Can it 
 be done ? From 2 hundreds take 1 hundred and change it 
 to tens. 1 hundred = how many tens ? Add 10 tens to 
 
 7 tens. How many tens does it make ? From 17 tens take 
 
 9 tens. How many tens are left ? Write 8 tens under 
 tens' column. 
 
 Since you have taken 1 hundred from 2 hundreds, how 
 many hundreds are left in the minuend ? From 1 hundred 
 take 5 hundreds. Can it be done ? From 4 thousands take 
 1 thousand. One thousand = how* many hundreds ? Add 
 
 10 hundreds to 1 hundred. How many hundreds does it 
 make ? From 11 hundreds take 5 hundreds. How many 
 hundreds are left ? Write 6 hundreds under hundreds' 
 column. 
 
 Since you have taken 1 thousand from 4 thousands, how 
 many thousands are left ? Write 3 thousands in thousands' 
 place in the remainder. 
 
 
SUBTRACTION 99 
 
 All this work may be expressed thus : 
 4285 Minuend. 
 
 597 Subtrahend. 
 = 3688 Remainder. 
 
 40. From the examples given above we may make the 
 following 
 
 Rule for Subtraction 
 
 1. Write the subtrahend under the minuend so that 
 units shall come under units. 
 
 2. From units take units, from. tens take tens, and 
 so on till each figure of the subtrahend has been sub- 
 tracted from the figure above it, writing the remainder, 
 every time, below the figures subtracted. 
 
 3. Whenever a figure of the minuend is less than 
 the figure of the subtrahend below it, take 1 from the 
 next figure to the left in the minuend, and add 10 to 
 the figure which is too small. Then subtract the sub- 
 trahend figure from the sum obtained. 
 
 4. To subtract Federal money, write the subtrahend 
 under the minuend so that the decimal point of the 
 subtrahend is under the decimal point of the minuends- 
 Then subtract the same as other numbers. 
 
 41. l. 12 ? = 7 ? Which terms of subtraction are given 
 in this question ? Which term are you asked to find ? How 
 do you find it ? When the minuend and remainder are given, 
 how can the subtrahend be found ? 
 
 2. ? 5 = 7 ? Which terms are given ? Which term are 
 you to find ? How do you find it ? When the subtrahend 
 and remainder are given, how can the minuend be found ? 
 
100 PRIMARY ARITHMETIC 
 
 42. The answers to these questions give us the following 
 
 Proof of Subtraction 
 
 1. Subtract the remainder from the minuend. If 
 the result is the same as the subtrahend, the subtrac- 
 tion is correct. Or, 
 
 2. Add the subtrahend and remainder. If the sum 
 is the same as the minuend, the subtraction is correct. 
 
 43. Subtract: 
 l. 2819 
 674 
 
 2. 
 
 8203 
 1276 
 
 3. 4295 
 597 
 
 4. 
 
 7306 
 
 1807 
 
 5. 
 
 2763 
 
 1289 
 
 6. 37284 
 
 9287 
 
 7. 36801 
 18463 
 
 8. 18003 
 921 
 
 9. 92874 
 11392 
 
 10. 94210 
 
 8206 
 
 13. 38264 
 
 29842 
 
 14. 19327 
 
 8291 
 
 u. $2.156 
 1.124 
 
 21. $34.28 
 24.28 
 
 18. $35.283 
 17.05 
 
 11. 42840 
 38706 
 
 is. 92593 
 
 87246 
 
 19. 25.18 
 1.155 
 
 12. 98301 
 26942 
 
 16. 27075 
 18092 
 
 20. $36.514 
 16.827 
 
 22. $39.216 
 27.134 
 
 23. $17.804 
 16.752 
 
 24. $75.005 
 24.325 
 
 25. From seventeen thousand sixteen, take nine thousand 
 four hundred eighty-seven. 
 
 26. From seventy-two thousand three hundred eleven, take 
 forty-six thousand nine hundred sixty-one. 
 
 27. Take eight thousand four, from thirty thousand. 
 
SUBTRACTION 101 
 
 28. Find the difference between sixteen thousand four 
 hundred seventy-five, and twenty thousand seven hundred 
 twenty-seven. 
 
 29. The minuend is 7026 and the subtrahend 987. Find 
 the difference. 
 
 30. Find the difference between 9284 and 13,411 
 
 31. $4216.56-11874.92 = ? 
 
 32. $149.725-169.417= ? 
 
 33. Take sixteen thousand eight hundred seventeen, from 
 twenty-four thousand five hundred forty-one. 
 
 34. The difference is 8037. The minuend is 19,406. Find 
 the subtrahend. 
 
 35. Take seventy-six dollars four "cents two mills, from 
 one hundred two dollars nine mills. 
 
 36. From sixty-five thousand three hundred sixteen, take 
 twenty-four thousand forty. 
 
 37. Take $86. 215 from $900. 09. 
 
 38. What must be added to $.67 to make $ 3 ? 
 
 39. From a farm of 263 acres of land 97 acres were sold. 
 How much was left ? 
 
 40. A man had $279, and spent $129.64. How much 
 had he left? 
 
 41. From a cask of vinegar, containing 44 gallons, 17 gal- 
 lons leaked out. How many gallons remained ? 
 
 42. From a box containing 200 oranges, 127 were sold. 
 How many oranges remained ? 
 
 43. A farmer having 250 acres of land, sold 87 acres. 
 How many acres did he have left ? 
 
 44. Two boys start together and run in the same direction. 
 How far apart are they when one has run 192 yards and the 
 other 156 yards ? 
 
 45. There were 83 sparrows on a limb, and 34 flew away. 
 How many remained ? 
 
102 PRIMARY ARITHMETIC 
 
 46. A boy having $ 2 spent $ .75 for a pair of skates. How 
 much had he left ? 
 
 47. Gene vie ve had $1, and gave Edith 37 cents. How 
 much had she left ? 
 
 48. There are 49 eggs in a basket. How many more 
 should be put in to make 144 eggs in all ? 
 
 49. John picked 40 quarts of berries, and James picked 13 
 quarts less than John. How many quarts did James pick ? 
 
 REVIEW PROBLEMS 
 ADDITION AND SUBTRACTION 
 
 44. 1. A farmer, having 456 bushels of corn, sold 84 
 bushels to one man and 135 bushels to another. How many 
 bushels did he have left ? 
 
 2. A man started to walk 112 miles in three days. He 
 walked 32 miles the first day, and 41 miles the second. How 
 far must he walk the third day to complete the journey ? 
 
 3. I bought a cow for $42, another for $48, and a third 
 for $56. For how much should I sell them to gain $28 ? 
 
 4. A lady bought sugar for 65 cents, tea for 55 cents, 
 molasses for 72 cents, butter for 84 cents, Starch for 25 cents, 
 and gave in payment a five-dollar bill. How much change 
 should she receive ? 
 
 5. John's father gave him $2.25, and his uncle gave him 
 $1.40. He earned enough besides so that he bought, with 
 the whole, a suit of clothes for $8. How much did he earn? 
 
 6. Two vessels start from points 850 miles apart, and 
 sail toward each other. How far are they apart when one 
 has sailed 246 miles and the other 352 miles ? 
 
 7. A man sold one horse for $145 and another for $182. 
 On the first he gained $ 23, and on the second $ 36. What 
 was the cost of both ? 
 
vT* * A *K 
 
 REVIEW^ PROBtgaaSITERSITY 
 
 8. A boy bought apples for $.45 amFpuaiis iU^HT.62, and 
 sold them all for $ 1.50. What was his profit ? 
 
 9. John sold 62 newspapers, Frank 48, and Henry 27 
 less than both of them. How many did Henry sell ? 
 
 10. A grocer sold butter for $45 and cheese for $62. On 
 the butter he lost $ 6 and on the cheese he gained $14. What 
 was the cost of both ? 
 
 11. In a school of 480 pupils, 13 were absent from the 
 primary department, 11 from the junior, and 9 from the 
 senior. How many were present in the whole school ? 
 
 12. A man earning $800 a year paid $208 for board, $175 
 for clothes, and $266 for other purposes. What does he 
 
 save 
 
 
 13. Mr. Clark's age, which is 50 years, is 17 years more 
 than the sum of the ages of his son and daughter. His 
 daughter is 18 years old. How old is his son ? 
 
 14. A farmer bought a barrel of flour for $6.35, sugar for 
 $2.15, coffee for $1.46, tea for $1.20, and gave in payment 
 $3.15 worth of butter and the remainder in cash. What 
 did he pay in money ? 
 
 15. The sum of 52 and 64 is how much greater than the 
 difference between 124 and 69? 
 
 16. From a flock of 320 sheep were sold at one time 76 
 and at another 112. How many remained ? 
 
 17. A man bought 148 bushels of potatoes of A, 216 
 bushels of B, 183 bushels of C, and afterwards sold all but 
 137 bushels. How many bushels did he sell ? 
 
 18. The sum of three numbers is 342. Two of the num- 
 bers are 84 and 96. What is the third number ? 
 
 19. A farmer having 215 acres of land, used 21 acres for 
 corn, 36 for oats, 29 for barley, 18 for potatoes, 52 for 
 meadow, and the rest for pasture. How many acres were 
 used for pasture ? 
 
MULTIPLICATION 
 
 45. Multiplication is finding a number which is a certain 
 number of times another number. Thus, 6 times 5 dollars 
 = 30 dollars. 
 
 46. The number multiplied is the Multiplicand. Thus, 7 
 times 9 = 63. 9 is the multiplicand. 
 
 47. The number by which we multiply is the Multiplier. 
 Thus, 12 times 7 = 84. 12 is the multiplier. 
 
 48. The result of multiplication is the Product. Thus, 6 
 times 3 feet =18 feet. 18 feet is the product. 
 
 49. The multiplicand, multiplier, and product are called 
 the Terms of Multiplication. 
 
 50. The Sign of Multiplication is an oblique cross placed 
 after the multiplicand. Thus, $12 x 6 means 6 times $12. 
 
 51. A number that is applied to some particular things or 
 objects is a Concrete Number. Thus, 10 cows, 5 books, 6 gal- 
 lons. 
 
 52. A number that is not applied to anything is an Abstract 
 Number. Thus, 10, 5, 6. 
 
 53. The product is always the same kind of a number as 
 the multiplicand. Thus, 12 pounds x 3 = 36 pounds. Both 
 the multiplicand and product are pounds. 
 
 54. The multiplier is always regarded as an abstract number. 
 
 104 
 
MULTIPLICATION 105 
 
 55. Tell products at sight : 
 
 3 
 
 4 
 
 5 
 
 9 
 
 8 
 
 4 
 
 6 
 
 5 
 
 8 
 
 6 
 
 7 
 
 8 
 
 6 
 
 5 
 
 8 
 
 8 
 
 4 
 
 3 
 
 9 
 
 5 
 
 6 
 
 3 
 
 6 
 
 7 
 
 4 
 
 
 
 7 
 
 2 
 
 6 
 
 4 
 
 7 
 
 6 
 
 6 
 
 
 
 4 
 
 10 
 
 9 
 
 3 
 
 4 
 
 10 
 
 10 
 
 11 
 
 11 
 
 12 
 
 12 
 
 8 
 
 7 
 
 10 
 
 2 
 
 7 
 
 2 
 
 7 
 
 2 
 
 7 
 
 3 
 
 5 
 
 4 
 
 5 
 
 9 
 
 7 
 
 3 
 
 4 
 
 10 
 
 8 
 
 8 
 
 5 
 
 3 
 
 9 
 
 7 
 
 5 
 
 11 
 
 3 
 
 10 
 
 11 
 
 11 
 
 12 
 
 12 
 
 9 
 
 5 
 
 4 
 
 6 
 
 8 
 
 3 
 
 8 
 
 3 
 
 8 
 
 3 
 
 9 
 
 6 
 
 4 
 
 9 
 
 3 
 
 4 
 
 10 
 
 10 
 
 11 
 
 11 
 
 12 
 
 12 
 
 10 
 
 9 
 
 12 
 
 4 
 
 9 
 
 4 
 
 9 
 
 4 
 
 9 
 
 10 
 
 10 
 
 4 
 
 6 
 
 9 
 
 4 
 
 10 
 
 10 
 
 11 
 
 3 
 
 5 
 
 7 
 
 6 
 
 10 
 
 8 
 
 5 
 
 10 
 
 5 
 
 11 
 
 11 
 
 10 
 
 12 
 
 12 
 
 8 
 
 5 
 
 8 
 
 3 
 
 10 
 
 5 
 
 11 
 
 5 
 
 10 
 
 7 
 
 9 
 
 2 
 
 7 
 
 9 
 
 3 
 
 4 
 
 8 
 
 9 
 
 5 
 
 12 
 
 4 
 
 12 
 
 12 
 
 12 
 
 7 
 
 8 
 
 9 
 
 5 
 
 12 
 
 4 
 
 11 
 
 56. 
 
 Oral. 
 
 
 
 
 
 
 
 
 1. 
 
 Multiply 
 
 these 
 
 numbers by 6. 
 
 By ; 
 
 8. By 
 
 9: 
 
 
 r , 
 
 q 4 
 
 V9 T:, 
 
 3, 
 
 8, 
 
 11, 5, 
 
 10, 
 
 12, 
 
 2, 
 
 6. 
 
 2. At 3 cents each, what will 5 oranges cost ? 
 
 3. Fred saves 8 cents a day. How much can he save in 
 9 days ? 
 
106 PRIMARY ARITHMETIC 
 
 4. At $ 5 each, what will 11 sheep cost ? 
 
 5. Eight five-cent tablets cost how much ? 
 
 6. How many trees must I plant to make a square orchard 
 with 7 trees on a side ? 
 
 7. At $4 a week, how much will a man's board bill 
 amount to in 11 weeks ? 
 
 8. There are 8 pints in a gallon. How many pints in 9 
 gallons ? 
 
 9. There are 4 pecks in a bushel. How many pecks in 6 
 bushels. 
 
 10. One horse eats 6 quarts of oats a day. How many 
 quarts will 10 horses eat in a day ? 
 
 11. What will a" dozen oranges cost at 3 cents each ? 
 
 12. A man can build 5 rods of fence in a day. How many 
 rods can he build in 12 days ? 
 
 13. Cloves cost 7 cents an ounce. What will 8 ounces 
 cost ? 
 
 14. How many quarts of water will be contained in 6 
 
 8-quart pails ? 
 i 
 
 15. On a card are 6 rows of buttons with 10 buttons in a 
 
 row. How many buttons on the card ? 
 
 16. James has 7 marbles, and Henry 6 times as many. 
 How many marbles has Henry ? 
 
 17. At 5 cents a quart, what is my milk bill for 7 days, if 
 I use 2 quarts a day ? 
 
 18. A steamer travels 12 miles an hour. How far can she 
 travel in 6 hours ? 
 
 19. There are 4 pecks in a bushel. How many pecks in 
 12 bushels ? 
 
MULTIPLICATION 107 
 
 20. John has 2 cents, Robert twice as many as John, and 
 Will 3 times as many as Robert. How many cents has 
 Will? 
 
 21. Ten mills make one cent. How many mills in 10 
 cents ? 
 
 22. At $.05 a quart, what will be the cost of 9 quarts of 
 bird seed ? 
 
 23. At 12 cents a quart, what will 10 quarts of molasses 
 cost? 
 
 57. Multiply 4127 
 by 6 
 
 6 times 7 units are how many units ? 42 units equal how 
 many tens and how many units over ? Write 2 units in 
 units' place in the product, and add the 4 tens to the product 
 of tens. 
 
 6 times 2 tens are how many tens ? 12 tens and 4 tens 
 are how many tens ? 16 tens equal how many hundreds and 
 how many tens over ? Write 6 tens in tens' place in the 
 product, and add 1 hundred to the product of hundreds. 
 
 6 times 1 hundred are how many hundreds ? 6 hundreds 
 and 1 hundred are how many hundreds ? Write 7 hundreds 
 in hundreds' place in the product. 
 
 6 times 4 thousands are how many thousands ? 24 thou- 
 sands = how many ten-thousands and how many thousands 
 over? Write 4 thousands in thousands' place and 2 ten- 
 thousands in ten-thousands' place in* the product. 
 
 The work may be expressed thus : 
 
 4127 Multiplicand, 
 x 6 Multiplier. 
 
 24762 Product. 
 
108 PRIMARY ARITHMETIC 
 
 58. Written. 
 
 Find the products : 
 
 1. 
 
 45 
 5 
 
 2. 36 
 
 4 
 
 3. 82 
 
 7 
 
 4. 63 
 
 6 
 
 5. 
 
 72 
 9 
 
 6. 84 
 5 
 
 7. 43 
 
 9 
 
 8. 35 
 
 8 
 
 9. 
 
 75 
 6 
 
 10. 98 
 
 9 
 
 11. 73 
 10 
 
 12. 68 
 11 
 
 13. 
 
 $123 
 9 
 
 14. $236 
 5 
 
 is. $384 
 
 8 
 
 16. $721 
 9 
 
 17. 
 
 1398 
 10 
 
 18. $4.32 
 5 
 
 19. $2.36 
 8 
 
 20. $3.95 
 4 
 
 21. 
 
 387 
 12 
 
 22. 792 
 
 7 
 
 23. 684 
 4 
 
 24. 199 
 
 12 
 
 25. 
 
 1306 
 5 
 
 26. 2908 
 9 
 
 27. 4908 
 6 
 
 28. 3967 
 
 7 
 
 29. 
 
 3872 
 8 
 
 so. 3963 
 11 
 
 31. 5984 
 
 7 
 
 32. 7983 
 10 
 
 33. 
 
 3161 
 11 
 
 34. 5184 
 
 9 
 
 35. 3872 
 5 
 
 36. 4560 
 
 8 
 
 Mu 
 
 Itiply these 
 
 numbers by 
 
 2, 5, 6, 9, 8, 7: 
 
 
 37. 42,608 39. 29,132 41. 18,736 43. 32,984 
 
 38. 36,975 40. 13,671 42. 28,416 44. 15,116 
 
MULTIPLICATION 109 
 
 59. 1. Write 536. In what place is the 6 ? The 3? The 5? 
 
 Annex a cipher to 536. Thus, 5360. 
 
 In 5360, what places do the 6, 3, and 5 occupy ? What 
 has been done to each figure ? 
 
 Moving a figure one place to the left affects its value how ? 
 (See principles of Arabic notation.) Since the value of each 
 figure has been multiplied by 10, what has been done to the 
 entire number ? 
 
 Since annexing a cipher to a number multiplies it by 10, 
 what would you do to multiply a number by ten ? 
 
 2. Multiply these numbers by 10 : 
 
 25, 342, 607, 4936, 8972, -400, 91. 
 
 How can you multiply a number by 100 ? By 1000 ? 
 By 10000 ? 
 
 3. Multiply the following numbers by 100, 1000, 10000 : 
 
 29, 341, 256, 9203, 4216, 899. 
 
 4. Multiply 876 by 80. 
 
 80 = 8 x 10. 876 x 80 = 876 x 8 x 10 
 First multiply 876 by 8, then by 10, thus : 
 
 876 
 
 80 How did we multiply by 10 ? 
 70080 Product. 
 
 5. Multiply 876 by 800. 
 
 800 = 8 x 100. 876 x 800 = 876 x 8 x 100, thus : 
 
 876 
 
 800 How did we multiply by 100 ? 
 700800 Product. 
 
 How could you multiply by 7000? 
 
 6. Multiply 1283 by 967. 
 
 967 = 900 + 60 + 7. 
 
110 PRIMARY ARITHMETIC 
 
 Multiply 1283 by 7, by 60, by 900, and add the three products, thus : 
 
 1283 
 
 967 
 
 8981 
 
 76980 
 
 1154700 
 
 1,240,661 Product. 
 
 The ciphers at the right of the partial products may be omitted, thus : 
 
 1283 
 967 
 8981 
 7698 
 11547 
 1,240,661 Product. 
 
 60. From the above examples we may make the following 
 
 Rule for Multiplication 
 
 1. Write the multiplier under the multiplicand. 
 
 2. Multiply the units in the multiplicand by the 
 multiplier. If this product is less than 10, write it in 
 units' place in the product. If 10 or greater than 10, 
 divide it by 10 and write the remainder in units' place 
 in the product, adding the quotient to the product of 
 the tens. Proceed in a similar way toward the left till 
 all the figures of the multiplicand have been multiplied. 
 
 3. If the multiplier contains more than one figure, 
 multiply the multiplicand by each figure of the multi- 
 plier separately, writing the first figure of each partial 
 product under the figure multiplied by, and add the 
 partial products. 
 
 4. In multiplying Federal money put the decimal 
 point in the product under the decimal point in the 
 multiplicand. 
 
MULTIPLICATION 111 
 
 61. Multiply 
 
 1. 324 x 24 12. 598 x 36 23. $36.915 x 45 
 
 2. 296 x 39 13. 287 x 49 24. $126.93 x 87 
 
 3. 387 x 45 14. 799 x 99 25. $17.856 x 48 
 
 4. 263 x 56 is. 296 x 28 26. $19.634 x 49 
 
 5. 892x63 is. 694x39 27. $75.105x97 
 
 6. 728 x 75 17. 206 x 54 28. $16.351 x 64 
 
 7. 398 x 84 is. $28.15 x 28 29. $280.52 x 36 
 
 8. 987 x 98 19. $34.98 x 27 30. $356.04 x 28 
 
 9. 516 x 31 20. $19.845 x 46 31. $987.62 x 75 
 
 10. 798 x 43 21. $7.852 x 124 32. $396.41 x 41 
 
 11. 896x79 22. $28.754x15 33. $806.04x79 
 
 62. i. 31 x 10 x 200 = ? 
 
 2. A has 172 sheep, and B 3 times as many. How many 
 has B? 
 
 3. There are 56 pounds in one bushel of salt. How 
 much will 7 bushels weigh ? 
 
 4. What will 6 acres of land cost, at $84 an acre ? 
 
 5. Find the cost of 8 bushels of potatoes at $ .45 a bushel. 
 
 6. There are 320 rods in 1 mile. How many rods in 9 
 miles ? 
 
 7. How many yards in 5 miles, there being 1760 yards 
 in one mile ? 
 
 8. At $1.75 a bushel, what will 10 bushels of walnuts 
 cost ? 
 
 9. If a train travels at the rate of 53 miles an hour, how 
 far will it travel in 11 hours ? 
 
 10. In an orchard there are 32 peach trees in a row, and 
 12 rows. How many trees in the orchard ? 
 
112 PRIMARY ARITHMETIC 
 
 11. At $2.50 a day, what will a man earn in 6 days ? 
 
 12. Find the cost of 9 yards of silk at $2.15 a yard. 
 
 13. How many pounds in 4 barrels of flour, there being 
 196 pounds in one barrel ? 
 
 14. If 1 sack of flour is worth $1.35, what must be paid 
 for 6 sacks of flour ? 
 
 15. At $5.25 a ton, what will 12 tons of coal cost ? 
 
 16. Find the cost of 10 tons of hay at $10.50 a ton. 
 
 17. There are 5280 feet in 1 mile. How many feet are 
 there in 7 miles ? 
 
 18. There are 2000 pounds in one ton. How many 
 pounds are there in 10 tons ? 
 
 19. If it costs $384 to pay the hands in a certain factory 
 for one day, what will be the amount of the weekly pay- 
 roll ? 
 
 20. What must be paid for 86 quarts of berries at 12 cents 
 a quart ? 
 
 21. The yearly expenses of a certain family are $642. 
 What are the expenses of a family using 3 times as much ? 
 
 22. If the average daily attendance at a certain school is 
 563, what is the attendance for 10 days ? 
 
 23. Mr. Smith has 174 acres of land, and his neighbor 5 
 times as much. How many acres has his neighbor ? 
 
 24. If a cord of wood costs $4.50, what will 11 cords 
 cost ? 
 
 25. There are 144 pens in 1 gross. How many pens are 
 there in 12 gross ? 
 
 26. How many pounds in 8 barrels of sugar, if each barrel 
 weighs 327 pounds ? 
 
DIVISION 
 
 63. Division is the process of finding how many times one 
 number is contained in another, or finding one of the equal 
 parts of a number. Thus, 5 cents is contained in 20 cents 
 4 times. One-fourth of 20 cents is five cents. 
 
 64. The number divided is the Dividend. The number by 
 which another number is divided is the Divisor. 
 
 65. The result of division is the Quotient. 
 
 dividend divisor quotient 
 
 Thus, 45 divided by 9 = 5. 
 
 The dividend, divisor, and quotient are called the Terms 
 of Division. 
 
 66. When the divisor is not exactly contained in the 
 dividend, the part of the dividend that is left is called the 
 remainder. Thus, 59 divided by 8 = 7 and 3 remainder. 
 
 67. The Sign of Division is a short horizontal line with a 
 dot above and a dot below it. When placed between two 
 numbers, it shows that the first is to be divided by the 
 second. Thus, 80 -* 10 = 8. 
 
 68. Division is also indicated by placing the dividend 
 above and the divisor below a horizontal line. Thus, -^ 
 means 12 -5- 3 ; or ^ means 1 -s- 3, or 1 whole thing divided 
 into 3 equal parts. 
 
 113 
 
114 PRIMARY ARITHMETIC 
 
 69. Tell quotients at sight : 
 
 4 x ? = 8 2 in 14=? ? x 2 = 12 
 
 6 x ? =18 4 in 48= ? ? x 5 = 45 
 
 7x ? =28 12in84=? ? x 6 = 30 
 
 4 x ? = 36 6 in 36 = ? ? x 4 = 36 
 
 2 x ? = 24 9 in 45 = ? ? x 8 = 40 
 
 3 x ? = 33 4 in 44 = ? ? x 7 = 63 
 
 6 x ? = 24 12 in 60 =? ? x 12 = 48 
 
 7 x ? = 56 9 in 36 =? ? x 8 = 32 
 
 4 x ? = 36 8 in 64 = ? ? x 9 = 81 
 
 120-12=? 99-9=? 120-10=? 
 
 100-10=? 66-11=? 80-8=? 
 
 90 - 9 = ? 44 - 4 = ? 108 - 9 = ? 
 
 80 - 10 = ? ' 54 - 9 = ? 48 - 4 = ? 
 
 48 - 8 = ? 84 - 12 = ? 90 - 10 = ? 
 
 63 - 7 = ? 50 - 5 = ? 72 - 12 = ? 
 
 81-9=? 54-6=? 49-7=? 
 
 72-6=? 24-8=? 25-5=? 
 
 28-7=? 24-2=? 64-8=? 
 
 35 - 7.= ? 40 - 4 = ? 60 - 5 = ? 
 
 132-11=? 22-11=? 63-7=? 
 
 108 - 12 =? 32 - 8 = ? 84 - 7 = ? 
 
 70. Oral. 
 
 1. At 12 cents each, how many books can be purchased 
 for 72 cents ? 
 
 2. How many dozen in 84 oranges ? 
 
 3. When 8 pounds of sugar cost 40 cents, what is the 
 price of a pound ? 
 
 4. Among how many boys can 45 cents be divided if 
 each boy receives 9 cents ? 
 
 5. There are 108 pencils in 108 equal packages. How 
 many pencils in each package ? 
 
LONG DIVISION 115 
 
 6. If 6 tons of hay cost 72 dollars, what will 1 ton cost ? 
 
 7. When milk is 5 cents a quart, how many quarts can 
 be purchased for 40 cents ? 
 
 8. Paid $55 for 11 tons of coal. What was the price of 
 1 ton? 
 
 9. There are 48 pecks of corn in a bin. There being 8 
 pecks in a bushel, how many bushels in a bin ? 
 
 10. There are 8 pints in a gallon. How many gallons in 
 96 pints of vinegar ? . 
 
 11. A dime is ten cents, and there are 10 dimes in a dollar. 
 How many dollars are there in 80 dimes ? 
 
 12. A laborer earns 56 dollars in 7 weeks. How much 
 does he earn in 1 week ? 
 
 13. If 11 boxes of berries sell for 77 cents, what is the 
 price of 1 box ? 
 
 14. I pay 77 cents for berries at 7 cents a box. How 
 many boxes do I purchase ? 
 
 15. Bought 9 yards of cloth for 108 cents. How much 
 did I pay for 1 yard ? 
 
 16. At 12 cents a yard, how many yards of cloth can be 
 bought for 108 cents ? 
 
 17. A boy wishes to buy a bicycle that costs 60 dollars. 
 In how many weeks can he earn money enough to pay for it 
 at $5 a week? 
 
 LONG DIVISION 
 
 71. l. Divide 4932 by 9. 
 
 Write the divisor at the left of the dividend with a line 014939 
 between, thus : 
 
 How many thousands times is 9 contained in 4 thousands? (No 
 thousand times.) 4 thousand 9 hundred make how many hundreds? 
 How many hundreds times is 9 contained in 49 hundreds? 
 
116 
 
 PRIMARY ARITHMETIC 
 
 Write 5 hundreds in the hundreds' place in the 
 quotient, thus : 
 
 5 hundred times 9 'are how many hundreds? 
 Write 45 hundreds under 49 hundreds and subtract, 
 thus : 
 
 How many hundreds over ? 
 
 Bring down three tens from the dividend, thus : 
 4 hundreds and 3 tens make how many tens? 
 How many tens times is 9 contained in 43 tens? 
 
 Write 4 tens in the quotient, thus : 
 
 4 tens times 9 are how many tens? Write 36 
 tens under 43 tens and subtract, thus : 
 How many tens over ? 
 
 Bring down 2 units from the dividend, thus : 
 
 5 Quotient. 
 9 1 4932 Dividend. 
 
 5 Quotient. 
 
 9 1 4932 Dividend. 
 
 45 
 
 4 
 
 5 Quotient. 
 
 9 1 4932 Dividend. 
 45 
 
 43 
 
 54 Quotient. 
 9)4932 Dividend. 
 45 
 
 43 
 
 54 Quotient. 
 9 1 4932 Dividend. 
 
 !5_ 
 43 
 
 36 
 
 7 
 
 54 Quotient. 
 9 1 4932 Dividend. 
 45 
 43 
 36 
 72 
 
 548 Quotient. 
 9 1 4932 Dividend. 
 45 
 43 
 36 
 72. 
 72 
 
 How many times will 72 units contain 9 ? Write 
 8 in units' place in the quotient; multiply 9 by 8 
 and write the product under 72, thus : 
 
 Subtract. How many over? What is the quo- 
 tient? 
 
 2. Divide 3553 by 17. 
 
 209 Quotient 
 
 17 1 3553 Dividend In this example, 17 is not contained any tens 
 
 34 times in 15 tens ; so we put in tens' place in the 
 
 153 quotient and bring down 3 units. 
 
 153 
 
LONG DIVISION 117 
 
 3. Divide 835,176 by 672. 
 
 1242 Quotient + 552 Remainder. 
 672 1 835176 Dividend. 
 672 
 
 In this example, the dividend does not contain 
 the divisor an exact number of times, hence there 
 9^00 is a remainder. This remainder may be written 
 
 over the divisor as part of the quotient thus: 
 
 1344 
 552 Rem. 
 
 72. From the foregoing examples, we may make the fol- 
 lowing 
 
 Rules for Long Division 
 
 1. Write the dividend at the right of the divisor 
 with a line between. 
 
 2. Beginning at the left, find how many figures of 
 the dividend are necessary to contain the divisor. 
 Divide the number represented by these figures by the 
 divisor, and write the quotient above the last figure 
 of the dividend used. 
 
 3. Multiply the divisor by the quotient just obtained, 
 and subtract that product from the partial dividend used. 
 
 4. Annex to the remainder the next figure of the 
 dividend, and use the number obtained as the next 
 partial dividend. Proceed as before and continue the 
 process until all the figures of the dividend have been 
 used. 
 
 5. In dividing Federal money, put the decimal point 
 in the quotient the same number of places from the 
 right-hand side as is the decimal point in the dividend. 
 
118 PRIMARY ARITHMETIC 
 
 73. Find the quotients : 
 
 1. 392-14 is. 5436-18 28. 1289-73 
 
 2. 1124-18 16. 1286-39 29. 16,428-84 
 
 3. 3726 -h 24 17. 2983-42 so. 12,582-58 
 
 4. 485-17 is. 1008-25 31. 1384-75 
 
 5. 793-15 19. 9436-^47 32. 6381-5-86 
 
 6. 851-27 20. 8059-36 33. 12,946-5-24 
 
 7. 507-^-16 21. 1583-46 34. 9273-91 
 
 8. 943-22 22. 4109-51 35. 7754-78 
 
 9. 1240-21 23. 2695-57 36. 10,846-^45 
 
 10. 1296^13 24. 3874-49 37. 21,431-36 
 
 11. 1364-19 25. 9003-25 38. 27,473-97 
 
 12. 3964-32 26. 5914-59 39. 35,702-53 
 
 13. 1289-16 27, 5630-62 40. 40,060-60 
 
 14. 5683-37 
 
 SHORT DIVISION 
 
 74. When the divisor is a small number, the work of divi- 
 sion may be shortened by omitting all the figures except 
 those of the dividend, divisor, and quotient, and writing 
 the quotient under, instead of over, the dividend. By this 
 method, all the processes are performed, just as in long divi- 
 sion, but are not written. 
 
 EXAMPLES 
 1. Divide 347,615 by 5. 
 
 51347615 Dividend. 
 
 69523 Quotient. 
 
SHORT DIVISION 119 
 
 2. Divide 20,076 by 12. 
 
 12 1 20076 Dividend. 
 1673 Quotient. 
 
 Every division by numbers not larger than 12 should be 
 performed by short division. 
 
 75. Written. Find the quotients-: 
 
 1. 2555-5 19. 30,005-*- 5 37. 31,493- 6 
 
 2. 2436 + 4 20. 288,012-12 38. 25,324- 5 
 
 3. 2845 -r- 5 21. 300,010 - 10 39. 28,764 - 4 
 
 36,099 - 9 
 14,412-12 
 36,930 - 11 
 24,003- 6 
 30,502 - 8 
 29,333 - 11 
 
 46. 675,262- 5 
 ,872- 8 
 
 48. 130,052- 2 
 
 13. H|JL8. 31. 82,956-10 49. 168,754- 9 
 
 14. iAjMJ. 32. 93,043- 7 so. 385,980- 5 
 is. jLLjpi 33. 65,407- 5 51. 769,520- 7 
 
 16. JUL|iMi 34 . 39,842- 9 52. 387,052-10 
 
 17. 2Ji|jy> 35. 27,391- 8 53. 943J69 - 12 
 
 18. M|Afi. 3 6 . 63,598 - 9 54. 748,131 - 4 
 
 4. 
 
 4503-f- 
 
 3 
 
 22. 
 
 99,011 - 
 
 11 
 
 40. 
 
 5. 
 
 2045- 
 
 5 
 
 23. 
 
 33,264- 
 
 11 
 
 41. 
 
 6. 
 
 2835- 
 
 7 
 
 24. 
 
 29,280 - 
 
 12 
 
 42. 
 
 7. 
 
 4986- 
 
 9 
 
 25. 
 
 36,550 - 
 
 10 
 
 43. 
 
 8. 
 
 2009- 
 
 7 
 
 26. 
 
 28,692 - 
 
 9 
 
 44. 
 
 9. 
 
 3504 - 
 
 8 
 
 27. 
 
 333,333 - 
 
 11 
 
 45. 
 
 10. 
 
 H1|JL8 
 
 
 28. 
 
 35,621 - 
 
 7 
 
 46. 
 
 11. 
 
 2_8|4_3 
 
 
 29. 
 
 42,963 ^ 
 
 6 
 
 47. 
 
 12. 
 
 .98.10 
 
 
 30. 
 
 50,725 - 
 
 3 
 
 48. 
 
 
120 PRIMARY ARITHMETIC 
 
 SPECIAL CASES IN DIVISION 
 
 76. Any number, as 34,765, may be analyzed as follows: 
 34,765 = 34,765 units; or, 3476 tens and 6 over; or, 347 
 
 hundreds and 65 over ; or, 34 thousands and 765 over ; or, 
 
 3 ten thousands and 4765 over. Therefore, 
 
 34,765 + 10 = 3476^ or 
 
 T 
 
 I9 ^ 
 
 Quotient. 
 
 3476 T % Quotient. 
 34,765 + 100 = 347^ or I9 ^ 
 
 34,765+1000 =34 T ^ or 
 
 Quotient. 
 
 34,765 +20 = Juyu + ^ or 
 
 j 5 o Quotient. 
 
 O 4 *7 f* C f A A Q A *7 R K. *J\JyJ ) OT: I yJfJ 
 
 34,765 -T- 500 = 5A1 + 65 or r ; 
 
 69|^-| Quotient. 
 
 77. Hence the 
 
 Rule for Special Cases in Division 
 
 1. To divide by 1 with any number of ciphers an- 
 nexed, cut off from the right-hand side of the dividend 
 as many figures as there are ciphers in the divisor. 
 The figures cut off will express the remainder, and the 
 figures not cut off will be the quotient. 
 
 2. To divide by any number ending in one or more 
 ciphers, cut off from the right-hand side of the dividend 
 as many figures as there are ciphers at the right side of 
 the divisor. Cut off the ciphers from the right of the 
 divisor. Divide the part of the dividend left by the 
 part of the divisor left, and prefix the remainder ob- 
 tained, if any, to the figures cut off, for a remainder to 
 the entire division. 
 
DIVISION 121 
 
 78. Find the quotients: 
 
 1. 
 
 1|OQ)369|QO 
 369 
 
 2. 1|QO)283|25 
 
 3. 
 
 1|000)36|954 
 
 4. 
 
 35,800 
 
 -r-10 
 
 10. 
 
 36,900 
 
 -100 
 
 16. 
 
 253,000 
 
 -1000 
 
 5. 
 
 78,563 
 
 -flO 
 
 11. 
 
 85,982 
 
 -100 
 
 17. 
 
 287,604 
 
 -*-1000 
 
 6. 
 
 50,625 
 
 + 10 
 
 12. 
 
 36,984 
 
 + 100 
 
 18. 
 
 129,832 
 
 -r-1000 
 
 7. 
 
 36,072 
 
 + 10 
 
 13. 
 
 28,305 
 
 -100 
 
 19. 
 
 172,001 
 
 ^1000 
 
 8. 
 
 25,600 
 
 + 10 
 
 14. 
 
 72,601 
 
 -f-100 
 
 20. 
 
 398,436 
 
 + 1000 
 
 9. 
 
 35,690 
 
 -10 
 
 15. 
 
 35,100 
 
 -i-100 
 
 21. 
 
 128,000 
 
 + 1000 
 
 
 22. 
 
 136,948 
 
 -50 
 
 23. 169,846 
 
 -80 
 
 
 
 24. 
 
 389,063 
 
 -* 
 
 200 
 
 25. 8,698,751-500 
 
 79. l. 24 ? = 8. Which terms of division are given ? 
 To find what ? How do you find it ? When the dividend 
 and quotient are given, how can the divisor be found ? 
 
 2. ? 3 = 8. Which terms are given ? To find what ? 
 How do you find it ? When the divisor and quotient are 
 given, how may the dividend be found ? State two ways. 
 
 80. These examples show the following 
 
 Proof of Division 
 
 1. Divide the dividend by the quotient. If the 
 result is the same as the divisor, the work is correct. 
 The remainder, if any, should be the same as in the 
 first division. 
 
 2. Multiply the quotient and divisor together. Add 
 the remainder, if there is any, to the product. If the 
 result obtained is the same as the dividend, the division 
 is correct. 
 
122 PRIMARY ARITHMETIC 
 
 81. 1. 9 x 2 = ? Which term is 9 ? Which term is 2 ? 
 2x9 = ? Which term is 9 ? Which term is 2 ? 
 Compare the results in the above examples. 
 
 2. ? x 2 = 18. Which terms are given ? Which term 
 to find ? How do you find it ? When the multiplier and 
 product are given, how can the multiplicand be found ? 
 
 9 x ? = 18. When the product and multiplicand are given, 
 how can the multiplier be found ? 
 
 82. These examples show the following 
 
 Proof of Multiplication 
 
 1. Multiply the multiplier by the multiplicand. If 
 the work is correct, the product obtained will agree 
 with the first product. Or, 
 
 2. Divide the product by the multiplier. If the 
 work is correct, the quotient will be the same as the 
 multiplicand. Or, 
 
 3. Divide the product by the multiplicand. If the 
 work is correct, the quotient will be the same as the 
 multiplier. 
 
 PROBLEMS IN DIVISION 
 83. Written. 
 
 1. If a steamboat ran 1440 miles in 4 days, what was the 
 average rate for a day? 
 
 2. A farmer put 1068 bushels of potatoes in 6 bins. How 
 many bushels were in each bin ? 
 
 3. A girl divided $4.50 among 10 poor children. How 
 much did she give to each? 
 
PROBLEMS IN DIVISION 123 
 
 4. How many tons of- coal at $ 5 a ton can be bought for 
 
 $765? 
 
 5. If 7 men can build 378 rods of fence in a week, how 
 many rods can one man build in the same time ? 
 
 6. How many days, at 11 miles a day, will it take a man 
 to walk 902 miles ? 
 
 7. The dividend is 981, the quotient 9. What is the 
 divisor? 
 
 8. How many ploughs at 1 12 each can be bought , for 
 
 $1008? 
 
 9. A man divided 2222 acres of land into 11 parts. How 
 many acres were there in each part ? ' 
 
 10. A farmer paid $46.25 for 10 sheep. What did he 
 pay for each? 
 
 11. There are 8 quarts in 1 peck. How many pecks are 
 there in 3320 quarts? 
 
 12. There are 7 days in 1 week. How many weeks in 
 364 days? 
 
 13. A man willed $19,722 to his 6 children. How much 
 did each receive, if they shared equally ? 
 
 14. What is the price of 1 yard of broadcloth, if 12 yards 
 cost $50.40? 
 
 15. There are 5280 feet in a mile, and 3 feet in 1 yard. 
 How many yards in a mile? 
 
 16. At $ 8 each, how many overcoats can be bought for 
 
 17. How many hours will be required to ride a bicycle 
 504 miles by riding 18 miles an hour? 
 
 18. At $ 15 each, how many suits of clothes can be bought 
 for $1080? 
 
124 PRIMARY ARITHMETIC 
 
 19. If a family consume 13 gallons of kerosene in a month, 
 in how many months will it consume 468 gallons? 
 
 20. At $16 a ton, how many tons of hay can be bought 
 for $1920? 
 
 21. If 1 acre of land yiejds 24 bushels of wheat, how 
 many will be required to yield 2544 bushels ? 
 
 22. At $27 each, how many stoves can be bought for 
 $648? 
 
 23. If a man can walk 30 miles in 1 day, in how many 
 days can he walk 1000 miles? 
 
 24. How many weeks will it take to pay a debt of $ 1225 
 by paying $ 25 a week ? 
 
 REVIEW EXERCISES 
 
 84. Oral. 
 
 1. A farmer sold 12 barrels of apples at $3 a barrel and 
 bought with the proceeds coal at $4 a ton. How many tons 
 did he buy ? 
 
 2. A .dealer bought 10 barrels of apples at $ 2 a barrel and 
 sold them so as to gain $10. What was the selling price 
 per barrel ? 
 
 3. In what time will a boy at $ 3 a week earn as much as 
 a man earns in 4 weeks at $9 a week? 
 
 4. John had $ 6, James 3 times as much, and Thomas J as 
 much as both. How much had Thomas ? 
 
 5. A man who carried 56 eggs to market found -| of them 
 broken. How many were not broken ? 
 
 6. Nell is three years old, and Will 5. Their sister is as 
 old as twice the sum of their ages. How old is their sister ? 
 
 7. A farmer sold 48 pecks of beans for $48. How much 
 did he receive a bushel, there being 4 pecks in a bushel ? 
 
REVIEW PROBLEMS 125 
 
 8. Bought a dozen oranges for 36 cents and sold them at 
 4 cents apiece. What was the entire profit ? 
 
 9. How many gallons of milk will a family use in 12 days 
 if they use 2 quarts a day, there being 4 quarts in a gallon ? 
 
 10. Mr. A owed a debt of $96. He made 5 payments of 
 $ 12 each. How much remained unpaid ? 
 
 11. Two boys 80 miles apart travel toward each other. 
 The first goes 5 miles an hour, and the second 3 miles an 
 hour. In how many hours will they meet ? 
 
 12. Two boys, travelling at the rate of 5 miles and 3 
 miles an hour respectively, go in the same direction. How 
 far apart are they at the end of 6 hours ? 
 
 13. If I can buy 7 oranges for 14 cents, how many can I 
 buy for 24 cents? 
 
 14. By selling 12 barrels of flour at $5 a barrel, a grocer 
 makes a profit of $12. What was the cost of the flour per 
 barrel ? 
 
 REVIEW PROBLEMS 
 
 85. Written. 
 
 1. If the dividend is 1821, the quotient 32, and the 
 remainder 29, what is the divisor ? 
 
 2. The product of three numbers is 1260, and two of 
 them are 12 and 7. What is the third? 
 
 3. A grocer buys 88 gallons of molasses at $.56 a gallon. 
 For how much per gallon must he sell it in order to gain 
 $12.32? 
 
 4. Two railway trains start at the same time from oppo- 
 site points, 1216 miles apart, and travel toward each other, 
 one going 35 miles an hour, and the other 41 miles an hour, 
 How many hours before they will meet ? 
 
126 PRIMARY ARITHMETIC 
 
 5. Two steamboats are 144 miles apart and going in the 
 same direction, one at the rate of 21 miles, and the other 15 
 miles, an hour. In how many hours will the former over- 
 take the latter ? 
 
 6. A merchant bought 8 pieces of cloth, each containing 
 52 yards, at 12 cents a yard, and 325 pounds of cotton 
 batting at 9 cents a pound. How much less than $100 did 
 it cost him ? 
 
 7. If 64 pounds of butter costs $15.36, what will 320 
 pounds cost at the same price ? 
 
 8. A grocer bought 123 gallons of molasses at 42 cents 
 a gallon and sold it at 60 cents a gallon. What was his 
 gain ? 
 
 9. A man bought 4 cows at one time for $168, 3 at 
 another for $153, and 6 at another for $225. What was 
 the average price paid ? 
 
 10. Divide the product of 27 and 32 by their sum. 
 
 11. If 18 men can build a wall in 120 days, in what time 
 can 24 men build it ? 
 
 12. A man, dying, left property amounting to $3500. 
 After paying $ 572 for funeral and other expenses, the 
 remainder was divided equally among 12 heirs. What did 
 each receive ? 
 
 13. Two vessels start from the same point and sail in 
 opposite directions, one at the rate of 18 miles, and the 
 other 23 miles, an hour. How far apart will they be in 16 
 hours ? 
 
 14. I bought 124 bushels of corn of A, 216 of B, and 96 
 of C, paying $.63 a bushel in each case. What will be my 
 profit if I sell the whole at $.72 a bushel ? 
 
REVIEW PROBLEMS 127 
 
 15. A man starts on a journey of 724 miles. When he 
 has travelled 12 hours at the rate of 32 miles an hour, how 
 far is he from his journey's end ? 
 
 16. A man bought 6 sacks of flour at $1.25 a sack, 24 
 pounds of sugar at 6 cents a pound, and 2 pounds of coffee 
 at 35 cents a pound, and paid for it in butter at 23 cents a 
 pound. How many pounds were there ? 
 
 17. If I sell 58 cows at $38 a head, and 200 sheep at 
 $4.30 a head, and invest the proceeds in 4 village lots, 
 what is the average price of each lot ? 
 
 18. I bought a city lot for $1750, built a house upon it at 
 a cost of $3275, and afterward sold the place for $6000. 
 What was my gain ? 
 
 19. A boy has $9.62 in his toy bank. How many times 
 can he take away 25 cents from it, and have 12 cents left ? 
 
 20. A man bought a house and lot for $3200. He paid 
 $1275 down, and agreed to pay the remainder in equal 
 monthly payments of $35 each. How many months will it 
 take to pay in full ? 
 
 21. The product of four numbers is 2880, and three of 
 them are 5, 6, and 8. What is the fourth ? 
 
 22. A teacher who receives a monthly salary of $125 
 for 10 months in a year will require how many years to 
 pay for 3 village lots at $645 each, if his yearly expenses 
 are $863? 
 
 23. A man having $783.58 in bank, drew out $132.75 at 
 one time, $175.50 at another, $216 at another. How much 
 then remained in the bank ? 
 
 24. How many tons of coal at $5 a ton will pay for 15 
 tons of hay at $11 a ton? 
 
128 PRIMARY ARITHMETIC 
 
 25. If a pupil in school uses 6 sheets of writing paper 
 each day, how many tablets containing 75 sheets will he 
 require for the school year of 40 weeks of 5 days each, if he 
 attends school every day, making no allowance for holidays? 
 
 26. I paid $365 for a horse and carriage, paying $1 more 
 for the horse than for the carriage. What did I pay for 
 each ? 
 
 27. A farmer paid $1125 for cows, horses, and farming 
 tools, and 8 times as much for a farm of 125 acres. What 
 was the price p^r acre ? 
 
 28. John, Edward, and Henry have together $12.80. 
 John has $2. 26 more than Henry, and Edward has $1.75 
 more than Henry. How much money has each ? 
 
 29. A man bought 84 acres of land at $65 an acre and 
 sold it all for $ 6552. What was his gain per acre ? 
 
 30. A merchant bought 172 yards of cashmere at $.45 a 
 yard, 504 yards of calico at $.05, 252 yards of flannel at 
 $ . 37, and paid for it in 3 equal payments. What was the 
 amount of each payment ? 
 
 31. A drover bought 27 COW T S for $1026. At what price 
 per head must he sell them to make a profit of $12 on each ? 
 
 32. There are 24 sheets of paper in a quire. How many 
 sheets in 2 reams, there being 20 quires in a ream ? 
 
 33. A man bought 1000 sheep and sold at one time 216, 
 at another 327, and at another 198. How many did he then 
 have left? 
 
 34. There are 640 acres in 1 square mile. Into how many 
 farms of 160 acres each can 10 square miles of land be 
 divided ? 
 
 35. A merchant bought dress goods at $1.26 a yard and 
 sold it at $2 a yard. What was his profit on 260 yards ? 
 
REVIEW PROBLEMS 129 
 
 36. I sold a farm for $ 1265 more than I paid for it, but 
 $ 325 less than my asking price. What would have been 
 my profit if I had sold at my asking price ? 
 
 37. How many more acres of land can I buy with $ 6048 
 at $56 an acre than at $ 72 an acre ? 
 
 38. A grocer bought 123 pounds of cheese at 10 cents a 
 pound and sold it for 13 cents a pound. What was his 
 profit ? 
 
 39. A lady bought 12 yards of dress goods at $ 1.75 a 
 yard, 8 yards of silesia at $.25 a yard, 2 pairs of gloves at 
 $1.45 a pair, 6 handkerchiefs at $.25 apiece, and 3 yards 
 of table linen at $.95 a yard. She pai'd $18.75 and left the 
 balance on account. What did she still owe ? 
 
 40. How many pounds of butter at 26 cents a pound 
 must be given for 3 barrels of flour at $4.20 a barrel? 
 
 41. At what rate per hour must a railway train run to 
 overtake, in 12 hours, another train 168 miles ahead running 
 at the rate of 32 miles an hour? 
 
 42. How many more revolutions will a wheel 10 feet in 
 circumference make in going 5280 feet, or a mile, than one 
 20 feet in circumference ? 
 
 43. How much more will 8 horses at $ 165 each cost than 
 23 cows at $ 37 a head ? 
 
 44. From a bin containing 324 bushels of wheat, 147 
 bushels were sold at $ .85, and the remainder at $.90 a 
 bushel. What did the wheat bring? 
 
 45. A man buys 32 cows for $1120 and sells them at a 
 gain of $192. What does he receive a head for them ? 
 
 46. How many hours will it take a horse, travelling 8 
 miles an hour, to go as far as a train of cars can go in 4 
 hours running at the rate of 35 miles an hour ? 
 
FACTORING 
 
 86. A number that will divide another number without 
 a remainder is an Exact Divisor of that number. 
 
 87. An exact divisor of a number is a Factor of that num- 
 ber. Thus, 5 is a factor of 15. Why ? What other factor 
 has 15 ? If a number has any factors, what is the least 
 number of factors it may have ? Which terms in division 
 are factors ? They are factors of what ? Which terms in 
 multiplication are factors ? They are factors of what ? 
 When one factor of a number is known, how can the other 
 factor be found ? 
 
 88. A number that has no factors but itself and one is a 
 Prime Number. Thus, 1, 3, 5, 7, 11, 13, 17, and 19 are prime 
 numbers. 
 
 89. A number that has other factors than itself and 1 is 
 a Composite Number. Thus, 4, 9, 12, and 21 are composite 
 numbers. 
 
 90. A factor that is a prime number is a Prime Factor. 
 
 Thus, 2, 3, and 5 are prime factors of 30. 
 
 91. A number that has two for a factor is an Even Num- 
 ber. Name all the even numbers from 2 to 30. 
 
 130 
 
FACTORING 131 
 
 92. A number of which 2 is not a factor is an Odd Number. 
 Name all the odd numbers from 1 to 29. 
 
 93. 
 
 Rule for finding whether a Number is Prime or not 
 
 1. Divide the given number by 2. 
 
 2. If 2 gives a / remainder, divide by 3. 
 
 3. Continue this process, using each prime number 
 in order as a divisor, until an exact divisor is found, or 
 until the divisor exceeds the quotient. If no exact divisor 
 is found until the divisor used exceeds the quotient, the 
 number is prime. Otherwise it is composite. 
 
 94. Find whether these numbers are prime or composite: 
 
 1. 143 5. 211 9. 121 13. 231 17. 437 
 
 2. 123 6. 221 10. 97 14. 161 is. 401 
 
 3. 324 7. 119 11. 213 15. 87 19. 593 
 
 4. 163 8. 208 12. 215 16. 78 20. 395 
 
 95. Finding the factors of numbers is called Factoring. 
 
 NOTE. Since 1 is a factor of every number, it is not generally men- 
 tioned among the factors of a number. 
 
 1. Find the prime factors of 1320. 
 2 1320 
 
 660 
 
 330 By what kind of numbers must we divide ? 
 
 lei Wh y ? 
 
 55 Which divisors do we use first ? 
 
 "~~jj What beside the divisors is a prime factor ? 
 
 2, 2, 2, 3, 5, 11. Ans. 
 
132 PRIMARY ARITHMETIC 
 
 96. 
 
 Rule for finding the Prime Factors of a Number 
 
 1. Divide the given number by its smallest prime 
 factor. Divide the quotient by the same factor, if 
 possible, and repeat the process as many times as that 
 divisor can be used. 
 
 2. Divide the last quotient obtained by the next 
 larger prime factor, and repeat if possible, as with 
 the first prime factor. 
 
 3. Continue in this way until the quotient is a prime 
 number. All the divisors and the last quotient are the 
 prime factors required. 
 
 97. Find the prime factors of : 
 
 l. 30 
 
 5. 110 
 
 9. 189 
 
 13. 414 
 
 2. 120 
 
 6. 105 
 
 10. 665 
 
 14. 3381 
 
 3. 42 
 
 7. 462 
 
 11. 429 
 
 15. 667 
 
 4. 66 
 
 8. 45 
 
 12. 425 
 
 
 CANCELLATION 
 
 98. 1. Divide 210 by 30. 
 
 210, Dividend ^ ~ ,. 
 
 ~j^-. = 7, Quotient. 
 
 30, Divisor 
 
 o-i A 9 i A- f What is done to the dividend? 
 
 ~^ = -^ = 7, Quotient. J To the divisor ? 
 
 [ How does it affect the quotient ? 
 
 ( What is done to the dividend? 
 10 5 ** - ~ = 7, Quotient. J To the divisor? 
 
 [ How does it affect the quotient ? 
 
 ^ T What is done to the dividend? 
 
 2pL2 =1 =7, Quotient. J To the divisor ? 
 
 [ How does it affect the quotient ? 
 
FACTORING 133 
 
 Dividing both dividend and divisor by the same number affects the 
 quotient how ? 
 
 210 2x3x5x7 x 3 x ^ x 7 
 
 80 s 2x3x5 ?x3x? = 7 ' Q " tlent 
 
 This example might be expressed thus : 
 
 7 
 W 
 
 w 
 
 % = 7, Quotient. 
 
 99. Taking out the same factor from both dividend and 
 divisor is Cancellation. 
 
 100. Find the answers to the following questions by 
 means of cancellation : 
 
 1. Divide 36 x 27 x 49 x 38 x 50 by 70 x 18 x 15. 
 
 2. (28 x 38 x 48) -=- (14 x 19 x 24 x 2 x 2) = ? 
 
 3. (26 x 5 x 54) - (13 x 5 x 6) = ? 
 
 4. What is the quotient of 36 x 48 x 16 divided by 
 27x24x8? 
 
 5. Divide 5 x 45 x 7 x 20 by 49 x 5 x 4 x 9. 
 
 6. Divide 5 x 51 x 7 x 9 x 4 by 17 x 20 x 12 x 7 x 2. 
 
 7. Divide 25 x 2 x 72 x 14 by 6 x 9 x 120. 
 
 8. How many bushels of potatoes at 50 cents a bushel 
 must be given in exchange for 15 pounds of tea at 40 cents 
 a pound ? 
 
 9. If 60 yards of cloth cost $120, how many yards can 
 be bought for 1 40? 
 
 10. 15 oranges cost 45 cents How much will 7 oranges 
 cost? 
 
134 PRIMARY ARITHMETIC 
 
 11. A dairyman sells 100 quarts of milk daily at 5 cents 
 a quart. How many bushels of corn at 45 cents a bushel can 
 he buy with 10 days' milk receipts ? 
 
 12. A farmer sold a grocer 45 bushels of apples at 50 cents 
 a bushel, taking his pay in flour at 90 cents a sack. How 
 many sacks did he receive ? 
 
 GREATEST COMMON DIVISOR 
 
 101. A number that will exactly divide two or more 
 numbers is a Common Divisor of those numbers. It is also 
 a Common Factor. Thus, 2 is a common divisor of 6 and 4 ; 
 5 cents is a common divisor of 10 cents, 25 cents, and 15 
 cents. 
 
 102. The largest number that will exactly divide two or 
 more numbers is the Greatest Common Divisor of those num- 
 bers. It is also the Greatest Common Factor. Thus, 6 is 
 the greatest common divisor of 12, 18, and 24 ; 15 is the 
 greatest common divisor of 45 and 60. 
 
 103. Numbers that have no common factor are Prime to 
 Each Other. Thus, 22 and 35 are prime to each other. 
 
 104. Find the greatest common divisor of 24, 36, and 72. 
 
 Name the common factors of 
 24, 36, and 72. Since 2, 2, and 
 
 79 A a 9 * Q 3 are all the common factors 
 
 of 24, 36, and 72, what will 
 you do with 2, 2, and 3 to find the greatest common factor ? 
 2x2x3 = what ? What is the greatest common factor ? 
 For convenience, we may find the common factors thus : 
 
GREATEST COMMON DIVISOR 135 
 
 24, 36, 72 
 
 3 
 
 12, 18, 36 
 
 6, 9, 18 
 
 2, 3, 6 
 2x2x3 = 12, greatest common divisor. Ans. 
 
 105. From this example we may make the following 
 
 Rule for finding the Greatest Common Divisor 
 
 1. Write the given numbers in a horizontal line. 
 
 2. Divide them by all their common factors in suc- 
 cession, beginning with the smallest. 
 
 3. Multiply the common factors together. 
 
 106. Find the greatest common divisor : 
 
 1. 84, 132 e. 40, 60, 80 11. 45, 60, 90 
 
 2. 63, 42 7. 64, 144, 560 12. 36, 72, 81 
 
 3. 90, 105 a 36, 48, 24 13. 44, 121, 132 
 
 4. 112, 168 9. 40, 56, 72 14. 63, 126, 189 
 
 5. 132, 156 10. 18, 54, 32 is. 36, 81, 135 
 
 LEAST COMMON MULTIPLE 
 
 107. A number that exactly contains another number is a 
 Multiple of that number. Thus, 30 is a multiple of 10. 
 
 108. A number that exactly contains two or more numbers 
 is a Common Multiple of those numbers. Thus, 60 is a com- 
 mon multiple of 15, 6, and 10. 
 
 109. The smallest number that exactly contains two 
 or more numbers is the Least Common Multiple of those 
 numbers. Thus, 30 is the least common multiple of 15, 
 6, and 10. 
 
Q ^ Q ~ ^ we f un( i ? A number to con- 
 
 = 
 
 136 PRIMARY ARITHMETIC 
 
 1. Find the least common multiple of 60, 90, 50, and 150. 
 fin 9 9 3 r What kind of factors have 
 
 \ Q ^ Q ~ ^ 
 
 X o X o X O . ->_ 
 
 __ 9 55 
 
 9 3 ^ ^ f actors ? To contain 90 ? To 
 
 contain 50 ? To contain 150 ? 
 
 To contain 60, 90, 50, and 150, a number must contain 
 how many factor 2's ? How many factor 3's ? How many 
 factor 5's ? What other factors ? What is the smallest 
 number that contains 2x2x3x3x5x5? What, then, 
 is the least common multiple of 90, 60, 50, and 150 ? 
 
 The necessary factors may be conveniently found thus : 
 
 2 
 3 
 5 
 5 
 
 90 
 
 50 
 
 60 
 
 150 
 
 45 
 
 25 
 
 30 
 
 75 
 
 15 
 
 25 
 
 10 
 
 25 
 
 3 
 
 5 
 
 2 
 
 5 
 
 31 21 
 
 2x3x5x5x3x2 = 900, least common multiple. Ans. 
 
 110. From this example we may make the following 
 
 Rule for finding the Least Common Multiple 
 
 1. Write the given numbers in a horizontal line. 
 
 2. Divide them by any prime number that will divide 
 two or more of them. It is best to begin with the 
 smallest. 
 
 3. If any number will not exactly contain the divisor, 
 bring that number down into the line with the quotients. 
 
 4. Continue this process until the quotients obtained 
 are prime to each other. 
 
 5. Multiply together all the divisors and the last line 
 of quotients. 
 
INDICATED OPERATIONS 137 
 
 111. Find the least common multiple : 
 
 1. 18, 27, 30 5. 36, 40, 48 9. 24, 42, 54, 360 
 
 2. 9, 12, 18 6. 18, 24, 36 10. 25, 20, 35, 40 
 
 3. 16, 48, 60 v. 15, 30, 21, 28 11. 14, 21, 35, 45 
 
 4. 21, 27, 36 a 15, 60, 140, 210 12. 24, 48, 96, 192 
 
 INDICATED OPERATIONS 
 
 112. The Parenthesis () indicates that all the numbers 
 included therein are to be subjected to the same operation. 
 
 Thus, (17 6) x 2 indicates that the difference between 6 
 and 17 is to be multiplied by 2. 17 - 6 = 11. 11 x 2 = 22. 
 Without the parenthesis, this would-be 17 6 x 2, and indi- 
 cates that 2 x 6 is to be taken from 17. 17 11 = 6. 
 
 (4 + 8) -T- 4 indicates that the sum of 8 and 4 is to be 
 divided by 4. The result is 3. If the parenthesis is omitted, 
 we have 4 + 8-5-4, which indicates that 8 -T- 4, or 2, is to be 
 added to 4. 4 + 4 = 8. 
 
 [(6 + 5) x 4 + 6] -T- 10 indicates that 6 + 5 is to be multi- 
 plied by 4, 6 added to the product, and the sum divided by 10. 
 6 + 5 = 11. 11 x 4 = 44. 44 + 6 = 50. 50 - 10 = 5. 
 
 113. Brackets [ ] and the Vinculum " " have the same 
 uses as the parenthesis. 
 
 [3 + 4] x 3, 3 + 4x3, mean the same as (3 + 4) x 3. 
 
 When the parenthesis or vinculum is included within the 
 brackets, the operations indicated within the parenthesis or 
 under the vinculum should be performed first. 
 
 114. When the parenthesis, vinculum, or brackets are not 
 used, or after they have been removed, operations indicated 
 by x or -i- must be performed first, then the operations indi- 
 cated by + and - . Thus, 12-5-4x2 + 36 --4-2x4 = ? 
 
 SOLUTION. 12-4x2 = 6. 36 - 4 = 9. 2x4 = 8. The statement 
 now reads, 6 + 98. The result is 7, 
 
138 PRIMARY ARITHMETIC 
 
 115. 
 
 1. 4 + 3x2 = ? 4. 4 x (3 + 2) = ? 
 
 2. (4 + 3) x 2 = ? 5. 8 + 4 -r- 2 = ? 
 
 3. 4x3 + 2 = ? 6. (8 + 4)-2 = ? 
 
 Find the value of : 
 
 7. 15 + 3x6 + 10-5. 
 
 a (6 + 4) x (3 + 2) - (8 x 5). 
 
 9 . 18-3 + 2 + 8x2 + 14-6. 
 
 10. 2 + 12 -5-4 -(10 + 16-5-4) -5-7. 
 
 11. 11 + 4 -3 + 6x4. 
 
 12. 3 + 4 x 6-*- (15 -18-*- 3). 
 
 13. 164 + 16-250-10 + 16x3. 
 
 14. 17 +3x4x6 + 3-5-3 + 3. 
 
 is. [39 + 8 -*- 2 + 7] x 6. 
 
 16. [6 + 15 x 3 - 6 + 16 -*- 8 + 4] - 3 + 5. 
 
 17. 7 + 8 10-2. 18 . 
 
 19. 
 
 4 
 
 20. Indicate the addition of 36, 15, 16, 38. 
 
 21. Indicate in two ways the division of 16 by 4. Of 
 
 5 + 17 divided by 11. 
 
 Indicate the operations of the following problems : 
 
 22. A lady found 3 roses on one bush, 5 on another, and 
 7 on another. How many roses did she find ? 
 
 23. James found 2 eggs in a hen's nest, 5 in another, and 
 
 6 in another. How many eggs did he find in all ? 
 
INDICATED OPERATIONS 139 
 
 24. A man spent $10.16 on Monday and $4.40 on Tues- 
 day. How much more did he spend on Monday than on 
 Tuesday ? 
 
 25. A boy had 36 marbles. He lost 6 one day and 11 the 
 next. How many had he left ? 
 
 36 -(6 + 11) = ? 
 
 26. If you have 60 cents and spend 18 cents for ribbon 
 and 12 cents for thread, how much have you left ? 
 
 27. James had 18 marbles and found 5 more. He after- 
 ward lost 8 marbles. How many were left ? 
 
 28. A boy deposited $1 in the savings bank on the 1st of 
 the month, 75^ on the 10th, and $2.50 on the 25th. On 
 the 30th he drew out $2.75. How much was left in the 
 bank? 
 
 29. John had $5.18 in the bank. He drew out $1.50 on 
 Monday and $.75 on Tuesday. How much had he left? 
 
 30. 4 increased by the product of 3 and 2. 
 
 31. The sum of 4 and 3, multiplied by 2. 
 
 32. The product of 4 and 3, increased by 2. 
 
 33. 4 multiplied by the sum of 3 and 2. 
 
 34. 84 less the product of 5 and 6. 
 
 35. The difference between 72 and 42, multiplied by 4. 
 
 36. 144 subtracted from the product of 18 and 18. 
 
 37. 6 multiplied by the difference between 11 and 6. 
 
 38. Henry has 58 ^, and John 63 ^. Charles has 4 times 
 as much as both. How much has Charles ? 
 
 39. Lucy and Mary went shopping. Lucy bought lace 
 for 55^, and Mary 5 yards of ribbon at 15^ a yard. What 
 was the amount of both purchases ? 
 
FRACTIONS 
 
 _Ji | ^_ 
 
 H * , M , M. 
 
 116. Draw a line. Divide it into 2 equal parts. What is 
 one of these parts ? How many halves in the line ? 
 
 Draw another line. Divide it into 3 'equal parts. What 
 is one part ? How many thirds in the line ? 
 
 Draw another line. Divide it into 4 equal parts. What 
 is one part ? How many fourths in the line ? 
 
 Draw another line. Divide it into 5 equal parts. One 
 of these parts is what ? Two of them are what ? Three of 
 them ? Four of them ? All of them ? 
 
 Which is larger, | or \ ? \ or \ ? 
 
 117. Make a square. Draw a line through the middle of 
 it from corner to corner. Into how many parts have you 
 divided the square ? What is one part ? 
 
 Connect the other corners by a line. Into how many 
 parts is the square now divided ? What is one of the parts 
 called ? What are two of them called ? Three of them ? 
 
 140 
 
FRACTIONS 
 
 141 
 
 118. Which piece of this pie would you rather have, |, |, 
 1, or | ? Why ? 
 
 One piece of the last pie is what part of it ? two pieces ? 
 8 pieces ? 5 pieces ? 
 
 Write the number that 
 represents 1 part of this 
 pear. Two parts. Write 
 the number that repre- 
 sents the whole pear. 
 
 How many small squares are there 
 in the large square ? One of the small 
 squares is what part of the large square ? 
 What part of the large square is yellow ? 
 White ? Yellow and white ? How many 
 ninths of the large square are red ? What 
 part of the large square is blue ? 
 
142 
 
 PRIMARY ARITHMETIC 
 
 How many oblongs are here ? 
 
 How many circles ? 
 
 One oblong is what part of all the oblongs. 
 
 What part of all the circles are in one oblong ? 
 
 ^ of all the circles are how many circles? ^ of 
 8 = ? | = ? 8 H- 4 = ? 
 
 What part of all the circles are red ? White ? 
 Yellow ? Green ? Red and white ? 
 
 J of all the circles are how many circles ? J- 
 = how many ? | = how many ? 
 
 119. A Fraction is one or more of the equal 
 parts of any thing. Thus, ^ of an inch ; -f^- ; * . 
 
 120. A fraction is also an expression of divi- 
 sion. Thus, -| means 1-5-4, or 1 whole thing 
 
 divided into 4 equal parts. 
 24 divided into 3 equal parts. 
 
 means 24 -^- 3, or 
 
 121. The number below the line in a fraction 
 is the Denominator. v It tells the number of parts 
 into which the whole is divided. Thus, 9 is the 
 denominator of ^. 
 
 122. The number above the line in a fraction 
 is the Numerator. It tells the number of parts 
 used. Thus, 3 is the numerator of f . 
 
 123. The numerator and denominator are the Terms of a 
 Fraction. What are the terms of J ? of f ? of | ? of f f ? 
 
 124. The quotient of the numerator divided by the de- 
 nominator is the Value of the Fraction. What is the value 
 off? off? of J^-? of -% 5 -? off? 
 
REDUCTION OF FRACTIONS 
 125. Read the following fractions : 
 
 2. | 6. f 10. T \ 14. 
 
 3. f 7. 1 11. 15. 
 
 4. I 8. | 12. 2*0 16 ' 
 
 143 
 
 126. Write in figures : 
 
 17. Four-fifths. 
 
 18. Seven-ninths. 
 
 19. Five-eighths. 
 
 20. Six-tenths. 
 
 21. Four-elevenths. 
 
 22. Six-thirteenths. 
 
 23. Four twenty-firsts. 
 
 24. Sixteen twenty-seconds. 
 
 25. Fifteen twenty-fifths. 
 
 26. Sixteen forty-fourths. 
 
 27. Eight thirty-thirds. 
 
 28. Six fifty-fourths. 
 
 29. Seventeen sixty-ninths. 
 
 30. Seven ninety-eighths. 
 
 31. Twenty-four eightieths. 
 
 32. Seven fiftieths. 
 
 33. Sixty-five seventieths. 
 
 34. 10 one-hundred-fifths. 
 
 35. 12 two-hundred-eighths. 
 
 REDUCTION OF FRACTIONS 
 Reduction of Fractions to Lowest Terms 
 
 127. Reduction is changing the form of numbers without 
 changing their value. Thus, f = 1 ; 10 cents = 1 dime. 
 
 128. Fractions are in their Lowest Terms when the numer- 
 ator and denominator have no common divisor. Thus, | is 
 in its lowest terms. - is not in its lowest terms. 
 
144 
 
 PRIMARY ARITHMETIC 
 FIRST ILLUSTRATION 
 
 How many squares are there in the oblong ? 
 
 One square is what part of the oblong ? 
 
 How many squares are red ? 
 
 How many ninths are red ? 
 
 How many colors are there in the oblong ? 
 
 Into how many parts do the colors divide the oblong? 
 How do these parts compare ? One of these parts is what 
 fraction of the oblong ? What fraction of the oblong is red ? 
 How many ninths are red ? How does | compare with J ? 
 Write | = ^. 
 
 What could you do to 3 to get 1 ? 
 
 What could 'you do to 9 to get 3 ? 
 
 What would you do to | to get ^ ? 
 
 Dividing both terms of a fraction' by the same number 
 affects the value of the fraction how ? 
 
 The terms of ^ have what common divisor ? Then ^ has 
 been reduced to what? (See definition, Art. 128.) 
 
 SECOND ILLUSTRATION 
 
 Into how many equal parts is this circle 
 divided by the black lines ? What is one 
 of the 8 equal parts called ? What part 
 of the circle is green ? How many eighths 
 are in the* green half ? -| of the circle 
 compares how with J ? What must you 
 do with 4 and 8 in the fraction |- to make 
 it ^ ? The terms of J have what common divisor ? 
 Then -| has been reduced to what ? 
 
REDUCTION OF FRACTIONS 
 
 145 
 
 129. Show by these cir- 
 cles that | = f That = f. 
 
 That T <V=f. 
 
 How are these fractions 
 reduced to lowest terms? 
 
 130. 
 
 Rule for Reduction of Fractions to Lowest Terms 
 
 Divide both numerator and denominator by common 
 divisors until they become prime to each other. 
 
 The numerator of a fraction is which term of division ? 
 The denominator ? The value of the fraction ? 
 
 Dividing both dividend and divisor by the same number af- 
 fects the quotient how ?* (See Cancellation, article No. 103.) 
 
 Dividing both numerator and denominator of a fraction by 
 the same number affects the value of the fraction how ? 
 
 Change the following to their lowest terms : 
 
 131. Mental. 
 
 1- I * I 
 
 2- I 5 - H 
 
 3. If 6. If 
 
 132. Written. 
 
 1- tl * tt 
 
 7 - I* 
 
 8. ff 
 
 9. || 
 
 10. 
 11. 
 
 13. 
 
 li 
 
 2- 
 
 3- 
 
 6. 
 
 7. 
 8. 
 9. 
 
 _72 
 12 S 
 
 12. 
 
146 PRIMARY ARITHMETIC 
 
 "" m 21. T& 25. 
 
 18 TVs 22. $fa 26. Kf 
 
 19 ' A\ 23. |fl 27. fOf 
 
 Hi 20. &$ 24. ^ 28 . 1|| 
 
 29. Express in lowest terms 230 -T- 345. 
 
 30. Express in lowest terms 98 divided by 392. 
 
 31. Express in lowest terms 437 -s- 2485. 
 
 32. Express in lowest terms the quotient of 288 divided 
 by 504. 
 
 33. What are the lowest terms of iff ? 
 
 Reduction of Integers and Mixed Numbers to Fractions 
 
 133. A number that is composed of whole units only is an 
 Integer. Thus, 5, 4, 1, 13, and 2000 are integers. 
 
 134. A number that is composed of an integer and a frac- 
 tion is a Mixed Number. Thus 8|, * 9 T ^, and 3| are mixed 
 numbers. 
 
 How many fourths in 1 circle ? In 2 circles ? In 3 circles ? 
 In 4 circles ? How do you find it ? 
 
 How many fourths in 4| circles ? In 2|- circles ? In 3| 
 circles ? How do you find it ? 
 
 How many eighths in 1 circle ? In 3 circles ? In 2 circles ? 
 In 4| circles ? In 2| circles ? How do you find it ? 
 
 How do you reduce an integer or a mixed number to a 
 fraction ? 
 
REDUCTION OF FRACTIONS 147 
 
 135. 
 
 Rule for Reduction of Integers and Mixed Numbers 
 to Fractions 
 
 1. Multiply the integer by the denominator of the 
 required fraction. 
 
 2. Add to the product the numerator of the given 
 fraction, if there is one. 
 
 3. Use this result as the numerator of the required 
 fraction. 
 
 4. For a denominator, take the denominator of the 
 given fraction or fraction required. 
 
 Reduce the following to fractions : 
 136. Mental. 
 
 1. 
 
 H 
 
 5. 
 
 H 
 
 9. 
 
 Q 4 
 
 &W 
 
 13. 
 
 8 9 
 
 2. 
 
 41 
 
 6. 
 
 2f 
 
 10. 
 
 4 9 
 
 14. 
 
 7 T \ 
 
 3. 
 
 3 f 
 
 7. 
 
 *t 
 
 11. 
 
 5 ! 
 
 15. 
 
 8 T^ 
 
 4. 
 
 &i 
 
 8. 
 
 2| 
 
 12. 
 
 6f 
 
 16. 
 
 i 
 
 137. 
 
 Written. 
 
 
 
 
 
 
 
 17. 
 
 251 
 
 24. 
 
 37 T% 
 
 31. 
 
 270|| 
 
 38. 
 
 491^ 
 
 18. 
 
 9 T \ 
 
 25. 
 
 49 1 7 5 
 
 32. 
 
 19 12 
 
 39. 
 
 35 5T 
 
 19. 
 
 17 i 
 
 26. 
 
 25 3T 
 
 33. 
 
 29 T 4 i 
 
 40. 
 
 191^ 
 
 20. 
 
 25f 
 
 27. 
 
 59& 
 
 34. 
 
 149f 
 
 41. 
 
 203 T % 
 
 21. 
 
 15 A 
 
 28. 
 
 67 T 5 6 
 
 35. 
 
 128| 
 
 42. 
 
 98 H 
 
 22. 
 
 23 A 
 
 29. 
 
 S 9 fi 
 
 36. 
 
 137^ 
 
 43. 
 
 87i| 
 
 23. 
 
 40* 
 
 30. 
 
 131^ 
 
 37. 
 
 238H 
 
 44. 
 
 138^ 
 
148 PRIMARY ARITHMETIC 
 
 ' Reduction of Fractions to Integers or Mixed Numbers 
 
 138. A fraction whose numerator is smaller than its de- 
 nominator is a Proper Fraction. Thus, |, f , and - are proper 
 fractions. 
 
 139. A fraction whose numerator equals or exceeds its 
 denominator is an Improper Fraction. Thus, f, -^-, ^-, and 
 -^L are improper fractions. 
 
 140. A boy has two half dollars. That is the same as 
 how many whole dollars ? Six half dollars equal how many 
 whole dollars ? How do you find it ? 
 
 Eleven half dollars make how many dollars and how many 
 halves over? How do you find it ? Write it. 
 
 How many quarters make a dollar ? 
 
 How many dollars would 8 quarters make ? 40 quarters ? 
 
 Fifteen quarters make how many dollars and how many 
 quarters over ? Write it. How do you find it ? 
 
 | = how many whole ones ? |- ? -^- ? |- ? 
 
 .| = how many wholes ? ^ ? -^ ? i^l ? 
 
 A fraction is an expression of what operation ? 
 
 How do you find the value of a fraction ? 
 
 Rule for Reduction of a Fraction to an Integer or a 
 
 Mixed Number 
 Divide the numerator by the denominator. 
 
 141. Mental. Find the values of : 
 
 1. | 5. Jjp- 9. If- 13. If- 17. 21JL 21. f| 
 
 2. f 6. I 10. -^ 14. f^ 18. {J 22. f| 
 
 3. f 7. Jj/L 11. -*/ 15. -V- 19. ff 23. ff 
 
 4. 8. - 12. -. 16. IA 20. 24. 
 
REDUCTION OF FRACTIONS 149 
 
 142. Written. Reduce to whole or mixed numbers: 
 
 1. JL 3. ^2 5. -Mf 7. JLBL 9 . 
 
 4 - 6 - - 8 - 
 
 11. -V_ 3 - 14. 48. 17. W 20. 
 
 1 o o 'to 
 
 12. 
 
 13. L 16. 2 19. 2 - 22. 
 
 To Least Common Denominator 
 
 143. Fractions whose denominators are alike have a 
 Common Denominator. Thus, ^, |~|, and ||- have a common 
 denominator. 
 
 144. Fractions having the smallest possible common de- 
 nominator are said to have their Least Common Denomi- 
 nator. Thus, 2^, ^, ^, and |^ have their least common 
 denominator. 
 
 145. Multiplying both dividend and divisor by the same 
 number affects the quotient how ? Multiplying both terms 
 of a fraction by the same number affects the value of the 
 fraction how ? 
 
 1. Reduce J, |, |, and | to fractions whose denominator 
 is 120. 
 
 | = y 6 ^. What must you do with the denominator 2 
 to make it 120 ? If you multiply 2 by 60, what must you 
 do with the numerator so that the value of the fraction may 
 not be changed ? 
 
 J = -j^j-. By what must you multiply the terms of f to 
 reduce it to 120ths ? How do you find that number to be 
 40? 
 
150 PRIMARY ARITHMETIC 
 
 I = i%V -^y what must you multiply the terms of | to 
 make it -$ ? How do you find that number to be 30 ? 
 
 | = y 4 ^. By what must you multiply the terms of f to 
 make it T 4 ^- ? How do you find*that number to be 24 ? 
 
 Since the common denominator must be divided by the 
 denominators of all the given fractions, it must be what of 
 their denominators ? 
 
 Then the least common denominator must be what of the 
 given denominators ? 
 
 These questions suggest the following 
 
 Rule for Reduction of Fractions to their Least Common 
 Denominator 
 
 1. Find the least common multiple of the denomi- 
 nators of the given fractions. This is the least common 
 denominator. 
 
 2. Divide the least common denominator by the de- 
 nominator of the first of the given fractions. Multiply 
 its numerator by the quotient obtained. The product 
 is the required numerator. 
 
 3. Proceed in the same way with each of the given 
 fractions. 
 
 THE RULE ILLUSTRATED 
 
 35 2 
 
 2. Reduce - - and - t '- to their least common denomi- 
 
 4 o o 
 
 nators. 
 
 
 4 
 
 6 
 
 3 
 
 = 12, 
 
 least common 
 
 denominator. 
 
 
 2 
 
 3 
 
 3 
 
 X 
 
 2 
 
 xl 
 
 xl 
 
ADDITION OF FRACTIONS 
 
 151 
 
 How many 12ths in 
 How many 12ths in 
 
 4x3 
 
 How many 12ths in 
 How many 12ths in 
 
 (12-6 = 
 
 /5x2 _ 10. 
 ~~ * 
 
 How many 12ths in ? (12 3 = 4.^ 
 How many 12ths in | ? (f-j = -f-% ) 
 
 Change the following to fractions having a least common 
 denominator : 
 
 146. 
 
 Mental. 
 
 
 
 
 1. |, 
 
 f 
 
 4- f , T V 2^ 
 
 7. 
 
 1' i iV 
 
 2. |, 
 
 f 
 
 5. 1, 1, T ^ 
 
 8. 
 
 i. I' f 
 
 3. J, 
 
 $ 
 
 e. J, f , Jy 
 
 9. 
 
 5' 6^ i- 
 
 147. 
 
 Written. 
 
 
 
 
 1. J, 
 
 3 5 
 5' 6 
 
 5. 1 |, f , T ^ 
 
 9. 
 
 f> 1' 9' 10 
 
 2. f, 
 
 1' 9 
 
 6. I, |, f , | 
 
 10. 
 
 f ' A' 1' 1 
 
 3. f, 
 
 T 9 0> J 
 
 7- 9,f, T Vf 
 
 11. 
 
 f i fr A 
 
 4. $, 
 
 I' 2 
 
 8- J,f fA 
 
 12. 
 
 f f i tf 
 
152 PRIMARY ARITHMETIC 
 
 ADDITION OF FRACTIONS 
 
 148. A proper fraction is in its simplest form when it is 
 in its lowest terms. 
 
 An improper fraction is in its simplest form when it is 
 reduced to an integer or a mixed number. 
 
 1*. , Add and A. + _ _ _ . An,. 
 
 ,,,362 ,1 
 
 2. Add -, -, -, and -. 
 
 | + | + 2 + l = 8 ll = ^ = 8. Ans. 
 
 23 5 
 
 3. Add -, -, and . 
 
 o 4 lo 
 
 7 
 
 2,3,5 32 , 36 , 15 32 + 36 4- 15 83 
 
 3 + 4 + l6 = r8 + 48 + r8 = - ~48 - = 48 
 
 328 
 
 X 3xl x4 = 48 
 
 Why do we reduce these fractions to their least common 
 denominator ? 
 
 150. The above examples illustrate the following 
 
 Rule for Addition of Fractions 
 
 1. Reduce the fractions to their least common de- 
 nominator. 
 
 2. Add the new numerators, and write the sum over 
 the least common denominator. 
 
 3. Reduce the result to its simplest form. 
 
ADDITION OF FRACTIONS 153 
 
 151. Addition of Mixed Numbers. 
 
 l. Add 3f, 5i and 
 
 152. 
 
 = = = . Ans. 
 
 Rule for Addition of Mixed Numbers 
 
 1. Add the integers and fractions separately. 
 
 2. Unite the sum of the integers and the sum of the 
 fractions. 
 
 3. Reduce the result to its simplest form. 
 
 153. Mental. Add the following: 
 
 1- i, * 5. 1, 1 9. f, , 3 13. 11, 21, 1 
 
 2. |, 1. 6. f, 1 10. 1, 1, 11 14. 3J, If, 5 
 
 3. f, I 7. l, i 11. 21, 41, 1 15. f, 31 4 
 4- |, 8- i, J 12. l, 1, 16. 2|, 3|, 21 
 
 17. A man paid $f for a book, f | for an inkstand, and 
 $ \ for writing paper. How much did he spend ? 
 
 18. Mary has $|; her mother gave her $3. How much 
 has she ? 
 
 154. Written. Addition : 
 
 1. f, Jj, | 7. |, ft, &, 1 13. 1, 2f, |, 6 
 
 2- \, A, A 8. |, |, ^j, ^ 14. f, |, 2|, ^ 
 
 3- f, i ^ 9- i, f, |, J 15. 4|, f, |, / T 
 * f' f, I 10. f, i 6, | 16. f, J, T ^, 4 
 5. , 1, | 11. |, A ^, | 17. 6|, 8|, f, I 
 6- i ^ L T 3 6 12- f, A, |, i 18- 3, f, }, | 
 
154 PRIMARY ARITHMETIC 
 
 19. f, 4, f, 1| 21. 6, 8J, 5|, 7f 23. j, f, f, |, 
 
 20 - I' I iV T 8 5 22 - 9 i> 5 f' 9 ' H 2*- 5}, 7|, 91, 45 
 
 25. 14f, 9|, 10J, 12if 
 
 26. A man travels 25| miles on Monday, 37^ miles on 
 Tuesday, on Wednesday as many miles as on Monday and 
 Tuesday. How many miles does he travel in three days ?* 
 
 27. A farmer has 27^ bushels of potatoes in one bin, 133$ 
 bushels in another, 47 T 5 ^ bushels in another. How many 
 bushels has he? 
 
 28. Mr. Brown has $13'0f-; his wife $25f more than he 
 has ; his son $78 T 9 ? , and his daughter $5| more than his son. 
 How much have all ? 
 
 29. How many yards of cloth will I have, if I buy 123 
 yards, 76| yards, and 58| yards ? 
 
 30. 6^ yards of cloth are required for a coat, 3| yards for 
 trousers, and ^ yards for a vest. How many yards are 
 required ? 
 
 31. Find what your mother spends if she pays 1 8^ for 
 your coat, $9J for your dress, 4| for your hat, f 2| for your 
 shoes, and $1^ for your gloves. 
 
 32. How much land in a farm of five fields if the first con- 
 tains 26i^ acres, the second 50|-| acres, the third 41^ acres, 
 the fourth 69| acres, and the fifth 52| acres ? 
 
 SUBTRACTION OF FRACTIONS 
 155. 1. From f take ^V 
 
 8 _ _7_ = 80 _ 21 = 59 
 
 3 [9 30 ""90 90 ""90* An$ * 
 
 x 3 x 10 = 90 
 
SUBTRACTION OF FRACTIONS 155 
 
 Rule for Subtraction of Fractions 
 
 1. Reduce the fractions to their least common denomi- 
 nator. 
 
 2. Subtract the numerator of the subtrahend from 
 that of the minuend and write the result over the least 
 common denominator. 
 
 3. Reduce to simplest form. 
 
 SUBTRACTION OF MIXED NUMBERS 
 156. 1. From 10^ take 3||. 
 
 6ff Ans. 
 
 Rule for Subtraction of Mixed Numbers 
 
 1. Subtract the integers and fractions separately. If 
 the fraction in the minuend is smaller than the fraction 
 in the subtrahend, take 1 from the integer of the minu- 
 end and add its value to the fraction of the minuend, 
 before subtracting. 
 
 157. Mental. Subtraction : 
 
 1. f-i 5. T \-f 9. 7- 1 13. 4 -1 
 
 2. |-i 6. f- 1 10. 8- f 14. 6J-4f 
 4- i-* 8- -i 12 - 22 ~i! 16 ' 19* -9* 
 
158. 
 
 Written. 
 
 
 1 
 
 
 
 
 |- 
 
 i 
 
 6. 
 
 15 
 
 -2J 
 
 
 2 
 
 
 
 
 H 
 
 I 
 
 7. 
 
 8* 
 
 -4i 
 
 
 3 
 
 
 
 
 1- 
 
 i 
 
 8. 
 
 10 
 
 5 
 f 
 
 
 4 
 
 
 
 <j 
 
 
 
 i 
 
 9. 
 
 12J 
 
 -6J 
 
 
 5 
 
 , 
 
 3 
 
 
 I 
 
 10. 
 
 81 
 
 -41 
 
 156 PRIMARY ARITHMETIC 
 
 11. if-f 
 
 12. f-1 
 
 13. JL-f 
 
 14. 11-1 
 
 is. if-i 
 
 16. Take l from f . From 1| take T 9 T . 
 
 17. From the sum of | and -| take their difference. 
 
 18. What must I add to 9| to make 20 T 8 ^ ? 
 
 19. The sum of two fractions is i| ; one of the fractions 
 is f . What is the other ? 
 
 MULTIPLICATION OF FRACTIONS 
 
 159. A fraction is an expression of what operation? The 
 numerator of a fraction is which term in division? The 
 denominator ? The value of the fraction ? 
 
 Principles 
 
 1. Multiplying the dividend multiplies the quotient. 
 Therefore, multiplying the numerator multiplies the 
 value of the fraction. 
 
 2. Multiplying the divisor divides the quotient. 
 Therefore, multiplying the denominator divides the 
 value of the fraction. 
 
 3. Dividing the dividend divides the quotient. 
 Therefore, dividing the numerator divides the value of 
 the fraction. 
 
 4. Dividing the divisor multiplies the quotient. 
 Therefore, dividing the denominator multiplies the value 
 of the fraction. 
 
MULTIPLICATION OF FRACTIONS 157 
 
 In what two ways may the value of a fraction be multi- 
 plied? Divided? 
 
 1. Multiply A by 8. 
 lo 
 
 State the principles applied in these operations. 
 160. 
 
 Rule for Multiplication of Fractions by Integers 
 
 1. Multiply the numerator of the fraction by the in- 
 teger ; or, divide the denominator of the fraction by 
 the integer. 
 
 2. Reduce the result to its simplest form. 
 
 161. Mental. Multiply: 
 
 1. I by 2 5. | by 5 9. f by 6 13. ^. by 4 
 
 2. | by 4 6. f by 7 10. f by 4 14. | by 3 
 
 3. | by 3 7. | by 9 11. ^ by 5 15. ^ by 5 
 
 4. | by 3 8. I by 2 12. f by 6 
 
 16. At $ I each, what will 8 books cost ? 
 
 17. If a horse eat | bushel of oats in a week, how much 
 will he eat in 4 weeks ? 
 
 18. If a pound of tea costs $ f , what will 6 pounds cost ? 
 
 19. Multiply the following fractions by 3 and give the 
 result in its simplest form : f, |, |, f , , f . 
 
 Multiply the fractions in example 19 by 5 ; by 6 ; by 10. 
 
158 PRIMARY ARITHMETIC 
 
 162 
 
 . Written. Multiply: 
 
 1. 
 
 if 
 
 by 
 
 7 
 
 7. 
 
 H by 
 
 6 
 
 13. 
 
 t 
 
 * 
 
 by 
 
 10 
 
 2. 
 
 | 
 
 by 
 
 6 
 
 8. 
 
 A b y 
 
 10 
 
 14. 
 
 1 
 
 i 
 
 b y 
 
 12 
 
 3. 
 
 2T 
 
 by 
 
 5 
 
 9. 
 
 M by 
 
 7 
 
 15. 
 
 i 
 
 *s 
 
 by 
 
 11 
 
 4. 
 
 u 
 
 by 
 
 7 
 
 10. 
 
 11 by 
 
 6 
 
 16. 
 
 
 \ 
 
 by 
 
 20 
 
 5. 
 
 H 
 
 by 
 
 9 
 
 11. 
 
 A by 
 
 15 
 
 17. 
 
 
 
 \ 
 
 by 
 
 18 
 
 6. 
 
 1! 
 
 by 
 
 8 
 
 12. 
 
 A by 
 
 25 
 
 18. 
 
 1 
 
 9 
 
 by 
 
 26 
 
 19. f of 12 == ? 
 
 SOLUTION. J of 12 = -\ 2 - = 3. 
 
 } of 12 = 3 x 3 = 9. Ans. 
 
 20. | of 7 = ? 
 
 SOLUTION. J of 7 = J. 
 
 | of 7 = 5 times J = = 4 f- ^ ns - 
 
 NOTE. | q/" 7 is the same as f ^wes 7, and the product is the same 
 as 7 times f . 
 
 21. f of 5 = ? -^ of 4 = ? | of 3 = ? of 6 = ? 
 
 22. $ 10 multiplied by | = ? ^ x 10 = ? 
 
 23. f x 8 = ? 4 x f = ? f x 4 = ? 
 
 24. Multiply 18| by 8, first reducing the mixed number 
 to an improper fraction. 
 
 25. Multiply 18| by 8 without reducing the mixed number 
 to an improper fraction. First multiply the fraction, then 
 the integer, by 8, and add the products. Thus : 
 
 18* 
 
 g SOLUTION. 
 
 8 times f = ^ = 6 
 8 times 18 = 144 
 
 144 150 
 
 150 
 
 26. 16| multiplied by 10. 29. Multiply 27 jf by 38. 
 
 27. 126| multiplied by 9. 30. Multiply 35J| by 46. 
 
 28. 326| multiplied by 5. 31. 9 times 2lf f = ? 
 
MULTIPLICATION OF FRACTIONS 159 
 
 32. Multiply 47 by 6|, first reducing the mixed number to 
 an improper fraction. 
 
 33. Multiply 65 by 7-|. 35. 4$ times 48 = ? 
 
 34. Multiply 125 by 14|. 36. 19f times 385 = ? 
 
 163. l. Multiply f by f . 
 
 Since ^ means 5 divided by 7, then to multiply f by f- is 
 to multiply it by 5 and divide it by 7. What is the easiest 
 
 way to multiply f by 5 ? f Y To divide it by 7 ? 
 
 2 x 5\ . 3 
 
 See principles, Article 164. Therefore 
 
 4 
 
 How was the work shortened in examples 2 and 3 ? 
 
 164. These examples illustrate the following 
 
 Rule for Multiplication of a Fraction by a Fraction 
 
 1. Multiply all the numerators together. 
 
 2. Multiply all the denominators together. 
 
 3. Cancel when possible. 
 
 4. Write the first product over the second and reduce 
 to simplest form. 
 
160 PRIMARY ARITHMETIC 
 
 KOTE 1. Any integer may be expressed as a fraction by writing it 
 over the denominator 1. 
 
 NOTE 2. The word of between fractions means the same as the sign 
 of multiplication. 
 
 Fractions joined by of form a Compound Fraction. 
 
 NOTE 3. Mixed numbers must be changed to improper fractions 
 before multiplying them together. 
 
 Oral. 
 
 1. How much is | of ^ of an inch ? 
 
 2. Illustrate that \ of \ of an apple is J of an apple. 
 
 3. Multiply f by 1 ; | by 1; 1 by I; J by f 
 
 4. How much is \ of f ? f of f ? \ of | ? l of T \ = ? 
 
 5. A man owned f of a farm and sold | of his share. 
 What part of the farm did he sell ? 
 
 6. James had $ |, and John \ as much. How much had 
 both ? 
 
 7. If a pound of tea costs $ |, what will \ pound cost ? 
 
 165. Written. Find the products : 
 
 1. 
 
 2. 
 3. 
 
 4. 
 
 1 x| 
 
 i.'kf 
 
 T 9 X | 
 
 i of A 
 
 7. 
 8. 
 9. 
 10. 
 
 1 
 i 
 
 of 
 of 
 
 V x 
 
 T 9 ^ | 
 12 X 7- 
 
 9X4 
 
 13. 
 14. 
 15. 
 16. 
 
 5f 
 
 71 
 
 i 
 
 X 
 X 
 X 
 
 X 
 
 2| x 20 
 ii x T 5 i 
 
 5. 
 
 |-of 
 
 ii 
 
 11. 
 
 9 \x 1 v 8 
 
 2T X -J- X g 
 
 17. 
 
 A 
 
 X 
 
 4 x 5| 
 
 6. 
 
 A* 
 
 : i 9 * 
 
 12. 
 
 1 
 
 f x 
 
 34 x f 
 
 18. 
 
 A 
 
 X 
 
 80 x 5J 
 
 Find the 
 
 value : 
 
 
 
 
 
 
 
 
 
 19. 
 
 ! f 
 
 40 
 
 22. 
 
 1 
 
 of 
 
 328 
 
 25. 
 
 11 
 
 of 
 
 342 
 
 20. 
 
 f of 
 
 42 
 
 23. 
 
 f 
 
 of 
 
 721 
 
 26. 
 
 15 
 16 
 
 of 
 
 800 
 
 21. 
 
 f of 
 
 16 
 
 24. 
 
 1 
 
 of 
 
 90 
 
 27. 
 
 A 
 
 of 
 
 2222 
 
, 
 
 DIVISION OF FRACTION 161 
 
 28. | of | of f of f of -| = ? $ of f of -V- of T \ = ? 
 
 29. ^Offfof^oflf Of| = ? f Of Jf Of | Of If = ? 
 
 30. Mr. Brown earns $40| a month, and his son | as 
 much. How much does the son earn ? 
 
 31. At $ 12| a ton, how much will 9^ tons of hay cost ? 
 
 32. What will be thg cost of 48| yards of cloth at $ | a 
 yard? 
 
 33. A man gave 124y 5 ^ acres of land to his two sons, giv- 
 ing | of it to the elder and | to the younger. How many 
 acres did each receive ? 
 
 34. If it requires 21| days for a man to dig a ditch, in 
 what time can he dig | of it ? 
 
 DIVISION OF FRACTIONS 
 
 166. What operations upon the dividend and divisor divide 
 the quotient ? 
 
 What operations on the numerator and denominator divide 
 the value of the fraction ? 
 
 l. y 9 y -7- 3 = ? What is the easiest way to divide -^ by 3 ? 
 
 2. ^g -r- 3 = ? What is the easiest way to divide ^ by 3 ? 
 -*- 3 = T&* = & 
 
 167. 
 
 Rule for Dividing a Fraction by an Integer 
 
 1. Divide the numerator or multiply the denominator 
 of the fraction by the given integer. 
 
 2. Reduce the result to its simplest form. 
 
162 PRIMARY ARITHMETIC 
 
 168 
 
 . Mental. Divide : 
 
 3. 
 
 I 
 
 by 3 
 
 7 16 
 '' 16 
 
 by 5 
 
 11. 
 
 1 5 
 21 
 
 by 
 
 8 
 
 15. 
 
 II 
 
 by 5 
 
 4. 
 
 I 
 
 by 3 
 
 8. 1 
 
 by 6 
 
 12. 
 
 ^ 
 
 by 
 
 10 
 
 16. 
 
 I 
 
 by 3 
 
 5. 
 
 l 
 
 9 
 
 by 4 
 
 9. f 
 
 by 3 
 
 13. 
 
 41 
 
 by 
 
 8 
 
 17. 
 
 I 5 o 
 
 by 4 
 
 6. 
 
 i 
 
 by 4 
 
 10. I 
 
 by 3 
 
 14. 
 
 A 
 
 by 
 
 7 
 
 18. 
 
 
 
 by 4 
 
 19. 
 
 A 
 
 man 
 
 divides $ 
 
 | equally 
 
 am<*ng 
 
 4 
 
 boys. 
 
 What 
 
 part 
 
 of a dollar does each receive ? 
 
 20. A boy wishes to put | of a bushel of chestnuts into 5 
 bags. How much will each bag contain ? 
 
 21. If 4 pounds of coffee cost $|, what will one pound 
 cost? 
 
 22. Divide $ | equally among 5 boys. What is the share 
 of each ? 
 
 23. How much is 1 -=- 4 ? \ divided by 5 ? 1 divided by 6 ? 
 
 -bj3 
 if by 6 
 ft by 2 
 ft by 7 
 II by 12 
 16. Divide 14 by 3. 
 
 : "3~ SOLUTION. We may change the 
 
 "V" ~*~ "3 = ^ = 4-| mixed number to an improper frac- 
 
 Q r tion and divide according to the 
 
 o rule, or we may divide without 
 
 ) "5" changing to an improper fraction. 
 
 4| 14| -r- 3 = 4 with a remainder of 2|. 
 
 69. Written. Divide: 
 
 1. 
 
 if 
 
 by 
 
 5 
 
 6. 
 
 fl 
 
 by 
 
 7 
 
 11. 
 
 2. 
 
 fl 
 
 by 
 
 6 
 
 7. 
 
 if 
 
 by 
 
 2 
 
 12. 
 
 3. 
 
 1! 
 
 by 
 
 5 
 
 8. 
 
 ii 
 
 by 
 
 3 
 
 13. 
 
 4. 
 
 1 3 T 
 
 by 
 
 7 
 
 9. 
 
 ti 
 
 by 
 
 10 
 
 14. 
 
 5. 
 
 
 
 by 
 
 4 
 
 10. 
 
 M 
 
 by 
 
 5 
 
 15. 
 
DIVISION OF FRACTIONS 163 
 
 Find the quotients : 
 
 17 . 476 _g_ 7 2CX 38 5| + 5 = ? 23< 2 64f -*- 4 = ? 
 
 18. 384f -g- 5 21. 16-| -s- 5 = ? 24. 9826-^ - 6 = ? 
 
 19. .287^ -*- 8 22. 30f -5- 7 = ? 
 
 25. If 16 bushels of apples cost $8|, what will 1 bushel 
 cost? 
 
 26. Five heirs shared equally in the division of a legacy 
 of $35,862f . What was the share of each ? 
 
 170. 
 
 | -r- 7 = 7 - . What principle is applied here ? We have 
 
 divided | by 7. The divisor given was -^ ; 7 is how many 
 times as large as -^ ? Since we have used a divisor 11 times 
 as large as the given divisor, how does the quotient compare 
 with the correct quotient ? State the principle. How shall 
 we correct the quotient ? What is the easiest way to 
 
 multiply 7 - by 11? The quotient then becomes -z -- =-. 
 o x 7 o x 7 
 
 This is the same as multiplying | by what fraction ? 
 
 I x = ft- Ans - 
 
 What do you do with ^- to get -y~ ? 
 
 2. 19^3 = ? 19^-V- -Y-^^ = i I ax = 1 F = 
 30|. Ans. 
 
 What is done with the integer before dividing ? 
 
 7 32 
 3 614 -*- - 1 - 7 - = ? 6lJr - 1 - li ^ x ^ ^4- 24^ J.TIS 
 
 u l '64"" u l^ * et~~ tg T7 ~ 9 9 * -aiw. 
 
 9 
 What is done with the mixed number before dividing ? 
 
164 PRIMARY ARITHMETIC 
 
 171. The above examples illustrate the following 
 
 Rule for the Division of a Fraction by a Fraction 
 
 1. Interchange the terms of the divisor. 
 
 2. Multiply the dividend by the divisor with terms 
 inverted. 
 
 3. Express integers and mixed numbers as fractions 
 before dividing. 
 
 172. Example 1 may be solved also by reducing both 
 dividend and divisor to a common denominator, thus : 
 
 3 7 3x11 7x5 
 
 5 11 5 x 11 11 x 5 
 
 The denominator 5 x 11 being common to both fractions, 
 we divide the numerator of the dividend by the numerator 
 of the divisor, thus, 
 
 3x 11 = 33 
 
 7x5 35' 
 
 This gives the same result as multiplying the dividend by 
 the divisor with terms interchanged, thus, f x ^ = ff . 
 
 173. Find the quotients : 
 
 4. 
 
 *+! 
 
 9. 
 
 3 2 -*- ii 
 
 14. 
 
 2-H| 
 
 19. 
 
 2f + 
 
 5 2 
 
 5. 
 
 tt-*f 
 
 10. 
 
 **i ~"~ A 
 
 15. 
 
 ^T 7 o 
 
 20. 
 
 7i- 
 
 !| 
 
 6. 
 
 T 5 *-t 
 
 11. 
 
 _3_ _^_ 51 
 11 U 4 
 
 16. 
 
 10- f 
 
 21. 
 
 2| + 
 
 T5 
 
 7. 
 
 1 ft O 
 
 JLfi. _s_ J. 
 
 2Y ' 3 
 
 12. 
 
 i 7 ?- 4 ! 
 
 17. 
 
 f-i-14 
 
 22. 
 
 2i + 
 
 3J 
 
 8. 
 
 1A _._ _T_ 
 15 ' 10 
 
 13. 
 
 tt + fi* 
 
 18. 
 
 M- 8 
 
 23. 
 
 8 i- 
 
 9 I 
 
* DIVISION OF FRACTIONS 165 
 
 24. | X f -*- f of f = ? 
 
 O o O O 
 
 SOLUTION. Inverting the divisor, indicating the operations, and can- 
 celling, we have 
 
 3 6 ^3 
 
 25. f Of 9 -f-f Of f 27. 3| -r- f X | Of 2 
 
 26. | Of -If -r- f Of 4 28. f X f X f -f- 71 
 
 29. Divide 3682 by 5J. 
 
 SOLUTION. When the dividend contains several figures and the 
 51^)3682 divisor is a mixed number, it is often more convenient to 
 2 2 divide as above. 
 
 TT \ 70^/1 ^ e mu ltiply both dividend and divisor by 2, when 
 
 the divisor becomes 11 (halves), and the dividend 7364 
 6 ^T 5 T (halves). Dividing, the quotient is 669 T 5 T . 
 
 Find the quotients: 
 
 30. 356-4J 33. 296 -v- 101 3 6. 76,582-91 
 
 31. 728-81 34. 39,846 -r-3 37. 28,769 -7f 
 
 32. 397 -f- 51 35. 44,077 H- 51 
 
 38. There are 51 yards in a rod. How many rods in 
 3158 yards ? 
 
 39. If a man walks 15^ miles a day, in how many days 
 can he walk 155 miles ? 
 
 40. What is the price of coal per ton when 16 tons cost 
 
 |73|? 
 
 41. How much does a man earn in a day if he earns f 84| 
 in a month of 26 days ? 
 
 42. When flour is |6| per barrel, how many barrels can 
 be bought for $297? 
 
166 PRIMARY ARITHMETIC 
 
 174. A fraction that has a fraction in either or both of its 
 terms is a Complex Fraction. Thus, 
 
 A JL M M i I -s-9 
 8f 16' 25' 7f If -| 
 
 are complex fractions. 
 
 A fraction whose terms are integers is a Simple Fraction. 
 Thus, 1J is a simple fraction. 
 
 1. Reduce to a simple fraction. 
 
 7 7 3 ft9 7 26 7 3 21 
 = 7 -f- 84 = i -- = - x = . Ans. 
 8f 1 3 1 26 26 
 
 JL 
 
 2. Reduce 1* to a simple fraction. 
 
 i = -*- 40 - ft - Ans 
 40 17 ' ~17x0~136' 
 
 8 
 7& 
 
 3. Reduce _ i. to its simplest form. 
 
 8 ' 20~ ji 53 
 2t 
 
 175. From the examples we may obtain the following 
 
 Rule for the Reduction of a Complex Fraction to its 
 Simplest Form 
 
 1. Perform the operations indicated in the numera- 
 tor, if there are any. 
 
 2. Perform the operations indicated in the denomi- 
 nator, if there are any. 
 
 3. Divide the numerator by the denominator, and 
 reduce the result to its simplest form. 
 
THE THREE QUESTIONS OF RELATION 167 
 
 176. Change to simple fractions : 
 
 A 9 fi 5 Q 
 
 I 18 
 
 13. 
 
 1 
 
 14. If | of an acre of land is worth $72^-, what is the 
 value of an acre at the same rate ? 
 
 15. There are 5J yards in a rod. How many rods in 70-| 
 yards ? 
 
 16. At $5J a ton, how many tons of coal can be bought 
 
 for 8731? 
 
 THE THREE QUESTIONS OF RELATION 
 
 177. 1. 3 times 4 equals what ? Am. 12. 
 
 2. 12 is how many times 4 ? Ans. 3. 
 
 3. 12 is 3 times what ? Ans. 4. 
 
 In question 1, we have two factors, to find their product. 
 In questions 2 and 3, we have the product and one factor, to 
 find the other factor. 
 
 1. Form questions like 2 and 3 from the following state- 
 ment : 5 x 6 = 30. 
 
 a. i of 8 equals what ? 
 
 Multiplying 8 by J, we have 4. Ans. 
 
 b. 4 is \ of what ? 
 
 Since Jx8 = 4, 4-s-J=8. Ans. 
 
 c. 4 is what part of 8 ? 
 
 Since x8 = 4,4-*-8 = . Ans. 
 
168 PRIMARY ARITHMETIC 
 
 Principle 
 
 The product of two numbers divided by one of them 
 gives the other. 
 
 To THE TEACHER. In such examples as question a, after the prod- 
 uct is found, it may be used with each of the two numbers to form 
 successively, question b and question c. Drill upon these three questions 
 of relation should be so thorough that each question will suggest its own 
 solution instantly. 
 
 2. J of 24 = what ? (Question a.) 
 
 3. After finding the product in example 2, form question 
 b. Question c. 
 
 4. 8 is J of what ? (Question 5.) 
 
 SOLUTION. From the question it is evident that 8 is the product of 
 two numbers, and that i is one of them. Therefore, 8 -H J = 24. 8 is 
 i of 24. 
 
 5. What part of 24 is 8 ? (Question c.} 
 
 SOLUTION. It is evident that 8 is the product of two numbers, and 
 24 is one of them. Therefore, 8 - 24 = & or J. 8 is J of 24. 
 
 Question a 
 Find the result, and form questions b and c : 
 
 6. How much is f of 12 ? 9. f of 15 = ? 
 
 7. How much is f of 16 ? 10. f of 21 = ? 
 
 8. How much is 4 of 20 ? 11. 4 of 40 = ? 
 
 O O 
 
 Question b 
 Find the result, and form questions a and c : 
 
 12. 15 is | of what ? 15. 18 is f of what ? 
 
 13. 4 is f of what ? 16. 24 is f of what ? 
 
 14. 9 is f of what ? 17. 25 is ^ of what ? 
 
THE THREE QUESTIONS OF RELATION 169 
 
 Question c 
 Find the result, and form questions a and b : 
 
 18. What part of 24 is 8 ? 21. 21 is what part of 35 ? 
 
 19. What part of 18 is 12 ? 22. 28 is what part of 63 ? 
 
 20. What part of 9 is 2 ? 23. 15 is what part of 25 ? 
 
 Find the result, form the other two questions, and solve 
 each: 
 
 24. | of 56 equals what ? 28. How much is fa of 96 ? 
 
 25. What part of 49 is 14 ? 29. 38 is T 2 T of what number ? 
 
 26. 26 is | of what ? 30. 16 is what part of 80 ? 
 
 27. 65 is what part of 120 ? 31. 1 8 is -f$ of what number? 
 
 REMARK. Each of the following problems contains one or more of 
 the three questions of relation. Before attempting to solve any of them, 
 the pupil should state the question in each of them. 
 
 32. James had 56 marbles, and John | as many. How 
 many had John ? 
 
 The question is, How much is | of 56 ? a. 
 
 33. John had 42 marbles, which was | as many as James 
 had. How many had James ? 
 
 The question is, 42 is f of what ? b. 
 
 34. James had 56 marbles, and John 42. John's marbles 
 are what part of James's ? 
 
 The question is, What part of 56 is 42 ? c. 
 
 35. A man sold 50 acres of land, which was f of all he 
 had. How many acres had he at first ? 
 
 36. A boy had 20 cents and spent 15 cents. What part 
 of his money did he spend ? What part was left ? 
 
 37. Mr. A has 640 sheep, and Mr. B -^ as many. How 
 many has Mr. B? 
 
170 PRIMARY ARITHMETIC 
 
 ALIQUOT PARTS 
 
 178. An aliquot part of a number is any integer or mixed 
 number that is exactly contained in it. 
 
 PARTS OF A DOLLAR 
 
 6J cents = i^g 37-| cents = $f 
 
 81 cents = $ ^ 50 cents = $ J 
 
 12 1 cents = I J 621 cents = f 
 
 16f cents = $ J 66 cents = $f 
 
 25 cents = $| 75 cents =$ 
 
 33J cents = | J 871 cen ts = if 
 
 What is the cost of 33 books at 16| ^ each ? 
 33 books cost 33 times 16f& or 33 times 
 
 $5.50. 
 
 Oral. Multiply : 
 
 1. 121 cents by 16 7. 371 cents by 8 
 
 2. 16| cents by 12 8. 50 cents by 15 
 
 3. 25 cents by 20 9. 621 cen ts by 8 
 
 4. 331 cents by 27 10. 66| cents by 9 
 
 5. 6J cents by 16 11. 75 cents by 4 
 
 6. 8J cents by 24 12. 871 cents by 8 
 
 13. What is the cost of : 
 
 16 pounds of bacon @ 12|^ a pound? 
 16 balls @ 50^ each? 
 36 yards of ribbon @ 331^ a yard ? 
 36 pounds of candy @ 25^ a pound? 
 8 pounds of tea @ 621 ^ a pound ? 
 
 The sign @ means at. The sign ^ means cents. 
 
ALIQUOT PARTS 171 
 
 Written. 
 
 What is the cost of : 
 
 14. 66 pounds of pork at 12^ cents a pound? 
 
 48 pounds of veal at 16| cents a pound? 
 
 65 boxes of strawberries at 25 cents a box? 
 
 15 yards of flannel at 831 cents a yard? 
 
 80 pounds of honey at 25 cents a pound? 
 
 48 pounds of tea at 50 cents a pound? 
 
 179. l. At 25^ a pound, how many pounds of butter can 
 be bought for $8? 
 
 As many pounds as 25^ or $^ is contained times in $8. 
 $8 -s- $| = 32 pounds. Ans. 
 
 Oral. Divide : 
 
 2. $3 by 33|^ 6. $lby6|^ 9. $4 by 12J* 
 
 3. |5 by 25^ 7. $10 by 50^ 10. $2 by 
 
 4. $2 by 8$ ft 8. 16 by 331^ 11. $3 by 
 
 5. $9 by 12^ 
 
 180. Written. t 
 
 12. At 25 cents apiece, how many hats can be bought for 
 $6? 
 
 13. At 25 cents a pound, how many pounds of cheese can 
 be bought for $ 5 ? 
 
 14. At 16| cents a dozen, how many dozen eggs can be 
 bought for $4? 
 
 15. How many pounds of beef can be bought for $4 at 
 $.16| a pound ? 
 
 16. At 33^ a yard, how many yards of linen can be 
 bought for $10? 
 
 17. How many penknives can be bought for $6 at 33| 
 cents apiece? 
 
 18. 24x1.12-1 = ? 19. 124 -1-$. 12J=? 
 
172 PRIMARY ARITHMETIC 
 
 REVIEW OF FRACTIONS 
 
 181. Oral. 
 
 1. Change J to sixths. To ninths. 
 
 2. Change J to sixths. To ninths. 
 
 3. Express ^ in larger terms. What operations did you 
 perform ? 
 
 Express | in smaller terms. What did you do ? 
 
 Change the following : 
 
 4. I to lOths 6. % to 27ths 8. 4- to 25ths 
 
 o 
 
 5. | to 9ths 7. I to 56ths 9. f to 84ths 
 
 o o / 
 
 Change to lowest terms : 
 
 10. f 12. 1| 14. ff 16. If 
 
 11. 1 13. f$ 15. || 17. Jf 
 
 18. Reduce 5J to halves. 71 to eighths. 4| to sixths. 
 4|^ to sevenths. 
 
 19. Change 41 to 9ths. 3| to 3ds. 5 T % to lOths. 8| to 
 5ths. 7- to llths. 
 
 Reduce to improper fractions : 
 
 20. 3f 22. 2| 24. 8^ 26. 12| 
 
 21. 41 23. 3 25. 9| 27. 
 
 28. How many dollars in $ - 2 /- ? in $ ! y 4 - ? in $ -\ 8 - ? 
 
 29. 12 fourths of a bushel are equal to how many bushels? 
 36 fourths ? 40 fourths ? 
 
 30. To how many dollars are 8 fourths of a dollar equal? 
 9 fourths? 11 fourths? 
 
 Reduce to integers or mixed numbers : 
 
 31. | 33. 35. ^ 37. iU. 
 
 32. f 34. %* 36. Af 38. 
 
REVIEW OF FRACTIONS 173 
 
 39. Change ^ and ^ so both may have 20 for a denomi- 
 nator. 
 
 40. Change J, J, and ^ each to 12ths. 
 
 41. Change f and | each to 24ths. 
 
 42. A boy paid -| of a dollar for a book and ^ of a dollar 
 for a paper. How much did he pay? 
 
 43. John saves J a dollar a week, and Charles f of a dol- 
 lar. How many fourths do both save ? 
 
 44. Henry gave J of his marbles to one boy and f of them 
 to another. How many twelfths do both receive ? 
 
 45. A clerk sold J a pound of tea to one customer, - to 
 another, and | to another. How many eighths did he sell? 
 
 46. A man pays ^ of his salary for rent, ^ for table ex- 
 penses, and T 2 Q- for clothing. What part of his 'money was 
 expended for rent, table, and clothing? 
 
 47. A boy had $ T 9 ^ and spent f J. What part of a dollar 
 had he left? 
 
 48. A owns | of a store, and B ^. How much of the store 
 does A own more than B ? 
 
 49. John runs J of a mile, and Jerry f of a mile. Which 
 runs farther, and what part of a mile ? 
 
 50. Mr. Ames owned ^ of a farm and sold ^ of it. What 
 part remained? 
 
 51. What is the difference between f of anything and -| 
 of it ? Which is greater ? 
 
 52. Lucy has $-|, and Alice $|. Which has the more, 
 and how much ? 
 
 53. How much is J of J of an orange? ^ of ^ of an 
 orange ? 
 
 54. At $ -| each, what will 8 books cost? 
 
174 PRIMARY ARITHMETIC 
 
 182. Written. 
 
 1. Find the cost of four pieces of cloth, measuring 231 
 yards, 25f yards, 22| yards, and 21| yards, at $ 2 a yard. 
 
 2. Charles has $ 15| in the bank. How much more must 
 he earn before he has $50? 
 
 3. From the sum of 2| and 31 J, take the difference of 5| 
 and 41. (Indicate.) 
 
 4. Which is greater, the product of | and 1, or the dif- 
 ference ? How much ? 
 
 5. A man drew from the bank $68, which was | of his 
 entire deposit. How much had he at first? (Question.) 
 
 6. A sum of money was divided between John and James. 
 John received |- of it, and James $300. How much did 
 John receive? 
 
 7. A merchant paid $272 for flour at $| a barrel. How 
 many barrels did he buy ? 
 
 8. Subtract 2 from both terms of the fraction |. Do you 
 increase or diminish the fraction, and how much ? Add 2 to 
 each term and find the difference. 
 
 9. What must be added to | + If + l to make 5 ? 
 
 10. What number multiplied by 25J will make 264 ? 
 
 11. A lady gave $| for ribbon, $ 1 for pins, $| for velvet, 
 and $^- for lining.* What change did she receive from a five- 
 dollar bill? 
 
 12. What will 4| pounds of raisins cost at 15^ a pound? 
 
 13. From 25 yards of cloth, a tailor used If yards for 
 making a vest, 21 yards for a pair of pantaloons, 3J yards 
 for a coat, and 4^ yards for an overcoat. How much cloth 
 was left? 
 
REVIEW OF FRACTIONS 175 
 
 14. I owned |- of a farm and sold ^ of my share. What 
 part of the farm did I sell, and what part did I retain ? 
 
 15. Henry had $78 in the bank. He withdrew $15 at one 
 time and $38 at another time. What part of his money did 
 he withdraw? (Question.) What part remained? (Ques- 
 tion.) 
 
 16. A man having 150 sheep sold ^ of them and kept the 
 remainder. How many were sold ? How many were kept ? 
 
 17. A man owning -| of a factory sold J of his share. 
 What part of the factory did he sell? 
 
 18. A man sold 50 sheep, which was | of his whole flock. 
 How many sheep had he at first? 
 
 19. If 4 yards of ribbon cost 35 1^, what is the price per 
 yard ? 
 
 20. If 20^ pounds of sugar cost 80 cents, what will 50 
 pounds cost? (Use cancellation.) 
 
 21. If 20|^ pounds of sugar cost 83^, how many pounds 
 can be bought for $2.00 ? 
 
 22. I bought 55 yards of cloth at $|- a yard, and sold it 
 at $-| a yard. What was the profit? 
 
 23. If an acre of land is worth $150, what part of an acre 
 will $ 50 buy ? 
 
 24. How long will it take a boy to pay for a $ 75 bicycle, 
 if he can pay $-| a day? 
 
 25. -| of a class are boys ; there are 30 girls. How many 
 pupils in the class ? 
 
 26. If 2J pounds of tea cost $1.00, how much will 3| 
 pounds cost ? 
 
 27. At $^ a pound, what is the cost of | pound of tea ? 
 
 28. Find the product of f , |-, 5|, and 2^. 
 
DECIMAL FRACTIONS 
 
 183. A Common Fraction is generally expressed by 
 placing the denominator below the numerator. 
 
 184. A Decimal Fraction has a denominator, but the 
 latter is not generally written. 
 
 The denominator of a common fraction may be any 
 number. 
 
 185. The denominator of a decimal fraction must be 10, 
 or 100, or 1000, etc. 
 
 NOTE. The word decimal comes from the Latin word decem, ten, 
 and so the denominator of every decimal fraction is 10, or 10 x 10, 
 or 10 x 10 x 10, etc. 
 
 186. A Decimal Fraction, or Decimal, is a fraction whose 
 unit is divided into tenths, hundredths, thousandths, etc. 
 
 187. A Decimal is always written at the right of a period 
 (.), called the Decimal Point. 
 
 We use the decimal point in writing U.S. money to sepa- 
 rate the dollars from the cents and mills. 5 dollars and 
 28 cents is written $5.28. But 28 cents is T 2 ^ of a dollar; 
 hundredths therefore are written like cents, with twc decimal 
 figures. 
 
 NOTE. Any figure at the right of the decimal point is a decimal 
 figure. 
 
 176 
 
DECIMAL FRACTIONS 177 
 
 Tenths are written like dimes, with one decimal figure. 
 
 Hundredths are written with two decimal figures, -f-^ 
 28; y 3 ^-=.39; y|-Q = . 06. 
 
 Thousandths are written with three decimal figures, 
 = .325; ^=.864; T ffo=.025. 
 
 Name the denominators : 
 
 1. .6 3. .105 5. .05 
 
 2. .17 4. .006 6. .225 
 
 188. Change to the decimal form : 
 
 ! ~^\ 6' - 8 oV H' Hfo^O ^. - 9 ?f 
 
 2 _8JL 7 _4JL 12 - 1 1- 17 - 1 
 
 100 100 100 10 
 
 3> T 8 OW 8 ' 1\ 13 ' T"00" 18 * 
 
 4 -.T 6 9 - Tto 14 - foOT 19 ' 
 
 5 - iVo 10 - iMo 15 - I 5 oo 20 - 
 
 189. Change to common fractions, and read : 
 
 21. .36 26. .485 31. 5.6 
 
 22. .7 27. .016 32. 5.06 
 
 23. .125 28. .16 33. 5.006 
 
 24. 12.2 29. .06 34. 5.600 
 
 25. 6.25 30. .6 35. 5.060 
 
 190. Write, first as common fractions, then as decimals : 
 
 36. Four tenths. 
 
 37. Seventy-five hundredths. 
 
 38. One hundred twenty-five thousandths. 
 
 39. Sixteen, and forty-eight hundredths. 
 
 40. Twelve, and four tenths. 
 
178 PRIMARY ARITHMETIC 
 
 41. Six tenths. 
 
 42. Six hundredths. 
 
 43. Six thousandths. 
 
 44. How many decimal figures are required to express 
 thousandths ? Hundredths ? Tenths ? 
 
 45. Read the numerators only in examples 36 to 43. 
 Write the following as decimals, and read the numerator 
 
 of each, then the denominator of each : 
 
 46. Two hundred eighty-two thousandths. 
 
 47. Fifty-six hundredths. 
 
 48. Seven tenths. 
 
 49. Six hundred thousandths. 
 
 191. Oral. 
 
 1. What part of 10 units is 1 unit ? 
 
 2. What part of 1 ten is 1 unit ? 
 
 3. What part of 2 hundreds is 2 tens ? 
 
 4. In the number 555, what is the value of the first 5 at 
 the right ? The second 5 ? The third 5 ? 
 
 5. Upon what does the value of any figure depend ? 
 
 6. The value of the first five is what part of the value 
 of the second five ? 
 
 7. -f^ is what part of 2 units ? 
 
 8. In the number 5.5, tne value of the right-hand 5 is 
 what part of the value of the. left-hand 5 ? 
 
 9. Write five and five-tenths decimally. 
 
 10. .5 is what part of 5? 
 
 11. In the decimal .555, what is the value of the first o 
 to the right ? The second 5 ? The third 5 ? 
 
 12. How much greater is the value of the third 5 than 
 the second 5 ? 
 
DECIMAL FRACTIONS 179 
 
 13. How much greater is the second 5 than the first 5 ? 
 In the number 555.555, we have found that the value of 
 
 each 5 is -^ as much as the next 5 to the left. Also that 
 the value of any 5 is 10 times as great as the value of the 
 next 5 to the right. 
 
 In decimals as in integers, any figure removed one place 
 to the right is diminished tenfold, and when removed one 
 place to the left is increased tenfold. 
 
 14. In the number 32.6, what would be the value of the 
 2 if it were removed one place to the right ? One place to 
 the left ? 
 
 Read: 15. .222 17. 22.2 
 
 16. 2.22 18. 222. 
 
 192. Integers and Decimals. 
 
 03 
 
 
 
 . S 
 
 02 02 +J M 
 
 2 Id . 09 1? 2 
 
 r^ 08 . 02 H ?j *^ 
 
 Ho203 ^3-M OlHw 
 
 i O M -^TS d JL 9 
 
 in !;,. in ill 
 
 i i flpQ ^o^ s3^o fl ^ r"i 
 
 WHH WHO HWH HffiS 
 
 4, 243, 684 . 268, 504 
 
 The number is read 4 million, 243 thousand, 684 and 268 
 thousand 504 millionths. 
 193. 
 
 Rule for Reading Decimals 
 
 1. For the numerator, read the decimal as an integer. 
 
 2. For the denominator, give the place name of 
 the last figure. 
 
 NOTE. The denominator of a decimal is always named, but seldom 
 written. 
 
180 PRIMARY ARITHMETIC 
 
 In reading an integer and a decimal, read " and " where 
 the decimal point occurs. 
 
 What is the denominator when the decimal has one figure ? 
 Two figures ? Three figures ? Four figures ? Five figures ? 
 Six figures ? Seven figures ? 
 
 194 
 
 , Read: 
 
 
 
 
 
 1. 
 
 .368 
 
 7. 
 
 28.3005 
 
 13. 
 
 .4983695 
 
 2. 
 
 .894 
 
 8. 
 
 .28962 
 
 14. 
 
 4.98369 
 
 3. 
 
 .5328 
 
 9. 
 
 15.60534 
 
 15. 
 
 49.8369 
 
 4. 
 
 .2053 
 
 10. 
 
 37.00537 
 
 16. 
 
 498.369 
 
 5. 
 
 25.623 
 
 11. 
 
 25.203602 
 
 17. 
 
 .000400 
 
 6. 
 
 7.0063 
 
 12. 
 
 38.000006 
 
 18. 
 
 .0004 
 
 19. In example 11 remove the point two places to the 
 right, and read. Four places to the right. One place to 
 the left. 
 
 20. Read the denominators only in the last five examples. 
 195. 
 
 Rule for Writing Decimals 
 
 Write the numerator, prefix naughts when necessary to 
 express the denominator, and place the point at the left. 
 
 How many decimal figures are required to express tenths ? 
 Hundredths? Thousandths? Ten-thousandths? Hundred- 
 thousandths ? Millionths ? Ten-millionths ? 
 
. WRITING DECIMALS 181 
 
 196. Write decimally : 
 
 1. Eight tenths. 
 
 2. 29 hundredths. 
 
 3. Sixteen, and 284 thousandths. 
 
 4. 4584 ten-thousandths. 
 
 5. Twenty-five hundredths. 
 
 6. Twenty-five thousandths. 
 
 7. Twenty-five ten-thousandths. 
 
 8. Twenty-five hundred-thousandths. 
 
 9. Twenty-five millionth*. 
 
 10. 1650, and 464 thousandths. 
 
 11. One thousand one, and 36 hundred-thousandths. 
 
 12. Sixteen, and six thousandths. 
 
 13. Seven hundred eighty-four millionths. 
 
 14. Twelve hundred-thousandths. 
 
 15. Seventy -five ten-thousandths. 
 
 197. Oral. 
 
 1. In the three decimals, .4, .40, .400, is there any differ- 
 ence in value ? 
 
 2. What is the effect when a cipher is annexed to a 
 decimal ? 
 
 3. What is the effect when a cipher is annexed to an inte- 
 ger ? Give an example. 
 
 4. In the decimals, .4, .04, .004, is there any difference in 
 value ? 
 
 5. What is the effect when a cipher is prefixed to a deci- 
 mal ? Two ciphers ? Give examples. 
 
 6. What is the effect when a cipher is prefixed to an 
 integer ? 
 
182 PRIMARY ARITHMETIC 
 
 198. 
 
 Principles 
 
 1. Ciphers annexed to decimals do not change their 
 values. 
 
 2. For each cipher prefixed to a decimal the value 
 is diminished tenfold. 
 
 3. The denominator of a decimal when expressed is 
 always 1 with as many ciphers as there are places in 
 the decimal. 
 
 REDUCTION OF DECIMALS 
 
 199. Decimals may be reduced to a common denominator 
 by annexing ciphers sufficient to give the same number of 
 decimal figures to all the decimals. 
 
 200. Reduce to a common denominator : 
 
 1. .5, .365, and .4689. 
 
 2. .18963, .5, 7.84, .16005. 
 
 3. .28, 3.5, .00005, .256. 
 
 4. .5, .05, .005, .0005, .00005. 
 
 5. .0463, .03, .1, .100010. 
 
 6. .38, 1.16, .4, 78.592. 
 
 201. 1. Reduce .375 to a common fraction. 
 SOLUTION. .375 as a common fraction is T 3 oW -375 = 
 
 Rule for reducing Decimals to Common Fractions 
 
 Write the numerator, omitting the decimal point, 
 supply the denominator, and reduce to lowest terms. 
 
 
REDUCTION OF DECIMALS 
 
 183 
 
 Reduce to common fractions : 
 
 2. 
 
 .25 
 
 8. 
 
 .125 
 
 14. 
 
 .368 
 
 3. 
 
 .35 
 
 9. 
 
 .875 
 
 15. 
 
 16.75 
 
 4. 
 
 .75 
 
 10. 
 
 .375 
 
 16. 
 
 .00125 
 
 5. 
 
 .64 
 
 11. 
 
 .455 
 
 17. 
 
 .054 
 
 6. 
 
 .52 
 
 12. 
 
 .025 
 
 18. 
 
 .0250 
 
 7. 
 
 .38 
 
 13. 
 
 .561 
 
 19. 
 
 .01375 
 
 20. Reduce .37| to a common fraction. 
 
 100 100 200 8 
 
 202. Reduce to common fractions 
 21. .121 24. .181 
 
 25. .03| 
 
 22. .62| 
 
 23. .06^ 
 
 26. .25f 
 
 27. .871 
 
 28. 
 29. 
 
 .66| 
 .36| 
 
 Reduce to mixed numbers : 
 so. 16.25, 2.331, 34.75. 
 
 203. Reduce | to a decimal. 
 
 | = 3 times ^. 3 = (3.0) 30 tenths. 
 
 ^ of 3.0 = (.7) 7 tenths and 2 tenths remainder. 
 
 2 tenths = 20 hundredths. 
 
 Hence f =.7 + .05 = .75. 
 
 Jof .20 = .05. 
 
 Rule for reducing Common Fractions to Decimals 
 
 Annex decimal ciphers to the numerator, and divide 
 by the denominator. Point off in the quotient as many 
 decimal places as there are ciphers annexed. 
 
184 PRIMARY ARITHMETIC 
 
 The division will not always be exact. In such cases, 
 write the remainder over the divisor as a common fraction, 
 or place the sign ( + ) after the decimal to show that the 
 result is incomplete. 
 
 Thus, |=.142f, or .142+. 
 
 204. Reduce to decimals : 
 
 2. | 6. f 
 
 3- i 7. f 
 
 4. I 8. f 
 
 205. ADDITION 
 
 Add: .35,4.375, 28.3065. 
 
 .35 
 4.375 
 
 28.3065 
 
 9 - tt 
 
 13. | 
 
 17. 
 
 10. M 
 
 14 ' ft 
 
 18. 
 
 11. if 
 
 15. 3^ 
 
 19. 
 
 12. -5-^ 
 
 16. | 
 
 20. 
 
 Rule for Addition of Decimals 
 
 Write the numbers so that the decimal points stand 
 in a column. Add as in integers, and place the point 
 in the sum directly under the points above. 
 
 Add: 2. 3.25 3. 4.5 4. .004 
 
 7.163 .168 4.1 
 15.0032 2.12 16.1563 
 
 5. .175 + 1.754-17.5 + 175. 
 
 6. 145 + 14.5 + 1.45 + .145 + .0145. 
 
 7. 3.2 + 14.0063 + .006 + 25.384 + .1. 
 
SUBTRACTION OF DECIMALS 185 
 
 8. .8 + .446 + 59.3 + 2.575 + 1.0056 + .3. 
 
 9. 1.45 + 2.365 + 96 + .96 + 15.863 + 4.3 + .0004. 
 
 10. 446 + 44.6 + 37562 + 9 + .8 + .321 + .16. 
 
 11. 21.0005 + .3842 + .1 + .005 + 3.6 + .158. 
 
 12. 1.0006 -J- 2001.1 + .003 + 5.5 + 11.1111. 
 
 206. SUBTRACTION 
 
 Rule for Subtraction of Decimals 
 
 Write the numbers so that the decimal point of the 
 subtrahend stands directly under the decimal point of 
 the minuend, subtract as in integers, and place the 
 point directly under the points above. 
 
 . It is sometimes convenient to give the decimals the same 
 denominator, by annexing decimal ciphers. 
 
 Subtract : 
 
 1. 24.3 2. 2.86 3. 4. 4. 2.46 
 
 4.5 1.325 1.15 .005 
 
 Find the remainders : 
 
 5. 7 -.15 10. 29.325-15.14 
 
 6. 1-.004 11. 3.852 -.125 
 
 7. 13-2.1 12. 1.1111 -.0011 
 
 8. 3.256-1.05 13. 500 -.05 
 
 9. 256.1-1.256 14. 25.3894-15.005 
 
 15. From twenty-eight, and twenty-five thousandths take 
 fourteen, and twenty-five hundredths. 
 
186 PRIMARY ARITHMETIC 
 
 16. From one tenth take one thousandth. 
 
 17. Which is the greater, fifty thousandths or five 
 hundredths ? 
 
 18. Take one thousandth from one thousand. 
 
 19. From 5 hundred take 5 hundredths. 
 
 MULTIPLICATION 
 207. Oral. 
 
 How much is 2 times .3 ? 3 times .3 ? 4 times .3 ? 
 7 times .02 = ? 12 times .06 = ? 12 times $.12 =? 
 
 iV x iV =100 5 1 x.l = .01. 
 
 ' .3 x. 05 = .015. 
 .3x.3=.09. 
 
 T 3 ^ = YO--Q How many ciphers in the denominator 
 
 of the product? 
 
 How many ciphers in the denominators of both factors ? 
 Every decimal has a corresponding common fraction, and 
 for each cipher in the denominator of the common fraction 
 there is a decimal figure in the decimal. 
 
 How many decimal figures in both 
 05 x. 3 = ,015 factors? 
 
 Rule for Multiplication of Decimals 
 
 Multiply as in integers, and point off from the right 
 of the product as many decimal figures as there are 
 decimal figures in both factors. 
 
 NOTE. If there are not figures enough, prefix ciphers. 
 
MULTIPLICATION OF DECIMALS 187 
 
 Ciphers at the right of a decimal have no value, and may 
 be omitted. 
 
 2.8 1.25 .005 25 
 
 x8 .6 .03 .06 
 
 22.4 .750 .00015 L50 
 
 Find the products: 
 
 1. .18 x.15 8. 13.3 xl.3 
 
 2. 1.0005 x .2 9. 100 x .01 
 
 3. 2.5 x .06 10. 100.56 x .0005 
 
 4. 56 x .005 11. 25.32 x 1.05 
 
 5. .005 x 1.6 12. 2.84 x 2| 
 
 6. 25.05 xl.15 is. "3.28 x 12 
 
 7. 2.863 x 100 14. 1.111 x 1000 
 
 208. 1. Multiply 1.265 by 100. 
 
 1.265 
 
 100 
 126.500 
 
 To Multiply by 10, 100, 1000, etc. 
 
 Remove the decimal point one place to the right for 
 every naught in the multiplier. 
 Do not write the multiplier. 
 
 Oral. Multiply: 
 
 2. 3.84 by 10 7. .3 by 100 
 
 3. 12.63 by 100 8. 1.869 by 100 
 
 4. 1.5555 by 1000 9. 32.856 by 1000 
 
 5. 1.358 by 10 10. 138.56 by 1000 
 
 6. .25 by 1000 11. 11.11 by 100 
 
188 PRIMARY ARITHMETIC 
 
 DIVISION 
 
 209. Since in multiplication there" are as many decimal 
 figures in the product as in both factors, in division the quo- 
 tient will have as many decimal figures as the number of 
 decimal figures in the dividend exceeds those in the divisor. 
 ^ 19 A5 Since there are three decimal figures in the 
 ^7~^ dividend and one in the divisor, there must be 
 two in the quotient. Prove by multiplying 
 dividend by quotient. 
 Divide 399.552 by 192. 
 
 2.081 
 
 192) 399.552 
 384 
 1555 
 1536 
 192 
 192 
 
 Rule for Division of Decimals 
 
 In all cases divide as in integers, then place the deci- 
 mal point. 
 
 When the divisor is an integer, place the point in the 
 quotient directly over the point in the dividend, in long 
 division (directly under in short division). 
 
 Prove by multiplying the divisor by the quotient. 
 
 When the divisor contains decimal figures, move the 
 point in both divisor and dividend as many places to 
 the right as there are decimal figures in the divisor, 
 then place the point in the quotient as if the divisor 
 were an integer. 
 
DIVISION OF DECIMALS 189 
 
 NOTE 1. The new point in both dividend and divisor may be placed 
 on a line with the tops of the figures, and the original point may stand, 
 to preserve the reading of the decimals. 
 
 NOTE 2. In the above example, the moving of the point two places 
 to the right in both dividend and divisor is equivalent to multiplying 
 each by 100. 
 
 NOTE 3. If the quotient does not have a sufficient number of figures, 
 prefix ciphers. 
 
 NOTE 4. Before commencing to divide see that there are at least as 
 many decimal places in the dividend as in the divisor. 
 
 NOTE 5. If there is a remainder, after all the figures of the dividend 
 are used, annex decimal ciphers and continue the division. 
 
 NOTE 6. It is not usually necessary to have "more than four decimal 
 figures in the quotient. 
 
 Divide 28.78884 by 1.25. 
 
 23.031 + 
 1.25*)28.78'884 
 250 
 378 
 375 
 388 
 375 
 134 
 125 
 9 
 
 Divide .125 by .5. 
 Divide 1.25 by .5. 
 Divide 12.5 by .5. 
 
 Divide at sight : 
 
 1. 3)3.33 4. .03). 333 7. .5)25 
 
 2. 3). 333 5. .003). 333 8. .05). 25 
 
 3. .03)333 6. 5)2.5 9. .07). 28 
 
190 
 
 PRIMARY ARITHMETIC 
 
 Find quotients and prove : 
 
 210. 10. 3. 57 -.7 
 .488 -s-.12 
 16.55 -f-. 05 
 13.13 -1.3 
 1.111 -.01 
 5555^.5 
 .875 -5- .05 
 73.5-1.05 
 
 11. 
 
 12. 
 13. 
 14. 
 15. 
 16. 
 17. 
 Divide : 
 
 26. Twenty-five ten-thousandths by 25 hundred ths. 
 
 27. 4678 hundred-thousandths by 9 ten-thousandths. 
 
 28. 3582 ten-thousandths by 3 hundredths. 
 
 18. 
 19. 
 20. 
 21. 
 22. 
 23. 
 24. 
 25. 
 
 376 -.6 
 376 -.06 
 37.6 -.6 
 3.76 -.06 
 1.875 -.005 
 15.55 -s- .1 
 l-.l 
 .1-1 
 
 To divide by 10, 100, 1000, etc. 
 
 Remove the decimal point one place to 
 each cipher in the divisor. 
 
 the left for 
 
 Divide at sight : 
 
 
 
 29. 10)365.8 33. 
 
 100)189.36 37. 
 
 1000)1698.45 
 
 30. 10)5 34. 
 
 100). 189 38. 
 
 1000)1.111 
 
 31. 10)148.963 35. 
 
 100)148.369 39. 
 
 1000)2948.36 
 
 32. 10)115.55 36. 
 
 100)4.983 40. 
 
 1000)39.85 
 
 Read and add : 
 
 
 
 i. 32.065 
 
 2. 36 
 
 .9486 
 
 6.006 
 
 2583 
 
 .04 
 
 4.25 
 
 4 
 
 .9602 
 
 .032 
 
 15 
 
 .15 
 
 .25 
 
 100 
 
 .001 
 
 25.01 
 
 56 
 
 .56 
 
 111.11 
 
 141 
 
 .141 
 
REVIEW OF DECIMALS 191 
 
 REVIEW OF DECIMALS 
 
 211. l. Tell where to place the decimal point in any 
 product. 
 
 2. In any quotient. 
 
 3. In any remainder. 
 
 4. In any sum. 
 
 5. From 1 take 1 millionth. 
 
 6. Add 1 tenth, 1 hundredth, and 1 thousandth. 
 
 7. Find the product of 1 multiplied by .15. 
 
 8. Multiply at sight : 36.984 by 1000. 
 
 9. Divide at sight : 159.83 by 1000. 
 
 Change to decimals : 
 
 10. |, f |, 16|, 25f 
 
 Change to common fractions : 
 
 11. .28, .38, .375, 15.125. 
 
 12. If John earns $8 in a week, how much can he earn 
 in 7.5 weeks? 
 
 13. If a barrel of flour costs $ 5.25, how many barrels can 
 be bought for $ 105 ? 
 
 14. What is the effect when a decimal figure is removed 
 one place to the left ? To the right ? 
 
 15. What is the effect when an integral figure is removed 
 one place to the left? One place to the right? 
 
 16. At 15^ a peck, how many pecks of pop-corn can be 
 bought for $3.75? 
 
 17. What is the cost of 28.78 yards of cloth at $ 3.15 a 
 yard? 
 
BILLS AND ACCOUNTS 
 
 212. An Account is a record of indebtedness for articles 
 bought or sold, cash paid or received, or services rendered. 
 
 213. A Debtor is a person who owes a debt. 
 
 214. A Creditor is a person to whom a debt is owed. 
 
 215. A Bill is a written statement of a debtor's account, 
 made by the creditor. 
 
 216. A Receipt is a creditor's written acknowledgment 
 that he has received payment of part or all of a debt. 
 
 217. A bill is Receipted when its payment is acknowledged 
 in writing, by the creditor, or b}^ some authorized person. 
 
 NOTE. The sign @ is for at, Dr. is for debtor, and Cr. for creditor. 
 
 1. BILL FORMS 
 
 DETROIT, MICH., July 1, 1901. 
 JAMES P. BARNES, 
 
 Bought of DEY BROS. & Co. 
 
 50 yards Brussels Carpet @ $ 1 15 
 
 24 " Oilcloth " 35 
 
 4 dozen pair Merino Hose " 3 50 
 
 2 Willow Chairs " 4 50 
 
BILLS AND ACCOUNTS 
 
 193 
 
 2. 
 
 JEROME A. PHELPS, 
 
 FORM OF A RECEIPTED BILL 
 
 NEW YORK, June 30, 1902. 
 
 In account with D. 0. POTTER & Co. 
 
 May 
 
 u 
 
 12 barrels Flour @ 
 
 $ 6.50 
 
 ft 
 f 
 
 
 (t 
 
 14 
 
 6 tubsButter,684pounds " 
 
 .24 
 
 
 
 June 
 
 10 
 
 5 barrels beef " 
 
 25.28 
 
 
 
 a 
 
 25 
 
 450 pounds Ham " 
 
 .09% 
 
 
 
 
 
 Received payment, 
 
 D. O. POTTER & Co. 
 
 3. 
 
 Mr. John Q. Adams buys of D. McCarthy & Co. : 
 
 4 pounds of coffee at 27 cents a pound. 
 18 pounds of sugar at 5J cents a pound. 
 5 gallons of molasses at 60 cents a gallon. 
 16 pounds of rice at 8^ cents a pound. 
 Make out the bill. 
 
 4. James Smith, farmer, sold Richard Dunn, grocer, the 
 following : 6 barrels of potatoes at 11.80 a barrel. 
 
 2 tons of hay at $16 a ton. 
 
 3 cords of wood at $4 a cord. 
 
 360 pounds of butter at 241 ^ a pound. 
 Make a receipted bill. 
 
 5. Syracuse, Dec. 5, 1898. Edward Smith, sold B. M. 
 Watson 65 yards of Brussels carpet at $1.25 ; 24 yards of oil- 
 cloth @ 35^; one dozen pair of merino hose @ $3.50; 2 willow 
 chairs @ $4.50. Make a bill, find the footing, and properly 
 receipt it. 
 
 6. Make out a bill of groceries. Foot it, and receipt it, 
 with F. H. Mead as creditor and Wm. H. Scott as debtor. 
 
 T 
 
 th " 
 
 To THE TEACHER. See that the prevailing prices are used, and that 
 the quantities are consistent. 
 
DENOMINATE NUMBERS 
 
 218. A number composed of units which belong to a table 
 of weights or measures is a Denominate Number. Thus, 2 feet, 
 7 gallons, 3 hours, are denominate numbers. 
 
 219. A number composed of two or more kinds of units 
 belonging to the same table is a Compound Number. Thus, 
 2 yards, 1 foot, 6 inches, and 1 ton, 50 pounds, 11 ounces, 
 are compound numbers. 
 
 LINEAR MEASURES 
 
 220. Measures used in measuring distances and dimen- 
 sions are Linear Measures. 
 
 221. The Yard is the standard unit of linear measure. 
 With a yardstick draw a line one yard long. Hold your 
 
 hands one yard apart. Name objects one yard apart. How 
 many yards apart are the windows of your schoolroom? 
 Without the measure, draw a line one yard long. Correct 
 it. Divide it into 3 equal parts. Each part is one foot long. 
 
 Hold your hands one foot apart. Measure a foot on your 
 arm. Name objects 1 foot long, wide, or high. 
 
 Draw a line one foot long. Correct it with a rule. 
 Divide it into 12 equal parts. Each part is 1 inch. Show 
 how long 1 inch is. Four inches. Six inches. 
 
 194 
 
DENOMINATE NUMBERS 195 
 
 With a yardstick, measure 5| yards on the schoolroom 
 floor. This is 1 rod. How many feet make a rod ? How 
 many rods long is your school ground? (Estimate it.) 
 How wide ? Where would you stop if you should walk 20 
 rods from the front door of your schoolhouse ? 
 
 320 rods make 1 mile. Name some places 1 mile from 
 your school. How many miles do you walk in coming to 
 school ? How many yards in 1 mile ? How many feet ? 
 How many inches ? 
 
 222. The answers to the above questions give us the 
 following 
 
 TABLE OF LINEAR 
 
 MEASURES 
 
 12 
 
 inches 
 
 (in.) make 
 
 1 
 
 foot 
 
 (ft,). 
 
 3 
 
 feet 
 
 make 
 
 1 
 
 yard 
 
 (yd-)- 
 
 PJ 
 
 yards 
 
 make 
 
 1 
 
 rod 
 
 (rd.). 
 
 320 
 
 rods 
 
 make 
 
 1 
 
 mile 
 
 (mi.). 
 
 5280 
 
 feet 
 
 make 
 
 1 
 
 mile. 
 
 
 Oral. 
 
 1. How many inches are there in 1 yd. ? 
 
 2. How many inches are there in 2 ft. ? 3 ft. ? 5 ft. ? 
 
 3. How many feet are there in 4 rd. ? 2 rd. ? 
 
 4. How many feet are there in 5 yd. ? 7 yd. ? 11 yd. ? 
 
 5. 24 feet are how many yards ? 
 
 6. How many feet around a picture 2 ft. long and 1 ft. 
 wide ? 
 
196 PRIMARY ARITHMETIC 
 
 7. How many inches in a half yard ? 
 
 8. At $.16 a yard, what will 1^ yd. of ribbon cost ? 
 
 9. 6 f t. -f 2 ft. -f- 4 ft. are how many yards ? 
 
 10. How many feet in 108 inches ? 
 
 11. John has a fish pole 4 yd. long. How many inches 
 long is it ? 
 
 12. How many rods in 5 miles ? 7 miles ? 1J miles ? 
 
 13. How many feet in ^ mile ? 3 miles ? 1^ miles ? 
 
 14. Stepping two feet at a step, how many steps will be 
 taken in walking 2 miles ? 
 
 SURFACE MEASURES 
 
 223. A Surface is that which has only length and breadth. 
 Thus, the top of a desk, the outside of a book, the upper and 
 under sides of a board, are surfaces. 
 
 224. An Angle is the difference in direction of two lines 
 that meet. Thus, 
 
 225. A Plane Surface is a surface which would be touched 
 by all the points of a straight line drawn in any direction 
 upon it. Thus, the top of a table is a plane surface. 
 
 226. A Plane Figure is a portion of a plane surface 
 bounded by lines. Thus, a triangle, an oblong, a circle, are 
 plane figures. 
 
SURFACE MEASUREMENTS 
 
 197 
 
 One 
 square 
 
 inch 
 
 227. A Square is a plane figure bounded 
 by four equal straight sides and having 
 four equal angles. 
 
 A square whose side is one inch is a 
 Square Inch. Thus, 
 
 A square whose side is one foot is a 
 Square Foot. Draw a square foot. 
 
 A square whose side is one yard is a 
 Square Yard. Draw a square yard. 
 
 A square whose side is one rod is a 
 Square Rod. Measure a square rod in your schoolroom. 
 
 A square whose side is one mile is a Square Mile. 
 Section of land is a square mile. 
 
 Draw a square yard 
 on the blackboard. 
 Divide each side into 
 feet and connect the 
 division marks as in 
 the figure. How many 
 squares are there ? 
 What is each square ? 
 How many square feet 
 are there in one square 
 yard ? 
 
 NOTE. Be sure to make 
 the figure on the black- 
 board full size. 
 
 Divide the sides of one of these square feet into twelve 
 equal parts. Connect the division marks. 
 
 How many squares have you made ? What is each square ? 
 
 How many square inches make one square foot ? 
 
 In a similar manner you might divide the sides of a square 
 mile into 320 rods each, making 320 x 320 = 102400 square 
 
198 PRIMARY ARITHMETIC 
 
 rods in one square mile. Each square mile, however, is 
 divided into 640 acres. This makes how many square rods 
 in one acre ? 
 
 You might also divide a square rod into 5^ x 5J = 30^ 
 square yards. 
 
 228. The foregoing demonstration gives us the following 
 
 TABLE OF SURFACE MEASURES 
 
 144 square inches (sq. in.) make 1 square foot (sq. ft.). 
 
 9 square feet make 1 square yard (sq. yd.). 
 30| square yards make 1 square rod (sq. rd.). 
 160 square rods make 1 acre (A.). 
 640 acres make 1 square mile (sq. mi.). 
 
 229. Written. 
 
 1. How many square inches in 3 sq. feet? in 6 sq. ft.? 
 
 2. How many square yards in 54 sq. feet ? in 108 sq. ft.? 
 
 3. In 12| sq. ft. how many sq. inches? 
 
 4. How many acres in 480 square rods? in 640 sq. rd.? 
 
 5. In 7212 sq. in., how many sq. feet? 
 
 6. In 40 acres, how many square rods? 
 
 7. In J of an acre, how many sq. rods? 
 
 8. A farmer had a section of land. He sold J of it to 
 one man and ^ to another. How many acres had he left ? 
 What part of the farm is left ? 
 
 9. 3 square feet is what part of a square yard ? 
 
 10. What part of a square foot is 36 square inches ? 108 
 sq. in.? 
 
 11. What part of an acre is 120 square rods ? 
 
CUBIC MEASURES 
 
 199 
 
 CUBIC MEASURES 
 
 230. That which has length breadth, and thickness is a 
 Solid. 
 
 231. A solid which has six equal 
 square faces is a Cube. 
 
 A cube whose edge is 
 one inch is a Cubic Inch. 
 
 A cube whose edge is 
 one foot is a Cubic Foot. 
 
 A cube whose edge is 
 
 Cube 
 
 Cubic inch 
 
 one yard is a Cubic Yard. 
 
 3 Feet 
 
 A solid 3 feet long, 1 foot wide, and 1 foot high contains 
 how many cubic feet? (3 x 1 x 1.) (See picture.) 
 
 A solid 3 feet long, 3 feet wide, and 1 foot high contains 
 how many cubic feet ? (3x3x1.) (See picture.) 
 
 A solid 3 feet long, 3 feet wide, and 3 feet high contains 
 how many cubic feet ? (See picture.) 
 
 A cubic yard is how many feet long, wide, and high ? 
 
 Therefore, a cubic yard contains how many cubic feet ? 
 
 A solid 12 inches long, 1 inch wide, and 1 inch high con- 
 tains how many cubic inches ? 
 
200 PRIMARY ARITHMETIC 
 
 A solid 12 inches long, 12 inches wide, and 1 inch high 
 contains how many cubic inches ? 
 
 A solid 12 inches long, 12 inches wide, and 12 inches high 
 contains how many cubic inches ? How many cubic feet ? 
 
 Therefore, a cubic foot contains how many cubic inches ? 
 
 232. The answers to the above questions give us the 
 following 
 
 TABLE OF CUBIC MEASURES 
 
 1728 cubic inches (cu. in.) make 1 cubic foot (cu. ft.). 
 27 cubic feet make 1 cubic yard (cu. yd.). 
 
 Written. 
 
 1. How many cu'bic inches in 6 cubic feet ? in 8 cu. ft. ? 
 
 2. How many cubic feet in 8640 cubic inches ? in 11,232 
 cu. in. ? 
 
 3. How many cubic inches in | of a cubic foot ? in | cu. ft. ? 
 
 4. What part of a cubic foot is 576 cubic inches ? 1152 
 cu. in. ? 
 
 5. What part of a cubic yard is 3 cubic feet ? 9 culjic feet? 
 
 6. What will it cost to remove an embankment containing 
 54,000 cu. ft. of earth at 12| cents a cubic yard ? 
 
 LIQUID MEASURES 
 
 1 Gill 1 Pint 1 Quart 1 Gallon 
 
LIQUID MEASURE 201 
 
 233. Fill a gill cup with water. Pour it into a pint cup. 
 Repeat until the pint cup is full. How many times have 
 you filled the gill cup ? How many gills in one pint ? Fill 
 a pint cup and pour into a quart cup until the quart cup is 
 full. How many pints in one quart ? Fill a gallon measure 
 with the quart cup. How many quarts in one gallon ? If 
 you should fill a barrel with the gallon measure, you would 
 need to fill the gallon measure 31|- times. How many gal- 
 lons make one barrel ? Two barrels of water would fill a 
 hogshead. How many gallons in a hogshead ? 
 
 234. From this work we may make the following 
 
 TABLE OF LIQUID MEASURES 
 
 4 gills (gi.) make 1 pint (pt.). 
 2 pints make 1 quart (qt.). 
 
 4 quarts make 1 gallon (gal.). 
 31 1 gallons make 1 barrel (bbl.). 
 2 barrels make 1 hogshead (hhd.). 
 
 These denominations are sometimes used : 
 
 2 hhd. = 1 pipe (pi.). 
 2 pi. =1 tun. 
 Oral. 
 
 1. How many pint cups can be filled from 8 quarts ? 
 
 2. A quart of milk was taken from a five-gallon pan. 
 How much was left ? 
 
 3. How many gallons in a hogshead ? 
 
 4. f of a gallon are how many quarts ? 
 
 5. How many hogsheads will 8 barrels of oil fill ? 
 
202 PRIMARY ARITHMETIC 
 
 DRY MEASURES 
 
 235, Fill a pint measure, which is used for dry measures, 
 and empty it into a quart measure, continuing until the 
 latter is full. How many times must you fill the pint 
 measure ? How many pints in 1 quart ? Fill the quart 
 (dry) measure and empty into a peck measure until the 
 latter is filled. How many quarts in 1 peck? In the same 
 way find how many pecks in 1 bushel. (Sawdust or oats 
 may be conveniently used for this measurement.) 
 
 236. From this work we may make the following : 
 
 TABLE OF DRY MEASURES 
 
 2 pints (pt.) make 1 quart (qt.). 
 8 quarts make 1 peck (pk.). 
 
 4 pecks make 1 bushel (bu.). 
 
 Oral. 
 
 1. How many pecks in 9 bushels ? 
 
 2. In 22 pints, how many quarts ? 
 
 3. A bushel of apples at $ .25 a peck will cost what ? 
 
 4. How many pints are in 6 qt. 1 pt. ? 
 
 5. What will a peck of chestnuts bring if sold at 10 f a 
 quart ? 
 
 6. How many times can a quart cup be filled from a 
 bushel of walnuts? 
 
 7. How many quarts are in 9 pecks ? 
 
AVOIRDUPOIS WEIGHT 
 
 203 
 
 AVOIRDUPOIS WEIGHT 
 
 237. Avoirdupois weight is used in weighing all common 
 articles, as coal, groceries, hay, etc. 
 
 TABLE OF AVOIRDUPOIS WEIGHT 
 
 16 drams (dr.) make 1 ounce (oz.). 
 
 16 ounces make 1 pound (lb.). 
 
 25 pounds make 1 quarter (qr.). 
 
 4 quarters make 1 hundred-weight (cwt.). 
 20 hundred-weight make 1 ton (T.). 
 
 2000 pounds make 1 ton. 
 
 The avoirdupois pound contains 7000 grains. 
 The hundred-weight is sometimes called a cental. 
 
204 PRIMARY ARITHMETIC 
 
 Oral. , 
 
 1. How many ounces are in 4 pounds ? 
 
 2. In 32 drams, how many ounces ? 
 
 3. What will a pound of candy cost at $.02 an ounce ? 
 
 4. How many pounds in 4 tons ? 
 
 5. In 6000 lb., how many tons ? 
 
 6. How many pounds are in a hundred-weight ? 
 
 7. Paid $ .48 a pound for candy. How much is that an 
 ounce ? 
 
 8. How many 3-pound packages can be made from 75 
 pounds of coffee ? 
 
 Written. 
 
 1. How many ounces are there in 25 lb. ? 
 
 2. In 7 1 tons, how many pounds ? 
 
 3. How many bullets weighing 2 oz. each can be made 
 from 32 lb. 4 oz. of lead ? 
 
 4. What will 2 J lb. dried peaches cost at $ .32 per pound ? 
 
 5. In 1364 drams, how many ounces ? 
 
 6. Five boys share equally 1 lb. 9 oz. of candy. How 
 many ounces do each receive ? 
 
 7. How many 4-ounce bags can I fill from a box holding 
 7 J lb. of candy ? 
 
 8. What is the difference in ounces between a hundred- 
 weight and 97 \ pounds? 
 
 9. What will 7| lb. of indigo cost at $.03 an ounce ? 
 
 10. Reduce 18^ lb. to ounces. 
 
 11. A hundred-weight is what part of a ton ? 
 
APOTHECARIES' WEIGHT 205 
 
 TROY WEIGHT 
 
 238. Troy weight is used for weighing gold, silver, and 
 precious stones. 
 
 TABLE OF TROY WEIGHT 
 
 24 grains (gr.) make 1 pennyweight (pwt.). 
 20 pennyweights make 1 ounce (oz.). 
 12 ounces make 1 pound (lb.). 
 
 Can you tell why Troy weight has no larger denomination 
 than pounds ? 
 
 Oral. 
 
 1. How many ounces in 2 lb. ? 5 lb. ? 10 lb. ? 
 
 2. How many ounces in 100 pwt. ? 200 pwt. ? 80 pwt.? 
 
 3. How many pwt. in 96 grains ? 72 gr. ? 
 
 4. How many gr. in 1 pwt. ? in 2 pwt. ? in 10 pwt. ? 
 
 5. How many lb. in 96 oz.? in 120 oz. ? 
 
 6. How many grains in half an ounce of gold ? 
 
 7. A watch chain weighs 10 pwt. What part of an ounce 
 does it weigh ? How many grains ? 
 
 APOTHECARIES' WEIGHT 
 
 239. Apothecaries' weight is used by physicians and drug- 
 gists in compounding medicines, and by druggists in selling 
 medicines in quantities smaller than one ounce. Medicines 
 in quantities of one ounce and more are bought and sold by 
 Avoirdupois weight. 
 
206 PRIMARY ARITHMETIC 
 
 TABLE OF APOTHECARIES' WEIGHT 
 20 grains (gr.) make 1 scruple (sc. or 3). 
 3 scruples make 1 dram (dr. or 3). 
 
 8 drams make 1 ounce (oz. or 5). 
 
 12 ounces make 1 pound (Ib. or Ib). 
 
 Oral. 
 
 1. How many grains in 1 dram ? in 1 ounce ? 
 
 2. How many drams in 1 Ib. ? in 30 scruples ? 
 
 3. How many pounds in 144 ounces ? in 292 drams ? 
 
 4. An ounce of quinine will make how many 4-grain 
 powders ? 
 
 5. How many drams will make sixty 3-grain tablets ? 
 
 240. FEDERAL MONEY 
 
 TABLE OF FEDERAL MONEY 
 
 10 mills (m.) make 1 cent (ct.). 
 10 cents make 1 dime (di.). 
 
 10 dimes make 1 dollar ($). 
 
 10 dollars make 1 eagle (E.). 
 
 Oral. 
 
 1. How many dimes in 6 dollars ? 
 
 2. 4 eagles are how many dollars ? 
 
 3. A man had $80 in eagles. How many eagles had he? 
 
 4. How many mills in 15 cents ? 
 
 5. In 5 dimes, how many cents ? 
 
 6. A dollar, a quarter, a dime, and a nickel are how 
 many cents ? 
 
 7. How many dollars are there in 130 dimes ? 
 
 8. How many dollars are there in 1300 cents? 
 
TIME 
 
 207 
 
 9. Divide 4 eagles among 5 men. How much will each 
 
 receive : 
 
 10. How many books at 50^ each can be bought for $2 ? 
 
 11. How many dollars in a double eagle ? 
 
 TIME 
 
 2*1. The solar year is 365^ days, nearly. 
 
 For convenience 365 days is taken for a common year. 
 The \ day, in 4 years, amounts to another day, making 
 every 4th year 366 days. This is called leap year. This 
 extra day is added to February. 
 
 Days in each month: 
 January 31 days. July 31 days. 
 February 28 or August 31 days. 
 
 29 days. September 30 days. 
 
 March 31 days. October 31 days. 
 April 30 days. November 30 days. 
 May 31 days. December 31 days. 
 June 30 days. 
 
 TABLE OF TIME 
 
 60 seconds (sec.) make 1 minute (min.). 
 
 60 minutes 
 24 hours 
 
 365 days 
 
 366 days 
 
 Also: 
 
 7 days 
 
 make 1 hour (h.). 
 make 1 day (da.), 
 make 1 common year (y.)- 
 make 1 leap year. 
 
 make 1 week (wk.). 
 
 12 months (mo.) make 1 year. 
 100 years make 1 century. 
 
208 PRIMARY ARITHMETIC 
 
 Oral. 
 
 1. How many minutes in 2 hours ? \ hour ? 2 hours ? 
 
 2. Reduce to hours : 180 minutes, 120 minutes, 30 min- 
 utes. 
 
 3. How many hours in a week ? 
 
 4. How many days in March and June ? 
 
 5. What 4 months have 30 days ? 
 
 6. How many have all the rest except February ? 
 
 7. What part of an hour is 45 minutes ? (Question.) 
 
 Written. 
 
 1. If a boy walk \ mile in ten minutes, how long will it 
 take him to walk 16 miles ? 
 
 2. How many hours in the month of August ? 
 
 The winter months are December, January, and Feb- 
 ruary. 
 
 The spring months are March, April, and May. 
 
 The summer months are June, July, and August. 
 
 The autumn months are September, October, November. 
 
 3. Which is the shortest season ? Why ? 
 
 4. Is it the shortest in leap year ? 
 
 5. How many more days in this year ? 
 
 MISCELLANEOUS 
 
 12 units or things, 1 dozen (doz.). 
 
 12 dozen, 1 gross (gro.). 
 
 20 units, 1 score. 
 196 lb., 1 barrel of flour. 
 200 lb., 1 bbl. of beef, pork, or fish. 
 280 lb., 1 barrel of salt. 
 
REDUCTION OF DENOMINATE NUMBERS 209 
 
 TABLE OF PAPER MEASURE 
 
 24 sheets make 1 quire. 
 20 quires make 1 ream. 
 
 2 reams make 1 bundle. 
 
 5 bundles make 1 bale. 
 
 242. Oral. 
 
 1. How many are 3 gross of pencils ? 
 
 2. What is the cost of \ gross of pens at 60 ^ a gross ? 
 
 3. How many are 3 score years ? 
 
 4. How many are 3 score and 10 years ? 
 
 5. How many are 5 dozen eggs ? 6| dozen eggs ? 
 
 6. How many sheets in 3 quires of paper ? 
 
 7. How many quires in ^ a ream ? 
 
 8. 84 eggs are how many dozen ? 
 
 9. How many reams in a bale of paper ? 
 
 10. How many pounds in ^ bbl. of flour ? 
 
 Written. 
 
 11. How many dozen in 66 cucumbers ? 
 
 12. What is 'the cost of 6 quires of paper at $4 a ream ? 
 
 13. What will 8 gross of copy-books cost at 10^ apiece ? 
 
 14. If paper is bought at $2 a ream and sold at 18^ a 
 quire, what is the gain on 6 reams ? 
 
 REDUCTION OF DENOMINATE NUMBERS 
 
 243. Changing numbers to smaller denominations is Re- 
 duction Descending. 
 
 Changing numbers to larger denominations is Reduction 
 Ascending. 
 
 What is reduction (see definition, Art. 129) ? In reduction 
 of numbers, what is changed ? What is not changed ? 
 
210 
 
 PRIMARY ARITHMETIC 
 
 l. Reduce 2 Ib. 7 oz. 5 pwt. 17 gr. to grains. 
 
 2. 
 
 2 (Ib.) 
 12 oz. 
 24 oz. 
 + 7 oz. 
 ~31 (oz.) 
 _20 pwt. 
 620 pwt. 
 + 5 pwt. 
 625 (pwt.) 
 24 gr. 
 2500 
 1250 
 
 15000 gr. 
 
 + 17 gr. 
 
 15017 gr. 
 
 How many oz. are there in 1 Ib. ? 
 How many oz. are there in 2 Ib. ? 
 24 oz. + 7 oz. = how many oz. ? 
 How many pwt. are there in 1 oz. ? 
 How many pwt. are there in 31 oz. ? 
 620 pwt. -f 5 pwt. = how many pwt. ? 
 How many gr. are there in 1 pwt. ? 
 How many gr. are there in 625 pwt. ? 
 15000 gr. + 17 gr. = how many gr. ? 
 
 Ans. 
 
 Reduce 2 mi. 51 rd. 2 yd. 2 ft. 7 in. to inches. 
 
 2 (mi.) 
 
 320 rd. 
 
 640 rd. 
 
 -f 51 rd. 
 
 2~|691 (rd.) 
 
 How many rods are there in 1 mi. In 2 mi.? 
 
 640 rd. + 51 rd. = how many rods ? 
 
 How many yd. in 1 rod ? In 691 rd. ? 
 
 38001 yd. + 2 yd. = how many yd. ? 
 
 How many feet in 1 yard? In 3802J yards? 
 
 11407J ft. + 2 ft. = how many feet ? 
 
 In 1 foot there are how many inches? IP 114091 
 
 feet? 
 136914 in. -f 7 in. = how many inches? 
 
 345| 
 3455 
 3800J yd. 
 
 -f 2 yd. 
 38021 (yd.) 
 3 
 
 11407| ft. 
 + 2 ft. 
 11409J (ft.) 
 12 
 
 6 in. 
 
 136908 in. 
 136914 in. 
 + 7 in. 
 136921 in. .4ns. 
 
REDUCTION DESCENDING 211 
 
 244. From the above examples we may make the following 
 
 Rule for Reduction Descending 
 
 Multiply the number of the largest denomination given 
 by the number of units of the next smaller denomina- 
 tion which are equal to one unit of the denomination 
 multiplied. To this product, add the given number of 
 the same denomination as the product. Proceed in the 
 same way with this and each succeeding result until 
 the required denomination is reached. 
 
 3. Reduce 2 sq. mi. 125 A. 71. sq. rd. 1 sq. yd. to square 
 
 yards. 
 
 2 (sq. mi.) 
 640 A. 
 1280 A. 
 + 125 A. 
 1405 (A.) 
 
 160 sq. rd. 
 84300 
 1405 
 
 224800 sq. rd. 
 + 71 sq. rd. 
 224871 (sq. rd.) 
 
 121 fourths sq. yd. NOTE. 30 sq. yd. = 
 224871 ifi sq. rd. 
 
 449742 
 224871 
 
 4 fourths | 27209391 fourths sq. yd. 
 68023471 sq. yd. Ans. 
 245. 
 
 Reduce to lower denominations : 
 
 4. 17 yd. 2 ft. 9 in. to inches. 
 
 5. 46 rd. 4 yd. 2 ft. to feet. 
 
212 PRIMARY ARITHMETIC 
 
 I 
 
 6. 3 mi. 75 rd. 4 ft. to inches. 
 
 7. 16 A. 140 sq. rd. 26 sq. yd. to square yards. 
 
 8. 4 A. 15 sq. rd. 4 sq. ft. to square inches. 
 
 9. 16 cu. yd. 25 cu. ft. 900 cu. in. to cubic inches. 
 
 10. 15 gal. 3 qt. 1 pt. to pints. 
 
 11. 7 bu. 3 pk. 5 qt. 1 pt. to pints. 
 
 12. 16^ bu. to quarts. 
 
 13. 25 Ib. 5 oz. 16 pwt. 10 gr. to grains. 
 
 14. 2 T. 6 cwt. 10 Ib. 14 oz. to ounces. 
 
 15. What will 3 reams of paper cost at 40 ^ a quire ? 
 
 16. Reduce 3 mi. 4 fur. 20 rd. 5 yd. 2 ft. 8 in. to inches. 
 
 17. Reduce 6 mi. 240 rd. to feet. 
 
 18. Reduce 3 A. 8 sq. rd. 5 sq. yd. 3 sq. ft. to square 
 inches. 
 
 19. Reduce 16 cu. yd. 9 cu. ft. 3 cu. in. to cubic inches. 
 
 20. Reduce 2 T. 3 ctl. 16 Ib. to ounces. 
 
 21. Reduce 3 Ib. 9 oz. 15 pwt. 12 gr. to grains. 
 
 22. Reduce 60 gal. 3 qt. 3 gi. to gills. 
 
 23. How many sheets in 5 bales of paper ? 
 
 24. Reduce 3 wk. 6 da. 5 hr. to minutes. 
 
 REDUCTION ASCENDING 
 246. 1. Reduce 5499 qt. to bushels. 
 
 8 qt. 
 4pk. 
 
 How many qt. in 1 pk. ? 
 
 5499 qt. 5499 qt. = how many pk. ? 
 
 687 pk. -f 3 qt. How many qt. over ? 
 171 bu. + 3 pk. How many pk. in 1 bu.? 
 J pk. 3 qt. Ans. 687 pk. how many bu.? 
 How many pk. over ? 
 
 A.I A ILIA. "| 
 
 How many pk. over 
 
REDUCTION ASCENDING 
 
 213 
 
 2. Reduce 241329 in. to larger denominations. 
 
 12 in. 
 
 3ft. 
 
 11 half 
 
 yd- 
 
 241329 in. 
 
 
 20110 ft. + 9 in. 
 
 6703 yd. + 1 ft. 
 2 
 
 13406 half yd. 
 
 1218 rd. + 8 half yd. 
 
 = 4 yd. 
 
 3 mi. + 258 rd. 
 
 320 rd.)121 rd. 
 96^ 
 258 rd. 
 
 3 mi. 258 rd. 4 yd. 1 ft. 9 in. Ans. 
 
 How many inches make 1 
 ft? 
 
 How many feet in 241329 
 in.? 
 
 How many inches left ? 
 
 How many ft. make 1 yd. ? 
 
 How many yd. in 6703 ft. ? 
 
 How many feet left? 
 
 How many yd. in 1 rd. ? 
 How many half yd. ? 
 
 How many half yd. in 6703 
 yd.? 
 
 How many rd. in 13406 half 
 yd.? 
 
 How many half yd. over? 
 8 half yd. = how many yd. ? 
 
 How many rd. in 1 mi.? 
 
 How many mi. in 1218 rd. ? 
 
 How many rd. left ? 
 
 3. 
 
 Reduce 208824 sq. in. to larger denominations. 
 
 1450 sq. ft. 
 144)208824 
 144 
 648 
 576 
 722 
 720 
 
 24 sq. in. 
 
 f sq. yd. = 6 sq. ft. 108 sq. in. 
 5 sq. rd. 9| sq. yd. 1 sq. ft. 24 sq. in. 
 5 sq. rd. 9 sq. yd. 7 sq. ft. 132 sq. in. Ans, 
 
 9 [1450 sq. ft. 
 
 161 sq. yd. -f 1 sq. ft. 
 
 4 
 121 fourths)_644 fourths sq. yd. 
 
 5sq. yd. + \ 9 sq. yd. = 9| sq. yd. 
 
214 PRIMARY ARITHMETIC 
 
 Rule for Reduction Ascending 
 
 Divide the given number by the number of units of 
 the denomination given which are equal to one unit of 
 the denomination next larger. Keep the remainder, 
 if any, as part of the answer. 
 
 Proceed in the same manner with this and each suc- 
 ceeding quotient till the required denomination has 
 been reached. 
 
 247. 4. Reduce 225932 inches to miles, etc. 
 
 5. How many miles and rods are there in 35640 ft. ? 
 
 6. Reduce 19922544 sq. in. to larger denominations. 
 
 7. Reduce 762051 cu. in. to cubic yards, etc. 
 
 8. Reduce 69056 oz. to tons, etc. 
 
 9. Reduce 21076 gr. to larger denominations. 
 
 10. Reduce 1947 gi. to gallons, etc. 
 
 11. How many bales in 24000 sheets of paper ? 
 
 12. Reduce 39180 min. to weeks, etc. 
 
 13. How many bushels, etc., in 35842 pints ? 
 
 14. How many pounds, etc. (Troy), in 32563 gr. ? 
 
 15. Reduce 39632 gr. to pounds, etc. (apoth.). 
 
 16. How many tons, etc., in 35682 Ib. ? 
 
 17. A box contains 75832 pens. How many great gross, 
 etc., in the box ? 
 
 18. Change 1384 dry pints to larger denominations. 
 
 19. In 139843 sq. in. how many square rods, etc. ? 
 
 20. Reduce 164808 in. to miles, etc. 
 
 21. In 12024 in. how many rods, etc. ? 
 
REVIEW OF REDUCTION 215 
 
 248. Written Review. 
 
 1. How many 2-quart cups can be filled from a barrel of 
 syrup ? 
 
 2. Change 7 gal. 2 qt. 1 pt. to gills. 
 
 3. In 276 pints how many gallons ? 
 
 4. A merchant paid $10 for a barrel of molasses, and 
 retailed it at $ .40 a gallon. What was his gain ? 
 
 5. How many ounces are there in 250 Ib. ? 
 
 6. In 17| tons how many pounds ? 
 
 7. How many bullets weighing | oz. each can be made 
 from 32 Ib. 4 oz. of lead ? 
 
 8. Reduce 118 Ib. 7 oz. to drams. 
 
 9. Reduce 15 pk. 7 qt. to pints. 
 
 10. How many quarts are in 846 pints ? 
 
 11. Henry gathered 16 bu. 2 qt. of walnuts, and sold 
 them at $ .08 a quart. What did he receive for them ? 
 
 12. In 8136 pt. how many bushels, etc. ? 
 
 13. What will 6 bu. 2 pk. of cranberries be worth at 
 1.75 a peck? 
 
 14. A half-barrel of vinegar was sold at 2^ a quart. 
 What was received for it ? 
 
 15. How many gallons in 16 quarts ? 
 
 16. 13| gallons have been sold from a barrel. How many 
 quarts are left ? 
 
 17. At 7 ^ a quart what will 15 gal. of vinegar cost ? 
 
 18. How many quarts are there in 7 bu. 3 pk. 7 qt. ? 
 
 19. A peck of peaches was sold .from a crate containing 
 a bushel. How many quarts were left ? 
 
 20. How many bushels are there in 576 pints ? 
 
216 PRIMARY ARITHMETIC 
 
 ADDITION OF COMPOUND NUMBERS 
 
 249. l. Add 14 Ib. 5 oz. 17 pwt. 12 gr., 18 Ib. 10 oz. 
 14 gr., 6 Ib. 4 oz. 8 pwt. 16 gr. 
 
 Ib. - oz. pwt. gr. 
 
 14 5 17 12 SOLUTION. The sum of the grains = 42 gr. 
 
 = 1 pwt. 18 gr. We place the 18 gr. under the 
 
 column of grains, and add the 1 pwt. to the column 
 
 6 4 8 16 of pennyweights. Add the other columns in like 
 
 39 8 6 18 manner - 
 
 rd. yd. ft. 
 2. 17 4 1 3. 
 
 12 4 2 
 
 6 5 21 
 
 832 
 46 1| li 
 
 46 2 
 
 
 bu. 
 
 P k. 
 
 qt. 
 
 4. 
 
 Add: 7 
 
 1 
 
 3 
 
 
 10 
 
 1 
 
 2 
 
 
 4 
 
 1 
 
 2 
 
 
 yd. 
 
 ft. 
 
 in. 
 
 6. 
 
 1 
 
 2 
 
 6 
 
 
 2 
 
 1 
 
 
 
 1 
 
 2 
 
 3 
 
 5. 
 
 7. 
 
 Find the sum : 
 
 8. 3 bu. 2 pk. 2 qt. 1 pt. ; 4 bu. 5 pk. 3 qt.; 7- bu. 1 pk. 
 4 qt. 1 pt. 
 
 9. 7 Ib. 8 oz. 6 dr. ; 4 Ib. 11 oz. 5 dr. ; 2 Ib.. 4 dr. 
 
 10. 1 bbl. 14 gal. 2 qt. 1 pt. ;. 2 bbl. 5 gal. 3 qt. ; 7 gal. 
 3 qt. 
 
 rd. 
 
 ft. 
 
 in. 
 
 6 
 
 12 
 
 6 
 
 4 
 
 14 
 
 11 
 
 17 
 
 15 
 
 9 
 
 6 
 
 12 
 
 8 
 
 36 
 
 5| 
 
 10 
 
 6 = ft. 
 
 36 
 
 6 
 
 4 
 
 bbl. 
 
 6 
 
 gal. 
 
 7 
 
 qt. 
 1 
 
 5 
 
 12 
 
 1 
 
 4 
 
 6 
 
 1 
 
 bbl. 
 4 
 
 gal 
 
 7 
 
 qt. pt. 
 4 1 
 
 6 
 
 2 
 
 1 
 
 3 
 
 5 
 
 1 1 
 
SUBTRACTION OF COMPOUND NUMBERS 217 
 
 SUBTRACTION OF COMPOUND NUMBERS 
 
 Ib. oz. pwt. gr. SOLUTION. 15 gr. - 12 gr. 
 
 250. 1. From 6 2 14 15 = 3 gr. As we cannot take 
 
 Take 4 10 18 12 18 pwt. from 14 pwt., we take 
 
 1 3 16 3 ^ oz> ' w h* c h equals 20 pwt., and 
 
 add to the 14 pwt. = 34 pwt.; 
 
 34 pwt. 18 pwt. 16 pwt. We have taken 1 oz. from the 2 oz., leaving 
 1 oz.; but as we cannot take 10 oz. from 1 oz., we take 1 Ib. = 12 oz., and 
 add it to 1 oz. = 13 oz., from which take 10 oz. = 3 oz. Since we took 1 
 of the 6 Ib., we have 5 Ib. left; from which take 4 Ib. = 1 Ib. 
 
 
 
 A. 
 
 sq. rd. 
 
 sq. ft. 
 
 hr. 
 
 min. 
 
 sec. 
 
 
 2. 
 
 From 
 
 10 
 
 50 
 
 7 
 
 4. 5 
 
 54 
 
 30 
 
 
 
 Take 
 
 4 
 
 106 
 
 5 
 
 1 
 
 71 
 
 50 
 
 
 
 da. 
 
 hr. 
 
 min. 
 
 sec. 
 
 T. 
 
 cwt. 
 
 Ib. 
 
 OZ. 
 
 3. 
 
 200 
 
 17 
 
 54 
 
 36 
 
 5. 20 
 
 15 
 
 75 
 
 10 
 
 
 135 
 
 20 
 
 24 
 
 48 
 
 5 
 
 16 
 
 25 
 
 12 
 
 Subtract : 
 
 6. 16 Ib. 8 oz. 3 dr. 8. 7 yd. 3 ft. 9 in. 
 
 542 257 
 
 7. 16 da. 5 hr. 36 min. 9. 27 gal. 3 qt. 1 pt. 2 gi. 
 
 5 7 18 18 2 S 
 
 10. From 6 dol. 7 di. 2 ct. 3 m. take 4 dol. 5 di. 8 ct. 1 m. 
 
 11. Find the difference between 4 Ib. 8 oz. 3 dr. and 2 Ib. 
 5 oz. 7 dr. 
 
 12. From a can containing 7 gal. 2 qt. 1 pt. of milk, 4 gal. 
 3 qt. were sold. How much was left ? 
 
 13. 6 ft. 11 in. were cut from a pole 18 ft. 9 in. long. How 
 long was the pole then ? 
 
218 PRIMARY ARITHMETIC 
 
 251. 1. Find the time from Jan. 25, 1842, to July 4, 1896. 
 It is customary to consider 30 days 
 
 yr. mo. da. 
 
 1896 7 4 to a month. July 4, 1896, is the 
 
 1842 1 25 1896th year, 7th month, 4th day of 
 
 54 5 g the Christian Era, and Jan. 25, 1842, 
 
 is the 1842d year, 1st month, and 
 
 25th day. Subtract, taking 30 days for a month. 
 
 2. What is the exact number of days between Dec. 16, 
 1895, and March 12, 1896 ? 
 
 Dec. 15 Do not count the first day mentioned. 
 
 Jan. 31 There are 15 days in December after the 
 
 Feb. 29 16th. January has 31 days, February 
 
 March 12 29 (leap year), and March 12, making 
 
 87 days Ans. 87 days. Always count the last day. 
 
 3. Find the time between Dec. 11, 1620, and July 4, 1776. 
 
 4. How much time elapsed from the beginning of the 
 Civil War, April 14, 1861, to the close of the war, April 9, 
 1865? 
 
 5. Washington was born Feb. 22, L732, and died Dec. 14, 
 1799. How long did he live ? 
 
 6. How much time since Oct. 12, 1492, to the present 
 time? 
 
 7. Mr. Griffith gave a note dated Feb. 25, 1896, and paid 
 it July 12, 1896. Find the exact number of days between 
 the giving and the paying of the note. 
 
 8. Find the exact number of days between June 25, 1900, 
 and Aug. 24, 1900. 
 
 Find the exact time between 
 
 9. Sept. 6, 1896, and April 7, 1897. 
 
 10. Nov. 11, 1898, and Dec. 4, 1898. 
 
 11. Aug. 16, 1900, and Dec. 21, 1900. 
 
MULTIPLICATION OF COMPOUND NUMBERS 219 
 
 12. July 4, 1896, and Aug. 10, 1896. 
 
 13. Feb. 23, 1897, and June 4, 1897. 
 
 14. Oct. 9, 1899, arid Feb. 6, 1900. 
 is. Nov. 8, 1894, and Oct. 6, 1895. 
 
 MULTIPLICATION OF COMPOUND NUMBERS 
 
 252. l. Multiply 4 yd. 2 ft. 8 in. by 8. 
 
 SOLUTION. 8 times Sin. = 64 in. = 5 ft. 4 in. Place 
 
 ' ' the 4 in. under the inches column, and reserve the 5 ft. 
 
 to be added to the product of 2 ft. by 8, which equals 
 
 (adding 5 ft.) 21 ft. 21 ft. 7 yd. with no remainder. 
 
 39 4 Place under the feet column and add 7 yd. to the 
 product of 4 yd. by 8, which -equals (adding the 7 yd.) 
 39 yd. The product, therefore, is 39 yd. 4 in. 
 
 2. 10 gal. 2 qt. 1 pt. 3 gi. 
 
 6 
 
 3. 12 bu. 2 pk. 5 qt. 1 pt. 
 
 4. How much hay in 6 loads if each load weighs 1 T. 
 
 2 cwt. 25 lb.? 
 
 5. What is the weight of 9 silver spoons if each weighs 
 
 3 oz. 14 pwt. 14 gr.? 
 
 6. How much oil in 5 barrels if each barrel contains 
 35 gal. 2 qt. 1 pt.? 
 
 7. What is the weight of 8 packages if each weighs 
 1 lb. 4 oz. (avoir.) ? 
 
 8. A farmer has 6 bins, each containing 58 bu. 3 pk. 2 qt. 
 How much wheat in the bins ? 
 
 9. A farmer can plough one acre of ground in 7 hr. 
 20 min. 6 sec. At the same rate how long will it take him 
 to plough 8 acres ? 
 
220 PRIMARY ARITHMETIC 
 
 DIVISION OF COMPOUND NUMBERS 
 253. 1. Divide 16 Ib. 9 oz. 17 pwt. 7 gr. by 5. 
 
 lb. oz. pwt. gr. SOLUTION.. J of 16 Ib. = 3 Ib. and 1 Ib. re- 
 5)16 9 17 7 maining. 1 lb. = 12 oz., which added to 9 oz. 
 g 4 *j JY 21 oz. \ of 21 oz. = 4 oz. with 1 oz. remain- 
 ing. 1 oz. = 20 pwt., which added to 17 pwt. 
 
 = 37 pwt. I of 37 pwt. = 7 pwt. and 2 pwt. remaining. 2 pwt. = 48 gr,. 
 which added to 7 gr. = 55 gr. -| of 55 gr. = 11 gr. 
 The quotient, therefore, is 3 lb. 4 oz. 7 pwt. 11 gr. 
 
 2. Divide 54 bu. 3 pk. 3 qt. by 5. 
 
 3. 8 persons share equally in the contents of a bin con- 
 taining 20 bu. 2 pk. of apples. What is the share of each ? 
 
 4. When $6 will buy 5 gal. 3 qt. 1 pt. of maple syrup, 
 how much will $ 1 buy ? 
 
 5. If a horse eats 8 qt. of oats per day, how long will 
 10 bu. 1 pk. 5 qt. last him ? 
 
 NOTE. When both dividend and divisor are compound, reduce them 
 to the same denomination and divide. The quotient will be abstract. 
 
 6. If a package weighs 4 cwt. 15 lb., how many such 
 packages will it take to weigh 3 T. 2 cwt. 25 lb. ? 
 
 7. Divide 102 T. 15 cwt. 27 lb. 8 oz. by 8. 
 
 8. I have 83 lb. 2 oz. of salt which I wish to put into 
 packages of 2 lb. 6 oz. each. How many packages will 
 there be ? 
 
 9. 113 gal. 2 qt. gi. -*- 4 = ? 
 
 10. 126 gal. 3 qt. 1 pt. -*- 6 = ? 
 
 11. 220 gal. 2 qt. -*- 7 = ? 
 
 12. 6 T. 1200 lb. -* 5 = ? 
 
 13. Divide 746 oz. 4 pwt. by 7. 
 
 14. Divide 10 wk. 4 da. 3 hr. 8 min. by 4. 
 
SURFACE MEASU: 
 
 221 
 
 6 IN. 
 
 SURFACE MEASUREMENTS 
 
 254. A plane figure having four straight sides and four 
 right angles is a rectangle. 
 
 The Area of a surface is the number of square units that 
 it contains. 
 
 What is the square unit 
 in this rectangle? 
 
 How many square inches 
 in it? 
 
 There are how many 
 square inches in a row? 
 There are how many rows ? 
 
 Therefore how many 
 square inches ? How do 
 you find it? 
 
 The length and breadth of a rectangle are called its 
 Dimensions. 
 
 NOTE. In finding areas, as in all multiplication, the multiplier is 
 abstract, and the unit of the product must be the same as the unit of 
 the multiplicand. 
 
 255. The answers to these questions give us the following: 
 
 Rule for Finding the Area of a Rectangle 
 
 Multiply the length by the breadth expressed in the 
 same denomination. The result will be the area ex- 
 pressed in square units of the denomination correspond- 
 ing to that of the dimensions. 
 
 Oral. 
 
 1. How many square feet in a surface 6 ft. long and 1 ft. 
 wide ? 
 
 2. In a surface 6 ft. long and 2 ft. wide ? 
 
222 PRIMARY ARITHMETIC 
 
 3. How many square feet in a platform 5 ft. long and 
 4 ft. wide ? 
 
 4. What is the area of a mirror 3 ft. long and 2 ft. wide ? 
 
 5. Draw a rectangle 4 inches long by 2 inches wide, and 
 divide it into square inches. 
 
 6. Draw a 2-inch square and divide it into square inches. 
 
 7. What is the difference between a 2-inch square and 2 
 square inches ? 
 
 8. How many square feet does a 5-foot square contain ? 
 Show the difference between a 5-ft. square and 5 square feet. 
 
 9. If the top of a table is 5 ft. long and 4 ft. wide, what 
 is its area? 
 
 10. If the area of a floor is 20 square yards, and the 
 length 5 yards, what is the width ? 
 
 Principles 
 
 1. Area is the product of length multiplied by 
 breadth. The numbers representing length and breadth 
 must be like numbers. 
 
 2. Area divided by either dimension gives the other. 
 
 256. Written. 
 
 1. How many square feet in the top of a table 5 J ft. long 
 and 4 feet wide ? How many square inches? 
 
 2. What is the area of a basement 36 ft. by 18|- ft.? 
 
 3. At 22^ a square foot, what is the cost of a flag walk 
 50 ft. x6 ft.? 
 
 4. How wide is a floor whose area is 300 sq. ft. and whose 
 length is 20 ft.? 
 
 5. 5 flag-stones, each 5| ft. by 6 ft., will cover how much 
 surface ? 
 
PLASTERING AND PAINTING 
 
 223 
 
 6. In a room are 4 doors, each 7 ft. 6 in. by 2 ft. 8. in. 
 How many square feet in the surface of the four doors? 
 How many square inches ? 
 
 7. A pasture containing 4 acres is 20 rods wide. How 
 long is it ? 
 
 8. A city lot containing 8400 sq. ft. is 140 ft. deep. 
 What is the frontage ? 
 
 9. How many acres in a field ^ mile square ? 
 
 10. Is there any difference between a mile square and a 
 square mile ? 
 
 PLASTERING AND PAINTING 
 
 257. Plastering and painting are usually done by the 
 square yard. 
 
 Deductions are frequently made for openings. 
 Windows and doors are openings. 
 
 l. A room is 18 ft. long, 12 ft. wide, and 10 ft. high. 
 How many square yards in the walls and ceiling ? 
 
 In problems of this kind first make a diagram represent- 
 ing the four walls in a line. 
 
 The ceiling may be represented as extend- r- _i2 FT. 
 
 ing from a side wall or an end wall. 
 
 Draw this diagram (enlarged) on stiff paper, 
 then cut and fold the pattern to represent the * 
 walls and ceiling of the room. 
 
 I 
 
 12 FT. 
 
 12 FT. 
 
 SOLUTION. The length of the four walls is 2 x (18 ft. + 12 ft.) = 
 60 feet. 
 
224 PRIMARY ARITHMETIC 
 
 Area of four walls, 60 ft. by 10 ft. = 600 sq. ft. 
 
 Area of ceiling, 18 ft. by 12 ft. = 216 sq. ft. 
 
 Area of four walls and ceiling = 816 sq. ft. = 90 f sq. yd. 
 
 2. If in the room mentioned above there are two doors, 
 3 ft. by 7 ft., and four windows 3 ft. by 6 ft., how many 
 square yards remain in the four walls and ceiling ? 
 
 Represent these doors and windows on the diagram. 
 
 3. How much will it cost at 25 cents a square yard to 
 plaster the room mentioned in example 1, full deductions 
 being made for openings ? 
 
 4. What will it cost at 33J cents a square yard to plaster 
 the walls and ceiling of a room 24 ft. long, 18 ft. wide, and 
 9 ft. high ? The room has 3 doors 3 ft. by 7 ft., and 6 
 windows 3 ft. by 6 ft. One-half of the openings deducted. 
 
 5. How many square yards of plastering in a room 40 ft. 
 long, 30 ft. wide, and 12 ft. high, deducting 80 sq. ft. for 
 openings ? 
 
 6. At 35 ^ a sq. yard, what will it cost to plaster a room 
 18 ft. square and 9 ft. high, having 3 doors 7 ft. by 3 ft., 
 and 5 windows 6 ft. by 3 ft., no allowance for openings ? 
 
 CARPETING ROOMS 
 
 258. In making a carpet, the carpeting is cut from a roll 
 into strips which are usually laid from end to end on the 
 floor, or lengthwise. Sometimes the strips are laid across 
 the room. 
 
 l. How much carpeting 1 yd. wide must I purchase to 
 cover a room 6 yd. long and 4| yd. wide, strips running 
 lengthwise ? 
 
 SOLUTION. It will be necessary to purchase as much carpeting as if 
 the room were 5 yd. wide, the excess of J yd. being turned under in the 
 last strip. 
 
 1 strip contains 6 yd. 5 strips = 5 times 6 yd. = 30 yd. A ns. 
 
CARPETING 225 
 
 2. How many yards must I 
 purchase, if the strips are laid 
 across the room ? 
 
 SOLUTION. 1 strip contains 4f 
 yd. 6 strips = 6 times 4f yd. = 28| 
 yd. Ans. 
 
 Carpeting is commonly 1 yd. 
 or | yd. wide. 
 
 NOTE. It is often necessary to 
 purchase more than enough carpeting 
 to cover a room, on account of the waste in matching patterns. 
 
 This diagram represents the floor in example 1, in which 
 the strips are laid lengthwise. Pupils should draw a simi- 
 lar diagram for each floor. 
 
 3. How many yards of carpet | yd. wide will be required 
 for a hall 18 ft. wide and 30 ft. long, the strips running the 
 long way of the hall ? 
 
 Make a diagram showing the strips or breadths. 
 How many linear yards in each strip ? 
 How many strips? 
 
 SOLUTION. Since one strip covers a space f yd. wide, it will take as 
 many strips to cover a space 6 yd. wide, as { yd. is contained times in 6 
 yd. 8 strips. 
 
 8 strips each 10 yd. long = 80 linear yards. 
 
 How many yards must be purchased if the strips run the 
 short way ? 
 
 4. At 11.25 a yard, what will it cost to carpet a hall 11^ 
 ft. wide and 28 ft. long, the carpet being 1 yard wide ? 
 
 How many yards long is each strip? 
 How many strips? 
 
 5. How much would the carpet cost if there were a waste 
 of 1^ yd. for matching ? (Ex. 4.) 
 
226 
 
 PRIMARY ARITHMETIC 
 
 7. 
 
 6. How many yards of ingrain carpet 1 yd. wide will be 
 required for a floor 17 ft. wide and 20 ft. long, strips run- 
 ning lengthwise? 
 
 How many yards long is each strip ? 
 
 How many strips would be needed if the room wera 15 ft. 
 wide ? How many if it were 18 ft. wide ? 
 
 It being 17 ft. wide, how many strips must be purchased ? 
 
 How much of the last strip is to be turned under ? 
 
 A sidewalk 10 ft. wide is to be laid on the 4 sides of 
 
 110 FT. t a lot 100 ft. square. At 
 
 25^ a sq. foot, what will 
 be the cost ? 
 
 The walk will be 110 
 ft. long on each of the 
 four sides, as shown by 
 the diagram. The entire 
 length of the walk is 4 x 
 110 ft. = 440 ft. ; this 
 multiplied by the width 
 of the walk will give its 
 area. 
 
 100 FT. 
 
 100 FT. 
 
 110 FT. 
 
 8. What will be the cost of a 5-foot walk laid on the 
 inside of the lot, close to the sides ? 
 
 9. A man builds a house 45 by 35 ft. on a lot 60 by 150 
 ft. How many sq. yards has he left for a lawn ? 
 
 10. What will it cost to build a tight fence 5 ft. high 
 around the above lot at 25 ^ a square yard ? 
 
 11. What is the cost of a farm 80 rods square at $ 50 an 
 acre ? 
 
 12. How long is a rectangular field that contains 50 acres 
 and is 80 rods wide ? 
 
PAPERING WALLS 227 
 
 PAPERING WALLS 
 
 259. A roll of paper is commonly 8 yards long and 18 
 inches wide. 
 
 A double roll is 16 yards long. 
 Borders are sold by the linear yard. 
 
 1. A room is 18 ft. by 15 ft., and 9 ft. high. Making no 
 deduction for openings, how many square yards in the four 
 walls and ceilings ? 
 
 How many square yards will one roll cover ? 
 
 How many rolls will be needed to paper the room ? 
 
 If the room has 2 doors 3 ft. by 8| ft., and 4 windows 
 5 ft. by 6| ft., how' many sq. yards "of surface are to be 
 covered ? 
 
 How many rolls will cover it ? 
 
 At 33 J ^ a roll, what will be the cost of papering ? 
 
 At 50 ^ a lineal yard, what will the border cost ? 
 
 2. A hall is 12 ft. wide, 38 ft. long, and 10 feet high. 
 The area of the openings is 117 sq. ft. 
 
 The paper costs 38 ^ a roll. 
 
 The border costs 66| ^ a yard. 
 
 Cost of putting on : 2 men 1| days each at $ 2 a day. 
 
 Full deductions made for openings. 
 
 Find the entire cost and make the bill. 
 
 3. A sitting room is 20 ft. by 17 ft., and 10 ft. high. It 
 has 3 doors 2 ft. 6 in. by 7 ft., and 4 windows 31 ft. by e> ft. 
 How many rolls of paper will cover the walls and ceiling, 
 deducting J the area of the openings ? 
 
 BOARD MEASURE 
 
 260. A Board Foot is a square foot of the surface of a 
 board 1 inch thick, or less. 
 
228 
 
 PRIMARY ARITHMETIC 
 
 A board 10 ft. long, 1 ft. wide, and 1 in. thick, or less, 
 contains 10 board feet ; but a beam 10 ft. long, 1 ft. wide, 
 and 8 in. thick contains 8 times 10 board feet, or 80 board 
 feet. 
 
 The number of board feet = Length (in feet) x Width 
 (in feet) x Thickness (in inches). 
 
 NOTE. When the thickness is 1 in., or less, the number of board feet 
 is the product of the length and width in feet. 
 
 1. How many board feet in a board 16 ft. long, 12 in. 
 wide, and 1 in. thick? 
 
 2. What will be the cost of 10 planks, each 12 ft. long, 
 10 in. wide, and 3 in. thick, at $ 12 a thousand? 
 
 3. How many board feet in a board 14 ft. long, 14 in. 
 wide, and | in. thick ? 
 
 4. How many board feet in 6 joists 16 ft. long, 12 in. 
 wide, and 3 in. thick ? 
 
 3 in. wide 
 
 VOLUME MEASUREMENTS 
 
 261. The Volume or Solidity of a body is the number of 
 cubic units that it contains. 
 
 How many cubic inches in a block 
 4 inches long, 3 inches wide, and 2 
 inches thick? 
 
 How many rows of cubic inches 
 are there in the bottom layer ? How 
 many cubic inches in each row? 
 How many cubic inches in the layer ? 
 How do you find it? How many 
 layers? How many cubic inches in 
 the 2 layers ? How do you find it ? 
 
VOLUME MEASUREMENTS 229 
 
 262. The answers to these questions give us the following 
 
 Rule for Finding the Volume of a Solid 
 
 Multiply together the length, breadth, and thickness, 
 all expressed in the same denomination. 
 
 The result will be the volume expressed in cubic 
 units corresponding to the unit of the dimensions. 
 
 1. How many cubic inches in a block 12 inches long, 6 
 inches wide, and 4 inches thick ? 
 
 2. What is the volume of a block of marble 6 ft. long, 
 
 5 ft. wide, and 4 ft. thick ? 
 
 3. What is the volume of 6 bricks, each being 8 in. by 
 4 in. by 2 in. ? 
 
 4. The solid contents of a block are 720 cubic feet. It 
 is 10 ft. high and 9 ft. wide. How thick is it ? 
 
 NOTE. To find one dimension when the solidity and the other two 
 dimensions are known, divide the solidity by the product of the two 
 given dimensions. 
 
 5. How many cubic inches of space in a box 10 in. long, 
 
 6 in. wide, and 4 in. high ? 
 
 What part of a cubic yard is the space in this box ? 
 
 6. A piece of marble 16 ft. long, 12 ft. wide, and 9 ft. 
 thick can be sawed into how many blocks of a cubic foot 
 each? 
 
 7. What will it cost to make an embankment containing 
 54,270 cu. ft. of earth at $.15 a cubic yard? 
 
 8. Find the number of cubic inches in a piece of ice 3 ft. 
 long, 2|- ft. wide, arid 18 inches thick. 
 
 9. What is the difference between 6 cubic inches and a 
 6-inch cube ? 
 
230 PRIMARY ARITHMETIC 
 
 10. If 300 cu. ft. of breathing space is required for a 
 pupil, how many pupils should be seated in a schoolroom 
 30 ft. square and 10 ft. high ? 
 
 11. How many cubic yards of earth will be removed in 
 digging a cellar 36 ft. square and 6 ft. deep ? 
 
 12. How many books 9 in. by 6 in. by 1| in. can be 
 packed into a chest 4 ft. by 2 ft. by 1| ft. ? (Indicate and 
 cancel.) 
 
 13. How many cubic "feet of snow on 18 square feet of 
 ground, the snow being 9 inches deep ? 
 
 14. How many bricks, 8x4x2 inches, will it take to 
 build a wall 16 x 8 x 1^ ft., no allowance for mortar? 
 (Cancel.) 
 
 15. How many cubic inches in a stick of timber 1 foot 
 square at the ends and 8 ft. long ? 
 
 16. How many 2-inch cubes may be made from a piece of 
 wood 6 ft. by 4 ft. by 2 ft. ? 
 
 17. How many loads of earth, each load containing a 
 cubic yard, in an excavation 30 ft. long, 26 ft. wide, and 14 
 feet deep? 
 
 18. A cubic yard of earth makes a load. How many 
 loads must be excavated for a cellar 32 ft. long, 30 ft. wide, 
 and 61 ft. deep ? 
 
 19. A brick is 8 in. long, 4 in. wide, and 2 in. thick. 
 How many will it take to build a wall 30 ft. long, 20 ft. 
 wide, and 1 1 ft. thick, making no allowance for mortar ? 
 
 20. The volume of a rectangular solid is 1200 cu. ft. It 
 is 20 ft. long and 4 ft. high. How wide is it ? 
 
 21. How high is a room that is 24J ft. long, 20 ft. wide, 
 and contains 4900 cubic feet? 
 
WOOD MEASURE 231 
 
 WOOD MEASURE 
 
 263. A pile of wood 4 feet wide, 4 feet high, and 1 foot long 
 is a Cord Foot. It contains how 
 
 many cubic feet ? 
 
 A pile of wood 4 feet wide, 
 4 feet high, and 8 feet long 
 contains how many cord feet ? 
 cubi feet 
 
 264. The answers to these questions give us the following 
 
 TABLE OF WOOD MEASURE 
 
 16 cubic feet make 1 cord foot (cd. ft.). 
 
 8 cord feet or ) 
 
 _, 00 , . r > make 1 cord (cd.). 
 
 128 cubic feet j 
 
 How many cords of wood in the following ? 
 
 1. A pile 18 ft. long, 4 ft. wide, 4 ft. high. 
 
 2. A pile 20 ft. long, 8 ft. wide, 8 ft. high. 
 
 3. A pile 50 ft. long, 12 ft. wide, and 17 ft. high. 
 
 4. What is the cost of a pile of wood 10 ft. long, 8 ft. 
 wide, and 8 ft. high at $4.50 a cord? 
 
 5. How high must a pile of wood be made to contain 20 
 cords, if the pile is 20 ft. long ? 
 
 6. How many cords of building stone in a pile 18 ft. long, 
 6 ft. wide, and 4 ft. high? 
 
 7. How many cords of wood can be piled into a shed 
 24 ft. long, 18 ft. wide, and 12 ft. high? 
 
232 PRIMARY ARITHMETIC 
 
 CAPACITY 
 
 265. Capacity of Cisterns. 
 
 1. A wine gallon fills 231 cubic inches of space. How 
 many gallons will fill a cubic foot of space? 
 
 JJg 2 - 8 - = about 7 J gallons. Ans. 
 
 NOTE. It is sufficiently accurate in estimating large liquid capacities 
 to reckon 7| gal. to the cubic foot. 
 
 2. A cistern is 5 ft. square and 6 ft. deep. How many 
 gallons of water will it contain? 
 
 Solve both ways and note the difference. 
 
 3. What is the capacity in barrels of the cistern in 
 Ex. 2? 
 
 4. How many barrels of water in a cistern 7 ft. long, 
 4| ft. wide, and 5| ft. deep ? (Indicate and cancel.) 
 
 5. What is the capacity in barrels of a tank 3 ft. by 4^ ft. 
 and 4| ft. deep? 
 
 6. How many gallons of water in a tank whose capacity 
 is 150 cubic feet ? 
 
 7. How many cubic feet in a cistern that will hold 1500 
 gallons of water? 
 
 266. Capacity of Bins. 
 
 8. A bushel fills 2150.42 cubic inches of space, which is 
 1^ cu. ft., nearly. 
 
 NOTE. In estimating large quantities of grain it is sufficiently accu- 
 rate to reckon 1J cu. ft. to the bushel. 
 
 9. How many bushels of grain will a bin hold that is 6 ft. 
 long, 5 ft. wide, and 4 ft. deep? (Indicate and cancel.) 
 
 Solve both ways and note the difference. 
 
 10. How many bushels in a bin that contains 150 cubic 
 feet? 
 
 11. How many cubic feet in a bin that holds 150 
 bushels? 
 
PERCENTAGE 
 
 267. To THE TEACHER. Before teaching percentage review thor- 
 oughly Questions of Relation and Division of Decimals. 
 
 Questions of Relation may be solved by means of hun- 
 dredths. 
 
 1. How much is -ffa of 20 ? Ans. 5. 
 
 2. 5 is fijfc of what ? Ans. 20. 
 
 3. 5 is how many hundredths of 20 ? Ans. -f 
 
 Another name for hundredths is per cent. Thus, -ffa is 25 
 per cent, yf^ is 8 per cent, .16 is 16 per cent, .05 is 5 per 
 cent. 
 
 Per cent means by the hundred or on the hundred. 
 
 The sign of per cent is Jo. 25 per cent is 25^, 6 per cent 
 is 6^>, 50 per cent is 50^. 
 
 In performing operations per cent is used generally as 
 decimal hundredths. 
 
 Using the sign ft, Examples 1, 2, and 3 become as follows : 
 
 NOTE. These questions may be solved as in Art. 177. 
 
 a. How much is 25 </o of 20 ? 
 
 20 x .25 = 5. Therefore 25 % of 20 = 5. 
 
 b. 5 is 25 Jfe of what number ? 
 
 Since 20 x .25 = 5 5 -* .25 = 20. Therefore 5 is 
 of 20. 
 
 233 
 
234 PRIMARY ARITHMETIC 
 
 c. 5 is what per cent of 20 ? 
 
 Since 20 x .25 = 5, 5 -*- 20 = .25. Therefore 5 is 
 25^ of 20. 
 
 What principle is used in solving questions b and c ? 
 
 Question a 
 Find the result and form questions b and c : 
 
 4. How much is 8^ of 50 ? 
 
 5. How much is 5/o of 200 ? 
 
 6. How much is 12 ^ of 150 ? 
 
 7. lOjfc of 60 sheep are how many sheep ? 
 
 8. 50^o of 300 men are how many men ? 
 
 9. 2 ft of 30 bushels are how many bushels ? 
 
 Question b 
 Find the result and form questions a and c 
 
 10. 16 is 25/o of what number ? 
 
 11. 15 is 10^) of what number ? 
 
 12. 210 is 1^) of what number? 
 
 13. 20 sheep are 5 ft of how many sheep ? 
 
 ' 14. 40 pupils are 10 ^ of how many pupils ? 
 
 15. 80 horses are 16^ of how many horses ? 
 
 Question c 
 
 Find the result and form questions a and b. 
 
 16. 20 is what % of 80 ? 
 
 17. 10 is what </o of 200 ? 
 
 18. 50 is what <fr of 500 ? 
 
 19. 25 boys are what per cent of 100 boys ? 
 
 20. 15 pounds are what per cent of 60 lb.? 
 
 21. What per cent of 80 men are 40 men ? 
 
 Find the result, form the other two questions, and solve 
 each. 
 
PERCENTAGE 235 
 
 22. 5</o of 40 apples are how many ? 
 
 23. $15 is 10/o of what? 
 
 24. 12 yd. is what <fo of 48 yd. ? 
 
 25. How much is 60 fo of 200 bushels ? 
 
 26. 40 men are 5^fc of how many men ? 
 
 268. Percentage is a process of solving questions of rela- 
 tion by means of hundredths. 
 
 269. Read the following Questions of Relation : 
 Question a. How much is 5% of 200 ? Am. 10. 
 Question b. 10 is 5% of what? Ans. 200. 
 Question c. 10 is what % of 200 ? .A^s. 5%. 
 
 These three kinds of questions form the basis of a great 
 variety of practical computations, which are classed under 
 the general head of Percentage. 
 
 270. Every question in percentage involves three elements: 
 the Rate per cent, the Base, and the Percentage. 
 
 271. The Rate per Cent is the number of hundredths taken. 
 In question a, what is the rate per cent ? 
 
 272. The Base is the number of which the hundredths are 
 taken. In question a, what is the base ? 
 
 273. The Percentage is the result obtained by taking a 
 certain per cent of a number. In question a, what is the 
 percentage ? 
 
 How much is 8% of $200 ? 
 
 SOLUTION. 8% of $200 = 200 x .08 = $ 16. We now have the three 
 elements, as follows : 
 
 8% is the rate, $200 is the base, and $16 is the percentage. 
 Since $200 x .08 = $16, the percentage; 
 $16 -4- .08 = $200, the base ; 
 and $16 + $200 = .08, the rate. 
 
236 PRIMARY ARITHMETIC 
 
 274. Therefore, when any two of these elements are given, 
 the other may be found, thus : 
 
 Base x Rate = Percentage ; 
 Percentage -5- Rate = Base ; 
 Percentage -*- Base = Rate. 
 
 275. Tell which elements are given, and which one is re- 
 quired, in question a ; in question b ; in question c. 
 
 To find the Percentage when the Base and the Rate 
 are given, multiply the Base by the Rate. 
 
 1. A boy had $4.00, and spent 10% of it for a book. 
 How much did the book cost ? 
 
 To THE TEACHER. In solving any problem in percentage, the pupil 
 should first state the question. The question in Ex. 1 is " How much 
 is 10% of $4.00? " 
 
 2. A farmer had 100 sheep and sold 20% of them. How 
 many did he sell? (Write the question, then solve.) 
 
 3. A man having 500 acres of land gave 20% to his son. 
 How many acres did his son receive ? (Question.) 
 
 4. If I buy goods for $400 and sell them at a loss of 5%, 
 how much do I lose? (Question.) 
 
 5. Write a problem having $500 for the base and 4% for 
 the rate. 
 
 To find the base when the Percentage and the Rate 
 are given, divide the Percentage by the Rate*. 
 
PERCENTAGE 237 
 
 6. $40 is 10% of what? 
 
 Solve, then state questions a and c. 
 
 7. A man sold goods at 50% profit, and thereby gained 
 1200. What was the cost ? 
 
 First state the question. ($200 is 50% of what?) 
 
 8. A boy paid 40 cents for a book, which was 10% of his 
 money. How much money had he ? (Question.) 
 
 9. A man sold 20 sheep, which was 20% of his flock. 
 How many sheep were there in the flock ? (Question.) 
 
 10. '10% of my salary is $160. What is my salary ? 
 (Question.) 
 
 11. By selling cotton at 5% below cost I lose $200. What 
 was the cost of the cotton? (Question.) 
 
 12. A grocer gained $50 by selling goods at 10% profit. 
 What did the goods cost ? (Question.) 
 
 13. I sold a bicycle at an advance on the cost of 20% and 
 thereby gained $10. What did I pay for the bicycle ? 
 (Question.) 
 
 14. A man pays $300 rent, which is 20% of his salary. 
 What is his salary ? (Question.) 
 
 To find the Rate when the Percentage and the Base 
 are given, divide the Percentage by the Base. 
 
 15. $50 is what per cent of $500 ? 
 Solve, then state questions a and b. 
 
 16. By selling a bicycle that cost $50, a dealer made a 
 profit of $10. What was his gain per cent ? First state the 
 question. ($10 is what per cent of $50 ?) 
 
 E'"S 
 
238 PRIMARY ARITHMETIC 
 
 17. In a school of 900 pupils 450 are girls. What per cent 
 of the pupils are girls ? (Question.) 
 
 18. A boy had 80 cents and spent 20 cents. What per 
 cent of his money did he spend? (Question.) What per 
 cent of his money did he save ? (Question.) 
 
 19. From a farm containing 400 acres 32 acres were sold. 
 What per cent of the farm was sold ? (Question.) 
 
 20. A farmer had 200 sheep and sold 50 sheep. What per 
 cent of his sheep were sold ? (Question.) What per cent 
 were not sold? (Question.) 
 
 21. In a spelling lesson of 20 words Lucy misspelled 5. 
 What per cent did she misspell? (Question.) What per 
 cent did she spell correctly? (Question.) 
 
 SIMPLE INTEREST 
 
 276. l. I borrow $500 for 1 year, and at the end of the 
 year I repay the money and 6^ for the use of it. How 
 much do I pay for the use of $ 500 ? 
 
 2. How much must be paid for the use of $ 50 for 1 year 
 at 5 ft? at 7fo? 
 
 3. How much at 5jfe per annum must I pay for the use 
 of $1000 for 1 year ? for 3 years ? 
 
 4. I loan James Barnes $500 at 6jfc. At the end of 2 
 years he pays me in full. How much does he pay me ? 
 
 277. Money that is paid for the use of money is called 
 Interest. The money for the use of which interest is paid 
 is called the Principal, and the sum of the principal and 
 interest is called the Amount. 
 
 Interest at 6 ft means 6 ^ of the principal for 1 year. 
 12 months of 30 days each are usually regarded as a year 
 in computing interest. 
 
SIMPLE INTEREST 239 
 
 Oral. 5. What is the interest of $ 100 for 3 years at 6 ft ? 
 
 SOLUTION. $100 Principal. 
 
 .06 Rate. 
 
 $ 6.00 Interest for 1 year. 
 3 
 
 $ 18.00 Interest for 3 years. 
 
 6. What is the interest of $ 80 at 5 ft for 2| years ? 
 
 7. What is the interest of $ 1000 at 5 Jo for 2 yr. 6 mo. ? 
 
 8. What is the interest of $100 at 6/0 for 1 year? For 
 1 year ? For 2 yr. 6 mo. ? For 3 yr. 3 mo. ? 
 
 278. When the time does not include days, find interest 
 as follows : 
 
 Rule for Finding Interest 
 
 Multiply the principal by the rate per annum and 
 that product by the time in years. 
 
 9. What is the interest of $ 297.62 for 5 yr. 3 mo. at 6 Jfe ? 
 SOLUTION. $ 297.62 
 
 r\n 
 
 NOTE. Final results should not in- 
 
 17.8572^ clude mins> Mi}ls are disregarded 
 
 I GSS than 5, and called another cent if 5 
 
 892860 or 
 
 $93.75. Ans. 
 Find the interest of : 
 
 10. $384.62 at 6 % for 2 yr. 
 
 11. 1463.75 at 7/o for 3 yr. 
 
 12. $250.50 at 8/0 for Syr. 
 
 13. $685.20 at 4% for 6 yr. 
 
 14. $596.15 at 5^ for 2 yr. 3 mo. 
 
240 PRIMARY ARITHMETIC 
 
 15. $386.42 at 5<fo for 6 yr. 5 mo. 
 
 16. $ 950.16 at 10 <fo for 4J yr. 
 
 17. $283.25 at 6/0 for 2 yr. 8 mo. 
 
 Find the amount of : 
 
 18. $284.10 for 3 yr. 2 mo. at 7fc. 
 
 19. $364.24 for 1 yr. 1 mo. at 6/0. 
 
 20. $282.50 for 5 yr. 9 mo. at 5/o. 
 
 21. $298 for 4 yr. 3 mo. at 6/0. 
 
 22. $ 389 for 7 yr. 10 mo. at 5 ft. 
 
 279. When the time includes clays, we find interest by the 
 following 
 
 Rule for Finding Exact Interest 
 
 To compute exact interest, find the exact time in 
 days and consider 1 day's interest as 3-^ of 1 year's 
 interest. 
 
 1. Find the exact interest of $358 for 74 days at 7/o. 
 
 SOLUTION. $358 x .07 = $25.06, 1 year's interest. 74 days' interest 
 is 3^ of 1 year's interest. ^ of $25.06 = $5.08. Ans. 
 
 Find the exact interest of : 
 
 2. $324 for 15 d. at 9%. 
 
 3. $253 for 98 d. at 4/o. 
 
 4. $624 for 117 d. at 1%. 
 
 5. $153.26 for 256 d. at 5%. 
 
 6. $620 from Aug. 15 to Nov. 12 at 670. 
 
 7. $540.25 from June 12 to Sept. 14 at 8fo. 
 
 8. $7560 for 90 days at 5fo. 
 
 9. Find the exact interest at 5 ft on a note dated Jan. 14, 
 1896, and paid March 31, 1896, for $ 832. 
 
TOPICAL REVIEW 
 
 280. l. Write in words 5007. 
 
 2. Write in figures fourteen thousand seventeen. 
 
 3. Write in figures CCXI. 
 
 4. Write in Roman 245. 
 
 5 Arid- COQOt-OiCOrHQOOit-OCD 
 
 o. 2i.uu. CM rt< T-H o t~ CM co co -O o 
 
 CO CM GO Ci t 
 
 6. From twenty-four thousand eight hundred eight take 
 twelve thousand nine hundred nine. 
 
 7. If you have 24 cents and spend 8 cents for a tablet 
 and 5 cents for a pencil, how many cents have you left? 
 Indicate the operation by signs. 
 
 8. Divide 35,702 by 53. 
 
 9. Write two prime numbers. 
 
 10. What is the quotient of 24 x 56 divided by 7 x 12 ? 
 Indicate and cancel. 
 
 COMMON FRACTIONS 
 
 281. 1. Write an improper fraction whose value is more 
 than 1. Write an improper fraction whose value is 1. 
 
 2. Change | to a fraction whose denominator is 40. 
 
 3. Change to lowest terms ^j-. 
 
 4. How many eighths in fifteen ? 
 
 5. Write two like fractions. 
 
 6. Change to common denominator and add : 9, f , |, ^. 
 
 241 
 
242 PRIMARY ARITHMETIC 
 
 7. $ 141 + $ 9 3 _ 1 1 6 1 = w hat ? Write a problem using 
 these numbers. 
 
 8. The sum of two fractions is ^. One of them is f . 
 What is the other ? 
 
 9. 15f-5i = ? 3|x5J = ? 28i-2f=? 
 10. Add: 28f, 171, 15|, 81. 
 
 282. l. Write a proper fraction, an improper fraction, a 
 mixed number, and an integer, and use them in one problem. 
 
 2. Write a complex fraction. 
 
 3. What is a factor of a number ? What is the greatest 
 common divisor of two or more numbers ? 
 
 4. If ^ of my money is invested in land, | in houses, and 
 the remainder is deposited in the bank, what fraction of my 
 money is in the bank ? 
 
 QJ3 
 
 5. Find the value of 9 * , + 1 of i -s- . 
 
 I ot I 
 
 6. Reduce to lowest terms ||-|. 
 
 7. The sum of two fractions is If. One of them is f . 
 What is the other ? 
 
 8. A man owned | of a ship and sold ^ of his share. 
 What part of the ship did he sell ? 
 
 9. A man had $500 in the bank. He drew out -I of it. 
 
 o 
 
 How much did he draw ? (Question.) 
 
 10. A man sold 50 sheep, which was ^ of his entire flock. 
 How many sheep in the flock ? (Question.) 
 
 DECIMAL FRACTIONS 
 
 283. 1. In the number 32.6, what would be the value of 
 the 2 if it were removed one place to the right ? What 
 would be its value if removed one place to the left ? 
 
TOPICAL REVIEW 243 
 
 2. Which is the greater, 50 thousandths or 5 hundredths? 
 
 3. Take one thousandth from one thousand. 
 
 4. Multiply 2 by 2.84. 
 
 5. Multiply 100 by .01. 
 
 6. 1.111 - .01 = ? 1 -f- .1 = ? .1 - 1 = ? 
 
 7. Change to decimals : |, |-, J, |. 
 
 8. Write .0000054 as a common fraction. 
 
 9. Write as a decimal fraction, thirty-four, and three 
 thousand four hundred six ten-millionths. 
 
 10. Write as a decimal, 15 5-10000. 
 
 284. 1. Make out a receipted bill of the following : 66 Ib. 
 pork at 121 ^ ; 143 ib. veal at 16| ^ ; 48 boxes strawberries at 
 16|^; 60 doz. eggs at 16|^. 
 
 Mr. A is the buyer, and Mr. B the seller. In multiply- 
 ing use the aliquot parts of $1. 
 
 2. How do you locate the decimal point in any product ? 
 In any sum ? 
 
 3. Change 62| and 83 J each to a common fraction. 
 
 4. Divide 28.78884 by 1.25 and have four decimal figures 
 in the quotient. 
 
 5. Divide .001 by 1000. 
 
 6. What cost 1650 oysters at 50 cents a hundred ? 
 
 7. What is the cost of 3783 ft. of pine lumber at $16 a 
 thousand ? 
 
 8. What is the cost of 7384 tons of coal at $5 a ton? 
 
 285. l. What is the cost of 80 tablets at 16f ^ each? 
 (Use the aliquot part.) 
 
 2. At 33^ a yard, how many yards of linen can be 
 bought for $9? (Use the aliquot part.) 
 
244 PRIMARY ARITHMETIC 
 
 3. In the number 66.6, what is the value of the first 6? 
 The second 6 ? The third 6 ? 
 
 4. Which is the greater, f or |, and how much ? 
 
 5. John spent .75 of his money. What part of his 
 money had he left? 
 
 6. Find the cost of these articles purchased by J. D. Fox 
 from John Grouse Jan. 10, 1882, and make out the bill in 
 proper form : 
 
 4 Ib. coffee at 25^ a pound. 
 18 Ib. sugar at 6^ ^ a pound. 
 4 gal. of molasses at 50^ a gallon. 
 16 Ib. of rice at 8^ ^ a pound. 
 
 7. How many bushels of wheat at $ .90 a bushel must be 
 given for 9 pieces of cloth, each containing 40 yards at $ .50 
 a yard ? (Cancellation.) 
 
 8. The lesser of two numbers is 4603.85 and their differ- 
 ence is 835.007. What is the greater number ? 
 
 9. John gave away 30 of his marbles. How many 
 remained if he had 200 marbles at first? 
 
 10. 200 is T 2 ^ of what ? 
 
 DENOMINATE NUMBERS 
 
 286. 1. How many bushels of apples at 50^ a bushel must 
 be given for 15 Ib. of tea at 40 j^ a Ib. ? (Cancellation.) 
 
 2. From 7 mi. 40 rd. 9 yd. 
 take 4 mi. 17 rd. 8 yd. 
 
 3. How long is a fence that extends around a field 124 
 rd. long and 78^ rd. wide ? (Draw diagram of field and 
 label each side.) 
 
 4. Define Compound Number and write one. 
 
TOPICAL REVIEW 245 
 
 5. If a peck measure is one-quarter full, how many 
 quarts does it contain ? 
 
 6. How many bushels in 1152 pints ? 
 
 7. Three quarts of milk are taken from a two-gallon 
 pail. How many quarts remain ? 
 
 8. How many tons in 6000 pounds ? 
 
 9. What will 4^ Ib. of indigo cost at $ .05 an ounce ? 
 
 10. What will it cost to build 15 yd. of fence <it 58^ a 
 foot? 
 
 287. 1. How much ro.pe is there in 3 balls, if there are 
 20 yd. 1 ft. in one, 18 yd. 1 ft. 8 in. in another, and 9 yd. 
 
 2 ft. 11 in. in the third ? 
 
 2. At $ 2.40 a dozen, what will 8 handkerchiefs cost ? 
 
 3. John had $25 and spent $15 for a suit of clothes. 
 What part of his money did he spend? (Question.) 
 
 4. The floor of a room 12 ft. wide is covered by 24 yd. 
 of carpet. How long is the room ? 
 
 5. At $ | a yard, how many yards of cloth can be bought 
 for $25? (Solve by cancellation.) 
 
 6. Reduce 25 sq. yd. 6 sq. ft. to square inches. 
 
 7. From 1J sq. miles of land I sold a farm 160 rd. long 
 by 100 rd. wide. How many acres are left ? 
 
 8. Reduce 36,940 pints to higher denominations. 
 
 9. How many feet in a mile ? 
 
 288. 1. How many acres in 640 sq. rods ? 
 
 2. Show the difference between a 3-foot square and 
 
 3 square feet. 
 
 3. A rectangle contains 320 sq. yards and is 20 yards 
 long. How wide is it ? (Make a drawing of the rectangle 
 and label the sides.) 
 
246 PRIMARY ARITHMETIC 
 
 4. At $18 a ton, what is the cost of 3000 Ib. of hay? 
 
 5. At $ -| a pound, what will 2 pounds of tea cost ? 
 
 6. What cost 3 Ib. 8 oz. of butter at 30 ^ a pound ? 
 
 7. I bought 8 cwt. 10 Ib. of sugar for $ 81 and sold it at 
 12 ^ a pound. What was the gain ? 
 
 8. Find the area of a floor 16J ft. long and 4 yd. wide. 
 
 9. How many gallons of water will a cistern contain 
 that is 7 ft. long, 4^ ft. wide, and 4| ft. deep ? 
 
 10. How many bushels of grain will a bin hold that is 
 
 6 ft. x 5 ft. x 4 ft. ? 
 
 289. l. How high is a room that is 24J ft. long, 20 ft. 
 wide, and contains 4410 cubic ft. ? 
 
 2. A square mile of land may be cut into how many 
 80-acre farms? (Show by a diagram as well as by figures.) 
 
 3. Change ^ of a ton to pounds. 
 
 4. 3 oz. is what part of a pound ? 
 
 5. Reduce to higher denominations 369,426 cu. inches. 
 
 6. How many cords of wood can be piled into a shed 
 16 ft. by 10 ft. by 8 ft. ? (Indicate and cancel.) 
 
 7. How many cords in a pile of wood 86 ft. 3 in. long, 
 
 7 ft. 6 in. high, and 4 ft. wide ? 
 
 8. How many bushels will a bin contain that is 9 ft. 
 long, 4 ft. wide, and 6 ft. deep? 
 
 9. Find the cost of 9^ tons of coal, if ^ of a ton cost 
 $3.00. 
 
 10. How many rods of fence are required to enclose a lot 
 20 rods wide and 3 times as long ? 
 
ANSWERS TO HEATH'S PRIMARY ARITHMETIC 
 
 Article 31. 4. 438. 5. 395. 6. 495. 7. 413. 8. 575. 9. 455. 
 
 10. 347. 11. 3196. 12. 3846. 13. 3549. 14. $2480.45. 15. 469. 
 16. 4139. 17. 5354. 18. $549.88. 19. $732.98. 20. 6115. 21. 8915. 
 
 22. 18,441. 23. 21,365. 24. .$771.40. 25. $1287.873. 26. $821.191. 
 
 27. $577.189. 28. 890,407. 29. 103,019. 30. $10,290.28. 31. 1364. 
 32. $240.75. 34. 31,014. 35. 273,420. 36. 875,935. 37. 51,543. 
 38. $41,981.17. 39. $136.09. 40. 373,915. 41. 176,880. 42. 651,021. 
 43. $511.233. 
 
 Article 32. 1. 41 peaches. 2. 41 scholars. 3. 98 sheep. 4. 87 bu. 
 
 5. $1.30. 6. 101 trees. 7. 80 qt. 8. 133 mi. 9. 126 fowls. 10. $2.20. 
 
 11. 62 years. 12. 71 houses. 13. 52 minutes. .14. 43 fish. 15. 2057 miles. 
 
 16. $54.05. 17. 521 bu. 18. 658 pages. 
 
 Article 43. 1. 2145. 2. 6927. 3. 3698. 4. 5499. 5. 1474. 
 
 6. 27,997. 7. 18,338. 8. 17,082. 9. 81,482. 10. 68,004. 11. 4134. 
 
 12. 71,359. 13. 8422. 14. 11,036. 15. 5347. 16. 8983. 17. $1.032. 
 18. $8.233. 19. $24.025. 20. $19.687. 21. $10. 22. $12.082. 
 
 23. $1.052. 24. $50.68. 25. 7529. 26. 25,350. 27. 21,996. 28. 3252. 
 29. 6039. 30. 4127. 31. $2341.64. 32. $80.308. 33. '7726. 34. 11,369. 
 35. $23.967. 36. 41,276. 37. $813.875. 38. $2.33. 39. 166 acres. 
 40. $149.36. 41. 27 gal. 42. 73 oranges. 43. 163 acres. 44. 36yd. 
 45. 49 sparrows. 46. $ 125. 47. 63 cents. 48. 95 eggs. 49. 27 qt. 
 
 Article 44. 1. 237 bu. 2. 39 mi. 3. $174. 4. $1.99. 5. $4.35. 
 6. 252 mi. 7. $268. 8. $.43. 9. 83 papers. 10. $99. 11. 447 pupils. 
 12. $151. 13. 15 years. 14. $8.01. 15. 61. 16. 132 sheep. 17. 410 bu. 
 18. 162. 19. 59 acres. 
 
 Article 61. 1. 7776. 2. 11,544. 3. 17,415. 4. 14,728. 5. 56,196. 
 
 6. 54,600. 7. 33,432. 8. 96,728. 9. 15,996. 10. 34,314. 11. 70,784. 
 12. 21,528. 13. 14,553. 14. 79,001. 15. 8288. 16. 27,006. 17. 11,124. 
 18. $788.20. 19. $944.46. 20. $912.87. 21. $973.648. 22. $431.31. 
 23. $1661.175. 24. $11,042.21. 25. $857.088. 26. $902.060. 27. $7285.185. 
 
 28. $1046.464. 29. $10,098.72. 30. $9967.12. 31. $73,671.50. 
 32. $16,252.81. 33. $63,677.16. 
 
 Article 62. 1. 62,000. 2. 516 sheep. 3. 392 pounds. 4. $504. 
 5. $3.60. 6. 2880 rods. 7. 8800yd. 8. $17.50. 9. 583 mi. 10. 384 trees. 
 11. $15. 12. $19.35. 13. 784 pounds. 14. $8.10. 15. $63. 16. $105. 
 
 17. 36,960ft. 18. 20,000 pounds. 19. $2304. 20. $10.32. 21. $1926. 
 22. 5030. 23. 870 acres. 24. $49.50. 25. 1728 pens. 26. 2616. 
 
 Article 73. 1. 28. 2. 62^. 3. 113^, 4. 28 r V 5. 52|3. 6. 5(y 7 . 
 
 7. 31 J}. 8. 1219. 9. 59^, 10 . 99 r \. 11. ll}-\. 12. 123ff. 13. 80 T %. 
 14. 153.22. 157302. 16. 32f4. 17. 71 ^ 18. 40^. 19. 200*. 
 20. 223f. 21. 34i|?-. 22. 80}f. 23. 47 H. 24. 79A- 25. 300^. 
 26. lOOlJ. 27. 00p. 28. 17f|. 29. 1664J. 30. 215J?. 31. 18fj. 
 32. 74U. 33. 63015. 34. 10l'-f. 35. 99f|. 36. 241 A. 37. 595JJ. 
 38. 283 jj. 39. 673$ j- 40. 687|f. 
 
 247 
 
248 PRIMARY ARITHMETIC 
 
 Article 83. 1. 360 mi. 2. 178 bu. 3. 45 cents. 4. 153 tons. 
 
 5. 54 rd. 6. 82 da. 7. 109. 8. 84 ploughs. 9. 202 acres. 10. $4.625. 
 
 11. 415 pk. 12. 52 wk. 13. $3287. 14. $4.20. 15. 1760yd. 
 
 16. 125 overcoats. 17. 38 hours. 18. 72. 19. 36 gal. 20. 120 tons. 
 21. 106 acres. 22. 24 stoves. 23. 33J da. 24. 49 wk. 
 
 Article 85. 1. 56. 2. 14. 3. 70 cents. 4. 16 hr. 5. 24 hr. 
 
 6. $20.83. 7. $76.80. 8. $22.14. 9. $42. 10. 14|f. 11. 90 da. 
 
 12. $244. 13. 656 mi. 14. $3924. 15. 340 miles. 16. 4fi pounds. 
 
 17. $768. 18. $965. 19. 38 times. 20. 55 months. 21. 12. 22. 5 years. 
 23. $159.33. 24. 33 tons. 25. 16 tablets. 26. Carriage 182, horse 183. 
 27. $72. 28. Edward $4.03, Henry $2.93, John $5.19. 29. $13. 
 30. $65.28. 31. $50. 32. 960 sheets. 33. 259 sheep. 34. 40 farms. 
 35. $192.40. 36. $1590. ' 37. 24 acres. 38. $3.69. 39. $11.50. 
 40. 48 T % pounds. 41. 46 miles an hour. 42. 264. 43. $469. 
 44. $284.25. 45. $41. 46. 70 hours. 
 
 Article 97. 1. 2-5-3. 2. 2.2-2.3.5. 3. 2 - 3 - 7. 4. 3-2.11. 
 5. 2-5-11. 6. 5-3-7. 7. 2.11-3.7. 8. 5.3.3. 9. 3.3.3.7. 
 
 10. 5.7-19. 11. 3-13.11. 12. 5-5.17. 13. 2-3-3-23. 
 
 14. 3.7.7.23. 15. 23-29. 
 
 Article 100. 1. 4788. 2. 2. 3. 18. 4. 5J. 5. 3f. 6. 1J. 7. 63J. 
 8. 12 bushels. 9. 20 yards. 10. 21 /v 11. 1 111 bushels. 12. 25 sacks. 
 
 Article 106. 1. 12. 2. 21. 3. 15. 4. 56. 5. 12. 6. 20. 7. 16. 
 8. 12. 9. 8. 10. 2. 11. 15. 12. 9. 13. 11. 14. 63. 15. 9. 
 
 Article 111. 1. 270. 2. 36. 3. 48. 4. 240. 5. 720. 6. 72. 
 
 7. 420. 8. 560. 9. 7560. 10. 1400. 11. 630. 12. 192. 
 
 Article 115. 1. 10. 2 14. 3. 17. 4. 20. 5. 10. 6. 6. 7. 35. 
 
 8. 20. 9. 10. 10. 3. 11. 29. 12. 3. 13. 218. 14. 93. 15. 300. 
 16. 18. 17. 9. 18. 40. 19. 5. 20. 36 + 15 + 16 + 38. 21. 16 - 4 ; y. 
 
 5+ 17 ; (5 + 17) -nil. 22.3 + 5+7. 23.2 + 5 + 6. 24. $ 10.16 - $4.40. 
 
 26. 60-(18+12). 27. (18 + 5)-8. 28. ($ 1.00 + $ .75 + $2.50) -$2.75. 
 29. $5.18- ($1.50 + $.75). 30. 4 + (3 x 2). 31. (4 + 3) x 2. 
 
 32. 4x3 + 2. 33. 4 x 
 36. 18 x 18 - 144. 37. 
 (5 x 150). 
 Article 132. 1. f. 
 8. A- 9. tff 10. i. 
 
 (3 + 2). 34. 84-5x6. 35. (72 
 6 x (11 - 6). 38. (53 + 63) x 4. 
 
 2. f. 3. i 4. T V 5. if- 6. 
 11. H. 12. fi 13. 1. 14. i 
 
 - 42) x 4. 
 39. 55^ + 
 
 i 7. J. 
 15. T ^. 
 
 16. 11. 17. M j 
 
 f. 18- & 
 
 19. T y 20. I 
 
 21. 4. 
 
 22. i. 
 
 23. J 
 
 
 24. i 25 
 
 . f 
 
 26. 11. 
 
 27 
 
 . i. 28. 11. 
 
 29. 
 
 |. 30. 
 
 i- 
 
 31. 
 
 i 32. 
 
 ' f 
 
 33. ff 
 
 
 
 
 
 
 
 
 
 
 
 
 Article 
 
 137.- 
 
 -17. -V-. 
 
 
 18. ^ 
 
 19. 1% 
 
 i. 20 
 
 . is- 1 -. 
 
 21. - 1 
 
 
 22. W-- 
 
 23. a; 
 
 !- 24. 
 
 4 T 8 "T 
 
 . 25. 
 
 
 26. 
 
 Vo 1 - 27 
 
 
 W-. 
 
 28. 1$ 
 
 "J 1 - 
 
 29. *f Ji. 
 
 30. i 
 
 -!<p. 31. 
 
 ~t 
 
 P. 32. 
 
 ~w~- 
 
 33. 
 
 32_3. 34> 11049 
 
 . 35. A 
 
 : !-- 
 
 38. ifp. 
 
 37. 
 
 fc#UL. 
 
 38. 
 
 2 W _2. 
 
 39. 
 
 if. 40. -^ff^. 41. -ff^-. 
 
 42. if p. 
 
 43. i 
 
 fi fl . 44. 
 
 4 
 
 IF- 
 
 
 
 
 
 
 
 
 Article 
 
 142.- 
 
 -1. 47}. 
 
 2 
 
 16&. 
 
 3. 20f. 4. 30^. 
 
 5. 
 
 30A- 
 
 , 6. 21 
 
 3T' 
 
 7. 60$. 8. 
 
 21 4 -, 
 
 , 9. 161f. 
 
 10. 134 
 
 Ii 11 
 
 . 52 
 
 iV 12- 
 
 24!}}V 
 
 13. 27 
 
 ir 
 
 14. 248JJ. 
 
 15. 
 
 26if 
 
 16. 191. 
 
 17. 
 
 19iJ 
 
 . 20. 
 
 
 
 21. 91 
 
 
 22. 2/4y^^; 
 
 
 
 
 
 
 
 
 
 
 
 
 Ar+ 14.' 
 
 7 1 
 
 15, 36, 
 
 50 
 
 2 30, 
 
 36, 20 
 
 3 
 
 25, 36, 
 
 20 
 
 4 
 
 14, 12, 
 
 27 > 
 
ANSWERS 249 
 
 6, 9, 10, 5 g 30, 72, 100, 105 - 360, 25, 36, 32 g 6, 9, 10, 7 
 
 12 120 40 12 
 
 135, 108, 80, 162 1Q 25, 28, 30, 32 n 15, 12, 20, 14 12 48, 45, 30, 110 
 
 180 40 30 120 
 
 Article 154. 1. If 2. 1. 3. 1JJ. 4. 2J. 5. 2J. 6. 1 T V 
 7. 1H. 8- 1J. 9- 2/2V 10. 7iJJ. 11- 2AVV 12. 2}J. 13. 9JJ. 
 14. 44. 15. 5f. 16. 6 AT. 17. 16 T %. 18. 4J. 19. 7-&. 20. 6J. 
 21. 28if. 22. 23f 23. 3f. 24. 66if. 25. 47||, 26. 126 T V mi. 
 27. 208|bu. 28. $240ff 29. 259^ yd. 30. lOfi yd. 31. $25ff. 
 32. 241}JJA. 
 
 Article 158. 1. &. 2. i. 3. |. 4. 5|. 5. 2|. 6. 12 T V 
 7. 4 T V 8. 9f 9. 6f. 10. 4J. 11. if. 12. T \. 13. 7 V 
 
 14. T %. 15- Ml- 16. iJ a %. 17. If 18. 10|. 19. 4J. 
 Article 162. 1. 61. 2. 3-*, 3. 2f 4. 3. 5. 6}. 6. 6if. 
 
 7. 5f. 8. 41. 9. 5-f. 10. 7f. 11. 1. 12. 41J. 13. 2f. 14. 11. 
 
 15. 4. 16. 15. 17. llj\. 18. 3 T V 26. 108. 27. 1139. 28. 1634J. 
 29. 1064 T V 30. 1616. 31. 26 r V 32. 3171. 33. 498J. 34. 1828J. 
 35. 234. 36. 7546. 
 
 Article 165. 1. ff. 2. |. 3. T \. 4.- 1. 5. i. 6. \. 7. \. 
 
 8. g. 9. ^ 2 T . 10. ^\. 11. if. 12. 15. 13^ 322. 14. 17J. 15. 2^. 
 
 16. 1}. 17. 9f. 18. 396. 19. 32. 20. 36. 21. 9f. 22. 205. 
 23. 309. 24. 72. 25. 323. 26. 750. 27. 1818. 28. f . 21J. 
 29. }J - if 30. $35fJ. 31. $115^. 32. .130Jf. 33. Elder, 74|^ ; 
 younger, 49|. 34. 15Jf days. 
 
 Article 169. 1. T 3 r . 2. \. 3. &. 4. T f 7 . 5. if. 6. T \. 
 
 7. if. 8. H. 9. T V. 10. i 11. f. 12. J. 13. ||. 14. A- 
 
 15. i. 17. 6|J, 18. 76|f. 19. 359J. 20. 77J. 21. 3^. 22. 4-i|. 
 23. 66^. 24. 1637|f. 25. ft-^V 26. 
 
 Article 173. 4. li. 5. 1 T V 6. if 7. f. 8. 1J. 9. 3J. 
 
 10. llf. 11. aVV 12. J. 13. AV 14. 21. 15. llf 16. 12. 
 17. T V 18. . 19. i. 20. 4J. 21. 3. 22. 2 T T . 23. fH- 
 25. 9^. 26. T V 27. 2J. 28. T V 30. 791. 31. 88}}. 32. 76if 
 33. 28^ 4 T . 34. 12,451|. 35. 8001 T \. 36. 8279/ 7 . 37. 3822Jf 
 38. 574 T 2 T rods. 39. 10 days. 40. $4f. 41. $31. 42. 44 barrels. 
 
 Article 176. 4. 27. 5. 23J. 6. 3}-|. 7. 2 VV 8. It}. 9. If. 10. 5. 
 
 11. 32. 12. Jft. 13. 4^ 4 T . 14. $1201. I 5 - 14 rods - 16. 14 tons. 
 Article 177. 6. 9. 7. 10. 8. 16. 9. 9. 10. 12. 11. 25. 
 
 12. 20. 13. 6. 14. 15. 15. 21. 16. 30. 17. 40. 18, i. 
 19. f. 20. f. 21. f. 22. f. 23. f. 24. 49. 25. f 26. 3<>. 
 27. i}. 28. 28. 29. 209. 30. i. 31. 20. 32. 42 marbles. 
 33. 56 marbles. 34. f . 35. 70 acres. 36. 1 left ; } spent. 37. 280 sheep. 
 
 Article 178. 14. $81 1. 
 
 Article 180. 12. 24 hats. 13. 20 pounds. 14. 24 doz. 15. 24 pounds. 
 16. 30yd. 17. 18 knives. 18. $3. 19. 112. 
 
 Article 182. 1. $ 1851. 2. $ 34J. 3. 32 J. 4. Difference i greater. 
 5. $90f. 6. $200. 7. 380^ barrels. 8. Diminish ^ ; ^ 9. 2JJ. 10. 10 T 6 7 . 
 11. $3i. 12. $.65f. 13. 13fyd. 14. f ; f. 15. f | ; ff. 16. 100 sheep ; 
 50 sheep. 17. T V 18. 125 sheep. 19. $.08}. 20. $2. 21. 51} Ib. 22. $6}. 
 23. i. 24. 120'days. 25. 50 pupils. 26. $1.50. 27. $f 28. 8^. 
 
 Article 188. 1. .25. 2. .85. 3. .326. 4. .6. 5. .16. 6. .384, 7. .49. 
 
250 PRIMARY ARITHMETIC 
 
 8. .5. 9. .06. 10. .015. 11. .025. 12. .11. 13. .09. 14. .500. 15. .50. 
 16. .9. 17. .1. 18. 5.40. 19. 8.2. 20. 64.683. 
 
 Article 189. -21. jfo. 22. ^. 23. ^V 24. 12 T V 25. 6ffo. 
 26. T VoV 27. T Jfo. 28. T W 29. ^. 30. A. 31. 5ft- 32. 5 T ^. 
 33. 5^. 34. 5 T %o_ 35. 5 r ^. 
 
 Article 190. 36. ^; .4. 37. ^ ; .75. 38. ^ ; -125. 
 
 39. 16rf&; 16.48. 40. 12& ; 12.4. 41. & ; .6. 42. ^ .06. 
 
 43. To 6 <ro; - 006 - 46. .282. 47. .56. 48. .7. 49. .600. 
 
 Article 194. 1. Three hundred sixty-eight thousandths. 
 
 2. Eight hundred ninety-four thousandths. 
 
 3. Five thousand three hundred twenty-eight ten-thousandths. 
 
 4. Two thousand fifty-three ten-thousandths. 
 
 5. Twenty-five and six hundred twenty-three thousandths. 
 
 6. Seven and sixty-three ten-thousandths. 
 
 7. Twenty-eight and three thousand five ten- thousandths. 
 
 8. Twenty-eight thousand nine hundred sixty-two hundred-thousandths. 
 
 9. Fifteen and sixty thousand five hundred thirty-four hundred-thou- 
 sandths. 10. Thirty-seven and five hundred thirty-seven hundred-thou- 
 sandths. 11. Twenty-five and two-hundred three thousand six hundred two 
 millionths. 12. Thirty-eight and six millionths. 13. Four million nine hun- 
 dred eighty-three thousand six hundred ninety -five ten-millionths. 14. Four 
 and ninety-eight thousand three hundred sixty-nine hundred-thousandths. 
 
 15. Forty-nine and eight thousand three hundred sixty-nine ten-thousandths. 
 
 16. Four hundred ninety-eight and three hundred sixty-nine thousandths. 
 
 17. Four hundred millionths. 18. Four ten-thousandths. 
 
 Article 196. 1. .8. 2. .29. 3. 16.284. 4. .4584. 5. .25. 
 6. .025. 7. .0025. 8. .00025. 9. .000025. 10. 1650.464. 
 
 11. 1001.00036. 12. 16.006. 13. .000784. 14. .00012. 15. .0075. 
 
 Article 200. 1. .5000; .3650; .4689. 2. .18963; .50000; 7.84000; 
 
 .16005. 3. .28000; 3.50000; .00005; .25600. 4. .50000; .05000; 
 
 .00500; .00050; .00005. 5. .046300; .030000; .100000; .100010. 
 
 6. .380; 1.160; .400; 78.592. 
 
 Article 201. -2. J. 3. &. 4. }. 5. if. 6. Jf- ? 
 8. i. 9. f 10. f. 11. ^ 12. ? V 13 
 
 15. 16}. 16. dr I?- i&V 18- & 19- *Vfr- 20. }. 
 
 Article 202. 21. |. 22. f. 23. T V 24. T 2 ^. 25. &. 
 
 26. i. 27. |. 28. f . 29. ?$. 30. 16J ; 2J ; 34}. 
 
 Article 209. 1. .8. 2. .75. 3. .44f. 4. .875. 5. .15. 6. .4. 
 7. .6. 8. ,55J. 9. .464. 10. 1J. 11. .30. 12. .5625. 13. .125. 
 14. 2.24. 15. 3.0625. 16. .375. 17. .0375. 18. .32. 19. .75. 
 20. 2.09375. 
 
 Article 210. 2. 25.4162. 3. 6.788. 4. 20.2603. 5. 194.425. 
 6. 161.1095. 7. 25401.3123. 8. 64.4266. 9. 120.9384. 10. 38062.881. 
 
 11. 25.2477. 12. 2018.7147. 
 
 Article 211. 1. 19.8. 2. 1.535. 3. 2.85. 4. 2.455. 5. 6.85. 
 
 6. .996. 7. 10.9. 8. 2.206. 9. 254.844. 10. 14.185. 11. 3.727. 
 
 12. 1.11. 13. 499.95. 14. 10.3844. 15. 13.775. 16. .099. 17. Same. 
 18. 999.999. 19. 499.95. 
 
 Article 212. 1. .027. 2. .2001. 3. .15. 4. .28. 5. .008. 6. 28.8075. 
 
 7. 286.3. 8. 17.29. 9. 1. 10. .05028. 11. 26.586. 12. 7.1. 13. 41. 
 14. 1111. 
 
 Article 215. 10. 5.1. 11. 4.06 + . 12. 331. 13. 10.1. 14. 111.1. 
 
ANSWERS 251 
 
 15. 11110. 16. 17.5. 17. 70. 18. 626.66}. 19. 6266. 66 J. 20. 62.664. 
 21. 62.66J. 22. 375. 23. 155.5. 24. 10. 25. .1. 26. .01. 27. 549.77. 
 28. 11.94. 
 
 Article 217. 7. .875; .71f ; .8; 16,75; 25.875. 8. A; M; t; 15 i- 
 9. $60. 10. 20bbl. 13. 25 pk. 14. $90.657. 
 
 Article 223. 1. .$88.90. 2. $410.18^. 3. $6.39. 4. $143. 
 
 5. 102.15. 7. $417.175. 
 
 Article 232. 1. 10,368; 13,825. 2. 5 ; 6J. 3. 216; 864. 4. } ; 4. 
 5. J; J. 6. $250. 
 
 Article 237. Written: 1. 400 oz. 2. 15,000 Ib. 3. 258 bullets. 4. 80^. 
 
 5. 85ioz. 6. 5 oz. 7. 30 bags. 8. 44 oz. 9. $3.72. 10. 292 oz. ,11. ^. 
 Article 241. Written:!. 5J hours. 2. 744 hours. 3. Winter. 4. Yes. 
 Article 242. 12. 5|. 13. $1-1. 14. $215.20. 15. $9.00. 
 Article 245. 4. 645 in. 5. 773ft. 6. 204,978 in. 7. 81,701 sq. yd. 
 
 8. 25,679,196 sq. in. 9. 790,596 cu. in. 10. 127 pt. 11. 507 pt. 
 
 12. 528 qt. 13. 146,794 gr: 14. 73,774 oz. 15. $24. 16. 225,932 in. 
 17. 35,640ft. 18. 19, 138,464 sq. in. 19. 762,051 cu. in. 20. 69,056 oz. 
 21. 21,972 gr. 22. 1947 gi. 23. 24,000 sheets. 24. 39,180 min. 
 
 Article 247. 4. 3 mi. 4 fur. 20 rd. 5 yd. 2 ft. 8 in. 5. 6 mi. 20 rd. 
 
 6. 17 A. 67 sq. rd. 3 sq. yd. 7 sq. ft. 72 sq. in. 7. 16 cu. yd. 9 cu. ft. 3 cu. in. 
 8. 2 tons 316 Ib. 9. 3 Ib. 7 oz. 18 pwt. 4 gr. 10. 60 gal. 3 qt. 3 gi. 
 11. 5 bales. 12. 3 wk. 6 da. 5 hr. 13. 560 bu. 1 qt. 14. 5 Ib. 7 oz. 16 pwt. 
 
 15. 7 Ib. 3 oz. 4 dr. 1 sc. 12 gr. 16. 17 tons 1682 Ib. 17. 43 G. gro. 10 gro. 
 
 7 doz. 4. 18. 21 bu. 2 pk. 4 qt. 19. 3 sq. rd. 18 sq. yd. 6 sq. ft. 27 sq. in. 
 20. 2 mi. 192 rd. 2 yd. 21. 60 rd. 4 yd. 
 
 Article 248. 1. 63. 2. 244 gi. 8. 34 \ gal. 4. $2.60. 5. 4000 oz. 
 
 6. 35,000 Ib. 7. 1032 bullets. 8. 30,320 dr. 9. 254 pt. 10. 423 qt. 
 11. $41.12. 12. 127 bu. 4qt. 13. $19.50. 14. $1.26. 15. 4 gal. 
 
 16. 72 qt. 17. $4.20. 18. 255 qt. 19. 24 qt. 20. 9 bu. 
 
 Article 249. 4. 21 bu. 3 pk. 7 qt. 5. 15 bbl. 25 gal. 3 qt. 6. 5 yd. 
 
 2 ft. 9 in. 7. 13 bbl. 15 gal. 2 qt. 1 pt. 8. 10 bu. 1 pk. 2 qt. 9. 14 Ib. 
 
 3 oz. 15 dr. 10. 3 bbl. 28 gal. 1 pt. 
 
 Article 250. 2. 5 A. 104 sq. rd. 2 sq. ft. 3. 54 da. 21 hr. 29 min. 48 sec. 
 
 4. 3 hr. 42 min. 40 sec. 5. 14 T. 19 cwt. 49 Ib. 14 oz. 6. 11 Ib. 4 oz. 1 dr. 
 
 7. 4yd. 1ft. 2 in. 8. 10 da. 22 hr. 18 min. 9. 9 gal. 1 pt. 3 gi. 10. 2 dollars 
 1 dime 4 cents 2 mills. 11. 2 Ib. 2 oz. 12 dr. 12. 2 gal. 3 qt. 1 pt. 
 
 13. 11 ft. 10 in. 
 
 Article 251. 3. 155 yr. 6 mo. 23 da. 4. 3 yr. 11 mo. 25 da. 
 
 5. 67 yr. 9 mo. 22 da. 7. 138 d. 8. 60 da. 9. 213 da. 10. 23 da. 
 
 11. 127 da. 12. 37 da. 13. 102 da. 14. 120 da. 15. 332 da. 
 Article 252. 2. 64 gal. 1 qt. 2 gi. 3. 101 bu. 1 pk. 4 qt. 
 
 4. 6 T. 13 cwt. 25 Ib. 5. 33 oz. 11 pwt. 6 gr. 6. 178 gal. 1 pt. 7. 10 Ib. 
 
 8. 352 bu. 3 pk;. 4 qt. 9. 58 hr. 40 min. 48 sec. 
 
 Article 253. 2. 10 bu. 3 pk. 7 qt. 3. 2 bu. 2 pk. 2 qt. 4. 3 qt. 1 pt. 3} gi. 
 
 5. 1 bu. 1 pk. 1 qt. \\ pt. 6. 15 packages. 7. 12 T. 16 cwt. 90 Ib. 15 oz. 
 
 8 35 packages. 9. 28 gal. 1 qt. 1 pt. 10. 21 gal. \\ pt. 11. 31 gal. 2 qt. 
 
 12. 1 T. 640 Ib. 13. 106 oz. 12 pwt. 14. 2 wk. 4 da. 13 hr. 122 min. 
 Article 256. 1. 22 sq. ft. ; 3168 sq. in. 2. 606 sq. ft. 3. $66.00. 
 
 4. 15 ft. - 5. 105 sq. ft. 6. 80 sq. ft. ; 11,520. 7. 32 rd. 8. 00 ft. 
 
 9. 100 A. 
 
 Article 257. 2. 64|sq. rd. 3. $ 16.16f . 4. $40.83J. 5. 311Jsq. yd. 
 8. $37.80. 
 
252 
 
 PRIMARY ARITHMETIC 
 
 Article 258. 3. 80 yd. ; 84 yd. 4. S46.66f. 5. $48.22}}. 6. 40yd. 
 8. $6475.00. 9. 825 sq. yd. 10. $58.33}. 11. 2000. 12. 100 rd. 
 
 Article 259. 1. 96 sq. yd. ; 4 sq. yd. ; 24 rolls ; 81| sq. yd. ; 20A rolls ; 
 $6.804; $11.00. 2. $ 35.79$. 3. 28& rolls. 
 
 Article 260. 1. 16 bd. ft. 2. $3.60. 3. 16} bd. ft. 4. 288 bd. ft. 
 
 Article 262. 1. 288 cu. in. 2. 120 cu. ft. 3. 384 cu. in. 4. 8 ft. thick. 
 5. 240 cu. in. 6. 1728 blocks. 7. $301.50. 8. 19,440. 9. 210 cu. in. 
 10. 30 pupils. 11. 288 cu. yd. 12. 256 books. 13. 13} cu. ft. 
 
 14. 4320 bricks. 15. 13,824 cu. in. 16. 10,368 cubes. 17. 404| loads. 
 18. 231} loads. 19. 24,300 bricks. 20. 15 ft. wide. 21. 10 ft. high. 
 
 Article 264. 1. 2} cd. 2. 10 cd. 3. 79J-J cd. 
 
 5. 32 ft. 6. 3| cd. 7. 40J cd. 
 
 Article 265. 1. 7} gal. 2. 1125 gal. 3. 35^ bbl. 
 5. 17^ bbl. 6. 1125 gal. 7. 200 cu. ft. 
 
 Article 266. 9. 96 bu. 10. 120 bu. 11. 187} cu. ft. 
 
 Article 267. 4. 4. 5. 10. 6. 18. 7. 6 sheep. 8. 150 men. 9. 6 bu. 
 10. 64. 11. 150. 12. 2100. 13. 400 sheep. 14. 400 pupils. 15. 500 horses. 
 16. 25%. 17. 5%. 18. 10%. 19. 25%. 20. 25%. 21. 50%. 22. 2 apples. 
 23. $150. 24. 25%. 25. 120 bu. 26. 800 men. 27. 50%. 
 
 Article 275. 1.40^. 2. 20 sheep. 3. 100 A. 4. $20. 
 7. $400. 8. $4. 9. 100 sheep. 10. $1600. 11. $4000. 
 13. $50. 14. $1500. 15. 10%. 16. 20%. 18. 25%; 75%. 
 20. 25%. 21. 25%; 75%. 
 
 $125. 8. $6; $9; $15; $19}. 
 
 11. $97.386. 12. $100.20. 13. $164.448. 
 16. $42.757. 17. $79.31. 18. $347.075. 
 21. $373.9! 
 3. $2.716. 
 
 4. $2250. 
 4. 41}bbl. 
 
 6. $400. 
 12. $500. 
 19. 80%. 
 
 Article 277. 6. $10. 7. 
 
 Article 278. 10. $46.146. 
 14. $67.066. 15. $123.976. 
 19. $387.915. 20. $363.698. 
 
 Article 279. 2. $1.198. 
 6. $9.07. 7. $13.498. 8. $93.205. 9. 
 
 Article 280. 1. Five thousand seven. 
 
 2. 
 
 17. 879.31. 
 22. $541.35. 
 4. $14.001. 
 .775. 
 14017. 3. 211. 
 
 5. $5.388. 
 4. CCXLX. 
 
 10. 16. 
 
 3. T V 4. 120. 6. 11}. 7. 7|. 8. f. 
 
 5. 7. 6. }Jf 7. T A- 8. J- 9. $300. 
 
 3. 999.999. 4. 7.10. 
 
 5. .000001. 
 
 5. 11899. 8. 673ff, 
 Article 281. 2. 
 
 9. 10}}; 21 A- ; 9|i. "10. 701." 
 Article 282. 4. 
 
 10. 70 sheep. 
 
 Article 283. 1. 2 tenths ; 2 tens. 2. Same. 
 
 5. 1. 6. 111.1; 10; .1. 7. .6; .25; .331; .625. 8. ^1 
 9. 34.0003406. 10. 15.0005. 
 
 Article 284. 1. 828.72. 3. f ; f . 4. 23.0310. 
 
 6. 8.25. 7. $60.525. 8. $36920. 
 
 Article 285. 1. $13.333. 2. 27yd. 3. 600 ; 60 ; 6 units. 
 T L greater. 5. }. 6. $5.61. 7. 200 bu. 8. 5438.857. 
 marbles. 10. 800. 
 
 Article 286. 1. 12 bu. 2. 3 mi. 23 rd. 1 yd. 3. 405 rd. 5. 2 qt. 
 6. 18 bu. 7. 5 qt. 8. 3 tons. 9. $3.60. 10. $26.10. 
 
 Article 287. 1. 48 yd. 2 ft. 7 in. 2. $1.60. 3. f< 4. 18ft. 
 5. 40yd. 6. 33264 sq. in. 7. 860 A. 8. 73 hhd. 18 gal. 2 qt. 9. 5280ft. 
 
 Article 288. 3. 16yd. 4. $27. 5. $}. 6. $1.05. 7. $16.20. 
 
 8. 198 sq.ft. 9. 1122 T % using 7J ; 1119 I 3 T using 231. 10. 96.427+ bu. 
 Article 289. 1. 9ft. 2. 8 farms. 3. 500 Ib. 4. T V 5. 7 cu. yd. 
 
 24 cu. ft. 1362 cu. in. 6. 10 cd. 7. 20^ cd. 8. 173.569+ bu. 
 
 9. $38. 10. 160 rd. 
 
 4. 
 9. 1 
 
 
 
. 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 
 C 17 1917 
 
 
 OCT 1? 
 
 30m-l,'15 
 
VB 17247 
 
 'OA/os 
 K/37 
 
 i