oJi-nson 
 
 SCHOOL ARITHMETIC 
 
 "Pri 
 
 rimar 
 
 IRLF 
 
 E7fi 
 
 Mi 
 
 \J&- 
 
 <M 
 
 Joh 
 Richmond -^Virginia 
 
IN MEMORIAM 
 FLOR1AN CAJORI 
 
SCHOOL ARITHMETIC 
 
 PRIMARY BOOK 
 
 BY 
 
 JOHN M. COLAW, A. M. 
 
 ASSOCIATE EDITOR OF THE AMERICAN MATHEMATICAL MONTHLY, 
 MONTEREY, VA. 
 
 J. K. ELLWOOD, A. M. 
 
 PRINCIPAL OF THE COLFAX PUBLIC SCHOOL, PITTSBURG, PA., AUTHOR OF 
 TABLE BOOK AND TEST PROBLEMS IN ELEMENTARY MATHEMATICS. 
 
 RICHMOND, VA. 
 B. F. JOHNSON PUBLISHING CO. 
 
 1900 
 
JOHNSON SERIES 
 
 SCHOOL ARITHMETICS 
 
 ..BY.. 
 COLAW AND ELLWOOD 
 
 Primary 
 
 Wnrfc 
 
 2i Pages Price, 35 Cents 
 ^ 
 
 Advanced Book 
 
 With an Introduction to Algebra 
 442 Pages Price, 60 Cents 
 
 < 
 HANDBOOK FOR TEACHERS 
 
 Containing Suggestions as to the best methods of 
 teachiTfc Arithmetic^ an* scl.urti6ns of diffi- 
 " ' 
 
 fook 
 t. (Jl l Prcjwation) ^ 
 
 CAJORI 
 
 Copyright, 1900. by 
 J. M. COLAW and J. K. ELLWOOD. 
 
PREFACE. 
 
 TTTO DEVELOP in the pupil's mind the idea of number and 
 its uses, to give* him facility in numerical operations, and 
 -k to lead him to grasp firmly the principles involved requires 
 the serious effort of the most skilful teacher. The most any 
 author can do to aid him is to present, in more or less detail, 
 an outline of a practical scheme of instruction based upon the 
 latest and best thought in number teaching; and even this is 
 a task that none but the superficial would undertake without 
 " fear and trembling." Neither theory nor practice alone is 
 a sufficient endowment for the work. Every theory, every 
 method, every device must be weighed in the class-room balance. 
 That which is to be taught is the child not arithmetic. 
 
 Holding these views, the writers of this book have spared 
 no effort in its preparation. With a wholesome respect for the 
 injunction, " Prove all things; hold fast that which is good," 
 they have endeavored to steer carefully between the Scylla of 
 modern fad and the Charybdis of mechanical drudgery and 
 stupefying monotony. Their aim has been to furnish for the 
 teacher a sound and practical work presenting the matter in 
 an approved order and suggesting rational methods of obtaining 
 the most desirable results. As to how well they have succeeded 
 the teacher must decide. 
 
 ARRANGEMENT. Before entering school the child learns a 
 little of a great many things, not a great deal about one thing. 
 There is no topical arrangement in nature. "And Nature, the 
 dear old nurse," permits the order of the child's mental develop- 
 ment to determine the arrangement of the material, which is 
 always a progressive one. The child learns a little about many 
 things to-day, a little more to-morrow, adds an increment to 
 his knowledge and widens his range of subjects day by day. 
 This arrangement keeps interest alive, without which there is 
 no substantial progress. This book aims to follow the natural 
 
 [v] 
 
 911274 
 
VI PREFACE. 
 
 order as closely as may be, considering the conditions under 
 which teachers are required to work. 
 
 " FBOM THE CONCRETE TO THE ABSTRACT." The child's mind 
 must be approached through those ever open doors, the senses. 
 Primary number teaching must be begun by the pupil's observ- 
 ing and handling objects, yet the mere presence of concrete 
 things does not guarantee the presence of definite numerical 
 ideas in the mind of the pupil. They must be so presented as 
 to stimulate and aid the mental movement of discriminating 
 and relating which leads to definite ideas of number. The 
 mind must (r/) recognize the like objects as distinct individuals, 
 and (/>) group (put together) the objects into a whole. The 
 child's own activity must conceive a whole of parts, and relate 
 the parts in a definite whole. It is not enough that he knows 
 our country as 45 states; he must know the 45 states as one 
 country. He should recognize five, for example, not only as 
 five ones, but also as one flue, considering the component ones 
 not chiefly for their own sake, but as giving definite value to 
 the whole, the group. By repeated acts of such measurement 
 or valuation the mind advances naturally and inevitably from 
 things to relations, from facts to principles, from the concrete 
 to the abstract. Believing that the concept of ratio an abstract 
 idea must be evolved in the young mind by its own activity, 
 and that therefore it should not be thrown at the child in the 
 earlier stages of his progress, the authors have not explicitly 
 stated the ratio idea until it has had time to grow into a 
 recognizable and useful product of the pupil's mind. 
 
 MATERIAL. The objects called for in this book, such as cubes, 
 splints, foot rules, quart measures, etc., can be provided by 
 the teacher with little trouble, and their use should precede 
 that of pictures and words. How long their use should be 
 continued with any given class must be determined by the 
 teacher. They should certainly not be laid aside until the child 
 can bring their images into consciousness without the presen- 
 tation of the actual objects to his senses; but when these images 
 are within easy reach, their use should supersede that of objects. 
 The number pictures given in this book are an important aid 
 to the child's mental movement of abstracting and relating, 
 and must be used for economy of energy. Five dots analytically 
 arranged ** are more easily grasped than five dots placed 
 
PREFACE. vil 
 
 promiscuously, or even in a row. Moreover, they are perceived 
 as one whole, rather than as separate, unrelated parts, and 
 they should symbolize any five units whatever five $2 or five 
 10-ft. as well as five $1 or five 1-ft. In the perceptive form 
 
 , twelve is seen as three fours and as four threes as four 
 
 9 
 
 three times and as three four times and the child's idea of the 
 number is more definite than when the whole was measured 
 by but one unit, the individual. Besides, this use of pictures 
 suggests to the pupil a method by which he can discover for 
 himself the measuring units of quantity or determine the definite 
 value of a whole. In notation, fractions, measurement of 
 surfaces, etc., the illustrations will be found highly beneficial; 
 their purpose is to aid, not to ornament. 
 
 COUNTING MEASURING. Dr. Harris says, " The first lessons 
 in arithmetic should be based on the practice of measuring in 
 its varied applications." In its earlier stages measurement is 
 a vague estimate, a crude guess. Later an undefined unit of 
 measure is used to make a whole more definite, as when a 
 class is measured by the unit boy an unmeasured unit. But 
 it is only when the unit itself is accurately defined that precise 
 numerical value is reached. The immediate purpose of measur- 
 ing is to make some whole more definite to find hoir much 
 there is of it. This can be done by learning how many units 
 are in it, and the " how many " can be found only by counting; 
 hence measuring involves rational counting the finding of the 
 SUM of the units that compose a whole. It seems clear, there- 
 fore, that the child learning to count should be led to number 
 the parts that make up some whole, as the desks in a row to 
 count with a definite cud in view; that the starting point should 
 be a group of things a whole to measure, parts to count and 
 relate. As soon as possible there should also be exact measure- 
 ments. The foot may be taken as the whole and measured by 
 4-inch units, 3-inch units, etc. Not only the idea of number 
 as the repetition of a unit of measure to equal a magnitude, 
 but also the law of commutation will be slowly, perhaps, but 
 surely developed through the use of the facts supplied by sense- 
 perception in the rational use of objects and number pictures. 
 
 FIGURE PROCESSES OXI.Y THE MEANS TO AN END. The child 
 must learn figure processes, not for their own sake, but as an aid 
 in discerning relation. Figures are not at all necessary to 
 
Vlll PREFACE. 
 
 numerical perception, but when this is to be supplanted by 
 numerical facility they should be employed as a cpnvenient 
 tool. The real subjects of thought are magnitudes (of value, of 
 space, of weight, etc.) and their relations; figures are mere 
 symbols of these. The essential thing is the discernment of 
 relation by comparing magnitudes; figure processes may or 
 may not be an aid in securing this end they can never be 
 anything more. It is evident, therefore, that the mere manipu- 
 lation of figures the mechanical work is of small value in 
 comparison with the thought processes the mental work; 
 yet as the means to an end it is of great importance, and to 
 secure absolute accuracy therein should be the constant aim 
 of every teacher. 
 
 SUGGESTIVE QUESTIONS AND DIRECTIONS. The exercises of 
 this book are more abundant and varied than is usual in books 
 of this kind, and much additional work will be called forth 
 by the suggestive nature of many of the questions and directions. 
 There is an especial need of an abundance of constructive 
 exercises. The pupil must be active, must do as well as see. 
 Knoiciny and doing are correlative. Things are grasped most 
 readily when there is a necessity, real or apparent, for knowing 
 them. Boys who sell papers or fruit on the streets, being under 
 the necessity of computing and making change, enter school 
 with a surprising stock of number facts. Excellent number 
 woik may be had in connection with the occupations of the 
 school-room passing pencils, making boxes, modeling, playing 
 number games, measuring things used in nature study and 
 manual training, etc. The questions and directions given 
 indicate the kind of>work that should be done, but the quantity 
 of it needed must be determined by the teacher, and by him 
 supplied when necessary. Figures and signs are not used until 
 the child has acquired some familiarity with the names of 
 numbers to twelve and with a few of the simpler processes and 
 facts. This should at least suggest that the figure symbol 
 should not be given until the child can understand that it is a 
 mere mechanical tool by which he can obtain rapid and at the 
 same time equally true results. 
 
 It is neither necessary nor desirable to keep this book out 
 of the hands of young pupils until they are able to read it 
 with ease. They should at least get the benefit of the number 
 pictures and the picture exercises. Anything too difficult for the 
 
PREFACE. IX 
 
 children should be read by the teacher, and answers only required 
 of the pupils. Formal analysis should be deferred; when 
 insisted upon at too early a stage, it interferes with progress 
 and deadens the pupil's interest. 
 
 It is believed that in plan, matter, and method this book is in 
 substantial accord with the views of progressive teachers in 
 the best schools, and that it will prove a suitable foundation 
 for and introduction to the more formal and rigorous treatment 
 presented in the Advanced book of the series. Its contents are 
 such, however, that pupils who can, complete only this book 
 will find themselves fitted to cope with the ordinary problems 
 of every-day life. 
 
 THE AUTHORS. 
 
 July 2, WOO. 
 
CONTENTS. 
 
 FIRST STEPS: 
 
 Indefinite Comparison, Form, Counting, Measuring 
 
 Use of Ruler, Concrete Exercises .... 1-43 
 
 PRIMARY NUMBER WORK : 
 
 Numbers to 10 Combinations (Emphasis on Adding 
 and Subtracting), Pint, Quart, Gallon, Half, Fourth, 
 
 Third, Peck, Bushel 44-74 
 
 Tens . . 74-83 
 
 Review and Drill 84-91 
 
 Writing and Reading Numbers from 1 to 100 . . 92-95 
 
 The Signs X and -h- 96-99 
 
 Numbers to 20 Tens and Ones, Combinations, Month, 
 
 Year, Roman Notation, Fifth, Ounce, Pound, Sixth, 100-134 
 
 Review and Drill 135-136 
 
 Twenty Two Tens, Tenth 137-142 
 
 Numbers to 100 Development of Tens and Ones . 143-147 
 
 Addition and Subtraction . . . . . . 148-154 
 
 Numbers to 30 Table of 3's, 'Square Foot, Easy Areas, 155-160 
 
 Numbers to 40 Table of 4's .'.... 161-168 
 
 Numbers to 50 Table of 5's, Square Yard . . . 169-173 
 
 Addition and Subtraction 174-188 
 
 Numbers to 60 Table of 6's, Hour, Minute, Second . 189-195 
 
 Numbers to 70 Table of 7' s 196-202 
 
 Numbers to 80 Table of 8's, Perimeter . . . 203-208 
 
 Numbers to 100-Table of 9's, Cubic Inch . . . 209-216 
 
 Review and Drill Work 217-227 
 
 Hundreds Cent, Dollar 228-232 
 
 Hundreds and Tens -. . 233-235 
 
 (xi) 
 
Xll 
 
 CONTENTS. 
 
 ARTICLE. 
 
 Hundreds, Tens, and Ones . . . . . . 236-238 
 
 Addition and Subtraction . . . . . 239-242 
 
 Multiplication and Division 243-250 
 
 U. S. Money Making Change 251-260 
 
 Numbers to Millions Unit of Measure, Notation and 
 
 Numeration 261-271 
 
 Addition and Subtraction 272-276 
 
 Multiplication and Division 277-295 
 
 Review Work . . 296-297 
 
 U. S. Money and Decimals 298-306 
 
 COMMON FRACTIONS : 
 
 Halves, Fourths, Eighths, Thirds, Sixths, Twelfths- 
 Fifths, Tenths, Hundredths Relations, Common 
 Denominator, Addition and Subtraction, Mtiltiplica- 
 
 and Division 307-333 
 
 COMPOUND NUMBERS 334-355 
 
 DECIMAL FRACTIONS 356-370 
 
 PERCENTAGE . 371-374 
 
 INTEREST 375-376 
 
 GENERAL REVIEW . 3/7-378 
 
SCHOOL ARITHMETIC. 
 
 FIRST STEPS. 
 
 Comparison. 
 -A 
 
 B 
 
 O- C 
 
 1. The line OB is longer than which line? 
 
 The line OB is shorter than which line? 
 
 The line OA is shorter than which lines? 
 
 The line OC is longer than which lines? 
 
 Which line is longer than the line OB? 
 
 Which lines are shorter than the line OC? 
 
 "Which line is shorter than the line OB? 
 
 Is any one of these lines longer than the line OC? 
 
 Is any one shorter than the line OA? 
 
 A 
 
 B 
 C 
 
 \l 
 
 
 
 
 
 
 
 
 P 
 
 2. Cut splints the same length as A, B ? and C. 
 
 Show me the longest. 
 Show me the next longest. 
 
SCHOOL ARITHMETIC. 
 
 Show me the shortest. 
 
 Show me the next shortest. 
 
 How many of these splints are longer than B? 
 
 How many of these splints are longer than A? 
 
 How many of these splints are shorter than B? 
 
 How many of these splints are shorter than C? 
 
 A B 
 
 3. Blocks of this shape are called cubes. 
 Which is the largest cube? 
 Which is the next largest cube? 
 Which is the smallest cube? 
 Which is the next smallest cube? 
 HOAV many cubes are larger than C? 
 How many cubes are smaller than A? 
 What can you tell me about B? 
 
 4 Which is longer, the length of your desk or its width ? 
 
 Which is wider, the sidewalk or the street? 
 
 Which is longer, your arithmetic or your slate? 
 
 Which is thicker, your book or your slate? 
 
 Which is larger, a boy or a man? 
 
 Which is higher, your house or the school-house? 
 
COMPARISON. 
 
 5. Here are two groups of cubes. fj| 
 "Which is the larger group? f|] 
 
 How many more cubes in the larger group than in the 
 smaller one? 
 
 AVliich of these rings has the most dots in it? 
 
 The ring on the left has how many more dots than the 
 one on the right? 
 
 Are there more girls than boys in the class? How many 
 more? 
 
 NOTE. Children should be given sufficient exercise in making 
 comparison to familiarize them with the use of the terms longer, 
 shorter, larger, smaller, JiiyJier, irider, etc. They may compare 
 solids, surfaces, lines, sounds, or any objects within reach or sight. 
 
 6. Here are pictures of a square, a circle, a triangle, 
 and a sphere. 
 
 Show me the square. Show me the circle. 
 
 Xow show me the triangle. Show me the sphere. 
 
 Take four sticks of the same length and make a square. 
 
 Cut a square out of paper. Xame something that 
 resembles a square in shape. 
 
4: SCHOOL ARITHMETIC. 
 
 From pasteboard cut out six equal squares. Make a 
 box of them. What have you? Name some object shaped, 
 like a cube. 
 
 Lay a penny on paper and draw a line around it. 
 
 Cut out the circle. Name something that is a circle 
 in shape. 
 
 Draw a square on the blackboard. Now draw a circle. 
 
 Did you draw straight lines in making the square? 
 What kind of line around the circle? 
 
 Here is a marble. What is it shaped like ? Is your ball 
 a sphere? What part of the body is almost a sphere? 
 
 NOTE. Have pupils observe and handle solids until they know 
 the familiar cube, sphere, square, triangle, circle. Have them 
 model simple forms, and cut squares, circles, etc., from paper. 
 
 Counting to Twelve. 
 
 7. How many boys are in the class? How many girls? 
 
 How many seats are in this row? 
 
 How many sides has this square? 
 
 Count the faces of this cube. 
 
 How many pairs of shoes in the class? 
 
 How many groups of three blocks? 
 
 m m 
 mmm mm mm 
 
 Here are twelve spools. Arrange them in pairs, and 
 count the number of pairs. 
 
 Arrange them in groups of three, and count the groups. 
 
MEASURING USE OF RULER. 
 
 Here are some dots. 
 How many twos? 
 How many threes? 
 How many fours? 
 
 Measuring Use of Ruler. 
 
 8. This line - - is an inch long. 
 
 Draw a line as long as the one above. 
 Cut four sticks each as long as the line. How long is 
 each stick? 
 
 How many sticks are as long as the line below? 
 
 Then how long is this line? 
 
 Find how many inches wide this book is. 
 
 How long is your pencil? 
 
 Draw a line four inches long. 
 
 An inch lower, draw another line four inches long. 
 
 Rule a page of this paper with lines an inch apart. 
 
 9. How long is this square? How wide 
 is it? 
 
 Are all four sides of the same length? 
 
 A square that is an inch on a side is 
 called a square inch. 
 
 Draw a square inch on paper. Cut it 
 out. 
 
6 
 
 SCHOOL ARITHMETIC. 
 
 Cut out a piece of paper two inches long and one inch 
 wide. 
 
 How many square inches can YOU make of it? 
 
 Draw a square two inches on a side. 
 
 Into how many square inches can you cut it? 
 
 8 9 
 
 II 12 
 
 10. This is a picture of a ruler reduced in size. 
 
 Here is a real foot-rule. It is a foot long. 
 
 Use the rule to find how long this table is. 
 
 How many feet wide is the table? 
 
 Measure this line on the blackboard. How long is it? 
 
 What is the length of this blackboard? 
 
 Cut a strip of paper an inch long. 
 
 Find how many strips are as long as the foot-rule. 
 
 There are twelve inches in a foot. 
 
 The Numbers One and Two. 
 
 11. How many dots are on the first card? 
 Hold up one finger. Hold up one more finger. 
 How many fingers are you holding up? 
 How many fingers are one finger and one finger? 
 Show me two hands. Show me two buttons* 
 Two boys are how many more than one boy? 
 
THE NUMBER THREE. 
 
 Here is a square. [H Make pictures of two squares. 
 
 How many stars are ^ and *fa ? 
 
 How many books are one book and one book? 
 
 How many are one and one? 
 
 Here are two squares. [] Q Push away the one on 
 the right. How many are left? 
 
 Make two marks on the board. Rub out one mark. 
 How many are left? 
 
 One marble from two marbles leaves how many marbles ? 
 
 How many more cents are @ ^p than ^p ? 
 
 How many cents must be put with one cent to have 
 two cents? 
 
 /\ and /\ are how many triangles? 
 
 O and O are how many circles? 
 
 from * leaves how many dots? 
 
 and - - are 
 
 How many ones in two? 
 
 The Number Three. 
 
 12. How many dots are two dots and one dot? 
 
 ]\lake the three dots on the board. 
 
 Show me three books. Three fingers. 
 
 Say school three times. 
 
 How many sides has this triangle? /\ 
 
8 SCHOOL ARITHMETIC. 
 
 What number comes before three? Before two? 
 
 What number is between one and three? 
 
 How many rings are O O and O $ 
 
 How many stars are ^f and ^ ^ ? 
 
 How many cows are two cows and one COW T ? 
 
 I have one cube. Give me enough to make three. 
 
 Here are three dots. Cover one dot. How many 
 are not covered? 
 
 Cover two dots. How many can you see? 
 _ ||| p| from p| |H| |p| leaves how many flags \ 
 
 ^A^. ^A^. ^fci. ^ ess </fc>. are ^ 10W man y tents 
 Measure this yardstick with your foot-rule. How long 
 is it? 
 
 13. How many ones in J* ? 
 How many twos in J J ? 
 
 How many pairs of tw r os in JJ JJ ? 
 Show me two threes, using splints. 
 Show me three twos with splints. 
 Make pictures of three groups of stars. 
 Make pictures of three pairs of tents. 
 
 14. Copy and complete: 
 A /\ o/rbd /\ 
 
 omxi^ 
 
 O O O llAA; O O CtA^, -- 
 
THE NUMBER FOUR. 9 
 
 15. Two dogs and one dog are how many dogs? 
 
 One foot and two feet are - - feet. 
 
 There were three birds on the fence, but one flew away. 
 How many were left? 
 
 Mary had three pennies, but now she has only two. How 
 many did she spend? 
 
 My hat cost three dollars. I have paid one dollar; how 
 much do I owe? 
 
 Tom ate one apple and had two left. How many had 
 he at first? 
 
 Charles has three rabbits, and Paul has one less. How 
 many has Paul? 
 
 The Number Pour. 
 
 16. Make a triangle Avith these three splints. 
 Now try to make a square with them. 
 How many more splints do you need? 
 How many dots are on the card to the right? 
 How many sides has a square ? 
 How many seasons in the year? 
 Tell me the names of four boys. 
 How many letters in the word four? 
 Take two cubes in each hand. How many cubes have 
 you? 
 
10 SCHOOL ARITHMETIC. 
 
 How many triangles can you make with these twelve 
 splints ? 
 
 I have one cube. Give me enough to make four. 
 
 If I give you one, how many will I have left? 
 
 Cover two of the dots on the right-hand card. How 
 many can you see? 
 
 Show me the number of splints these words stand for: 
 three, two, four. 
 
 Copy these pictures, and write under each group the 
 word for the number (how many) in each group: 
 
 # nnnn oo AAA 
 
 17. How many tops are and 
 
 How many marbles are ^) and 
 How many cents are ^p ^p and 
 Q) from (^ Q^ (^ (^ leaves how many apples? 
 O O O O I GSS O O are now many circles? 
 There are four splints. Give me half of them. 
 How many have I? How many have you? 
 This line - ' - is one inch long. 
 In one inch there are - half inches. 
 This line - - ' - 1 - ' - is two inches 
 long. 
 
 In two inches there are - half inches. 
 
 In fj there are Q M (half -circles). 
 In two circles there are - half-circles. 
 
THE NUMBER FOTJK. 11 
 
 18. How many ones in J J ? How many twos ? 
 Show me four twos with splints. 
 
 ^lake pictures of four pairs of tents. 
 
 Here are four tops. ^ ^ ^ ^ How many boys 
 can have one top each? 
 
 Here are four pears. (^ ^3 & & How many girls 
 can have two pears each? 
 
 Cut a strip of paper three inches long. 
 
 Find how many strips are as long as your foot-rule. 
 
 Cut a strip of paper four inches long and one inch wide. 
 
 Find how many square inches will cover it. 
 
 Ask your papa how many quarters make a dollar. 
 
 Ask your mamma how many quarts in a gallon. 
 
 19. Copy and complete, then read: 
 
 LJLJ ED o/nxL CH oA/t/ . 
 
 O aW, O O O ct/be, - -. 
 i^^iZ aW, - - o/u, 
 A A A A te^fc, A a/bo 
 
 20. Three boys and one boy are how many boys? 
 One tree and three trees are how many trees? 
 Two sheep and two sheep are - - sheep. 
 
12 SCHOOL ARITHMETIC. 
 
 Harry had four apples, but gave one to May. How 
 many had he left? 
 
 You have four fingers on one hand. If two were cut 
 off, how many would you have left on? 
 
 Alice had four kittens, but three of them died. How 
 many has she left? 
 
 How many ears have two rabbits? 
 
 How many boys have four heads? 
 
 How many bicycles have as many wheels as a wagon? 
 
 The Number Five. 
 
 21. How many dots on the left-hand card? 
 
 How many more are on the other card? 
 
 How many fingers on your left hand? 
 
 How many, counting the thumb? 
 
 Tell me the names of five boys. 
 
 How many cents is a nickel worth? 
 
 What number follows four? 
 
 What number is between three and five? 
 
 I have four beans. Give me enough to make five. 
 
 Take three blocks. Now take enough more to make five. 
 
 Take five beans. Separate them into two piles, thus: 
 
 Two beans and three beans are how many beans? 
 
THE NUMBER FIVE. 13 
 
 Take one bean from the smaller pile and put it into 
 the larger. 
 
 'Now what two numbers make five? 
 
 Here are five rings. O O O O O Cover one of 
 them. How many are not covered? 
 
 Cover two of them. How many can you see? 
 
 Ask your papa how many nickels make a quarter. 
 
 22. How many ones in JJ ? 
 Show me two fives with beans. 
 Show me five twos with beans. 
 
 I 
 
 ABC 
 
 By how many squares is D larger than C? Than B? 
 Than A? 
 
 A and B together are as large as . 
 
 How can we make C as large as D? 
 
 Take one square from D and put it with B. 
 
 B is now as large as - - or - . 
 
 Draw a line five inches long on paper. 
 
 Draw a line five feet long on the blackboard. 
 
14 SCHOOL ARITHMETIC. 
 
 23. Copy and complete, then read: 
 
 O O O O o/rbd O o/u, - . 
 A A A CLmxL A A o/u, - -. 
 
 a/ue, 
 
 (Q/vu, 
 
 24. Four dolls and one doll are how many dolls? 
 
 One finger and four fingers are - - fingers. 
 
 How many splints will make a triangle and a tent, if 
 the tent is made like this A 
 
 Sam had five cents. He spent one cent for candy. How 
 many has he left? 
 
 Fred had five marbles and lost four. How many has 
 he left? 
 
 We have school five days each week. If you stay at 
 home two days, how many days do you come to school? 
 
 Ned had five chickens. The cat killed three of them. 
 How many has he left? 
 
 If your papa gives you a cent every day, in how many 
 days will you have a nickel. 
 
 Jennie bought a tablet for four cents. She gave the 
 clerk a nickel. How many cents should she receive back? 
 
THE NUMBER SIX. 
 
 15 
 
 The Number Six. 
 
 25. Here are .five splints. Make a triangle and then 
 make a tent like this /\. 
 
 Can you make two triangles with the same splints? 
 
 How many more splints do you need? 
 
 How many dots are on the card to the left? 
 
 How many more dots are on the other card? 
 
 Five dots and one dot are how many dots? 
 
 Hold up six fingers. 
 
 Here are twelve splints. Make as many tents like that 
 above as you can with them. JsTow count them. 
 
 What number follows five? What number comes 
 before six? Before five? 
 
 I have five cubes. Give me enough to make six cubes. 
 
 Take six blocks. Put four in one pile, two in another. 
 
 Are six blocks as many as four blocks and two blocks? 
 
 Now arrange the six blocks in two equal rows. 
 
 How many are in each row? 
 
 Three blocks and three blocks are how many blocks? 
 
 How many dots are here? | Cover one of 
 them. How many do you see? 
 
16 SCHOOL ARITHMETIC. 
 
 One dot from six dots leaves how many dots? 
 Cover two of them. Tell me what you see. " 
 Two dots from six dots leaves how many dots? 
 Cover three dots. How many can you see? 
 Three dots from six dots leaves how many dots? 
 How many dots can you see if you cover four of them ? 
 Cover five of them. Tell me what you see. 
 Copy the cards below, and put in the dots needed to 
 make six dots on each card. 
 
 26. How many twos in J J 5 ? How many threes? 
 
 Show me two sixes with cubes. 
 
 How many cubes have you used? _ 
 
 Cut a strip of paper two inches long. 
 
 How many strips are as long as your foot-rule? 
 
 Cut a strip of paper six inches long and one inch wide. 
 
 Into how many square inches can you cut it? 
 
 Draw a line six feet long on the blackboard. 
 
 Measure the line with this yardstick. How many yards 
 long is it? 
 
 A line six feet ]ong is - yards long. 
 
 Ask your mamma how many eggs there are in a half- 
 dozen. 
 
THE NUMBER SIX. 17 
 
 27. Copy and complete, then read: 
 
 o/uo - . 
 
 n n c^^d, n a a a ^ -. 
 
 / / / a/rbd / / / aA^ - -- . 
 a/nxL -r - a/u> J J I . 
 
 O O O O O O f*A^ O O 
 AAAAAA 
 
 A A A A A A 
 
 28. How many days in a week, not counting Sunday? 
 
 George gave me five roses and Ed gave me one. How 
 many did I then have? 
 
 One pig and five pigs are 3 pigs- 
 
 Robert is four years old. How old will he be in two 
 years ? 
 
 Two bears and four bears are how many bears? 
 
 There are three cows on each side of a fence. How 
 many cows are there? 
 
 Name two numbers that make six. Two other numbers. 
 
 From six blocks take away two blocks. How many are 
 left? 
 
 How many more are six cents than one cent? 
 
 Then what two pieces of money make six cents? 
 
 This morning I had six apples, Kow I have only three. 
 How many have I eaten? 
 
18 SCHOOL ARITHMETIC. 
 
 What part of them have I eaten? What part have I 
 left? 
 
 Make six dots on your slate. Put a ring around one- 
 half of them. 
 
 One-half of six dots is - dots. 
 
 Ask your papa how many cents will pay for three two- 
 cent stamps. 
 
 The Number Seven. 
 
 29. Make two A/s with these six splints. 
 Can you make a triangle and a square with the same 
 six splints? Why not? 
 
 How many more splints do you need? 
 Six dots and one dot are how many dots? 
 Show me seven dots. Seven cubes. 
 Copy these cards: 
 
 I want you to make each card have seven dots. 
 Name two numbers that together make seven. Two 
 other numbers. 
 
 Here are four blocks. Add enough to make seven. 
 Now take two away. How many remain? 
 
THE NUMBER SEVEN. 19 
 
 Here are one-cent, two-cent, three-cent, four-cent, and 
 five-cent postage stamps. Pick out any two that you can 
 buy with seven cents. 
 
 30. Make pictures of seven tents. 
 
 Draw a line around three of them. How many are 
 outside ? 
 
 Show me two sevens with dots. 
 
 Cut out a strip of paper seven inches long and one inch 
 wide. 
 
 Into how many square inches can you cut it? 
 
 Draw a line one inch long. Close to the right end draw 
 a line six inches long. 
 
 Xow draw a line below them as long as both. 
 
 How many inches long is this line? 
 
 This line - - is two inches 
 
 long. How much longer is a seven-inch line? 
 
 31. Copy and complete: 
 
 O O O O O oWy O O o/u, -- . 
 
 nnnnnnn ^^ an *** -. 
 
 AAAAAAAf^-- - a/u, AA- 
 
20 
 
 SCHOOL ARITHMETIC. 
 
 32. How many days in a week? 
 
 Name the days of the week, beginning with' Sunday. 
 
 The middle of the week is "W . 
 
 On Wednesday morning how many days of the week 
 are gone? How many are left? 
 
 How many sides have a /\ and a | | ? 
 
 Five girls and two boys went out. How many are out? 
 
 When one comes in, how many will be out? 
 
 Each week we come to school five days and stay at 
 home - - days. 
 
 Joe had seven cakes. The cat took three of them. How 
 many had he left? 
 
 Here are seven apples. OOOOOOO Name 
 each number of apples that you can take away, and tell 
 how many will remain. 
 
 The Number Eight. 
 
 33. Make a triangle and a square with splints. How 
 many splints have you used? 
 
 Try to make two squares with the splints. 
 
 How many more splints must you have ? 
 
 Seven splints and one splint are how many splints? 
 
 Show me eight dots. Show me eight buttons. Point 
 to eight corners in this room, 
 
THE NUMBER EIGHT. 21 
 
 Make a pile of eight blocks. 
 
 Now make two piles of them, putting the same number 
 in each. How many in each pile? 
 . Four blocks and four blocks are how many blocks? 
 
 Take a block from one pile and place it on the other. 
 Xow how many in each pile? 
 
 Five blocks and three blocks are how many blocks? 
 
 Take another block from the smaller pile and place it 
 on the larger. How many in each pile? 
 
 Six blocks and two blocks are how many blocks? 
 
 Name two numbers that make eight. Two other 
 numbers. Who can name still two other numbers? 
 
 What number comes before eight? Before seven? 
 Before six? Before five? 
 
 What number is between five and seven? Between six 
 and eight? 
 
 A nickel and how many cents make eight cents? 
 
 Copy these blank cards, and put in each the number of 
 dots indicated by the word written under it: 
 
 eight six seven five four three 
 
 34. Make four dots, thus: J 2 Draw a line around 
 one-half of them. 
 
 Into how many equal parts have you divided them? 
 One-half of four dots is dots. 
 
22 SCHOOL ARITHMETIC. 
 
 Make eight clots, thus: I I Z J 
 
 Draw a square around one-half of them. Draw a line 
 around the other half. 
 
 One-half of eight dots is dots. 
 
 Show me one-half of six dots. 
 
 How many squares are there here? 
 
 What part of them is black? 
 
 Four squares are one-half of - - squares. 
 
 How much of this circle is black? 
 
 A dollar is worth how many half-dollars? 
 
 Find by trial to-night how many quarts in a half-gallon. 
 
 35. How many fours in 5 I How many twos? 
 
 Show me eight shoes. How many pairs are there? 
 
 Draw four rings above a line, and four below it. How 
 many times did you draw four rings? 
 
 Draw a line around one-half of the rings. How many 
 rings are inside of the line? 
 
 Make pictures of eight tents, four in a row. Cross 
 out one-half of them. How many are left? 
 
 Make pictures of eight stars, two in a row. How many 
 rows have you? 
 
 Make pictures of one-half of eight squares. 
 
 Tell all you can about these figures. 
 
 Two horses need - - pairs of shoes. In four pairs 
 there are - - shoes. 
 
 The spider has - - legs. How many pairs of legs 
 
 does the spider have? 
 
THE NUMBER EIGHT. 23 
 
 36. Copy and complete: 
 
 A A A A A ci/YuL A A A o/u, - . 
 
 CX/YbcL -- OJ\JL> 
 
 X X X X a/Ybd X X X X 
 
 '/////// O/YUL / 
 
 
 
 37. Seven bugs and one bug are how many bugs? 
 
 One bean and seven beans are - - beans. 
 
 A man has six white sheep and two black sheep. How 
 many sheep has he? 
 
 There are five eggs in a dish. We need eight for dinner. 
 How many more must we find? 
 
 Mr. Jones has eight horses in two fields. There are 
 four in one field. How many are in the other field? 
 
 Eight birds were sitting on a fence. A bad boy shot 
 one. How many were left? 
 
 A boy had two fingers cut off. How many were left on? 
 
 We have two gallons of milk. How many quarts have 
 we? Find by trial. 
 
 Draw T a figure four squares long and two squares wide. 
 
 This figure contains - - squares. 
 
SCHOOL ARITHMETIC. 
 
 The Number Nine. 
 
 38. Make two squares with splints. How many splints 
 have you used? 
 
 Try to make three triangles with the splints. How 
 many more splints do. you need? 
 
 How many more than eight dots are on the card to the 
 right? 
 
 Eight dots and one dot are how many dots? 
 
 Take nine blocks and lay them in a row. 
 
 Push one away. How many are left? 
 
 One block and eight blocks are how many blocks? 
 
 One block from nine blocks leaves how many blocks? 
 
 If you push three blocks away, how many will be left? 
 
 Take away all but two. How many have you taken? 
 /Lay the nine blocks in three rows, three in a row. 
 I Now tell me how many threes make nine. 
 
 Copy these cards: 
 
 Add enough dots to make each card have nine. 
 Name two numbers that together make nine. Two other 
 numbers. 
 
THE NUMBER NINE. 
 
 How many splints will make three triangles? 
 
 Draw a square like this: 
 
 How many of the nine small 
 squares are white? 
 
 Make another black. Two black squares and 
 
 white squares are nine squares. 
 
 Cut out a paper triangle three inches on a side. How 
 long are all the sides? 
 
 Copy these squares, and put in each square the number 
 of dots indicated bv the word written under it : 
 
 none 
 
 four 
 
 six 
 
 eight 
 
 nine 
 
 39. There are eight pigs in the pen and one on the 
 road. How many pigs? 
 
 The white hen has seven chicks, the black hen has two. 
 How many chicks? 
 
 There are six eggs in one nest and three in another. 
 How many eggs in both nests? 
 
 Five boys and four girls are how many children? 
 
 Dan has three pennies, Nell has three, and Kate has 
 three. How many have they all? 
 
 Nine sheep were in a field, but one jumped out. How 
 many were left in? 
 
26 SCHOOL ARITHMETIC. 
 
 Here are nine tents, 
 
 If the wind blows two down, how many will remain 
 standing? 
 
 If I take three of them away, how many will be left? 
 
 How many times can you take three tents away? 
 
 If a book costs nine cents, it will take a nickel and 
 pennies to pay for it. 
 
 This line on the blackboard is nine feet long. Find 
 how many yards long it is. 
 
 The Number Ten. 
 
 40. How many fingers and thumbs have you? How 
 many more than nine? 
 
 Make a pile of ten blocks. 
 
 How many cents is this dime worth? 
 
 Copy, and add dots enough to make ten dots on each 
 card: 
 
 Make eight tents and two tents. How many have you 
 made? 
 
 Make seven stars and three stars. How many? 
 
THE NUMBER TEN. 2 
 
 Draw six rings and four rings. How many rings? 
 
 Five fingers and five fingers are how many fingers? 
 
 How many dots on the right-hand card? 
 
 How many fives do you see on it? 
 
 How many nickels make a dime? 
 
 How many tents can you make with ten splints, if the 
 tents are made like this /\ ? 
 
 Xame two numbers that make ten. Two other numbers. 
 
 Lay ten blocks in a row. Push one away. How many 
 are left? 
 
 If you take two away, how many will be left? 
 
 Two blocks from ten blocks leaves hoAV many blocks ? 
 
 Draw a square. Make ten dots. Now put one half of 
 the dots inside the square. 
 
 One-half of ten dots is how many dots? 
 
 Make two piles of ten blocks each. How many tens? 
 
 Two tens and three tens are how many tens? 
 
 Nine fives and one five are how many fives? 
 
 Use dots to show me three twos. 
 
 Four twos and one two are how many twos? 
 
 Show me five twos with dots. How many ones? 
 
 How many fingers have two boys? 
 
 How many clocks have ten hands? 
 
 Find whether this room is ten yards long. 
 
 How many feet less or more? 
 
 41. Willie had nine cents and his uncle gave him one 
 
 more. He then had cents, or one . 
 
 How many children are eight boys and two girls? 
 
Ao SCHOOL ARITHMETIC. 
 
 A week and three days are how many days ? 
 
 This line on the blackboard is ten inches long, and this 
 one is nine inches long. How much longer is one than 
 the other? 
 
 Dan had ten cents. He spent two cents for a pencil. 
 How many cents had he left? 
 
 A man had three of his toes cut ofT. How many were 
 left on? 
 
 Bessie started to the store with ten cents (two nickels), 
 but lost one-half of her money. How much had she left? 
 
 How many two-cent stamps are worth a dime ? 
 
 If you have ten cents, how often can you spend five 
 cents ? 
 
 If one orange costs five cents, how much money will be 
 needed to buy two oranges? 
 
 The Numbers Eleven and Twelve. 
 
 42. How many dots are on the left-hand card? How 
 many more than ten? 
 
 Ten dots and one dot are how many dots? 
 A dime and a penny are how many cents? 
 
THE NUMBERS ELEVEN AND TWELVE. 29 
 
 Here is one block. Put enough more here to make 
 eleven. 
 
 Kame two numbers that make eleven. Two other 
 numbers. 
 
 Make two squares and a triangle with splints. How 
 many splints have you used? 
 
 Try to make three squares with the same splints. How 
 many more do you need ? 
 
 Eleven splints and one splint are how many splints? 
 
 Make a pile of twelve blocks. 
 
 Xow take two blocks away. How many are left? 
 
 Twelve blocks are how many more than ten blocks? 
 
 How many dots do you see here? !!!!!! 
 
 How many sixes in twelve? How many twos? How 
 many fours? 
 
 Cut a strip of paper six inches long. How many strips 
 are as long as your foot-rule? 
 
 How many six-inches in twelve inches? 
 
 Find how many strips each four inches long are as long 
 as your ruler. 
 
 How many four-inches make twelve inches? How many 
 two-inches? 
 
 Make twelve tents with splints. Let the wind blow 
 down one-half of them. How many are left? 
 
 43. Twelve boys are how many more than eleven boys? 
 There are ten eggs in a nest. When the hen lays two 
 more there will be - - eggs in the nest. 
 
30 SCHOOL ARITHMETIC. 
 
 My two horses ate twelve ears of corn. The gray horse 
 ate six ears. How many ears did the bay horse' eat? 
 
 Mamma bought a dozen oranges at the store. We ate 
 six for breakfast. How many were left? 
 
 I found a nest with twelve eggs in it. I took out all 
 but one. How many did I take? 
 
 Twelve of Mr. Smith's sheep were sick. Two of them 
 died. How many got well? 
 
 Six boys were playing soldiers on one side and five on 
 the other. How many boys were there altogether? 
 
 Henry's father gave him a dozen pencils. How many 
 had he left after using four? 
 
 Marvin has a five-cent piece and three pennies. How 
 many more cents must he have to pay for a top worth 
 eleven cents? 
 
 Harry's knife has two blades. How many blades do six 
 such knives have? 
 
 We learned five new words yesterday. If we learn one 
 more to-day than Ave did yesterday, how many have we 
 learned in both days? 
 
PRIMARY NUMBER WORK. 
 
 44. How many ones on the middle card? How many 
 
 twos? 
 
 Two dots are how many more than one dot? 
 Three dots are how many more than two dots? 
 How many dots on the first two cards? 
 Cover two of the dots on the last card. How many do 
 you see? 
 
 One dot and one dot are - - dots. 
 
 Two tents and one tent are - tents. 
 
 One square and two squares are - - squares. 
 
 Two stars less one star are - - star. 
 
 Three tents less one tent are - - tents. 
 Make pictures of: 
 
 Two stars and one star are three stars. 
 
 One tent and two tents are three tents. 
 
 Three dots less one dot are two dots. 
 
 Three rings less two rings are one ring. 
 
 How many ones in two? In three? What two numbers 
 make three? 
 
 [31] 
 
32 SCHOOL ARITHMETIC. 
 
 Make the figure that stands for the number one 
 Make the figure that stands for the number two 
 Make the figure that stands for the number three 
 Use figures instead of these pictures : 
 
 less 
 
 D D D iess D D are Q- 
 2 dots and 1 dot are - - dots. 
 
 1 star and 1 star are - - stars. 
 
 2 tents less 1 tent are - - tent. 
 
 3 cents less 1 cent are - - cents. 
 
 3 squares less two squares are - - square. 
 
 45. Here are some squares: 
 
 n i 
 
 DP a 
 ODD 3 
 
 Write the figure for the number of squares in the 
 upper row. 
 
 Under this write the figure for the number of squares 
 in the second row. 
 
 One square and two squares are - squares. 
 
 Write 3 under the 2 with a line between. Is 3 the 
 number of squares in both upper rows? 
 
 Three squares is the sum of one square and two squares. 
 
 Finding the sum of two or more numbers is called 
 adding. 
 
NUMBERS 1 TO 3. 
 
 Add these numbers: 
 
 33 
 
 DD 
 
 nn 
 
 Take one square from 3 squares. How many are left? 
 Taking one number from another is called subtracting. 
 
 Subtract the following: 
 
 2 3 
 
 1 1 
 
 46. Add: 
 
 1 foot 
 
 2 feet 
 
 2 cents 
 1 cent 
 
 1 yard 
 1 yard 
 
 Subtract: 
 
 
 
 
 2 feet 
 1 foot 
 
 3 yards 
 1 yard 
 
 3 cents 
 2 cents 
 
 2 tops 
 2 tops 
 
 Complete : 
 
 1 and 1 are ( ). 2 less 1 are ( ). 3 less 2 are ( ). 
 
 2 and 1 are ( ). 2 and ( ) are 3. 
 1 and 2 are ( ). 3 less 1 are ( ]. 
 
 3 less ( ) are 2. 
 3 less ( ) are 1. 
 
34 SCHOOL ARITHMETIC. 
 
 47. Make a picture for 2 and 1 are 3. (J and are J ). 
 Tell a story about 1 and 1 are 2. 
 
 ANS. My dolly had 1 dress, and I made her 1 more. She then 
 had 2 dresses. 
 
 Tell a story about 1 and 2 are 3. 
 
 Emma has two pairs of shoes, and Lillie has one pair. 
 How many pairs have they both? 
 
 Mary had three dimes, but lost one. How many had 
 she left? 
 
 Tell another story about 3 less 1 are 2. 
 
 My hat cost two dollars. I have paid one dollar. How 
 much do I owe ? 
 
 We have three quarts of milk for sale. How many 
 times can we sell one quart? 
 
 Then how many quarts are 3 times 1 quart? 
 
 How many fives are one five and two fives? 
 
 Clara ate one peach, and has two left. How many had 
 she at first? 
 
 John had three marbles and gave one to Sam. Ask a 
 question and answer it. 
 
 Here are 3 pears. & (^ & How many boys can 
 each have 1 pear? 
 
 How many ones in 3? 
 
 Count forwards to three, then backwards to one. 
 
 Tell me some things you have learned about the number 
 three, 
 
FOUR 4. 35 
 
 Four 
 
 48. How many ones are pictured on this card? How 
 many twos? 
 
 Four dots are how many more than three dots? How 
 many more than two dots? 
 
 Name two numbers whose sum is four. Two other 
 numbers. 
 
 Show with splints that your answers are correct. 
 
 Here are four tents. Cover one. How many are not 
 covered ? 
 
 If two tents were taken away, how many would be left? 
 
 How many times can one tent be taken away? 
 
 Then four times one tent are - - tents. 
 
 Here are four blocks. Eva may take two blocks. Now 
 she may take two more. 
 
 How many times has she taken two blocks? -How 
 many blocks has she? 
 
 Then two times two blocks are blocks. 
 
 Show with pegs that two twos are as many as four ones. 
 
 Here are four cents. ^p (gP (QP How many 
 
 girls can have one cent each? How many ones in four? 
 
 How many boys can have two cents each? How many 
 twos in four? 
 
36 SCHOOL ARITHMETIC. 
 
 49. Separate four blocks ^^ 
 into two equal parts, thus: 
 
 What is one part called? 
 
 What must you do with an apple to get one-half of it? 
 (Divide it into two equal parts.) 
 
 What must you do with four blocks to find one-half of 
 them? 
 
 If anything is divided into two equal parts, what is 
 one of the parts called? 
 
 In an apple there are - half -apples. 
 
 How many halves make a whole pie? 
 
 One half from two halves leaves - - half. 
 
 Draw two squares and divide them into halves. 
 
 In two squares there are - - half-squares. 
 
 We write one-half thus: \. 
 
 Two blocks are J of - - blocks. 
 
 Write the figure that stands for the number four - 
 
 50. The sign + stands for and. Copy the following, 
 using + instead of and: 
 
 1 and 1 are 2. 3 and 1 are 4. 
 
 2 and 1 are 3. 2 and 2 are 4. 
 
 Kead these: 
 
 1 + 2 are 3. 1 + 3 are 4. 
 
 1 + 1 are 2. 2 + 2 are 4. 
 
FOUR 4. 37 
 
 The sign stands for less. Copy the following, using 
 instead of less: 
 
 2 less 1 are 1. 3 less 2 are 1. 
 
 3 less 1 are 2. 4 less 1 are 3. 
 
 Read these: 
 
 3 1 are 2. 4 2 are 2. 
 
 3 2 are 1. 4 3 are 1. 
 
 We may use the sign = for are. 
 
 Read these: 
 
 2 + 2 = 4. 42 = 2. 
 
 Copy and complete: 
 
 1 + 3 = (). l + () = 4. 4-l = O. 
 
 2 + 2 = ( ). 2 + O_ = 4. * 3 = ( ). 
 4 = 3 + O- 4-() = 3. 4-() = 2. 
 4-1 + O- 4-O = l. 4 = 2 + O. 
 
 NOTE. To secure facility on the part of the pupils the teacher 
 should, as often as may be found necessary, require them to an- 
 nounce results at ftiyJit. He should also train them to give answers 
 immediately upon hearing the numbers and operations named. 
 This applies to all exercises involving the " combinations." 
 
38 SCHOOL ARITHMETIC. 
 
 51. Make a picture for 2 + 2 = 4. 
 
 How many boys together have as many legs as a horse? 
 
 George earned one quarter on Monday and three 
 quarters on Tuesday. How much did he earn in both days ? 
 
 Ask your papa how many quarters there are in a dollar. 
 
 Tell a story about 8 + 1 == 4. 
 
 I bought four pounds of meat. Two pounds of it was 
 pork and the rest beef. Ask a question and answer it. 
 
 Charlie has four rabbits and Paul has one less. How 
 many has Paul? 
 
 How many more fingers than thumbs has your hand ? 
 
 Count from one to four; then count from four back 
 to one. 
 
 If one-half of a lemon is worth two cents, how much is 
 the lemon worth? 
 
 If a cake is worth four cents, how much is one-half of 
 it worth? 
 
 One half-dollar and one half-dollar are - . 
 
 PINT QUART GALLON 
 
 52. Which of these measures is the largest? Which 
 is the smallest? 
 
 Fill each measure with water, then tell me which is 
 the heaviest. 
 
FOUR 4. 39 
 
 The gallon measure is full of water. Find how many 
 times it will fill the quart measure. 
 
 Find how many times you can fill the quart measure 
 and empty it into the gallon measure. 
 
 One gallon is as much as - - quarts. 
 4 quarts make 1 gallon. 
 
 Mabel had a gallon of milk, but fell and spilled a quart. 
 She had quarts left. 
 
 Papa brought home a gallon of oil in a can. There is 
 only one quart in it now. How much has been used? 
 
 Fill the pint measure and empty it into the quart 
 measure. How many times must you do this to fill the 
 quart measure? 
 
 One quart is as much as - - pints. 
 
 2 pints make 1 quart. 
 
 A pint is what part of a quart? 
 
 Two quarts are what part of a gallon? 
 
 When milk is two cents a pint, how much does a quart 
 cost? 
 
 Jennie paid four cents for a quart of vinegar. How 
 much did a pint cost? 
 
 Mamma gave four quarters for a gallon of molasses. 
 How much did a quart cost ? 
 
 Tell a story about a quart and a gallon. 
 
 Tell me some things you have learned about the 
 number four. 
 
40 SCHOOL ARITHMETIC. 
 
 Five 
 
 53. How many dots on this card? Of what number 
 are they a picture? 
 
 Without the one in the center, how many are there? 
 
 Cover the two at the right. How many can you see? 
 
 Are three dots and two dots as many as four dots and 
 one dot? 
 
 Name two numbers whose sum is five. Two other 
 numbers. 
 
 What number is one less than five? Two less? 
 
 Are five ones as many as one five? 
 
 Which would you rather have five pennies or a 
 nickel? Why? 
 
 Count these squares, beginning ; it the left. Q |5 [H d d 
 
 Which square did you call one? Which did you call 
 two? 
 
 Is the black square really two squares, or merely 
 another one square? 
 
 The first square and the second square are how many 
 squares? 
 
 Make the figure that stands for the number five J~. 
 
 54. Here are five balls. () 
 
 If Owen takes 1 ball at a time for 5 times, how many 
 balls will he have? 
 
 Then 5 times 1 ball are how many balls? 
 
FIVE 5. 
 
 5 times 1 are how many? 
 Here are five cents. 
 
 How many boys can have 1 cent apiece? 
 How many ones in 5 ? 
 How many boys can have 2 cents apiece? 
 How many will -be left for another boy? 
 Two 2's and 1 are . 
 
 -B 
 C 
 
 -E 
 
 -D 
 
 The line D and the line A equal which line? 
 
 The line B and the line C equal which line? 
 
 The line B is how many times as long as the line A? 
 
 The line D is how r many times as long as the line B? 
 
 If from the line E we take a line equal to the line A, 
 which line will the remainder equal? 
 
 Show me the number of blocks these figures represent: 
 3, 5, 1, 4, 2. 
 
 Now make the figures that represent the number of 
 blocks I show you. (Show blocks.) 
 
 55. Copy, complete, and read: 
 
 4 + !-=(). 5 != = (). 4 + () = 5. 5 ( ) = 3. 
 
 1 + 4 = (). 5 -4==(). 3 + () = 5. 5-() = 2. 
 3 + 2 = (). 5 2 (). 5 (. ) = 4. 5 = 4 + ( ). 
 
 2 + 3 = (). 5 3=(). 5 () = !. 5 = 2 + (). 
 
42 SCHOOL ARITHMETIC. 
 
 56. Make a picture for 3 + 2 = 5. 
 
 Four little toes and one great toe are toes. 
 
 My hat cost three dollars and my shoes two dollars. 
 How much did both cost? 
 
 A lady bought two pounds of coffee at one store and 
 three pounds at another. Ask a question and answer it. 
 
 2 pounds 4" 3 pounds = pounds. 
 
 We have school five days each week. If you stay at 
 home two days, how 7 many days do you come to school? 
 
 Tell a story about 5 4 == 1. 
 
 It is five miles to Salem. When we have traveled 
 three miles, how far have we yet to go ? 
 
 This line on the blackboard is one foot long, and this 
 one is five feet long. Tell me all you can about the two 
 lines. 
 
 In O O an( i Dj how many half-circles are there? 
 For a nickel I can buy - - 2-cent stamps and - 
 1-cent stamp. 
 
 Tell some other things you can buy with a nickeL 
 Helen, please tell all you know about four. 
 
 ANS. 3 and 1 are four, 2 and 2 are four, 1 and 3 are four ; two twos 
 are four ; 4 less 1 are three, 2 from 4 leaves two, etc., etc. 
 
 James, be kind enough to state what you know about 
 five. 
 
six 6. 43 
 
 Six 6 
 
 57. How many cents can you get for a nickel? 
 
 If I should give you one more penny, how many cents 
 would you have? 
 
 Would you have a cent for every dot on this card? 
 
 Show me five fingers and one finger. How many? 
 
 Draw a line four inches long. At one end of it draw 
 
 a line two inches long. Both together make a line 
 
 inches long. 
 
 Here are six tops. ^ ^ ^ ^ ^ ^ 
 
 If Ben takes two tops at a time for three times, how 
 many tops will he have? 
 
 Then how many tops are 3 times 2 tops? 
 
 Here are six balls. <) <) I <D 
 
 Jack may take 3 balls; then 3 more. 
 
 How many times has Jack taken 3 balls? 
 
 Here are 6 marbles. Q Q Q Q Q Q 
 
 How many boys can have 1 marble each? 
 
 How many ones in 6? 
 
 How many boys can have 2 marbles each? 
 
 How many twos in six? 
 
 How many boys can have 3 marbles each? 
 
 How many threes in six? 
 
44 SCHOOL ARITHMETIC. 
 
 How many threes do you see on the card? Two threes 
 are . 
 
 How many twos are on the card ? Three twos are - . 
 
 Show me with blocks that two threes are as many as 
 three twos. 
 
 Here are four squares. How many 
 
 more must we draw to have six? 
 
 The sum of five and one is six. Name two other num- 
 bers whose sum is six. Two others. 
 
 Draw a line six inches long on your slate. Rub out 
 one inch of it. How long is the remainder? 
 
 If two dots are taken from six dots, how many dots will 
 remain ? 
 
 Make the figure that stands for the number six <f. 
 58. Divide 6 dots into three equal parts thus: 
 
 How many dots are there in each part? 
 When a number of things is divided into three equal 
 parts, each part is one-third of the whole number. 
 
 What is one-third of 6 dots? One-third is written -?,. 
 J of 6 cents is - - cents. 
 
 Into how many equal parts is the first 
 circle divided? The second? 
 
 What part of the first circle is dark? 
 
 What part is light? 
 
 How much of the second circle is dark? 
 
six 6. 45 
 
 Which is greater one-half or one-third of anything? 
 
 Two thirds of a pie and one third of a pie are how much 
 of the pie? 
 
 Cut this apple, giving one-third to John, one-third to 
 Charley, and keeping one-third yourself. In one apple 
 how many thirds of an apple? 
 
 Tii 2 apples there are - - thirds of an apple? 
 
 59. Copy, complete and read: 
 
 5 + ! = (). 3 + 8 = O< 6 4 = (). 2 + () = 6. 
 
 1 + 5==(). 6-l = (). 6 3 = (). 6-() = 4. 
 
 4 + 2 = ( ). 6 5 = ( ). 4 + ( ) = 6. 1 + ( ) = 6. 
 
 2 + 4 = (). 6 2 = O- 6 () = 2. Jof 6 = O- 
 
 3 + ( ) = 6. 6 ( ) = 3. i of 6 = ( ). J of 3 = ( ). 
 
 60. Make a picture for 3 + 3 = 6. 
 
 Harry made five rings and Stella made one. How 
 many did both make? 
 
 Maud, you may draw two circles. Annie may draw 
 four. How many have both drawn? 
 
 The black cow gives a gallon of milk, the red cow two 
 quarts. How much do both give? 
 
 There are three horses on each side of a fence. How 
 many horses are there? Draw the picture. 
 
 Draw a line two yards long. How many feet long is it? 
 
 A lady who had six dollars gave one dollar for gloves. 
 Ask a question and answer it. 
 
 A man had six ten-dollar bills, but spent two of them. 
 How many had he left? 
 
46 SCHOOL ARITHMETIC. 
 
 Henry gets two dollars a day. How much does he earn 
 in three days? 
 
 Our hens lay three eggs a day. How many do they lay 
 in two days? 
 
 A man gets six dollars for working a day. How much 
 does he get for working half a day? 
 
 Tell a story about 6 3 = 3. 
 
 If one orange costs 3 cents, what does one-third of the 
 orange cost? 
 
 If one-third of a melon is worth 2 cents, what is the 
 whole melon worth? 
 
 Alice has one-half of 6 cents and Frances has one-third 
 of 6 cents. Which has the more money? 
 
 Who wants to tell me all about six? James may tell. 
 
 Now you may all go to the board and write what he has 
 told us. 
 
 Seven 
 
 61. Make two triangles with splints. How many have 
 you used? 
 
 Can you make a triangle and a square with the same 
 splints? How many more do you need? 
 
 Six dots and one dot are - - dots. 
 
 How many days in a week? Name them. 
 
 Draw a line six inches long, and another one inch long. 
 What is the length of both lines? 
 
SEVEN 7. 4:7 
 
 Take seven blocks. Take two of them away. How many 
 are left? 
 
 Five blocks and two blocks are blocks. 
 
 Now take three blocks from the seven. How many in 
 each pile? 
 
 Cut out a strip of paper seven inches long. Cut off an 
 inch from one end. "What is the length of the part left? 
 
 This line on the blackboard is four feet long. Make 
 it seven feet long. How long is the line you have drawn? 
 
 Draw a line seven inches long on the blackboard. Helen 
 may rub out one inch of her line. How long is the part 
 left? 
 
 Tom may rub out two inches of his line. How much 
 of the line is left? 
 
 Hester may erase three inches of her line. Tell me 
 something about the part left. 
 
 Xame two numbers whose sum is seven. Two other 
 numbers. 
 
 How many are Q Q and Q Q and Q Q and Q ? 
 
 Can you name three numbers that together make seven ? 
 
 Show me the number of blocks these figures stand for: 
 6, 7, 5, 4, 3. 
 
 Make the figures that stand for the number of balls I 
 hold up. 
 
 62. Copy, complete and read: 
 
 6 + l = (). 5 + () = 7. 7-l = (). 7-3 = (). 
 5 + 2 = O- 3 + () = 7. 7-6 = (). 7-4 = O- 
 4 + 3 = - l + = 7. 7 2 = . 7- = 5. 
 
4:8 SCHOOL ARITHMETIC. 
 
 Add quickly: 
 
 564123 
 
 213654 
 
 Subtract at sight: 
 
 777777 
 162534 
 
 63. You come to school five days each week. How 
 many days do you stay at home? 
 
 What two pieces of money make seven cents? 
 
 There are half a dozen eggs in one nest and one in 
 another. How many eggs in both? 
 
 Tell a story about 7 1 = 6. 
 
 Four boys and three girls are how many children? 
 
 How many sides have a triangle and a square? 
 
 Seven boys went to town, but only five returned. How 
 many stayed in town? 
 
 This is Tuesday. How many more days in this week? 
 
 There were seven windows in a room, arid two of them 
 were open. How many were shut? 
 
 How many quarts are a gallon and three quarts? 
 
EIGHT 8. 
 
 Eight 
 
 8 
 
 64. How many dots are on this card? 
 
 How many large dots? How many small dots? 
 
 Eight dots are one more than what? 
 
 Here are six blocks. Give me enough to make eight. 
 
 Now make two piles of them with the same number in 
 each. How many blocks in each pile? 
 
 Take one block from one pile and place it on the other. 
 Now how many in each pile? 
 
 Take one block from the smaller pile and place it on 
 the larger. Now how many in each pile? 
 
 Make eight dots on your slate. 
 
 Albert may erase one and tell how many are left. 
 
 Carrie may erase two and tell how many she has left. 
 
 Jack may erase three and tell us about the others. 
 
 Jill may erase four and tell us how many she did not 
 rub out. 
 
 Count to eight, then back to one. 
 
 Count to eight by twos. How many twos in eight? 
 
 Show me one half of eight blocks. 
 
 How many fours in eight? 
 
 Two blocks are what part of four blocks? 
 
 65. Here are eight stars. 
 
 ft 
 
 ft 
 
 ft 
 
 ft 
 
 Into how many parts are they divided? 
 *4 
 
50 SCHOOL ARITHMETIC. 
 
 Has each part the same number of stars? 
 
 One of the four equal parts of anything is called 
 one-fourth. (Fourths are often called quartet's.) 
 
 One fourth of eight stars is - - stars. 
 
 Make eight tents. Draw a ring around one fourth of 
 them. 
 
 Make eight dots. Call them pigs. Put one fourth of 
 them into a pen. 
 
 Now put another fourth of them into a pen. 
 
 How many pigs are not in a pen? 
 
 What part of the eight pigs are not in a pen? 
 
 How many fourths of the eight pigs are penned up? 
 
 Are two fourths of the pigs as many as one half of them? 
 
 Ask your mamma to show you a fourth of a dollar, and 
 tell me all you can about it to-morrow. 
 
 One fourth (J) of eight cents is - - cents. 
 
 A quart is what part of a gallon? 
 
 Ask your papa to-night what measures are used to 
 measure potatoes, and tell me something about them 
 to-morrow. 
 
 Make the figure that stands for the number eight cf 
 
 66. Copy, complete and read: 
 
 7 + l = (); 5 + 3 = (). 8-l = (). 8 4 = ( ). 
 
 6 + 2 = (). 4 + 4 = O- 8 2 = (). 8-3 = (). 
 
 1 + ( ) = 8. 3 + ( ) = 8. 8 () = l. 8 = 4. 
 
 2 + () = 8. 4 + () = 8. 8-() = 2. 8 = 3. 
 
 Jof8 = (). i of 4 = O. * of 8 = O. 
 
EIGHT 8. 51 
 
 67. How many pints are there in a gallon of milk? 
 
 If you drink two pints of it, how much will be left? 
 
 What part of the gallon will be gone? 
 
 Six rats were caught in one trap and two in another. 
 How many rats were caught? 
 
 Tell a story about 5 + 3 = 8. 
 
 Dick has four marbles and John has four. How many 
 have they both? 
 
 How many fourths of this square .are black \ 
 
 Is one half of the square white? 
 
 One square is what part of four squares? 
 
 Two squares are what part of four squares? 
 
 Which is more one half of four apples, or one fourth 
 of them? Draw the picture. 
 
 One half of anything is as much as fourths of it. 
 
 Tell a story about 8 5 = 3. 
 
 A boy has eight rabbits. Four of them are white. The 
 rest are black. How many are black? 
 
 This line on the blackboard is two yards and two feet 
 long. What is its length in feet? 
 
 Ray has eight cents and Elsie has a nickel. Ask a 
 question and answer it. 
 
SCHOOL ARITHMETIC. 
 
 68. Have you ever seen these measures 2 Which 
 measure is the largest? 
 
 Clyde may tell me some of the things he has seen 
 measured by them. Who can tell me something more 
 about them? 
 
 The bushel basket is full of corn. Find how many 
 times you can fill the peck measure from it. 
 
 Find how many times you can fill the peck measure and 
 empty it into the bushel measure. 
 
 In one bushel there are - - pecks. 
 4 pecks make 1 bushel. 
 
 When you buy a bushel of potatoes, how many pecks 
 do you get? 
 
 A peck is one - - of a bushel. 
 
 How many pecks will fill the half -bushel? 
 
 If a bushel basket is half-full of potatoes, how many 
 more pecks of potatoes will it hold? 
 
 Fill the peck and the half-bushel with apples, and 
 empty them into the bushel basket. Is the basket full? 
 How much more will it hold? 
 
 How many half -bushels does it take to fill the bushel? 
 
 Two pecks are what part of a bushel? 
 
N i NE _ 9. 53 
 
 When nuts are a dollar a peck, how much does a bushel 
 cost? 
 
 If plums are worth two dollars a bushel, how much 
 must I pay for a half-bushel? 
 
 There are eight pecks of wheat in a sack. How many 
 bushels are in it? 
 
 If we eat a peck of apples each week, how long will a 
 bushel last? 
 
 How many half-pecks will fill the bushel? 
 
 A peck is one fourth of a bushel. 
 
 Two pecks are fourths of a bushel. 
 
 Three pecks are - - fourths of a bushel. 
 
 A half : bushel and a peck are - - pecks, or 
 
 fourths of a bushel. 
 
 Papa bought a bushel and a half of beets. How many 
 pecks did he get? 
 
 How much must you pay for four bushels of clover 
 seed at two dollars a bushel? 
 
 Nine 9 
 
 69. How many more than eight dots are on this card? 
 
 Eight dots and one dot are dots. 
 
 There are three dots in one row. How many in two 
 rows? In three? 
 
 How many splints are needed to make three triangles? 
 How many threes in nine? 
 
SCHOOL ARITHMETIC. 
 
 This line on the board is seven inches long, and this 
 one is two inches long. What is their combined length? 
 
 Put five blocks in one pile and four in another. Put 
 the piles together. How many blocks? 
 
 Take three blocks away. How many now in each pile? 
 
 Six blocks and three blocks are - - blocks. 
 
 Make nine tents with splints. Take away two. How 
 many are left? 
 
 Cover three of the dots on the card. How many can 
 you see? 
 
 Here are nine beans. Take away all but four. How 
 many have you taken? 
 
 Use blocks to find answers: 
 
 Two blocks from nine blocks leaves - blocks. 
 Seven blocks from nine blocks leaves - blocks. 
 Three blocks from nine blocks leaves - blocks. 
 Six blocks from nine blocks leaves - - blocks. 
 Four blocks from nine blocks leaves - - blocks. 
 Five blocks from nine blocks leaves blocks. 
 
 Make the figure that stands for the number nine ?. 
 70. Into how many equal parts are these nine dots 
 
 divided? |:.|:.|:. 
 
 One of the three equal parts of anything is called 
 one, third. 
 
 One third of nine dots is dots. 
 
 One third of six stars is - - stars. ^f 2/ JA! 
 
NIKE -- 9. 
 
 Into what is this circle divided? 
 
 What part of it is black? How many thirds of it are 
 white ? 
 
 One third of the circle and two thirds of it are how 
 much of the circle? 
 
 In anything there are - - thirds. 
 
 Make 9 dots. Draw a ring around one-third (!) of 
 them. 
 
 1 J- * * 
 
 4- of == - . % of = - . 
 
 Draw a line 3 of 9 inches long. 
 Draw a line f of 9 inches long. 
 Show me t of six splints. 
 Show me % of six splints. 
 Show me J- of six splints (all of them). 
 One third of six dollars is - dollars. 
 Two thirds of six dollars is - dollars. 
 Here are some squares. DDD DDD DDD 
 Henry may make 3 squares at a time for 3 times. 
 How many squares has he made? 
 How many squares, then, are 3 times 3 squares? 
 How many are 3 times 3, or 3 threes? 
 How many times is 3 squares found in 9 squares? 
 Draw a line 9 inches long. Measure it with a 3-inch 
 measure. 
 
 How many times does it contain the 3-inch line? 
 
SCHOOL ARITHMETIC. 
 
 XXX 
 
 
 
 
 
 
 
 D 
 
 How many times does C contain A? 
 
 C is how many times A? 
 
 How many times does I) contain B? 
 
 D is how many times B? 
 
 B is what part of D? 
 
 A is what part of C ? 
 
 D is how many times A? 
 
 A is what part of D? 
 
 C is what part of D? 
 
 71. Copy, complete and read: 
 
 8 + l==(.). 4 + () = 9. 9-l = (). 9-4 = (). 
 
 7 +.2 ( ). 2 + () = 9. 9 8 = (). 9 6 = (). 
 
 6 + 3 = ( ). 1 + ( ) = 9. 9 - 2 = ( ). 9 3 = ( ). 
 
 5 + 4 = ( ). 3 + ( ) = 9. 9 7 = ( ). 9 ( ) = 4. 
 
 3 times = 
 3 times 3 = 
 
 00 =t 
 
 2 times A A A A 
 2 times 4 
 
 **( ). 
 
 2 times D D D = 
 
 2 times 3 
 
 A A A = * of ( ). 
 
NINE __ 9. 57 
 
 72. Make a story for 8 + 1 = 9. 
 
 Seven days and two days are how many days? 
 
 There are six eggs in a dish. If I put in three more, 
 how many will be there ? 
 
 Bertha came to school five days last week and four days 
 this week. How -many days did she come ? 
 
 Albert had nine marbles but lost two. Ask a question 
 and answer it. 
 
 Ada broke three of her nine eggs. How many had 
 she left? 
 
 Homer had nine dimes. He gave six dimes for a book. 
 How much had he left? 
 
 Mamma bought nine pairs of gloves, and gave Susie 
 four pairs. How many pairs did she keep? 
 
 Papa had nine dollars; he spent all but two dollars for 
 shoes. How much did the shoes cost? 
 
 Three girls wear six shoes. How many does one girl 
 wear? 
 
 Mamma took nine yards of cloth to make three dresses 
 for Bessie. How many yards in each dress? 
 
 Frank walked nine miles in three days. How far did 
 he walk in one day? 
 
 Tell a story about J of 9 = 3. 
 
SCHOOL ARITHMETIC. 
 
 Zero 
 
 73. How many dots do you see on this card? 
 
 If your two hands were cut off, how many would you 
 have left? 
 
 Draw a line four inches long on your slate. Rub out 
 four inches of the line. How much of it is left? 
 
 Ida had two pennies. She spent them for a pencil. 
 How many pennies had she left? 
 
 Albert had four apples. He ate one and gave three 
 to John. Ask a question and answer it. 
 
 Make a picture of no stars. 
 
 Make the figure that stands for none 6>. 
 
 The figure is called zero, naught, or cipher. 
 When it stands alone it means none to count; but we 
 shall soon make it work hard in a " double team." 
 Tell a story about 5 5 = 0. 
 
 Ten 
 
 10 
 
 74. How many more than nine dots are on this card? 
 Nine dots and one dot are - - dots. 
 How many fingers and thumbs have you? 
 How many fives do you see on the card? 
 Put eight pegs in one pile and two in another. ll<>\v 
 many pegs in both piles? 
 
TEN 10. 59 
 
 Put one peg from the larger pile into the smaller. Now 
 how many in each pile? In both? 
 
 Five pegs and five pegs are - - pegs. 
 
 Lay ten blocks in a row. Take one away. How many 
 are left? 
 
 Use the ten blocks to find these answers: 
 
 Two blocks from ten blocks leaves - - blocks. 
 Eight blocks from ten blocks leaves - blocks. 
 Three blocks from ten blocks leaves - - blocks. 
 
 Seven blocks from ten blocks leaves blocks. 
 
 Four blocks from ten blocks leaves - - blocks. 
 Six blocks from ten blocks leaves - blocks. 
 Five blocks from ten blocks leaves blocks. 
 
 Make ten dots, thus: 
 
 How many times did you make five dotGf 
 
 Two times 5 dots are dots. 
 
 How many times did you make two dots? 
 
 Five times '2 dots are dots. 
 
 Divide ten blocks into piles, putting 2 blocks in each 
 pile. How many times have you found 2 blocks in 10 
 blocks? 
 
 Then 10 blocks contains 2 blocks - times. 
 
 10 blocks divided by 2 blocks = 5. 
 
 10 blocks divided by 5 blocks = 2. 
 
60 SCHOOL ARITHMETIC. 
 
 Show me ten splints. Tie them in a bundle. 
 How many splints in the bundle? How 'many ones 
 in it? How many tens? 
 
 Ten ones ^nake one ten. 
 
 One ten and one ten are - - tens. 
 
 How many are 5 tens and 5 tens? 
 
 It takes more than one figure to stand for the number 
 ten. We must now make go to work. Ten is written 
 thus: 
 
 Make ten dots. Draw a ring around one-half of them. 
 How many are in the ring? 
 
 75. Copy and complete: 
 
 8+2 ( ). 1+ 9 ( ). 7+( )=10. 10 2=( ). 
 
 6+4 ( ). 4+()=10. 5+( )=10. 10 4=( ). 
 
 7+3=( ). 6+()= 10. 2+( )=10. 10 6 ( ). 
 
 5+5=( ). 3+( )=1Q. 8+( )=10. 10 3 ( ). 
 
 10 5 ( ). 10 ()= 7. 10 ( )= 8. J of 10 ( ). 
 
 76. Write with proper signs: 
 
 From 10 take 3; 5; 7; 6; 8; 4. 
 
 From 9 take 4; 3; 6; 8; 5; 7. 
 
 To 3 add 4; 6; 5; 7; 2; 3. 
 
 To 2 add 5; 8; 7; 6; 4; 0. 
 
 Find one-half of 10; 8; D; 4; 1. 
 
 Find one-third of 9; 6; 3; 1. 
 Find one-fourth of 8; 4; 1. 
 
TEN - 10. 61 
 
 77. Dan walked 8 miles on Monday and 2 miles on 
 Tuesday. How far did he walk in both days? 
 
 Tell a story about 10 2 = 8. 
 
 The white hen has seven chicks and the black hen has 
 3. How many have they both? 
 
 Give a story for 10 3 = 7. 
 
 George worked 6 days last week arid 4 days this week. 
 How many days did he work? 
 
 Sadie bought 10 yards of gingham. She used 4 yards 
 for aprons, and had - -- yards left. 
 
 How many nickels are worth 10 cents? 
 
 If you wish to pay me 10 cents, how many times must 
 you give me 5 cents? 
 
 Two times 5 cents = - cents. 
 
 How many 5-cents in 10 cents? 
 
 If I give you 2 cents five times, how much money will 
 you have? 
 
 Five times 2 cents =='- - cents. 
 
 ooo ooo ooo ooo 
 
 If one hat costs 3 dollars, three hats will cost - 
 dollars. 
 
 How much w y ill five 2-cent stamps cost? 
 
 For 9 cents I can buy - - 2-cent stamps, and I shall 
 have - # left. 
 
 How many 2-cents in 10 cents ? (Make the picture.) 
 divided by 2^ means, how many 2$ are there in 
 
SCHOOL ARITHMETIC. 
 
 How often can you cut 2 yards of silk from a piece 10 
 yards long? 10 yd. divided by 2 yd. = ( ). - 
 
 Mamie went to the store with 10 cents in her pocket. 
 She spent one-half of it. How much money had she left? 
 
 Tens. 
 
 78. How many cents equal a dime? 
 
 Then how many ten-cents is a dime worth? 
 
 How many ten-cents are the dimes on the left-hand 
 card worth? On the right-hand card? 
 
 Two ten-cents and three ten-cents are - - ten-cents. 
 
 Eight dimes and two dimes are - - dimes. 
 
 Two dimes are worth twenty cents. 
 
 Place ten blocks in a column as in the picture. 
 
 Make another column of ten blocks. How 
 many blocks in both columns? 
 
 10 blocks and 10 blocks are - - blocks. 
 
 One ten and one ten are - - tens, or twenty. We 
 write twenty thus -^^. 
 
 Make another column of ten blocks. How many tens 
 have you now? 
 
 2 tens and 1 ten are - - tens, or thirty. 
 20 blocks and 10 blocks are blocks. 
 
 Twenty means two tens; what does thirty mean? 
 
TENS. 
 
 63 
 
 In 20 the figure 2 stands for two tens, the for no ones. 
 Now who can write thirty, or three tens and no ones? 
 Let me see who can write forty, or four tens and no 
 ones? 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 1 = one ten. 
 
 
 
 
 
 
 
 
 
 
 
 = one ten. 
 
 
 
 
 
 
 
 
 
 
 = one ten. 
 
 3 tens = 30. 
 
 79. Supply the figures needed: 
 
 One ten and no one is written thus 10. Ten. 
 
 Two tens and no ones is written thus 20. Twenty. 
 Three tens and no ones is written -thus 30. Thirty. 
 Four tens and no ones is written thus Forty. 
 
 Five tens and no ones is written thus Fifty. 
 
 Six tens and no ones is written thus Sixty. 
 
 Seven tens and no ones is written thus Seventy. 
 
 Eight tens and no ones is written thus Eighty. 
 
 Nine tens and no ones is written thus Ninety. 
 
 Ten tens and no ones is written thus 100. One hundred. 
 
 Sixty means six tens. What does seventy mean? 
 Eighty? Ninety? 
 
 80. Count by tens to one hundred. 
 How many tens make 100? 
 
 How many cents in a dollar? How many dimes? 
 How many tens make fifty? 
 
64 SCHOOL ARITHMETIC. 
 
 How many dimes are worth 50 cents? 
 Six ten-cent pieces are worth - - cents. 
 Four dimes and three dimes are - - dimes, or - 
 cents. 
 
 Five tens and four tens are -- tens, or - . 
 
 Ten tens less two tens are - tens, or - . 
 
 Three tens from eight tens leaves - - tens, or - . 
 
 One-half of 6 tens is - - tens, or - . 
 
 We gave 2 ten-dollar bills for our cow. How many 
 dollars was that? (Twenty dollars is written thus $20.) 
 
 This book is worth 4 dimes, or - - cents. 
 
 Dora had 10 dimes. She spent 4 of them, and had 
 left - dimes, or - cents. 
 
 20 No ones and no ones are how many ones ? 2 tens and 3 tens 
 30 are how many tens ? Then 20 + 30 = 5 tens and no ones, or 50. 
 50 
 
 81. Add: 
 
 2 dimes 20^ 4 dimes 
 
 3 dimes 30^ 4 dimes 
 
 5 dimes 50^ 2 dimes 20^ 
 
 1 dime 10^ 5 dimes 
 
 3 dimes 30^ 3 dimes 
 
 3 dimes 30^ 4 dimes 
 
 4 tens 40 5 tens 50 
 
 2 tens 20 3 tens 30 
 
TENS. 
 
 65 
 
 30 days 
 
 30 days 
 
 70 bushels 
 
 30 bushels 
 
 10 ft. 
 60 ft. 
 
 $50 
 
 $50 
 
 $40 
 $50 
 
 70 yd. 
 20 yd. 
 
 $60 
 
 $40 
 
 20 
 60 
 
 82. Subtract 
 
 4 dimes 
 1 dime 
 
 40^ 
 
 7 dimes 
 1 dime 
 
 6 dimes 
 3 dimes 
 
 7 dimes 
 2 dimes 
 
 20^ 
 
 8 tens 
 4 tens 
 
 $60 
 
 $20 
 
 80 
 40 
 
 80 ft. 
 20 ft. 
 
 10 tens 
 5 tens 
 
 90 pecks 
 80 pecks 
 
 100 
 50 
 
 $100 
 $ 10 
 
 83. Copy and complete: 
 
 10 + 10 = ( ). 
 
 20 + 20 ( ). 
 
 50 + 30 ( ). 
 
 20 + 10 = ( ). 
 
 30 + 20 = ( ). 
 
 60 + 30 ( ). 
 
 30 + 10- ( ). 
 
 40 + 20 ( ). 
 
 70 + 30 ( ). 
 
 40 + 10 ( ). 
 
 50 + 20 ( ). 
 
 40 + 40 ( ). 
 
 50 + 10 = ( ). 
 
 60 + 20 ( ). 
 
 50 + 40 ( ). 
 
 60 + 10 = ( ) 
 
 70 + 20 ( ). 
 
 60 + 40 ( ). 
 
 70 + 10 ( ). 
 
 80 + 20 ( ). 
 
 50 + 50 = ( ). 
 
 80 + 10 = ( ). 
 
 30 + 30 ( ). 
 
 20 + 10 ( ). 
 
 90 + 10 (), 
 
 40 + 30 ( ). 
 
 30 + 10 = ( ). 
 
66 
 
 SCHOOL ARITHMETIC. 
 
 Review and Drill. 
 84. Copy and add: 
 
 $3 
 
 4 gal. 3 
 
 ft. 1 ten 
 
 10 
 
 $1 
 
 2 gal. 4 
 
 ft. 2 tens 
 
 20 
 
 2 gal. 
 
 3 in. 4^ 
 
 ' 4 tens 
 
 40 
 
 3 gal. 
 
 2 in. 2< 
 
 5 3 tens 
 
 30 
 
 $7 
 
 6 doz. 5 
 
 in. 8 tens 
 
 80 
 
 $1 
 
 1 doz. 4 
 
 in. 2 tens 
 
 20 
 
 85. Copy 
 
 and subtract: 
 
 
 
 7 ft. 
 
 6 doz. 5^ 
 
 * 6 tens 
 
 60 
 
 3 ft. 
 
 4 doz. 2^ 
 
 2 tens 
 
 20 
 
 $8 
 
 7 in. 8 
 
 gal. 5 tens 
 
 50 
 
 $5 
 
 4 in. 6 
 
 gal. 3 tens 
 
 30 
 
 9 yd. 
 
 $9 10 qt. 10 tens 
 
 100 
 
 6 yd. 
 
 $4 7 
 
 qt. 8 tens 
 
 80 
 
 86. Copy 
 
 and complete: 
 
 
 
 3+2 ( ). 
 
 3+4 ( ). 
 
 3+6=( ). 
 
 6 2=( 
 
 4+1 ( ). 
 
 7+1 ( ). 
 
 5+4=( ). 
 
 5 3=^=( 
 
 l+5=( ). 
 
 2+6 ( ). 
 
 9+1 ( ). 
 
 7-5-( 
 
 2+4 ( ). 
 
 5+3 ( ). 
 
 2+8 ( ). 
 
 6 4 ( 
 
 3+3 ( ). 
 
 4+4 ( ). 
 
 7+3 ( ). 
 
 8 5 ( 
 
 6+1 ( ). 
 
 1+8 ( ). 
 
 4+6 ( ). 
 
 7 3=( 
 
 2+5=( ). 
 
 7+2 ( ), 
 
 5+5=( ), 
 
 8 6=( 
 
REVIEW AND DRILL. 67 
 
 5+( )=8. 
 
 8 3=( ). 
 
 10 2=( ). 
 
 10-( )=7. 
 
 7+( )=9. 
 
 9 2=( ). 
 
 10 7=( ), 
 
 10 ( )=2. 
 
 3+( )=7. 
 
 7 4=( ). 
 
 10 4=( ). 
 
 10-( )=6. 
 
 4+( )=8. 
 
 8 3=( ). 
 
 10 5=( ). 
 
 10 ( )=4. 
 
 6+( >=9. 
 
 9 7=( ). 
 
 10 6=( ). 
 
 10 ( )=8. 
 
 2+( )=7. 
 
 7-5=( ). 
 
 10 8=( ). 
 
 10_( )=l. 
 
 8=2+( ). 
 
 7=2+( ). 
 
 3=7 ( ). 
 
 i of 4=( ). 
 
 6=4+( ). 
 
 9=5+( ). 
 
 2=5 ( ). 
 
 i of 8=( ). 
 
 9=6+(- ). 
 
 6=4+( ). 
 
 1=8 ( ). 
 
 i of 8=( ). 
 
 7=3+( ). 
 
 8=3+( ). 
 
 3=6 ( ). 
 
 i of 6=( ). 
 
 9=7+( ). 
 
 10=6+( ). 
 
 4=9 ( ). 
 
 Jof 10=( ). 
 
 8=5+( ). 
 
 10=3+( ). 
 
 6=9 ( ). 
 
 i of 9=( ). 
 
 87. Add quickly: 
 
 4 
 
 2 
 
 1 
 
 3 
 
 4 
 
 2 
 
 6 
 
 4 
 
 3 
 
 2 
 
 3 
 
 4 
 
 3 
 
 3 
 
 5 
 
 1 
 
 4 
 
 5 
 
 6 
 
 1 
 
 2 
 
 1 
 
 3 
 
 7 
 
 4 
 
 1 
 
 2 
 
 2 
 
 7 
 
 7 
 
 8 
 
 6 
 
 2 
 
 5 
 
 9 
 
 8 
 
 88. Subtract quickly: 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 
 
 6 
 
 6 
 
 6 
 
 7 
 
 1 
 
 2 
 
 2 
 
 3 
 
 2 
 
 4 
 
 3 
 
 5 
 
 1 
 
 7 
 
 7 
 
 7 
 
 7 
 
 7 
 
 8 
 
 8 
 
 8 
 
 8 
 
 6 
 
 2 
 
 5 
 
 3 
 
 4 
 
 4 
 
 2 
 
 3 
 
 5 
 
 8 
 
 8 
 
 9 
 
 9 
 
 9 
 
 9 
 
 10 
 
 10 
 
 10 
 
 6 
 
 7 
 
 2 
 
 7 
 
 3 
 
 4 
 
 4 
 
 6 
 
 7 
 
68 
 
 SCHOOL ARITHMETIC. 
 
 89. Add the number in the center to each of the other 
 numbers in the same square. Name results at sight: 
 
 9 
 
 7 
 
 4 
 
 6 
 
 1 
 
 8 
 
 3 
 
 5 
 
 2 
 
 8 
 
 4 
 
 5 
 
 1 
 
 2 
 
 3 
 
 6 
 
 2 
 
 7 
 
 5 
 
 4 
 
 7 
 
 1 
 
 3 
 
 2 
 
 6 
 
 
 
 3 
 
 90. Subtract the number in the center from each of 
 the other numbers in the same square. Name results 
 quickly : 
 
 7 
 
 4 
 
 3 
 
 5 
 
 2 
 
 10 
 
 9 
 
 8 
 
 6 
 
 6 
 
 8 
 
 4 
 
 10 
 
 3 
 
 7 
 
 5 
 
 3 
 
 9 
 
 5 
 
 6 
 
 8 
 
 9 
 
 4 
 
 9 
 
 4 
 
 10 
 
 7 
 
 n n 
 n 
 n n 
 
 n 
 
 n n 
 
 Q 
 Q Q 
 
 Q 
 
 Q 
 
 91. Rob made 5 squares and Roy made 3. How many 
 did both make? Draw the picture. 
 
 Dick had six marbles. He gave 2 to Ned. How many 
 had he left? Draw the picture. 
 
 There are 5 boys and 4 girls in a class. How many 
 children ? 
 
 May had 7 apples. She ate 2. How many had she left? 
 Draw the picture. 
 
WRITING AND BEADING NUMBERS TO 100. 69 
 
 How many feet are there in 3 yards? 
 
 How many 2-dollar bills should I get for a 10-dollar bill? 
 
 A man had ten sick sheep. One-half of them died. 
 How many got well ? 
 
 A lady sold 8 pounds of butter, 2 pounds in a roll. How 
 many rolls? 
 
 It is 2 miles from Harry's home to school. How far 
 does Harry walk each day? How far in two days? 
 
 Two wagons and a bicycle have how many wheels? 
 
 A farmer has 9 acres of wheat. One-third of it is cut. 
 How much has he to cut yet? How many thirds? 
 
 Bert has a dime. How can he give me J of it? 
 
 At two cents each, what will 5 oranges cost? 
 
 If $4 is J of my money, how much have I? 
 
 Two years is i of John's age. How old is he? 
 
 Writing and Reading Numbers from 1 to 100. 
 
 : : 
 
 
 
 
 11 12 13 14 15 
 
 Eleven Twelve Thirteen Fourteen Fifteen 
 
 92. Look at the number picture on the left. What 
 do you see over the 1 at the right in this picture? (1 one.) 
 
 Over the one at the left? (1 ten.) Then It means 1 len 
 and 1 one. (The figures 11 stand for the number eleven.) 
 
 What do you see over the 2 in the second number pic- 
 ture? (2 ones.) Over the 1? Then 12 means 1 ten and 
 2 ones. (The figures 12 stand for the number twelve.) 
 
70 
 
 SCHOOL ARITHMETIC. 
 
 What does 13 mean? 17? 18? 
 
 How would you write one ten and three ones (thirteen) ? 
 One ten and four ones (fourteen) ? Qne ten and five ones 
 (fifteen)? 
 
 How many figures do you write for each number? 
 
 What does the figure on the left show? 
 
 What does the figure on the right show? 
 
 In which place do we write the ones ? The tens ? 
 
 If we call the number expressed by 16, sixteen, what 
 shall we call the number expressed by 17? By 18? By 19? 
 
 93. Read, supplying blanks: 
 
 11 = 1 ten and 1 one. 16 = -- ten and -- ones. 
 
 12 = ten and ones. 
 
 13 = ten and ones. 
 
 14 = - ten and ones. 
 
 15 = ten and ones. 
 
 17 = ten and ones. 
 
 18 = ten and ones. 
 
 19 = ten and ones. 
 
 20 = - tens (and no ones). 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 = 1 ten. 
 = 1 ten. 
 = 1 one. 
 
 
 
 
 
 
 
 
 
 
 
 
 jj 
 
 94. You have already learned that two tens and no 
 ones is written thus 20. 
 
 Try to write two tens and one one. 
 
 Now write two tens and two ones. 
 
 What do we call 2 tens? 
 
 If we call two tens and one one, twenty-one, what shall 
 we call two tens and two ones? 
 
 What shall we call two tens and three ones? Two tens 
 and four ones? Two tens and five ones? Two tens and 
 
WRITING AND READING NUMBERS TO 100. 
 
 71 
 
 six ones? Two tens and seven ones? Two tens and eight 
 ones? Two tens and nine ones? 
 Copy and complete this table:* 
 
 
 
 10 
 
 20 
 
 30 
 
 40 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 1 
 
 11 
 
 21 
 
 31 
 
 
 
 
 
 
 
 2 
 
 12 
 
 22 
 
 
 
 
 
 
 
 
 3 
 
 13 
 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 
 
 
 7 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 95. How many numbers are in each column? 
 How many columns are there? 
 
 Name the numbers in the second column, beginning at 
 the top. 
 
 What does 16 express? (One ten and ones.) 
 
 What does 14 express? 18? 15? 
 
 * The pupils should be able to complete this table without help. 
 When they have it finished, they should learn the number names 
 that is, count to one hundred. 
 
SCHOOL ARITHMETIC. 
 
 Name the numbers in the third column. 
 
 What does 21 express? 23? 25? 29? 
 
 What do we call 3 tens ? Wliat then is the number made 
 up of 3 tens and 1 one? (Thirty-one.) 
 
 Now name the numbers in the fourth column. 
 
 What does 31 express? 32? 36? 38? 
 
 Name the numbers in the fifth column. 
 
 What does 41 express? 43? 44? 49? 
 
 Name the numbers in each of the other columns. 
 
 Count to one hundred without looking at the table. 
 
 What number is written at the right of 14? At the 
 left of it? 
 
 What number is written at the left of 25? At the right 
 of it? 
 
 Begin at the number 2 and name each number to the 
 right of it. 
 
 Begin with 6 and read across to 96. 
 
 Name all the numbers in the table that end in 8. In 
 4. In 7. In 9. 
 
 What does 
 ones? 
 
 express? Who can write 9 tens and 10 
 
 The Sign x. 
 C D 
 
 E 
 
 96. How many squares in A? B is how many times A? 
 
 A is 2. How many 2's in B? 2 2's are - . 
 
 2X2 = 4. This is read, 2 2's are 4, or 2 times 2 are 4. 
 
 (The sign X stands for the word times.) 
 
THE SIGN X 73 
 
 How many 2's in C? How many ones? 
 
 Eead this: 3X2 = 6. 
 
 How many 2's in D? How many ones? How many 
 fours ? 
 
 Complete and read: 4 X 2 = ( ). 2 X 4 =( ). 
 
 How many 2's in E? How many ones? How many 
 fives? 
 
 Complete and read: 5X2 = ( ). 2 X 5 = ( ). 
 
 How many twos on the card to the left? 
 How many threes on the other card? 
 Are 3 2's as many as 2 3's? 
 Show with blocks that your answer is correct. 
 Read these: 3X2 = 2X3. 3X2 or 2X3 = 6. 
 Call the dots on the first card cents. How many of 
 them will pay for a 2-cent stamp? 
 
 How many of them will pay for 3 stamps? 
 
 97. 
 
 
 1 
 
 X2 
 
 = 
 
 2 
 
 2 
 
 X 
 
 1 = 
 
 2 
 
 
 
 4 
 
 
 
 2 
 
 X2 
 
 = 
 
 4 
 
 2 
 
 X 
 
 2 = 
 
 4 
 
 
 
 I 
 
 
 3 
 
 X2 
 
 = 
 
 6 
 
 or 2 
 
 X 
 
 3 = 
 
 6 
 
 
 
 
 
 .:: 
 
 4 
 
 4 
 
 K 
 
 X2 
 
 V 9 
 
 = 
 
 8 
 i n 
 
 2 
 
 9 
 
 X 
 
 4 = 
 K 
 
 8 
 
 
 
 How i 
 
 in 
 
 my 
 
 /\ ^ 
 
 are 
 
 2 i 
 
 1 U 
 
 2 4's? 
 
 2 
 
 3's? 
 
 2 5 
 
 <, 
 
 2 1 
 
 Copy and complete: 
 
 2X() = 4 2 X ( ) = 2 2 X ( ) = 10 
 3X() = 6 4X() = 8 5X() = 10 
 
SCHOOL AKITHMETIC. 
 
 98. How many dots on the card at the left? How 
 many 3's? 
 
 How many 3's do you see on the second card? On the 
 third card? 
 
 Two 3's are how many ones? 2 X 3 = ( ). 
 
 Three 3's are how many ones? 3 X 3 = ( ). 
 
 Nine dots are how many times 3 dots? 
 
 Call each dot on the middle card a foot. How many 
 of them are a yard ? How many yards in 6 feet ? In 9 feet ? 
 3X2 (). 2X() = 6. 3X() = 9. 
 
 An orange costs 3 cents. How much must I pay for 
 3 of them? 
 
 How many sides have three triangles? Three squares? 
 
 The Sign -T-. 
 
 How many 2-cent stamps can 
 How many 
 
 99. Here are 6 cents. 
 I buy with them? 
 
 How many 2^ do you see in the 
 
 How often must 2^ be taken to make 
 
 Then 6^ divided by 2^ = 3 times. This may be writ- 
 ten, 60-^-2^ = 3. 
 
 It means that 2 cents are found in 6 cents 3 times. 
 6^ divided by 3# == ( ). 6^ -=- 3^ = ( ). 
 
 What may stand for the words divided by? 
 
THE SIGN 
 
 Here are 8 stars. V, ^ ^ ow manv 
 
 can I give 2 stars each? 4 stars each? 
 
 8 stars -f- 2 stars = ( ). 8 stars -r- 4 stars = ( ). 
 
 If I divide the stars into two equal parts, how many 
 stars will be in each group? 
 
 Then 8 stars -+- 2 = 4 stars. 8 stars -r- 4 = ( ). 
 
 How many 2's in 4? In 6? In 8? In 10? 
 
 How many 3's in 6 ? How many in 9 ? 
 
 How many 4's in 8? How many 5's in 10? 
 
 How often are 4^ contained in 8^? 
 
 Nine quarts contains 3 quarts - - times. 
 
 4-7-2 = ( ). 6-f-2 = ( ). 8-7-4 = ( ). 
 
 8 -5-2 ==(*). 6-^-3 = ( ). 10-7-5 = ( ) 
 
 i of 4 = ( ). J of 6 = ( ). i of 8 = ( ). 
 
 An orange costs 3^. How many can I buy for 
 
 If I must pay 5^ for a quart of milk, how many quarts 
 will I get for this dime? 
 
 Hettie had 9 buttons, 3 in a row. How many rows 
 were there? 
 
 How many 2-cent tops can you buy for 8 cents? 
 
 Cut a stick 9 inches long and one 3 inches long. Com- 
 pare them. 
 
 The longer stick is times as long as the other. 
 
 The shorter stick is : as long as the other. 
 
 How many times can a 2-inch line be measured off on 
 a 10-inch line? 
 
76 
 
 SCHOOL ARITHMETIC. 
 
 NUMBERS TO 20. 
 Eleven. 
 
 
 
 
 
 
 11. 
 
 100. Ten dots and one dot are 
 Eleven is made up of 1 ten and 
 
 dots. 
 
 one. 
 
 How many splints are in the bundle? How many loose 
 splints are there? 
 
 What figure will tell the number of bundles, or tens? 
 The number of single splints, or ones ? 
 
 Take 11 pegs. Place them in two piles, putting 9 in 
 one pile. 
 
 How many pegs in each pile? How many in both? 
 
 What is the sum of 9 pegs and 2 pegs ? Of 9 and 2 ? 
 
 Put one peg from the larger pile on the smaller. Xow 
 how many in each pile? 
 
 The sum of 8 pegs and 3 pegs is pegs. 
 
 Take another peg from the larger pile and place it on 
 the smaller. Now tell me about the two piles. 
 
 Show me with the pegs how many 6 and 5 are. 
 
 Take one peg away from the 11. How many are left? 
 
 Show me with the pegs how many 2 from 11 leaves. 
 3 from 11. 4 from 11. 5 from 11. 6 from 11. 7 
 from 11. 
 
 Cut a string a foot long. Cut off 1 inch of it. Measure 
 the piece that is left. 
 
 Mary may tell us all she can about 11. 
 
TWELVE. 
 
 77 
 
 101. Copy and complete: 
 
 10 + 1= 11 1= 11 6= 11 ()= 8 
 
 3 + 8 = 11 4= 11 7 = 4 + ( ) = 11 
 
 7 + 4 = 11 3= 11 9= 11 ( )= 6 
 5 + 6= 11 5= 1110= !! ()= 4 
 
 102. Make a story for 5 + 6. 
 
 A stick of candy costs a cent. How many sticks can 
 you get for a dime and a cent? 
 
 What two pieces of money make 11 cents? 
 
 How much must you pay for three 3-cent stamps and a 
 2-cent stamp? 
 
 If you have been at school two weeks and one day this 
 month, how many days have you been at school? 
 
 Three yards and two feet are how^many feet? 
 
 We have 2 bushels and 3 pecks of apples. How many 
 pecks have we? 
 
 If we use 3 pecks of them, how many pecks will we 
 have left? How many busnels? 
 
 A rail 11 feet long was cut in two. One part was 7 
 feet long. What was the length of the other part? 
 
 There are 11 eggs in two nests. In one nest there are 
 5 eggs. How many in the other? 
 
 Twelve. 
 
 103. Ten dots and 2 dots are 
 Twelve dots are 1 more than 
 
 - dots, 
 dots. 
 
78 SCHOOL ARITHMETIC. 
 
 There are 12 dots on the card at the right. Call them 
 pigs. How many are in each pen? 
 
 Six and six, or two sixes, are . How many 6's 
 
 in 12? 
 
 Put one little pig into the pen with the big ones. How 
 many pigs in each pen now? 
 
 Seven and five are how many? 
 
 Put another little pig in with the big ones. Now how 
 many pigs in each pen? 
 
 Eight and four are how many? 
 
 When 9 of them are in one pen, how many are in 
 the other? 
 
 When only two little pigs remain in one pen, how many 
 are in the other? 
 
 Who can name three numbers that added together 
 make 12? 
 
 Write twelve and tell what each figure stands for. 
 
 Use your foot rule to find these answers : 
 
 One inch from 12 inches leaves - - inches. 
 Two inches from 12 inches leaves - - inches. 
 Four inches from 12 inches leaves - - inches. 
 
 Eight inches from 1 2 inches leaves inches. 
 
 Three inches from 12 inches leaves inches. 
 
 Five inches from 12 inches leaves - inches. 
 Six inches from 12 inches leaves - inches. 
 
 How many triangles can you make with 12 splints? 
 How many squares? 
 
 Measure your rule with a stick 2 inches long. How 
 many 2-inches make 12 inches? 
 
 @ X 2 inches = inches. 
 
TWELVE. 79 
 
 How many times could you cut 2 inches off your rule? 
 How many 2's in 12? 
 
 12 inches -f- 2 inches = - . 
 Use splints to show me J of 12. J of 12. f of 12. 
 
 104. Measure with the foot rule: 
 
 The. length of this book. 
 The width of your desk. 
 The length of this chart. 
 The height of this boy. 
 The length of this yardstick. 
 
 Measure with the yardstick: 
 
 The length of this room. 
 The width of this room. 
 The length of this house. 
 
 Your foot rule is marked off into 12 equal parts. What 
 is each part called? 
 
 In 1 foot there are inches. In 1 of a foot there 
 
 are inches. 
 
 How many inches in -J of a foot? In J of a foot? 
 
 Draw a line on the board 12 inches long, without 
 measuring. 
 
 Now measure it and find out how long it really is. 
 
 Who can draw a line a yard long without measuring it? 
 
 Draw a rectangle (an oblong) four inches long and 
 three inches wide. 
 
 Draw lines across it, as in the picture. 
 Draw them an inch apart. 
 
 What is a square 1 inch on a side 
 called? 
 
80 SCHOOL ARITHMETIC. 
 
 How many square inches are there in the upper row? 
 
 How many rows are there? Then how many square 
 inches in the three rows? 
 
 3X4 square inches = - square inches. 
 
 How many square inches in the left-hand row? How 
 many rows are there? 
 
 Then how many square inches in the four rows? 
 4X3 square inches = - - square inches. 
 
 Cut out a square inch and find how many of them will 
 cover your rectangle. 
 
 Draw a rectangle 6 inches long and 2 inches wide. Find 
 how many square inches there are in it. 
 
 105. Copy and complete: 
 
 10 
 
 + 2 = 
 
 12 
 
 
 
 12 () 
 
 = 2 
 
 9 
 
 + 2 
 
 11 
 
 + 1 = 
 
 12 
 
 -4 
 
 12 () 
 
 -4 
 
 7 
 
 + 4 
 
 9 
 
 + 3 = 
 
 12 
 
 -4 = 
 
 12 ( ) 
 
 = 3 
 
 i 
 
 4 
 
 of 12 
 
 4 
 
 + 
 O 
 
 12 
 
 -3 = 
 
 12 ( ) 
 
 =r 5 
 
 i 
 
 of 12 
 
 7 
 
 + 5 = 
 
 12 
 
 -5 = 
 
 12-( ) 
 
 = 7 
 
 i 
 
 of 12 
 
 6 
 
 + 6 = 
 
 12 
 
 /> 
 
 12 () 
 
 1 = 8 
 
 ^ 
 
 of 9 
 
 2 
 
 X 6 = 
 
 12 
 
 -4-2 = 
 
 12 -^ 3 
 
 = 
 
 i 
 
 of 12 
 
 3 
 
 X4 = 
 
 12 
 
 -5-6 = 
 
 12 -T- 4 
 
 = 
 
 1 
 
 of 12 
 
 106. There are 9 quarts of milk in one pail and 3 
 quarts in another. How much milk? 
 
 Tell a story about 8 + 4 = 12. 
 
 How many days are a week and 5 days? 
 
 Seven cents and a nickel are how much money? 
 
 Henry had 12 goats. A bad boy stole 4 of them. Ask 
 a question and answer it. 
 
 Make a story about 12 5 = 7. 
 
TWELVE. 81 
 
 A boy who had 12 cents gave two nickels for a book. 
 He had left cents. 
 
 How many cows have 12 tails? How many have 12 
 horns ? 
 
 Six girls wear - shoes. 
 
 How many shoes do 3 horses wear? 
 
 In 1 yard there are feet. In 4 yards there are 
 
 feet. 
 
 Twelve pecks of plums are how many bushels? 
 
 A log is 12 feet long. How many yards is that? 
 
 If you divide 12 nuts equally among 4 boys, how many 
 will each have? 
 
 How many quarts of milk in 12 pints? 
 
 If we had a dozen eggs, boys could have 2 apiece. 
 
 107. Name the months of the year. 
 
 In a year there are months. In half a year there 
 
 are - - months. 
 
 What is the first month? The second? The twelfth? 
 
 What is the name of the present month? In what 
 month is your birthday? 
 
 During what months is school held? 
 
 March, April, and May are called the spring months. 
 Name the summer months. The fall or autumn months. 
 The winter months. 
 
 How many seasons in a year? Then how many months 
 in a season? 
 
 What part of a year are the spring months? The 
 summer months? 
 
 What part of a year are the spring and summer months 
 together ? 
 
82 
 
 SCHOOL ARITHMETIC. 
 
 108. Some things to remember: 
 
 Jan. stands for January. Sept. stands for September. 
 
 Feb. stands for February. Oct. stands for October. 
 
 Mar. stands for March. Nov. stands for November. 
 
 Aug. stands for August. Dec. stands for December. 
 
 12 inches make 1 foot. 
 12 things make 1 dozen. 
 12 months make 1 year. 
 
 Ct. or $ stands for cent. 
 Qt. stands for quart. 
 Gal. stands for gallon. 
 
 In. stands for inch or inches. 
 Ft. stands for foot or feet. 
 Doz. stands for dozen. 
 
 Sq. in. stands for square inch. 
 Yd. stands for yard. 
 Bu. stands for bushel. 
 
 109. It is noon at 12 o'clock. Look 
 at the 'clock face and tell how many 
 hours it is from noon to midnight. 
 
 Show me to what the short hand 
 points at 1 o'clock. At 2 o'clock. 
 
 What stands for one on the clock 
 face? For two? For three? For 
 fivel For ten\ 
 
 I stands for 1. 
 
 II stands for 2. 
 
 Ill stands for 3. 
 
 V stands for 
 X stands for 
 What stands 
 
 5. 
 10. 
 for 4? 
 
 In Roman notation IV always stands for 4 except on 
 clock faces, where IIII is commonly used. 
 
 You know that 5 1 means 4, or 1 less than 5. When 
 I is written before V, the two letters (IV) mean one less 
 than five, or 4. 
 
THIRTEEN. 
 
 83 
 
 What do you think IX means? 
 What does 5 + 1 mean? 
 
 When I is written after V, the two letters (VI) mean 
 one more than five, or 6. 
 
 What do you think VII means? VIII? XI? XII? 
 
 IV stands for 4. X stands for 10. 
 
 VI stands for 6. IX stands for 9. 
 
 VII stands for 7. XI stands for 11. 
 
 VIII stands for 8. XII stands for 12. 
 
 If we eat dinner at 12 o'clock and supper at 6 o'clock, 
 how long is it between meals? 
 
 Look at a nickel to-night and tell me to-morrow what 
 shows the number of cents it is worth. 
 
 Thirteen. 
 
 110. What number follows 12? 
 
 One ten and 3 ones are . 
 
 Name two numbers less than 10 whose sum is 13. Two 
 other numbers. Now two others. (Use splints to find 
 the numbers.) 
 
 Take 13 splints. Show how many are left when 4 are 
 taken away. When 5 are taken away. When 6 are taken 
 away. 
 
 This line on the board is 13 inches long. How much 
 longer is it than your foot rule? 
 
 How many splints are in the bundle? How many tens? 
 
 How many loose splints, or ones, do you see? 
 
84 
 
 SCHOOL ARITHMETIC. 
 
 Write on the board the figures that stand for the 
 number thirteen. 
 
 Which figure stands for the tens? Which for the ones? 
 
 Three and ten are - . (The word thirteen means 
 three and ten.) 
 
 111. Copy and complete: 
 
 10 + 3= 13 4- 11 + 2= 8 + 2 + 3 = 
 
 9 + 4= 13 6= 13 ( ) = 9 5 + 4 + 4 = 
 
 5 + 8= 13 7= 13 ( ) = 7 4 + 3 + 6 = 
 
 7 + 6= 13 5= 13 () = 5 5 + 3 + 5 = 
 
 112. Add quickly: 
 
 532 
 8 10 11 
 
 Subtract at sight: 
 
 13 13 13 13 13 13 13 12 12 12 
 
 465789 10 354 
 
 Subtract each number in the rim of the 
 wheel from the 13 in the center. 
 
 113. Three bushels and a peck are how 
 many pecks? 
 
 There are 8 qt. of milk in one pail and 5 qt. in another. 
 How much milk 111 both ? 
 
FOUKTKKX. 
 
 85 
 
 Look at the flag and tell a 
 story about 7 -|- 6. 
 
 How many 4's in 13, and 
 how many left over ? Draw the 
 picture, using dots. 
 
 A log is 4 yd. and 1 ft. long. 
 
 It is feet longer than a pole 
 
 ten feet long. 
 
 Fourteen 
 
 114. One ten and 4 ones are 
 
 How many squares do you see in the figure? 
 
 How many more than 10? How many more 
 than 9? Than 8? Than 7? 
 
 If 5 were taken away, how many would be left? 
 
 Take six away from 14. How many remain? 
 
 Count by twos to 14. !!!!!!! 
 
 How many dots are in each row? How many 
 rows ? 
 
 Two times 7 dots are dots. 
 
 Show that 7 times 2 dots are as many as 2 X 7 dots. 
 
 One-half of 14 dots is dots. 
 
 How many 7's make 14? How many 2's? 
 
 Take 9 splints and 5 splints and show that they are as 
 many as one ten and four ones. 
 
 Write the figures that stand for the number fourteen. 
 
 Which figure stands for the ones? On which side of 
 the 1 must it stand? 
 
86 SCHOOL ARITHMETIC. 
 
 115. Copy and complete: 
 
 9 + 5= 146= 5 + ( ) = 14 2X7 = 
 
 6 + 8= 14 7 = 8 + ( ) == 14 7X2-= 
 
 7 + 7= 14 8= 14 ()= 9 14 -f- 2 = 
 14 5= 14 ,9= 14 ()= 6 14 -v- 7 = 
 
 2 qt. + 1 pt. = - - pt. 3 ga.. + 2 qi. = - - qt. 
 7 bu. + 3 bu. = - $10 + $4 = 
 
 1 ft. +2 in. = - - in. 5 qt. + 3 pt. = pt. 
 
 3 yd. -4- 5 ft. = ft. i doz. + 5 
 
 116. James earned 8 cents on Friday and 6 cents on 
 Saturday. On both days he earned - - cents. 
 
 How much will 6 eggs cost at 14 cents a dozen? 
 
 In 14 there are 3 ? s and - over. 
 
 Make a story for 7 + 7 = 14. 
 
 How many days are there in two weeks? 
 
 How many gloves are 7 pairs of gloves? 
 
 Fourteen months are how many more months than a 
 year ? 
 
 A boy had a ten-cent piece and four pennies. He spent 
 5 cents for peanuts. How much had he left? 
 
 A spider has 8 legs. A spider and a fly together have 
 14 legs. How many legs has a fly? 
 
 Three gallons and 2 quarts of milk are how many quarts? 
 
 How many half -bushels of oats make 7 bushels ? 
 
 If a milkman has 7 qt. of milk, to how many persons 
 can he sell a pint each? 
 
 A man has 14 miles to travel. When he has gone 8 
 miles, how far has he yet to go? 
 
FIFTEEN. 
 
 Fifteen. 
 
 87 
 
 117. One ten and 5 ones, or one ten and 1 five, are - . 
 
 Lay 10 blocks in one row and 5 in another, as in the 
 picture above. Use them to find the missing number in 
 the following: 
 
 15=9+( ). l5=8+(). 15=6+( ). 15=7+( ). 
 15 6=( ). 15 8=( J'). 15 7=( ). 15 9=( ). 
 15=3 X( ). 15=5X( ). 15-HJ==< ). 15-^3=( ). 
 
 How many dots are on the card? What part of them 
 are on the right of the line? On the left of the line? 
 Are 3 fives as many as 5 threes? Show with counters. 
 
 118. This circle is divided into 
 
 equal parts. 
 
 What do you think one of these parts is called? 
 What part of the rectangle is dark? 
 One of the 5 equal parts of anything is called one-fifth 
 
 To find one-fifth of 
 into - - equal parts. 
 
 anything we must divide it 
 
 How many small squares are there in the rectangle? 
 Are the 3 dark squares one of the 5 equal parts of the 
 rectangle? 
 
88 SCHOOL ARITHMETIC. 
 
 Then J of 15 squares is - - squares. 
 
 One-fifth of 5 cents is - - cent. 
 
 One-fifth of 10 feet is - - feet. 
 
 Make 15 dots. Draw a line around i of them. Now 
 draw a line around another fifth of them. 
 
 How many fifths have lines around them? How many 
 fifths have no lines around them? 
 
 How many dots in one fifth? How many in two fifths? 
 
 Then f of 15 dots = - dots. 
 
 119. Copy and complete: 
 
 9+6= 
 
 156= 
 
 7+( )=15. 
 
 3X5: 
 
 7+8= 
 
 157= 
 
 9+( )=15. 
 
 5X3 
 
 1 of 15= 
 
 159= 
 
 15 ( )=10. 
 
 15-^5= 
 
 I of 15= 
 
 158= 
 
 15-( )= 6. 
 
 15-=-3 : 
 
 i of 15= 
 
 J of 15= 
 
 f of 15= 
 
 t of 15 
 
 120. A man has 3 five-dollar bills. How much money 
 has he? 
 
 What two pieces of paper money make $15? What 3 
 pieces ? 
 
 Fifteen eggs are how many more than a dozen? 
 
 Tell a story about 9 boys + 6 girls = 15 children. 
 
 Punch has 8 dimes and Judy 7. Ask a question and 
 answer it. 
 
 Jennie has 5 yd. of cloth for a dress. How many feet 
 long is the cloth? 
 
 Tell a story about 15 6 == 9. 
 
 Stella had 15 jacks. She lost 7 of them. She had 
 
 left. 
 
 Harry may tell all he can about 15. 
 
 Find out at home to-night how many ounces make a 
 pound. 
 
SIXTEEN. 
 
 Sixteen. 
 
 89 
 
 121. One ten and six ones are - . 
 Show with blocks how many 9 and 7 are. 
 How many ones do you see on the card? How many 
 8's? How many 4's? How many 2's? 
 Show with blocks how many 16 7 are. 
 How many times 4 dots make 16 dots? 
 How often does the card contain 8 dots? 
 If the dots were shoes, how many pairs could you take? 
 If they were quarts, how many gallons would you have? 
 What part of the dots is on each side of the line? 
 What part of the 16 dots are large? 
 How many fourths of them are small? 
 Sixteen means six and . 
 
 122. Copy and complete: 
 
 + 7= iof!6= 
 
 8 + 8= 
 10 + 6= 
 
 |- of 16= 
 of 16- 
 
 2X8 
 8X2 
 4X4 
 
 16-^-8 
 16-^-2 
 
 16 ~- 4 
 
 123. Tom had 9 cents and Sam had 7 cents. They 
 both had -- cents. 
 
 They gave ten cents of it for a dime. How many 
 pennies had they left? 
 
 Cora carried 2 gallons of water and Delia carried" 8 
 quarts. How much did both carry? 
 
 We have 4 cows. Each cow gives 4 quarts of milk. 
 They all give - quarts. 
 
90 
 
 SCHOOL ARITHMETIC. 
 
 Mr. Brown had 16 sheep, but one-half of them died. 
 Ask a question and answer it. 
 
 How many wheels have 8 bicycles? 
 
 I have 16 apples. To how many girls can I give two 
 apples each ? 
 
 124. Where have you seen these weights used? 
 Which is the largest weight? The smallest? 
 How many of the smallest are equal to the largest? 
 How many ounces make a pound? 
 
 16 ounces (oz.) make 1 pound (lb.) 
 
 What stands for the word ounce or ounces? For the 
 word pound or pounds? 
 
 How many ounces in ^ of a pound? In J of a pound? 
 
 What part of a pound are 8 ounces? 4 ounces? 
 
 How many ounces in a quarter of a pound of starch? 
 
 How many 4-ounce weights are equal to the 1 -pound 
 weight? How many 2-ounce weights? 
 
 When butter is 16 cents a pound, how much must I 
 pay for 8 ounces? For 4 ounces? For 12 ounces, or f 
 of a pound? 
 
 Seventeen. 
 
 125, Ten and seven are how many? How many more 
 would make 2 tens? 
 
 What does the word seventeen mean? 
 
SEVENTEEN. 
 
 91 
 
 How many dots are on the card? How many on each 
 end of it? 
 
 Nine dots and eight dots are dots. 
 
 If 8 dots were taken off the card, how many would 
 remain? How many if 9 dots were removed? 
 
 Count 12 by twos. What other numbers can you count 
 by twos? Can you count 9 by twos? 
 
 Numbers that can be counted by twos are called even 
 numbers; all others are called odd numbers. 
 
 Did you ever play " Odd or Even" ? How do you play it? 
 
 Is 5 odd or even f 
 
 Name all the odd numbers less than 17. 
 
 Tell at sight what number put with 
 each of the outer numbers will make 17. 
 
 126. Add: 
 9 10 
 
 8 7 
 
 10 
 
 8 
 
 14 
 
 12 
 
 17 
 
 7 
 
 15 
 
 11 
 
 9 
 
 11 
 
 6 
 
 5 
 12 
 
 13 
 4 
 
 3 
 14 
 
 15 
 
 2 
 
 Subtract: 
 17 17 
 8 10 
 
 17 
 9 
 
 16 
 
 16 
 
 9 
 
 16 
 6 
 
 16 
 
 7 
 
 15 
 
 6 
 
 127, Is 9 odd or even? How many 2's in 9? 
 
 y - 
 
 >j 
 
 2 
 
 
 
 - ana - 
 
 - leit over. 
 
 i 
 
 1 ^ 
 
 
 
 
 
 J.O 
 
 14. 
 
 
 
 
 
 17 
 
 A 
 
 
 
 -L t 
 17 
 
 T 
 ft 
 
 
 
92 SCHOOL ARITHMETIC. 
 
 128. Nine cents + eight cents = 1 dime + cents. 
 
 Five yards and 2 feet are how many feet ? - 
 
 My brother is 17 years old. How old was he 8 years 
 
 If sugar is 5^ a pound, how many pounds can you buy 
 with a dime and a nickel? 
 
 A string 17 ft. long was cut in two in the middle. What 
 was the length of each part? Find by measuring. 
 
 How many gallons of oil at 8 cents a gallon can you 
 buy with 17 cents? How many cents left over? 
 
 Eighteen. 
 
 129. Ten and eight, or 1 ten and 8 ones, are - . 
 
 Nine dots and nine dots are how many dots? 
 
 If- nine dots are taken from 18 dots, how many will 
 remain ? 
 
 How many small dots are on the card? How many sixes 
 do you see on it? How many threes? How many nines? 
 
 Find how many twos make eighteen. 
 
 One-half of 18 dots is - - dots. 
 
 One-third of 18 dots is - - dots. 
 
 Two-thirds of 18 dots are - - dots. 
 
 Make dots for the following: 18, 6, 12, 9, J of 18. 
 
 Count to 18 by 2's. By 3's. By 6's. 
 
 Is 18 an even or an odd number? 
 
 How many 2's in 18? How many 3's? How many 6's? 
 
 How many 9's can you take from 18? Then how many 
 9's are in 18? 
 
EIGHTEEN. 
 
 93 
 
 Take 18 sticks and find how many 8's in 18, and how 
 many left over. 
 
 What part of 18 is 9? What part of 18 is 6? 
 
 
 
 '/s 
 
 * 
 
 
 
 
 equal parts. Show 
 
 130. The circle is divided into - 
 me one-sixth (4) of the circle. 
 
 To find 4 of anything we must divide it into equal 
 
 parts. 
 
 Show me 4 of the dots on the card, 
 i of 12 dots = - dots. 
 How many sixths of the dots are large? 
 . f of 12 dots - - dots. 
 
 | of 12 dots - - dots. 
 Is J of the rectangle as much as -f of it? 
 Is \ of 12 dots as many as f of them? 
 Find 4 of 12 dots and compare it with f of them. 
 Which is larger, 4 of 12 or 4 of 12? 
 Show me 4 of 18 blocks. 4 of 18 = 
 What part of 12 is 2? Of 6 is 1? 
 
 131. Copy and complete: 
 
 9 + 9= 9X2= 18^-6= 18 ( ) = 9 
 
 2X9= 18 H- 3 = 18 -*- 9 = 8 + 8 + 2 = 
 
 18 9= 18-^2= 3X6= 6 X ( ) = 18 
 
 10 = 
 4 = 
 
 i of 18 = 
 
 \ of 18 = 
 
 f of 18 
 | of 18 
 
 6 = 
 5 = 
 
 f of 18 = 
 | of 18 = 
 
 1+ i 
 1- 1 
 
94: 
 
 SCHOOL ARITHMETIC. 
 
 132. A boy bought 2 books at 9 cents apiece. They 
 cost him - - cents. 
 
 Barnet put 18 nuts on a fence. A squirrel carried off 
 2 of them each day for days. Then all were gone. 
 
 How many days are 2 weeks and 4 days? 
 
 Four bushels and 2 pecks, or 4f bu., are - - pecks. 
 
 Draw a line 18 in. long. Show that it is - - ft. long. 
 
 Mary sold eggs at a cent apiece. How much did she 
 get for a dozen and a half? 
 
 Find the cost of a gallon of milk at 4^ a quart. 
 
 If 1 orange costs 2 cents, what will 9 oranges cost? 
 
 How many yards in a piece of cloth 18 feet long? 
 
 I want to buy a book for 18 cents. I have a dime. I 
 need cents more. 
 
 Maud has 18 jacks. She gave | of them to Jane. How 
 many had she left? 
 
 How many squares can you make with 18 splints? How 
 many triangles? 
 
 Nineteen. 
 
 133. One ten and 9 ones, or 10 and 9, are - . 
 How many dots are 2X9 dots, and 1 dot? 
 How many dots are 6X3 dots, and 1 dot? 
 Nineteen dots are how many more than 3X6 dots? 
 How many tens in 19? How many ones left over? 
 How many 2's in 19, and how many ones left over? 
 How many 9's in 19, and how many left over? 
 
REVIEW AND DRILL. 95 
 
 Show that 10 is less than .19. 
 
 Nineteen is how many more than 11? 
 Show that 12 and - - are 19. 
 Show that 19 is - - more than 13. 
 To each of the following add the number that will make 
 the sum 19: 8, 11, 7, 9, 15, 17, 16. 
 
 134. Copy and complete: 
 
 10+9=- 9 + 9 + 1- 8 + 8 + 3 = 
 
 199= 2X9 + 1= 2X8 + 3 = 
 
 19 -=-10= 19 -f- 9 = 19-^-8 = 
 
 Review and Drill. 
 135. 
 
 a 
 
 I 
 
 c 
 
 11 + 1 = 
 
 12 + 2 = 
 
 13 + 3 
 
 11 + 3 = 
 
 12 + 4 = 
 
 13 + 5 
 
 11 + 2 = 
 
 12 + 6 = 
 
 13 + 6 
 
 11 + 5 = 
 
 12 + 3 = 
 
 14 + 5 
 
 11 + 4 = 
 
 12 + 5 = 
 
 14 + 4 
 
 11 + 7 = 
 
 12 + 7 = 
 
 14 + 2 
 
 11 + 6 = 
 
 13 + 2 = 
 
 14 + 3 
 
 11 + 8= 13 + 4= 15 + 2 = 
 
 d e f 
 
 15 + 3= 9 + 3= 8 + 9 = 
 15+4= 9 + 5= 9 + 9 = 
 
 16 + 3= 9 + 4= 8 + 5 = 
 
 16 + 2= 9 + 6= 8 + 8 = 
 
 17 + 2= 9 + 7= 8 + 4 = 
 
96 SCHOOL ARITHMETIC. 
 
 9 
 
 o ~~ f~ o 
 
 1 fj 
 
 8 + 8 = 
 7 + 4 = 
 7 + 6 = 
 7 + 5 = 
 7 + 3 = 
 7 + 7 = 
 
 6 
 6 
 6 
 6 
 6 
 5 
 5 
 5 
 
 ^ t 
 
 +2= 5+5= 
 +4= 4+4= 
 +6= 4+2= 
 +3= 4+3= 
 + 5 = 3 + 4 = 
 +4= 3+2= 
 +2= 7+9= 
 +3= 8+7= 
 
 
 
 j 
 
 
 fc 
 
 
 i 
 
 
 m 
 
 
 2 
 
 X 
 
 2 = 
 
 2 
 
 X 8 = 
 
 3 
 
 X 5 = 
 
 5 
 
 X 
 
 3 
 
 2 
 
 X 
 
 3 = 
 
 2 
 
 X 9 = 
 
 3 
 
 X 6 = 
 
 6 
 
 X 
 
 2 
 
 2 
 
 X 
 
 4 = 
 
 2 
 
 X 10 = 
 
 4 
 
 X 2 = 
 
 6 
 
 X 
 
 3 
 
 2 
 
 X 
 
 5 = 
 
 3 
 
 X 2 = 
 
 4 
 
 X 3 = 
 
 7 
 
 X 
 
 2 
 
 2 
 
 X 
 
 6 
 
 3 
 
 X 3 = 
 
 4 
 
 X 4 = 
 
 8 
 
 X 
 
 2 
 
 2 
 
 X 
 
 7 = 
 
 3 
 
 X 4 = 
 
 5 
 
 X 2 = 
 
 9 
 
 X 
 
 2 
 
 
 
 n 
 
 
 
 
 
 P 
 
 
 g 
 
 
 9 
 
 
 
 2 = 
 
 8 
 
 2 = 
 
 7 
 
 o 
 
 10 
 
 
 
 2 
 
 9 
 
 
 
 7 = 
 
 8 
 
 6 = 
 
 7 
 
 o 
 
 10 
 
 
 
 8 
 
 9 
 
 
 
 3 = 
 
 8 
 
 o 
 
 7 
 
 4 = 
 
 10 
 
 
 
 3 
 
 9 
 
 
 
 6 = 
 
 8 
 
 5 = 
 
 6 
 
 2 = 
 
 10 
 
 
 
 7 
 
 9 
 
 
 
 4 = 
 
 8 
 
 4 = 
 
 6 
 
 4 = 
 
 10 
 
 
 
 4 
 
 9 
 
 
 
 O " - - 1 
 
 7 
 
 2 = 
 
 6 
 
 3 = 
 
 10 
 
 
 
 3 
 
 r 
 
 s 
 
 
 i 
 
 
 u 
 
 
 10 
 
 
 
 5 = 
 
 12 
 
 o 
 
 13 
 
 2 = 
 
 14 
 
 
 
 2 
 
 11 
 
 
 
 2 = 
 
 12 
 
 -10 = 
 
 13 
 
 -11 = 
 
 14 
 
 
 
 3 
 
 11 
 
 
 
 9 = 
 
 12 
 
 3 = 
 
 13 
 
 Q 
 
 14 
 
 
 
 4 
 
 11 
 
 
 
 o 
 
 12 
 
 Q 
 
 13 
 
 4 = 
 
 14 
 
 
 
 5 
 
 11 
 
 
 
 o 
 
 12 
 
 4 = 
 
 13 
 
 9 = 
 
 14 
 
 
 
 9 
 
 11 
 
 
 
 4 = 
 
 12 
 
 8 = 
 
 13 
 
 5 = 
 
 14 
 
 
 
 6 
 
 11 
 
 
 
 J-r 
 
 12 
 
 5 = 
 
 13 
 
 8 = 
 
 14 
 
 
 
 8 
 
 11 
 
 
 
 5 = 
 
 12 
 
 Y 
 
 13 
 
 6 = 
 
 14 
 
 
 
 7 
 
 11 
 
 
 
 6 = 
 
 12 
 
 $ = 
 
 13 
 
 - 7- 
 
 14 
 
 
 
 10 
 
REVIEW AND DKILL. 
 
 97 
 
 V 
 
 w 
 
 4- 
 
 Q 
 
 14- 
 
 - 2 
 
 9- 
 
 - 
 
 16- 
 
 - 2 
 
 6- 
 
 -2-= 
 
 18- 
 
 - 2 
 
 8- 
 
 -2 = 
 
 4 - 
 
 - 4 
 
 10- 
 
 -2 = 
 
 
 
 - 4 
 
 12- 
 
 -2 = 
 
 1*2- 
 
 - 4 
 
 
 X 
 
 
 
 
 12- 
 
 - 6=. 
 
 18- 
 
 - 3 
 
 18- 
 
 - 6 = 
 
 10- 
 
 - 5 
 
 6- 
 
 - 3 = 
 
 15- 
 
 - 5 
 
 9- 
 
 - 3 = 
 
 12- 
 
 - 6 
 
 12- 
 
 Q 
 
 18- 
 
 - 6 
 
 15- 
 
 - 3 = 
 
 14- 
 
 - 7 
 
 136. A farmer has 7 Jersey cows and 8 Durham 
 cows. How many cows has he? 
 
 Willie caught 1 trout and Harry caught 9 trout. How 
 many did both catch? 
 
 School begins at 9 o'clock in the morning, and continues 
 3 hours. What time is it when school is dismissed? 
 
 In a game of baseball 9 persons play on each side. How 
 many players are there in the game? 
 
 A table is 6 feet long and 3 feet wide. What is the 
 number of feet around it? 
 
 From a dozen and a half cans of peaches 3 cans were 
 used. How many cans were left? 
 
 A farmer had 19 lambs and sold 7 of them. How many 
 lambs had he left? 
 
 One sash of a window has 2 rows of panes, and 3 panes 
 in a row. How many panes are there in the sash? 
 
 Hunter has 8 rabbits; Jack has half as many. How 
 many rabbits have both together? 
 
 How many legs have 6 three-legged stools? 
 
 From a brood of 19 chickens, 6 were sold, and half a 
 dozen were eaten. How many chickens were left? 
 
 How many times does the sun rise and set in 1 week? 
 
 Divide 18 peaches among 6 girls. How many peaches 
 does each receive? 
 
 *7 
 
98 
 
 9OHOOL ARITHMETIC. 
 
 A plank is 18 inches long. If you saw off a Half foot, 
 how long is the plank then? 
 
 Make a rectangle 5 inches long and 3 inches wide, and 
 divide it into inch squares. How many square inches in 
 the rectangle? 
 
 How many quart bottles will it take to hold 16 pints? 
 
 If you have | of a dollar and spend J, how many fourths 
 have you left? How many quarters? 
 
 Nineteen ounces are how many more ounces than one 
 pound? 
 
 Draw a line 17 inches long. How many more inches long 
 is it than 1 foot? 
 
 How many strokes will a clock make in striking 8 and 9 ? 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 I 
 
 
 
 
 
 3 
 
 
 
 
 
 4 
 
 
 
 
 
 1 
 
 fwe 
 
 nt; 
 
 tn 
 
 F* 
 
 I) 
 
 
 ( 
 
 
 
 
 
 
 
 
 
 
 
 
 137. Ten and ten, or two tens, are . 
 
 How many squares in the upper row? How many 
 rows are there? How many squares in all the rows? 
 
 Then 4 times 5 squares are squares. 
 
 Show that 5 times 4 squares are 20 squares. 
 
 Two tens are as many as fives or fours. 
 
 Find from the card how many twos in twenty. 
 What does the figure mean in the number 20? 
 What figure shows that there are two 10's in twenty? 
 Show that 20 is more than 10. 
 
TWENTY. 99 
 
 Show that 16 is - - less than 20. 
 Show that is 5 less than 20. 
 
 One-half of 20 dots is dots. 
 
 Two dots are found in 20 dots - - times. 
 
 One-fourth of 20 squares is squares. 
 
 Two-fourths of 20 squares are squares. 
 
 Three-fourths of 20 squares are squares. 
 
 138. One-half of anything is one of its two equal parts. 
 
 One-third of anything is one of its equal parts. 
 
 What is meant by i of anything? J? 
 
 Divide 10 blocks into 10 equal parts. How many 
 blocks in each part? 
 
 What is one of the equal parts called? (One-tenth.) 
 
 One- tenth of 10 blocks is block. 
 
 How many ones make one ten? Then one one is what 
 part of one ten? 
 
 Show me one-tenth ( T V) of 20 dots. 
 
 One cent is what part of 10 cents? One is what part 
 of 10? 
 
 Draw a line 10 inches long. Under it draw a line T ^ 
 as long. 
 
 Into how many equal parts is this circle 
 divided? 
 
 What is each part called? 
 
 How many tenths are dark? How many 
 are light? 
 
 T 3 of the circle -f- -^ of the circle = of the 
 
 circle, or the whole circle. 
 
 How many tenths are -fa and ^ ? 
 
 Make two rows of 10 dots each. Draw a ring around 
 j-V of the dots. Draw a ring around | of the 20 dots. 
 
100 SCHOOL ARITHMETIC. 
 
 "Which is more, | of 20 dots or ^ of 20 dots ?'" 
 
 If you take T 3 of anything away, how many tenths 
 remain ? 
 
 One of the ten equal parts of anything is called one-tenth. 
 
 What are 3 of the parts called? Four of the parts? 
 Seven of the parts? 
 
 How many tenths are there in anything? How many 
 halves? Show that J = &. 
 
 One tenth means one out of ten. What does -$ mean ? 
 
 A? W 
 
 How many dimes make a dollar? A dime is what part 
 of a dollar? 
 
 What part of a dollar are 3 dimes? 5 dimes? 
 
 Is one half-dollar as much as 5 dimes? 
 
 Is one j half as much as 5 tenths? 
 
 Twenty things are sometimes called a score. How many 
 things in half a score ? In -^ of a score 2 
 
 139. Complete the process: 
 
 10 + 10 = 
 
 20 10 = 
 
 20 = 10 + 
 
 18+2 = 
 
 20- 2 = 
 
 20 -=18 + 
 
 16+4 = 
 
 20- 4 = 
 
 20 =F 16 + 
 
 17+3 = 
 
 20- 3 = 
 
 20 = 17 + 
 
 15+5 = 
 
 20- 5 = 
 
 20 = 15 + 
 
 14+ 6 = 
 
 20- 6 = 
 
 20 == 14 + 
 
 12+8 = 
 
 20- 8 = 
 
 20 == 12 + 
 
 13+7 = 
 
 20- 7 = 
 
 20 = 13 + 
 
 2X10 = 
 
 20 -f- 10 = 
 
 4 of 20 = 
 
 10 X 2 = 
 
 20^-2 = 
 
 i of 20 = 
 
 4X 5 = 
 
 20-^-5 = 
 
 i of 20 = 
 
 5X4 = 
 
 20 -f- 4 = 
 
 T V of 20 = 
 
TWENTY. 
 
 140. 10 is contained in 20 times and over. 
 
 9 is contained in 20 times and over. 
 
 8 is contained in 20 times and over. 
 
 7 is contained in 20 times and - over. 
 
 6 is contained in 20 times and over. 
 
 5 is contained in 20 times and - - over. 
 
 3 is contained in 20 times and over. 
 
 4 is contained in 20 times and over. 
 
 2 is contained in 20 times and 
 
 141. Count by fives to 20. - fives are 20. 
 Count by twos to 20. twos are 20. 
 Count by fours to 20. fours are 20. 
 
 Count by threes to 18. threes and 2 are 20. 
 
 Count by sixes to 18. sixes and 2 are 20. 
 Count by tens to 10^. tens are 100. 
 
 142. How many shoes will be required to shoe 5 
 horses? 10 men? 
 
 If you had 10 cents and your mother gave you a ten- 
 cent piece, how much money would you have? 
 
 A farmer owns 3 horses, 8 cows, and 9 sheep. How 
 many animals has he? 
 
 If a strip of paper is 5 inches long and 4 inches wide, 
 how many square inches does it contain? 
 
 Two dimes equal how many nickels? 
 
 If 20 bananas were divided equally among 4 girls, how 
 many would each have? 
 
 If a strip of paper contains 20 square inches, and it is 
 5 inches long, how wide is it? 
 
 Marvin had 20 cents and spent i of them for ink, and 
 the rest for paper. What did the paper cost? 
 
102 
 
 SCHOOL ARITHMETIC. 
 
 How many school days in 4 weeks? 
 
 If I cut 5 apples into quarters, to how many children 
 can I give a piece? 
 
 Is 20 odd or even? How much must you add to it to 
 make it odd? 
 
 Take 20 cents and give -^ of them to each of 5 of your 
 classmates. How many have you left ? 
 
 Draw 11 vertical lines 2 inches apart on the blackboard. 
 How far apart are the two outside lines? 
 
 Harry had 20 marbles. He put i of them into one pile, 
 of them into another pile, and the rest in the third pile. 
 How many in each pile? 
 
 Eggs are 10^ a dozen. How many dozen can be bought 
 for 2(#? 
 
 We have found out that X stands for 10. What do you 
 think XX stands for? 
 
 How many years are 3 score years ? 
 
 How old is a man who is 3 score and ten years of age? 
 
 Numbers to 100. 
 
 
 =21. 10+10+5=25. 10+10+10=30. 10+10+10+4=34. 
 
 143. Here t stands for the tens. What does o stand for? 
 Draw squares like these to represent 23, 27, 36, 39. 
 Draw squares to represent 2 + 6 o, 3 + 8 o, 2 / + 2 . 
 
NUMBERS TO 100. 
 
 103 
 
 Complete: 
 
 20 + 1 =21 20 + 8= 25 = 22+50 
 
 20 + 2 = 30 + 1 = 26 = 
 
 20 + 4 30 + 3 = 32 = 
 
 20 + 6 = 30 + 5 = 37 = 
 
 22+6o= 32 + 50= 39 = 
 
 5 t + 3 t = 8 t = 80 6 o + 5 o = llo = 12 + lo, or 11 
 
 J 
 
 10+10+10+10+10+6=56. 
 
 10+10+10+10+3=43. 
 
 144. Draw squares to represent 45, 57, 52, 64, 66. 
 Draw squares to represent 4+6 o, 5 + 8 o, 6 +1 
 
104 
 
 Complete : 
 
 40 + 1 = 41 
 
 40 + 4 = 
 
 50 + = 
 50 + 5 = 
 50 + 9 = 
 60 + 3 = 
 60 + 8 = 
 
 42 = 4 + 2< 
 
 45 = 
 
 47 = 
 
 53 = 
 
 56 = 
 
 58 = 
 
 64 = 
 
 67 = 
 
 SCHOOL ARITHMETIC. 
 
 4 t + 1 o =41 o 41 = 4 t + 1 o 
 
 4 t + 4 o = 44 = 
 
 4 * + 8 o = 48 = 
 5 + Oc= 50 = 
 
 5 t + 5 o = 55 = 
 5 + 9o = 59 = 
 
 6 * + 3 = 63 = 
 Gt + 8o = 68 = 
 
 18 o + 3 o = 21 o = 2 J + 1 o, or 21 
 15 o + 50 = 
 
 30 o + 2 = 
 40 o + 7 = 
 
 60 o + 5 o = 
 
 10+10+10+104-10+10+10+5=75. 
 
 Draw squares to represent 73, 84, 89, 92. 
 Draw squares to represent 7 t + 4 o, 8 + 10 o, 
 
NUMBERS TO 100. 105 
 
 145. Complete : 
 
 70+ 1 = 71 7 + 10 = 7lo 71 = 7* + lo 
 
 80+3= 8 + 3o = 83 = 
 
 80+8= 8 + 80 = 88 = 
 
 90+0= 9 + 00 = 90 = 
 
 90+5=' 9 + 5o = 95 = 
 
 60 + 20= 6+2 = 80 = 
 
 76 = 7 t + 6 o 70 o + 4 o = 74 o = 7 +4o, or 74 
 
 79= 70o+7o = 
 
 81= 80 o+ 5o = 
 
 87= 800 + 100 = 
 
 93= 900+ 3 o = 
 
 96 = 90 o + 10 o = 100 o =10 t, or 100 
 
 1 dime + 5^=15^ 1 1-\- 5 o=15 12^=1 dime + 2$ 
 
 2 dimes + 5^= 2^+50= 
 
 4 dimes + 2^= 4^+2 o= 
 
 5 dimes + 8^= 5^+80= 25^= 
 
 7 dimes + 5j= 7 t+ 50= 38^=- 
 
 8 dimes + 7^= 8 + 7 0= 53^= 
 
 9 dimes + 9^= 9 t-}- 9 o= 81tf= 
 9 dimes +10^= 9 ^+10 o= 98^= 
 
 146. Write and read the numbers to 100. 
 Count backwards from 20 to 0. From 50 to 20. 
 Count by 2's to 50; then backwards to 2. 
 Count by 10's from to 100; then backwards to 0. 
 Count by 10's from 1 to 91. .From 2 to 92. 
 In 25 what does the 2 stand for? The 5? 
 In 33 the figures are alike. Do they mean the same 
 thing? 
 
106 
 
 Complete : 
 
 24=20 
 27 = 
 22 = 
 31 = 
 34 = 
 39 = 
 
 SCHOOL ARITHMETIC. 
 
 46 = 
 
 48 = 
 52 = 
 55 = 
 68 = 
 71 = 
 
 74 
 
 77 
 79 
 
 82 
 85 
 87 
 
 88 
 89 
 67 
 94 
 96 
 99 
 
 24 + 3= 32 + 4 = 
 
 147. Add: 
 
 24 
 3 
 
 32 
 4 
 
 24 
 4 
 
 32 
 
 5 
 
 25 3 = 
 
 21 
 
 33 
 4 
 
 37 4 = 
 
 33 
 5 
 
 34 
 
 2 
 
 26 
 3 
 
 35 
 3 
 
 46 
 
 2 
 
 44 
 4 
 
 51 
 
 7 
 
 62 
 6 
 
 65 
 4 
 
 52 
 7 
 
 74 
 3 
 
 83 
 6 
 
 77 
 2 
 
 86 
 2 
 
 94 
 5 
 
NUMBERS TO 100. 
 
 107 
 
 Subtract: 
 
 25 
 3 
 
 37 
 
 4 
 
 26 
 
 2 
 
 47 
 4 
 
 36 
 
 2 
 
 35 
 3 
 
 19 
 4 
 
 29 
 4 
 
 39 
 
 4 
 
 49 
 4 
 
 59 
 4 
 
 69 
 4 
 
 79 
 4 
 
 28 
 5 
 
 38 
 5 
 
 48 
 5 
 
 57 
 3 
 
 67 
 3 
 
 77 
 3 
 
 87 
 3 
 
 Name results quickly: 
 
 21 + 1 = 
 
 21 + 2 = 
 
 21 + 3 
 
 81 + 1 = 
 
 31 + 2 = 
 
 31 + 3 
 
 41 + 1 = 
 
 51 + 2 = 
 
 41 + 3 
 
 51 + 1 = 
 
 71 + 2 = 
 
 51 + 3 
 
 71 + 1 = 
 
 22 + 2 = 
 
 22 + 3 
 
 91 + 1 = 
 
 32 + 2 = 
 
 32 + 3 
 
 61 + 1 = 
 
 42 + 2 = 
 
 42 + 3 
 
 81 + 1 = 
 
 52 + 2 = 
 
 52 + 3 
 
 21 + 4 
 
 31 + 4 
 
 41 + 4 
 
 51 + 4 
 
 22 + 4 
 
 32 + 4 
 
 42 + 4 
 
 52 + 4 
 
 If you add 1 to numbers ending in 1 ? with what figure 
 does the sum end? 
 
 If you add 2 to numbers ending in 1, with what figure 
 does the sum end? 
 
 If you add 2 to numbers ending in 2, with what figure 
 does the sum end? ' 
 
 If you add 3 to numbers ending in 1 ? with what figure 
 does the sum end? 
 
 If you add 3 to numbers ending in 2, with what figure 
 does the sum end? 
 
108 SCHOOL ARITHMETIC. 
 
 
 
 If you add 4 to numbers ending in 2; with what figure 
 does the sum end? 
 
 If you add 4 to numbers ending in 3, with what figure 
 does the sum end? 
 
 When you increase 31 by 2 ? do you add 2 to the 1 or 
 to the 3? 
 
 21 + 5 = 
 
 21 + 6 = 
 
 21 + 7 = 
 
 21+8 = 
 
 31 + 5 = 
 
 31 + 6 = 
 
 31 + 7 = 
 
 31+8 = 
 
 41 + 5 = 
 
 41 + 6 = 
 
 41 + 7 = 
 
 51+8 = 
 
 51 + 5 = 
 
 51 + 6 = 
 
 51 + 7 = 
 
 71+8 = 
 
 22 + 5 = 
 
 22 + 6 = 
 
 22 + 7 = 
 
 73 + 6 = 
 
 32 + 5 = 
 
 32 + 6 = 
 
 32 + 7 = 
 
 84 + 5 = 
 
 42 + 5 = 
 
 42 + 6 = 
 
 42 + 7 = 
 
 92+7 = 
 
 52 + 5 = 
 
 52 + 6 = 
 
 52 + 7 = 
 
 65 + 3 = 
 
 If you subtract 1 from numbers ending in 2, with what 
 figure does each answer end? 
 
 If you subtract 1 from numbers ending in 3, with what 
 figure does each answer end? 
 
 Add 3 to numbers ending in 5. What is the ending 
 figure ? 
 
 Subtract 5 from numbers ending in 8. What is the 
 ending figure? 
 
 Find the value of : 
 
 24- 
 
 1 
 
 26 
 
 -3 
 
 87 
 
 4 
 
 49 
 
 7 
 
 16 
 
 5 
 
 34- 
 
 1 
 
 46 
 
 -3 
 
 18 
 
 5 
 
 79 
 
 -7 
 
 26 
 
 -5 
 
 74- 
 
 1 
 
 86 
 
 -3 
 
 28 
 
 5 
 
 88 
 
 -6 
 
 66 
 
 5 
 
 15- 
 
 2 
 
 17 
 
 -3 
 
 48 
 
 5 
 
 58 
 
 -6 
 
 18 
 
 8 
 
 25 
 
 2 
 
 27 
 
 -3 
 
 19 
 
 -6 
 
 39 
 
 8 
 
 28 
 
 g 
 
 35- 
 
 2 
 
 57 
 
 -3 
 
 29 
 
 -6 
 
 28 
 
 -3 
 
 49 
 
 9 
 
 65- 
 
 2 
 
 77 
 
 -4 
 
 39 
 
 -6 
 
 47 
 
 -4 
 
 86 
 
 -6 
 
 16 
 
 3 
 
 97 
 
 4 
 
 89 
 
 7 
 
 56 
 
 5 
 
 99 
 
 7 
 
ADDITION AND SUBTRACTION. 
 
 109 
 
 5 
 
 15 
 
 25 
 
 35 
 
 2 
 
 45 
 
 55 
 
 65 
 
 75 
 
 6 
 
 16 
 
 26 
 
 36 
 
 3 
 
 46 
 
 56 
 
 66 
 
 76 
 
 4 
 
 14 
 
 24 
 
 34 
 
 4 
 
 44 
 
 54 
 
 64 
 
 74 
 
 Add numbers in center of each square to each of the 
 other numbers. Subtract central number from each of the 
 others. 
 
 Addition and Subtraction. 
 
 20 + 15 
 
 14 + 22 
 
 31 + 26 
 
 148. If we put these splints all together, how many 
 loose splints will we have? How many bundles, or tens? 
 
 20 = 2 t + o 
 15 = 1 * + 5 o 
 
 = 3 + 50 
 
 31 = 
 
 Four ones and 2 ones are 6 ones. One ten 
 and 2 tens are 3 tens. Where is the 6 
 written? The 3? Which then is the ones' 
 place? The tens' place? 
 
 No ones and 5 ones are ones. Two 
 
 tens and 1 ten are tens. Show me the 
 
 5 ones in the picture. The 2 tens. The 1 
 ten. The 3 tens. Which do we add first 
 the ones or the tensf 
 
 Show me the 6 ones in the picture. The 
 7 ones. The 3 tens. The 2 tens. The 5 tens. 
 
 57 = 
 
HO SCHOOL ARITHMETIC. 
 
 149. Add: 
 
 13 12 20 16 21 10 15 23 
 24 13 11 22 15 12 23 14 
 
 24 27 18 25 32 30 26 34 
 
 14 31 31 42 24 10 32 33 
 
 43 41 20 51 62 75 17 54 
 
 26 28 40 31 25 23 82 35 
 
 64 45 17 50 73 69 40 26 
 
 23 53 42 40 16 20 50 72 
 
 150. Find the value of: 
 
 32 + 26 
 
 12 + 14 
 
 34 + 25 
 
 15 + 10 
 
 54+15 
 
 36 + 23 
 
 17 + 50 
 
 25 + 10 
 
 67 + 21 
 
 60 + 15 
 
 24 + 34 
 
 35 + 10 
 
 23 + 70 
 
 54 + 33 
 
 31 + 51 
 
 12 + 12 
 
 42 + 27 
 
 62 + 17 
 
 63 + 25 
 
 24 + 12 
 
 36 + 12 
 
 41 + 24 
 
 56 + 42 
 
 36 + 12 
 
 11 + 11 
 
 70 + 16 
 
 40 + 21 
 
 22 + 11 
 
 40 + 40 
 
 50 + 31 
 
 24+ 12 
 
 33 + 11 
 
 A boy has 30 hens and 12 roosters. How many chickens 
 has he? 
 
 A man paid a barber 25^ for a hair-cut and 10^ for a 
 shave. For both he paid #. 
 
 A farmer drove 14 miles to town and then drove home. 
 How far did he drive? 
 
 Helen's papa gave her 50f5 and her marnma gave her 
 a quarter. She then had cents. 
 
ADDITION AND SUBTRACTION. 
 
 Ill 
 
 There are 24 hours in a day. In two days there are 
 hours. 
 
 There were 20 cents in a box, when George put in 14 
 cents, and Ada 5 cents. How many cents were in the 
 box then? 
 
 How many days in May and June together? 
 
 There are 45 pupils in one school and 42 in another. 
 In both schools there are - pupils. 
 
 Hallie's book has 23 pages more than there are in Odie's. 
 There are 42 pages in Odie's book. How many pages are 
 there in Hallie's book? 
 
 There are 33 frogs in one pond, and 24 in another. How 
 many are there in both? 
 
 25 5 = 
 
 36 4 = 
 
 151. Here are 24 splints (2 tens and 4 ones). Take 
 4 away. How many are left? 
 
 Did you take the 4 from the loose splints (the ones) 
 or from the tens? How many ones were left? 
 
 24 = 2 t + 4 o 
 4= 4o 
 
 = 2^ + 50 
 = 5o 
 
 20 = 2 +00 20 2 - 
 
 Show with splints how many 16 6 are. 
 Draw squares to represent 18 8. 
 
112 
 
 SCHOOL ARITHMETIC. 
 
 Show me 3 tens and 5 ones with splints. Take 3 away 
 and tell me what you have left. 
 
 From what did you take the 3 splints? How many 
 ones were left? How many tens? 
 
 3= 3o 
 
 32 = 3 t + 2 o 
 
 4:= 
 
 4:0 
 
 Show with splints how many 17 4 are. 
 Draw squares to represent 24 3. 
 
 152. Subtract: 
 
 16 
 
 26 
 
 36 
 
 46 
 
 18 
 
 28 
 
 38 
 
 48 
 
 4 
 
 4 
 
 4 
 
 4 
 
 5 
 
 5 
 
 5 
 
 5 
 
 18 
 
 27 
 
 26 
 
 37 
 
 49 
 
 68 
 
 75 
 
 89 
 
 8 
 
 3 
 
 2 
 
 4 
 
 7 
 
 3 
 
 5 
 
 a 
 
 36 12 = 24. 
 
 153. Here are 36 splints. How many tens? How 
 many ones? 
 
 Take away 12 splints (2 ones and 1 ten). 
 
ADDITION AND SUBTRACTION. 113 
 
 How many ones are left? How many tens? How many 
 splints ? 
 
 Two ones from 6 ones leaves ones. One ten from 3 tens 
 
 leaves tens. Two tens and 4 ones are . Which do 
 
 24- we subtract first the ones or the tenst 
 
 When 12 is subtracted from 36, what is the remainder? 
 Show me the squares that represent it. 
 
 Take 25 splints (2 tens and 5 ones.) Take away 13 
 splints (1 ten and 3 ones). How many ones remain? How 
 many tens? How many splints? 25 13 = 
 
 Draw squares to represent 25 10. 
 
 154. Subtract: 
 
 13 16 26 34 45 24 27 30 
 2 4 14 14 12 12 15 10 
 
 
 37 44 56 63 58 76 69 75 
 
 14 12 24 21 33 25 36 50 
 
 86 93 77 68 84 50 95 98 
 41 21 34 58 62 30 70 23 
 
 80 72 97 48 59 76 81 99 
 60 52 60 18 21 41 31 44 
 
114 SCHOOL ARITHMETIC. 
 
 23 
 
 42 4 ones, 2 ones, and 3 ones are ones. 
 
 14. I ten, 4 tens, and 2 tens are tens. 
 
 The sum is tens and ones, or ." 
 
 Find the sum: 
 
 12 14 11 20 30 25 13 21 
 24 31 42 45 27 40 35 16 
 51 23 45 13 32 14 40 51 
 
 23 27 18 25 32 30 26 34 
 31 42 54 26 28 20 17 64 
 
 24 30 21 11 31 13 2 10 
 
 Jane had 3 dimes and a nickel. She gave a dime and a 
 nickel for a slate. How much money had she left ? 
 
 William earned 45 cents on Friday and 30 cents on 
 Saturday. On both days he earned cents. 
 
 There are 24 hours in a day. If you work 10 hours, 
 how many hours do you have for rest? 
 
 If you cut 12 feet from a fish line 36 feet long, how 
 many feet of line will be left? 
 
 This week there are 69 pupils in school; last week there 
 were 48. How many new pupils have come this week? 
 
 Eobert had 40 cents, Mack had 30 cents, and Clyde 
 had 10 cents HOAV many more cents did the three boys 
 need to make a dollar? 
 
 George has 14 marbles and Tom has 10 more. They 
 both have marbles? 
 
 The white hen has 15 chicks, and the black hen has 5 
 less. They both have chicks. 
 
 John had a knife worth 45 cents, which he traded to 
 Walter for his knife and 2 nickels. What was Walter's 
 knife worth? 
 
NUMBERS TO 30. 
 
 115 
 
 Numbers to 30. 
 
 33333333 
 
 156. What is the name of the number made up of 2 
 tens and 1? 
 
 2 tens and 2? 2 tens and 3? 2 tens and 4? 2 tens 
 and 5? 2 tens and 6? 2 tens and 7? 2 tens and 8? 2 
 tens and 9? 
 
 How many squares in the rectangle? How many 
 threes? Then 8 threes are . 
 
 How many squares in the upper row? How many 
 rows? Then 3X8 squares = squares. 
 
 Show that 8X3 squares = 3X8 squares. 
 
 The dark row is what part of the rectangle? One part 
 out of 8 parts is called one . 
 
 Show how many eighths of the rectangle make J of it. 
 
 J of 24 squares = - - squares, 
 f- of 24 squares = - squares. 
 
 i of 24 squares = squares. 
 
 \ of the rectangle = - squares. 
 
 The upper row is what part of the rectangle? 
 
 of 24 squares = 
 of 24 squares = 
 
 How many light squares are there? 
 make 21? How many 7's? 
 
 squares, 
 squares. 
 
 How many 3's 
 
 \ of 21 squares = - - squares, 
 f of 21 squares = squares. 
 
116 SCHOOL ARITHMETIC. 
 
 Make 4 dots six times. How many dots have you? 
 
 How many 4's make 24? 
 
 Arrange 5 rows of 5 dots each in square, 
 
 as in the number picture at the left. Tell 
 
 how many 5's in 25. 
 
 Count by 5's to 25. 5 X 5 = . 
 Make 3 dots 9 times. How many 
 
 dots have you? How many 3's make 
 27? How many 9' s? 
 
 Show by the picture at the right that 
 4X7 dots ==7X4 dots. 
 
 How many 4's in 28 ? How many 7's in 28 ? 
 
 Count by 3's to 30. How many 3's make 30? 
 
 156. Complete and memorize: 
 
 1X3 = 3. 3X1 = 3. 
 
 2X3= 3X2 = 
 
 3X3= 3X3 = 
 
 4X3= 3X4 = 
 
 5X3= 3X5 = 
 
 6X3= 3X6 = 
 
 7X3= 3X7 = 
 
 8X3= 3 X 8 = 
 
 9X3= 3X9 = 
 
 10 X 3 = 3 X 10 = 
 
 157. 3 squares are found in 18 squares - - times. 
 3 squares are found in 24 squares - - times. 
 3 squares are found in 30 squares - - times. 
 3 squares are found in 21 squares - times. 
 
 What added to 2 tens makes 22? 23? 26? 29? 
 Find 1 of 22 splints. J of 22 = - . 
 How many elevens make 22? 
 Find how many 12's make 24? 
 
NUMBERS TO 30. 
 
 158. Find the value of: 
 
 117 
 
 9- 
 
 -3 
 
 30- 
 
 -3 
 
 20- 
 
 -2 
 
 15- 
 
 -3 
 
 27- 
 
 -3 
 
 24- 
 
 -2 
 
 12- 
 
 - 3 
 
 12- 
 
 - 2 
 
 22- 
 
 -2 
 
 18- 
 
 -3 
 
 18- 
 
 -2 
 
 20- 
 
 -3 
 
 24- 
 
 -3 
 
 16- 
 
 -2 
 
 16- 
 
 -3 
 
 21- 
 
 -3 
 
 14- 
 
 -2 
 
 22- 
 
 -3 
 
 20 
 40 
 
 60 
 50 
 30 
 
 80 
 
 10 
 10 
 10 
 10 
 10 
 10 
 
 4 / 
 4> 
 5> 
 
 6> 
 91 
 
 ^ D - 
 
 <7 = 
 
 25-4- 
 
 28- 
 
 OPC 
 
 - D 
 
 -7 = 
 
 t oi 
 iof 
 
 4 of 
 
 iof 
 -1-of 
 iof 
 
 4nf 
 
 Zl 
 
 24 = 
 
 O'T 
 
 zo 
 28 
 27 
 26 
 29 
 30 
 9^ 
 
 10 
 
 = 20 
 01 
 
 T - 
 
 j 
 
 1 
 
 f b 
 
 z/b 
 
 OA 
 
 5 
 
 A 
 
 A ( - 
 O/i 
 
 oo 
 
 i 
 4_ 
 
 4: 
 
 Ij 
 
 Zi* 
 00 
 
 
 ^ 
 
 OQ - 
 
 01 
 
 1 
 J_ 
 
 zi 
 
 C)A 
 
 8- 
 
 ZiO 
 C)A 
 
 
 4O 
 
 ore 
 
 on 
 
 1 ~ 
 4^ 
 
 Zl 1 ! 
 
 9ft 
 
 K 
 
 A* 
 
 9ft 
 
 \ 
 
 ^it) 
 
 94- 
 
 19 
 
 1 
 4-. 
 
 159. Find the cost of 10 pints of milk at 3^ a pint. 
 
 A boy walks 3 miles a day. In 7 days he walks 
 
 miles. 
 
 A man who had 24 bushels of potatoes sold J of them. 
 How many had he left? 
 
 Mr. Jones had 27 sheep but 3 of them died. He then 
 had sheep left. 
 
 What will 2 dozen eggs cost at a cent apiece? 
 
 How many ounces in i of a pound? In | of a pound? 
 
 A blacksmith has 24 horseshoes. He can shoe 
 
 horses with them. 
 
 With 25 cents I can buy - - 3-cent stamps, and I shall 
 have left. 
 
 A man had $30. He gave T V of it for a pair of shoes. 
 Find the cost of the shoes. 
 
118 
 
 SCHOOL ARITHMETIC. 
 
 A room is 27 feet long. How many yards long is it? 
 
 Divide 21 apples equally among 3 boys. How many 
 apples will each boy have? 
 
 If you have 25 oranges, how many times can you give 
 away oranges if you give 5 each time? 
 
 If it takes 4 men 7 days to dig a certain ditch, how long 
 will it take 1 man to dig the ditch? 
 
 How many weeks are there in 28 days? 
 
 If you sleep 8 hours every day, what part of the whole 
 day do you sleep? In 1 day there are - - hours. 
 
 How many days has February? When a week of this 
 month has passed, how many days of it will be left? 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 How many squares in the upper row of this rectangle? 
 How many rows? 
 
 3X7 squares = - - squares. 
 
 Draw a rectangle 7 inches long and 3 inches wide. Draw 
 lines to divide it into square inches. 
 
 How many sq. in. in 1 row? How many rows? 
 3 X 7 sq. in. = sq. in. 
 
 Find how many square inches in each of the following: 
 
 A square, 5 inches on a side. 
 A rectangle, 6 inches by 4 inches. 
 A rectangle, 7 inches by 4 inches. 
 A rectangle, 10 inches by 3 inches. 
 
NUMBERS TO 30. 119 
 
 160. In this picture the line jib is a vertical line. 
 Which other lines are vertical? 
 
 The line mn is a horizontal line. Point out the other 
 horizontal lines. 
 
 Draw on the blackboard a square 3 feet on each side. 
 Draw two horizontal lines to divide it into 3 equal parts. 
 
 Then draw two vertical lines to divide it into 9 equal 
 parts. How long is each of the 9 parts? How wide? 
 
 What is the shape of each part? 
 
 A square that is a foot on each side is called a square 
 foot (sq. ft.). 
 
 How many square feet are there in your large square? 
 
 Measure the large square with the yardstick. What is 
 the length in yards? The width? 
 
 A square that is a yard on each side is called a square 
 yard (sq. yd.). 
 
 Kow who can tell how many square feet in a square 
 yard? 
 
 In 3 square yards there are square feet. 
 
 A rug is 5 ft. square. How many square feet in it? 
 
 A strip of carpet is 9 yards long and 1 yard wide. It 
 contains - - square yards. 
 
 There are 4 strips of carpet on our bedroom. Each 
 strip is 5 yards long and a yard wide. How many square 
 yards of carpet are there? 
 
120 
 
 SCHOOL ARITHMETIC. 
 
 Numbers to 40. 
 
 444444:4:44:4 
 
 161. What is the name of the number made up of 3 
 tens and 1? 3 tens and 2? 3 tens and 3? 
 
 Head the numbers: 34; 35; 36; 37; 38; 39. 
 In 5 rows of 6 dots each there are dots. 
 
 5X6 = 
 
 6 X 5 = 
 
 30 H- 5 = 
 dots. 
 
 In 5 rows of 7 dots each there are 
 
 5 times 7 are - . 7 times 5 are - . 
 
 Show by the dots at the right how many 7's in 35. How 
 many 5's in 35? 
 
 How many squares in this rectangle? How many tens? 
 How many fours? 
 
 Show that 4 X 10 squares = 10 X 4 squares. 
 
 The upper row is what part of the rectangle? Then 
 1 of 40 squares is squares. 
 
 The left-hand column is what part of the rectangle? 
 then -^ of 40 squares is squares. 
 
 162. How many squares are there in 7 columns ? Then 
 7X4 squares are - - squares. 
 
 Make 4 rows of 7 dots each. How many dots? 
 
 How many 4 ? s make 28? How many 7's? 
 
 Draw a ring around i of the dots. J of 28 = . 
 
NUMBERS TO 40. 121 
 
 163. How many squares are there in 8 columns? Then 
 8X4 are - - squares. 
 
 Here are 32 blocks. Give me i of them, i of 32 = . 
 
 Now divide these 32 blocks into 4 equal parts. How 
 many in each part? i of 32 = . 
 
 164. How many squares in 1 column ? How many 
 columns are light? How many squares are light? 
 
 9X4 squares = - squares. 9X4= . 
 
 Divide 36 splints into 4 equal piles. How many splints 
 in each pile? 
 
 36 splints -r- 4 = - - splints. 
 
 Separate 36 splints into 9 equal piles. How many 
 splints in each pile? 
 
 36 splints -T- 9 = splints. 
 
 Lay 3.6 blocks in 3 equal rows. How many 3's make 
 36? How many 12's? 
 
 Make a square of dots, having six dots on each side. 
 
 In 6 rows of 6 dots each there are dots. 
 
 Count by 4's to 36. Count by 6's to 36. 
 Count by 4's to 40. How many 4's make 40? 
 
 165. Complete and memorize: 
 
 1X4 = 4. 4X1 = 4. 
 
 2X4= 4X 2 = 
 
 3X4= .4X3 = 
 
 4X4= 4X 4 = 
 
 5 X4= 4X5 = 
 
 6X4= 4X6 = 
 
 7X4 = 4X 7 = 
 
 8 X4= 4X8 = 
 
 9X4= 4X9 = 
 
 10X4= 4X10 = 
 
122 
 
 SCHOOL AEITHMETIC. 
 
 times, 
 times, 
 times, 
 times. 
 
 166. 4 squares are contained in 24 squares - 
 4 squares are contained in 32 squares - 
 4 squares are contained in 28 squares 
 4 squares are contained in 36 squares - 
 
 Show by dots how many 3's make 33. How many ll's? 
 
 1 of 33 dots - dots. 
 What added to 3 tens makes 34? 37? 
 
 Count by 3's from to 36, then backwards to 3. 
 
 Count by 4's from to 40, then backwards to 4. 
 
 Count by 3's from 1 to 37, then backwards to 1. 
 
 Count by 4's from 1 to 41, then backwards to 1. 
 
 Count by 4's from 2 to 38, then backwards to 2. 
 
 167. Find the value of: 
 
 8- 
 
 -4 
 
 32- 
 
 -4 
 
 28- 
 
 -2 
 
 30-^3 
 
 16- 
 
 -4 
 
 36- 
 
 -4 
 
 26- 
 
 -2 
 
 40-^2 
 
 12- 
 
 -4 
 
 40- 
 
 -4 
 
 34- 
 
 -2 
 
 iof40 
 
 20- 
 
 -4 
 
 32- 
 
 -2 
 
 24- 
 
 -2 
 
 4 of 36 
 
 28- 
 
 -4 
 
 36- 
 
 -2 
 
 33- 
 
 -3 
 
 i of 40 
 
 24- 
 
 -4 
 
 30- 
 
 -2 
 
 36- 
 
 -3 
 
 iof 36 
 
 5 X 6 30 6 of 30 = 37 ( ) X 4 + 
 
 5X7 32 8 i of 30 81 = ( ) X ,-+ 
 
 6X6 35 7 Jof35 34 ( ) X 4 + 
 
 5X5 36 9 iof36 38 ( ) X 4 + 
 
 168. Our hens lay 4 eggs a day. How many will they 
 lay in 10 days? 
 
 How many quarts in 6 gal. ? In 9 gal. ? 
 
 How many months in 2 yr.? In 3 yr.? In \ of a year? 
 
 I have 4 rows of peach trees, 8 in each row. How many 
 trees have I? 
 
 Mr. Wilson has 11 barrels of apples, 3 bushels in each 
 barrel. He has bushels of apples. 
 
NUMBERS TO 50. 123 
 
 In 35 days there are - - weeks. 
 
 How many cents are 6 five-cent pieces? 
 
 How many eggs are there in 3 dozen eggs? 
 
 From the 8th to the 29th of May there are - - days, 
 or - weeks. 
 
 How many inches long is the yard-stick? 
 
 A line is 3 feet 2 inches long. How many inches is it? 
 
 John took 3 6. pecks of potatoes to the store. How many 
 bushels was that? 
 
 How many 5-cent stamps can you buy for 30 cents? 
 
 A farmer has 32 horses. How many 4-horse teams can 
 he form? 
 
 At 5 cents a ride, how many street-car rides can be 
 taken for 30 cents? 
 
 Mr. Henry gave 30 cents to his children. Each child 
 got a dime. How many children has he? 
 
 A bushel of oats weighs 32 pounds. How much does 
 a peck weigh? 
 
 Eight quarts make a peck. How many quarts in a 
 bushel? 4 X 8 qt. = - qt. 
 
 Numbers to 50. 
 
 169. How many dots do you see here? How many 
 fives? 
 
 10 X 5 dots = dots. 
 
 5 X 10 dots = dots. 
 
 Find from the picture how many 5 times 5 dots are. 
 6 times 5 dots. 8 times 5 dots. 7 times 5 dots. 9 times 
 5 dots. 
 
 Count by 5's from 5 to 50, then backwards to 5. 
 
124 
 
 SCHOOL ARITHMETIC. 
 
 Complete and memorize: 
 
 1 five =5. 
 
 2 fives = 
 
 3 fives = 
 
 4 fives = 
 
 5 fives = 
 
 6 fives = 
 
 7 fives = 
 
 8 fives = 
 
 9 fives = 
 10 fives = 
 
 !Find the value of: 
 
 4X5 + 5 5X4+6 
 
 5X5 + 3 7X4 + 2 
 
 7X5 + 1 8X3 + 5 
 
 8X5 + 2 9X4 + 2 
 
 5 blocks are conl 
 blocks. 
 
 5 blocks are conl 
 blocks. 
 
 5 pegs are contained in 30 
 pegs. 
 
 5 inches are conta 
 
 5 is contained in 5 
 
 5 is contained in 10 
 
 5 is contained in 20 
 
 5 is contained in 25 
 
 5 is contained in 40 
 
 5 is contained in 50 
 
 5 is contained in 45 
 
 Point out one of the 5 equal parts of 50 dots. 
 
 1 X5 = 5. 
 
 5X 1 = 5. 
 
 2X5 = 
 
 5X -2=*= 
 
 3X5 = 
 
 5X3 = 
 
 4X5 = 
 
 5 X 4 = 
 
 5X5 = 
 
 5X5 = 
 
 6X5 = 
 
 5X6 = 
 
 7X5 = 
 
 5X 7 = 
 
 8 X 5 = 
 
 5X8 = 
 
 9X5 = 
 
 5X 9 = 
 
 10 X 5 = 
 
 5 X 10 = 
 
 4 of 24 i 
 
 
 1 P C\f\ 
 
 
 t oi 20 
 
 
 f of 20 
 
 
 4 of 21 8 
 
 
 
 
 
 
 
 y times 5 
 
 
 
 
 id in 15 6 
 
 
 
 
 
 
 J r\ * 
 
 
 id m 25 
 
 
 8 
 
 
 
 A 
 
 
 in ^fl 
 
 
 111 OU 
 
 
 
 
 in 10 inches 
 
 i 
 
 one time. 
 
 5 5 = . 
 
 , 
 
 
 - times. 
 
 
 times. 
 
 
 , 
 
 OK K - 
 
 
 
 times. 
 
 KA K 
 
 
 Ov > - ' 
 
 A& Z : 
 
NUMBERS TO 50. 
 
 125 
 
 171. Is i of 50 dots the same as 50 dots -f- 5 ? Prove it. 
 How much is i of 25 cents? | of 25 cents? 
 
 How many dots in each row of dots at the left? 
 
 How many rows are there? 
 
 In 6 rows of 7 dots each there are dots. 
 
 i /\ . O /\ i . 
 
 Add to 42 by 6's. How many 6's in 42? 
 Add to 42 by 7's. How many 7's in 42? 
 
 In 6 rows of 8 dots each there are dots. 
 
 By aid of the middle picture, complete: 
 6X8= .8X6= . 48-^6= . 48-f-8= 
 
 In a square made of dots, 7 dots on each side, 
 are dots. 
 
 7X7= . 
 172. Copy and complete: 
 
 there 
 
 50.-T- 5 = 
 30-^-5 = 
 40-^5 = 
 20 -=-5 = 
 
 25 -r- 5 = 
 45 -i- 5 = 
 
 40 -f- 8 = 
 45-:-9 = 
 40 -=-4 = 
 48-^-6 = 
 
 35 5 = 
 15 5 = 
 17 5 = 
 21 5 = 
 
 28 5 = 
 32 5 = 
 
 6X7 = 
 7X 7 = 
 8X5 = 
 4X 9 = 
 
 "t7 . 4 - . 
 
 50 10 = -jV of 50 = 
 
 30- 
 
 -10 = 
 
 ^ of 50 
 
 40- 
 
 -10 = 
 
 | of 50 = 
 
 20- 
 
 -10 = 
 
 ^ of 50 = 
 
 25- 
 
 -10 = 
 
 i of 50 = 
 
 45- 
 
 -10 = 
 
 | of 50 = 
 
 42- 
 
 -7 = 
 
 6X8 = 
 
 42- 
 
 -6 = 
 
 7X 6 = 
 
 48- 
 
 -8 = 
 
 4X10 = 
 
 49- 
 
 -7 = 
 
 41-J- 5 
 
126 
 
 SCHOOL ARITHMETIC. 
 
 173. How many cents are 6 nickels worth? 
 
 Our cow gives 10 quarts of milk a day. In 5 days she 
 gives quarts. 
 
 How many flags at 5 cents apiece can I buy for 17 cents? 
 How many cents shall I have left? 
 
 For 17 cents I can buy - - flags. I shall have 
 
 cents left. 
 
 How many 5-cent stamps can I buy for 30^? Draw 
 the picture. 
 
 Forty pecks of onions are how many bushels? 
 A house is 12 yards long. It is - - feet long. 
 At 6 dollars a ton, how many tons of coal can be bought 
 for 42 dollars? 
 
 What will 7 yards of cloth cost at 7 cents a yard? 
 A pansy has five petals. How many petals do 9 pansies 
 have? 
 
 How many times can a 5-inch line be measured off on 
 a line 40 inches long? 
 
 Ben had 30 cents and gave J of it for candy. How much 
 money had he left? Show by drawing. 
 
 What are 3 dozen eggs worth at 1 cent apiece? 
 
 What will a pound and a half of butter cost at 16 cents 
 a pound? 
 
 Draw a rectangle 10 inches long and 4 inches wide. 
 Divide it into square inches. How many are there? 
 
 How many rows are there running lengthwise? 
 
 How many inch squares in each row? 
 
 How many square inches, then, are 4 times 10 square 
 inches ? 
 
ADDITION AND SUBTRACTION. 
 
 127 
 
 Find the number of square inches in the following: 
 
 A square, measuring 7 inches on a side. 
 A rectangle, 10 inches by 5 inches. 
 A rectangle, 10 inches by 4 inches. 
 A rectangle, 9 inches by 5 inches. 
 
 9 square feet make 1 square yard. How many square 
 yards are there in 45 sq. ft.? 
 
 Addition and Subtraction. 
 
 1 -f- 90 + 1 o = 2* -f Oo 
 19 + 1 = 20 
 
 174. Take 19 splints. Make a bundle of 10. How 
 many do you need to make another ten? 
 
 19 = It 
 1 = 
 
 lo 
 
 29 = 2 t 
 1 = 
 
 9 o 
 lo 
 
 20 = 2 + o 30 = 3 + o 
 
 Show with splints how many 39 and 1 are. 49 and 1. 
 Add: 
 
 49 
 
 1 
 
 59 
 1 
 
 79 
 1 
 
 89 
 1 
 
 69 
 1 
 
 99 
 1 
 
 How many splints must you put with 18 to make 2 tens? 
 With 28 to make 3 tens? 
 
 18 = 
 
 2 = 
 
 20 
 
 28 = 2^ + 80 
 2 = 20 
 
128 
 
 SCHOOL ARITHMETIC. 
 
 Show with splints how many 38 and 2 are. 48 and 2. 
 Add: 
 
 38 48 78 58 88 68 ' 98 
 
 2222222 
 
 Name results quickly: 
 
 9 + 1 
 
 28 + 2 
 
 59 + 1 
 
 78 + 2 
 
 8 + 2 
 
 39 + 1 
 
 58 + 2 
 
 89 + 1 
 
 19 + 1 
 
 38 + 2 
 
 69 + 1 
 
 88 + 2 
 
 18 + 2 
 
 49 + 1 
 
 68 + 2 
 
 99 + 1 
 
 29 + 1 
 
 48 + 2 
 
 79 + 1 
 
 98 + 2 
 
 How many tens in one hundred? How many tens in 
 half a hundred? How many ones? 
 
 J of 100 = tens, or ones. 
 
 9 + 2 = 
 
 19 + 2 = 
 
 175. Nine splints and 2 splints are 
 Nineteen splints and 2 splints are - 
 
 splints. 
 
 splints. 
 
 Take one splint from the two and put it with the nine. 
 You now have 1 ten and 1 one, or . 
 
 Take one splint from the other two and put it with 
 the nine. You now have tens and - one, or . 
 
 Show by splints how many 29 and 2 are. 
 49 and 2. 
 
 19 
 
 2 
 
 29 
 
 2 
 
 39 
 
 2 
 
 49 
 
 2 
 
 59 
 
 2 
 
 69 
 
 2 
 
 39 and 2. 
 
 79 
 
 2 
 
ADDITION AND SUBTRACTION. 129 
 
 176. Take 11 splints (a ten and a one). How can you 
 take 2 splints away from the 11? How many must you 
 take from the ten? How many will be left? 
 
 Take 21 splints 2 tens and a one. Take away 2 splints. 
 Ho\v many must you take from one of the tens? How 
 many tens and how many ones will be left? 
 
 Show by splints how many 31 less 2 are. 41 2. 
 512. 61 2. 
 
 11 21 
 
 31 41 
 
 51 
 
 61 
 
 71 
 
 81 
 
 2 2 
 
 2 2 
 
 2 
 
 2 
 
 2 
 
 2 
 
 ~9 
 
 
 
 
 
 
 177. Find 
 
 the value of: 
 
 
 
 
 
 9 + 2 
 
 8 + 2 
 
 11 
 
 2 
 
 10- 
 
 2 
 
 19 + 2 
 
 18 + 2 
 
 21 
 
 2 
 
 20 
 
 2 
 
 39 + 2 
 
 48 + 2 
 
 41 
 
 2 
 
 30 
 
 2 
 
 49 + 2 
 
 28 + 2 
 
 61 
 
 2 
 
 50 
 
 2 
 
 29 + 2 
 
 68 + 2 
 
 31 
 
 2 
 
 60 
 
 2 
 
 69 + 2 
 
 38 + 2 
 
 51 
 
 2 
 
 40- 
 
 2 
 
 89 + 2 
 
 58 + 2 
 
 71 
 
 2 
 
 70- 
 
 2 
 
 79 + 2 
 
 78 + 2 
 
 81 
 
 2i 
 
 90 
 
 2 
 
 59 + 2 
 
 98 + 2 
 
 91 
 
 2 
 
 80 
 
 2 
 
 Add by 2's from 2 to 50. 
 Subtract by 2's from 40 to 18. 
 Add by 2's from 9 to 61. 
 Subtract by 2's from 49 to 9. 
 
130 
 
 SCHOOL ARITHMETIC. 
 
 8 + 3 
 
 17 + 4 
 
 19 
 
 178. Show with blocks that 8 + 3 = 1 ten and 1 
 
 one, or 11. 
 
 Show that 18 + 3 = 
 Show that 28 + 3 = 
 Show that 17 + 4 = 
 Show that 19 + 3 = 
 
 tens and 
 tens and 
 tens and 
 tens and 
 
 one, or 
 one, or 
 one, or 
 ones, or 
 
 179. How many squares do you see in the picture at 
 the left? How many of them will be left if you take 
 away the 3 dark ones? 
 
 How many squares in the next picture? How many 
 light ones? 
 
 1 ten and 8 ones, or 18. 
 
 tens and 8 ones, or - . 
 
 ten and ones, or . 
 
 Show that 21 3 = 
 Show that 31 3 = 
 Show that 21 4 
 Show that 22 -- 3 = 
 
 ten and 
 
 Add; also, subtract: 
 
 11 
 3 
 
 21 
 3 
 
 31 
 3 
 
 41 
 3 
 
 61 
 3 
 
 81 
 3 
 
 ones, or 
 
 71 
 3 
 
 51 
 3 
 
ADDITION AND SUBTRACTION. 131 
 
 21 
 
 31 
 
 41 
 
 51 
 
 71 
 
 61 
 
 91 
 
 
 81 
 
 4 
 
 4 
 
 4 
 
 
 4 
 
 4 
 
 4 
 
 4 
 
 
 4 
 
 22 
 
 32 
 
 42 
 
 62 
 
 52 
 
 72 
 
 82 
 
 
 92 
 
 3 
 
 3 
 
 3 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 
 3 
 
 180. 
 
 N 
 
 ame results at 
 
 sight : 
 
 
 
 
 
 - 
 
 8 
 
 + 
 
 3 
 
 . 7 
 
 + 
 
 4 
 
 11 
 
 g 
 
 11- 
 
 4 
 
 
 
 18 
 
 + 
 
 3 
 
 17 
 
 + 
 
 4 
 
 21 
 
 3 
 
 214 
 
 
 28 
 
 + 
 
 3 
 
 27 
 
 + 
 
 4 
 
 31 
 
 3 
 
 31- 
 
 4 
 
 
 
 58 
 
 + 
 
 3 
 
 37 
 
 + 
 
 4 
 
 51 
 
 3 
 
 41- 
 
 4 
 
 
 
 48 
 
 + 
 
 3 
 
 67 
 
 + 
 
 4 
 
 61 
 
 3 
 
 614 
 
 
 68 
 
 + 
 
 3 
 
 87 
 
 + 
 
 4 
 
 41 
 
 -3 
 
 81- 
 
 4 
 
 
 
 38 
 
 + 
 
 3 
 
 47 
 
 + 
 
 4 
 
 81 
 
 -3 
 
 71- 
 
 4 
 
 
 
 88 
 
 + 
 
 3 
 
 57 
 
 + 
 
 4 
 
 71 
 
 -3 
 
 51- 
 
 4 
 
 
 
 78 
 
 + 
 
 3 
 
 77 
 
 + 
 
 4 
 
 91 
 
 -3 
 
 91- 
 
 4 
 
 
 Add by 3's from 
 
 to 
 
 51 
 
 . From 
 
 2 to 50 
 
 
 
 
 Subtract 
 
 by 
 
 4's from 48 
 
 to 0. From 45 
 
 to 1. 
 
 
 
 181. 
 
 Name 
 
 results at sight: 
 
 
 8 
 
 + 
 
 4 
 
 9 
 
 + 
 
 4 
 
 12 
 
 -4 
 
 13- 
 
 4 
 
 
 
 18 
 
 + 
 
 4 
 
 19 
 
 + 
 
 4 
 
 22 
 
 A 
 
 23 
 
 4 
 
 
 
 28 
 
 + 
 
 4 
 
 29 
 
 + 
 
 4 
 
 32 
 
 -4 
 
 43- 
 
 4 
 
 
 
 38 
 
 + 
 
 4 
 
 49 
 
 + 
 
 4 
 
 42 
 
 -4 
 
 53 
 
 4 
 
 
 
 48 
 
 + 
 
 4 
 
 39 
 
 + 
 
 4 
 
 62 
 
 -4 
 
 33 
 
 4 
 
 
 
 68 
 
 + 
 
 4 
 
 79 
 
 + 
 
 4 
 
 82 
 
 4 
 
 73 
 
 4 
 
 
 
 88 
 
 + 
 
 4 
 
 89 
 
 + 
 
 4 
 
 52 
 
 -4 
 
 93 
 
 4 
 
 
 
 78 
 
 + 
 
 4 
 
 69 
 
 + 
 
 4 
 
 72 
 
 -4 
 
 63 
 
 4 
 
 
 
 58 
 
 + 
 
 4 
 
 59 
 
 + 
 
 4 
 
 92 
 
 4 
 
 83 
 
 4 
 
 
 Add 5 to 16, 26, 36, 46, 56, 66, 76, 86. 
 Subtract 5 from 21, 31, 41, 51, 61, 71, 81, 91 
 
132 
 
 SCHOOL ARITHMETIC. 
 
 15 + 7 = 19 
 
 182. Find the sum of 15 and 7. 
 
 15 = 
 
 Write 15 and then write the 7 ones under the 5 ones. 15 
 7 ones and 5 ones are - - ones, or 1 ten and 2 ones. 1 
 
 Write the 2 ones in ones' place under 7. 22 
 
 What shall be done with the ten ? Add it to the 1 ten in 
 
 15. 1 ten and 1 ten are tens. 
 
 In what place do we write the tens ? 
 
 Find the sum of 19 and 15. 
 
 5 ones -\- 9 ones = 14 ones, or 1 ten and 4 ones. 
 1 ten + 1 ten -f- 1 ten = tens. 
 
 Copy and 
 
 add: 
 
 18 38 
 
 29 
 
 4 4 
 
 15 
 
 25 35 
 
 27 
 
 56 48 
 
 16 
 
 63 42 
 
 74 
 
 28 39 
 
 17 
 
 32 
 19 
 
 64 
 
 18 
 
 31 
 
 49 
 
 63 
 
 28 
 
 43 
 32 
 
 28 
 64 
 
 42 
 39 
 
 57 
 25 
 
 36 
 
 58 
 
 19 
 15 
 
 34 
 
 78 
 14 
 
 68 
 17 
 
 43 
 37 
 
 69 
 24 
 
 34 
 
 38 
 
 54 
 39 
 
ADDITION AND SUBTRACTION. 133 
 
 26 57 44 87 65 39 76 58 
 
 58 27 37 15 26 47 18 37 
 
 15 16 23 14 26 32 29 40 
 
 23 34 42 37 38 18 29 27 
 
 47 26 18 25 14 47 30 19 
 
 183. Find the value of: 
 
 36 + 14 
 
 25 + 45 
 
 33 + 49 
 
 26 + 35 + 18 
 
 33 + 17 
 
 81 + 19 
 
 62 + 28 
 
 17 + 23 + 46 
 
 42 + 18 
 
 46 + 37 
 
 71 + 29 
 
 35 + 18 + 26 
 
 82 + 18 
 
 34 + 58 
 
 80 + 18 
 
 24 + 39 + 27 
 
 47 + 14 76 + 17 46 + 35 31 + 17 + 46 
 
 184. There are 31 days in May and 30 in June. In 
 both months there are - - days. 
 
 Mr. Jones has 58 sheep in one field and 37 in another. 
 In both fields he has - - sheep. 
 
 Ella is 18 years old and her mother is 36 years older. 
 How old is her mother? 
 
 Our black horse cost $65 and our red cow cost $25. 
 How much did both cost? 
 
 If a room is 18 feet long and 16 feet wide, how many 
 feet is it around the room? 
 
 A Christmas tree held 13 dolls. 27 balls, 37 flags, and 
 17 bags. How many articles were there in all? 
 
 Edith paid 35 cents for a book, 15 cents for paper, and 
 3 cents for a ruler. How much did they all cost her? 
 
 Mr. White's wagon cost $42. His buggy cost $29 more 
 than the wagon. How much did the buggy cost? 
 
 How many days are there in October, November, and 
 December? 
 
134 
 
 SCHOOL ARITHMETIC. 
 
 2t 
 
 2o 
 
 22 5 = 
 
 185. Take 22 splints (2 tens and 2 ones). How many 
 ones can you take away without taking any from a bundle ? 
 
 If you wish to take 5 splints away, how many ones must 
 you take from one of the tens? How many ones will be 
 left? One ten and 7 ones are - . 
 
 Take 32 splints (3 tens and 2 ones). How can you take 
 7 splints away? Can you take 7 ones from the 2 ones? 
 
 Take the string from one of the bundles. Xow how 
 many ones have you? Take 7 splints away. How many 
 ones are left ? How many tens ? 
 
 22 = 2 
 5 = 
 
 t + 
 
 2 
 5 
 
 = 
 
 + 
 
 12 
 
 5 
 
 0. 
 0. 
 
 n = 
 
 7 
 
 
 
 17 = 
 
 
 
 = lt 
 
 + 
 
 7 
 
 0. 
 
 25 = 
 
 
 
 7 o = 7 o. 
 
 = 2+ 50. 
 
 How many squares do you see in the picture ? 
 How many tens? How many ones? 
 
 We cannot take 5 squares from the 3 
 squares, so we must take one of the tens and 
 and put it with the 3 ones, making 13 ones. 
 We then have 2 tens and 13 ones. What is 
 left when 5 ones are taken away? 
 
 Show with splints how many 23 less 5 are. 
 31 less 7. 
 
ADDITION AND SUBTRACTION. 
 
 Subtract : 
 
 24 25 
 6 
 
 32 
 
 26 
 
 8 
 
 21 
 
 n 
 
 34 
 
 35 
 
 31 
 
 16 
 
 15 
 
 We cannot take 6 from 1, so we put one of the tens with 
 the 1, and take 6 from 11. There are only 2 tens left, 
 so we take the 1 ten from 2 tens. 
 
 31 = = 20 + 11 
 16 = : 10+ 6 
 
 15 = 10+ 5 
 
 NOTE. Of course, as soon as the pupils understand the process, 
 they should do the work without any change of figures. 
 
 Show with splints how to subtract 12 from 31. 15 from 
 32. Use splints to show how many 25 less 15 are. 45 
 less 20. 
 
 186. Copy and subtract: 
 
 23 31 34 42 63 54 36 75 
 8 6 16 25 34 28 19 47 
 
 60 
 29 
 
 91 
 16 
 
 40 
 25 
 
 53 
 15 
 
 68 
 35 
 
 90 
 50 
 
 84 
 30 
 
 93 
 
 48 
 
 44 
 
 28 
 
 55 
 37 
 
 64 
 26 
 
 45 
 
 28 
 
 74 
 24 
 
 80 
 51 
 
 100 
 50 
 
 100 
 80 
 
44 
 
 19 
 
 52 
 
 27 
 
 41 
 
 16 
 
 50 
 
 -38 
 
 75 
 
 -36 
 
 5"2 
 
 27 
 
 72 
 
 22 
 
 44 
 
 -18 
 
 63- 
 
 38 
 
 67 
 
 28 
 
 63 
 
 -45 
 
 74- 
 
 49 
 
 83 
 
 -38 
 
 81 
 
 -50 
 
 85 
 
 56 
 
 62 
 
 -43 
 
 27 
 
 9 
 
 96- 
 
 67 
 
 91 
 
 56 
 
 50 
 
 13 
 
 43 
 
 15 
 
 136 SCHOOL ARITHMETIC. 
 
 187. Find the value of: 
 34 16 
 
 42 15 
 61 24 
 83 15 
 21 12 
 75 54 
 92 65 
 
 188. How many more days are there in this month?' 
 A man wants to buy a watch for $32. He has only $25. 
 
 How much more does he need? 
 
 Julia bought a doll for 29 cents, and gave the store- 
 keeper a half-dollar. How much change did she get? 
 
 In a school there are 45 pupils. There are 26 boys. 
 How many girls are there? 
 
 What number must you add to 14 to get 21? 
 
 What number must you subtract from 32 to get 24? 
 
 A man paid $94 for a horse and cart. He paid $18 
 for the cart and $ - for the horse. 
 
 Grandma is 83 years old, and Lizzie is 7 years old. How 
 much older is grandma than Lizzie? 
 
 If your mamma had 2 dozen eggs, and used all of them 
 at Easter but a half-dozen, how many did she use? 
 
 How many days from the llth of June to the 9th of 
 July? 
 
 A barrel of oil contained 53 gallons but 5 gallons leaked 
 out. There were - - gallons left in. 
 
 Mrs. Hill had 62 hens. She sold 27 of them and had 
 
 left. 
 
 Tom weighs 96 pounds and Warren 78 pounds. How 
 many more pounds does Tom weigh than Warren? 
 
NUMBERS TO SIXTY. 137 
 
 Numbers to Sixty. 
 
 189. How many dots in the picture? How many rows 
 of 10 dots each? 
 
 6 X 10 dots - - dots. 
 
 How many large dots do you see? How many sixes are 
 there? 
 
 10 X 6 dots = - dots. 
 In 60 there are - tens or - sixes. 
 How many times can you take 10 dots from 60 dots? 
 00 dots -f- 10 dots = - - times. 
 
 The large dots are what part of the 60 dots? T V of 60 
 dots = dots. 
 
 How many tenths of the 60 dots equal \ of the 60 dots? 
 Ten dots are what part of 60 dots? \ of 60 dots = 
 dots. 
 
 How many sixths of 60 equal i of 60? 
 
 In 60 there are twelves. 
 
 In 60 there are fives. 
 
 190. How many small dots in the picture? How many 
 rows of 9 dots each? How many columns of 6 dots each? 
 
 6X9 dots = - dots. 9X6 dots = - dots. 
 
 Draw a rectangle 9 inches long and 6 inches wide, and 
 draw horizontal and vertical lines to divide it into square 
 inches. 
 
138 SCHOOL ARITHMETIC. 
 
 How many squares inches does it contain? How many 
 times 6 sq. in. ? How many times 9 sq. in. ? 
 
 How many sq. in. in one-sixth of the rectangle? i of 
 54 = - . 54 sq. in. -r- 6 = sq. in. 
 
 In -J- of the rectangle how many sq. in. ? -Jof 54 = 
 . 54 sq. in. ~- 9 = sq. in. 
 
 Show how many sixths of the rectangle equal i of it. 
 
 Count by 4's to 60. By 5's. By 6's. 
 
 191. Complete and memorize: 
 
 1 
 
 six = 6 
 
 1 
 
 X 
 
 6 6. 
 
 6 
 
 X 
 
 1 = 6. 
 
 2 
 
 sixes = 
 
 2 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 2 = 
 
 3 
 
 sixes = 
 
 3 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 r> 
 
 4 
 
 sixes = 
 
 4 
 
 X 
 
 6== 
 
 6 
 
 X 
 
 4 = 
 
 5 
 
 sixes = 
 
 5 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 5 = 
 
 6 
 
 sixes = 
 
 6 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 6 = 
 
 7 
 
 sixes = 
 
 7 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 7 = 
 
 8 
 
 sixes = 
 
 8 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 8 = 
 
 9 
 
 sixes = 
 
 9 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 9 = 
 
 10 
 
 sixes = 
 
 10 
 
 X 
 
 6 = 
 
 6 
 
 X 
 
 10 = 
 
 192, Find how many times: 
 
 6 dots are contained in 18 dots. 
 
 6 squares are contained in 30 squares 
 
 6 eggs are contained in 48 eggs. 
 
 6 blocks are contained in 36 blocks. 
 
 6 inches are contained in 42 inches. 
 
 6 beans are contained in 54 beans. 
 
 6 feet are contained in 24 feet. 
 
 9 sq. ft. are contained in 36 sq. ft. 
 
 9 sq. ft. are contained in 54 sq. ft. 
 
 9 dollars are contained in 45 dollars. 
 
NUMBERS TO SIXTY. 
 
 139 
 
 193. In 7 rows of 8 squares each 
 there are - - squares. 
 
 How many times 7 squares make 56 
 squares ? 
 
 Show that 7X8 squares = = 8X7 
 squares. 
 
 How many times are 8 squares found in the 56 squares? 
 7 squares? 
 
 56 squares *-r- 8 squares = - times. 56 squares 
 
 -r- 7 squares = - - times. 
 
 What part of the rectangle is found in the upper row? 
 
 Two rows are what part of the rectangle? Three rows? 
 
 Four-sevenths of 56 squares are - - squares. 
 
 Seven squares are what part of the 56 squares? 14 
 squares ? 
 
 Compare f of the squares with i of them. 
 
 56 squares -r- 8 = squares. 56 squares -r- 7 = 
 squares. 
 
 How many 9's in 56, and how many over? 
 
 How many 5's in 56, and how many over? 
 
 How many 10's in 56, and how many over? 
 
 Find the value of: 
 
 12- 
 
 -6 
 
 4 
 
 X 
 
 7 
 
 t 
 
 of 
 
 60 
 
 60 = 
 
 7X 
 
 8 + 
 
 ( ) 
 
 30- 
 
 -6 
 
 6 
 
 X 
 
 8 
 
 1 
 
 of 
 
 60 
 
 53 = 
 
 10 X 
 
 5 + 
 
 () 
 
 48- 
 
 -6 
 
 7 
 
 X 
 
 7 
 
 3 
 f 
 
 of 
 
 60 
 
 54- 
 
 7X 
 
 T + 
 
 () 
 
 42- 
 
 -6 
 
 4 
 
 X 
 
 8 
 
 1 
 
 of 
 
 60 
 
 K Q 
 OO = 
 
 8 X 
 
 7 + 
 
 ( ) 
 
 54- 
 
 -6 
 
 3 
 
 X 
 
 9 
 
 i 
 
 of 
 
 21 
 
 55 = 
 
 6X 
 
 9 + 
 
 ( ) 
 
 36- 
 
 -6 
 
 5 
 
 X 
 
 8 
 
 t 
 
 of 
 
 40 
 
 59 = 
 
 11 X 
 
 5 + 
 
 () 
 
 24- 
 
 -6 
 
 7 
 
 X 
 
 5 
 
 j 
 
 of 
 
 60 
 
 51 = 
 
 8 X 
 
 6 + 
 
 ( ) 
 
 60-^-6 
 
 5 
 
 X 
 
 9 
 
 1 
 
 of 
 
 60 
 
 52 = 
 
 6 X 
 
 8 + 
 
 ( ). 
 
140 
 
 SCHOOL ARITHMETIC. 
 
 194. Here is a picture of a watch 
 face. 
 
 When the pointer in the little 
 circle has gone round once, how many 
 minutes have passed? 
 
 The little circle is divided into how 
 many spaces? 
 
 Sixty seconds make a minute. 
 
 "When the longer hand in the large circle has gone round 
 once, what time has passed? 
 
 Into how many spaces is the large circle divided? 
 Sixty minutes make an hour. 
 
 Which is the hour-hand? Which the minute-hand? 
 The second-hand? 
 
 How often does the hour-hand go round from midnight 
 to midnight? 
 
 Then how many hours make a day? 
 
 What time of day is shown on the watch-face? 
 
 How many minutes in a half of an hour? In a quarter 
 of an hour? 
 
 What part of an hour are 30 minutes? 15 minutes? 10 
 minutes ? 
 
 From noon to midnight is what part of 48 hours? 
 
 In half a minute how many seconds? 
 
 What part of a minute are 15 seconds? 10 seconds? 
 6 seconds? 
 
 In what time does the hour-hand go round four times? 
 
 How many hours in a half of a day? 
 
 How many hours is it from 6 A. M. on Monday till 
 6 A. M. on Tuesday? 
 
NUMBERS TO SIXTY. 141 
 
 195. How much money will buy 10 pounds of sugar 
 at 6 cents a pound? 
 
 Five boys bought a ball for 50 cents. No one gave 
 more money than another. How much did each give? 
 
 In 8 weeks there are days. 
 
 We had 48 eggs on Sunday. On Monday we got a 
 dozen more. How many eggs had we then? How many 
 dozens ? 
 
 9 quarts of milk at 6 cents a quart will cost - cents. 
 
 Maud had 11 nickels. She gave 50 cents for a doll, and 
 had - - cents left. 
 
 A house is 30 feet long and 18 feet wide. What is the 
 distance around the house? 
 
 A rug is 9 feet long and 6 feet wide. It contains 
 
 square feet, or square yards. 
 
 There are 52 weeks in a year. How many weeks in 
 half a year? 
 
 A bushel of wheat weighs 60 pounds. What is the 
 weight of a peck? A half -bushel? 
 
 Six windows contain 48 panes of glass. How many 
 panes are there in each window? 
 
 If each of 7 boys makes 8 balls of snow, how many will 
 they have together? 
 
 Roy borrowed 60 cents from his brother, and paid him 
 back 6 cents of it every week. How many weeks did it 
 take to pay the whole? 
 
 If a man works 8 hours a day, what part of the day 
 does he work? 
 
 If a horse walks a mile in 15 minutes, how many miles 
 at that rate will he walk in an hour? 
 
 If a railway train runs one mile in 2 minutes, how many 
 miles will it go in an hour? 
 
142 SCHOOL ARITHMETIC. 
 
 Numbers to Seventy. 
 
 196. We have - - rows of 10 dots each; there are 
 dots in all the rows. 7 X 10 dots = - - dots. 
 
 There are 10 columns of - - dots each. 10 X Y dots 
 
 = dots. 
 
 We see that there are - - tens or - - sevens in YO. 
 
 YO -r- 10 = YO -r- Y = 
 
 The large dots are one - - of the YO dots. T V of YO = 
 The small dots are nine - - of the YO dots. T 9 ^of Y0=r 
 On one side of the vertical line there are - - tenths 
 
 of the YO dots] on the other side we find J of the YO dots. 
 
 One side has as many dots as the other. (-J- = y-g-.) 
 
 197. There are - - small dots in the picture seven 
 rows of - - dots each. Y X 9 dots == - - dots. 
 
 There are 9 columns of - dots each. 9 X Y dots = 
 
 dots. 
 
 We can take Y small dots away - - times; we can 
 take away 9 small dots - - times. 
 
 63 dots -f- Y dots = - times. 63 dots -^ 9 dots = 
 
 times. 
 
 Show by a drawing that 9 sevens = Y nines. 
 Count by 5's to YO. By 10's. By Y's, 
 
NUMBERS TO SEVENTY. 
 
 143 
 
 198. Complete and memorize: 
 
 .1 seven = 7, 
 
 2 sevens = 
 
 3 sevens = 
 
 4 sevens = 
 
 5 sevens = 
 
 6 sevens == 
 
 7 sevens = 
 
 8 sevens = 
 
 9 sevens = 
 10 sevens = 
 
 1X7 = 7. 
 2X7 = 
 3X7 = 
 4X7 = 
 5X7 = 
 6X7 = 
 7X7 = 
 8X7 = 
 9X7 = 
 10 X 7 = 
 
 7X 
 
 7X 
 X 
 X 
 X 
 X 
 X 
 X 
 X 
 
 7 X 10 = 
 
 199. 7 dots are contained in 21 dots - - times. 
 7 days are contained in 70 days - - times. 
 7 pints are contained in 35 pints - - times. 
 7 yards are contained in 63 yards - - times. 
 9 sq. ft. are contained in 36 sq. ft. - - times. 
 9 eggs are contained in 63 eggs - - times. 
 7 pounds are contained in 66 pounds - - times, and 
 3 pounds over. 
 
 6 
 
 200. Here is a square. How 
 many small squares in the upper 
 row? How many rows? 
 
 8X8 squares === - - squares. 
 
 How many times can 8 squares 
 be found in the 64 squares? 
 
 In one-half of the large square how many small squares ? 
 i of 64 squares = - - squares. 
 64 squares -r- 2 = - - squares. 
 64 squares -r- 8 = squares, 
 
144 SCHOOL ARITHMETIC. 
 
 The upper row is what part of the large square? 
 How many eighths of the large square are on each side 
 of the dark line? 
 
 J of 64 squares - - squares. 
 
 -f of 64 squares - - squares. 
 
 201. Find the value of: 
 
 14 7 7X6 iof64 64= 9X 7 + ( ). 
 
 28 7 9X5 of 64 62 = .7 X 8 + ( ). 
 
 35 7 8X7 f of 64 69 = 8 X 8 + ( ). 
 
 21 7 7X9 A of 70 68 = 7 X 9 + ( ). 
 
 70 7 8X8 A of 70 61 = 8 X 7 + ( ). 
 
 42 7 6X7 iV of 70 67 = 10 X 7 ( ). 
 
 49 7 9X6 A of 70 65-= 6 X'10 + ( ). 
 
 56 7 6X8 \ of 70 66 = 7 X 10 ( ). 
 
 63 7 9X7 -f- of 70 70 = 8 X 8 + ( ). 
 
 202. In 10 weeks there are - - days. 
 
 Tom has 65 cents. How much more than 50^ is that? 
 
 Maria has 40 cents and Martha has a quarter. How 
 much have they both? 
 
 At 8 cents a quart how much will 8 quarts of chestnuts 
 cost? 
 
 How much will 3 yards of wire cost at 7 cents a foot? 
 
 10 cents is \ of my money. How much have I? 
 
 A nickel is \ of my money. How much have I? 
 
 I gave A ^ m y m oney for a 5-cent stamp. How much 
 had I? 
 
 7 children give 9 cents each to a Children's Aid Society. 
 How much money is given by all together? 
 
NUMBERS TO EIGHTY. 
 
 145 
 
 In a school-room there are 63 seats arranged in 7 rows. 
 How many seats in each row? 
 
 Robert has 56 cents. How many quarts of peanuts can 
 he buy at 7 cents a quart? 
 
 How old is a man who has lived 3 score and 10 years? 
 
 Numbers to Eighty. 
 10 
 
 8 
 
 203. How many squares in this rectangle? How many 
 rows of 10 squares each? How many columns of 8 squares 
 each? 8'X 10= 10 X 8 = 
 
 Find how many squares in 9 columns. 9X8= 8X9== 
 How often do 80 squares contain 10 squares? SO-^-10 11 ^ 
 How many times are 8 squares contained in 80 squares? 
 How many tens make 80? How many tens make i of 80? 
 
 ^ of 80 = | of 80 = 
 
 How many 8's make 80? How many 8's make \ of 80? 
 Which is more, T 5 of 80 or % of 80 I 
 Make 6 rows of 12 dots each,, and tell how many six 
 12's are. 12 X 6 = 
 
 Show that 9 X 8 = 6 X 12. 
 
 In 50 there are - - 5's; in 25 there are 5's. 
 
 Count by 6's to 78. By 7's to 77. 
 Count by 8's to 80. By 5's to 80, 
 *io 
 
146 SCHOOL ARITHMETIC 
 
 204. Complete and memorize: 
 
 1 
 
 eight =8 
 
 1 
 
 X 
 
 8 = 8 
 
 8 
 
 X 
 
 1 = 8 
 
 2 
 
 eights = 
 
 2 
 
 X 
 
 o 
 
 8 
 
 X 
 
 '2= . 
 
 3 
 
 eights = 
 
 3 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 ? = 
 
 4 
 
 eights = 
 
 4 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 4 = 
 
 5 
 
 eights = 
 
 5 
 
 X 
 
 Q 
 
 8 
 
 X 
 
 5 = 
 
 6 
 
 eights = 
 
 6 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 6 = 
 
 7 
 
 eights = 
 
 7 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 7 = 
 
 8 
 
 eights = 
 
 8 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 8 = 
 
 9 
 
 eights = 
 
 9 
 
 X 
 
 o 
 
 8 
 
 X 
 
 9 = 
 
 10 
 
 eights = 
 
 10 
 
 X 
 
 8 = 
 
 8 
 
 X 
 
 10 = 
 
 205. Find how many times : 
 
 8 squares are contained in 24 squares. 
 
 8 squares are contained in 40 squares. 
 
 8 squares are contained in 72 squares. 
 
 9 squares are contained in 72 squares. 
 
 6 pegs are contained in 66 pegs. 
 
 7 days are contained in 77 days. 
 
 8 pounds are contained in 64 pounds. 
 
 206. Find the value of: 
 
 16 8 5X7 I of 36 75= 7X10 + () 
 
 32 8 4X9 f of 36 72 = 9 X 8 + ( ) 
 
 40 8 6X8 iof40 76 = 8 X 9 + ( ) 
 
 80 8 7X9 | of 40 71 = 8 X 8 + ( ) 
 
 72 8 8X8 f of 40 74 = 50 + 20 -f ( ) 
 
 24 8 6X7 i of 44 79 = 40 + 25 + ( ) 
 
 48 8 9X8 5 of 44 77 = 7 X 10 + ( ) 
 
 64 8 8X7 |of80 . 73 = 50 + 14 + () 
 
 56 8 7X7 i of 80 78 = 7 X 11 + ( ) 
 
NUMBERS TO EIGHTY. 
 
 147 
 
 TRIANGLE 
 
 SQUARE 
 
 RECTANGLE 
 
 HEXAGON 
 
 207. If each side of the triangle is an inch long, what 
 is the distance around the triangle? (The distance around 
 it is called the perimeter.) 
 
 How many sides make the perimeter of the square? 
 
 What is the perimeter of a square inch? 
 
 A table is 2 feet square. Tho perimeter is feet. 
 
 If the rectangle is 1 inch long and 1 inch wide, its 
 perimeter is - - inches. 
 
 How many sides has the hexagon? If each side is half 
 
 an inch long, the perimeter is - - half inches, or 
 
 inches. 
 
 A rectangle is 3 feet long and 2 feet wide. What is 
 the perimeter? 
 
 The perimeter of a square is 4 feet. What is the length 
 of a side? What is the figure called? 
 
 The perimeter of a triangle is 15 feet. One side is 8 
 inches, another is 5 inches. How long is the third side? 
 
 Find the perimeter of this room. Of this table. 
 
 Find the perimeter of a room 16 feet long and 16 feet 
 wide. 
 
 208. In 8 dimes there are 
 
 cents. 
 
 I gave 50^ for a book and 22^ for a slate. How much 
 did I give for both ? 
 
 ^ Tattie had 8 climes. She gave 5 cents for candy, and 
 then had cents left. 
 
148 SCHOOL AKITHMETIC. 
 
 A bushel of wheat weighs 60 pounds. A bushel and a 
 peck weigh pounds. 
 
 How many gallons must be added to 65 gallons to make 
 78 gallons? 
 
 If I have 70 cents, to how many boys can I give a dime 
 each? 
 
 Uncle Henry is 50 years old. How old will he be in 24 
 years ? 
 
 The perimeter of a square is 12 inches. Draw the 
 square and show how many square inches it contains. 
 
 If you had 65 cents and each of 5 boys gave you 2 
 cents, how many cents would you have? 
 
 Wilbur earns 53 cents in a day and Oscar 44 cents. 
 How much more does Wilbur earn than Oscar in 8 days? 
 
 Numbers to One Hundred. 
 
 209. Draw a square 9 inches on a side. Mark it off 
 into square inches. 
 
 How many squares inches are there? How many in 1 
 row? How many rows? 
 
 9X9 square inches = - squares inches. 
 
 81 square inches contains 9 square inches - - times. 
 
 10 X 9 sq. in. = - sq. in. 9 X 10 = 
 
 90 -^10 == 90 -^ 9 = T V of 90 = 
 
 Make 7 rows of 12 dots each, and tell how many seven 
 12's are. How many are twelve 7's? 
 
 How many 12's make 84? How many 7's? 
 
 Add by 7's to 84. By 8's to 96. By 9's to 99. By 
 10's to 100. 
 
NUMBERS TO ONE HUNDRED. 
 
 149 
 
 Write a number which has 9 in the ones' place. Can 
 you write a number which has ten in the ones' place ? 
 
 What is the smallest number that is written with two 
 figures ? 
 
 What is the largest number that can be expressed by 
 two figures? 
 
 210. 
 
 Complete and memorize: 
 
 1 
 
 nine = 9 
 
 1 
 
 X 
 
 9 = 9 
 
 9 
 
 X 
 
 1 
 
 = 
 
 2 
 
 nines = 
 
 2 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 2 
 
 = 
 
 3 
 
 nines = 
 
 3 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 3 
 
 = 
 
 4 
 
 nines = 
 
 4 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 4 
 
 = 
 
 5 
 
 nines = 
 
 5 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 5 
 
 = 
 
 6 
 
 nines = 
 
 6 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 6 
 
 = 
 
 7 
 
 nines = 
 
 7 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 7 
 
 = 
 
 8 
 
 nines = 
 
 8 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 8 
 
 == 
 
 9 
 
 nines = 
 
 9 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 9 
 
 = 
 
 10 
 
 nines = 
 
 10 
 
 X 
 
 9 = 
 
 9 
 
 X 
 
 10 
 
 = 
 
 11 
 
 nines = 
 
 11 
 
 X 
 
 9 = 
 
 9 
 
 x 
 
 11 
 
 
 
 Multiply 10 by 3, 7, 5, 4, 8, 6, 9, 10. 
 How many 10's in 50, 30, 70, 90, 60, 100? 
 How many 9's in 36, 45, 63, 72, 90, 81? 
 How many 8's in 40, 56, 64, 80, 72, 88, 96? 
 
 211. Find 
 
 the value of: 
 
 
 
 90- 
 
 -9 
 
 80- 
 
 -10 
 
 77- 
 
 - 7 
 
 72- 
 
 - 9 
 
 36- 
 
 -9 
 
 60- 
 
 -10 
 
 63- 
 
 -7 
 
 64- 
 
 - 8 
 
 63- 
 
 -9 
 
 30- 
 
 -10 
 
 84- 
 
 -7 
 
 56- 
 
 - 7 
 
 45- 
 
 -9 
 
 90- 
 
 -10 
 
 66 
 
 -6 
 
 54- 
 
 - 6 
 
 54- 
 
 -9 
 
 88- 
 
 -11 
 
 72- 
 
 -6 
 
 49- 
 
 - 7 
 
 72- 
 
 -9 
 
 99- 
 
 -11 
 
 88- 
 
 -8 
 
 42- 
 
 - 6 
 
 81- 
 
 -9 
 
 84- 
 
 -12 
 
 96- 
 
 -8 
 
 60- 
 
 -12 
 
 99- 
 
 -9 
 
 96- 
 
 -12 
 
 72- 
 
 -8 
 
 72- 
 
 -12 
 
150 SCHOOL ARITHMETIC. 
 
 212. How many 10-cent dishes can I buy for a dollar? 
 A bath room is 9 feet square. It contains - - square 
 feet. 
 
 Mr. Hall has 12 bushels of turnips. To how many 
 persons can he sell 1 peck each? 
 
 A milkman has 9 gal. 1 qt. of milk. He can sell 1 qt. 
 to each of - customers. 
 
 What are 7 dozen eggs worth at a cent apiece? 
 
 How many days are there in 11 weeks? 
 
 Twelve men paid 2 dollars apiece to hire a sail boat. How 
 much did they all pay? 
 
 If a boy's suit costs 9 dollars, how much will 10 such 
 suits cost? 
 
 A man paid 81 dollars for a horse and -g as much for 
 a saddle. How much did the saddle cost him? 
 
 If the whole of anything costs 81 cents, how much 
 does -f of it cost 1 
 
 At his last birthday Edward had lived 96 months. How 
 many years old was he? 
 
 Add the days in the month in which Thanksgiving comes 
 to those in the month after and the month before. 
 
 Slate Work. 
 
 213. How many dollars are $32 and $32 and $32, or 
 3 X $32? 
 
 Three times 2 ones are 6 ones. Write the 6 
 
 $96 
 
 in ones' place. Three times 3 tens are 9 tens. 
 Where do we write the 9 ? 
 
SLATE WOKK. 
 
 151 
 
 Multiply: 
 42 ' 23 
 
 2 3 
 
 34 
 
 2 
 
 31 
 3 
 
 44 
 
 2 
 
 21 
 3 
 
 32 
 
 2 
 
 The perimeter of a square room is 48 feet. What is the 
 length of each side? 
 
 ' f ee t Each side is I of the perimeter. J of 4 tens is 1 
 
 12 feet ^ en > an< ^ * ^ ^ nes is 2 ones. ^ of 48 feet is 12 feet. 
 
 Find 1 of $84, J of 66 yd., 1 of 46 gal., i of 96^. 
 How many 3's in 36? 
 3 ) 36 3 ) 36 
 12 
 
 10 
 
 12 
 
 Find how many: 
 2's in 28. 
 3*s in 96. 
 
 Divide : 
 
 2) 68 3) 69 
 
 In 3 tens there are 10 threes. In 6 ones 
 there are 2 threes. 10 threes and 2 threes 
 are 12 threes. 
 
 3's in 63. 
 
 4's in 88. 
 
 2) 86 
 
 3)96 
 
 2) 64 
 9)99 
 
 4)44 
 
 4)88 
 
 4's in 48. 
 2's in 84. 
 
 5) 55 7) 77 
 
 6) 66 
 
 8) 88 
 
 214. This is a cube. How 
 many sides, or faces, has it \ 
 
 What is the length of each 
 face \ The width \ 
 
 Are the faces all of the same 
 size \ Each face is a inch. 
 
 A cube that is an inch long., 
 an inch wide, and an inch thick 
 is called a cubic inch (cu. in.). 
 
SCHOOL ARITHMETIC. 
 
 Find a block that is a cubic inch. 
 
 Place 4 such blocks in a row. How many cubic inches 
 in the row? 
 
 Place 4 more cubes beside these. How many cubic 
 inches in the 2 rows? 
 
 Place 8 more cubes on top of these. How S /' S S^"*^ 
 many cubic inches in each layer? How [\ I I P^ 
 many in both layers? 
 
 215. With one-inch cubes build a cube 2 inches on 
 each side. 
 
 How many layers are there? How many rows in each 
 layer? How many one-inch cubes in each row? 
 
 How many cubes in both rows? In both layers? 
 
 How many cubic inches in the cube you have built? 
 
 A cube 2 inches on a side is a two-inch cube. It con- 
 tains cubic inches. 
 
 A one-inch cube is what part of a two-inch cube? 
 
 A two-inch cube is how many times a one-inch cube ? 
 
 Point out | of a two-inch cube. \ of it. 
 
 How many fourths of the two-inch cube equal \ of it? 
 
 How many eighths of the two-inch cube equal i of it? 
 
 One-fourth is what part of one-half? 
 
 One-half of one-half is one . 
 
 216. Build a cube having 3 layers, 3 rows in each 
 layer, and 3 one-inch cubes in each row. 
 
 This cube is - - inches on each side, and contains 
 cubic inches. 
 
 It is a three-inch cube and contains one-inch cubes. 
 
 Nine one-inch cubes are what part of the 3-inch cube? 
 18 one-inch cubes are what part? 
 
REVIEW AND DRILL WORK. 
 
 153 
 
 How many square inches in each face of the 3-inch cube? 
 In 3 faces? In all the faces? 
 
 How many inch cubes will be needed to make a pile 6 
 in. long, 3 in. wide, and 2 in. high? 
 
 Review and Drill Work. 
 
 217, 
 
 1. 
 
 2. 
 3. 
 
 4. 
 5. 
 6. 
 
 7. 
 8. 
 
 a 
 
 4 
 7 
 5 
 6 
 8 
 4 
 6 
 9 
 
 b 
 
 8 
 4 
 ' 6 
 5 
 4 
 6 
 7 
 5 
 
 c 
 
 7 
 8 
 7 
 4 
 5 
 8 
 9 
 6 
 
 d 
 
 4 
 6 
 
 8 
 3 
 6 
 
 7 
 4 
 
 8 
 
 e 
 
 9 
 
 2 
 
 7 
 5 
 4 
 6 
 
 8 
 
 f-r 
 < 
 
 f 
 
 6 
 5 
 4 
 
 7 
 5 
 4 
 
 7 
 6 
 
 g 
 
 8 
 2 
 6 
 5 
 7 
 3 
 8 
 5 
 
 h 
 5 
 
 7 
 4 
 6 
 3 
 8 
 5 
 4 
 
 i 
 4 
 
 8 
 3 
 8 
 4 
 
 7 
 6 
 5 
 
 i 
 
 7 
 4 
 5 
 7 
 3 
 9 
 2 
 6 
 
 k 
 
 6 
 5 
 
 7 
 5 
 8 
 5 
 
 8 
 
 7 
 
 1 
 8 
 3 
 8 
 4 
 9 
 4 
 7 
 8 
 
 m 
 9 
 
 2 
 9 
 2 
 8 
 6 
 5 
 6 
 
 n 
 
 6 
 
 / 
 i 
 
 6 
 4 
 
 8 
 7 
 6 
 8 
 
 8 
 
 Add the numbers in each line. 
 
 Add the numbers in each column. 
 
 Multiply the numbers in each column by 3 ; 4 ? 5 ? 6, 7, 
 
 . 9 - 
 
 Multiply the numbers in column h by 8, and those in 
 column m by 7, and find the sums and differences of each 
 two corresponding results. 
 
 218. Complete: 
 
 -2 = 
 
 49- 
 
 -7 = 
 
 42- 
 
 -6 = 
 
 63 -f- 9 
 
 4 = 
 
 48- 
 
 -8 = 
 
 27- 
 
 -3 = 
 
 54^-9 
 
 5 = 
 
 84- 
 
 -7 = 
 
 28- 
 
 -4 = 
 
 81-*- 9 
 
 -3== 
 
 18- 
 
 -3 = 
 
 40- 
 
 -4 = 
 
 56 -f- 7 
 
 -9 = 
 
 33- 
 
 -3 = 
 
 63- 
 
 -7-= 
 
 84-^12 
 
 -3 = 
 
 64- 
 
 -8 = 
 
 72- 
 
 o 
 
 45 -f- 3 
 
154 SCHOOL ARITHMETIC. 
 
 219. How many 
 
 yards in 30 ft.? dimes in 90^? 
 
 pecks in 24 qt.? gallons in 28 qt.? 
 
 feet in 96 in.? dollars in 30 dimes? 
 
 bushels in 32 pk.? pints in 44 qt.? 
 
 weeks in 49 days? yards in 27 feet? 
 
 ounces in 2 lb.? half -pecks in 2 bu.? 
 
 quarts in 48 pt. ? shoes in 30 pairs? 
 
 dimes in 33^? tens in 35 ones? 
 
 220. Find the cost of: 
 
 9 lb. of sugar at 6^ a pound. 
 
 4 quires of paper at 10^ a quire. 
 
 8 qt. of peanuts at 6^ a quart. 
 
 9 yd. of silk at $4 a yard. 
 
 1 dozen papers at 3# each. 
 
 2 bu. of salt at 4^ a quarter-peck. 
 
 221. Find the perimeter and area of: 
 
 A rectangle, 7 inches by 4 inches. 
 A rectangle, 8 inches by 3 inches. 
 A rectangle, 9 inches by 4 inches. 
 A rectangle, 12 inches by 5 inches. 
 A square, measuring 3 inches on a side. 
 A square, measuring 4 inches on a side. 
 
 222. Take inch cubes and build a pile 4 blocks long, 
 3 blocks wide, and 2 blocks high. Then fill out the 
 following: 
 
REVIEW AND DRILL WORK. 155 
 
 Length of one side = - - inches. 
 
 Height of one side = - - inches. 
 
 Area of one side = sq. in. 
 
 Width of one end = inches. 
 
 Area of one end = sq. in. 
 
 Area of the top sq. in. 
 
 Area of all six sides = sq. in. 
 
 Xumber of cubes in the pile = . 
 
 223. Draw a square that contains 49 square inches. 
 
 Draw a rectangle that contains 30 square inches. 
 
 James is 10 years old. His age is i of his father's age. 
 How old is his father? 
 
 When oil is worth 20 cents a gallon, how much can be 
 bought for 5 cents? 
 
 If you take 2 quarts of milk a day at 6^ a quart, how 
 much will your milk cost you for a week? 
 
 How much must you pay if you buy 7 yards of cloth 
 at 9^ a yard? 
 
 If there are 4 sq. in. in the face of a cube, how many 
 square inches are there in all the faces? 
 
 24 sheets of paper make, a quire. Find how many 
 sheets there are in a quire and a half of a quire. 
 
 Xaine all the months of the year that have 31 days. 
 
 From 1 o'clock in the morning until nine o'clock in 
 the evening is how many hours? 
 
 If your oil can holds 2 gal. and your lamp holds 2 
 quarts, how many times can you fill your lamp from your 
 can? 
 
 Show by lines that -J-, |, and -| are the same in value. 
 
156 SCHOOL ARITHMETIC. 
 
 Hundreds. 
 
 one ten hundred 
 
 224. How many ones make 1 ten? How many tens 
 make 1 hundred 1 
 
 Show me 10 tens with splints. Put a band around them. 
 How many ones are in the bundle? 
 
 Make another bundle of 100. How many ones are in 
 both bundles? How many hundreds? 
 
 One hundred and 4 hundreds are - - hundreds. 
 
 Four hundreds and 5 hundreds are - - hundreds. 
 
 How many cents make 1 clime ? How many dimes make 
 a dollar? How many cents make a dollar? 
 
 One hundred cents make a, dollar. 
 
 How many cents in 5 dollars? In 8 dollars? 
 
 In what place, counting from the right, do wo write the 
 figure for the number of tens? 
 
 In what place do you think we should write the hundreds 
 of a number? 
 
 225. Supply the figures needed: 
 
 One hundred is written thus 100. 
 Two hundred is written thus 200. 
 Three hundred is written thus 
 
HUNDREDS. 157 
 
 Four hundred is written thus 
 Five hundred is written thus 
 Six hundred is written thus 
 Seven hundred is written thus 
 Eight hundred is written thus 
 Nine hundred is written thus 
 Ten hundred is written thus 1000. One thousand. 
 
 226. Copy and complete: 
 
 10 tens make 100. 60 tens make - . 
 
 20 tens make - . 80 tens make . 
 
 30 tens make - . 70 tens make - . 
 
 40 tens make - . 90 tens make - . 
 
 50 tens make - . 100 tens make - . 
 
 100 ~- 10 tens. 600 = - tens. 
 
 500 = - - tens. 800 = - tens. 
 
 300 = - - tens. 700 = - tens. 
 
 400 = - tens. 900 = - tens. 
 
 200 = - tens. 1000 = - tens. 
 
 227. Add: 
 
 $5 50o</ $4 
 
 3 3000 5 
 
 4 hundreds 
 3 " 
 
 40 tens 
 30 " 
 
 200 sheep 
 400 " 
 300 " 
 
 400 ones 
 300 " 
 
 100 miles 
 300 " 
 500 " 
 
 $100 
 600 
 200 
 
158 
 
 SCHOOL ARITHMETIC. 
 
 228. Subtract: 
 $6 600^ 
 
 $2 200# 
 
 7 hundreds 
 3 " 
 
 60 dimes 
 
 20 " 
 
 70 tens 
 30 " 
 
 700 ones 
 300 
 
 900 
 200 
 
 700 
 400 
 
 600 
 100 
 
 800 
 500 
 
 900 
 TOO 
 
 229. Copy and complete: 
 
 100 + 300 = 
 
 500 + 100 = 
 
 300 + 600 
 
 200 + 400 - 
 
 400 + 300 - 
 
 500 + 400 
 
 400 + 200 = 
 
 700 + 200 - 
 
 100 + 800 
 
 600 + 300 = 
 
 100 + GOO = 
 
 300 + 500 
 
 300 + 200 = 
 
 200 + 500 = 
 
 400 + 600 
 
 Hundreds and Tens. 
 
 t 
 
 
 
 
 h 
 
 t 
 
 o 
 
 
 h t 
 
 \ 
 
 
 
 1 
 
 
 
 1 
 
 
 
 
 
 i | t 
 
 
 
 230. In writing ten in figures, why do we put in ones' 
 place ? 
 
 In writing one hundred in figures we put in two 
 places. Why? 
 
 How many ones can be written with one figure? How 
 many tens? How many hundreds? 
 
 How do you write 1 ten and 1 one in figures? 
 
 How do you think 1 hundred and 1 ten should be 
 written? 
 
HUNDREDS AND TENS. 159 
 
 One hundred and one ten is written thus 110. 
 One hundred and two tens is written thus 120. 
 One hundred and three tens is written thus 130. 
 One hundred and ten tens is written thus 200. 
 Two hundreds and one ten is written thus 210. 
 Three hundreds and five tens is written thus 350. 
 
 231. Copy and complete: 
 
 1 hundred + 1 ten -- = 110. 1 hundred +9 tens 
 
 1 hundred + 3 tens = 2 hundreds + 3 tens = 
 
 1 hundred + 7 tens = 2 hundreds + 6 tens = 
 
 1 hundred + 5 tens = 2 hundreds + 5 tens = 
 
 1 hundred + 4 tens = 3 hundreds + 1 ten = 
 
 1 hundred + 8 tens = 3 hundreds + 4 tens = 
 100 + 80 = 300 + 40 = 
 
 One hundred and two tens, or 120, is read one hundred 
 twenty. 
 
 How then should 140 be read? 250? 230? 360? 
 510? 74G? 
 
 Count by 10's from 100 to 300. From 300 to 500. 
 From 500 to 1000. 
 
 How many hundreds and how many tens in 240? In 
 360? In 580? 
 
 232. Copy and complete: 
 
 260 = 2 h + 6 t 430 = 4 h + 3 t 
 
 320 = 680 = 
 
 410 = 740 = 
 
 630 == 590 = 
 
 540 = 860 = 
 
 . 720 = 770 = 
 
 810= 990 = 
 
 950= 870 = 
 
160 
 
 SCHOOL ARITHMETIC. 
 
 What number contains 4 hundreds and 3 tens? Two 
 hundreds and 5 tens? 
 
 Count by 10's from 300 to 600, and write the numbers 
 as you count. 
 
 Show with sticks what is expressed by each figure in 
 140. In 250. 
 
 How many tens in 100? In 200? In 500? In 250? 
 In 120? In 210? 
 
 233. Read: 
 
 150, 180, 210, 
 280, 470, 390, 
 
 234. Write in figures: 
 One hundred forty. 
 One hundred sixty. 
 Two hundred thirty. 
 
 320, 
 
 760, 
 
 430, 540, 
 920, 650, 
 
 360, 
 
 870. 
 
 Four hundred fifty. 
 
 Six hundred ten. 
 
 Eight hundred seventy. 
 Two hundred twenty. Seven hundred eighty. 
 Three hundred eighty. Nine hundred forty. 
 Five hundred ninety. Nine hundred ninety. 
 
 Hundreds, Tens, and Ones. 
 
 h 
 
 t 
 
 
 
 1 
 
 
 
 1 
 
 k 
 
 t 
 
 
 
 1 
 
 2 
 
 4 
 
 235. In writing 1 hundred and 1 one, or 1 more than 
 100, what do we write in the ones' place? In the tens' 
 place ? 
 
 In writing 124 what do we write in ones' place? In 
 tens' place? 
 
 Count from 100 to 200, and write the numbers as you 
 count. 
 
HUNDREDS 
 
 161 
 
 Numbers from 100 to 1000 are written as follows: 
 One hundred, 100. 
 
 One hundred one, 101. 
 
 One hundred two, 102. 
 
 Two hundred one, 201. 
 
 Two hundred twelve, 212. 
 
 Two hundred forty-six, 246. 
 
 Nine hundred ninety-nine, 999. 
 One thousand, 1000. 
 
 How many hundreds in 132? How many tens? How 
 many ones? 
 
 How many hundreds, tens, and ones in 245? In 328? 
 In 612? 
 
 236. Eead: 
 
 25 
 
 42 
 
 30 
 
 90 
 
 81 
 
 325 
 
 542 
 
 130 
 
 290 
 
 781 
 
 16 
 
 23 
 
 17 
 
 84 
 
 10 
 
 216 
 
 423 
 
 217 
 
 484 
 
 810 
 
 37 
 
 66 
 
 36 
 
 3 
 
 98 
 
 437 
 
 666 
 
 336 
 
 303 
 
 898 
 
 237. Write in figures: 
 
 Forty-one. 
 
 Two hundred forty-one. 
 
 Sixty-four. 
 
 Six hundred sixty-four. 
 
 Eighty-nine. 
 
 Four hundred eighty-nine. 
 
 Eleven. 
 
 Five hundred eleven. 
 
 Thirty-six. 
 
 Three hundred thirty-six. 
 
 Ninety. 
 
 Nine hundred ninetv. 
 
100- 
 
 h30H 
 
 h 2 = 132 
 
 100- 
 
 h20H 
 
 r 5 = 
 
 200- 
 
 I-10H 
 
 h 6" = 
 
 200- 
 
 h40H 
 
 h7 = 
 
 500- 
 
 h30H 
 
 r 8 = 
 
 300- 
 
 h60H 
 
 h4 = 
 
 400- 
 
 h40- 
 
 h4 = 
 
 700- 
 
 h80- 
 
 hV = 
 
 600- 
 
 1-20H 
 
 hO = 
 
 800- 
 
 h OH 
 
 h8 - = 
 
 162 SCHOOL ARITHMETIC. 
 
 238. Copy and complete: 
 Hundreds tens ones 
 
 1 + 3 + 2 = = 132. 
 1+2 
 
 2 -f 
 
 2 -f 
 
 5 -i 
 4 -+ 
 
 6 -i 
 
 8 -i 
 
 3 H- 
 
 9 -I 
 
 Dollars dimes cents cerits Dollars dimes cents cents 
 
 1 + 5 + 5 = 155 2 + 3 + 1 = = 231 
 
 1+4 + 2= 3+5 + 4 = 
 
 3+2 + 8= 5+7 + 5 = 
 
 4+6 + 0= 6+9 + = 
 
 2+0 + 5= ' 7+0 + 8 = 
 
 5+0 + 0= 4+4 + 4 = 
 
 In 325 cents, the 5 represents cents, the 2 represents 
 dimes, and the 3 represents dollars, or hundreds of cents. 
 
 What does each figure in 427 cents represent? 
 
 In 555 cents, which five represents the greatest value? 
 Which represents the least value? 
 
 Which 5 represents 50 cents? Which represents 5 
 cents? 
 
 Then the middle 5 represents 10 times as much as 
 which 5? 
 
 Which 5 represents 10 times as much as the middle 5? 
 
ADDITION AND SUBTRACTION. 163 
 
 Show how many dollars, dimes, and cents there are in 
 215 cents. 
 
 How many hundreds, tens, and ones are there in 348? 
 In 592? In 402? 
 
 How many figures are needed to write hundreds? How 
 many to write hundreds, tens, and ones? 
 
 Addition and Subtraction. 
 239. Add: 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 24 
 
 92 
 
 57 
 
 68 
 
 90 
 
 27 
 
 87 
 
 87 
 
 86 
 
 94 
 
 76 
 
 46 
 
 68 
 
 69 
 
 75 
 
 76 
 
 84 
 
 84 
 
 96 
 
 34 
 
 68 
 
 45 
 
 59 
 
 68 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 49 
 
 94 
 
 84 
 
 65 
 
 7 
 
 92 
 
 74 
 
 87 
 
 76 
 
 29 
 
 84 
 
 37 
 
 98 
 
 39 
 
 18 
 
 84 
 
 68 
 
 48 
 
 65 
 
 65 
 
 54 
 
 76 
 
 42 
 
 51 
 
 83 
 
 56 
 
 63 
 
 17 
 
 79 
 
 76 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 28 
 
 81 
 
 63 
 
 37 
 
 97 
 
 28 
 
 46 
 
 63 
 
 81 
 
 96 
 
 2 
 
 84 
 
 92 
 
 9 
 
 5 
 
 42 
 
 85 
 
 61 
 
 74 
 
 27 
 
 37 
 
 88 
 
 46 
 
 79 
 
 19 
 
 45 
 
 19 
 
 4 
 
 58 
 
 46 
 
 37 76 46 73 39 3T 
 
164 SCHOOL ARITHMETIC. 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 76 
 
 64 
 
 95 
 
 76 
 
 12 
 
 74 
 
 32 
 
 93 
 
 26 
 
 90 
 
 37 
 
 29 
 
 23 
 
 89 
 
 7 
 
 39 
 
 45 
 
 83 
 
 67 
 
 46 
 
 80 
 
 68 
 
 79 
 
 ^8 
 
 51 
 
 57 
 
 78 
 
 85 
 
 28 
 
 45 
 
 24 
 
 54 
 
 38 
 
 42 
 
 55 
 
 45 
 
 36 
 
 36 
 
 47 
 
 36 
 
 84 
 
 83 
 
 45 
 
 79 
 
 62 
 
 7 
 
 83 
 
 37 
 
 240. Subtract 286 from 753. 
 
 753 We cannot take 6 ones from 3 ones, so we add 10 ones to 
 
 286 the 3 ones, and take 6 from 13. Where do we get the 10 
 
 ones ? How many tens are left ? 
 467 Can we take 8 tens from 4 tens? Then we must add 10 
 
 tens to the 4 tens, and take 8 from 14. Where do we get 
 the 10 tens? How many hundreds are left? 2 hundreds from 6 
 hundreds leaves 4 hundreds. 
 
 Add 467 and 286. If the sum is 753, the subtraction 
 is correct. 
 
 Subtract and prove: 
 
 123 456 
 
 714 635 582 . 745 827 610 
 362 271 175 476 572 247 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 921 
 
 824 
 
 732 
 
 .672 
 
 523 
 
 624 
 
 473 
 
 547 
 
 435 
 
 48 
 
 149 
 
 258 
 
ADDITION AND SUBTRACTION. 
 
 165 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 362 
 
 521 
 
 607 
 
 300 
 
 815 
 
 935 
 
 57 
 
 412 
 
 278 
 
 27 
 
 726 
 
 786 
 
 19 
 
 20 
 
 21 
 
 22 
 
 23 
 
 24 
 
 872 
 
 360 
 
 706 
 
 982 
 
 617 
 
 308 
 
 375 
 
 97 
 
 418 
 
 387 
 
 419 
 
 199 
 
 241. Copy and 
 
 1. 475+65= ' 
 
 2. 582+78= 
 
 3. 368+53= 
 
 4. 729+94= 
 
 5. 647+85= 
 
 6. 768+74= 
 
 7. 526+59= 
 
 8. 395+67= 
 
 complete : 
 
 9. 248+376: 
 
 10. 426+187: 
 
 11. 519+183: 
 
 12. 372+439: 
 
 13. 582+276: 
 
 14. 766+180: 
 
 15. 647+273: 
 
 16. 504+396; 
 
 17. 527348-= 
 
 18. 716297= 
 
 19. 432186= 
 
 20. 666378 = 
 
 21. 500275= 
 
 22. 807508= 
 
 23. 431276= 
 
 24. 760498= 
 
 242. 1. How much will a span of horses cost if one 
 horse costs 85 dollars and the other 105 dollars? 
 
 2. In a box were 85 oranges. If the box would hold 
 125, how many more oranges would it take to fill it? 
 
 3. A boy shoots one arrow 97 yards up the road, and 
 another 65 yards down the road. How many yards apart 
 are the two arrows? 
 
 4. Mr. Thomas paid $625 for a lot, and sold it for 
 $900. How much did he make? 
 
 5. Three men have $980. One has $145, another 
 has $321. How much has the third man? 
 
 6. I can buy a candy store for $825, but I have only 
 
 How much more do I need? 
 
166 SCHOOL ARITHMETIC. 
 
 7. Mr. Johnson raised 345 bushels of corn, 475 bushels 
 of oats, and 128 bushels of wheat. He raised - 
 bushels in all. 
 
 8. One week a milkman sold 284 qt. of milk, the next 
 week 296 qt., the next week 318 qt., and the, next week 
 72 qt. In the four weeks he sold quarts. 
 
 9. Martin weighs 128 lb., Frank 96 lb., Jack 116 
 lb., Rob 87 lb., and Will 131 lb. How much do all five 
 boys weigh? 
 
 10. A storekeeper had 970 bushels of potatoes. One 
 week he sold 265 bu., and the next week 325 bu. How 
 many bushels had he left? 
 
 11. On Monday morning a freight train started to run 
 962 miles. The first day it ran 316 miles, the second day 
 it ran 373 miles. It still had - - miles to run. 
 
 12. September, April, June, and November each has 
 30 days. February has 28 days except in leap years, when 
 it has 29. All other months have each 31 days. How 
 many days in all the months, or in a year? 
 
 Multiplication and Division. 
 243. Multiply: 
 
 243 321 434 233 212 
 
 23234 
 
 211 322 423 534 412 
 
 54324 
 
 Take 46 splints, 4 tens and 6 ones. How many would 
 you have if you had 4 times as many? 
 
MULTIPLICATION AND DIVISION. 167 
 
 Four times 6 splints = 24 splints. How many tens and 
 how many ones in the 24 splints. 
 
 Four times 4 tens = 16 tens. 16 tens and 2 tens are 
 18 tens. You would have 18 tens and 4 ones, or 184 
 splints. 
 
 46 = 4 t + 6 o 
 4 4 
 
 184 = 16* + 24o = 18* +4<? 
 
 Multiply 246 by 4. 
 
 246' 246 = 2 A + t + So 
 
 246 4 4 
 
 984 = 9 h + 8 * + 4 -9 
 
 984 
 
 We can find the result by adding, but there is a snorter process. 
 4 times 6 ones = 24 ones. We write the 4 ones under the 6 ones, 
 and "carry" the 2 tens to add with the tens. 4 times 4 tens = 16 
 tens. The 2 ones we had to carry make 18 tens, or 1 hundred and 8 
 tens. We write the 8 tens under the 4 tens, and carry the 1 hundred. 
 4 times 2 hundreds are 8 hundreds and the 1 hundred makes 9 hun- 
 dreds. Where is the 9 hundreds written ? 
 
 MI 
 
 Multiply : 
 
 123456 
 
 45. 36 25 35 143 125 
 
 345345 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 216 
 
 117 
 
 228 
 
 170 
 
 280 
 
 181 
 
 4 
 
 5 
 
 3 
 
 2 
 
 3 
 
 4 
 
168 SCHOOL ARITHMETIC. 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 242 
 
 5 
 
 162 
 
 6 
 
 136 
 6 
 
 172 
 5 
 
 196 
 4 
 
 23 
 
 167 
 5 
 
 19 
 
 20 
 
 21 
 
 22 
 
 24 
 
 152 
 6 
 
 138 
 7 
 
 126 
 
 8 
 
 119 
 
 7 
 
 137 
 
 7 
 
 128 
 
 7 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 108 
 
 8 
 
 107 
 
 9 
 
 117 
 
 8 
 
 163 
 
 6 
 
 69 
 
 8 
 
 76 
 9 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 36 
 
 35 
 12 
 
 24 
 12 
 
 32 
 11 
 
 51 
 11 
 
 62 
 12 
 
 44 
 12 
 
 244. Examine carefully: 
 
 5 multiplied by 10 - 50. 10 X 7 = 70. 
 
 8 multiplied by 10 =80. 10 X 2 - 20. 
 
 10 multiplied by 10 == 100. 10 X 9 = 90. 
 
 12 multiplied by 10 = 120. 10 X 20 = 200. 
 
 15 multiplied by 10 == 150. 10 X 50 = 500. 
 
 Annexing to a number multiplies it by 10. 
 
 Announce results at sight: 
 
 10 X 7 10 X 25 10 X 60 
 
 10 X 11 10 X 30 10 X 66 
 
 10X14 10X36 10X70 
 
 10 X 18 10 X 40 10 X 75 
 
 10 X 20 10 X 48 10 X 87 
 
 10 X 24 10 X 50 10 X 98 
 
MULTIPLICATION AND DIVISION. 
 
 245. Divide: 
 
 169 
 
 (a) 
 00 
 
 to 
 (*) 
 w 
 
 ( f ) 
 (*) 
 
 ( h ) 
 
 (i) 
 
 2)486 
 
 2) 682 
 
 2)248 
 
 3) 636 
 
 6)660 
 
 3)369 
 
 4) 844 
 
 4)480 
 
 5) 555 
 
 8)888 
 
 2)100 
 
 2)128 
 
 3) 126 
 
 3) 150 
 
 3) 189 
 
 4) 168 
 
 4)204 
 
 4)284 
 
 4) 320 
 
 4)368 
 
 5) 105 
 
 5) 150 
 
 5) 200 
 
 5)355 
 
 5) 550 
 
 6)126 
 
 6)240 
 
 6)366 
 
 6)420 
 
 6) 546 
 
 7) 140 
 
 ' 7)217 
 
 7)280 
 
 7)357 
 
 7) 630 
 
 8) 160 
 
 8) 248 
 
 8)400 
 
 8) 560 
 
 8)728 
 
 9) 639 
 
 9) 720 
 
 9) 810 
 
 9) 909 
 
 9) 990 
 
 246. Examine carefully: 
 
 50^-10= 5 
 
 30.-f-10= 3 
 
 80-^10=- 8 
 
 100 -f- 10 -=10 
 
 120 -f- 10 = 12 
 
 150 -r- 10 = 15 
 200-^-10 = 20 
 250-^10 = 25 
 
 Annexing a cipher to a number multiplies that number 
 by 10. Show that cutting oft' zero divides a number by 10. 
 
 247. Name results at sight: 
 
 50 10 
 
 70 10 
 
 40 10 
 
 60 10 
 
 110 10 
 
 130 10 
 
 140 10 
 180 10 
 200 10 
 270 10 
 300 10 
 320 10 
 
 400 
 460 
 510 
 680 
 790 
 940 
 
 10 
 10 
 10 
 10 
 10 
 10 
 
170 SCHOOL ARITHMETIC. 
 
 248. To find i of 75 splints, take 7 tens and 5 ones, and 
 divide them into 5 equal piles. Each pile will contain 
 i of the 75. How shall we proceed to make the 5 piles? 
 
 5) 75 $ of 7 tens = 1 ten for each pile, but there are 2 tens 
 ~~T left out. 2 tens and 5 ones = 25 ones. Of 25 ones == 5 
 
 ones for each pile. Hence each pile has 1 ten -f 5 ones, 
 or 15 splints. 
 
 1. Divide 738 by 6. 
 
 6) 738 7 hundreds -=-6 1 hundred, and 1 hundred remain- 
 
 ~ls ing * 
 
 The remainder 1 hundred equals 10 tens, which with 
 the 3 tens makes 13 tens. 
 
 13 tens -4-6 = 2 tens, and 1 ten remaining. 1 ten and 8 ones = 18 
 ones. 18 ones -=-6 = 3 ones. 
 Explain this division by using splints. 
 
 2. Divide 375 by 5. 
 
 Since 3 does not contain 5, we take the 3 hundreds or 
 5) 375 30 tens and put them with the 7 tens, making 37 tens. 
 Then 37 tens -=-5 = 7 tens, and 2 tens remaining. 
 
 * ^ The 2 tens or 20 ones put with the 5 ones make 25 ones. 
 
 25 ones -5-5 = 5 ones. 
 
 Divide : 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 2)236 
 
 2)112 
 
 2)154 
 
 2) 178 
 
 2)192 
 
 2) 254 
 
 9 
 
 10 
 
 11 
 
 12 
 
 13 
 
 14 
 
 2) 176 
 
 2)452 
 
 2) 634 
 
 2) 816 
 
 2)412 
 
 2)630 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 3)168 
 
 3)195 
 
 3)351 
 
 3) 642 
 
 3)975 
 
 3)678 
 
 21 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 3)426 3)753 3)826 3)525 3)432 3)528 
 
MULTIPLICATION AND DIVISION. 171 
 
 27 
 
 4)452 
 
 28 
 
 4)896 
 
 29 
 
 4)568 
 
 30 
 
 4)604 
 
 31 
 
 4)720 
 
 32 
 
 4) 956 
 
 33 
 
 5)625 
 
 34 
 
 5)675 
 
 35 
 
 5)720 
 
 36 
 
 5)835 
 
 37 
 
 5)960 
 
 38 
 
 5) 985 
 
 39 
 
 6) 132 
 
 45 
 
 7)154 
 
 40 
 
 6)198 
 
 41 
 
 6)252 
 
 42 
 
 6) 618 
 
 48 
 7)714 
 
 43 
 
 6)714 
 
 44 
 
 6)804 
 
 46 
 
 7)112 
 
 47 
 
 7)105 
 
 49 
 
 7)798 
 
 50 
 
 7)861 
 
 51 
 
 8)176 
 
 52 
 
 8)104 
 
 53 
 
 8) 256' 
 
 54 
 
 8)736 
 
 55 
 
 8)984 
 
 56 
 
 8) 992 
 
 57 
 
 9)117 
 
 58 
 
 9)198 
 
 59 
 
 9)288 
 
 60 
 
 9)657 
 
 61 
 
 9)765 
 
 62 
 
 9) 846 
 
 249. 1. What number multiplied by 7 is equal to 84? 
 
 2. What number divided by 6 is equal to 72? To 720? 
 
 3. Find one of the 4 equal parts of 96. Of 240. 
 
 4. Of what number is 25 one-fourth? One-eighth? 
 
 5. Fifty is ^ of what number? y^ of what "number? 
 
 6. If 24 is f of some number, what is ^ of the number? 
 
 7. If $20 is of my money, how much money have I? 
 
 8. A train runs 315 miles in 9 hours. How far does 
 it run in 1 hour? 
 
 9. If 3 organs cost $180, how much does one cost? 
 
 10. If 1 organ costs $60, how much will 10 cost? 
 
 11. At the rate of 2 for 5 cents, what will a dozen 
 lemons cost? (12 = how many 2's?) 
 
 12. What will 10 books cost if 2 books cost $3 \ 10 is 
 how many times 2? The cost of 10 books will be how 
 many times $3? 
 
172 
 
 SCHOOL ARITHMETIC. 
 
 13. If you read 23 pages each day, how many pages 
 will you read in a week? 
 
 14. How many boxes will hold 117 pounds of candy, 
 if 3 pounds are put in each box? 
 
 15. In a year there are 365 days. How much more 
 than 52 weeks is that? 
 
 16. At $7 a barrel, how many barrels of flour can be 
 bought for $413? 
 
 17. A rectangle is 81 inches long and 7 inches wide. 
 How many square inches does it contain? 
 
 18. Three boys have 43 quarts of nuts, and they 
 gather 32 quarts more. If they divide them equally 
 among themselves, how many quarts will each receive? 
 
 19. How many inch-cubes can you put into a box that 
 measures in the inside 5 inches long, 4 inches wide, and 
 3 inches deep? 
 
 United States Money. 
 
 250. How many cents make a dime? 
 How many dimes make a dollar? 
 Then how many cents make a dollar? 
 
 10 cents make 1 dime. 
 
 10 dimes, or 10O cents, make 1 dollar. 
 
 One dollar is written $1, or $1.00. The sign $ is called 
 
UNITED STATES MONEY. 173 
 
 the dollar mark, and is placed before the figures express- 
 ing dollars. Four dollars and twenty-five cents is written 
 $4.25. The dot after the $4 in $4.25 means that the two 
 figures on the right stand for cents, and the figures on the 
 left stand for dollars. This dot is called the decimal point. 
 
 251. Head the following: 
 
 $4.75 
 
 $6.20 
 
 $8.10 
 
 $2.05 
 
 $5.05 
 
 $4.50 
 
 $2.84 
 
 $1.90 
 
 $3.60 
 
 $4.40 
 
 $3.25 
 
 $7.15 
 
 $5.35 
 
 $9.01 
 
 $8.16 
 
 Write the following: 
 
 Two dollars and fifty cents. One dollar and twenty-five 
 cents. One dollar. Five dollars and forty cents. Eight 
 dollars and five cents. Ten dollars and seventy-five cents. 
 Six dollars and two cents. Nine dollars and fifteen cents. 
 
 252. When there are no dimes or cents we do not need 
 to use the dot unless we write ciphers in the place of dimes 
 and cents. 
 
 Read the following: 
 
 $5 $10 $50 $100 $125 $500 
 
 $1 $25 $75 $110 $206 $640 
 
 $4.00 $2.00 $8.00 $105 $30.00 $75.00 
 
 When there are no dollars to write we place the dot 
 between the dimes and the dollar mark. 
 
 Read the following: 
 
 $.25 $.75 $.10 $.01 $.07 $.09 
 
 $.50 $.90 $.05 $.20 $.85 $.99 
 
174: SCHOOL ARITHMETIC. 
 
 Write in figures: 
 
 Thirty dollars. One hundred five dollars. Four hun- 
 dred ten dollars. Five hundred dollars. Twenty-five cents. 
 Sixty cents. Ten cents. Five cents. Thirty cents. One 
 cent. Eighty-eight cents. Seven cents. Twelve cents.. 
 Five dollars and five cents. 
 
 253. Write as dollars and cents : 
 
 150^ 175^ 225^ 360$* 105^ 310^ 
 
 420^ 500^ 713^ 609^ 220# 666^ 
 
 = $3.25 
 
 Complete and 
 
 read: 
 
 
 Dollars 
 
 Dimes 
 
 Cents 
 
 3 
 
 2 
 
 5 
 
 5 
 
 1 
 
 6 
 
 
 
 7 
 
 
 
 2 
 
 4 
 
 8 
 
 8 
 
 3 
 
 
 
 
 
 
 
 4 
 
 4 
 
 
 
 
 
 
 
 5 
 
 2 
 
 9 
 
 6 
 
 7 
 
 254. Dollars, dimes, and cents are added just as hun- 
 dreds, tens, and ones are added. 
 
 Dol. Dimes $ What is written in the first 
 
 o . K _ too AK. column? In the second ? In 
 
 ^' 4t the third? 
 
 4 5 8 = 4.58 Are the dots all in one 
 
 7 6 . = 7.60 column? 
 
 How do we get 14 dollars 
 
 14 6 3 =$14.63 in the sum? 
 
UNITED STATES MONEY. 175 
 
 Find the sums: 
 
 $12.15 
 
 $16.52 
 
 $21.45 
 
 $60.76 
 
 7.06 
 
 5.01 
 
 8.72 
 
 28.09 
 
 8.29 
 
 7.75 
 
 6.34 
 
 7.84 
 
 4.80 
 
 30.40 
 
 5.80 
 
 3.63 
 
 36.94 
 
 28.89 
 
 10.10 
 
 5.00 
 
 Find the differences: 
 
 $84.75 
 
 $70.20 
 
 $37.00 
 
 $64.03 
 
 26.38 
 
 8.05 
 
 25.25 
 
 28.85 
 
 Multiply: 
 
 
 
 
 $14.16 
 
 $15.10 
 
 $12.25 
 
 $24.75 
 
 3 
 
 4 
 
 5 
 
 3 
 
 $42.48 
 
 
 
 
 $51.80 
 
 $42.34 
 
 $28.04 
 
 $37.43 
 
 6 
 
 5 
 
 7 
 
 8 
 
 Divide : 
 
 
 
 
 2) $48.76 
 
 3) $48.51 
 
 2) $75.20 
 
 2) $25.00 
 
 $24.38 
 
 
 
 
 255. 1. One month Mr. Gray paid $22.50 for rent, 
 $4.80 for milk, $26.78 for groceries, and $6.37 for gas. 
 How much did he pay for all ? 
 
 2. I owe $32.20 for coal, If I pay $25 now, how much 
 shall I still owe $ 
 
176 SCHOOL ARITHMETIC. 
 
 3. A man bought 6 cows at $24.75 each. He paid 
 $ for all. 
 
 4. A dealer paid $112.25 for 5 stoves. What was the 
 price of one? 
 
 5. A farmer paid $328 for two horses. He sold one 
 for $197.50, and the other for $187.50. What was his 
 profit? 
 
 6. Find the cost of 10 acres of land at $85 an acre. 
 
 * 
 
 7. Mrs. Brown gave $320 for 10 cows. How much 
 did she pay for one cow? 
 
 8. How many pounds of sugar at 5^ a pound can you 
 buy for 75^? 
 
 9. If I can buy 2 oranges for 5^, how many can I buy 
 for a half-dollar? 
 
 Oral Exercises. 
 256. How much money in : 
 
 a. 1 5-dollar bill, 3 2-dollar bills, 1 silver dollar, 1 half 
 dollar, and 1 quarter? 
 
 b. 1 10-dollar bill, 2 5-dollar bills, 3 silver dollars, 3 
 quarters, and 2 dimes? 
 
 c. 3 20-dollar bills, 6 5~-dollar bills, 2 1-dollar bills, 2 
 half dollar bills, 5 dimes, and 6 nickels? 
 
 d. 5 10-dollar bills, 10 2-dollar bills, 1 5-dollar gold 
 piece, 6 half dollars, 8 dimes, and 5 cents? 
 
 How many half dollars are therein $2? $5? $10? $12? 
 How many quarters are there in $2? $3? $5? $10? 
 How many dimes are there in $2? $3? $5? $15? 
 How many quarters are there in 2 half dollars? 5 half 
 dollars? 12 half dollars? 
 
ORAL EXERCISES. 
 
 177 
 
 How many dimes are there in 2 quarters ? 2 half dollars ? 
 6 quarters? 3 half dollars? 
 
 How many dimes are therein 30*? 80*? 120*? 250*? 
 10 nickels? 
 
 How many dollars are there in 20 dimes? 50 dimes? 
 60 dimes? 75 dimes? 40 nickels? 600 cents? 
 
 257. Copy and complete: 
 
 i of $1 = 50* 
 i of $1 = 
 I of $1 = 
 of $1 = 
 
 A- ^ $1 = 
 
 25* = 
 
 of $1 
 of $1 
 of $1 
 of $1 
 of $1 
 
 258. Two dollars and <a half means $2.50; a dollar and 
 a quarter means $1.25. 
 
 Complete and read: 
 
 $1 + 4 of $1 = 
 
 $2 + i of $1 = 
 $5 + i of $1 - 
 $3 + t of $1 = 
 
 $4 + of $1 = 
 $7 + T V of $1 = 
 
 $9 + -A- of $1 = 
 
 259. Find the amount of this bill: 
 
 
 6 Ib. steak at .... $ .15 
 5 yd. silk at 1.35 
 
 
 
 
 4 gal. milk at 30 
 9 doz. eggs at .... .14 
 
 
 
178 SCHOOL ARITHMETIC. 
 
 260. A lady bought 3 Ib. of sugar for 18 cents, and 
 gave the grocer a half dollar. He made the " change " 
 as follows: 
 
 Saying 18, he handed her 2#, and said 20; gave her a 
 nickel, and said 25; then gave her a quarter, and said 50. 
 Did she get the correct change? 
 
 Change is usually made by counting up from the 
 amount of the purchase to the amount given in pay- 
 ment. 
 
 Find the change by counting up: 
 
 Bought candy for 3^; gave a dime in payment. 
 Bought sugar for 83^; gave $1 in payment. 
 Bought shoes for $3.25; gave $5 in payment. 
 Bought books for $8.12; gave $10 in payment. 
 
NUMBERS TO MILLIONS. 179 
 
 NUMBERS TO MILLIONS. 
 
 261. Measure with the quart measure the water in 
 this pail. How many quarts are there? One quart is 
 called the unit of measure. 
 
 Measure with a ruler the length of your book. How 
 many inches long is it? What unit of measure did you 
 use? 
 
 When we say w have ten apples, the unit used in count- 
 ing them is one apple. 
 
 One of any kind (or any group regarded as one) by com- 
 parison with which we count or measure is called a unit. 
 
 262. You have already learned that when three figures 
 are written side by side, the one at the right represents 
 ones, the second figure represents tens, and the one at the 
 left represents hundreds. 
 
 Can you write 10 hundred with three figures? 
 The number 10 hundred is called a thousand. 
 A thousand is written 1,000. Then how many figures 
 are required to write thousands? 
 
 263. One thousand one hundred is written 1,100. 
 Twenty-five thousand is written 25,000. 
 
 Ten thousand five hundred is written 10,500. 
 
 One hundred twenty thousand three hundred is writ- 
 ten 120,300. 
 
 How many thousands and how many hundreds in 
 1,500? 2,600? 8,200? 3,800? 9,300? 18/TOO? 115,400? 
 
180 SCHOOL ARITHMETIC. 
 
 264. One thousand one hundred ten is written 1,110. 
 One thousand one hundred eleven is written 1,111. 
 One thousand twenty-five is written 1,025. 
 
 One thousand four is written 1,004. 
 
 How many thousands and tens in 1,130? 1,480? 
 2,140? 3,250? 4,890? 7,620? 6,970? 5,710? 
 
 How many thousands, hundreds, tens, and ones in 1,235? 
 1,346? 1,472? 2,125? 3,521? 6,275? 2,017? 12,534? 
 
 Write in figures and read all the numbers from 1,002 
 to 1,020; from 10,995 to 11,001; from 125,090 to 125,160. 
 
 265. Complete: 
 
 2 ? 743 = 2000 + 700 + 40 + 3 = 2th + 7h + i + 3o 
 5,271 = 
 1,075 r= 
 12,004 = 
 
 25,378 = 
 
 3000 + 500 + 60 + 2 = Mh + 6h + 6t + 2o = 3,562. 
 6000 + 200 + 70 + 5 = 
 5000 + 800 + 20 + = 
 4000 + 000 + 50 + 4 = 
 8000 + 300 + 00 + 7 = 
 
 266. Compare 1, 10, 100, 1000. 
 
 How many ones make 1 ten? 
 
 How many tens make 1 hundred? 
 
 How many hundreds make 1 thousand? 
 
 When 1 stands alone how many ones does it express? 
 When it stands at the left of a cipher? At the left of two 
 ciphers ? 
 
NUMBERS TO MILLIONS. 181 
 
 In the number 11 which 1 expresses the greater value? 
 How many times as great? In the number 111? 
 
 REMEMBER : Any figure represents ten times the 
 value it would represent in the next place to the right. 
 
 267. In counting by ones the unit is one. 
 
 In counting the tens of a number, we may regard one 
 ten as the unit for the tens. 
 
 May one hundred be regarded as the unit for the 
 hundreds of a number? 
 
 The ones of a number are called units of the first order, 
 or simply units; the tens are called units of the second 
 order; the hundreds are called units of the third order, 
 and so on. 
 
 268. One more than 999,999 is 1000 thousands, which 
 is called a million, and is written thus 1,000,000. 
 
 When we wrote thousands, what did we put after the 
 last figure of the thousands? 
 
 Do we place a second comma after the figure for 
 millions ? 
 
 Into groups of how many figures each do the commas 
 divide the figures? 
 
 For convenience in reading numbers the figures are 
 divided into groups of three figures each, beginning at the 
 right. Each group is called a period. The right-hand 
 group is called the period of units, the second group, the 
 period of thousands, the third group, the period of 
 millions. 
 
182 
 
 SCHOOL ARITHMETIC. 
 
 269. "What we have learned about the manner of 
 writing numbers is shown in the following 
 
 
 CO 
 
 _- 
 
 
 1 1 
 
 
 a 
 
 .2 
 
 g o 
 W H H 
 
 in 
 
 rH . IT? W 
 
 3 
 
 840 
 
 532 
 
 3d 
 
 Y 
 
 2nd 
 
 1st 
 
 Period. 
 
 Period. 
 
 Period. 
 
 Millions 
 
 Thousands 
 
 Units 
 
 The number in the table is read three million 7 eight 
 hundred forty thousand, five hundred thirty-two. 
 
 Examine the table and tell: 
 
 How many figures are required to write ten-thou- 
 sands \ Hundred -thousands \ 
 
 How many figures are required to write millions? 
 Are the tens and ones of each group read together? 
 How many figures has the left-hand group? 
 How many figures must the other groups contain? 
 
 Each period has three places ones, tens, and hun- 
 dreds. The first period has ones, tens, and hun- 
 dreds of ones; the second has ones, tens, and 
 hundreds of thousands; and so on. 
 
NUMBERS TO MILLIONS. 183 
 
 270. Eead the following: , 
 
 507 101 340 300 999 
 
 2,100 1,310 2,136 3,204 5,060 
 
 6,400 3,240 1,275 6,308 ' 8,401 
 
 12,800 15,890 12,581 16,035 14,008 
 
 234,600 616,720 321,476 695,182 999,999 
 
 3,005,008 2,452,320 1,982,200 2,879,079 1,121,001 
 
 Write in figures: 
 
 Two thousand five hundred. Five thousand eight hun- 
 dred. Four thousand two hundred ten. Six thousand one 
 hundred ninety. Three thousand four hundred forty-six. 
 Eight thousand seven hundred thirty-five. Four thousand 
 three hundred eight. Nine thousand twenty-four. Two 
 thousand ten. Six thousand twenty. Seven thousand five. 
 Ten thousand fifty-eight. Eight thousand two hundred 
 six. One million. 
 
 271. I V X L C D M 
 
 1 5 10 50 100 500 1000 
 
 You have already learned how numbers are written in 
 the Roman notation up to 12. 
 
 Now state what the new letters L, C, D, and M each 
 stand for. 
 
 I represents 1; II represents 2; X stands for 10; XX 
 stands for 20. Then what is the effect of repeating a letter? 
 
 Y stands for 5; IY stands for 4; X stands for 10; IX 
 stands for 9. "What then is the effect of writing a letter of 
 less value before a greater? 
 
184: SCHOOL ARITHMETIC. 
 
 What does XL stand for? XC? 
 
 YI stands for 6; XI stands for 11. What is the effect 
 of writing a letter of less value after a greater? 
 What does LX stand for? CX? 
 
 Complete : 
 
 1= I 
 
 11 XI 
 
 21 = XXI 
 
 35 = XXXV 
 
 2 = 
 
 12 = 
 
 22 = 
 
 45 = 
 
 3 = 
 
 13 = 
 
 23 = 
 
 75 = 
 
 4 = 
 
 14 = 
 
 24 = 
 
 95 = 
 
 5 = 
 
 15 
 
 25 = 
 
 34 = 
 
 6 = 
 
 16 = 
 
 26 = 
 
 46 = 
 
 7 = 
 
 17 = 
 
 27 = 
 
 77 = 
 
 8 = 
 
 18 = 
 
 28 = 
 
 88 = 
 
 9 = 
 
 19 = 
 
 29 = 
 
 99 = 
 
 20= 30= 101 = 
 
 Addition and Subtraction. 
 
 272. Add 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 3,725 
 
 7,618 
 
 5,392 
 
 6,728 
 
 8,796 
 
 5,287 
 
 4,376 
 
 2,763 
 
 8,276 
 
 6,978 
 
 7,392 
 
 2,914 
 
 4,827 
 
 4,937 
 
 3,547 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 $7,246 
 
 $2769 
 
 $3486 
 
 $16.38 
 
 $70.35 
 
 3,983 
 
 8478 
 
 7615 
 
 29.15 
 
 25.97 
 
 2,762 
 
 9192 
 
 5307 
 
 85.72 
 
 64.78 
 
 6,219 
 
 7581 
 
 8590 
 
 72.40 
 
 59.24 
 
 8,768 
 
 4803 
 
 6925 
 
 69.17 
 
 91.39 
 
ADDITION AND SUBTRACTION. 
 
 185 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 87535 
 
 29413 
 
 44777 
 
 67890 
 
 36925 
 
 62914 
 
 72694 
 
 32416 
 
 12345 
 
 81470 
 
 4728 
 
 547 
 
 87324 
 
 34251 
 
 14703 
 
 872 
 
 84062 
 
 4715 
 
 26076 
 
 69258 
 
 53389 
 
 7618 
 
 982 
 
 8907 
 
 58147 
 
 7604 
 
 385 
 
 5639 
 
 73529 
 
 3692 
 
 5881 
 
 92764 
 
 76248 
 
 982 
 
 81470 
 
 3627 
 
 8270 
 
 39571 
 
 8076 
 
 369 
 
 98376 
 
 64936 
 
 50867 
 
 93745 
 
 70487 
 
 273. Find the. sum of: 
 
 16. 72384 + 2984 + 37038 + 920 + 8006. 
 
 17. 60572 + 3751 + 807 + 73092 + 46075. 
 
 18. 19283 + 47650 + 2006 + 8372 + 50098. 
 
 19. 53761 + 6807 + 924 + 7354 + 89763. 
 
 20. 40516 + 27385 + 6607 + 4481 + 90876. 
 
 21. Four thousand six, twenty thousand seven hundred 
 fourteen, eighty-nine, five hundred ninety-four, eighty- 
 four thousand nineteen. 
 
 274. Subtract: 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7,236 
 4,753 
 
 5,176 
 2,849 
 
 8,352 
 5,178 
 
 6015 
 2376 
 
 9200 
 2914 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 $3520 
 1750 
 
 $7245 
 2754 
 
 $6321 
 4576 
 
 $4000 
 2545 
 
 $8007 
 7129 
 
 11 
 
 12 
 
 13 
 
 14 
 
 15 
 
 8003 
 2347 
 
 6004 
 5706 
 
 7005 
 5717 
 
 3004 
 1068 
 
 45216 
 
 27089 
 
186 
 
 SCHOOL ARITHMETIC. 
 
 16 
 
 17 
 
 18 19 
 
 20 
 
 37002 
 
 56214 
 
 73014 18001 
 
 20450 
 
 19008 
 
 42657 
 
 34025 7608 
 
 16784 
 
 21 
 
 22 
 
 23 
 
 24 
 
 870623 
 
 601540 
 
 803002 
 
 500000 
 
 581539 
 
 403862 
 
 80305 
 
 423167 
 
 275. The Minuend is the number from which another 
 number is subtracted; the Subtrahend is the number that 
 is subtracted. What is ihej'emainder f 
 
 1. The minuend is 825, the subtrahend is 368. Find 
 the remainder. 
 
 2. The minuend is 7215, the remainder 2345. What is 
 the subtrahend? 
 
 3. The subtrahend is 4527, the remainder is 1328. 
 What is the minuend? 
 
 4. To what number must 572 be added to make the 
 sum 1420? 
 
 5. If 365 be subtracted from - , the remainder 
 will be 1824. 
 
 276. 1. There are 365 days in a common year. In 
 10 common years there are - - days. 
 
 2. In 1860 there were 177,840 people living in Boston; 
 in 1890, there were 448,477. What was the increase in 
 30 years? 
 
 3. From 1860 to 1890 the population of Baltimore 
 grew from 212,418 to 434,439. Find the gain. 
 
 4. In 1890 how much larger was the population of 
 Boston than that of Baltimore? 
 
ILLUSTRATION. $5 -f $5 -f $5 -f- $5 = $20. This is addition. 
 4 X $5 == $20. This is multiplication. $5 is the multiplicand. It is 
 taken 4 times, hence 4 is the multiplier. Which is the product? 
 
 The multiplicand and the multiplier are called factors 
 of the product. Thus, in 2 X 5 = 10, 2 and 5 are factors 
 of 10. 
 
 Of what number are 8 and 11 the factors? 5 and 7? 
 
 One factor of 21 is 3. What is the other factor? 
 
 What is the product of the factors 7 and 9? 10 and 12? 
 
 The product is 48, and one factor is 4. What is the 
 other factor? 
 
279. 
 
 1 
 
 Find the products: 
 
 20 
 9 
 
 4 
 
 5 
 
 $1250 
 5 
 
 $2348 $3176 
 3 4 
 
 $5267 
 6 
 
 $24,639 
 5 
 
 6 
 
 7 8 
 
 9 
 
 10 
 
 6314 
 
 7 
 
 11 
 
 8273 
 9 
 
 5283 7489 
 6 7 
 
 36,458 
 6 
 
 57,926 
 8 
 
 12 13 
 
 6742 9275 
 
 8 8 
 
 14 
 7364 
 9 
 
 15 
 
 69,078 
 9 
 
MULTIPLICATION. 189 
 
 16 17 
 
 18 19 
 
 20 
 
 3906 4075 
 
 8 ' 9 
 
 7766 8594 
 
 7 8 
 
 99,888 
 9 
 
 21 22 
 
 23 24 
 
 25 
 
 5604 3817 
 6 8 
 
 6670 4096 
 
 9 7 
 
 124,762 
 6 
 
 26. Multiplier 8, 
 27. Multiplicand 
 
 multiplicand 50,725. 
 23,450, multiplier 7. 
 
 
 28(K 1. If a man earns $125 a month, how much 
 does he earn in 6 months? 
 
 $125 in one month. 
 
 6 In 6 months he earns 6 times 
 
 $125, or $750. 
 $750 in six months. 
 
 2. A grocer bought 8 barrels of sugar each weighing 
 284 Ib. How many pounds did he buy? 
 
 3. Mr. Henry pays $425 a year for rent. How much 
 does he pay in 3 years? 
 
 4. If a teacher is paid $270 each year, how much is 
 paid in 8 years? 
 
 5. How many strokes does a clock strike in 12 hours? 
 In 24 hours? In a week? 
 
 6. If a train runs 386 miles a day, how far does it 
 run in 7 days? 
 
 7. The distance from Pit.tsburg to Philadelphia is 354 
 miles. How many miles does a man travel who makes 
 2 round trips between the two cities? 
 
 8. A man sold 48 bales of cotton, which was T V of his 
 crop. How many bales had he left? 
 
190 SCHOOL ARITHMETIC. 
 
 281. 1. Multiply $48 by 12. 
 
 $48 
 12 
 
 ~~QA - O V Are 2 times $ 48 + 10 times 
 
 480 = 10 X 
 
 $576 = 12 X 
 
 2. Multiply $32, $54, $66, and $75 each by 12. 
 
 3. Multiply 225 by 15. By 23. 
 
 225 225 
 
 15 23 
 
 1125= 5X225 675= 3X225 
 
 2250 = 10 X 225 . 4500 = 20 X 225 
 
 3375 = 15 X 225 5175 = 23 X 225 
 
 4. Multiply 314 by 13. By 24. 
 Find the produces: 
 
 5. 36 X 12. 10. 124 X 22. 15. 413 X 18. 
 
 6. 45 X 13. 11. 143 X 25. 16. 625 X 23. 
 
 7. 63 X 15. 12. 216 X 32. 17. 842 X 26. 
 
 8. 72 X 18. 13. 244 X 36. 18. 736 X 33. 
 
 9. 88 X 23. 14. 326 X 43. 19. 534 X 44. 
 
 20. Multiply 648 by 164. 
 
 648 648 
 
 164 164 
 
 2592= 4X648 2592 
 38880= 60 X 648 3888* 
 64800 = 100 X 648 648 
 
 106272 = 164 X 648 106272 
 
 * In multiplying by tens it is not customary to put the in ones' 
 place. 60 X 648 = 38880 ones, or 3888 tens. 
 
 In multiplying by hundreds how many ciphers may we omit? 
 When we multiply by tens and omit the 0, in what place does the 
 
MULTIPLICATION. 191 
 
 first figure of the partial product stand ? In what place when we 
 multiply by hundreds and omit the two ciphers? 
 
 Observe that the ones, tens, and hundreds of the multiplicand, in order, 
 are multiplied by the ones, tens, and hundreds of the multiplier, in order, 
 and that the first figure of each product is put directly under the figure of 
 the multiplier used in obtaining it, and that the products are then added. 
 
 282. Multiply: 
 
 1 
 
 2 
 
 3 4 
 
 5 
 
 362 
 
 264 
 
 218 264 
 
 317 
 
 24 
 
 26 
 
 32 34 
 
 25 
 
 7 
 
 8 
 
 9 10 
 
 11 
 
 523 
 
 417 
 
 643 527 
 
 486 
 
 44 
 
 35 
 
 38 46 
 
 53 
 
 13 
 
 14 
 
 15 
 
 16 
 
 5247 
 
 6351 
 
 2583 
 
 4286 
 
 54 
 
 68 
 
 65 
 
 73 
 
 18 
 
 19 
 
 20 
 
 21 
 
 6304 
 
 7023 
 
 5230 
 
 4076 
 
 36 
 
 47 
 
 84 
 
 63 
 
 23 
 
 24 
 
 25 
 
 26 
 
 325 
 
 761 
 
 248 
 
 691 
 
 143 
 
 235 
 
 534 
 
 346 
 
 28 
 
 29 
 
 30 
 
 31 
 
 2317 
 
 3465 
 
 4263 
 
 6375 
 
 324 
 
 125 
 
 217 
 
 264 
 
 27 
 
 835 
 462 
 
 32 
 
 8729 
 536 
 
 33. Multiply 325 by 103. 
 325 
 
 If either factor is 0, what is the product? 
 Multiply 103 by 325 and compare the 
 products. 
 
 33475 
 
192 
 
 SCHOOL ARITHMETIC. 
 
 283. Find the 
 
 product : 
 
 
 1. 7430 X 53. 
 
 10. 2108 X 93. 
 
 19. 62425 X 55. 
 
 2. 9625 X 49. 
 
 11. 3206 X 57. 
 
 20. 23507 X 68. 
 
 3. 6275 X 56. 
 
 12. 4004 X 68. 
 
 21. 75310 X 39. 
 
 4. 4760 X 72. 
 
 13. 5760 X 74. 
 
 22. 38672 X 74. 
 
 5. 3586 X 63. 
 
 14. 3090 X 85. 
 
 23. 50836 X 83. 
 
 6. 8274 X 76. 
 
 15. 6805 X 39. 
 
 24. 40078 X 95. 
 
 7. 6407 X 81. 
 
 16. 7273 X 47. 
 
 25. 82036 X 78. 
 
 8. 496 X 237. 
 
 17. 638 X 524. 
 
 26. 3726 X 485. 
 
 9. 738 X 346. 
 
 18. 857 X 432. 
 
 27. 4385 X 724. 
 
 284. 1. Multiply 72 by 30. 
 
 72 72 
 
 30 or 
 
 30 
 
 2160 
 
 2160 
 
 Here we multiply by 3 tens 
 and no ones. 
 
 Multiply : 
 
 2. 74 X 20. 
 3. 48 X 30. 
 4. 65 X 40. 
 5. 142 X 30. 
 
 6. 59 X 30. 
 
 7. 38 X 60. 
 8. 67 X 50. 
 9. 234 X 40. 
 
 10. 75 X 80. 
 11. 83 X 70. 
 12. 96 X 90. 
 13. 456 X 150. 
 
 285. 1. If a man takes 180 steps a minute, how 
 many steps will he take in an hour? 
 
 2. If a train runs 35 miles an hour, how far will it 
 run in 20 hours? 
 
 3. How much will 8 months' wages amount to at $27 
 a month? 
 
 4. When you know the cost of one orange, how can 
 you find the cost of 10 oranges? 
 
 5. A steamer sails 275 miles a day. How far does she 
 sail in 9 days? 
 
MULTIPLICATION. 193 
 
 6. In an orchard there are 18 rows and 12 trees in a 
 row. How many trees in the orchard? 
 
 7. My parlor is 18 feet square. How many square 
 yards of carpet will it require? 
 
 8. How many lines are there on this page of your 
 book? How many on 27 such pages? 
 
 9. There are 144 pens in a box. How many pens in 
 2 dozen boxes? 
 
 10. A lot is 175 feet long and 60 feet wide. How 
 many square feet does it contain? 
 
 11. There are 28 regiments in an army. If there are 
 875 men in each regiment, how many men in the army? 
 
 12. If a bushel of wheat weighs 60 pounds, what will 
 150 bushels weigh? 
 
 13. An army used 48512 pounds of meat each week. 
 How much was used in 13 weeks? 
 
 Find the cost of: 
 
 14. 245 dozen fresh eggs at 9^ a dozen. 
 
 15. 384 pounds of sugar at 6^ a pound. 
 
 16. 18 pianos at $275 each. 
 
 17. 75 tons of clover hay at $14 a ton. 
 
 18. 286 bushels of wheat at 70^ a bushel. 
 
 19. 524 sheep at $4 a head. 
 
 20. 4 barrels of molasses, 42 gal. each, at 35^ a 
 gallon. 
 
 21. 65 barrels of apples, 3 bu. each, at 45^ a bushel. 
 
 22. 2 rolls of carpet, 59 yd. each, at 75^ a yard. 
 
 23. 8 loads of coal, 45 bu. each, at 8^ a bushel. 
 
194 SCHOOL ARITHMETIC. 
 
 Division. 
 
 286. When we divide one number by another, the 
 result is called the Quotient ; the number divided is called 
 the Dividend; and the number by which we divide is called 
 the Divisor. 
 
 In multiplication we have two factors to find the product. 
 In division we have a product and one factor to find the 
 other factor. The dividend is the product, the divisor 
 one factor. What is the other factor? 
 
 2X$5 = $10. $10 -r-2 = $5. $10 -^-$5 = 2, 
 
 Point out the factors in this example. The product. 
 The dividend. The divisors. The quotients. 
 
 287. Division includes 
 
 (A). Finding one of the equal parts of a number; as, -J 
 /of $10 = $5. $10 -f- 2 = $5. 
 
 (B). Finding how many times one number contains 
 .another; as, $20 -r- $5 = 4. 12 ft. -4- 3 ft. == 4. 
 
 1. What is one of the 3 equal parts of $24? 
 
 $24 -r- 3 = $8. 
 
 2. How many times is $3 contained in $24? 
 
 $24 -=-$3 = 8. 
 
 In these examples $24 is the dividend. In the first 3 is the divisor 
 and $8 the quotient. In the second $3 is the divisor and 8 the 
 quotient. 
 
 3. When 50 Ib. is the dividend and 5 the divisor, what 
 is the quotient? 
 
 What is required in this example ? Do we also find the number of 
 pounds in each part? Is the quotient of the same kind (pounds) as 
 the dividend? 
 
DIVISION. 
 
 195 
 
 4. When 40^ is the dividend and 5^ the divisor, what 
 is the quotient? 
 
 Are the dividend and divisor of the same kind in this example? 
 Does the quotient denote the number of times the divisor must be 
 taken to equal the dividend? 
 
 5. Find by trial whether the product of the quotient 
 and divisor is equal to the dividend. 
 
 6. When $36 is the dividend and $4 the quotient, what 
 is the divisor? 
 
 7. When $7 is the divisor and 5 the quotient, what is 
 the dividend? 
 
 8. If you have a dozen eggs and wish to give me J of 
 them, you must give me one of the 3 equal parts of 12 
 eggs. That is, you must divide 12 eggs by 3. 
 
 9. Divide 30 gallons by 3. By 5. By 6. By 10. 
 
 10. What is 4 of 36 feet? J? \l T V? 
 
 288. Divide: 
 12 3 45 6 
 
 3) 369 5) 550 6) 126 5) 205 4) 328 6) 426 
 
 7 
 4)368 
 
 8 
 
 5)400 
 
 9 
 
 7)427 
 
 10 
 
 6) 540 
 
 11 
 
 8)720 
 
 12 
 
 8)818 
 
 13 14 15 16 
 
 6) 612 7) 714 5) 300 9) 36 
 
 17 18 
 
 8) 808 9) 918 
 
 19 
 
 4) 8044 
 
 20 
 
 5) 1050 
 
 21 
 
 3) 9126 
 
 22 
 
 6) 1206 
 
 23 
 
 7)14014 
 
 289. Find the quotients: 
 
 1. 
 
 3096- 
 
 -3. 
 
 7. 
 
 18618- 
 
 -6. 
 
 13. 
 
 305100- 
 
 -5. 
 
 2. 
 
 4015- 
 
 -5. 
 
 8. 
 
 20515 - 
 
 -5. 
 
 14. 
 
 180120- 
 
 -3. 
 
 3. 
 
 1421- 
 
 -7. 
 
 9. 
 
 16812- 
 
 -4. 
 
 15. 
 
 363636- 
 
 -6. 
 
 4. 
 
 1224- 
 
 -6. 
 
 10. 
 
 14721 - 
 
 -7. 
 
 16. 
 
 281435 - 
 
 -9. 
 
 5. 
 
 1612- 
 
 -4. 
 
 11. 
 
 24816- 
 
 -8. 
 
 17. 
 
 271836 - 
 
 -9. 
 
 6. 
 
 3240- 
 
 -8. 
 
 12. 
 
 18924- 
 
 -9. 
 
 18. 
 
 321632- 
 
 -8. 
 
196 SCHOOL ARITHMETIC. 
 
 19. What is the difference between i of 824 and 824 
 -5- 4? 
 
 20. Which would you rather have i of $1200 or 
 $1200-^- 3? 
 
 290. Are 5 tens and 6 ones equal to 4 tens and 16 ones? 
 Complete : 
 
 34 = 3 tens + 4 ones = 2 tens + ones. 
 
 78 = 7 tens + 8 ones = 6 tens + - - ones. 
 
 42 = 4 tens + 2 ones = 3 tens + ones. 
 
 87 = 8 tens + 7 ones = 6 tens + - ones. 
 
 95 = 9 tens + 5 ones = 5 tens + ones. 
 
 126 = 12 tens + 6 ones = 7 tens + - - ones. 
 
 1. Divide 34 by 2, or find i of 34. 
 
 2) 34 = 2 tens + 14 ones. j O f 2 tens- 1 ten. 
 17 = 1 ten + 7 ones. i of 14 ones - 7 ones. 
 
 Complete: 
 
 
 
 
 2. 4 of 78 = 
 
 6. 
 
 | of 126 = 
 
 10. 76-^-2 
 
 3. J of 42 = 
 
 7. 
 
 i of 52 = 
 
 11. 51 -f- 3 
 
 4. ^ of 87 = 
 
 8. 
 
 i of 65 = 
 
 12. 80 -H 5 
 
 5. 4 of 95 = 
 
 9. 
 
 i of 64 = 
 
 13. 78 -T- 6 
 
 291. 1. Divide 968 by 8. 
 
 8)968 = Sh + 16* + So 
 121 = 1ft + 2* + lo 
 
 Divide : 
 
 2. 
 
 568 
 
 by 
 
 4. 
 
 6. 
 
 655 
 
 by 
 
 5. 
 
 10. 
 
 516 
 
 by 
 
 3. 
 
 3. 
 
 605 
 
 by 
 
 5. 
 
 7. 
 
 968 
 
 by 
 
 8. 
 
 11. 
 
 750 
 
 by 
 
 5. 
 
 4. 
 
 847 
 
 by 
 
 7. 
 
 8. 
 
 780 
 
 by 
 
 6. 
 
 12. 
 
 684 
 
 by 
 
 4. 
 
 5. 
 
 726 
 
 by 
 
 6. 
 
 9. 
 
 648 
 
 by 
 
 4. 
 
 13. 
 
 846 
 
 by 
 
 6. 
 
DIVISION. 19T 
 
 292. 1. Divide 945 by 7. 
 
 7)945 = = 7/i + 2t + 5o= 7fe + 21* + 35o 
 135 = Ife + 3* + 5o 
 
 9/1 -r- 7 = Ih, and 2ft or 20* remaining; 24* --5- 7 = 3, and 3? or 
 30 o remaining ; 35 o -f- 7 = 5 o. 
 
 'Divide : 
 
 
 
 2 3 
 
 456 
 
 7 
 
 5) 625 4) 548 
 
 3) 525 6) 756 5) 725 
 
 4)632 
 
 8 9 
 
 10 11 12 
 
 13 
 
 6) 852 3) 534 
 
 8) 984 7) 952 8) 992 
 
 6)948 
 
 14 15 
 
 16 17 
 
 18 
 
 4) 8524 3) 6471 
 
 2) 2756 5) 5620 
 
 6) 6804 
 
 19 20 
 
 21 22 
 
 23 
 
 4) 9256 3) 7260 
 
 2) 3674 5) 6705 
 
 6) 7344 
 
 293. 1. Divide 
 
 7356 by 12. 
 
 
 (a) 
 12) 7356 
 
 613 
 
 w 
 
 12) 7356 ( 613 
 72 
 
 quotient. 
 
 73 hundreds +- 12 = 6 hundreds, 
 
 and 1 hundred remaining. 
 15 tens -5- 12 = 1 ten, and 3 tens 35 
 
 remaining. og 
 
 36 ones -r- 12 = 3 ones. 
 
 A common way of proceeding is something like the following : 
 12 in 73 6 times and 1 over ; 12 in 15 once and 3 over ; 12 in 36 3 
 times. 
 
 The process as shown in (a) is called short division; as shown in 
 (b) is long division. Wherein do they differ? In what ways are 
 they alike? 
 
198 SCHOOL AEITHMETIC. 
 
 2. Divide 864 by 24. 
 
 24) 864 (36 
 
 72 
 
 144 
 144 
 
 86 tens ^- 24 = 3 tens and a remainder. 24 X 3 
 tens = 72 tens. 14 tens and 4 ones are 144 ones. 
 144 ones -f- 24 6 ones. 24 X 6 ones = 144 ones. 
 
 Find the quotients: 
 
 3. 5670 6. 
 
 4. 7212 6. 
 
 5. 6315 5. 
 
 6. 3507 7. 
 
 7. 2536 8. 
 
 8. 9208 8. 
 
 9. 7452 12. 
 
 10. 3744 12'. 
 
 11. 4956 12. 
 
 12. 6276 12. 
 
 13. 
 
 3454- 
 
 -11. 
 
 23. 
 
 7072- 
 
 -52. 
 
 14. 
 
 4565- 
 
 -11. 
 
 24. 
 
 3536- 
 
 -26. 
 
 15. 
 
 4851- 
 
 -21. 
 
 25. 
 
 5346- 
 
 -22. 
 
 16. 
 
 9702- 
 
 -21. 
 
 26. 
 
 14624- 
 
 -32. 
 
 17. 
 
 3844- 
 
 -31. 
 
 27. 
 
 14616- 
 
 -42. 
 
 18. 
 
 7688- 
 
 -31. 
 
 28. 
 
 25599- 
 
 -53. 
 
 19. 
 
 9963- 
 
 -41. 
 
 29. 
 
 62350- 
 
 -25. 
 
 20. 
 
 7488- 
 
 -24. 
 
 30. 
 
 20020 - 
 
 -35. 
 
 21. 
 
 6908- 
 
 -22. 
 
 31. 
 
 10368- 
 
 -36. 
 
 22. 
 
 9050- 
 
 -25. 
 
 32. 
 
 30576- 
 
 -48. 
 
 294. 1. 
 
 2) $49 
 
 Find one half of 
 
 = $40 + $9 
 
 ^ of 4 tens, or $40, = $20. 
 $ of 9 ones, or $9, = $4, or 
 
 $4.50. 
 
 When there is a remainder we may write the quotient and re- 
 mainder as a complete quotient, as $24 above. 
 
 Find: 
 
 2. i 
 
 3. J of 10 yd. 
 
 4. ^ of 45 qt. 
 
 5. J of 75 bu. 
 6. 
 
 7. iof 45 gal. 
 
 8. Jofl5pk. 
 
 9. iof 69 bu. 
 
 10. -^ of $21. 
 
 11. iof 145 Ib. 
 
 12. Jof 127. 
 
 13. J of 214. 
 
 14. iof 366. 
 
 15. | of 329. 
 
 16. T Vof 501. 
 
DIVISION. 199 
 
 295. 1. At 60^ a gallon, what is the value of a quart 
 of molasses? 
 
 2. How many times can you fill an 8-gallon jug from a 
 barrel that holds 48 gallons? 
 
 3. A crate holds 1728 eggs. How many dozen eggs 
 are there in the crate? 
 
 4. When you know the cost of 10 apples, how can you 
 find the cost of one apple? 
 
 5. A cattle dealer paid $682 for 22 head of cattle. 
 What was the average price? 
 
 6. How many years old is a man who has lived 900 
 months ? 
 
 7. Tommy Jones weighs 100 Ib. A ton of hay weighs 
 as much as 20 such boys. How many pounds in a ton? 
 
 8. If .there are 60,000 Ib. of coal in a car, how many 
 tons are in it? 
 
 9. A nine-acre field produced 375 bushels of oats. 
 How many bushels to the acre did it yield? 
 
 10. In 4 years the President receives salary to the 
 amount of $200,000. What is his yearly salary? 
 
 11. There are 5280 ft. in a mile. How many yards 
 in a mile? 
 
 12. If a man saves $12 a month, in how many months 
 will he save $1440? In how many years? 
 
 13. One day the fares on a certain street car amounted 
 to 2450 cents. Each passenger paid 5 cents. How many 
 persons rode on the car that day? 
 
 14. If a man on a bicycle rides 48 miles each day in 
 June, how much farther will he have to travel to make 
 1500 miles? 
 
 15. Mr. Butler divided $19500 equally among his 3 
 children. The daughter divided her share equally among 
 her 5 children. How much did each grandchild get? 
 
200 SCHOOL ARITHMETIC. 
 
 REVIEW WORK. 
 Oral Exercises. 
 
 296. 1. If 6 oranges cost 30 cents, what will 3 
 oranges cost? 
 
 If 6 oranges cost 30 ct., 1 orange will cost of 30 ct., or 5 ct.; and 
 3 oranges will cost 3 X 5 ct., or 15 ct. 
 
 2. If 9 cords of wood cost $36, what will 1 cord cost? 
 What will 12 cords cost? 
 
 3. If 4 knives cost 96 cents, what will 9 knives cost? 
 
 4. If -i of a pound of candy costs 10 cents, how much 
 must I pay for 2 pounds? 
 
 5. If -J of a pound of cheese costs 5 cents, how much 
 will 2 pounds cost? 
 
 6. If 4 men can do a piece of work in 6 days, how many 
 days will it take 3 men to do it? 
 
 If it takes 4 men 6 days to do the work, it will take 1 man 4X6 
 days, or 24 days ; if it takes 1 man 24 days, it will take 3 men of 
 24 days, or 8 days. 
 
 7. If 8 men can mow a field in 9 days, how many days 
 will it take 6 men to mow the field? 
 
 8. If 4 men can dig a ditch in 5 days, how many men 
 will be required to dig it in 4 days? 
 
 9. T is 1 of what number? 
 
 10. At 10 cents a dozen, what will 60 apples cost? 
 
 11. How many oranges at the rate of 2 for 5 cents 
 can I buy for 20 cents? 
 
 12. How many coats can.be cut from 21 yards of cloth, 
 if 3 coats can be cut from 9 yards? 
 
 13. How many pounds of sugar at 6 cents a pound 
 must be given for 2 pounds of coffee at 15 cents a pound? 
 
 14. If you divide 36 marbles among 6 boys, how many 
 marbles will 2 boys have? 
 
WRITTEN EXERCISES. 201 
 
 15. If a railroad car has 8 wheels, how many cars will 
 40 wheels supply? 
 
 16. A boy bought 6 lead pencils at 4^ each and ex- 
 changed them for erasers at 3^ each. How many erasers 
 did he get? 
 
 17. If 7 men can do a piece of work in 9 days, how 
 many men will it take to do the same work in 1 day? 
 
 18. If you buy 3 dozen pencils at 20^ a dozen, and sell 
 them at 3^ each, how much do you gain? 
 
 19. John is 9 years old, and his father is 3 times as old 
 and 9 years more. How old is his father? 
 
 20. If a man pays $30 for 6 sheep, how much at the 
 same rate does he pay for 5 sheep? 
 
 21. How many square yards in the floor of a room 15 
 yards long and 9 yards wide? 
 
 22. Alice's father gave her $2 every 2 months. How 
 many dollars did he give her in a year? 
 
 23. If a cow gives 6 qt. of milk a day, how many 
 gallons does she give in six days? 
 
 24. $28 is $7 more than the cost of 3 tons of coal. 
 What does 1 ton cost? 
 
 25. A man pays $3 a month for his room rent and $9 
 a month for his office rent. How much rent does he pay 
 a year? 
 
 26. If 2 oranges are worth 4 apples, how many oranges 
 are worth 12 apples? 
 
 Written Exercises. 
 
 297. . 1. A man gave $35 for a wagon, and paid $4 
 for repairing it. For how much must he sell it to gain 
 $11? 
 
 2. There are CL Psalms. When you have read XC, 
 how many more have you to read? 
 
 3. The earth moves in its orbit 19 miles a second. How 
 manv miles does it move a minute? 
 
202 . SCHOOL ARITHMETIC. 
 
 4. B and C start from the same place and travel in 
 opposite directions. B travels 5 miles an hour, and C 4 
 miles an hour. How far apart are they in 15 hours? 
 
 5. A clock strikes 156 times a day. How often will it 
 strike in a year of 365 days? 
 
 6. A barrel of flour weighs 196 pounds. What is the 
 weight of J a barrel? 
 
 7. Sound travels 1120 feet a second. How far off is a 
 cannon, the report of which is heard in 13 seconds? 
 
 8. How many times will 500 oranges fill a fruit dish 
 that holds 1 dozen oranges, and how many will be left 
 over? 
 
 9. If you purchase a horse for $100, and pay $40 in 
 cash, how long must you work at the rate of $12 a week 
 to pay the balance? 
 
 10. If your pulse beats 4320 times in an hour, how 
 many times will it beat in a day? 
 
 11. In what number is 225 contained 25 times? 
 
 12. Gold was discovered in California in 1848. How 
 many years ago was that? 
 
 13. A farmer sold 60 bushels of apples at $2 a bushel. 
 How many pigs can he buy at $4 each with the money? 
 
 14. One farmer gets $200 for his wood, and his neigh- 
 bor gets $248. The price is $8 a cord. How many cords 
 do they both sell ? 
 
 15. A boy takes 9 subscriptions to the " Youth's Com- 
 panion " at $1.75 each. How much money does he receive 
 for them all? 
 
 16. A building is 240 feet long and 200 feet wide. 
 How many yards is it around the building? 
 
 17. A man owed $5000. He made three payments, 
 one of $1375, another of $964, and another of $2484. 
 How much did he still owe? 
 
WRITTEN EXERCISES. 203 
 
 18. A car line is 12 miles long. If a car makes 6 
 round trips daily, how many miles will it run during the 
 month of July? 
 
 19. If 8 cords of wood are worth $32, what are 19 
 cords worth? 
 
 20. America was discovered in 1492; the Pilgrims 
 landed at Plymouth in 1620. How many years from the 
 discovery of America to the landing of the Pilgrims? 
 
 21. A man paid $175 for a horse, which was 5 tinies 
 as much as he paid for a cow. How much did he pay 
 for both? 
 
 22. The multiplicand was 3962; the multiplier was 
 186. What was the product? 
 
 23. If the divisor is 55, and the dividend is 9625, what 
 is the quotient? 
 
 24. The floor of a room 16 ft. long contains 192 square 
 feet. What is the width? 
 
 25. How many marble slabs each 10 in. by 2 ft. will 
 cover a floor 10 ft. square? 
 
 26. A baker has 200 loaves of bread. He sells f of 
 them at 6^ each, and the remainder at 5^ each. How 
 much does he get for his bread? 
 
 27. If 3 oranges cost 10^', how many times 10^ must 
 be paid for a dozen oranges? 
 
 28. A farmer clipped 1000 Ib. of wool from his sheep. 
 If each fleece weighed 5 Ib., how many sheep had he? 
 
 29. A sugar plantation produces 2000 barrels of sugar, 
 averaging 250 Ib. in weight. At 2^ a pound, what is the 
 value of the sugar? 
 
 30. A man earns $2.50 a day and pays 50^ a day for 
 board. If he does not work on Sundays, how much will 
 he have left this month after paying his board? 
 
204 SCHOOL ARITHMETIC. 
 
 U. S. Money and Decimals. 
 Ten dimes make a dollar. 
 
 298. What part of a dollar is 1 dime? 2 dimes? 3 
 dimes? 5 dimes? 10 dimes? 
 
 How many tenths of a dollar make a dollar? 
 
 How many tenths make 1 one? 
 
 A dime is 1 tenth of a dollar. We write dimes (tenths 
 of dollars) in the first place to the right of dollars. 
 
 Where with reference to ones' place should we write 
 tenths of ones? 
 
 What do we place between the figures for dollars and 
 the figures for dimes? 
 
 Should we place the decimal point after ones and before 
 tenths ? 
 
 Tenths occupy the first place to the right of the decimal 
 point. 
 
 The number five and three-tenths is written 5.3. 
 
 The number .3, or 0.3, is read three tenths. 
 
 299. What part of a dollar is 1 cent? 
 
 How many hundredths of a dollar are 3^? 5^? 10#? 
 
 of a dollar=.01 of a dollar. 
 2^=1.02=^ of a dollar = .02 of a dollar. 
 
 of a dollar = .05 of a dollar. 
 
 of a dollar = .10 (or .1) of a dollar. 
 20^=1.20 = ^ of a dollar = .20 (or .2) of a dollar. 
 25^=1.25 = of a dollar = .25 of a dollar. 
 
 Which is easier to wrie, y-J-g- of a dollar or .01 of a 
 dollar? 
 
U. S. MONEY AND DECIMALS. 205 
 
 There are two ways of writing hundredths and tenths. 
 
 and .01 are both read one-hundredth. 
 
 an d -05 are both read five-hundredths. 
 -fa and .1 are both read one-tenth. 
 fa and .5 are both read five-tenths. 
 -fa and .2 are both r^ad two-tenths. 
 
 and .25 -are both read twenty- five-hundredths. 
 
 300. How many tenths of a dollar are 10 cents (1 
 dime)? 
 
 How many hundredths of a dollar are 10 cents? 
 Then how many hundredths make 1 tenth? 
 
 10 hundredths make 1 tenth. 
 10 tenths make 1 one. 
 
 What is written between tens and 
 tenths f 
 
 The places to the right of ones are 
 called decimal places. Compare the 
 names of the decimal places with 
 those of the corresponding places on 
 the left of the decimal point. 
 How many of each place make 1 of the next place to 
 the left? 
 
 Does the figure next to the decimal point express tenths 
 or hundredths? Which figure expresses hundredths? 
 
 When there are five hundredths and no tenths, what is 
 written in tenths 7 place? 
 
 When there are tenths and no hundredths, is it neces- 
 sary to put a zero in hundredths' place? Why not? 
 
 Is 1 tenth (.1) of a dollar equal to 10 hundredths of a 
 dollar? Is 1 dime equal to 10 cents? 
 
206 SCHOOL ARITHMETIC. 
 
 301. How many dimes and cents in: 
 
 $.05 $.04 $.50 $.25 $.05 
 
 $.20 $.30 $.08 $.05 $.75 
 
 $.25 $.34 $.58 $.30 $.80. 
 
 How many tenths and hundredths in: 
 
 .04 .4 .05 *.7 .1 A5 
 
 .2 .03 .6 .05 .35 .12 
 
 .24 .43 .65 .75 .45 .57 
 
 302. Copy and complete: 
 
 4 hundredths of a dollar == 4^ = $.04. 
 
 6 hundredths of a dollar = 
 9 hundredths of a dollar = 
 
 3 tenths of a dollar = 
 
 7 tenths of a dollar = 
 
 2 tenths and 5 hundredths of a dollar = 
 25 hundredths of a dollar = 
 
 5 tenths and 8 hundredths of a dollar = 
 
 303. Write with the decimal point: 
 
 4 hundredths 4 tenths and 2 hundredths 
 
 7 hundredths 3 tenths and 6 hundredths 
 
 5 tenths 7 tenths and 5 hundredths 
 
 8 tenths 1 tenth and hundredths 
 36 hundredths 10 hundredths 
 
 65 hundredths 50 hundredths 
 
 304. Two dimes and 5 cents are how many cents? 
 Two tenths and 5 hundredths are how many hundredths? 
 
 Two dimes are how many cents? Two tenths are how 
 many hundredths? 
 
 How many hundredths of a dollar make a dime? .10=.!. 
 
U. S. MONEY AND DECIMALS. 207 
 
 A quarter is equal to how many hundredths of a dollar? 
 
 A silver dollar is worth how many hundredths of a 
 
 dollar? How many tenths of a dollar? 10 tenths = 
 
 hundredths. 
 
 How many tenths of a dollar make a half dollar? How 
 many hundredths? .5 = .50. 
 
 75 cents * = 7 dimes and - - cents. 
 
 75 hundredths 7 tenths and hundredths. 
 
 Write with the decimal point: 
 
 4 
 
 TOT TOT 100 i o TOT 
 
 TOT TOT TOT TO TOT 
 
 TOT TOT ITT TO" TOT 
 
 305. What part of a dime is a cent? 
 
 One-tenth of a dime is what part of a dollar? 
 
 One-tenth of .1 of $1 is one - - of a dollar. 
 
 Compare $10 and $1. 10 ft. and 1 ft. 
 
 Six minutes is what part of an hour? 12 minutes? 
 
 How many tenths of an hour are thirty minutes? 
 
 What part of $500 is $50? $5? 
 
 What is .01 of $100? Of $200? Of $500? 
 
 One foot is what part of 100 feet? 10 feet? 
 
 A dollar, 3 dimes, and 2 nickels are how many tenths 
 of a dollar? 
 
 Two dimes, a nickel, and 3 pennies are how many hun- 
 dredths of a dollar? 
 
 How many ones in 30 tens? In 30 tenths? 
 
 How many ones and tenths are there in 25 tenths? 
 Write it decimally. 
 
 How many ones, tenths, and hundredths in each of 
 these: 1.11, 1.05, .05, .44, 55.55? 
 
208 SCHOOL ARITHMETIC. 
 
 Draw a square and divide it into 10 equal parts. Point 
 out .2 of the square. .5 of it. .7 of it. 
 
 Add: 
 
 (a) 
 37.5 
 
 w 
 
 26.8 
 
 62.4 
 
 (*) 
 
 81.92 
 
 25.65 
 
 25.6 
 
 34.2 
 
 13.7 
 
 34.34 
 
 43.37 
 
 47.5 
 
 51.3 
 
 45.6 
 
 56.87 
 
 68.98 
 
 Subtract : 
 
 62.55 
 
 (*) 
 
 48.75 
 
 00 
 
 72.44 
 
 49.8 
 
 (J) 
 
 85.3 
 
 12.42 
 
 25.30 
 
 36.23 
 
 37.5 
 
 62.9 
 
 Where do we place the decimal point in the result ? 
 
 306. 1. At 5^ each how many oranges can I buy 
 for .5 of a dollar? 
 
 2. A farmer who had 100 sheep sold .1 of them to a 
 butcher and .5 of them to a drover. How many did he 
 sell? 
 
 3. Mr. Hall gave .3 of $50 to his daughter and .7 of 
 $50 to his son. How much did each receive? 
 
 4. Clark spent $4, which was .1 of his money. How 
 much money had he? 
 
 5. If $15 is .3 of my cash, what is .1 of it? 
 
 6. From 2.2 take .22. From 4 take .45. 
 
 7. Add 7.6, 7.8, 5.9, 3.4, and 5.7. 
 
 8. Bertha gave .2 of her money for a 10-cent doll. 
 How much had she left? 
 
COMMON FRACTIONS. 
 
 209 
 
 COMMON FRACTIONS. 
 
 
 
 H 
 
 307. What part of A is dark? "What part is light? 
 
 Into how many equal parts is A divided? 
 
 Is B one of the equal parts ? What part of the rectangle 
 isB? 
 
 How do we find i of anything? 
 
 How does the line CD divide the rectangle E? What 
 part of E is to the right of CD? 
 
 What part of this half is H? What part is G? 
 
 What part of the whole rectangle is H? Then may we 
 find i of a thing by dividing half of it into 2 equal parts? 
 
 One-fourth is what part of a half? How many fourths 
 are equal to a half? 
 
 What is 2 times i? 3 times i? 4 times i? 
 
 How many times must I take i to make f ? f ? -f-1 
 
 What part of E are Gr and H together? 
 
 One-half of A is how many times i of it? 
 
 What part of A is B + O + M? 
 
 How many fourths of E is J of it + i of it? 
 
 o 
 
 ''///''S, -'/,'y''', 
 
 
 H 
 
 E 
 
 
 
 A 
 
 F 
 
 308. This rectangle is divided into 
 Point out | of it, f of it. | of it. 
 
 *i4 
 
 equal parts. 
 
210 
 
 SCHOOL, ARITHMETIC. 
 
 How many eighths of it are dark? How many are light? 
 
 How many fourths of it are dark? How many are light? 
 
 One-eight is what part of a fourth? How many eighths 
 are equal to i? Tof? To|? 
 
 How is -J obtained from i? 
 
 What is 2 times -J? 3 times i? 4 times i? 6 times ? 
 
 How many eighths are there in the rectangle? How 
 many have letters? How many have none? f f = 
 
 How many fourths of the rectangle have letters ? These 
 3 fourths are equal to how many eighths ? f = ? 
 
 What part of the whole rectangle is H + A + E + F? 
 How many fourths? How many eighths? f = -g- - 
 
 Show that | of the rectangle = f or | of it. 
 
 What part of the rectangle is O? What part is D? 
 What part is O + D? 
 
 What is -J of J ? i is equal to how many eighths ? J ? f ? 
 
 How many eighths of the rectangle is i of it + -J of it? 
 
 Six quarters are worth how many half dollars? f are 
 equal to how many halves? 
 
 12 
 
 309. What part of the circle is shaded? How many 
 thirds of it are not shaded? 
 
 The dotted line divides one of the thirds into 2 equal 
 parts. What is each part called? 
 
COMMON FRACTIONS. 211 
 
 One-sixth is what part of one-third? How many sixths 
 are equal to J? To f ? Tof? 
 
 What part of the circle is below EH? Above EH? 
 
 Then which is larger, J of the circle or J of it? How 
 much larger? 
 
 How many times must I take J of the circle to make 
 -f- of it? To make the whole circle? 
 
 What part of the rectangle isA + B + C + D? "Then 
 C + D is what part? 
 
 What part of the rectangle is D ? Then C + D = how 
 many twelfths? i of & (or |) = ^. 
 
 How many ^y s are there in the rectangle ? In of the 
 rectangle ? -J- = TT . 
 
 What part of the rectangle is A + O + K? 
 
 Which is larger, i of the rectangle or 4 of it? Show 
 how much larger. 
 
 How many ^'s of the rectangle = 1 of it -f ^ of it ? 
 
 Find how many -j^'s of the rectangle are equal to f of 
 it. To f of it. 
 
 Find how much larger i of the rectangle is than J of it. 
 
 310. Copy and complete: 
 
 
 i 
 
 : T 
 
 
 i 
 
 r z= 
 
 "6T 
 
 i=T* f 
 
 
 
 
 i 
 
 
 
 T 
 
 
 i 
 
 - z^ 
 
 -g- 
 
 f =TF f 
 
 = 
 
 
 i- 
 
 T 
 
 
 i 
 
 r = 
 
 TF 
 
 *=TF * 
 
 "6" 
 
 
 1 
 
 
 
 
 
 
 
 2 - 2 
 
 
 
 T 
 
 r TT 
 
 
 T 
 < 
 
 
 T2~ 
 
 IT " TT f 
 
 ~ TF 
 
 
 311. 
 
 What 
 
 part 
 
 
 of 
 
 this 
 
 rectangle 
 
 
 is 
 
 dark? 
 
 How many fifths 
 
 are light ? 
 
 B H 
 
 
 How 
 
 many tenths 
 
 of 
 
 the 
 
 rectangle 
 
 E D " 
 
 make i 
 
 of it? 
 
 
 
 
 
 
 
 
 One-half of 
 
 the 
 
 dark 
 
 portion is what part of 
 
 the whole 
 
 figure? ofi = 
 
212 SCHOOL ARITHMETIC. 
 
 What part of the figure is on each side of AH? 
 
 Show how many tenths of the rectangle make | of it.. 
 
 What part of the figure is E+B+C? 
 
 If D were removed, what part of the whole would 
 remain? 
 
 How many times C+D make up the figure? How many 
 times J = 1 ? 
 
 How many fifths of a nickel make a dime (two nickels) ? 
 How many J's in 2? 
 
 Point out i of half the rectangle. It is what part of 
 the whole? J of \ = 
 
 B+C+D+E = -- how many i's of the figure? How 
 many^'s? f = TT . 
 
 How many -^'s make f ? f ? f ? | ? 
 
 How many y^'s of the rectangle = -|- of it + y 1 ^- of it? 
 
 Which is larger, f of the rectangle or y 3 ^ of it? How 
 much larger? 
 
 Draw a 10-inch square and divide it into square inches. 
 
 Each small square is what part of the whole? 
 
 How many hundredths in the upper row? Then how 
 many hundredths make 1 tenth? 
 
 Find how many hundredths make y 3 ^, or ^. y^, or ^. 
 
 One-tenth is how many times as much as one-hundredth? 
 
 Find how many hundredths in i of the large square. 
 In f of it. 
 
 One-hundredth is what part of 1 tenth? 
 
 Point out y^j- of one-tenth of the large square, and tell 
 what it is called. 
 
 Complete: = T =^ = T = T1F =-^ ^ 
 Complete: l=f = T = T = -$ = Tir = 
 
COMMON FRACTIONS. 213 
 
 BCD 
 
 312. A, B, C, and D are equal squares. What part of 
 each is dark? Are the dark parts equal? 
 
 Into how many equal parts is B divided? How many 
 of the dark parts are equal to the dark part of A? Then 
 how do -J and i compare in size? 
 
 How does i of A compare in size with -f of C? Then 
 what can you say of ^ and f ? 
 
 Compare ^ of A with -f of D, and state what you learn. 
 
 Are 2 of the equal parts of B equal to 4 of the equal 
 parts of D? Is | greater than f ? Is f ? 
 
 Arrange the fractions J, f , -J , and J- in six groups of two 
 fractions each. Compare each two, and tell what you. learn. 
 
 In the fractions and -f-, what does the 2 show ? The 1 ? 
 The 8 ? The 4 ? 
 
 In the fraction f , which figure indicates the number 
 of equal parts into which a whole is divided? What shows 
 us how many of the parts are taken? 
 
 The number below the line of a fraction shows into how 
 many equal parts anything is divided. It is called the 
 Denominator. 
 
 The number above the line shows how many of the parts 
 are taken. It is called the Numerator. 
 
 In f of the rectangle, what does the 8 show ? The 5 ? 
 
 Draw on the board a line 4 ft. long. Measure it with 
 your foot rule, which is -J yd. in length. The line is how 
 many thirds of a yard long? 
 
214 SCHOOL ARITHMETIC; 
 
 What does the 3 show? What does the 4 show? 
 Grive the meaning of the numerator and of the denomi- 
 nator in f . In f. in. In f yd. In . 
 
 313. What is the sum of a quarter and a half dollar? 
 The half-dollar = 2 quarters. 2 quarters + 1 quarter = 3 quarters. 
 
 What is the sum of 4 bu. and a peck? 
 
 Add J gal. and i gal. 4 + i = T . 
 
 Can you add halves and fourths without changing the 
 halves to fourths? 
 
 Use your foot-rule to find the sum of i in. and i in. 
 To find the sum of ^ in. and % in. 
 
 i + i = T- f +*==* 
 
 What must be done with i before it can be added to 
 i? With 4? 
 
 Only like numbers can be added. Fractions to be added 
 
 must have the same denominator. 
 
 
 314. With a foot-rule complete: 
 
 . = T n. n.-- n. = n. n.-- n. = n. 
 | in. -f| in. =-5- in. | in. +1 in. = F in. |in.+Jin.=- B -in. 
 | in. -fi in. = in. \ in. +| in. = in. f in. +|- in. =-g in. 
 
 When one fraction is to be subtracted from another, both 
 must have the same denominator. 
 
 . =-g-in. -|in. -Jin. ^in. 1 in. Jin. = T in. 
 . i=-g-in. 1 in. -f-in. =--in. fin. J-in. =-g-in. 
 in. in. in. =in. -in. -in. =-in. 
 
COMMON FRACTIONS. 215 
 
 315. Find the value of: 
 
 3 +i i 
 
 T T T f ~T ~T g- "2 i f+t T 
 
 3 
 T 
 
 f + 
 
 '+ i + i I - 
 
 316. Copy and complete: 
 
 2 times J = J or J. 3 X f = -g- or T . 
 
 2 times | = f or T . 2 X f = -g- or T . 
 
 2 times i = T or T . 4 X f = T or T . 
 
 2 times f = -g- or -g-. 8 X -g- = -- or 
 4 times 
 
 317. How many |'s = -J-? How many |'s = -J-? 
 |- r= how many times ^ ? |- = how many times ^- < 
 How many times is 1 ft. contained in 3 ft ? 
 
 3 ft. -=- 1 ft. = - . 3 fourths -f- 1 fourth = - 
 
 6 yd. -T- 2 yd. = times, f -f- f times. 
 
 i of 2 qt. = - - qt. t of J = T . 
 
 1. of 3 ft. - ft. tof| = T . 
 
 i is contained in i - times, 
 
 i is contained in i - - times. 
 
 i is contained in \ how many times? 
 
 i is contained in f how many times? 
 
 f is contained in -J how many times? 
 
 f is contained in f how many times? 
 
 i is contained in 1 how many times? 
 J is contained in 2 how many times? 
 
216 SCHOOL ARITHMETIC. 
 
 How many J's are there in 1? In 2? In 5? 
 How many 's are there in 2? In 5? In 12? 
 How many -J's are there in 1? In 2? In 3? 
 How many eighths of an inch in 4 inches? In 12 inches? 
 
 318. Complete and read: 
 
 1 in. + | in. = 14 in. (one and one-half inches), or 
 ir m - 
 
 2 in. + i in. = 3 in. + f in. = 
 1 in. + 4 in. = 1 hr. + f hr. - 
 5 in. + f in. = 4 gal. + J gal. = 
 
 319. In 1| gal. how many fourths? How many quarts? 
 In 2J bu. how many halves? How many pecks? 
 
 In 1-J in. how many eighths? In 2-J inches? 
 
 In $3f how many fourths, or quarters? 
 
 In 2^ yd. how many halves? How many fourths? 
 
 Change to fourths : 
 
 i n 4* i if v- 
 
 H 3 i I. I si V 
 
 Six half -inches = how many inches? 
 
 Twelve quarter-inches = how many inches? 
 
 Three half inches = how many inches and half -inches? 
 
 How many inches in f in.? In | in.? In f- in.? 
 
 How many inches and half -inches in f in.? In % in.? 
 
 320. 1. If a horse eats three times a day ; and eats 
 2 pk. of oats at a time, how many half -pecks will he eat 
 in 6 days? How many pecks? How many bushels? 
 
 2. When milk is 3^ a pint, how much must be paid 
 for li quarts? 
 
COMMON FRACTIONS. 
 
 217 
 
 3. If \ of a yard of cloth costs 24^, what does \ of a 
 cost? 
 
 4. How many sheets of paper at J# apiece can you 
 buy for 5^? 
 
 5. If | of a yard of ribbon costs 18#, what is the cost 
 of 1 of a yard? Of J of a yard? 
 
 6. Tom earned i of a dollar on Monday and J of a 
 dollar on Tuesday. How much did he earn? 
 
 7. A box is | yd. long and -J yd. wide. By how much 
 does the length exceed the width? 
 
 8. Each side of a square is f ft. long. What is the 
 perimeter? 
 
 9. A lady who had J of a gallon of milk sold a quart 
 to a neighbor. What part of a gallon had she left? 
 
 10. A man who had $40 spent $10. What part of his 
 money had he left? 
 
 11. Tillie had f of a yard of velvet and gave Nell J 
 of it. What part of a yard had Tillie left? 
 
 12. Draw a rectangle 12 in. long and i as wide- How 
 many square inches in \ of it? In j of it? 
 
 Common Denominator. 
 
 A B C 
 
 321. How many J's are eqiial to 4? Then -J is how 
 many times \\ 
 
 Multiply numerator and denominator of -J by 2. What 
 is the result? 
 
 When 4 is changed to f, how is the size of the parts 
 changed? Are more of them taken? 
 
218 SCHOOL ARITHMETIC. 
 
 By what must numerator and denominator of i be 
 multiplied to change it to -f- 1 
 
 The part on the left of CD is how many times as large 
 as one of the parts on the right? 
 
 The number of parts on the right of CD is - - times 
 the number of parts on the left. 
 
 Multiply numerator and denominator of i by 3, and 
 explain the result. 
 
 Divide numerator and denominator of f by 4. Is the 
 result equal to -| 3 
 
 By what must you divide numerator and denominator 
 of T 5 Q- to change it to \\ 
 
 Show that the following is true: 
 
 If both numerator and denominator of a fraction are 
 multiplied, or divided, by the same number, the value of 
 the fraction is not changed. 
 
 322. Change i ? J, and f to 12ths. 
 
 Both numerator and denominator of i must be multi- 
 plied by 12 -f- 2, or 6. 
 
 Both numerator and denominator of f must be multi- 
 plied by 12-S-3, or 4. 
 
 By what must both numerator and denominator of f be 
 multiplied? 
 
 Change : 
 
 1. , , and to 12ths. 
 
 2. i, f , and to 8ths. 
 
 3. i, f, and ^ to lOths. 
 4 ? | ? | 5 and | to 12ths. 
 5*. i, I, i, and ^ to 20ths. 
 
 6. t, |, i, and ^ to 40ths. 
 
 7. |, t, f, and T V to lOOths. 
 
 8. f, A, , and ^ to 4ths. 
 
COMMON FRACTIONS. 219 
 
 323. Change to smaller denominators: 
 
 9. f, f, T W? 12. A.M.-H.M- 
 
 in 466 8 10 102040 
 
 - LU - 65 8' 10' T2 *> 25' 30' ~5"0~' 
 
 11- t, TV ii, H I*- T, TV 
 
 15. In ^ of a dozen how many half dozen? 
 
 16. In f of a dozen how many y^'s of a dozen? 
 
 17. In -J- of a- dozen how many y^'s of a dozen? 
 
 18. How many more oranges are ^ of a dozen than ^ of 
 a dozen ? What part of a dozen more ? 
 
 19. How many 12ths of a foot (inches) in ^ foot? In 
 | foot ? 
 
 20. In 1-J- yards how many thirds ? How many feet ? 
 
 21. How many yards in f yd. ? How many feet ? 
 
 22. How many ones are equal to -- ? -^ 2 - ? T |- ? 
 
 23. How many ones and thirds in JJ In -J? ^-? 
 
 24. In f how many fourths ? In J how many halves ? 
 
 25. Change 1^ bu. and J bu. to pecks, or fourths (of a 
 bushel). 
 
 Addition and Subtraction. 
 
 324. Fractions that have a common denominator are 
 called Similar fractions. Only similar fractions can be 
 added or subtracted. Change to similar fractions and add 
 or subtract as indicated: 
 
 1- *+ i = e 9- f +A=T7 17. t - - i = 
 
 2. *+i=ir 10. i+ T V=T2 18- t--i= T 
 
 3- H-i= T 11. i+A=n 19- i - - t = T 
 
 4- *+i==lT 12- 1+TV=TT 20. i--TV=T2 
 
 5. *+* = T 13. t+A=TT 21. f--A=TT 
 
 6. *+t- T 14. i+A=TT 22. |--TV=TT 
 
 7- i+A=T^ 16. t+*=TT 23. A--i=n 
 
 8. = ie---= 24. --= 
 
30. 
 
 i+i+- 
 
 ro 
 
 35. 
 
 1 -A 
 
 31. 
 
 1+1+ 
 
 \ 
 
 36. 
 
 7 2 
 TTF 5 
 
 32. 
 
 1+1+ 
 
 i 
 
 37. 
 
 i - i 
 
 33. 
 
 i+t+ 
 
 ! 
 
 38. 
 
 i - i 
 
 34. 
 
 A+i + : 
 
 ro 
 
 39. 
 
 l^-T 5 
 
 220 SCHOOL ARITHMETIC. 
 
 Find the value of: 
 
 25. 
 26. 
 27. 
 28. 
 29. 
 
 In the following exercises add the integers and frac 
 tions separately, and then add the results: 
 
 40. 3f + 7| 45. 6i + 2| + 1 
 
 41. 2i + 5| 46. 9| + 3 + 
 
 42. 6| + 3i 47. 8 + 7^ + 
 
 43. i| _j_ 45 48. 2f + 5 T 7 7 + 
 
 44. 8^5- + 5| 49. 10 + 9| + 26 T y o 
 
 50. Subtract 2f from 5^. 
 
 5 if = ^T : ^T The fractions are first made similar. We can- 
 
 2J = 2 J = 2J no t take f from f , so we take 1 one, or f , from 
 
 the 5 ones, and add it to the f . We then take f 
 
 c\ Q O ^ 
 
 ^4: *T from f , and 2 from 4. 
 
 Subtract : 
 
 51. 1% from 10^ 56. 12J- from 16J 
 
 52. 3| from 6 57. 22^ from 30| 
 
 53. Sffrom 9J 58. 31f from 42 
 
 54. 2ifrom 7| 59. 16 T 7 o from 2 Of 
 
 55. 4f from 8^ 60. 37-^- from 62^ 
 
COMMON FRACTIONS. 221 
 
 Multiplication and Division. 
 .325. Complete: 
 
 3 times -i- = -g- or T 2 X T V = TT O1 * ^ 
 
 2 times ^- = g- or ^ 3 X yV ~ T2 or T 
 
 2 times f = or 3- -i X -^ T2 or ^ 
 
 3 times -| = -g- or 6 X yV = TT or 2" 
 3 times ^ = ^ or 8 X -^ TT or 3- 
 1 times -| -g- or 9 X -^ T T or T 
 6 times -J- = -g- or 6 X -% = TT or 
 
 326. How many -i-'s = -J-? How many y^-'s = -J? 
 -| how many times -J-? |- := how many -J-'s? iV' 8 ^ 
 How maii^ times is 1 contained in |-, or 4- ? 
 
 t/ b b " 
 
 3 sixths -r- 1 sixth = times, f -r- -g- = times. 
 
 ^ is contained in -J times. -J- -j- ^- = 
 
 jr is contained in 1 times. 1 -=- ^ = 
 
 y^- is contained in ^ times. ^ -f- ^ =: 
 
 y^ is contained in -J- times. -J- -f- T V = 
 
 ^ of 2 sixths -s-. i of -I =---. 
 
 b - b b 
 
 i f f = IT" i f A = TT 01 * -6 ' 
 
 -1 OT ~ JL syr 6 ___ OT* 
 
 How many ^'s are there inl? In 2? In 4? 
 How many -J-'s are there in 1 ? In 2 ? In 5 1 
 How many y^-'s are there in 1 \ In 2 ? In. 3 \ 
 How many y^'s of a foot in 2 inches ? In 6 inches ? 
 Four inches is what part of a foot \ 
 How many inches = f of a foot ? f of a foot \ 
 
222 
 
 SCHOOL ARITHMETIC. 
 
 327. If each third of A is divided into 2 equal parts, 
 as in B, how many parts will there be? 
 
 What is each part of B called? -J of -J =-g. 
 
 How many fifths of E are there to the left of CD? 
 
 How many thirds of this part of E are dark? 
 
 How many fifteenths of E are dark ? 
 
 Thenfof f== Tir . tXf = 
 
 In finding f of f how was the 15 obtained? How was 
 the numerator obtained? 
 
 To multiply one fraction by another 
 
 We take the product of the numerators for the required 
 numerator, and of the denominators for the denominator. 
 
 Find the product of: 
 
 1. 
 
 f X f 
 
 7. 
 
 2. 
 
 J x i 
 
 8. 
 
 3. 
 
 f x i 
 
 9. 
 
 4. 
 
 fx 1 
 
 10. 
 
 5. 
 
 *x| 
 
 11. 
 
 6. 
 
 t.x 4 
 
 12. 
 
 i x I x ! 
 i x 1 X | 
 I x t x f 
 I x t x i 
 
 f X f Xf 
 
 4 x I x^ 
 
 13. 
 14. 
 15. 
 16. 
 17. 
 
 x ! 
 
 t x 
 tx 
 f x 
 
COMMON FRACTIONS. 223 
 
 19. Multiply 34 by 6. 
 
 34 
 6 
 
 18 = 6 X 3 We multiply the integral part, then the 
 
 3 =0^1 fractional, and add the results. 
 
 21 = 6 X 34 
 Find the products: 
 
 20. 
 
 6 
 
 X 
 
 44 
 
 25. 
 
 7 
 
 X 6f 
 
 30. 
 
 4 
 
 X 
 
 124 
 
 21. 
 
 9 
 
 X 
 
 H 
 
 26. 
 
 4 
 
 X 5| 
 
 31. 
 
 6 
 
 X 
 
 374 
 
 22. 
 
 5 
 
 X 
 
 ^ 
 
 27. 
 
 8 
 
 v 3 5 
 
 /\ ""J" 
 
 32. 
 
 6 
 
 X 
 
 16| 
 
 23. 
 
 4 
 
 X 
 
 3* 
 
 28. 
 
 6 
 
 v 4 ^ 
 
 33. 
 
 3 
 
 X 
 
 33 
 
 24. 
 
 3 
 
 X 
 
 9| 
 
 29. 
 
 9 
 
 X Tf 
 
 34. 
 
 8 
 
 X 
 
 624 
 
 328, 1. Divide 4 ft. by 2 ft. 4 thirds by 2 thirds. 
 
 2. Find 4 of 4 thirds. -f -=- 2 = f . 
 
 3. How many f 's in f ? -| -=- f = times. 
 
 Find the quotients: 
 
 4. | -j- 2 9. -J -T- f 14. I -T- T V 
 
 5. | - 3 10. f - | 15. 4 - yV 
 
 6. A -5 11. I- I 16. I- A 
 
 7. 1-4 12. | - f 17. 4 -=- l 
 
 8. T V -7-2 13. | - I 18. | - f 
 
 19. Write these fractions in a line, placing the largest 
 
 first, the next largest second, and so on: J, 4? 4 7 4? yV? 
 i i i A 3 i 
 
 T> TS~5 "S"' 85 T' TFO"' 
 
224 
 
 SCHOOL ARITHMETIC. 
 
 What does it contain -J, 
 
 329. How many sixths of A are shaded? How many 
 times is f- contained in A \ Can you find out by inverting -| \ 
 
 Find how many times A contains (the light part). 
 What does A contain 6 times ? 
 or 2 times? 
 
 B contains -J how many times ? Can you tell by invert- 
 
 ing I? 
 
 Invert -| and show how many times it is contained in the 
 whole of B. 
 
 In B, I- is contained 2f times, or 4 times. 
 
 ' o *-> o 
 
 Can we find how many times a fraction is contained in a 
 whole or 1 by inverting the fraction '{ 
 
 Find how many times 1 contains i, i, -J, f , T 5 T , f . 
 
 One-half is contained in one, 2 times; in four it is con- 
 tained - times. 
 
 How many times is \ contained in 1? In 2? In 5? 
 In I? 
 
 To divide by a fraction 
 
 Multiply the inverted divisor l)y the dividend. 
 
 330. 1. Divide 4 by f. 
 
 I = the number of f's in 1. 
 4X1 = -VS or 6, the number of f's in 4. 
 
 Divide : 
 
 2. 
 
 5 b; 
 
 7 i 
 
 8. 
 
 6 
 
 by 1 
 
 14. 
 
 10 
 
 by 
 
 f 
 
 3. 
 
 3b; 
 
 Y \ 
 
 9. 
 
 2 
 
 by f 
 
 15. 
 
 3 
 
 by 
 
 i 
 
 4. 
 
 6b; 
 
 n 
 
 10. 
 
 5 
 
 by I 
 
 16. 
 
 2 
 
 by 
 
 1 
 
 5. 
 
 4b; 
 
 Y i 
 
 11. 
 
 8 
 
 by I 
 
 17. 
 
 5 
 
 by 
 
 A 
 
 6. 
 
 7b 
 
 y i 
 
 12. 
 
 3 
 
 by I 
 
 18. 
 
 4 
 
 by 
 
 1 
 
 7. 
 
 5 b; 
 
 7 -nr 
 
 13. 
 
 4 
 
 by A 
 
 19. 
 
 2 
 
 by 
 
 9 
 TTT 
 
COMMON FRACTIONS. 225 
 
 20. Divide J by . 
 
 Inverted divisor f = the number of f's in 1. 
 f X I = I, or 1$, the number of f's in f . 
 
 Find the quotients: 
 
 21. | -* i 25. * - T V 29. | -4- i 
 
 22. i -=- f 26. | - i 30. | ^ f 
 
 23. i-i 27. f-*- * 31. 4-5- | 
 
 24. i - i 28-1-1 32. | -s- 'A 
 
 331. 1. Ella picked i gal. berries and Nora picked f 
 gal. They both picked gal. 
 
 2. What is the difference between J of an hour and 
 J of an hour? 
 
 3. How much will 3^ quarts of milk cost, if 1 pint 
 is worth 3 cents? 
 
 4. If carpet is f yd. wide, how wide a room will 6 
 widths cover? 
 
 5. If i of a yard of ribbon costs 2$, how many yards 
 can you buy for 32 cents? 
 
 6. If I had J of a yard of ribbon, and used i of a yard, 
 what part of a yard have I left? 
 
 7. At y^Q- of a dollar a peck, how many pecks of apples 
 can be bought for $f ? For $1? 
 
 8. If a boy earns $| a day, in 12 days he will earn 
 
 9. How many 12 7 s of a foot are equal to a yard? 
 
 10. At i of a dollar a pound, how many pounds of 
 coffee can I buy for $1? For $5? 
 
 11. James sold 2 bushels of apples at 10^ a half -peck. 
 How much did he get for them? 
 
 *i5 
 
226 SCHOOL ARITHMETIC. 
 
 12. 4 horses are J of - - horses. (Show by dots.) 
 
 13. One-third of 12 sheep is - - sheep." f of 12 
 sheep are sheep. 
 
 14. 8 quarts are of how many quarts? (Show by 
 dots or squares.) 
 
 15. Bell bought a book for 10^, which was i of her 
 money. How much had she? 
 
 16. There are 36 gallons of cider in a barrel which is 
 f full. How many gallons will the barrel hold? 
 
 17. A 3-gallon pail was full of water, but 2 quarts were 
 taken out. What part of the water was taken out? What 
 part was left? 
 
 18. If f of a yard of cloth cost 15^, what is the cost of 
 
 1 of a yard? Of 1 yard? Of 2 yards? 
 
 19. If T 3 F of the cost of a wagon was $12, what was 
 the entire cost? 
 
 20. If -i bu. of corn is worth 20^, what is the value of 
 
 2 bushels? Of 2i bu.? 
 
 21. Adam's house is f of a mile south of the school- 
 house, and Dick's is f of a mile north, How far apart do 
 the boys live? 
 
 22. In a school of 48 scholars f are girls. How many 
 boys are there? 
 
 23. If \ lb. of coffee costs $.15, what will 2 pounds 
 cost? 
 
 24. How many pieces of velvet, each half a yard long, 
 can be cut from a piece 9J yards long? 
 
 25. I have a jointed fishing rod in 3 parts. One part 
 is 2J feet long, another 2f feet, and the other 3} feet. 
 How long is the rod? 
 
 26. f of the days in April are how many days? 
 
RELATIONS RATIO. 227 
 
 27. From a piece of ribbon J ft. long a piece -f^ ft. 
 long was cut off. Show the length of the remainder. 
 
 28. A rectangle is i ft. long and i ft. wide. What is 
 the perimeter? How many square inches does it contain? 
 
 29. A box is li ft. long and f ft. wide. Find how 
 many square inches in the lid. 
 
 30. A lady bought 3j yd. of ribbon, and divided it 
 equally among 5 girls. What part of a yard did each girl 
 get? (3J yd. -f- 5 = - 1 / J d - + 5 )- 
 
 31. Draw an 8-inch square. In it draw a square i 
 as large. How many square inches between the two 
 perimeters ? 
 
 Relations Ratio. 
 
 332. 1. One line is 12 ft. long, another is 3 ft. long. 
 Compare their lengths. 
 
 (a] The 3-ft. line must be taken (repeated) times to make 
 
 up the 12-ft. line. 
 (6) The 12-ft. line is times as long as the 3-ft. line. 
 
 (c) The 12-ft. line is composed of 3-ft. lines. 
 
 (d) The 3-ft. line is one as long as the 12-ft. line. 
 
 By comparing or measuring we find the answers required. When 
 we know the answers to a and fc, we know the relation (ratio] of 12 
 ft. to 3 ft. The ratio is 4. 
 
 When we know the answers to c and d, we know the ratio of 3 ft. 
 to 12 ft. It is J. 
 
 2. One package weighs 2 lb., another 8 Ib. Make four 
 statements similar to the four above, and find the ratio of 
 each weight to the other. 
 
 3. Measure your foot-rule with a 4-inch unit. Tell 
 what you can about the ratios. 
 
 4. Find the ratio of your foot-rule to a 6-inch unit. 
 A 2-inch unit. A 1-inch unit. 
 
228 SCHOOL ARITHMETIC. 
 
 5. What is the ratio of the 6-inch unit to the foot-rule? 
 Of the 2-inch unit? The 1-inch unit? 
 
 6. Find two ratios by comparing a yardstick and a 
 foot-rule. 
 
 7. What two ratios can be found by comparing a 
 gallon and a quart? 
 
 8. Draw a 2-in. square and a 
 4-in. square. Divide them into 
 square inches, and find the ratio of 
 each to the other. 
 
 9. What is the ratio of a dollar 
 to a dime? Of a dime to a dollar? 
 
 10. Ten is how many times 2? Then what is the ratio 
 of 10 to 2? Of 2 to 10? 
 
 11. How many times must one be taken to make ten? 
 
 Then the ratio of 10 to 1 is , and the ratio of 1 to 
 
 10 is - . 
 
 12. The ratio of 10^ to - tf is 2. The ratio of - j 
 to 10# is J. 
 
 13. A man counting a roll of 5-dollar bills says, $5, 
 $10, $15, $20. How many equal parts make up his $20? 
 How many times must one of the parts be taken to equal 
 his $20? What is the ratio of $20 to $5? Of $5 to $20? 
 
 14. $50 is how many times $10? That is, what is the 
 ratio of $50 to $10? 
 
 15. Four feet is what part of 20 feet? That is, what 
 is the ratio of 4 ft. to 20 ft? 
 
 16. Five inches is one-half of what? That is, the ratio 
 of 5 in. to in. is -J. 
 
 17. Thirty dollars is five times what? That is, the 
 ratio of $30 to $ is 5. 
 
RELATIONS RATIO. 229 
 
 18. What is the ratio of i (f ) to | ? Of to ? Of 
 |- to ^ ? Show by drawing. 
 
 19. Find the ratio of 24 to 8. Of 42 to 6. 
 
 20. By what process do you find the ratio of one num- 
 ber to another? (See Division.) 
 
 21. Select any number you please, and state its ratio 
 to one. To two. 
 
 333, 
 
 ARTICLE COST ARTICLE COST 
 
 1 apple 2 cents 2 apples 5 cents 
 
 5 apples 10 cents 8 apples 20 cents 
 
 Five apples are how many times 1 apple? Then they 
 will cost how many times as much? Point out two ratios 
 that are equal. Eight apples are how many times 2 apples ? 
 How many times as much will they cost? Point out the 
 ratios. 
 
 1. At 3^ each, what will be the cost of a dozen oranges? 
 . 2. When lemons are selling at the rate of 3 for 5#, 
 what will a dozen cost? 
 
 3. If 11 lb. of sugar cost 50^, what will 22 Ib. cost? 
 
 4. When you can buy 3 handkerchiefs for 25^, how 
 many can you buy for $1? 
 
 5. A lady paid 30^ for a dozen eggs. How much would 
 4 eggs cost at that rate? 
 
 6. A boy running takes 3 steps every 10 ft. How 
 many steps does he take in miming 100 ft.? 
 
 7. A man earns $21 every two weeks. How much 
 does he earn in six weeks? 
 
 8. How much do I gain by buying 10 pigs at $2 each, 
 and selling them at $3 each? 
 
 (a) How much do I gain on 1 pig? On 10? 
 
 (b) How much do I pay for the 10 pigs? How much do I get 
 
 for them ? Then how much do I gain ? 
 
230 SCHOOL ARITHMETIC. 
 
 9. If 5 apples cost 10 cents, what is the cost of 1 apple? 
 
 10. If 4 sheep are worth $20, what are 3 sheep worth?. 
 
 11. A girl bought 3 pairs of shoes for $6. At the 
 same rate, what would 5 pairs cost? 
 
 12. Draw two lines showing the ratios 4 and \. 
 
 13. What is the ratio of a rectangle 4 in. by 5 in. to 
 one 2 in. by 5 in.? 
 
 Review. 
 
 334. 1. Find the cost of a ton of hay, when f of a 
 ton costs $6. 
 
 2. 9 is f of what number? 
 
 3. 15 is f of what number? 
 
 4. 14 is f of what number? 
 
 5. 20 is -| of what number? 
 
 6. 3J is f of what number? 
 
 7. If | of a yard of satin costs 80^, what is the cost 
 of one yard? Of 5 yards? 
 
 8. If | of a ton of coal occupies 24 cubic feet, how 
 many cubic feet will 1 ton occupy? 
 
 9. If f of a barrel of fish cost $10, what will 1 barrel 
 cost? 
 
 10. What is the price of a dozen, when f of a dozen 
 oranges sell for 20^? 
 
 11. 2 times f are how many fourths? 
 
 12. i of 18 is i of what number? 
 
 13. If f of a pound of rice costs 6 cents, what will 5 
 pounds cost? 
 
 14. What is the cost of 6i gallons of molasses at $.40 
 a gallon? 
 
 15. A woman has 15 yards of muslin. How much will 
 she have after she uses 14| yards? 
 
 16. What is the cost of of a pound of candy at 
 a pound? 
 
REVIEW. 231 
 
 17. What will 15i dozen eggs cost at 20^ a dozen? 
 
 18. A boy after selling -J and i of his marbles had 12 
 marbles left. How many had he at first? 
 
 19. A boy has of a peck of nuts. If he gives away 
 | of them, what part of a peck will he have left? 
 
 20. If i of an ounce of tea costs 5^, what will 1 pound 
 cost? 
 
 21. Four fifths of 20 is f of what number? 
 
 22. If I can buy 7 pencils for -$ of a dollar, how many 
 can I buy for -f^ of a dollar? 
 
 23. If | of a cord of wood is sold for $4, what will 5 
 cords bring? 
 
 24. If f of a barrel of sugar costs $12, what will f 
 of a barrel cost? 
 
 25. If y 1 ^ of a lot of goods is worth $360, what is 4 
 of the lot .worth? 
 
 26. $40 is equal to i of my house rent for 1 year. How 
 much do I pay a month? 
 
 27. If -J of a ton of coal lasts 2 days, how long will J 
 of a ton last? 
 
 28. What will J of a pound of tea cost at f of a dollar 
 a pound? 
 
 29. At i of a dollar a bushel, how many bushels of 
 apples can be bought for 10 dollars? 
 
 30. One third of a pole is blue, J of it is red, and the 
 rest is white. What part of the pole is white? 
 
 31. If 5i pounds of nuts are divided equally among 
 7 boys, what part of a pound will each boy receive? 
 
 32. When a furnace consumes coal at the rate of f of 
 a ton a day, how much will it consume in 4-| weeks? 
 
 33. When f of a yard of ribbon is put into a loop, how 
 many loops can be made from 3 yards? 
 
 34. At f of a cent a square foot, what will it cost to 
 paint a blackboard 24 feet long and 4| feet wide? 
 
COMPOUND NUMBERS. 233 
 
 COMPOUND NUMBERS. 
 
 Liquid Measure. 
 
 335. Liquid Measure is used in measuring liquids, as 
 water, milk, etc. 
 
 PINT QUART GALLON 
 
 2 pints (pt.) = 1 quart (qt.). 
 4 quarts = 1 gallon (gal.). 
 
 1. How many pints are there in 3 qt.? In 5 qt.? 
 
 2. How many quarts are there in 3 .gal.? In 10 gal.? 
 
 3. How many pints in 5 gal. 3 qt. and 1 pt.? 
 5 gal. =5X4 qt., or 20 qt. ; 20 qt. + 3 qt. = 23 qt. 
 23 qt. = 23 X 2 pt., or 46 pt.; 46 pt. -f 1 pt. = 47 pt. 
 
 4. How many pints in 4 gal. 2 qt. 1 pt.? 
 
 5. How many gallons are there in 24 qt.? In 40 qt. ? 
 
 6. How many quarts are there in 12 pt.? In 16 pt.? 
 
 7. How many gallons are there in 110 pints? 
 
 1 pt. of a qt., and 110 pt. = 110 X $ qt., or 55 qt. 
 
 1 qt. = \ of a gal., and 55 qt. = 55 X i gal., or 13 gal. and 3 qt. 
 
 8. How many gallons in 129 pints? 
 
 9. How many pints in 1 gal. ? In -J gal. ? 
 
 10. How many gallons in 40 quarts? In 75 qt.? 
 
 336. 1. How many quart jars will hold 2-J gallons 
 of milk? 
 
 2. How many half-pint bottles can you fill with a 
 gallon of olive oil? 
 
234 
 
 SCHOOL ARITHMETIC. 
 
 3. A milkman sold 18 gal. of milk at 6^ a qtfart. How 
 much did he get for it? 
 
 4. At 10^ a pint, how much syrup can be bought for 
 $3.60? 
 
 5. How many pint bottles will hold 2 gal. 1 qt. of oil? 
 
 6. If a gallon of molasses costs 80^, how much will 6 
 pints cost? 
 
 7. A man bought 2 cans of mineral water, each con- 
 taining a gallon and a half. The price was 20^ a gallon. 
 How much did he pay? 
 
 8. There are 231 cu. in. in a gallon. How many cubic 
 inches in a quart? 
 
 9. A lady sold 2 gal. 3 qt. 1 pt. of vinegar at 6# a 
 quart. How much did she get for it? 
 
 10. A man paid 52^ for 1 gal. 2 qt. 1 pt. of milk. He 
 paid - # a quart. 
 
 11. If a family pays 8^ a quart for milk and uses 3 
 pt. a day, what is the milk bill for the month of March? 
 
 12. If a barrel holds 31-| gallons, and a hogshead holds 
 twice as much, what does a hogshead hold? 
 
 Dry Measure. 
 
 337. Dry Measure is used in measuring dry articles, 
 as grain, seeds, fruit, vegetables. 
 
 UP 
 
 PINT 
 
 QUART 
 
 PECK 
 
 2 pints (pt.) = 1 quart (qt.). 
 8 quarts = 1 peck (pk.). 
 4 pecks = 1 bushel (bu.). 
 
 BUSHEL 
 
COMPOUND NUMBERS. 235 
 
 1. How many pints in 3 qt.? In 5 qt.? 
 
 2. How many qt. in 4 pk. ? In 5 pk. ? 
 
 3. How many pk. in 3 bu.? In 7 bu.? 
 
 4. How many quarts in 5 bu. 3 pk. 4 qt.? 
 
 5. How many pecks in 8 bu. 3 pk.? 
 
 6. How many pecks in 32 qt. ? In 20 qt. ? 
 
 7. How many bushels in 4096 pints? 
 
 8. How many pecks in J bu. ? In i bu.? 
 
 9. In 32i pecks how many bushels? 
 10. In 784 quarts how many bushels? 
 
 338. 1. When potatoes are worth 80^ a bushel, what 
 is i peck worth? 
 
 2. If apples are selling at 10^ a quarter-peck, how 
 much will a bushel cost? 
 
 3. A boy sold -J bu. of berries at 5^ a quart. He 
 received - # for them. 
 
 4. Two bushels of cherries were divided equally among 
 4 persons. How many quarts did each receive? 
 
 5. A man bought 5 bu. 3 pk. of corn at 40^ a bushel. 
 How much did it cost him? 
 
 6. How many peck baskets can you fill with 64 qt. 
 of onions? 
 
 7. A woman bought 2 bu. 1 pk. 3 qt. of strawberries 
 at 5^ a quart. She paid for them with a $5-bill, and got 
 $ - in change. 
 
 8. How many pint packages can a seedsman make 
 from 2 bu. 2 pk. and 2 qt. of seeds? 
 
 9. A grocer bought 10^ bu. of apples at 60^ a bushel, 
 and sold them at 10^ a half -peck. What was his profit 
 on them ? 
 
236 
 
 SCHOOL ARITHMETIC. 
 
 Avoirdupois Weight. 
 
 339. Avoirdupois Weight is used in weighing all corn 
 mon articles. 
 
 16 ounces (oz.) = 1 pound (lb.). 
 2000 pounds = 1 ton (T.). 
 
 1. How many ounces in 4 lb. ? In 2J lb.? 
 
 2. In 2 lb. 8 oz. how many ounces? 
 
 3. What part of a pound are 4 oz.? 10 oz.? 
 
 4. How many pounds in 160 ounces? In 336 oz.? 
 
 5. What part of a ton is 500 lb.? 200 lb.? 
 
 6. A barrel of flour weighs 196 lb. What is the 
 weight of a sack of flour containing J of a barrel? 
 
 7. A bushel of wheat weighs 60 lb. What does a peck 
 weigh? 
 
 8. From a firkin of butter containing 42 lb. a grocer 
 sold 13 lb. 10 oz. How much was left? 
 
 \\) m oz. lb. oz. We cannot take 10 oz. from 
 
 40 Q _ j_-j -, p oz , so we take 1 lb. from the 
 
 1 A 1 Q 42 lb. and change it to ounces. 
 
 16 oz. - 10 oz. = 6 oz., 
 
 286 28 6 and 41 lb - 13 lb - = 28 lb - 
 
 9. A butcher sold 24 lb. 12 oz. of lard from a can 
 containing 40 lb. How much was left? 
 
 10. One crock of butter weighed 8 lb. 10 oz., and 
 another 9 lb. 14 oz. How much did both weigh? 
 
 340. 1. Find the cost of 3i lb. of cheese at 12^ a 
 pound. 
 
 2. What will 3 lb. 8 oz. of butter cost at 20^ a pound? 
 
COMPOUND NUMBERS. 237 
 
 3. How many hundred pounds make a ton? 
 
 4. If hay is worth $20 a ton, what is 100 Ib. worth? 
 
 5. A bushel of wheat weighs 60 Ib. How many bushels 
 in a bag weighing 120 Ib.? 
 
 6. A bin contains 6^ bu. of wheat. What is the weight 
 of the wheat? 
 
 7. Three boys bought 2 Ib. 4 oz. of candy. Each paid 
 15^. How many ounces should each one receive? 
 
 8. If a man eats 3 8-ounce loaves of bread in one day, 
 how many pounds will he eat in one week? 
 
 9. A bushel of oats weighs 32 Ib. Find the weight of 
 2 bu. 2 pk. 
 
 10. A sack of oats weighs 96 Ib. What is it worth 
 at 30^ a bushel? 
 
 11. At $4 a ton, how much coal can be bought for $25 ? 
 
 12. What is the value, at $2 a ton, of 7000 Ib. of coal? 
 
 Time Measure. 
 341. Time Measure is used in measuring duration. 
 
 60 seconds (sec.) = 1 minute (min.). 
 60 minutes = 1 hour (hr.). 
 
 24 hours 1 day (da.). 
 
 7 days = 1 week (wk.). 
 
 365 days = 1 year (jr.). 
 
 12 months (mo.) = 1 year. 
 
238 SCHOOL ARITHMETIC. 
 
 1. How many seconds are 'there in 5 "min. ? In 
 10 min.? 
 
 2. How many hours are there in 2 da.? In ^ da.? 
 
 3. How many days are there in 2 weeks? In 4 wk? 
 
 4. How many days are there in 4 wk. 3 da.? 
 
 5. How many hours in 240 min.? In 180 min.? 
 
 6. 100 years make 1 century. How many centuries 
 in 1900 yr.? 
 
 7. In 1^ hr. how many minutes? 
 
 8. What part of a day is 6 hours? 16 hours? 
 
 9. How many days in this month? How many weeks? 
 
 342. 1. How many days in 52 weeks? Then ,a year 
 is how much longer than 52 weeks? 
 
 2. How long is it from Christmas to E"ew Year's Day? 
 
 3. How many months is it from one Christmas to 
 another? 
 
 4. How many years and months have you lived? 
 
 5. How many weeks and days in May? 
 
 6. How many times does the clock strike 12 every day? 
 
 7. When we have daylight 14 hours, how long is the 
 night? 
 
 8. How many centuries are there between 1300 and 
 1900? 
 
 9. If you go to bed at 9 o'clock at night and get up at 
 6 in the morning, how long are you in bed? 
 
 10. Eight hours is what part of a day? 16 hr.? 
 
 11. Cousin Fred came to our house on Monday arid 
 stayed 2 weeks. On what day did he start home? 
 
 12. If a train runs 30 miles an hour, how far does it 
 run in 2 hours and a half? 
 
 13. How many times does the second hand of a watch 
 go around while the minute hand goes once around? 
 
COMPOUND NUMBERS. 239 
 
 14. While the hour hand goes once around, the minute 
 hand goes around - - times. 
 
 15. How often does the hour hand go around in a day? 
 The minute hand? 
 
 16. How many minutes in f of an hour? 
 
 17. Are the two hands of a clock together 12 times or 
 13 times in 12 hours? 
 
 18. If a boy saves 10^ a day, how much will he save 
 in a year? 
 
 19. If a man earns $30 a month, how much does he 
 earn in a year? 
 
 20. A girl walked J mile and back in 20 minutes. 
 How far would she walk in an hour at that rate? 
 
 21. How many days is it from October 24 to November 
 3* From Dec. 25 to Jan. 10? 
 
 22. If a man gets $2 for working 8 hours, how much 
 should he get for 44 hours? 
 
 23. If a horse can trot a mile in 3 minutes, how far 
 can he trot in an hour? 
 
 24. If a boy walks 3 miles an hour, how far does he 
 walk in 4 hr. 40 min.? 
 
 Long Measure. 
 
 343. Long Measure is used in measuring lines and 
 distances. 
 
 * i * l i * i * i * i * i * i * i * 
 21 3| 4| S| 6| 7| 8| 9| 
 
 12 inches (in.) = 1 foot (ft.). 
 
 3 feet = 1 yard (yd.). 
 
 54- yards ) 
 
 16* feet } =lrod(rd.). 
 
 320 rods = 1 mile (mi.). 
 
24:0 SCHOOL ARITHMETIC. 
 
 How many feet are there in 5 yards? In -J of a yard? 
 In 5J yards? 
 
 A distance of 5-| yards is called a rod. How many feet 
 in a rod? 
 
 A barn 4 rods long is how many yards in length? How 
 many feet? 
 
 How many rods long is your schoolroom? Find by 
 measuring. 
 
 Find the perimeter of a field 32 rods long and 25 rods 
 wide. 
 
 Name a place about a mile from your home. One about 
 2 miles. One about half a mile. 
 
 A distance of 320 rods is called a mile. How many rods 
 in J of a mile? 
 
 In J of a mile there are rods ; in f of a mile there 
 
 are rods. 
 
 What part of a mile is 160 rods? 80 rods? 
 
 Complete: 
 
 1. 1 rd. 2 yd. = yd. 6. 1 mi. 40 rd. = - - rd. 
 
 2. 3 ft. 2 in. = in. 7. 6 yd. 2 ft. = - -ft. 
 
 3. 2 yd. 1 ft. = ft. 8. 1 rd. 8 ft. = - -ft. 
 
 4. 1 yd. 4 in. = in. 9. 1 mi. 80 rd. = mi. 
 
 5. 2 rd. 2 ft. = ft. 10. 1 yd. 1 ft. 1 in.=- in. 
 
 344. If you walk 20 rd. a minute, how long will it 
 take you to walk a mile? 
 
 What is the perimeter of a field 80 rods square? 
 
 If a boy walks a mile to school in 20 minutes, he walks 
 at the rate of rods a minute or miles an hour. 
 
COMPOUND NUMBERS. 241 
 
 What is the length of this line? If 1 inch represents 3 
 feet, what does the line represent? Then to what scale 
 is the line drawn? 
 
 A line 6 in. long is drawn to the scale of 1 inch to 3 feet. 
 What length does the line represent? 
 
 Draw a line 5^ in. long. Let each inch represent 3 feet. 
 What length does the whole line represent? 
 
 What would the line represent if the scale were 12 feet 
 to 1 inch? 
 
 ^Making each inch represent 10 feet, draw a line to 
 represent 30 feet. 40 feet. 25 feet. 
 
 A field is 48 rods long and 36 rods wide. Represent it 
 on a scale of 12 rods to the inch. 
 
 A township in some states is a mile square. Draw a 
 map of one on a scale of 1 inch to 80 rods. 
 
 345. 1. A room 18 ft. long is how many yards long? 
 
 2. A fence is 11 yards or feet or rods long. 
 
 3. The perimeter of a rectangle is 40 feet. If the 
 length is 12 feet, what is the width? 
 
 4. Ten rods is how much greater length than 50 yards? 
 
 5. Find the distance around the schoolhouse in feet. 
 In yards. In rods. 
 
 6. Frank can walk 3 miles in an hour. In what time 
 can he walk 160 rods? 
 
 7. A room is 16J ft. square. What is the distance 
 around it? 
 
 8. What part of a yard is 1 ft. 6 in. ? 
 
 9. How many feet and inches in -J of a rod? 
 *i6 
 
24:2 SCHOOL ARITHMETIC. 
 
 10. The distance to the moon is 240,000 miles. If a 
 bullet traveled 1000 miles an hour, it would reach the 
 moon in hours. 
 
 B 
 
 E 
 
 D 
 
 These lines represent a part of a road. They are 
 drawn to a scale of 1 inch to 3 miles. 
 
 11. How far is it from A to B? From B to C? 
 
 12. How many miles is it from D to E? From 
 C to D? 
 
 13. Find the distance from F to C. From F to A. 
 
 14. The distance from E to D is what part of the dis- 
 tance from B to C? 
 
 15. A man wishes to drive from A to C. When he 
 reaches B, what part of the distance has he gone? 
 
 16. If the wheels of a bicycle turn twice around in 
 going one rod, how many times will they turn in going 
 from F to E? 
 
 17. A room is 18 ft. long and 15 ft. wide. The carpet 
 is laid lengthwise and is a yard wide. How many strips 
 are there on the floor? "What is the length of each strip? 
 How many yards in all the strips? 
 
 18. If the carpet is a yard wide, and is laid lengthwise, 
 how many yards will cover the floor of a room 12 ft. wide 
 and 16 ft. long? 
 
COMPOUND NUMBERS. 
 
 243 
 
 Square Measure. 
 346. Square Measure is used in measuring surfaces. 
 
 144 square inches (sq. in.) = 1 square foot (sq. ft.). 
 9 square feet = 1 square yard (sq.yd.). 
 
 30-J- square yards = 1 square rod (sq. rd.). 
 
 160 square rods = 1 acre (A.). 
 
 We have learned what a square foot is. Draw one, and 
 divide it into square inches. 
 
 How many square inches in one row? In all rows? 
 
 Then how many square inches make 1 square foot? 
 
 How many square inches in 2 sq. ft. ? In \ of a square 
 foot? 
 
 What part of a square foot is 72 sq. in.? 36 sq. in.? 
 
 How many square feet are there in 288 sq. in.? 
 
 Draw a square yard, divide it into square feet, and find 
 how many square feet make 1 square yard. 
 
 In 2 sq. yd. how many square feet? In 5 sq. yd.? 
 
 A square 1 rod long and 1 rod wide is called a square 
 rod. 
 
 How many square rods in a garden 5 rd. long and 3 rd. 
 wide ? Make a map of the garden, letting 1 inch represent 
 a rod. 
 
244 
 
 SCHOOL ARITHMETIC. 
 
 Areas. 
 
 347. The Area of a surface is 
 
 the number of square units of All B 
 
 measure it contains. 
 
 If each side of one of the small 
 squares in the figure is one inch 
 long, then each part is 1 square 
 inch (square unit of measure). 
 
 The area of the strip AB is 4 X 1 sq. in., or 4 sq. in. 7 
 and the total area is 3 X 4 sq. in., or 12 sq. in. 
 
 The area of a rectangle is expressed by the product of 
 the numbers that represent its length and width. 
 
 348. 1. How many square feet in a strip of carpet a 
 yard wide and 10 yards long? 
 
 2. A table is 6 ft. long and 3 ft. wide. It contains 
 - sq. ft., or sq. yd. " 
 
 3. How many square feet of oilcloth will cover a floor 
 15 ft. square? How many square yards? 
 
 4. Find how many square yards would be needed to 
 cover your kitchen at home. What would it cost at 30# 
 a square yard? 
 
 5. A lot is 16 rd. long and 5 rd. wide. How many 
 square rods in it? What part of an acre? 
 
 6. What part of an acre is 40 sq. rd.? 120 sq. rd.? 
 
 7. In 2 acres how many square rods? In 5 A.? In 
 10 A.? 
 
 8. An acre and 40 sq. rd. = - - A. 
 
 9. A field is 16 rd. by 20 rd. How many acres in it? 
 
 10. A rug is 9 feet square. How many square feet in it? 
 
 11. The area of a rectangle 8 ft. long is 40 sq. ft. 
 What is the width? 
 
COMPOUND NUMBERS. 
 
 245 
 
 12. The perimeter of a square is 12 yards. What is 
 the area in square feet? 
 
 13. A rectangular lot is 50 ft. by 75 ft. The house on 
 the lot is 25 ft. by 50 ft. How many square feet are there 
 in the yard? 
 
 14. How many square inches are there in the surface 
 of a common brick, which is 8 inches long, 4 inches wide, 
 and 2 inches thick? 
 
 15. A farmer wishes to make a grain bin 8 ft. long, 5 
 ft. wide, and 4 ft. deep. Ho\v many square feet of boards 
 will he have in the bottom? In one end? In one side? 
 
 B 
 
 D 
 
 This figure is drawn to a scale of 12 ft. to 1 inch. 
 
 349. To find the area of the entire figure we divide it 
 into four rectangles and find the area of each separately. 
 
 1. What is the length of A? The width? The area 
 in square feet? In square yards? 
 
 2. Find the area of B in square feet. In square yards. 
 What is the area of C? The area of D? 
 
 Find the area of the entire figure in square yards. 
 How does the area of A compare with that of C? 
 A is what part of D? D is what part of B? 
 What part of the entire figure is B? What part is D? 
 Copy the figure, omitting the dotted lines. Make 
 
 3. 
 4. 
 5. 
 6. 
 
 7. 
 8. 
 
 other dotted lines dividing the figure into 3 rectangles. 
 
 Find the area of each rectangle. 
 
246 
 
 SCHOOL ARITHMETIC. 
 
 350. Draw a rectangle 4 in. long and 3 in. wide, and 
 divide it into square inches. How many sq. in. have you? 
 
 Draw another rectangle 6 in. long and 2 in. wide. Is its 
 area equal to that of the first rectangle? Has it the same 
 dimensions (length and width)? 
 
 Draw a third rectangle 12 in. long and wide enough 
 to have the same area. What is its width? 
 
 Draw a rectangle 6 in. by 8 in. Draw another twice as 
 long, but only half as wide. Are their areas equal? 
 
 Draw another twice as wide as the first, but only half 
 as long. Compare the areas. 
 
 What may be the dimensions of a rectangle containing 
 24 sq.ft.? 36 sq.ft.? 64 sq.ft.? 
 
 Complete : 
 
 A rectangle 6 in. by 3 in. equals another 3 in. by - in. 
 A rectangle 20 ft. by 2 ft. equals another 10 ft. by - - ft. 
 A rectangle 5 in. by 4 in . equals another 2-J in. by - - in. 
 
 A rectangle 4 in. by 7 in. is how many times one that is 
 2 in. by 7 in. ? 
 
 A rectangle that is 6 in. by 5 in. is what part of one that 
 is 9 in. by 5 in. ? 
 
 HOW T many rectangles each 2 in. by 3 in. are equal to one 
 that is 6 in. by 3 in. ? To one 10 in. by 3 in. ? 
 
 D 
 
 B 
 
 BASE 
 
 351. Point out the base of the shaded triangle. The 
 altitude. 
 
COMPOUND NUMBERS. 247 
 
 What part of the rectangle is the triangle? 
 
 What is the area of the rectangle ? What, then, must be 
 the area of the triangle? 
 
 The area of the rectangle is 3 X 4 sq. units. 
 
 The area of the triangle is -J of 3 X 4 sq. units. 
 
 The area of a triangle is expressed by one-half of the pro- 
 duct of the numbers that represent its base and altitude. 
 
 1. If the base of a triangle is 6 inches and the altitude 
 3 inches, what is its area? 
 
 of ( 3 X 6 ) sq. in. = 9 sq. in. 
 
 Find the area of the following triangles: 
 
 2. Altitude 8 inches, base 6 inches. 
 
 3. Altitude 10 inches, base 8 inches. 
 
 4. Altitude 12 inches, base 12 inches. 
 
 5. Altitude 9 inches, base 16 inches. 
 
 6. Altitude 5 inches, base 3 inches. 
 
 Cubic Measure. 
 352. Cubic Measure is used in measuring solids. 
 
 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.). 
 27 cubic feet = 1 cubic yard feu. yd.). 
 
 Figure 1 represents a cubic 
 inch. Each face is an inch 
 square. Is each face a rectangle ? 
 
 Suppose Fig. 1 is drawn to 
 a scale of 1 foot to 1 inch. Then 
 OD represents what length? 
 
 What is the area of each 
 face? Does the figure repre- 
 sent a cubic foot ? FIG. 1 
 
 A solid that is 1 foot long, 1 foot wide, and 1 foot thick 
 is called a cubic foot. 
 
248 
 
 SCHOOL ARITHMETIC. 
 
 Find a block of wood, a stone, or a box that is about as 
 large as a cubic foot. 
 
 Suppose Fig. 1 is drawn to a scale of 1 inch to 3 feet, 
 or 1 yard. Then OD represents what length? 
 
 What is the area of each face? Does the figure represent 
 a cubic yard? 
 
 A solid that is 1 yard long, 1 yard wide, and 1 yard 
 thick is called a cubic yard. 
 
 353. Figure 2 represents 
 a cubic yard. If we cut it 
 into cubes as indicated, what 
 will be the size of each cube ? 
 
 Each cube is a cubic foot. 
 How many of them are 
 there in one layer? In the 3 
 layers? Then how many 
 cubic feet in a cubic yard? 
 
 2. 
 
 FIG. 3. 
 
 354. Fig. 3 represents a 
 cubic foot. If we cut off a 
 piece an inch thick and divide 
 it into inch cubes, how many 
 of them shall we have? 
 
 How many such pieces can 
 be cut from a cubic foot ? Then 
 how many cubic inches in a 
 cubic foot? 
 
 A cubic yard is 3 ft. long, 3 
 ft. wide, and 3 ft. thick. Find 
 the value of 3 X 3 X 3. Is 
 
 the product the number of cubic feet in a cubic yard? 
 
COMPOUND NUMBERS. 
 
 249 
 
 What are the dimensions of a cubic foot? Find the 
 value of 12 X 12 X 12, and compare it with the number 
 of cubic inches in a cubic foot. 
 
 Find how many cubic inches in a cube that measures 4 
 inches on each side. Build the cube with blocks (inch 
 cubes). 
 
 Volumes. 
 
 355. How many faces has a cube? Are they all equal? 
 Is each face a rectangle? 
 
 FIG. 4 
 
 Figure 4 represents a solid 6 inches long, 4 inches wide, 
 and 3 inches thick. 
 
 How many faces has the solid ? Is each face a rectangle ? 
 
 A solid bounded by 6 rectangles is called a rectangular 
 solid. 
 
 In Figure 4 each little cube represents 1 cubic inch. 
 Find how many cubic inches there are. 
 
 There are three layers, each containing 4 rows of the little cubes, 
 as ABCD. Each row contains 6 little cubes, or cubic inches, hence 
 the 4 rows contain 24 cubic inches. 
 
 Since there are 24 cu. in. in each layer, in the 3 layers there are 
 3 X 24 cu. in., or 72 cu. in., which is the volume. 
 
 Find the value of 6 X 4 X 3. Does the product equal 
 the number of cubic inches in Fig. 4? (6 X 3 X 4) X 
 1 cu. in. = - - cu. in. 
 
 The volume of a rectangular solid is expressed by the 
 
250 SCHOOL ARITHMETIC. 
 
 product of the numbers that represent its length, breadth, 
 and thickness. 
 
 The number of cubic units (cu. in., cu. ft., cu. yd., etc.) in a solid 
 is called its volume. 
 
 1. How many cubic inches in a brick 8 in. long, 4 in. 
 wide, and 2 in. thick? 
 
 2. How many cubic feet in a wall 16 ft. long, 4 ft. 
 high, and 2 ft. thick? 
 
 3. A hole is 3 ft. long, 2 ft. wide, and 6 ft. deep. How 
 many cubic feet of earth have been removed? 
 
 4. A cistern is 6 ft. square and 9 ft. deep. How many 
 cubic feet of water will it hold? How many cubic yards? 
 
 5. How many cubic feet in a cord? 
 
 A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high is called a cord. 
 
 6. How many cords are there in a pile of wood 16 ft. 
 long, 4 ft. wide, and 4 ft. high? 
 
 7. A cubic foot of water weighs 1000 oz. What is the 
 weight of a cubic yard of water? 
 
 8. Find the dimensions of a box that will hold 24 cu. 
 in. of water. 
 
 9. What are the width and depth of a cistern 6 ft. long 
 that will hold 144 cu. ft. of water? 
 
 10. An ice box holds 20 cu. ft. of ice. It is 4 ft. long 
 and 2 ft. deep. How wide is it ? 
 
DECIMAL FRACTIONS. 
 
 251 
 
 Decimal Fractions. 
 A B 
 
 356. What part of A is dark? Into how many parts is 
 each strip divided in B? 
 
 What part of each strip is the shaded square ? What part 
 of the large square? 
 
 Then -^ of one-tenth of B is one - - of B. 
 
 When anything is divided into ten equal parts, what is 
 each part called? 
 
 When each of these ten parts is divided into ten parts, 
 how many parts are there? 
 
 When each of these hundred parts is divided into ten 
 parts, how many parts are there? 
 
 When anything is divided into tenths, hundredths, thousandths, etc., 
 the parts are called decimal parts ; that is, tenth-parts. 
 
 357. You have already learned that 10 hundredths 
 make 1 tenth, and that 10 tenths make 1 one, just as 10 
 ones make 1 ten, 10 tens 1 hundred, and so on. You have 
 also learned that tenths and hundredths may be written 
 with the decimal point and without denominators. Frac- 
 tions so written are called Decimals or Decimal Fractions. 
 
 358. Tenths must stand next to ones, because 10 of 
 them make 1 one; hundredths next to tenths, because 10 
 
252 
 
 SCHOOL ARITHMETIC. 
 
 of them make 1 tenth. Kext to hundredths we must write 
 thousandths, because 10 of them make 1 hundredth, etc. 
 
 359. In decimals, as in integers (whole numbers), the 
 position of the figures indicates their value. Thus, in 3.15 
 we know that the 1 is one-tenth, because tenths are written 
 only in the first place to the right of ones; and that the 5 
 is five hundredths, because it is in the second place. 
 
 360. One-tenth of a cent is called a mill; then how 
 many mills make 1 cent ? 
 
 How many mills in 10 cents? In 100 cents, or $1? 
 Then 1 mill is what part of a dollar? 
 
 What part of a cent are 5 mills, or 5 thousandths of a 
 dollar? 
 
 In $.125, how many dimes, cents, and mills? Which 
 figure is in tenths' place ? In hundredths' ? In thousandths' ? 
 
 How many mills make 1 cent, or 1 hundredth of a dollar ? 
 
 How many mills in 1 dime? In 2 cents? Then may 
 $.125 be read as 125 mills, or as 125 thousandths of a 
 dollar? 
 
 1 ^ S * 
 3 O g s 2 
 o> ~ L R o> fl 
 
 a) .2 w 
 
 2 gc5 
 
 H PH H H 
 12345. 6789 
 
 Integers. Decimals. 
 
 361, Examine this table. Ten of any order make one 
 of the next higher order. With reference to ones, wliciv 
 
DECIMAL FRACTIONS. 253 
 
 are tens and tenths written? Hundreds and hundredths? 
 In what place is the 8? What does it express? 
 
 In the decimal .125, there are 1 tenth, 2 hundredths, and 
 5 thousandths, or 125 thousandths. When there are no 
 tenths or hundredths, we write thousandths in the third 
 place, and put ciphers in the first two places. 
 
 Thus, 5 thousandths is written .005. 
 
 What decimal place is occupied by tenths? By thou- 
 sandths? By hundredths? 
 
 What occupies the second decimal place? The fourth? 
 The third? 
 
 Extend tho table, and tell what occupies the fifth place. 
 The sixth place. 
 
 362. In reading integers we omit the name, which is 
 ones, the name of the lowest integral order. Decimals are 
 read just as integers are, except that the name of the lowest 
 decimal order is given. 
 
 In reading an integer and decimal, use the word and 
 between the integral and decimal parts of the number, but 
 nowhere else. 
 
 325.46 is read 325 and 46 hundredths. 
 
 73.05 is read 73 and 5 hundredths. 
 
 .08 is read 8 hundredths. 
 517.325 is read 517 and 325 thousandths. 
 
 82.073 is read 82 and 73 thousandths. 
 716.0034 is read 716 and 34 ten-thousandths. 
 
254: SCHOOL ARITHMETIC. 
 
 363. Eead the following: 
 
 x. .7 10. .225 19. 278.35 
 
 2. .15 11. .600 20. 51.07 
 
 3. .38 12. .012 21. 39.50 
 
 4. .03 13. .708 22. 624.054 
 
 5. .44 14. .1325 23. 516.0027 
 
 6. .044 15. .4016 24. 88.0008 
 
 7. .444 16. .7203 25. 200.0200 
 
 8. .707 17. .0518 26. 765.4004 
 
 9. .005 18. .0024 27. 394.3275 
 
 364. Write 7 thousandths as a decimal. 
 
 Thousandths occupy the third place, hence we write the 7 and put 
 ciphers in the first two places, thus : .007. 
 
 Express 25 thousandths as a decimal. 
 
 25 thousandths = 2 hundredths and 5 thousandths. There are no 
 tenths, hence we put a cipher in the first place, thus : .025. 
 
 Write as decimal fractions : 
 
 5 tenths 216 thousandths 75 thousandths 
 
 7 hundredths 103 thousandths 40 thousandths 
 42 hundredths 68 hundredths 90 hundredths 
 
 8 thousandths 50 hundredths 6 thousandths 
 36 thousandths 9 thousandths 82 thousandths 
 
 5 and 37 hundredths 46 and 7 thousandths 
 
 24 and 5 hundredths 75 and 14 thousandths 
 
 17 and 9 tenths 8 and 125 thousandths 
 
 32 and 8 hundredths 92 and 8 thousandths 
 
 40 and 40 hundredths 72 and 72 thousandths 
 
DECIMAL FRACTIONS. 255 
 
 Addition and Subtraction. 
 
 365. 1. Add .7, .42, .05, 2.7, and 15.48. 
 .7 
 
 Are the tenths all written in the same column ? Where 
 05 are the hundredths written? How are the decimal 
 2 . T points arranged ? 
 
 15.48 Are decimals added just as integers are added ? 
 
 19.35 
 
 2. Subtract .17 from .56, and .24 from .8. 
 
 .56 .8 Are tenths written in one column? Can you 
 
 .17 .24 ta> ke 4 hundredths from no hundredths? What 
 
 must you do ? Do we subtract as in whole 'num- 
 
 39 .56 bers? 
 
 Add: 
 
 
 
 
 3 
 
 4 
 
 5 
 
 6 
 
 42.3 
 
 13.256 
 
 7.0296 
 
 .032 
 
 16.07 
 
 6.09 
 
 5.724 
 
 .85 
 
 5.45 
 
 54.307 
 
 38.602 
 
 .027 
 
 .08 
 
 8.9 
 
 3.08 
 
 .645 
 
 24.06 
 
 36.005 
 
 6.7043 
 
 .930 
 
 Subtract : 
 
 
 
 
 
 7 
 
 8 
 
 9 
 
 10 
 
 11 
 
 37.42 
 
 51.63 
 
 7.15 
 
 .672 
 
 .0072 
 
 12.51 
 
 28.35 
 
 6.47 
 
 .348 
 
 .0036 
 
 12 
 
 13 
 
 14 
 
 15 
 
 16 
 
 2.57 
 
 5.02 
 
 16.3 
 
 .207 
 
 .87 
 
 .39 
 
 2.75 
 
 2.14 
 
 .0525 
 
 .254 
 
256 SCHOOL ARITHMETIC. 
 
 Find the value of: 
 
 17. 72.5 + .324 + 5.07 23. 6.08 + .027 4.44 
 
 18. 61.3 + 2.79 + .008 24. 8.72 + .803 .75 
 
 19. 26.7 +.41.3 + .802 25. 3.60 + 34.2 .016 
 
 20. 5.34 + .534 + 53.4 26. .542 + 7.61 3.25 
 
 21. .016 + 0.16 + .024 27. 9.27 3.45 .005 
 
 22. 7.03 + .300 +5.04 28. .172 + 61.5 2.64 
 
 Multiplication and Division. 
 
 366. How many tenths are 5X6 tenths? 30 tenths 
 are equal to how many ones? 3.0 = 30 tenths. 
 
 How many tenths are 8X5 tenths ? 40 tenths = - 
 ones. 
 
 5 x .6 = 30 tenths, or 3. 8X5 tenths = 40 tenths, or 4. 
 
 In 25 tenths, how many ones and tenths? 
 
 1. Multiply 4.2 by 6. 
 
 4. 2 6X2 tenths = 12 tenths, or 1.2. Where do we write 
 
 * the 2 ? What is done with the 1 ? Do we multiply as 
 
 in whole numbers ? How many decimal places in the 
 
 25.2 factors ? How many in the product ? 
 
 There must be as many decimal places in the product as 
 there are in both factors. 
 
 Find the products: 
 
 2. 5 X 3.7 7. 2 X .24 12. 4 X 1.36 
 
 3. 7 X 2.3 8. 5 X .13 13. 7 X 3.35 
 
 4. 4 X 5.6 9. 4 X .23 14. 3 X 8.72 
 
 5. 6X1.7 10. 7.X .14 15. .12 X .48 
 
 6. 8 X 4.2 11. 8 X .06 16. 2.4 X 1.2 
 
DECIMAL FRACTIONS. 257 
 
 17. Multiply .14 by .7. 
 
 7 X 14 = 98, only two places. What must we do 
 7 to make three places ? How do we know there should 
 
 be three decimal places? 
 
 Find the products: 
 
 18. .5 X .5 23. 12.5 X .5 28. .48 X .4 
 
 19. .8 X .4 24. 16.3 X .2 29. .25 X .5 
 
 20. .6 X .6 25. 24.6 X .3 . 30. .32 X .3 
 
 21. .9 X .3 26. 33.2 X .4 31. .17 X .5- 
 
 22. .7X.8 27. 53,2 X .5 32. .55 X .3 
 33. Multiply 142 by .06. 
 
 on How many decimal places in the factors? Then how 
 
 many must we point off in the product? 
 
 8.52 
 
 .Multiply: 
 
 34. 125 by .03 39. 376 by .05 
 
 35. 234 by .06 40. 428 by .03 
 
 36. 145 by .05 41. 706 by .06 
 
 37. 421 by .04 42. 250 by .07 
 
 38. 845 by .06 43. 625 by .05 
 367. 'What is i of 8 tenths? -J of .8 = 
 
 What is i of 9 tenths? J of .9 = 
 What is i of 24 hundredths? i of .24 = 
 What is ^ of 18 tenths? i of 1.8 = 
 What is i of 36 tenths? J of 3.6 = 
 Copy and find: 
 
 1. i of .6 4. 4 of 2.4 7. 4 of 36 tenths, or 3.6 
 2.- ]of .8 5. -J of 3.9 8. i of 52 tenths, or 5.2 
 3. -J of .6 6. i of 8.4 9. -J of 42 tenths, or 4.2 
 
258 SCHOOL ARITHMETIC. 
 
 Copy* and complete: 
 
 10. 
 
 11. 
 
 12. 
 13. 
 14. 
 15. 
 
 3)126 
 
 3) 12.6 
 
 3) 13.5 
 
 3) 13.8 
 
 4)168 
 
 4) 16.8 
 
 4) 17.2 
 
 4) 17.6 
 
 6) 126 
 
 6) 12.6 
 
 6) 13.2 
 
 6) 14.4 
 
 8) 168 
 
 8) 16.8 
 
 8) 17.6 
 
 8) 18.4 
 
 7)217 
 
 7) 21.7 
 
 7) 22.4 
 
 7) 23.1 
 
 4)568 
 
 4) 56.8 
 
 4) 57.2 
 
 4) 59.6 
 
 16. Divide 75 by 4. 
 
 4) 75. 00 7 tens -=-4=1 ten, and 3 tens remaining. 
 
 35 ones -^4 = 8 ones, and 3 ones remaining. 
 L8.75 3 oneg and Q tenths = 30 tenths. 30 tenths -r- 4 = 
 
 7 tenths, and 2 tenths remaining. 2 tenths and 
 hundredths = 20 hundredths. 20 hundredths -j- 4 = 5 hundredths. 
 
 Find the quotients: 
 
 17. 49 -r- 4 21. 71 -T- 5 25. 121 -r- 8 
 
 18. 67 -f- 4 22. 79-^4 26. 130^-8 
 
 19. 53-^-4 23. 35 -f- 2 27. 146 -f- 4 
 
 20. 66 -f- 5 24. 87-^-2 28, 255-^-6 
 368. How many tenths in 1? In 2? In 4? In 2J < 
 How many hundredths in 1? In J? In i? 
 
 Write as decimals: , i, }, J, f, f , T V, iV 
 
 How many thousandths in 1? In J? In i? 
 
 Write as decimals: -J, f, f, 5, -j^V 
 
 Change to common fractions: .5, .25, .75, .2, .075. 
 
 The following exercises will show you that 
 
 (a) Moving the decimal point one place to (lie right 
 multiplies a number by 10. 
 
 (b) Moving the decimal point one place to the left 
 divides a number by 10. 
 
DECIMAL FRACTIONS. 259 
 
 1. 10X2.5 = 25. 6. 25.0 -4- 10 = 2.5 
 
 2. 10X1.25 = 12.5 7. 12.5-^10 = 1.25 
 
 3. 10 X. 25 = 2.5 8. 2.5 -=- 10 = .25 
 
 4. 10 X. 5 = 5.0 9. 5.0 -4- 10 = .5 
 
 5. 10 X .05 = .5 10. .5 10 = .05 
 
 Find the products and quotients by moving the decimal 
 
 point : 
 
 11. 
 
 10 
 
 X 
 
 2.7 
 
 17. 
 
 27- 
 
 _i_ 
 
 10 
 
 23. 
 
 10 
 
 X 
 
 4.265 
 
 12. 
 
 10 
 
 X 
 
 2.45 
 
 18. 
 
 24. 
 
 5- 
 
 4-10 
 
 24. 
 
 10 
 
 X 
 
 30.74 
 
 13. 
 
 10 
 
 X 
 
 .36 
 
 19. 
 
 3.6 
 
 -4-10 
 
 25. 
 
 10 
 
 X 
 
 261.7 
 
 14. 
 
 10 
 
 X 
 
 .8 
 
 20. 
 
 8. - 
 
 
 10 
 
 26. 
 
 37 
 
 5 X 10 
 
 15. 
 
 10 
 
 X 
 
 .07 
 
 21. 
 
 .7 - 
 
 5 
 
 10 
 
 27. 
 
 62 
 
 5.4 
 
 X 10 
 
 16. 
 
 10 
 
 X 
 
 1.03 
 
 22. 
 
 10.3 
 
 4-10 
 
 28. 
 
 71 
 
 .68 
 
 X 10 
 
 Complete the following and show that 
 
 (c) MDriiif/ the decimal point two places to the riyht 
 m ultqdi-es a number by 100. 
 
 (d) Moving the decimal point two places to the left 
 divides a number by 100. 
 
 29. 100 X 25.0 = 39. 2500 -f- 100 = 
 
 30. 100 X 1.25 = 40. 1 25 -4- 100 = 
 
 31. 100 -X 12.5= 41. 1250-^-100 = 
 
 32. 100 X. 125= 42. 12.5-4-100 = 
 
 33. 100 X .042 = 43. 4.2 -4- 100 = 
 
 34. 100 X. 005= 44. .5-4-100 = 
 
 35. 100 X 3.07 = 45. 307 -4- 100 = 
 
 36. 100 X. 5= 46. 50-^-100 = 
 
 37. 100 X .25 = 47. 25 -4- 100 - 
 
 38. 100 X .05= 48. 5-1-100 = 
 
260 SCHOOL ARITHMETIC. 
 
 369. 1. Divide .098 by .7. 
 
 .098 -i- .7 = .14 Is - 098 tne product of .7 (the divisor) and 
 
 .14 (the quotient) ? Does it contain as 
 many decimal places as both the factors. 
 
 The dividend contains 3 decimal places, the divisor 1. How many 
 must the quotient contain ? 
 
 There must be as many decimal places in the quotient 
 <as the number of such places in the dividend exceeds the 
 number in the divisor. 
 
 Find the products: Find the quotients: 
 
 1. .6 X .7 8. .42 -*- .6 
 
 2. .3 X .15 9. .45 + .3 
 
 3. .5 X 4.3 10. 2.15 -5- .5 
 
 4. 3.6.X .$ 11. 3.24 -f- .9 
 
 5. .7 X .05 12. .035 ~ .7 
 
 6. .9 X -017 13. .0153 -*- .0 
 
 7. 310 X .05 14. 15.50 ~ .05 
 
 370. Another name for hundredths is per cent. Instead 
 of saying 5 hundredths of $250, we may say 5 per cent of 
 $250. 
 
 To find 1 hundredth of a number we divide it by 100. 
 Hence, to find 1 per cent of a number we divide the num- 
 ber by 100. 
 
 What is the easiest way to divide by 100? 
 
 1. Find 1 per cent of $125. 
 
 $125 -f- 100 = $1.25. 
 
 2. Find 1 per cent of $275. Of $325. Of $152.50. 
 
 3. What is 1 per cent of $200? What is 2 per cent 
 of $200? 
 
 4. Tind 2 per cent of $300. Of $500. Of $250. 
 
PERCENTAGE. 
 
 261 
 
 5. What is 3 per cent of $217.50? Of $187.50? 
 
 6. When you know what 1 per cent of a number is, 
 how do you find 4 per cent of the number? 
 
 7. Find 4 per cent of $732.50. Of $364.25. 
 
 8. What is 6 per cent of $75? Of $87.25? 
 
 9. Find 5 per cent of 200. Of 800. Of 24.5. 
 
 10. What per cent of a number equals 100 hundredths 
 of the number? 
 
 11. Multiply $125 by .05, and compare the product 
 with 5 per cent of $125. 
 
 12. Find 6 per cent of $240; multiply $240 by .06. 
 Are the results equal? 
 
 13. Compare .04 X $325 with 4 per cent of $325. Are 
 they equal? 
 
 14. In how many ways can you find a per cent of a 
 number? 
 
 15. If you borrow money, do you have to pay anything 
 for its use? 
 
 16. Find out at home all you can about what is paid for 
 the use of money. 
 
 Percentage. 
 
 371. This square is di- 
 vided into equal parts. 
 Each part is 1 - - of the 
 square. 
 
 What part of the square 
 is A + B? 
 
 How many hundredths of 
 the square in each horizon- 
 tal strip? Each strip is what 
 part of the square? 
 
262 SCHOOL ARITHMETIC. 
 
 Instead of hundredths we may use the term per cent, 
 because per cent means hundredths. 
 
 Then what per cent of the square is A ? A + B ? 
 
 How many per cent are there in the square? In any- 
 thing? 
 
 One hundred per cent of a number is the number itself. 
 
 What per cent of the square is above the line KIM 
 What part of anything is 50 per cent of it? 
 
 What part of the square is shaded ? What per cent of it 
 is shaded? 
 
 How many small squares in 10 per cent of the large 
 square? In 20 per cent? 
 
 The sign % stands for the term per cent, and means 
 either per cent or hundredths. Thus, 5% of the square 
 means 5 per cent, or 5 hundredths of it. 
 
 What per cent of the square isA + B + C + D + E? 
 
 What part of the square is 10$ of it? 20$? 4<K/< 
 50$? 60$? 6$? 
 
 Cover 25% of the square. What % is not covered? 
 
 372. What % of $100 is $5? $10? $25? 
 
 Draw a rectangle and divide so as to show 50% of it. 
 25%. 12^%. 
 
 Divide a square so as to show that 50% = 2? and that 
 25% =J. 
 
 ' Draw a line an inch long, and another line 50% as long. 
 ; This line is an inch long. . Draw 
 
 another line 100% as long. 
 
 How many times a number is 200% of it? 300%? 
 
 3^ of a number is what % of it ? 
 
 How do you find 1 hundredth, or 1%, of a 
 
PERCENTAGE. 263 
 
 What is the effect of moving the decimal point two places 
 to the left? 
 
 When you have found 1% of a number, how do you find 
 3% of it? 5%? 
 
 Find 1% of 200. Of 500. Of 250. Of 12.5. 
 
 Find 5% of 200. Of 125. Of 315. Of 41.2. 
 
 State the simplest way of finding 10%, or y 1 ^-, of a num- 
 ber. What is the effect of moving the decimal point one 
 place to the left? 
 
 Find 10% of 50. Of 12.5. Of 345. Of 624. 
 
 What is the ratio of 200% to 100%? 100% to 50%? 
 25% to 100%? 
 
 What .is 100% of 5^? Of $10? Of 25 gal.? 
 
 373. 1. Find 2^% of $400. 
 
 \% of $400 = ^4.00. 
 2\% of $400 = 2| X $4.00, or $10. 
 
 Find: 
 
 2. 1J % of $1200. 6. 334 % of 900 ft. 
 
 3. 12^% O f $000. 7. 2i% of $1500. 
 
 4. 16| % of 120 bu. 8. 4 % of $1000. 
 
 5. 17 % of $320. 9. f % of $2000. 
 
 374. Be sure you understand the following: 
 100 % of a number = all of it. 
 
 200 % of a number = twice the number. 
 
 25. % of a number | of it. 
 
 12i% of a number = | of it, 
 
 37^-% of a number = f of it. 
 
 33i% of a number = 4 of it. 
 
 1. Find 200% of $5. Of 3 ft. Of gal. 
 
 2. What is 25% of 24 in.? Of 16 ft.? Of 
 
264 SCHOOL ARITHMETIC. 
 
 3. Find 50% of $20. Of $.40. Of a dime. Of a gallon. 
 
 4. Find 12^% of 40^. Of 8 yd. Of 4 bu. Of 72 ft. 
 
 5. What is 33-J% of a yard? Of 12 qt? Of $300? 
 
 6. A man who had $10 spent 50% of it. How much 
 had he left? 
 
 7. Mr. Lee has 40 acres of land. If he plants 25% 
 of it in corn, how many acres does he plant? 
 
 8. How many days in 33^% of the month of June? 
 
 9. If $6 is 50% of my cash, how much have I? 
 
 10. is i of what number? 6 is 20% of what number? 
 
 11. A farmer had 80 chickens, but a hawk caught 25% 
 of them. How many did the farmer have left? 
 
 12. What is the difference in hours between 1G|% 
 and 12^% o f one a ay $ 
 
 13. Eva's age is 75% of the age of Ethel, who is 16 
 years old. How old is Eva? 
 
 14. Pencils bought at 48^ a dozen were sold at a gain 
 of 25%. Find the selling price of each pencil. 
 
 15. A girl spelled correctly 99% of 200 words. How 
 many did she miss? 
 
 16. Some boys bought a pie, and each ate 25% of it. 
 If the whole pie was consumed, how many boys were there ? 
 
 17. What is the distance between two towns if 5 miles 
 is 33^% of the distance? 
 
 18. I had $20, but spent $10 of it for a dress. What 
 per cent of rny money did I spend? 
 
 19. A farmer who had 8 cows sold 2 of them. \Ylml, 
 per cent of them did he sell? 
 
 20. I bought a stove for $12 and sold it so as to gnin 
 $3. What per cent of the cost did I gain? 
 
 Gain or loss is always some per cent of the cost. 
 
PEKCENTAGE. 205 
 
 21. A boy bought a watch for $12 and sold it for $9. 
 How much did he lose? What per cent of the cost? 
 
 22. Robert paid $15 for an overcoat and sold it for 
 $20. What per cent did he gain? 
 
 23. If I pay. $2 for an article and sell it for $1, what 
 per cent do I lose ? 
 
 24. If a sheep is bought for $4 and sold at a gain of 
 _!r>%, for how much is it sold? 
 
 25. A man paid 50^ for a knife and sold it at a loss of 
 10%. What did he get for it? 
 
 26. If a grocer buys sugar at 4# a pound and sells it at 
 r>^ a pound, what per cent does he gain? 
 
 27. At what price must coffee which cost 15^ a pound 
 be sold to make a profit of 20%? 
 
 28. How much must be paid for a book marked $2, if 
 25% is taken off the marked price? 
 
 29. If $12 is 37 2% of my money, how much have I? 
 
 30. An organ which was marked $70 I bought for 
 10% less. Tell me what I paid for it. 
 
 31. Of a regiment of 1000 soldiers 5% were made 
 prisoners. How many escaped? 
 
 32. How much must be paid for a bicycle, if the marked 
 price is $75, and the discount, or the sum taken off, is 40% ? 
 
 33. What per cent of the day has passed at 6 o'clock 
 A. M.? 
 
 34. Oranges were bought at the rate of 2 for 5#, and 
 sold at 3^ apiece. What per cent was gained? 
 
 35. A man who earned $60 a month had his salary 
 increased 25%. He then earned $ - a month. 
 
 36. If you get 6 cents interest for every 100 cents you 
 loan for a year, what per cent are you getting? 
 
266 SCHOOL ARITHMETIC. 
 
 Interest. 
 
 375. If a man borrows a horse, he does not pay for its 
 use; if he hires the horse, he must pay the owner whatever 
 is agreed upon. 
 
 When a man borrows money, he is usually required to 
 pay something for its use. Money paid for the use of 
 money is called Interest. 
 
 1. If you borrow $100 from me and agree to pay me 
 6% a year for its use, at the end of the year you must 
 give me back the $100 and pay me the interest, which is 
 
 6% of $100, or $- . 
 
 2. If you borrow $100 at 4% a year, how much interest 
 will you owe at the end of one year? 
 
 3. What is the interest of $100 for 1 year at 5%? 
 
 4. At 6%, what i.s the interest of $200 for 1 year? 
 Of $500? Of $300? 
 
 5. At 4%, what is the interest of $300 for 1 year? 
 For 2 years? 
 
 6. At 3%, what is the interest of $400 for 1 year? 
 For 2 years? 
 
 7. Find the interest of $300 for 1 year at 6%. For 
 2 years. 
 
 8. At 6%, what is the interest of $200 for 6 months ^ 
 
 9. At 5%, what is the interest of $600 for 4 months 
 (iyr.)? 
 
 10. At 6%, what is the interest of $200 for 1 year 
 and 6 months (1J yr.)? 
 
INTEREST. 267 
 
 376. Find the interest of $200 for 
 
 1. 2 yr. @ 6% 7. 2 yr. @ 8% 
 
 2. 5 yr. @ 6% 8, 6 yr. @ 8% 
 
 3. 6 mo. @ Q% 9. 3 yr. @ 3% 
 
 4. 3 mo. @ 6% 10. 4 mo. @ 3% 
 
 5. 2 mo. @ 6% 11. 6 mo. @ 4% 
 
 6. 9 mo. @ 6% 12. 9 mo. @ 4% 
 
 13. Find the interest of $150 at 4% for 2 yr. 3 mo. 
 
 $1.50 = interest for 1 yr. at \%. 
 4 
 
 $6.00 = interest for 1 yr. at 4%. 
 2 
 
 $12.00 = interest for 2 yr. at 4$. 
 
 1.50 = interest for 3 mo. (\ yr. ) at 4%. 
 
 $13.50 = interest for 2 yr. 3 mo. at 4%. 
 
 Find the interest of $150 for 
 
 14. 3 yr. 4 mo. @ 4% 16. 2 yr. 9 mo. @ 4-.% 
 
 15. 4 yr. 6 mo. @ 4% 17. 5 yr. 2 mo. @ 4% 
 
 Find the interest of $240 for 
 
 18. 1 yr. 3 mo. @ 5% 25. 5 yr. 2 mo. @ 2% 
 
 19. 3 yr. mo. @ 6% 26. 7 yr. 4 mo. @ 8% 
 
 20. 2 yr. 4 mo. @ 4% 27. 1 yr. 1 mo. @ 4% 
 
 21. 4 yr. 8 mo. @ 4% 28. 3 yr. 9 mo. @ 6% 
 
 22. 1 yr. 9 mo. @ 6% 29. 4 yr. 2 mo. @ 5% 
 
 23. 6 yr. 6 mo. @ 3% 30. 10 yr. 4 mo. @ 7% 
 
 24. 8 yr. 4 mo. @ 5% 31. 16 yr. 8 mo. @ 6% 
 
208 SCHOOL ARITHMETIC. 
 
 GENERAL REVIEW. 
 Oral Work. 
 
 377, 1. A man bought a book for 56^ and gave a 
 silver dollar in payment. Count up the change. 
 
 2. How many handkerchiefs at 25^ each can be bought 
 for $3? 
 
 3. Find the perimeter of a rectangle 8 ft. long and 50% 
 as wide. 
 
 4. If C men can build a stable in 8 days, how long 
 would it take one man? 
 
 5. If one man can build a wall in 32 days, how long 
 would it take 4 men? 
 
 6. If 5 cows are worth 25 sheep, 8 cows are worth' 
 sheep. 
 
 7. How many pounds of butter at 12# a pound must be 
 given for 3 Ib. of coffee at 16^ a pound? 
 
 8. At the rate of 3 for 5#, how many oranges can be 
 bought f or $1? 
 
 9. James bought 3 bushels of pears at $2 a bushel. 
 Henry bought twice as many at the same price. How 
 much did both pay? 
 
 10. Lemons were bought at the rate of 2 for 5#, and 
 sold at 3^ apiece. Find the gain on a dozen. 
 
 11. A grocer paid 75^ a bushel for potatoes and sold 
 them at 25^ a peck. How much did he gain on 10 bushels? 
 
 12. What is the ratio of a gallon to a pint? 
 
 13. A farmer had 40 sheep. Dogs killed one out of 
 every 8. How many were not killed? 
 
 14. If 10 men weigh a ton, what is the average weight 
 of each man? 
 
GENERAL REVIEW. 2<>9 
 
 15. How many square inches in a rectangle 8 in. long 
 and 25% as wide? 
 
 16. A rectangle 6 ft. long contains 18 sq. ft. What is 
 its width ? Draw the figure. 
 
 17. What is the perimeter of a square garden contain- 
 ing 25 square rods? 
 
 18. A man bought a hat for $2.65. What 4 pieces of 
 money would exactly pay for it? 
 
 19. How many 2-inch squares are equal to a 6-inch 
 square? 
 
 20. A lady having $20 gave 50% of it to her son and 
 50% of the remainder to her daughter. How much had 
 she left?. 
 
 21. If a horse trots 10 miles in an hour, how far does 
 he trot in 6 minutes? 
 
 22. A man sold a cow for J of her cost. What per 
 cent did he lose? 
 
 23. If $50 is f of my cash, how much have I? 
 
 24. Helen's age is 25% of her father's. If Helen's 
 nge is 8 years, what is her father's age? 
 
 25. Mr. Jones pays $300 a year for rent, which is 10% 
 of the value of the house. In how many years will his 
 rent amount to the value of the house? 
 
 Written Work. 
 
 378. 1. Find the cost of 25 bushels of wheat at $1.1 5 
 a bushel. 
 
 2. A sheep cost $4, a cow 6 times as much, and a horse 
 3 times as much as the cow. They all cost $ . 
 
 3. A grocer bought a barrel of vinegar containing 42 
 gallons at 15# a gallon. He sold it at 6^ a quart. How 
 much did he gain? 
 
270 SCHOOL ARITHMETIC. 
 
 4. The distance from Pittsburg to Philadelphia is 354 
 miles. At 2^ a mile, what is the fare for a round trip? 
 
 5. How long is the side of a square whose area is 12J% 
 of that of a rectangle 8 ft. by 16 ft.? 
 
 6. A lady bought 8 yd. of silk @ $1.25 a yard, 3 pairs 
 of shoes @ $2.50, 6 Ib. of butter @ 15#, and li pk. of 
 apples @ 20^ a half peck. Make out the bill. 
 
 7. A field is 40 rods long and 16 rods wide. How many 
 square rods does it contain? How many acres? 
 
 8. A 2-foot cube of marble was polished at a cost of 
 25^ a square foot. How much was paid for polishing? 
 
 9. How many square yards of oilcloth will cover a room 
 18 ft. long and 16 ft. wide? 
 
 10. At 12J^ a yard, what will be the cost of 36 yards 
 of cloth? 
 
 11. What number divided by 12 will give the quotient 
 144? 
 
 12. How many boards, each 12 ft. long, will be required 
 for a fence 600 ft. long, and 5 boards high? 
 
 13. From a cheese which weighed 75 Ib. a grocer cut 
 42 Ib. 8 oz. How much remained? 
 
 14. There are 16.5 ft. in a rod. How many feet are 
 there in 320 rods, or 1 mile? 
 
 15. How many rails, each 30 ft. long, will be required 
 for a mile of railroad? 
 
 16. A fence is 120 ft. long and the posts are 8 ft. apart. 
 Find how many posts there are. Make a drawing. 
 
 17. If 2 bushels of oats cost 64^, what is the cost of 2 
 pecks? 
 
 18. At 12i^ a quart, how many quarts of molasses will 
 $2 buy? 
 
GENERAL REVIEW. 271 
 
 19. How many eggs, at 10^ a dozen, can be bought for 
 $2.50? 
 
 20. Find two numbers whose product is 105. Two 
 other numbers. 
 
 21. In an orchard -J of the trees are apple, 3 peach, 
 and the remainder pear. There are 10 pear trees. How 
 many peach trees? 
 
 22. On Friday a man started on a trip. He was gone 
 24 days. On. what day of the week did he return? 
 
 23. A man feeds his horse 6 qt. of oats 3 times a day. 
 How long will 9 bushels of oats last? 
 
 24. Does your pulse beat 76 times in a minute? If it 
 does, how many times does it beat in a day? 
 
 25. How many pint bottles will it take to hold 9i 
 gal. of ink? 
 
 26. How many cubic feet of water can be put into a 
 trough 6 ft. long, 2 ft. wide, and 1 ft. deep? 
 
 27. At $2.40 a square yard, what will it cost to lay a 
 pavement 90 ft. long and 6 ft. wide? 
 
 28. Find the interest of $50 for 4 mo. at 6%. 
 
 29. I lost $5 by selling a wagon for $35. What per 
 cent did I lose? 
 
 30. What is the length and width of your schoolroom \ 
 Find the cost of painting the ceiling at 5^ a square yard. 
 

PRICE-LIST OF TEXT BOOKS. 
 
 1. Johnson's Primer lin colors), Paper Binding, 
 
 2. Johnson's Primer (in colors), Bound in Hoards 
 
 3. Johnson's First Header, Hound in Hoards 
 
 4. Johnson's First Header, Hound in Cloth 
 
 5. Johnson's Second Header. Hound in Boards 
 
 ti. JobnsOn'a Second Reader. Hound in Cloth 
 
 7. Johnson's Third Header, Hound in Cloth 
 
 8. Johnson's Fourth Header, Bound in Cloth 
 
 9. Johnson's Fifth Header, Bound in Cloth 
 
 10. Branson's Common School Speller, First Book (In Boards). 
 
 11. Branson's Common School Speller, Second Book (In Boards) . 
 
 12. Branson's Common School Speller. Complete (In Cloth) 
 
 13. Lee's New Primary History of the United States (formerly Lee's 
 
 Primary) 
 
 3 hool History of the United States, Cloth 
 
 Now Scl 1 History of the United States. Half Morocco 
 
 16. Lee's Advanced School History of the United States 
 
 17. Smithdeal's Slant Writing-Books, (six numbers), each 
 
 J* ** in's Vertical Writing-Books (Nos. 1,2, 3, 4), each. 
 
 Retail 
 price. 
 
 911274 
 
 10 
 15 
 16 
 20 
 25 
 30 
 35 
 45 
 60 
 ir, 
 20 
 30 
 
 50 
 75 
 85 
 
 100! 
 05 
 04 
 
 Kxch'ge 
 
 price. 
 
 THE UNIVERSITY OF CALIFORNIA LIBRARY 
 
 52. Southern Literature (from 1579 to 1895) 
 
 53. History of Vindnia (Maurv's) 
 
 54. Geography of Virginia (Henning's) 
 
 55- Moses' First Phonetic Reader, by Prof. E. P. Moses, Raleigh, N. C. 
 (Other numbers in course of preparation) 
 
 oli. Some Birds and Their Ways, cloth 
 
 57. Grimm's Fairy Tales, by P". P. Claxton and Winifred Haliburton. Cloth 
 
 I 00 ' 
 75 
 
 35 
 
 For Examination, with compliments of 
 
 B. F. JOHNSON PUBLISHING CO., Publishers, 
 
 RicHi-i-iorid, Virginia.