HALCS mAmEM/JJICAL SERi |;Hi!ti;ni ELEME/iTARY FRAN K-rt-n ALL OMlnimiM^lt uwnminoi liilliiiil ■twitijiiiiniiiitiiiliiiiuii •«wnt t — < *—»mn ■>**»» >»»■ ■■— ■*—»<—>— »M—»>» EDUCATIONAL PUSUS«ERS YOR K • Ci\ I CmO 'BOST* 3% DEP M). Digitized by the Internet Archive in 2008 with funding from IVIicrosoft Corporation http://www.archive.org/details/elementaryarithmOOhallrich HALL'S MATHEMATICAL SERIES ''.' \ , A^ : \\''^'UJl\l AN ELEMENTARY AEITHMETIC ORAL AND WRITTEN FRANK H. HALL AUTHOR OF "THE WERNER ARITHMETICS," "THE ARITHMETIC READERS," J STC. WERNER SCHOOL BOOK COMPANY NEW YORK CHICAGO BOSTON G A lA^ HALL'S MATHEMATICAL SERIES THE WERNER ARITHMETICS A Three-Book Course for -Graded Schools Book I. For third and fourth grades, cloth, 256 pages, 40c. Book II. For fifth and sixth grades, cloth, 288 pages, 40c. Book III. For seventh and eighth grades, cloth, 288 pages, 50c. TEACHERS' HAND BOOK giving oral work preparatory for Book I, suggestions to teachers who are using the Werner Arithmetics, answers to problems in Books II and III, and a large amount of supple- mentary seat-work. Cloth, 131 pages, 25c. THE HALL ARITHMETICS A Tiiio-Book Course /or Graded or Ungraded Schools Hall's Elementary Arithmetic, cloth, 248 pages, , 35c. Hall's Complete Arithmetic, cloth, 448 pages, , . 60c. Copyright, 1899 By WERNER SCHOOL BOOK COMPANY Typography by R. R. Donnelly Sons Co., Chicago PREFACE. The prominent feature of this book is the spiral advance- ment plan upon which it is built. The basis of the spiral is the five fundamental thought processes of arithmetic, viz.: 1. The uniting of numbers (of things) — addition. 2. The separating of numbers (of things) — subtraction. 3. The taking of numbers (of things) a given number of times — multiplication. 4. The finding of how many times one number (of things) is contained in another number (of things) — ■ division. 5. The finding of one of the equal parts of a number (of things) — division; or, as it is sometimes cslled, partition. These five processes appear in groups, — five times on page 9 in problems so simple that the tyro will find little difficulty in understanding them; twice on page 10; five times on page 11; four times on page 23; twice on page 25 ; three times on page 89 ; twice on page 96; three times on page 109 ; twice on page 114 ; three times on page 119; twice on page 146, and at least once on nearly one fourth of the pages of the book. Each of these "spirals" is a little more difficult than the preceding one, and each is preparation for the one that follows. The variety in the book comes (1) from the introduction of new terms, (2) from the gradual increase in the difficulty of the problems, and (3) from the different magnitudes (things) to which these processes are applied. The plan of the book provides that the pupil may become familiar with the terms peculiar to mathematics 54! 4 in '/, /4v ' PREFACE. cc r c •by'l'Kfeit'iti^e rather taan by definition. See the words sum, "^''' *' di'ff evince, product, quotient, — pages 18, 19, 20, 21, 22, 156, 157, 158, 159 ; the words t7nangle, ohlong, x>entagon, square, perimeter, area, — pages 63, 73, 83, 93, 103, 113. On pagiBS 10 and 12 the fundamental processes are applied to inches, feet, and yards; on page 23, to apples, cents, trees, and degrees; on page 35, to halves and fourths; on page 36, to half-inches and fourth-inches; on page 37, to half-dollars and fourth- dollars ; on page 45, to halves and sixths; on page 55, to halves, fourths, and eighths; on page 89, to inches, sixths, and tenths written decimally, etc. In no part of the book is the pupil allowed to lose sight of the fact that his arithmetic work is mainly adding, sub- tracting, multiplying, dividing, and "parting"; and he soon learns to take great delight in applying these processes to new magnitudes. So close is the connection between the oral and the written work (see pp. 112, 122, 132, 142, 155, 156, 157, 165, 170, 209, etc.), that the former becomes a preparation for, and a stepping stone to, the latter. It is all "mental " arithmetic, some of the problems of which are to be solved without and some with the aid of a pencil. There is such an abundance of concrete problems that the pupil never leaves out of his thought, for any consider- able length of time, the magnitude idea. But if, in the learning of the merely mechanical processes, he for the moment loses sight of quantity, he is able quickly to pro- ject into the abstract problem the notion of magnitude and magnitude relation. The book thus becomes, not simply an arithmetic, but a first book in mathematics. F. H. H. Jacksonville, Illinois, April, 1899. NUMBER FACTS To be taught orally before the book is put into the hands of the pupil. Each fact of separation or combina- tion here given should be worked out with objects and measurements, then memorized — perfectly memorized. THIRTY-THREE FACTS OF ADDITIOX. 1 1 2 1 3 1 2 2 4 1 3 2 5 1 4 2 3 3 6 1 5 2 2 3 4 4 5 5 6 6 6 7 7 4 3 7 1 6 2 5 3 4 4 8 1 7 2 6 3 5 4 9 1 8 2 7 8 8 8 8 9 9 9 9 10 10 7 3 6 4 5 5 9 2 8 3 7 4 6 5 9 3 8 4 7 5 6 6 10 10 10 11 11 11 11 12 12 12 12 If the thirty-three facts of addition given above are taught properly, the pupil will, at the same time, acquire a knowledge of the corresponding facts of subtraction ; thus, if it is clear to the pupil that 7 and 5 are 12, he will also know that 12 less 7 are 5, and that 12 less 5 are 7. TWELVE FACTS OF MULTIPLICATION. 2 twos = 4 3 twos = 6 4 twos = 8 5 twos =10 6 twos = 12 2 threes = 6 3 threes = 9 4 threes = 12 2 fours = 8 3 fours = 12 2 fives = 10 2 sixes = 12 If these twelve facts of multiplication are taught prop- erly, the pupil will, at the same time, acquire a knowledge of twelve facts of division ; thus, if it is clear to him that 3 twos are 6, it must be equally clear that 6 is 3 twos ; or, 5 6 ELEMENTARY ARITHMETIC. to use the ordinary mathematical expression of this fact, that 2 is contained in 6 three times. These twelve facts of multiplication will also give to the thoughtful pupil twelve other facts of division, often called FACTS OF PARTITION. 1 of 4 = 2 J of 6 = 2 i of 8 = 2 i of 10 == 2 lof 12 ^2 J of 6 = 3 i of 9 = 3 J of 12 = 3 iof 8 = 4 J of 12 = 4 i of 10 r= 5 i of 12 ■= 6 SEVEN DENOMINATE NUMBER FACTS. 1 foot = 12 inches. 3 feet = 1 yard. 2 nickels = 1 dime. 10 dimes = 1 dollar. 2 pints = 1 quart. 4 quarts = 1 gallon. 100 cents = 1 dollar. FACTS OF PARTITION AND MULTIPLICATION. 4 is f of 6. 6 is I of 9. 8 is | of 12. 6 is f of 8. 9 is f of 12. 4 is f of 10. It will be observed that these facts are combinations of facts given before. The work should be performed first with objects. It is very desirable that the pupil shall give the answer to such questions as, 6 is f of hoio many? not from memory, but by thinking 6 objects divided into two equal groups, and by adding to the two groups another similar group : thus, (111 111) 111. OTHER FACTS OF PARTITION. i of 3 = If J of 5 =• 2^. i of 7 = 31. i of 9 = 4L. i of 11 = B\. i of 7 = 21 Not by definition, but by frequent use, the pupil should become familiar with the following terms and expressions : add, subtract, multiply, divide, sum, difference, product, quotient, square, oblong, triangle, square inch, 2-inch square, 3-inch square, is contained in. Do not use the sign (x) for the word times. Whenever this sign is employed in the lower grades, it should be used for the words multiplied by. CONTENTS. PRIMARY NUMBER PACTS PAGES Outline of work to be done orally 5,6 PART I. Primary Number Pacts applied to linear magnitudes, — inch, foot, yard; to magnitudes of capacity,— pm^, quart; to magnitudes of value, — cent, nickel, dime, dollar; to magnitudes of time, — day, week; to sur- face magnitudes, — 1-inch square, 2-inch square, 3-inch square ; to fractional units, — half, third, fourth ; to inexact units of measurement, — apple, ball, egg, pie, tree, etc 9-40 PART II. Primary Number Facts 41, 51, 61, 71, 81, 91, etc Primary Number Pacts applied to a variety of magni- tudes 42, 52, 62, 72, 82, 92, etc. Primary Number Pacts applied to linear and surface measurements 43, 53, 63, 73, 83, 93, etc. Miscellaneous Problems 44, 54, 64, 74, 84, 94, etc. Common Fractions 45, 55, 65, 75, 85, 95, etc. Common Fractions applied to a variety of magnitudes, 46, 56, 66, 76, 86, 96, etc. Denominate Numbers 47, 48, 57, 58, 68, 78, 88, 98 Miscellaneous Problems 49, 50, 59, 60, 79 Adding by 2's, 3's, 4's, etc 67, 77, 87, 97, 107, 117, etc. Tenths written decimally 70, 80, 90 The meaning of certain arithmetical expressions . 89, 99, 109, 119, 129 Time Problems 100, 110,114, 120, 124, 130, 134, 140, 144 Review 147, 149, 152 7 8 ELEMENTARY ARITHMETIC. PART III. PAGES Decimals — tenths 153-172 Denominate Numbers 174, 184 Fractions 175, 176, 177; 185, 186, 187 Surface Measurements 178, 179; 188, 189 Ratio and Proportion 180, 181; 190, 191 Miscellaneous Problems , 182, 192 PART IV. Decimals -hundredths 193-212 Terms in multiplication and division 213, 223 Denominate Numbers ; 214, 224 Fractions 215, 216; 225, 226 Miscellaneous Problems 217, 222, 227 Surface Measurements 218, 219; 228, 229 Ratio and Proportion 220, 221 Problems in Addition, Subtraction, Multiplication, and Division 230, 231, 232 Definitions and Explanations 233-240 Suggestions to Teachers . 241-248 PROBLEMS At bottom of pages, beginning with p. 11. Addition pp. 11, 16, 21, 26, 31, 36, etc. Subtraction pp. 12, 17, 22, 27, 32, 37, etc. Multiplication pp. 13, 18, 23, 28, 33, 38, etc. Division pp. 14, 19, 24, 29, 34, 39, etc. Division (" Partition ") pp. 15, 20, 25, 30, 35, 40, etc. ^ ■> ■> i ■> , l' J 1 J J 5 , 3 o e » ARITHMETIC. PAET I. •••« •• 1. Four and two are . 2. Five less two are . •••oo 3. Three times two are . *• ** 4. Six is twos. •• •• 5 . One half of six is . ••• ••• 6. Five and three are . 5 and 3 = 7. Seven less four are . 7 less 4 = 8. Four times two are . 4 times 2 = 9. Eight is twos. 8 is 2's. 10. One half of four is . | of 4 = 11. William earned 5 cents and his brother earned 6 cents; together they earned cents. 12. James had 12 cents; he gave his sister 4 cents; he then had cents. 13. John paid 2 cents each for 5 pencils; for all he paid cents. 14. Harry has 10 cents; oranges cost 5 cents each ; he can buy oranges . 15. Richard paid 8 cents for 2 lemons; one lemon cost cents. 9 JO KL.EMENTARY ARITHMETIC. One fourth of a foot. 1. Tioelve inches are one foot. 2. Six inches are of a foot. 3. Three inches are of a foot. 4. One half of a foot and 2 inches = 5. One half of a foot less 2 inches = 6. Three times 2 inches are inches. 7. 2 inches are contained in 8 inches times. 8. One half of 6 inches is inches. 9. Mary's pencil is 3 inches long; Alice's pen- cil is 4 inches long; together they are inches long. 10. Jane had a pencil 8 inches long ; she broke off a piece 2 inches long ; what remained was inches long. 11. Think of a square. A square has sides. One side of a 2-inch square measures inches. All the sides of a 2-inch square together measure inches. 12. Ann had a piece of ribbon 10 inches long; she cut it into 2-inch pieces; there were pieces. 13. I am thinking of a square. It has equal sides. All its sides together measure 12 inches. It is a inch square. PAKT I, 11 1. Ten and two are — 2. Ten less two are — 3. Three times ten are 4. Forty is tens. 5. One half of forty is 10 and 3 = -. 10 less 4 = . 5 times 10 = 60 is lO's. . 10 is 1 of 6. Twenty and 10 are — 7. Twenty less 2 are 8. Four times 10 are — 9. Seventy is tens. 10. One third of 30 is -. 20 and 20 = . 30 less 2 = 6 times 10 — 50 is lO's. . t of 30 = 11. A boy paid 2 dimes for a slate and 3 dimes for a book; for both he paid cents. 12. The price of Susie's book was 38 cents; she gave the salesman 4 dimes ; she should receive in change cents. 13. At 10 cents a yard, 2 yards of ribbon cost cents; one half of a yard costs cents; two and one half yards cost cents. 14. For some railroad tickets I paid 60 cents; each ticket cost 10 cents; there were tickets. 15. For 4 melons James j^aid 40 cents; one melon cost cents. One fourth of 40 cents is cents. (1) Read, and give sums. (2) Copy and add. 20 21 23 22 22 4 4 4 6 2 28 2 12 ELEMENTARY ARITHMETIC. 1. One foot is inclies. 2. Two feet are 24 inches. 3. Three feet are 36 inches. — feet. — inches. 4. One yard is One yard is 5. 6. One half of a yard is 7. One third of a yard is — 8. Two thirds of a yard are 9. Six inches and 6 inches are inches. 10. One foot less 6 inches are inches. 11. Fonr times 3 inches are inches. 12. 3 inches are contained in 12 inches — times. 13. One third of twelve inches is inches. 14. Two feet and 2 inches are 15. One yard less 2 inches are inches, inches. 16. Think of a line 6 feet Ions;. Six feet are yards. Nine feet are 17. One yard and 1 foot are — 18. One yard and 2 feet are — 19. Seven feet are yards and yards. — feet. — feet. foot. 20. Three times 2 feet are feet, or yards. 21. Two 12's are . Three 12's are - (1) Kead, and give differences. (2) Copy and subtract. 26 28 29 25 27 30 4 3 6 4 7 2 PART I. J3 A 1-inch Square. 1. Think of a 2-incli square. Think of a 2-inch square divided into 1-inch squares. A 2-inch square is equal to 1-inch squares. 2. Think of a 3-inch square. Think of a 3-inch square divided into 1-inch squares. A 3 -inch square is equal to 1-inch squares. 3 . Think of an oblong 1 inch wide and 4 inches long. Think of this oblong divided into 1-inch squares. Such an oblong is equal to 1-inch squares. 4. An oblong 2 inches wide and 4 inches long is equal to 1-inch squares. 5. An oblong 2 inches wide and 3 inches long is equal to 1-inch squares. 6. An oblong 2 inches wide and 5 inches long is equal to 1-inch squares. 7. One fourth of a 2-inch square = 8. One half of a 2-inch square = (1) Eead, and give products. (2) Copy and multiply. 20 12 21 32 34 35 2 2 2 2 2 2 14 ELEMENTARY ARITHMETIC. 1. Four times 2 balls are balls. 2. 2 balls are contained in 8 balls times. 3. Three times 3 tops are tops. 4. 3 tops are contained in 9 tops * * • • times. * * * * 5. Two times 4 stars are stars. 6. 4 stars are contained in 8 stars times. • • • • • • • • 7. Four times 3 dots are dots. 8. 3 dots are contained in 12 dots • • • times. 9. Five times 2 eggs are — 10. 2 eggs are contained in 10 eggs eggs. 11. Three times 4 hats are hats. 12. 4 hats are contained in 12 hats times. times. (1) Eead, and give quotients. (2) Copy and divide. 2 balls)12 balls 2 stars)20 stars 2)40 — times 2)42 2)44 — times 2)46 2)48 PART I. 15 1. One half of 4 cents is cents. 2. Two cents are contained in 4^ times. 3. One half of 6 cents is cents. 4. Two cents are contained in 6^ times. 5. One half of 8 cents is cents. 6. Two cents are contained in 8^ times. 7. One half of 10 cents is cents. 8. Two cents are contained in 10^ times. 9. One half of 12 cents is cents. 10. Two cents are contained in 12^ times. 11. One half of 20 cents is cents.. 12. Two cents are contained in 20^ times. 13. One half of 40 cents is cents. 14. Two cents are contained in 40^ times. 15. One liaK of 60 cents is cents. 16. Two cents are contained in 60^ times. 17. One half of 80 cents is cents. 18. Two cents are contained in 80^ times. (1) Eead, and give quotients. (2) Copy and divide. 2 )12 cents 2 )14 cents 2)20 cents — cents — cents — cents 2)24^' 2)26^ 2)28j^ 2)80^ 2)40^ 16 ELEMEKTABY AKITHMETIC. 1 pint. 1 quart. 1. Two pints are one quart. 2. Six pints are quarts. 3. Two quarts are pints. 4. Six quarts are pints. 5. Four quarts are pints. — quarts. — quarts. — pints. 6. Four pints are — 7. Ten pints are — 8. Ten quarts are — 9. Mr. Smith sold 1 pint of milk to each of 4 customers ; to all he sold quarts. 10. At 3 cents a pint^ one quart of milk costs 11. At 4 cents a quart, one pint of milk costs 12. At 4 cents a quart, two quarts and one pint of milk cost cents. 13. 2 quarts are contained in 6 quarts times. 14. 1 pint is contained in 3 quarts times. (1) Eead, and give sums. (2) Copy and add. 28 28 28 38 38 38 3 4 5 2 3 4 PART 1. 17 1. One third of 6 balls is balls. 2. Two thirds of 6 balls are balls. 3. One third of 9 balls is balls. 4. Two thirds of 9 balls are balls. 5. Arrange 12 balls so that it will be easy to think the number of balls in one third of 12 balls, and the number of balls in two thirds of 12 balls. 6. One third of 12 balls is balls. 7. Two thirds of 12 balls are balls. •••• •• •• oo 8. Four balls are two thirds of balls. •••••• ••• ••• ooo 9. Six balls are two thirds of balls. 10. Arrange 8 balls so that it will be easy to think the number of balls of which 8 balls are two thirds. 11. Eight balls are two thirds of balls. — . 1 of 9 is . — . i of 12 is . — . 10 is 1 of . — . 6 is i of . (1) Read, and give differences. (2) Copy and subtract. 30 40 50 30 40 50 3 3 3 4 4 4 12. |- of 6 is 13. i of 8 is 14. i of 10 is 15. A of 6 is 18 ELEMENTARY ARITHMETIC. 1. The sum of 7 and 4 is . 2. The sum of 20 and 6 is . 3. The sum of 21 and 4 is . 4. The sum of 32 and 4 is . 5. The sum of 43 and 2 is . 6. Peter and Harry together had 12 marbles; Harry had 7 ; Peter had . 7. The sum of two numbers is 8; one of the numbers is 5 ; the other number is . 8. Joseph has a new bicycle. There is a cyclometer on it. When Joseph had used the bicycle two days the cyclometer showed that he had ridden 11 miles; he rode 5 miles the first day; the second day he rode miles. 9. The sum of two numbers is 10; one of the numbers is 6 ; the other number is . 10. Joseph rode 8 miles in the morning and 4 miles in the afternoon ; in all he rode miles. 11. Mary paid 6^ for 2 thirds of a yard of rib- bon; at the same rate, 1 yard would cost cents. 12. ^ of 6 is . 6 is i of -. 13. f of 6 are . 6 is f of . 14. 1 of 3 is . 3 is i of . 15. I of 9 are . 8 is f of . (1) Eead, and give products. (2) Copy and multiply. 25 35 45 21 22 23 2 2 2 3 3 3 PART I. 19 1. The difference of 6 and 4 is — 2. The difference of 12 and 8 is - 3. The difference of 5 and 9 is — 4. The difference of 26 and 24 is 5. The difference of 27 and 30 is 6. The difference of 35 and 40 is 7. The temperature at 9 o'clock in the morning was 65 degrees above zero; at noon it was 75 ,- the difference was degrees. 8. The temperature inside the schoolroom was 70 degrees above zero; outdoors it was 50; the difference was degrees. 9. The temperature at noon was 80 degrees above zero; at 4 o'clock in the afternoon it was 10 degrees lower ; at 4 o'clock it was . 10. The greater of two numbers is 90; their difference is 10 ; the less number is . 11. The temperature at 10 o'clock was 85 de- grees above zero; at noon it was 10 degrees higher; at noon it was . 12. The less of two numbers is 55; their differ- ence is 10; the greater number is . (1) Eead, and give quotients. (2) Copy and divide. 3 dollars) 12 dollars 4 cents) 12 cents — times — times 3)15 3)33 3)36 3)39 3)63 20 ELEMENTARY ARITHMETIC. 1. The product of 4 and 2 is — 2. The product of 6 and 2 is ■ 3. The product of 5 and 2 is 4. The product of 3 and 4 is 5. The product of 3 and 2 is 6. The product of 10 and 2 is . 7. The product of 20 and 2 is . 8. I have an orchard in which there are four rows of trees; in each row there are 10 trees; in all there are trees. 4 tens are . 5 tens are . 9. The length of one side of a 3-inch square is inches; the length of all its sides together is inches. 4 threes are . 3 threes are . 2 threes are . 10. The product of two numbers is 8; one of the numbers is 2 ; the other number is . 11. The product of two numbers is 40; one of the numbers is 2 ; the other number is . 12. Ten and ten and ten are . Three tens are . The product of 3 and 10 is . Twenty is the product of 10 and . Forty is the product of 10 and . (1) Eead, and give quotients. (2) Copy and divide. 3 )12 dollars 3 )15 dollars 3 )36 dollars — dollars — dollars — dollars 3)18 3)39 3)60 3)63 3)66 PART I. 21 1. The quotient of 6 divided by 2 is . 2. The quotient of 8 divided by 4 is . 3. The quotient of 10 divided by 2 is . 4. The quotient of 12 divided by 3 is . 5. The quotient of 12 divided by 6 is ■ . 6. The quotient of 20 divided by 10 is . 7. The quotient of 40 divided by 4 is . 8. I have an orchard in which there are 60 trees ; these trees are in 6 equal rows ; in each row there are trees. Sixty divided by 6 equals 9. Edward paid 60 cents for 6 pounds of nuts; one pound cost . One sixth of 60 is . 10. Byron sold papers for which he received 40 cents; he sold the papers at 2 cents each; he sold papers. Two cents are contained in 40 cents times. 11. One half of 12 is . 2 is contained in 12 times. 12. One half of 20 is . 2 is contained in 20 times. 13. One third of 12 is . 3 is contained in 12 times. 14. One half of 60 is . 2 is contained in 60 times. (1) Read, and give sums. (2) Copy and add. 26 26 35 47 17 52 10 20 20 20 20 20 22 ELEMENTARY ARITHMETIC. 1. The sum of 6 and 2 is . 2. The difference of 6 and 2 is 3. The product of 6 and 2 is 4. The quotient of 6 divided by 2 is 5. The sum of 40 and 20 is . 6. The difference of 40 and 20 is 7. The jDroduct of 20 and 2 is 8. The quotient of 20 divided by 2 is 9. The sum of 30 and 20 is . 10. The difference of 30 and 20 is 11. The product of 30 and 3 is - — 12. The quotient of 30 divided by 3 is 13. The sum of 27 and 3 is . 14. The difference of 27 and 3 is 15. The product of 12 and 2 is 16. The quotient of 12 divided by 2 is 17. The sum of 30 and 5 is . 18. The difference of 30 and 5 is 19. The product of 10 and 5 is 20. The quotient of 10 divided by 5 is 21. One half of 3 feet is . 22. One half of 5 apples is . 23. One half of 7 inches is . (1) Eead, and give differences. (2) Copy and subtract. 30 35 52 44 57 63 10 10 10 20 20 20 PART I. 23 1. Six apples and 3 apples are apples. 2. Seven apples less 2 apples are apples. 3. Three times 2 apples are apples. 4. Three apples are contained in 9 apples . 5. One half of 7 apples is apples. 6. Eight cents and 3 cents are cents. 7. Nine cents less 2 cents are cents. 8. Four times 3 cents are cents. 9. Four cents are contained in 12 cents . 10. One third of 12 cents is cents. 11. Twenty trees and 7 trees are trees. 12. Twenty trees less 2 trees are trees. 13. Two times 20 trees are trees. 14. Two trees are contained in 40 trees . 15. One half of 60 trees is trees. 16. Sixty-eight degrees and 4 degrees are . 17. Sixty-eight degrees less 4 degrees are . 18. Four times 20 degrees are degrees. 19. Two degrees are contained in 12 degrees 20. One third of 30 degrees is degrees. 21. i of 4 is . 4 is i of . 22. 1 of 3 is . 3 is i of . 23. i of 5 is . 5 is 1 of . (1) Kead, and give products. (2) Copy and. multiply. 31 32 33 11 12 13 3 3 3 3 3 3 24 ELEMENTARY ARITHMETIC. 1. In 6 there are - 2. In 7 there are - 3. In 8 there are - 4. In 9 there are - 5. In 10 there are 6. In 11 there are 7. In 8 there are - 8. In 9 there are - 9. In 10 there are 10. In 11 there are 11. In 10 there are 12. In 12 there are 13. In 9 there are - 14. In 11 there are 15. In 23 there are 16. In 35 there are 17. In 21 there are 18. In 41 there are 19. One half of 20 is 20. One half of 40 is 21. Onehalf of 50 is 22. One half of 60 is — twos. -- twos and — twos. — twos and - twos. - twos and fonrs. fours and - - fours and - fours and - fives. - fives and threes. - threes and - tens and - - tens and - twos and - - twos and - of 21 1 1 of 41 = 1 of 51 = i of 61 = (1) Eead, and give quotients. (2) Copy and divide. 4 apples) 12 apples 5 cents) 25 cents 5)20 — times 5)30 5)35 ■ — times 3)69 2)64 PART I. 25 1. John had 22 cents, and his mother gave him 5 cents more ; he then had cents. 2. AYilliam had 36 cents; he spent 5 cents; he then had cents. 3. David paid 20 cents each for 2 books; the books cost cents. 4. George paid 50 cents for some tablets; the price of the tablets was 10 cents each; there were tablets. 5. Harry's new drawing-pencils cost 40 cents; there were 4 of them ; each pencil cost cents. 6. In one coop there were 21 little chickens; in another coop there were 8 ; in both there were chickens. 7. Susan had 36 chickens; 4 of them died; she then had chickens. 8. In each of three coops there were 20 chick- ens; in all there were chickens. 9. Mrs. Brown has 36 chickens equally divided among 3 mother hens; each hen cares for chickens. 10. Mrs. Harris had 30 chickens; she divided them equally and put them into 3 coops; in each coop there were chickens. (1) Read, and give quotients. (2) Copy and divide. 2 )$14 2 ) $42 2 ) $44 2 ) $46 2 ) $48 2)24 2)26 2)28 2)62 2)64 26 ELEMENTARY ARITHMETIC. 1 . If one quart of milk is worth 6 centSj 1 pint is worth cents. 2. When milk costs 4 cents a quart, 1 pint costs cents ; 1 quart and 1 pint cost cents; 2 quarts cost cents; 2 quarts and 1 pint cost cents. 3. When milk costs 6 cents a quart, 9 cents will pay for . 4. When milk costs 4 cents a quart, 6 cents will pay for ; 10 cents will pay for ; 12 cents will pay for . 5. When milk costs 6 cents a quart, 12 cents will pay for . 6. Herbert paid 6 cents for a ball, and half as many cents for an orange; the orange cost cents; the orange and the ball together cost . The sum of 6 and 3 is . 7. Four two-cent stamps cost cents. 8. Two four-cent stamps cost cents. 9. George had 11 cents; he bought 3 two-cent stamps ; he then had cents. 10. My j)en-holder cost 8 cents; my pencil cost half as much as my pen-holder; my pencil cost cents; my pen-holder and pencil together cost cents. (1) Bead, and give sums. (2) Copy and add. 30 40 20 50 60 70 15 12 17 14 13 18 PART I. 27 1 . William had six cents ; lie paid one third of his money for a tablet; he then had cents. 2. Jane had six cents; she paid two thirds of her money for an orange; she then had cents. 3. Henry earned some money; he spent one half of what he earned and had 5 cents left; he earned cents ; he spent cents. 4. James earned some money; he spent two thirds of what he earned and had 3 cents left; he earned cents; he spent cents. 5. Peter earned some money; he spent one third of what he earned and had 6 cents left; he earned cents; he spent cents. 6. A hen came off her nest with a nice brood of chicks; but there came a rain storm and three fourths of them were drowned; the poor hen then had only three chicks ; she came off her nest with chicks; the rain' killed chicks. 7. Mary had a whole family of dolls; she gave away three fourths of them and had only 2 dolls left ; before she gave any away she had dolls; she gave away dolls. (1) Read, and give differences. (2) Copy and subtract. 30 40 50 30 40 60 12 12 12 13 13 13 35 45 55 35 45 55 12 12 12 13 13 13 28 ELEMENTARY ARITHMETIC. 1. One half of 4 apples is apples. 2. Four apples are one half of apples. 3. One half of 6 oranges is oranges. 4. Six oranges are one half of oranges. 5. One half of three toothpicks is . 6. Three toothpicks are one half of . 7. One half of 5 inches is inches. 8. Five inches are one half of inches. 9. One half of 7 square inches is . 10. One half of 8 square inches is . 11. One half of 9 square inches is . 12. One half of 10 square inches is . 13. One third of three blocks is block. 14. Three blocks are one third of blocks. 15. One third of 6 balls is balls. 16. One third of 9 balls is balls. 17. One third of 12 balls is balls. 18. One fourth of 8 boys is boys. 19. One fourth of 12 boys is boys. 20. One fifth of 10 girls is girls. 21. Two fifths of 10 girls are girls. 22. One sixth of 12 hats is hats. (1) Kead, and give products. (2) Copy and multiply. 30 40 50 60 20 30 2 2 2 2 3 3 PART I. 29 1. I obtain a sum by 2. I obtain a difference by 3. I obtain a product by - 4. I obtain a quotient by - 5. The answer in addition is a 6. The answer in subtraction is a — 7. The answer in multiplication is a 8. The answer in division is a . 9. The sum of 8 and 2 is 10. The difference of 8 and 2 is 11. The product of 8 and 2 is 12. The quotient of 8 divided by 2 is . 13. When I put two numbers together, I . 14. When I take one number from another, I 15. When I take a number a certain number of times, I . 16. When I find how many times one number is contained in another, I . 17. When I find a certain part of a number, as one half of it, or one third of it, or one fourth of it, I . (1) Eead, and give quotients. (2) Copy and divide. $2)$12 $2)$2Q $2)$24 $2)$26 $2 )$28 2)14 2)22 2)18 2)40 2)42 30 ELEMENTAKY ARITHMETIC . 1. 2)6 Two apples are contained in 6 apples One half of 6 apples is . 2. 3 )12 Three dollars are contained in 12 dollars One third of 12 dollars is . 3. 4 )12 Four cents are contained in 12 cents One fourth of 12 cents is . 4. 5 )10 Five oranges are contained in 10 oranges One fifth of 10 oranges is . 5. 6 )12 Six inches are contained in 12 inches — One sixth of 12 inches is . 6. 4 )40 Four cents are contained in 40 cents One fourth of 40 cents is . 7. 2 )24 Two peaches are contained in 24 peaches ■ . One half of 24 peaches is . One third of 24 peaches is . (1) Read, and give quotients. (2) Copy and divide. 2)22 ft. 3)36 ft. 2)44 ft. 3)66 ft. 2)28 ft. IS PART I. 31 1. One half of 1 quart is . 2. One half of 1 foot is — — inches. 3. One half of 1 yard is . 4. One half of 1 dollar is cents. 5. One half of 1 dime is . 6. One half of 7 quarts is . 7. One half of a 2-inch square is . 8. One half of a 3-inch square is . 9. One half of 5 feet is . 10. One half of an oblong 2 inches by 4 inches 11. Two quarts are one third of 12. Four inches are one third of- 13. One foot is one third of 14. Three inches are one fourth of 15. Twenty-five cents are one fourth of 16. One pint is one fourth of . 17. One dime is one third of . 18. One quart is one fourth of 2 19. ^ of 4 is . 4 is i- of 1 of 9 is 20. 1 of 6 is 21. i of 8 is 22. i of 10 is 23. i of 12 is i of 12 is 10 is i of 12 is i of (1) Read, and give sums. (2) Copy and add. 30 30 30 20 20 20 22 23 24 23 24 25 32 ELEMENTARY ARITHMETIC. 1. 2. 3. 4. 5. 6. Two is one fourth of . Four is of eight. Six is of eight. Three is one fourth of . Six is of twelve. Nine is of twelve. 7. Three times 2 are 8. Three times 4 are 9. Four times 3 are - 10. Two times 6 are - 11. Two times 4 are - 12. Two times 2 are - 2 is i of - 4 is ^ of - 6 is ^ of - 3 is I of - 5 is i of - 8 is I of - 3 times 3 4 times 2 6 times 2 2 times 5 2 times 3 5 times 2 FOR DRILL IN ADDING. 5 5 4 2 8 2 2 3 4 8 9 2 5 5 1 2 3 1 3 2 1 2 8 6 6 3 5 5 6 4 4 4 2 3 4 3 3 1 4 8 9 7 7 9 7 1 4 3 2 4 3 1 2 1 (1) Eead, and give differences. (2) Copy and subtract. 20 30 40 50 60 70 14 14 14 15 15 15 PART I. 33 1. Imagine 12 marks on the blackboard; then imagine that you erase half of them ; then imagine that you erase one half of the remainder. How many marks do you now seem to see upon the blackboard ? 2. Imagine a 4-inch square drawn upon the blackboard ; imagine it divided into equal parts by a vertical line ; also imagine a horizontal line that would divide the square into two equal parts. Into how many equal parts does the square now seem to be divided? Each part is what kind of a square? How many 2-inch squares in a 4-inch square ? 3. Imagine a 1-inch square drawn upon your slate. It has how many sides? Each side is how long? How far is it around a 1-inch square? 4. Imagine a 2 -inch square drawn upon the blackboard. It has how many sides? Each side is how long ? How far is it around a 2-inch square? 5. Imagine a 3-incli square drawn upon the blackboard. It has sides. Each side is inches long. How far is it around a 3-inch square ? 6. How far is it around a 4-inch square? (1) Eead, and give products. (2) Copy and multiply. 20 21 22 20 30 31 4 4 4 5 4 4 34 ELEMENTAKY ARITHMETIC. 1. Imagine that you have a stick of candy 1 foot long; imagine that you give one third of it to your brother; imagine that you break the remain- der into two equal pieces. How many inches long is each piece? 2. Imagine an oblong bounded by two vertical lines each 1 inch long, and two horizontal lines each 3 inches long. How many such oblongs would be equal to a 3-inch square? 3. Imagine four 1-inch squares cut from paper. So arrange them that they together will make a square. What kind of a square is it? 4. Imagine nine 1-inch squares cut from paper. So arrange them that they together will make a square. What kind of a square is it? 5. Imagine an oblong 1 inch wide and 3 inches long. Imagine this oblong divided into 1-inch squares. How many 1-incli squares do you seem to see? 6. Imagine eight 1-inch squares cut from paper. So arrange them that they together will make an oblong 2 inches wide. How long is the oblong? 7. How many inches around an oblong 4 inches long and 2 inches wide? (1) Read, and give quotients. (2) Copy and divide. 3^)60^ 3^)66^ 3^)69^ 4^)80^ 4^)88^ PART I. 35 1. In one whole there are 2. In one whole there are 3. In one half there are - - halves. - fourths, fourths. fourths. fourth. 4. One half and 1 fourth are 5. One half less 1 fourth is — 6. One half of one half is one 7. Jane ate one half of a j^ie; Harold ate one fourth of a pie; together they ate of a pie. 8. Webb had one half of a pie; he gave one fourth of a pie to his sister ; he then had of a pie. 9 . Robert had one fourth of a pie ; Arthur had three times as much; Arthur had of a pie. 10. Mrs. Johnson divided a pie equally among some children, giving to each child one fourth of a pie; there were children. 11. Mrs. Clark divided one half of a pie equally between two children; each child received of a pie. (1) Read, and give quotients. (2) Copy and divide. 2)60^ 3)60^ 4)80^ 2)84^ 4)84^ 36 ELEMENTARY ARITHMETIC. I I I.I 1. One inch is half-inches. 2. One inch is fourth-inches. 3. One half -inch is fourth inches. 4. Two half -inches are inch. 5. Four fourth-inches are inch. 6. Two fourth-inches are of an inch. 7 . One half -inch and 1 fourth-inch . are fourth-inches. 8. One half -inch less 1 fourth-inch is . 9. Two times 1 fourth-inch are fourth- inches, or half -inch. 10. One fourth-inch is contained in one half- inch times. 11. Alice's pencil is two and one half inches long; Jane's pencil is two and one fourth inches long; together they are inches long. 12. Sarah's pencil is two and one fourth inches long; Mary's is three times as long; Mary's pencil is ■ inches long. 13. Laura had a pencil two and one half inches long ; she broke it into pieces, each piece being one half -inch long; there were pieces. (1) Bead, and give sums. (2) Copy and add. 2 fourths 2| 23| 3| 24| 1 fourth 2| 10| Si 104- PART I. 37 1. One dollar is equal in value to half- dollars. 2 . One dollar is equal in value to fourth- dollars. 3. One half-dollar is equal in value to fourth-dollars. A fourth-dollar is sometimes called a " quarter," or a quarter of a dollar. 4. One half of a dollar and one fourth of a dollar are — fourths of a dollar. 5. One half of a dollar less one fourth of a dollar is of a dollar. 6. Four times one fourth of a dollar equals fourths of a dollar, or dollar. 7. One fourth of a dollar is contained in one half of a dollar times. 8. One half of one half of a dollar is of a dollar. (1) Read, and give differences. (2) Copy and subtract. 3 fourths 3f 25f 8i 27i 1 fourth li lOi 5i lOi 38 ELEMENTARY ARITHMETIC. 1. One half of a foot and one fourth of a foot are inches. 2. One half of a dollar and one fourth of a dol- lar are cents. 3. One half of a pie and one fourth of a pie are fourths of a pie. 4. One half of an inch and one fourth of an inch are fourths of an inch. 5. One half of a square inch and one fourth of a square inch are fourths of a square inch. 6. Fred bought a knife; the price was half a dollar; he gave the salesman one dollar; Fred should receive in change . 7. At a quarter of a dollar a pound, 4 pounds of coifee cost . 8. I paid half a dollar for butter at one fourth of a dollar a pound; I bought pounds. 9. Bessie had a pencil two and one half inches long ; she broke it into two equal parts ; each part was inches long. 10. One half of 2^ inches is . Acid. Subtract. Multiply. Divide. 1 fourth 3 fourths 2 fourths 2)4 fourths 3 fourths 1 fourth 2 (1) Read, and give products. (2) Copy and multiply. 3 fourths 5i 23i 3i 23i 2 2 • 2 2 2 PART I. 39 1. There are seven clays in a tveek. 2. Eight days are 1 week and day. 3. Nine days are 1 week and days. 4. Twelve days are 1 week and days. 5. Eleven days are 1 week and days. 6. Ten days are 1 week and days. 7. One w^eek and 2 days are 8. One week and 5 days are 9. One week and 3 days are 10. One week and 4 days are 11. One dime and 1 cent are days, days, days, days. cents. — cents. 12. Twelve cents and 1 dime are — 13. Two dimes are cents. 3 dimes = 14. Six dimes are cents. 4 dimes = 15. Two dimes and 2 cents are cents. 16. Two dimes and 5 cents are cents. 17. Two quarts and 1 pint are j)ints. 18. Four quarts and 1 pint are pints. 19. Five pints are quarts and 1 pint. 20. Nine pints are quarts and 1 pint. 21. Two yards and 1 foot are 22. Two yards and 2 feet are feet, feet. (1) Eead, and give quotients. (2) Copy and divide. 3 ft. )36 ft. 2ft .)24ft. 4ft. )48ft. 5 ft.) 25 ft. — times 40 ELEMENTARY ARITHMETIC. 1. If Harry steps 2 feet at each step, how many steps will he take in walking 12 feet? 20 feet? 40 feet? 100 feet? 2. If Mary steps H feet at each step, how many steps will she take in walking 3 feet? 6 feet? 9 feet? 12 feet? 3. If Harry's father steps 2^ feet at each step, how many steps will he take in walking 5 feet? 10 feet? 15 feet? 20 feet? 4. One half of seven feet is feet. 5. One half of nine feet is — feet. 6. One half of eleven feet is feet. 7. One third of six feet is feet. 8. One third of seven feet is — — ■ feet. 9. One third of nine feet is feet. 10. One third of ten feet is — — feet. (1) Read, and give quotients. (2) Copy and divide. 2)24 feet 2 )25 feet 2 )26 feet 2 )27 feet 2)44 feet 2)45 feet 2)46 feet 2)47 feet PART II. 9 8 7 4 5 6 13 13 13 1. Nine and 4 are . 8 and 4 are 2. Seven and 5 are . 8 and 5 are 3. Nine and 3 are . 6 and 5 are 4. Seven and 6 are . 7 and 4 are 5. Thirteen less 9 are . 13 less 7 are 6. Thirteen less 8 are . 13 less 4 are 7. Thirteen less 6 are . 13 less 5 are 8. Twelve units, or ones, make one dozen. 9. Thirteen is one dozen and . 10. Thirteen inches are 1 foot and . 11. Thirteen cents are 1 dime and cents. 12. Thirteen days are one week and ■ days. 13. Thirteen pints are 6 quarts and pint. 14. Thirteen feet are 4 yards and foot. Copy and add: 25 26 27 28 26 28 25 26 25 23 24 24 41 42 ELEMENTARY ARITHMETIC. 1. Seven quarts of milk and 6 quarts of milk are quarts of milk. 2. Eight pounds of sugar and 4 pounds of sugar are pounds of sugar. 3. Twelve loads of gravel less 7 loads of gravel are loads of gravel. 4. Thirteen pairs of horses less 6 pairs of horses are pairs of horses. 5. Three times 4 books are books. 6. Two times 6 birds are birds. 7. Three inches are contained in 12 inches times. 8. Three inches are contained in 13 inches times with one inch remainder. 9. One third of 12 inches is inches. 10. One third of 13 inches is . 11. Four inches are contained in 12 inches times. 12. Four inches are contained in 13 inches times with inch remainder. 13. One fourth of 12 inches is inches. 14. One fourth of 13 inches is . 15. Five inches are contained in 10 inches . 16. Five inches are contained in 13 inches times with inches remainder. Copy and subtract: 42 52 62 72 82 92 16 16 16 16 16 16 PART II. 43 ■D 1. The line A B is long. 2. The line C D is inches long. 3. How many inches longer is C D than A B? C D is inches longer than A B. 4. A B and C D together are inches long. 5. C D is how many times as long as A B? C D is times as long as A B. 6. A B is equal to what part of C D? A B is equal to of C D. 7. The sum of 8 and 5 is . 8. The difference of 8 and 5 is . 9. The product of 40 and 2 is . 10. The quotient of 8 divided by 2 is -. 11. The sum of two numbers is 13; one of the numbers is 9 ; the other number is . 12. The difference of two numbers is 5; the greater number is 13; the less number is . 13. The difference of two numbers is 4; the less number is 9 ; the greater number is . Copy and multiply : 26 36 46 25 24 15 2 2 2 3 3 3 44 ELEMENTARY ARITHMETIC. 1. Mary had 13 canaries; slie sold 8 of them; she then had canaries. 2 . Henry lives 9 miles north of Aurora ; James lives 4 miles south of Aurora ; from Henry's home to James's home it is miles. 3. William had 13 cents; he bought two or- anges at 5 cents each; he then had cents. 4. A ton of coal cost 6 dollars; a cord of wood cost 4 dollars; the coal cost dollars more than the wood; the wood and coal together cost dollars. 5. Robert is 8 years old, and his sister is 5 years older than he is; Robert's sister is years old. 6. John gathered 13 roses and gave 6 of them to his sister; he kept roses. 7. One fourth of 8 inches is inches. 8. One fourth of 9 inches is inches. 9. One half of 13 inches is . 10. If one barrel of apples costs $2 J, two bar- rels cost ; three barrels cost ; four barrels cost . 11. If one ton of coal is worth $6-|^, two tons are worth . 12. If one cord of wood is worth $4^, two cords are worth . Copy and divide : $2)$30 $2)$50 $2)$70 . $2)$90 PART II. 45 IS 1. One whole is 2. One whole is fourths. sixths. 3. One half is how many fourths? fourths. One half 4. One half is how many sixths? One half is — sixths. 5. One half and one fourth are fourths. 6. One half and one sixth are sixths. 7. One half less one fourth is 8. One half less one sixth are 9. One half less two sixths is 10. Two times one fourth are - 11. Two times one sixth are — 12. Two times two sixths are - 13. Three times two sixths are 14. One fourth is contained in 1 half 15. One sixth is contained in 1 half 16. One half of one half is — 17. One third of one half is — fourth. — sixths. — sixth. — fourths, sixths. — sixths. — sixths. times, times. Copy and divide : 2)|30 2 )$50 — dollars 2)$70 2)$90 46 ELEMENTARY ARITHMETIC. 1. One half of a pie and one fourth of a pie are fourths of a pie. 2. One half of a pie and one sixth of a pie are sixths of a pie. 3. One half of a pie less one fourth of a pie is fourth of a pie. 4. One half of a pie less one sixth of a pie are sixths of a pie. 5. Three times 2 sixths of a pie are . 6. Two sixths of a pie are contained in one whole pie times. 7. One third of one half of a pie is . 8. Webb had one half of a pie; he gave one sixth of a pie to his sister; he then had of a pie. 9. Mrs. Johnson divided a pie equally among some children, giving to each child one sixth of a pie; there were children. 10. Mrs. Clark divided one half of a j)ie equally among three children; each child received oi a pie. Copy and add: 125 127 126 129 128 15 16 14 11 14 l^ART 11. 47 1 pint. 1 quart. 1 gallon. 1. Four quarts are one gallon. 2. Eight quarts are gallons. 3. Twelve quarts are gallons. 4. Two gallons are quarts. 6. Two quarts are of a gallon. 6. Three quarts are of a gallon. crallons, ^— o"allons. gal- 7. Five quarts are 8. Six quarts are and and 9. Seven quarts are and Ions. costs 10. At 5 cents a quart, one half -gallon of milk cents. 11. At 12 cents a gallon, two quarts of milk cost cents. Copy and subtract: 140 140 140 130 130 15 16 17 18 19 48 ELEMENTARY ARITHMETIC. 1. One quart and one pint are pints. 2. One gallon and one quart are quarts « 3. One foot and one inch are inches. 4. One yard and one foot are feet. 5. One dime and one cent are cents. 6. One half and one fourth are fourths. 7. One half and one sixth are sixths. 8. One nickel and one cent are cents. 9. At 40 cents a gallon, two quarts of syrup cost cents. 10. At 20 cents a quart, one half -gallon of lard oil costs cents. 11. At 12 cents a gallon, one quart of kerosene costs cents. 12. At 2 cents a quart, one gallon of skimmed milk costs cents. 13. Will Blake carried to Mr. Jones a pint of milk each day for two weeks; in all he carried pints, or quarts, or one gallon and quarts. 14. Mrs. Bean buys two quarts of milk each day, for which she pays 5 cents a quart ; each day the milk costs cents; for one week the milk costs cents. Copy and multiply : 126 136 146 125 124 2 2 2 3 3 PART II. 49 . 1. Nine books and 4 books are books. 2. Six apples and five apples are apples. 3. My book is inches wide. 4. If I slioiild draw an oblong 3 inches wide and 4 inches long, and then divide it into 1-inch squares, there would be rows of squares, and in each row there would be squares. An oblong 3 inches by 4 inches contains ■ square inches. 5. Three times 4 square inches are . 6. Four times 3 square inches are . 7. Jane had a piece of ribbon 13 inches long; she cut from it pieces 3 inches long; when she had cut off 4 pieces, she had left. 8. Byron pays 2 cents each for oranges, and sells them for 4 cents each; on 1 orange he gains cents ; on 6 oranges he gains cents. 9. Harry pays 10 cents a dozen for eggs and sells them at 13 cents a dozen; on 1 dozen he gains cents; on 4 dozen he gains cents. 10. Ten days are one week and days. 11. To-day is Monday. Seven days from to-day will be . Eight days from to-day will be 12. An old hen sat upon 13 eggs; all the eggs hatched except 4 ; there were chickens. Copy and divide : $2)$32 $2)$52 $2)$72 $2)$92 50 ELEMENTARY ARITHMETIC. 1. Howard has a string 2 and 1 half feet long; David has a string 2 and 1 fourth feet long; to- gether the strings are and fourths feet long. 2. Draw an oblong 2 and 1 half inches wide; make it twice as long as it is wide ; it will be inches long. 3. The teacher bought 2 and 1 half yards of ribbon; she cut it into pieces 1 fourth of a yard long ; there were pieces. 4. Mary had a stick of molasses candy 1 and 1 half feet long ; she cut it into pieces 1 sixth of a foot long; there were pieces. 5. One half of 2 and 1 half inches is . 6. One third of 6 and 1 half inches is . 7. Ellen had a piece of ribbon 1 half of a yard long; Sarah had a piece 1 sixth of a yard long; together they had of a yard. 8. Emma lives 1 half of a mile north of the schoolhouse; Eva lives one fourth of a mile south of the schoolhouse; from Emma's home to Eva's home it is of a mile. 9. The cyclometer on Willie's bicycle showed that he had ridden 10 and 1 half miles; James had ridden twice as far; James had ridden miles. Copy and divide: 2)$32 2)$52 2)$72 2)$92 14 PART II. 9 5 8 6 7 7 7 twos are 14 — 2 sevens are 14 14 51 14 1. Nine and 5 are - 2. Seven and 6 are 3. Seven and 5 are 4. Fourteen 5. Fourteen 6. Fourteen 7. Fourteen 8. Fourteen 9. 14 is — 10. Fourteen 11. Fourteen 12. Fourteen 13. Fourteen 14. Fourteen 15. Fourteen 16. Foin^teen 17. Fourteen quarts. 18. Fourteen 19. Fourteen 20. Fourteen Copy and add : 135 132 25 28 less 9 are . less 5 are . less 6 are . less 12 are . less 4 are . - 7's. 14 is — is one dozen and 8 and 5 are 7 and 7 are 8 and 6 are 14 less 7 = 14 less 8 = 14 less 10 = -. 14 less 11 = 14 less 2's. inches are 1 foot and — cents are 1 dime and - days are weeks. pints are quarts. pints. 2 = inches, cents. quarts are — feet are 3 yards and feet. quarts are 3 gallons and eggs are 1 dozen and — cents are 2 nickels and - sixths are 2 wholes and eggs. - cents. 134 36 137 25 136 26 52 ELEMENTARY ARITHMETIC. 1. Eight gallons of milk and 6 gallons of milk are — — - gallons of milk. 2. Nine pairs of ponies and 4 pairs of ponies are pairs of ponies. 3. Fourteen loads of hay less 9 loads of hay are loads of hay. 4. Fourteen boxes of berries less 8 boxes of berries are boxes of berries. 5. Two times 7 marbles are marbles. 6. Seven times 2 horses are horses. 7. 7 inches are contained in 14 inches . 8. 2 inches are contained in 14 inches . 9. 6 inches are contained in 14 inches times with a remainder of inches. 10. 5 inches are contained in 14 inches times with a remainder of inches. 11. 4 inches are contained in 14 inches times with a remainder of inches. 12. 3 inches are contained in 14 inches times with a remainder of inches. 13. One half of 14 inches is inches. 14. One seventh of fourteen inches is inches. 15. Three sevenths of 14 inches are inches. 16. Two sevenths of 14 inches are inches. 17. Five sevenths of 14 inches are inches. Copy and subtract: 150 150 150 150 150 25 27 24 28 23 PART II. 53 1 in. .2 Ftg. 1. 1. The jwrwietei' of a figure is the distance around it. 2. The perimeter of a 1-incli square is inches. 3. The perimeter of a 2-inch square is inches. 4. The perimeter of a 3-inch square is inches. 5. The perimeter of Fig. 2, at the beginning of this page, is inches. 6. The sum of 9 and 5 is . 7. The difference of 14 and 9 is . 8. The product of 7 and 2 is . 9. The quotient of 140 divided by 2 is . 10. The sum of two numbers is 14; one of the numbers is 8 ; the other number is . 1 1 . The difference of two numbers is 4 ; the less number is 10 ; the greater number is . 12. The difference of two numbers is 5 ; the greater number is 14 ; the less number is . Copy and multipl}^ : 127 137 147 227 2 2 2 2 237 54 ELEMENTARY ARITHMETIC. 1. A hen had 14 chickens; a hawk killed 6 of them; she then had chickens. 2. Peter lives 5 miles west of Anrora; his cousin lives 14 miles west of Aurora; from Peter's home to his cousin's it is miles. Peter lives of his cousin. 3. At 7 cents each, 2 melons cost cents. 4. Charles pays 3 cents a bag for pop-corn and sells it at 5 cents a bag ; on one bag he gains cents; on three bags he gains cents. 5. When oranges cost 2 cents each, for 14 cents I can buy oranges. 6. Willie paid 70 cents each for two books; for both he paid . 7. I paid 1 dollar and 20 cents (120^) for 2 yards of lace; one yard cost cents. 8. One fifth of 10 inches is inches. 9. One fifth of 11 inches is inches. 10. One fifth of 12 inches is inches. 11. If one barrel of flour costs $3^, two barrels cost ; three barrels cost ; four barrels cost . 12. If one ton of coal is worth $6^, two tons are worth . 13. Two times 5^ are . 2 times 5J = Copy and divide: 2^ )34^ 2^ )54^ 2^ )74^ 2^ )94^ — times PART II. 55 1. One whole is 2. One half is - 3. One fourth is — eighths. — eighths. — eighths. 4. Three fourths are eighths. 5. One half and one eighth are — — 6. One fourth and one eighth are — 7. One half and two eighths are — 8. One fourth and two eighths are — 9. One half and three eighths are — 10. One half less one eighth are 11. One fourth less one eighth is - — - 12. One half less three eighths is — eighths. - eighths, eighths. - eighths. - eighths. eighths. eighth. - eighth. 13. Two times one eighth are eighths. 14. Two times two eighths are eighths. 15. Two times three eighths are eighths. 16. One eighth is contained in one half times. 17. One eighth is contained in one fourth times. 18. One half of one fourth is eighth. Copy and divide: 2)34^ 2)54^ 2)74^ 2)94^ 56 ELEMENTARY ARITHMETIC. 1. One half of an inch and one eighth of an inch are eighths of an inch. 2. One fourth of an inch and one eighth of an inch are eighths of an inch. 3. One inch less one eighth of an inch are eighths of an inch. 4. One half of an inch less one eighth of an inch are eighths of an inch. 5. One fourth of an inch less one eighth of an inch is eighth of an inch. 6. Three times three eighths of an inch are 7. Two times five eighths of an inch are 8. Four times three eighths of an inch are 9. Three eighths of an inch are contained in one and one eighth inches (9 eighths) times. 10. Three eighths of an inch are contained in one and one half inches times. 11. Johnnie had a S23linter in his finger one fourth of an inch long. In getting it out his mother broke it into two equal pieces. Each piece was of an inch long. Johnnie cried. Copy and add: 230 250 240 220 221 120 132 128 136 131 PART II. 57 1. 2. pecks. 3 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 1 peck. Eight quarts are one jpeck. Twelve quarts are and Four jpeeks are one husliel. Eight pecks are - Twelve pecks are One quart is Three quarts are Five quarts are - Seven quarts are One peck is bushels. - bushels. - of a peck. of a peck. of a peck. of a peck. Two pecks are - Three pecks are Five pecks are - Two bushels are of a bushel. — of a bushel. of a bushel. — pecks. One bushel and 3 pecks are pecks. Copy and subtract: 270 206 309 120 104 105 425 102 536 124 58 ELEMENTARY ARITHMETIC. 1. Two 2. Two 3. Two 4. Two 5. Two 6. Two 7. Two 8. Two 9. Two 10. Two 11. Two 12. Two eighths. quarts and one pmt are - gallons and one quart are feet and one inch are - — pints. - quarts. yards and one foot are — dimes and one cent are — pecks and one quart are - bushels and one peck are - nickels and one cent are - halves and one fourth are - halves and one sixth are - halves and one eighth are - fourths and one eighth are inches. — feet. — cents. — quarts. — pecks. — cents. — fourths. — sixths. eighths. 13. How many of the class can read the first 12 statements on this page, filling each blank with the right number, in one minute or less? 14. Can you read the first eight statements on page 48 in thirty seconds or less? Try it. 15. At 20 cents a peck, one bushel of potatoes costs cents. 16. At 10 cents a quart, one peck of beans costs cents. 17. At 40 cents a bushel, one peck of apples costs cents. Copy and multiply : 206 207 205 2 2 2 215 2 216 2 PART It. 59 1. Nine slates and five slates are slates. 2. Seven dollars and six dollars are . 3. My book is inches long. 4. If I should draw an oblong 2 inches wide a^nd 7 inches long, and then divide it into 1-inch squares, there would be rows of squares, and in each row there would be squares. An oblong 2 inches by 7 inches contains square inches. 5. Two times 7 square inches are . 6. SeA'en times 2 square inches are . 7. Henry is 5 feet 1 inch tall; his sister is 4 feet 6 inches tall; Henry is inches taller than his sister. 8. Jane had a piece of red ribbon 14 inches long; she cut from it pieces 4 inches long; when she had cut off 3 pieces, she had left. 9. In 14 there are fours and . 10. In 14 there are sixes and . 1 1 . Byron buys apples at 1 half a cent each and sells them for 1 cent each; on one apple he gains ; on 14 apples he gains cents. 12. Fourteen days are weeks. To-day is Two weeks from to-day will be Fifteen days from to-day will be . Thirteen days from to-day will be . Copy and divide: 2 qt.)120 qt. 2 qt.)124 qt. 2 qt.)140 qt. 60 ELEMENTARY ARITHMETIC. 1 . Howard has two pieces of board ; . one piece is 1 and one eighth inches thick ; the other is 1 and one fourth inches thick; together they are and inches thick. 2. Draw an oblong 2 and three eighths inches wide; make it twice as long as it is wide. It will be and ■ inches long. 3 . Two times 2 and three eighths = 4. Draw a line 1 and one half inches long; divide it into parts each one eighth of an inch long; there are parts. 5. Two eighths of an inch are contained in 1 and one half inches (12 eighths) times. 6. One half of 4 and one fourth is — . 7. Harry pays 12 J cents a dozen for eggs; he sells them at 15 cents a dozen; on one dozen he gains ; on two dozen he gains cents. 8. In 14 there are threes and . 9. In 14 there are fives and . 10. One seventh of 14 cents is cents. 11. Two sevenths of 14 cents are cents. 12. Three sevenths of 14 cents are one half of cents. 13. Clyde had 14 cents; he spent 4 sevenths of his money; he spent cents and had cents left. Copy and divide: 2)120 qt. 2)124 qt. 2)140 qt. 2)144 qt. PART 11 • 61 9 8 g 7 3 fives are 15 5 threes are 15 15 15 1. Nine and 6 are . 8 and 6 are — 2. Nine and 5 are . 8 and 7 are — • 3. Fifteen less 9 are . 15 less 7 are 4. Fifteen less 8 are . 15 less 6 are . 5. Fifteen less 3 are . 15 less 10 are , 6. Fifteen less 4 are . 15 less 12 are • 7. 15 is 5's. 15 is 5 3's. 8. Fifteen is one dozen and . 9. Fifteen inches are — — foot and -. 10. Fifteen cents are • dime and cents. 11. Fifteen days are weeks and — — - day. 12. Fifteen pints are quarts and pint. 13. Fifteen quarts are — — pints. 14. Fifteen feet are vards. 15. Fifteen quarts are — — gallons and - — -. 16. Fifteen quarts are — — peck and ■ — — . 17. Fifteen pecks are — — bushels and . 18. Fifteen halves are — — wholes and - . 19. Fifteen thirds are — wholes. 20. Fifteen fourths are — — - wholes and • Copy and add: 208 206 209 207 208 205 107 206 107 207 62 ELEMENTARY ARITHMETIC. 1. Nine bushels of potatoes and 6 bushels of potatoes are bushels of potatoes. 2. Eight rows of trees and 6 rows of trees are rows of trees. 3. Fifteen pounds of butter less 7 pounds of butter are pounds of butter. 4. Fifteen quarts of walnuts less 9 quarts of walnuts are quarts of walnuts. 5. Three times 5 lemons are lemons. 6. Five times 3 oranges are oranges. 7. Five quarts are contained in 1 peck and 7 quarts (15 quarts) times. 8. Three quarts are contained in 1 peck and 4 quarts times. 9. One half of 15 inches is inches. 10. Fifteen inches are one half of inches. 11. One third of 15 inches is inches. 12. Two thirds of 15 inches are inches. 13. One fifth of 15 feet is feet. 14. Two fifths of 15 feet are feet. 15. Three fifths of 15 feet are feet. 16. Alice had 15 apples; she gave two fifths of them to her sister ; she gave her sister apples and had apples left. 17. Ten balls are two thirds of balls. Copy and subtract: 215 214 213 215 215 107 107 105 109 106 PART II. 63 lin. .2 Fig. 5. 1. A triangle has sides. 2. An oblong has sides. 3. A pentagon has sides. 4. A square has sides. 5. Figure 3 has sides. It is a 6. Figure 4 has sides. It is a 7. Figure 5 has sides. It is a 8. Figure 6 has sides. It is a 9. The perimeter of figure 3 is 10. The perimeter of figure 4 is 11. The perimeter of figure 5 is 12. The perimeter of figure 6 is Copy and multiply : 205 204 215 214 3 3 3 3 inches, inches, inches, inches. 225 3 64 ELEMENTARY ARITHMETIC. 1. 3 cents) 12 cents This means, find lioiu many twies S cents are contained in 12 cents. Three cents are contained in 12 cents times. 2. 3)12 cents This means, find one third of 12 cents. One third of 12 cents is cents. 3. 3 cents) 15 cents This means, r-. 4. 3)15 cents This means, . 5. James lives 8 miles north of the Court House; Joseph lives 7 miles south of the Court House ; from James's home to Joseph's home it is miles. 6. At night the out-door temperature was 9 degrees above zero; the next morning it was 6 degrees below zero; the temperature had fallen — — degrees. What was the season of the year? 7. In the morning the out-door temperature was 80 degrees above zero; at noon it was 90 de grees above zero; the temperature had risen degrees. What was the season of the year? Copy and divide : 3 ft.)120 ft. 3 ft.)126 ft. 5 ft.)150 ft. PAET II. 65 One whole is One half is - - tenths, tenths. 1. 2. 3. 4. 5. One half and three tenths are 6. One half and two tenths are - One and one half are One half and one tenth are tenths. tenths. — tenths. - tenths. 7. One half less one tenth are 8. One whole less three tenths are 9. One half less two tenths are — tenths. — tenths. - tenths. 10. Two times three tenths are tenths. 11. Four times two tenths are tenths. 12. Three times four tenths are . 13. Two tenths are contained in six tenths — 14. Two tenths are contained in one whole — 15. One tenth is contained in one half . 16. One fifth of one half is — 17. One fifth of one whole is tenths. 18. One tenth is contained in two wholes . 19. One half is contained in two wholes . Copy and divide : 3)120 ft. 3)126 ft. 5)150 ft. 5)155 ft. 66 ELEMENTARY ARITHMETIC. 1. One dime is one tenth of a dollar. 2. One half-dollar is tenths of a dollar. 3. One half of a dollar and one tenth of a dollar are tenths of a dollar. 4. One half of a dollar and three tenths of a dollar are tenths of a dollar. 5. One half of a dollar less one tenth of a dollar are tenths of a dollar. 6. One half of a dollar less three tenths of a dollar are tenths of a dollar. 7. Three times three tenths of a dollar are tenths of a dollar. 8. Four times three tenths of a dollar are tenths dollars, or one and tenths dollars. 9. Two tenths of a dollar are contained in one dollar times. 10. One tenth of a dollar is contained in one half of a dollar times. 1 1 . One fifth of one Irnlf of a dollar is of a dollar. Copy and add: 218 216 105 107 219 106 217 107 218 107 PART II. 67 1. Can you add column (a) in fifteen seconds, beginning at the top ? 2. Can you add column (a) in fifteen seconds, beginning at the bottom ? 3. Can you add column (b) in fifteen seconds? 4. Can you add column (c) in fifteen seconds? 5. Ten twos are . 6. Fifteen twos are . 7. Twenty twos are . 8. Twenty-five 2's are — 9. Thirty twos are 10. Forty twos are . 11. Fifty twos are . 12. Two fifties are . 13. Four 25's are . 14. One fourth of 100 is 15. One fifth of 100 is — 16. 75 is three fourths of 17. 40 is two fifths of — 18. Harry had one dollar (100 cents); he spent three fourths of his money; he then had cents. a b c 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 Copy and subtract : 245 244 243 245 245 107 107 105 109 106 68 ELEMENTAEY AKITHMETIC. 1. Three quarts and 1 pint are pints. 2. Three gallons and 1 quart are quartSo 3. Three feet and 1 inch are inches. 4. Three yards and 1 foot are feet. 5. Three dimes and 1 cent are cents. 6. Three bushels and 1 peck are pecks. 7. Three nickels and 1 cent are cents. 8. Three halves and 1 fourth are fourths. 9. Three halves and 1 sixth are sixths. 10. There were 100 trees in a park; one fifth of them were elms ; one fifth were maples, and the remainder were oaks. There were elms, maples, and oaks. 11. There were 100 people at a banquet; one fourth of them were men, one fourth were women, and the remainder were children. There were men, women, and children. 12. Sarah bought a doll; the price was 75 cents; she gave . the salesman one dollar ; she should re- ceive in change cents. 13. Howard bought seven boxes of berries at 10 cents a box; he gave the salesman one dollar; he should receive in change cents. 14. For fifty cents I can buy two-cent stamps. Copy and multiply : 53 42 74 32 31 21 3 3 2 4 5 6 PART II. 69 1. Nine pens and six pens are pens. 2. Eight desks and seven desks are desks. 3. My desk is inches wide. 4. If I should draw an oblong 3 inches wide and 5 inches long and then divide it into 1 inch squares, there would be rows of squares, and in each row there would be squares. An oblong 3 inches by 5 inches contains square inches. 5. Three times 5 square inches are . 6. Five times 3 square inches are ■ . 7. Robert's father is 6 feet 2 inches tall; Rob- ert is 5 feet 1 inch tall. How much taller is Robert's father than Robert? 8. Alice had a 23iece of green ribbon 15 inches long; she cut from it pieces four inches long; when she had cut off 3 pieces she had inches left. 9. Byron buys peanuts at 3 cents a bag; he sells them at 5 cents a bag; on one bag he gains • cents; on 50 bags he gains . 10. In 1 and 1 fourth feet there are inches. 11. If a melon costs 15 cents, 1 fifth of a melon costs • ■ cents. 12. If I drink 1 pint of milk each day, in 2 weeks I shall drink quarts of milk. Copy and divide : 3^)42^ 3^)72^ 3^)45^ 3^)75^ 70 ELEMENTARY ARITHMETIC. 1. Notice that tenths may be written in more than one way : 3 tenths -^^ -3 5 tenths -^^ .5 12 tenths If 1.2 1 and 2 tenths 1^-^ 1-2 2. When the period is used as above in writing numbers, it is called a^;om^, or a decimal point. 3. Write the following in figures, using the decimal point: 4 tenths 1 and 4 tenths 7 tenths 2 and 5 tenths 9 tenths 3 and 8 tenths 11 tenths 1 and 3 tenths 15 tenths 2 and 1 tenth 4. Each of the following may be read in two ways: 1.6 is 1 and 6 tenths, or 16 tenths. 1.3 is 1.4 is • 2.5 is ■ 3.4 is — 1.9 is — 2.1 is 3.5 is 2.7 is • — Copy and divide: 3 )42^ 3 )72^ 3 )45^ 3)75^ PART II. 71 9 7 16 8 8 l6 8 twos are 16 4 fours are 16 1. Nine and 7 are - 2. Eight and 8 are ■ 3. Sixteen less 7 are 4. Sixteen less 8 are 5 . Sixteen less 5 are 6 . Sixteen less 4 are 8 and 7 are - 9 and 6 are — 7. 16 is 8's. 16 is 16 less 9 are 16 less 10 are 16 less 12 are 16 less 11 are — - 4's. 8. Sixteen 9. Sixteen 10. Sixteen 11. Sixteen 12. Sixteen 13. Sixteen 14. Sixteen 15. Sixteen 16. Sixteen 17. Sixteen 18. Sixteen 19. Sixteen 20. Sixteen is one dozen and inches are - cents are — days are — pints are - quarts are feet are — quarts are quarts are pecks are - tenths are eio^hths are fifths are - — foot and — ■ dime and - weeks and — quarts. — pints, yards and — gallons. — - pecks. — bushels. — and inches. - cents. - days. foot. wholes. and tenths. fifth. 24 3 Q1 5 Copy and add: 31.3 23.5 26.2 22.4 21.4 43.3 46.1 12.2 72 ELEMENTARY ARITHMETIC. 1. Nine sj)ans of horses and 7 spans of horses are spans of horses. 2. Eight loads of coal and 7 loads of coal are loads of coal. 3. Sixteen gallons of oil less 9 gallons of oil are gallons of oil. 4. Sixteen pounds of cheese less 8 pounds of cheese are pounds of cheese. 5. Two times 8 days are days. 6. Four times 4 bushels are bushels. 7. Two inches are contained in one foot and 4 inches (16 inches) times. 8. Four inches are contained in 1 foot and 4 inches times. 9. Five inches are contained in 16 inches times with a remainder of inch. 10. Six inches are contained in 16 inches times with a remainder of" — inches. 11. Seven inches are contained in 16 inches times with a remainder of inches. 12. One third of 16 feet is and • feet. 13. Two thirds of 16 feet are . 14. One eighth of 16 feet is feet. 15. Three eighths of 16 feet are feet. Copy and subtract: 363-V 48.4 66.8 35.5 73.7 223-V 23.2 14.2 10.2 21.4 PART II. Fig. 7. 73 lin. d •r-( 1—1 lin. lin. d • 1-1 1 . By the area of a figure we mean the amount of its surface. The area of Fig. 7 is sq. in. 2. The 23erimeter of Fig. 7 is inches. 3. The perimeter of a 2-inch square is inches. The area of a 2-inch square is sq. in. 4. The perimeter of a 3-inch square is inches. The area of a 3-inch square is sq. in. 5. The area of a 4-inch square is sq. in. 6. The perimeter of an oblong 2 inches by 3 inches is inches. The area of an oblong 2 inches by 3 inches is sq. in. 7. The sum of two numbers is 16; one of the numbers is 9 ; the other number is -. 8. The difference of two numbers is 5 ; the less number is 11; the greater number is . Copy and multiply: 2Sj\ 24.3 33.3 2 24.4 2 12.2 3 74 ELEMENTARY ARITHMETIC. 1. 4 inches) 12 inches This means, find lioio many thnes Jf inches are contained in 12 inches. Four inches are contained in 12 inches times. 2. 4)12 inches This means, find one fourth of 12 inches. fourth of 12 inches is inches. One 3. 4 inches) 16 inches This means, This means. 4)16 inches 5. Hattie lives 7 miles south of Waukegan; Elsie lives 9 miles south of Hattie's home; from Waukegan to Elsie's home it is miles. 6. When the top of the mercury column in a thermometer is at 32 degrees above zero, water will begin to freeze. Thirty-two degrees above zero is called "the freezing point." When the top of the mercury column is at 40 degrees above zero, it is degrees above the freezing point. When the top of the mercury column is at 26 degrees above zero, it is degrees below the freezing point. Copy and divide: 2 miles) 3 6 miles 2 miles) 56 miles PART II. 75 1 . One whole is twelfths. 2. One half is twelfths. 3. One fourth is : twelfths. 4. Three fourths are twelfths. 5. One half and 1 twelfth are twelfths. 6. One half and 5 twelfths are twelfths. 7. One fourth and 1 twelfth are twelfths. twelfths, twelfth. — twelfths. are 8. One half less 1 twelfth are 9. One half less 5 twelfths is 10. One fourth less 1 tweKth are — 11. Three fourths less 1 twelfth twelfths. 12. Two times 5 twelfths are twelfths. 13. Three times 2 twelfths are . 14. Two twelfths are contained in 1 half — times. 15. One third of 1 fourth is — 16. Two thirds of 1 fourth are Copy and divide: 2)$46V TT 2)$48.6 2)$62.4 2)$84. 76 ELEMENTARY ARITHMETIC. njuzii \ » \ , \ are 1. One inch is 1 twelfth of a foot. 2. One half of a foot is twelfths of a foot. 3. One half of a foot and 1 twelfth of a foot — twelfths of a foot. are 4. One half of a foot and 5 twelfths of a foot twelfths of a foot. 5. One half of a foot less 1 twelfth of a foot — twelfths of a foot. are — 6. One half of a foot less 5 twelfths of a foot is twelfth of a foot. 7. Two times 5 twelfths of a foot are twelfths of a foot. 8. Three times 5 twelfths of a foot are twelfths feet, or 1 and twelfths feet. 9. Two twelfths of a foot are contained in 1 half of a foot times. Copy and add : 32^ 24.6 33.8 51.6 42.7 243-V 12.6 24.5 • 23.7 23.7 PART II. 77 1. Can you add each of these cohimns in fifteen seconds, beginning at the top? 2. Can you add each of these cohimns in fifteen seconds, beginning at the bottom? 3. Ten threes are . 4. Fifteen threes are . 5. Twenty threes are . abed 6. Twenty-five threes are 7. Thirty threes are 8. Forty threes are 9. 28 and 3 = 10. 48 and 3 = 11. 78 and 3 = 12. 29 and 3 = 13. 49 and 3 = 14. 79 and 3 = 15. 37 and 3 = 16. 47 and 3 = 17. 77 and 3 = 18. Three lO's : 19. Three 30's : 58 and 3 = 38 and 3 = 98 and 3 = 59 and 3 = 39 and 3 = 99 and 3 = 57 and 3 = 67 and 3 = 97 and 3 = 3 20's = 3 40's = 3 3 3 3 3 3 3 3 o O o O o O 3 3 3 3 o O 3 3 3 o o O O 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 1 3 2 3 1 3 2 3 2 1 o O 3 1 2 1 3 3 3 3 2 3 2 3 1 3 3 3 3 3 2 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 o O Copy and subtract: 64 48 54 21-1^ 32.6 21.7 57 22.3 45 24.4 78 ELEMENTARY ARITHMETIC. 1. Four quarts and 1 pint are pints. 2. Four gallons and 1 quart are quarts. 3. Four feet and 1 inch are inches. 4. Four yards and 1 foot are — feet. 5. Four bushels and 1 peck are pecks. 6. Four nickels and 1 cent are cents. 7. There were 90 trees in an orchard; one third of them were apple trees ; one third of them were pear trees, and the remainder were peach trees. There were apple trees, pear trees, and peach trees. 8. Three fourths of the trees in a park were maples; the remainder were oaks; there were 75 maples. There were trees in the park. There were oaks in the park. 9. Seventy-five is three fourths of . 10. Thirty is three fourths of . 11. William bought 30 oranges at 3 cents each; he gave the salesman 1 dollar; he should receive in change cents. 12. Herbert bought 2 packages of paper at 20 cents each ; he gave the salesman half a dollar ; he should receive in change cents. 13. Twenty 3-cent stamps cost cents. 14. For 90 cents I can buy 3-cent stamps. Copy and multiply : 223-V 32.7 24.5 31.6 43.7 2 2 2 2 2 PART II. 79 1. Think of a 1-foot square. Think of a 3-foot square. Think of a 3-foot square divided into 1-foot squares. A 3-foot square contains square feet. 2. A 3-foot square is sometimes called a square yard. A square yard contains square feet. 3. One third of a square yard is sq. ft. 4. Two thirds of a square yard are sq. ft. 5. If I should draw an oblong 3 feet wide and 4 feet long and divide it into 1-foot squares there would be rows of squares, and in each row there would be squares. An oblong 3 feet by 4 feet contains square feet. 6. Three times 4 square feet are sq. it. 7. An oblong 3 feet by 4 feet contains 1 and ■ square yards. 8. A 4-foot square contains square feet. 9. A 4-foot square contains 1 square yard and square feet. 10. Six square feet are of a square yard. 11. One square foot is contained in 1 square yard times. 12. Three square feet are contained in 1 square yard times. Copy and divide: 2 tenths )36 tenths .2 )2.4^ .2 )4.8 .2)6.4 * 2 tenths in 24 tenths. 80 ELEMENTARY ARITHMETIC. 1. Write the following in figures, using tlie decimal point: 34 tenths 2 and seven tenths 45 tenths 4 and two tenths 23 tenths 3 and five tenths 19 tenths 1 and seven tenths 2. Each of the following may be read in two ways: 3.2 is 3 and two tenths, or 32 tenths. 2.7 is . 5.1 is . 4.4 is . 3. .3 are contained in 1.5 times. 4. .2 are contained in 1.6 times. 5. .4 are contained in 1.6 times. 6. .5 are contained in 1.5 times. 7. Draw an oblong 3 and one fourth inches wide; make it twice as long as it is wide; it is ' and inches long. 8. Draw an oblong 4 and one half inches wide; make it twice as long as it is wide; it is inches long. 9. I of 12 are . 12 is f of . 10. i of 12 is . 12 is i of . Copy and divide : 2)$46|- 2)$48.4 2)$28|- 2)$68.2 PART II. 9 •^ 3 sixes are 18 8 6 threes axe 18 T i Q 9 twos are 18 81 17 1. Nine and 8 are 2. Nine and 7 are 3. Seventeen less 8 are 4. Seventeen less 7 are 5. Eio^liteen less 9 are - 6. Eig:liteen less 8 are - 7. 18 is 9's. 8. Seventeen inches are 9. Seventeen dimes are 10. Seventeen days are - 11. Seventeen pints are - 12. Seventeen quarts are 13. Seventeen quarts are 14. Seventeen feet are — 15. Eighteen tenths are - 16. Ei2;hteen fifths are — 17. Eis^hteen fourths are 18. Eighteen feet are — 19. Eiofhteen cents are — 20. Eighteen days are — 9 and 9 are 9 and 6 are -. 17 less 12 = -. 17 less 11 = 18 less 12 .= 18 less 15 = 18 is 6's. - foot and - - dollar and weeks and - - quarts and - pecks and - gallons and yards and — - and . and -. - and -. yards, dime and weeks and Copy and add: 35i 43.2 37.3 46.4 55.6 36i 29.1 27.4 28.2 17.1 S2 ELEMEKTAEY AKITHMETIC. 9 9 8 7 4 6 8 6 9 7 9 8 9 7 7 6 8 8 9 9 5 7 5 8 FOR DRILL IN ADDING. Review and drill until pupils can give the sums in any order in 12 seconds. It provides an excellent exercise to put the figures found in this table upon 12 cards, 2 figures on each card; then allow the pupils to handle the cards and name the sums as rapidly as possible. Suspend a pendulum 39 inches long, and see how many pupils can recite these sums while it vibrates 12 times. FOR DRILL IN MULTIPLYING. This is a review of the 23 facts of multiplication that have already been presented. 2 times 2 are 4 times 2 are 6 times 2 are 3 times 2 are 5 times 2 are 8 times 2 are 7 times 2 are 9 times 2 are 3 times 3 are 2 times 4 are 2 times 3 are 4 times 4 are 2 times 5 are 3 times 6 are 2 times 7 are 3 times 5 are 2 times 9 are 2 times 8 are 2 times 6 are 4 times 3 are 5 times 3 are 6 times 3 are 3 times 4 are Copy and subtract: 43 35 21| 12| 57 23| 48 31f 59 24.6 PART II. 83 1. Henry drew an oblong upon his slate. It contained 10 square inches. It was 5 inches long. It was inches wide. 2. A square that contains 4 square inches is a inch square. 3. A square that contains 9 square inches is a inch square. 4. Mary drew a square upon her slate; the area of the square was 16 square inches. It was a< square inch. 5. The sum of 8 cents and 2 cents is ^. 6. The difference of 8 cents and 2 cents is cents. 7. There can he 7io j^roduct of 8 cents and 2 cents. 8. The product of 8 cents and 2 is ^. 9. The quotient of 8^ divided by 2^ is . 10. The quotient of 8^ divided by 2 is 11. The quotient of 15^ divided by 3^ is 12. The quotient of 15^ divided by 3 is ^ 13. The quotient of 16^ divided by 4^ is 14. The quotient of 16^ divided by 4 is ^ 15. The quotient of 15^ divided by 5^ is — 16. The quotient of 15^ divided by 5 is Copy and multiply : \^ 321 3 2 2 2 3 22| 32|- 43|- 21|- 21.6 84 ELEMENTARY ARITHMETIC. 1. 5 quarts) 15 quarts This means, find how r}iany thnes 5 quarts are contained in 1 5 quarts. Five quarts are contained in 15 quarts times. 2. 5)15 quarts This means, find one fifth of 15 quarts. One fifth of 15 quarts is quarts. 3. Highland Park is 11 miles north of Evans- ton; Waukegan is 12^ miles north of Highland Park ; from Evanston to Waukegan it is miles. 4. In the evening the outdoor temperature was 8 degrees above the freezing point ; the next morn- ing it was 9 degrees below the freezing point; during the night it had fallen degrees. 5. When the temperature is 2 degrees below the freezing point, it is degrees above zero. 6. When the temperature is 28 degrees above zero, it is degrees below the freezing point. 7. 18 is 4 4's and . 18 is 3 5's and . 8. 18 is 2 7's and . 18 is 2 8's and . 9. 17 is 8 2's and . 17 is 5 3's and . 10. 17 is 7 2's and . 17 is 2 6's and . Copy and divide : 3 fifth s)15 fifths 3 fourths )18 fourths 3 halves) 3 6 halves 3 tenths) 3 6 tenths PART II. 85 thirds. sixths, sixths. — sixths. 1. One whole is — 2. One whole is — 3. One third is — 4. Two thirds are 5. One third and 1 sixth are - 6. Two thirds and 1 sixth are 7. One third less 1 sixth is — 8. Two thirds less 1 sixth are 9. Two times 2 sixths are — 10. Three times 2 sixths are — sixths. - sixths. sixth. — sixths. sixths. 11. Two sixths are contained in 1 whole 12. One half of 1 third is sixth. 13. 1 and | = 4- less 1 = 1 and 1 == 14. 4- less 1 = 4" and i = |less 1 = 15. 1 and ^V = 1 ipcjtj 1 ._ -g- less YlT — 4" and y^^ = 16. 1 less yV = 4- and 1 = -g- less -^ = 17. i and -^\ = Y ^^^^ T^ = i and ,% - 18. I less ,V - 1 and 3^ - ■F 1^^^ TO" = Copy and divide: 2)24 thirds 2)46 tenths 3)36 fifths 86 ELEMENTARY ARITHMETIC. 1. One third of a pie is 2 sixths of a pie. 2. Two thirds of a pie are 4 sixths of a pie. 3 . Harry had a whole pie ; he ate 1 third of it for his lunch and 1 sixth of it at dinner time ; he then had of a pie. 4. Sarah had 1 third of a -pie; she gave 1 sixth of a pie to her little brother ; she then had of a pie. 5. Mrs. Smith's boarders ate 2^ pies at dinner and 2^ pies at supper; in all they ate pies. 6. Hattie divided 2^ pies among her play- mates, giving to each ^ of a pie; she had playmates. 7. If I should divide 1 half of a pie equally among three children, each child would receive of a pie. 8. If I should divide 1 half of a pie equally between two children, each child would receive of a pie. 9. If I had two thirds of a pie and gave away 1 sixth of a pie, I should then have of a pie. Copy and add: 24| 261 245 374 18.6 32| 162 182 131 32.2 PART II. 87 1. Can you add each of these cohimns in fifteen mng at the top? seconds, begin- a 4 b 2 c 4 d 3 2. Can vou add cohimns m fifteen [ each of these seconds, begm- 4 4 4 4 4 4 4 4 4 4 2 1 ning at the bottom? 4 4 1 1 4 4 4 3 3. Ten fours are . 4 4 4 4 4. Eleven fours ; are -. 4 4 4 2 5. Twelve fours are . 4 4 4 4 4 2 3 1 6. 28 and 4 = 38 and 4 =. 4 4 4 4 7. 48 a.nd 4 = 58 and 4 = 4 4 4 4 4 4 4 4 4 2 2 1 8. 68 and 4 = 78 and 4 = 9. 29 and 4 = 39 and 4 = 4 4 4 4 4 4 3 4 10. 49 and 4 = 59 and 4 = JL 4 4 _L 4 2 11. 69 and 4 = 79 and 4 = 4 4 3 4 4 4 4 3 12. 26 and 4 = 36 and 4 = 4 4 4 1 13. 46 and 4 = 56 and 4 = 4 4 4 2 14. 66 and 4 = 76 and 4 =: 4 4 4 4 4 4 4 2 15. 27 and 4 = 37 and 4 = 4 4 4 3 16. 47 and 4 = 57 and 4 = 1 3 4 4 17. 67 and 4 = 77 and 4 = Copy and subtract: 247 209 207 325 346 63 82 43 62 84 88 ELEMENTARY ARITHMETIC. 1. Five quarts and 1 pint are pints. 2. Five yards and 1 foot are feet. 3. Five dimes and 1 cent are cents. 4. Five halves and 1 fourth are fourths. 5. Five halves and 1 sixth are sixths. 6. Five nickels and 1 cent are cents. 7. Seven pints are and quarts. 8. Two is contained in 7 times. 9. Two is contained in 9 times. 10. Seven feet are and yards. 11. Three is contained in 7 times. 12. Three is contained in 10 times. 13. Nine pecks are and bushels. 14. Four is contained in 9 times. 15. Four is contained in 13 times. 16. In 11 there are — 5's and remain- der. 17. Five is contained in 11 times. 18. Five is contained in 16 times. 19. In 13 there are 6's and remain- der. 20. Six is contained in 13 times. 21. Six is contained in 19 times. 283 25.3 2 2 Copy and multiply : 32i 263 3 2 273 2 PART II. 89 1. 8 + 2, means, 8 and 2 ; 8 and 2 are . 2. 8 — 2, means, 8 less 2; 8 less 2 are . 3. 8 inches x 2, means, 2 times 8 inches; 2 times 8 inches are — - — - inches. 4. 8 inches -^ 2 inches, means, find lioio many times 2 inches are contained in 8 inches; 2 inches are contained in 8 inches times. 5. 8 inches ^ 2, means, ^nc? one half of 8 inches; one half of 8 inches is inches. 6. 4 sixths + 2 sixths, means 7. 4 sixths — 2 sixths, means 8. 4 sixths X 2, means . 9. 4 sixths -=- 2 sixths, means 10. 4 sixths -^ 2, means . 11. 6 tenths + 2 tenths, means 12. 6 tenths — 2 tenths, means 13. 6 tenths x 2, means . 14. 6 tenths ~ 2 tenths, means 15. 6 tenths -^ 2, means . 16. 12^ + 3^, means . 12^ ^+ 2 _ T — 4 2 — 6 |x 2 = 4 . 2 — 4 . "B" ~ 2 = .6 + .2 = ,6- .2 = .6 X 2 = .6- .2 = .6- 2 = D(t, means 17. 12^ X 3^ = nonsense. 12^ x 3, means 18. 12^ -^ 3, means . 12^ -^ 3^, means Copy and divide: $ 4)$804 $ 4)$408 $ 4)$448 $4 )$488 - — times 90 ELEMENTARY ARITHMETIC. 1. Write the following in figures, using the decimal point: 275 tenths 23 and 4 tenths 146 tenths 13 and 5 tenths 224 tenths 26 and 3 tenths 346 tenths 15 and 6 tenths 2. Each of the following may be read in two ways : 24.2 is 24 and 2 tenths, or 242 tenths. 37.5 is — — . 25.6 is . 14.5 is . 3. Draw an oblong 6 and 1 half inches long; make it one half as wide as it is long; it is and inches wide. 6 J inches h- 2 means . 6^ inches ^ 2 = 4. Draw an oblong 4 and 1 half inches long; make it half as wide as it is long; it is and inches wide. 4J inches -^ 2 means -. 4^ inches -i- 2 = 5. f of 12 are . 12 is f of . 6. J of 8 are . 9 is f of . 7. i of 7 is . 7 is i of . Copy and divide : 4)$804 4)$408 4)$448^ 4)$488 PART II. 91 4 fives are 20 3 sevens are 21 3 eights are 24 1. Twenty pecks are 2. Twenty fifths are 3. Twenty-one days are — 4. Twenty-one feet are — 5. Twenty-four quarts are 6. Twenty-fonr feet are — 5 fours are 20 7 threes are 21 8 threes are 24 bushels, wholes. — weeks. — yards. pecks. yards. 7. Three pecks are 8. Three weeks are — 9. Eight yards are 10. Five bushels are — 11. Nineteen inches are 12. Nineteen quarts are 13. Twenty days are — 14. 15. quarts. days, feet. pecks. 2 pecks = 2 weeks = 7 yards = 4 bushels = Twenty-one dimes are — Twenty-two pecks are — 16. Twenty-two feet are — 17. Twenty-four cents are - 18. Twenty-four tenths are — foot and — — pecks and - weeks and dollars and bushels and — yards and dimes and — and and 19. Twenty-four sevenths are - 20. Twenty-four fifths are 21. Twenty-four days are weeks and and Copy and add: 23i 362 375 284 27.4 35i 241 143 172 35.1 92 ELEMENTARY ARITHMETIC. 1. Twelve pairs of boots are boots. 2. Three spiders have legs. 3. Three house-flies have legs. 4. Three cats have feet. 5. Eleven spans of horses are horses. 6. Five butterflies have wings. 7. A cat has toes on each front foot and toes on each hind foot. A cat has toes. 8. Eight three-cent stamps cost cents. 9. Eight 2-cent stamps cost cents. 10. A boy wears 2 shoes. A horse wears 4 shoes. An ox wears 8 shoes. Three boys need shoes. 3 horses need shoes. 3 oxen need shoes. 11. What day of the week is it? It is . One week from to-day will be ; 14 days from to-day will be ; 21 days from to- day will be ; 22 days from to-day will be ; 20 days from to-day will be . 12. At 3^ each, 7 oranges cost cents. 13. At 8^ each, 3 melons cost cents. 14. At 7^ each, 3 balls cost cents. 15. At 3^ each, 8 pencils cost cents. 16. When 2 oranges cost 8^, 3 oranges cost . ^17. When 3 lemons cost 6^, 4 lemons cost . Copy and subtract: 45i 264 363 268 36.5 17i 83 91 72 8.2 PART II. 93 1. Henry drew an oblong upon liis slate. It contained 20 square inches. It Avas 5 inches long. It was inches wide. 2. An oblong that is 3 inches by 7 inches con- tains square inches. Its perimeter is inches. 3. The area of an oblong that is 2 inches by 8 inches is square inches. 8 sq. in. x 2 = 4. The perimeter of an oblong that is 2 inches by 8 inches is inches. 5. A square whose area is 16 square inches is a inch square. 6. I am thinking of an oblong whose area is 21 square inches. It is 7 inches long. It is inches wide. 7. The perimeter of a figure is 18 feet; each side is 6 feet; the figure is a . 8. The sum of 10 feet and 2 feet is ft. 9. The difference of 10 feet and 2 feet is ft. 10. There can he no product of 10 feet and ^ feet. 11. The product of 10 feet and 2 is ft. 12. The quotient of 10 feet divided by 2 feet is 13. The quotient of 10 feet divided by 2 is — ft. Copy and multiply: 22^ 132 231 123 12.3 4 4 4 4 4 94 ELEMENTARY ARITHMETIC. 1. 3 pecks) 24 pecks This means, find how many times 8 jpecks are contained in ^^ pecks. Three pecks are contained in 24 pecks times. 2. 3 )24 pecks This means, find one third of ^Jf pecks. One third of 24 pecks is pecks. 3. Peter lives 4^ miles west of Lake Michigan; Herbert lives 2f miles west of Peter \ Herbert lives miles west of the lake. 4. When the temperature is 6 degrees below the freezing |)oint, it is • degrees above zero. 5. Samuel has two pieces of rope; one piece is 8 feet long; the other piece is 3 yards long; together they are feet long. 6. AYlien apples cost 2^ dollars a barrel, 3 barrels cost dollars. 7. I am thinking of a triangle, each side of which is 2 inches long. The perimeter of the triangle is inches. 8. I am thinking of a triangle, each side of which is 4 feet long. The perimeter of the triangle is feet. 9. Twelve feet equal yards. Copy and divide: $3 )$426 $3 )$456 $3 )$486 $3 )$786 times PART II. 95 1. One whole is 2. One third is ninths, ninths. — ■ ninths. 3. Two thirds are — 4. One third and 1 ninth are — 5. One third less 1 ninth are — 6. Two thirds and 1 ninth are 7. Two thirds less 1 ninth are - 8. One third and 2 ninths are - 9. One third less 2 ninths is — 10. Two thirds and 2 ninths are 11. Two thirds less 2 ninths are 12. Four times 2 ninths are - 13. Three times 2 ninths are ninths, ninths. — ninths. — ninths. — ninths, ninth. — ninths. — ninths. ninths. - ninths. 14. Two ninths are contained in 8 ninths times. 15. Two ninths are contained in 1^^ times. 16. One half of 1 third is 17. One third of 1 third is Copy and divide: 3)$426 3)$456 3)$486 3)$786 96 ELEMENTARY ARITHMETIC. 1. If each third of a pie should be divided into 3 equal pieces, each piece would be of a pie. A hungry boy would think these very small pieces. 2 . 4^ of a pie -\-^ oi Si pie = 2| + 2^ — 3. ^ oi Sb pie — -^ of a pie = 4| — 2^ = 4. 2f of a pie X 4 = 3f x 4 = 5. 2^ pies -^ ^ oi a, pie = 2| -^ 4- = 6. 4| pies - 2 = 8| - 2 = 7. I of a yard and -J- of a yard = 2| + 2|- = 8. |- of a yard less -g- of a yard = 4f — 2^ = 9. I of a yard x 3 = 2|- x 3 = 10. 1-^ yards -^ i of a yard = 2^ -^ 4- = 11. 6| yards -3:= 9| - 3 = 12. Henry had two pieces of rope; one was 2^ yards long ; the other was 3|- yards long ; together they were and yards long. 13. One and -^ yards and 1^ yards are . 14. The sum of 5| yards and 2^ yards is and yards. 15. One foot is of a yard. 16. One third of a foot is 1 ninth of a yard. Copy and add: 34| 624 736 832 92.2 23| 625 721 822 93.5 PART II. 97 1. Can you add column (a) in fifteen seconds, beginning at the top? 2. Can you add column (a) in fifteen seconds, beginning at the bottom? 3 . Practice until you can do this with each column. 4. Ten fives are . 5. Eleven fives are 6. Twelve fives are — 7. Twenty fives are — 8. 28 + 5= 38 + 5 9. 48 + 5= 58 + 5 10. 68 + 5= 78 + 5 11. 19 + 5= 39 + 5 12. 49 + 5= 29 + 5 13. 69 + 5= 89 + 5 14. 67 + 5= 37 + 5 15. 27 + 5= 17 + 5 16. 16 + 5 = 36 + 5: 17. 26 + 5 = 56 + 5: Copy and subtract : 54| 253 355 26| 72 82 a b c d e 5 2 4 5 5 5 5 5 5 4 5 5 5 5 3 5 5 5 4 2 5 5 5 5 1 5 6 5 5 3 5 5 5 5 4 5 5 3 2 5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 2 3 5 5 5 5 4 5 5 5 5 2 5 5 5 5 1 5 5 5 1 5 5 5 5 5 4 5 5 5 5 2 5 5 5 5 3 5 5 5 4 4 1 3 5 3 257 24.6 92 8.2 98 ELEMENTARY ARITHMETIC. 1. Six quarts and 1 pint are pints. 2. Six yards and 1 foot are ■ feet. 3. Six dimes and 1 cent are cents. 4. Six halves and 1 fourth are fourths. 5. Six nickels and 1 cent are ■ cents. 6. Eight feet are and 7. Three is contained in 8 - 8. Three is contained in 11 9. Ten pecks are and - 10. Four is contained in 10 - 11. Four is contained in 14 - 12. der. In 12 there are 5's and 13. Five is contained in 12 14. Five is contained in 17 15. Five is contained in 21 16. Five is contained in 22 17. Five is contained in 23 18. Five is contained in 24 — yards, times. times. - bushels. times, times. - remain- times, times, times, times, times, times. 19. 4 12's are 48. 20. 4 ll's are 44. 21. 3 ll's are 33. Copy and multiply : 231 104 5 5 5 12'sare 60 5 ll's are 55. 2 ll's are 22. 103 5 102 5 10.5 5 PART II. 99 1. $9 + $7, means 2. 3. 4. $9 — ^i , means X 2, means - $2, means 5. 6. 7. 8. 9. 10. 11. 12. 13. ^ 9, means 1 05 means 11+ )|- — $y\j-j means )^ X 5, means - 9 TIT )y%, means 'T ^Q- -=- 2, means $9 and $7 = $9 less $7 =. 2 times $9 = $2 are . I- of $9 = $i and -$yV = $i less $yV = 5 times $yV = $yV are . iof $A = ..6 + $.3, means - • 1 — $.3, means - 1.5 X 4, means — 14. $1.5 - $.3, means 15. $1.8 -^ 3, means — .3 $.6 + $1-! 4 times $.5 = .3 .3 are 16. Arthur had had and — .2; he earned dollars. I of 1.5: he then 17. Fred had $3.6; he spent $1.5; he then had — and dollars. 18. James earned $.3 each day; in 4 days he earned . 19. When coffee costs $.3 a pomid, for $1.2 I can buy pounds. Copy and divide : $ 2)$412 $2 )$616 $2 )$214 $2 )$418 times 100 ELEMENTARY ARITHMETIC. 1. 2. 3. 4. 5. 6. 60 seconds are 1 minute. 60 minutes are 1 hour. 24 hours are 1 day. One half-hour is — One fourth-hour is minutes. — minutes. When the long hand of a clock points to KII and the short hand to IX, it is o'clock. 7. When the long hand points to XII and the short hand to Yl, it is o'clock. 8. At 5 minutes past 9, the long hand points to . At " half past 3/' the long hand points to . At " quarter past 6/' the long hand points to . At 20 minutes past 8, the long hand points to . 9. '' Half past 9 " is usually printed 9:30. 10. " Quarter past 9 " is usually printed 9:15. 11. '' Quarter of ten " is usually printed 9:45. Copy and divide: 2)$412 2)$616 2^S214 2)$418 PART II. 4 sixes are 24 6 fours are 24 3 nines are 27 9 threes are 27 5 fives are 25 ^ ' 101 1. Twenty-four pecks are — 2. Twenty-four sixths are - 3. Twenty-seven feet are — 4. Twenty-seven ninths are 5. Twenty-five fifths are — bushels. - wholes, yards. — wholes, wholes. 6. 25 is 7. 27 is 8. 28 is 9. 29 is 6's and 4's and 9's and 6's and 26 is 26 is 29 is 29 is 4's and 6's and 3's and 4's and 10. 6 bushels are 11. 9 yards are - pecks. feet. 12. Twenty-five inches are 13. Twenty-five quarts are 14. Twenty-six days are — 5 bushels 8 yards = — feet and — pecks and weeks and - — dollars and 15. Twenty-six dimes are — 16. Six bushels and 2 pecks are pecks. 17. Five bushels and 3 pecks are pecks. 18. Nine yards and 2 feet are feet. 19. Eight yards and 1 foot are feet. 20. Three feet and 3 inches are inches. 26| 221 Copy and add: 605 508 704 609 803 708 90.7 60.5 102 ELEMENTARY ARITHMETIC. 1. Two tliirds of 18 apples are apples. 2. Eighteen apples are two tliirds of . 3. Three fourths of 12 oranges are or- anges. 4. Twelve oranges are three fourths of ■. 5. Eight is two thirds of . 12 is two thirds of . 18 is two thirds of . 6. The first day of August, 1898, was Monday; the next Monday was the th ; the ninth was ; the seventh was . 7. Nine 3-cent stamps cost cents. 8. Six 4-cent stamps cost cents. 9. Five 5-cent stamps cost cents. 10. At $9 a ton, 3 tons of hay cost dollars. 11. At $6 a ton, 4 tons of coal cost dollars. 12. At $3 each, 9 hats cost dollars. 13. Six spoons are a set; 24 spoons are — sets; 18 spoons are sets. 14. When kerosene is 9^ a gallon, for 27^ I can buy gallons. 15. When wood is $6 a cord, for $24 I can buy cords; for $27 I can buy cords. 16. When sugar is 4^ a pound, for 24^ I can buy pounds; for 26^ I can buy pounds. 383 32.6 191 16.3 Copy and subtract: 62| 365 374 16^ 183 182 PART II. 103 1. If I should draw an oblong 3 inches wide and 9 inches long, and then divide it into 1-inch squares, there would be ■ • rows of squares. An oblong 3 inches by 9 inches contains square inches. 2. Three times 9 square inches are . 3. Nine times 3 square inches are . 4. A square whose area is 25 square inches is a inch square. 5. The perimeter of a 5-inch square is inches. 6. I am thinking of a pentagon, each side of which is 4 inches. The perimeter of this pentagon is inches. 7. The sum of 9 inches and 3 inches = 8. The difference of 9 inches and 3 inches = 9. There can he no 'product of 9 inches and 3 inches. 10. The product of 9 inches and 3 = 11. The quotient of 27 inches divided by 3 inches = 12. The quotient of 27 inches divided by 3 = 13. The quotient of 24 inches divided by 4 inches = 14. The quotient of 24 inches divided by 4 = Copy and multiply : 311 131 141 151 12.1 5 5 5 5 104 ELEMEN^TARY ARITHMETIC. 1. Four and one half times 6, means, Jf sixes and 1 half of six. 4^ times 6 = 2. 6 X 2^, means, 2^ times 6, or 2 sixes and \ of six. 2 J times 6 — 6x2^ — 3. Notice carefully the following: 3 tons at $8 a ton; $8x3 = 2 tons at $8 a ton; $8x2 = 1 ton at $8 a ton; $8x1 = i ton at $8 a ton; $8 x i = i ton at $8 a ton; $8 x i = 21 tons at $8 a ton; $8 x 2i = 2i tons at $8 a ton; $8 x 2i = 4. Remeiiiber that to niidtiioly a number hy \ is to (jet i of that number; to multiply by J . 5. 10 X i, means, ^ of ten. 10 x |, means 6. 10 multiplied by 2^ = 7. 12 multiplied by 2^ = 8. 20 multiplied by 2i = 9. 30 multiplied by 2^ = 10. 4 X 21= 5 X 21 = 11. 3 X 24= 7 X 21 = 12. At $6 a ton, 2^ tons of coal cost dollars. Copy and divide: $4 )$524 $4 )$564 $4 )$604 $4)$608 * The sign of multiplicatiou in this book is to be read multi- plied by. PART II. 105 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. times. 17. 18. 19. 20. One whole is - One fifth is — Two fifths are - tenths, tenths. - tenths, tentlis. — tenths. Three fiftlis are Four fifths are - One fifth and 1 tenth are One fifth less 1 tenth is - tenths. tenth. tenths, tenths. — tenths. — tenths. Four fifths and three tenths are tenths. Three fifths and 1 tenth are Three fifths less 1 tenth are Four fifths and 1 tenth are Four fifths less 1 tenth are Four fifths less 3 tenths are Four times 2 tenths are - — - Three times 3 tenths are — tenths. — tenths. — tenths. Two tenths are contained in 6 tenths One tenth is contained in 1 fifth One half of 1 fifth is One half of 3 fifths is One half of 2 fifths is times. Copy and divide: 4)$524 4)$564 4)$604 4)$608 106 ELEMENTARY ARITHMETIC. [ I I I I [TT I I I I I I I I I iq: 1 . Sometimes inches are divided into fifths and tenths. Perhaps the teacher can show you a rule so divided. 2. -^ of an inch + y^ of ^^ i^- = ^i + ^tw — 3. 4- of an inch — -^^ of an in. = i\ — 2^^^ = 4. yV c>f an inch x 3 = 2^^^ x 3 = 5. 2|- in. ^ 4^ of an inch = 1| -^ y^ = 6. 6|in. -2= 8|-2 = 7. Draw a line 3 inches long; erase from it \^jj inches \ the line that is left is ■ and tenths inches long. 3 — IfV = 8. William drew a square. Each side of it was ly^ inches. We might call it a ly^-inch square. The perimeter of the square was — — and inches. ly\j- x 4 = 9. Egbert had a piece of copper wire 1-|- inches long. He divided it into pieces each of which was y^Q of an inch long. There were pieces. -■-2 • 10 10. Herbert had a piece of silver wire 1.2 inches long. He divided it into 3 equal parts. Each part was ■ of an inch long. 1.2 in. ^ 3 = lA in. - 3 = Copy and add: 35| 515 617 714 81.4 24y^ 607 505 408 30.8 PART II, 107 12 sixes are 72 11 sixes are G6 6 twelves are 72 6 elevens are 66 1. Can you add column (a) in fifteen seconds, beginning at the top? abode 6 2 4 6 6 2. Can you add column (a) q q q q 2 in fifteen seconds, beginning at 6 6 6 6 1 the bottom? 6 6 6 5 3 6 6 6 6 5 3 . Practice until you can do 6 6 6 6 4 this with each column. 6 6 6 6 6 6 6 6 4 3 4. Ten sixes are . 6 6 6 6 2 5. Eleven sixes are . 6 6 6 6 5 6. Twelve sixes are . b b b 6 1 7. Twenty sixes are . n n r^ ^ t D D 8. 27 + 6= 37 + 6= 6 6 6 6 1 9. 17 + 6= 47 + 6= I t ^c t t 10. 87 + 6= 67 + 6= 6 6 6 2 3 11. 86 + 6= 46 + 6 = 12. 36 + 6= 56 + 6 = 1 J J 6 2 6 3 13. 16 + 6= 26 + 6= 1 2 14. 48 + 6 = 58 + 6 = 18 + 6 = 5 15. 28 + 6 = 38 + 6 = 68 + 6 = 4 _3 Copy and subtract: 48-1, 423 532 643 75.2 23tV 165 . 196 286 28.6 108 ELEMENTARY ARITHMETIC. 1. 2 is contained in 11 - 2. 2 is contained in 11 - 3. 3 is contained in 13 - 4. 3 is contained in 13 - 5. 3 is contained in 11 - 6. 3 is contained in 11 - 7. 3 is contained in 14 - 8o 3 is contained in 14 - 9. 4 is contained in 17 - 10. 4 is contained in 17 - 11. 4 is contained in 19 - 12. 4 is contained in 19 - 13. 5 is contained in 22 - 14. 5 is contained in 22 - 15. 5 is contained in 33 - 16. 5 is contained in 33 - 17. 5 is contained in 42 - 18. 5 is contained in 42 - 19. 21 is — 5's and — . 20. 23 is — lO's-and — . 21. 22 is — 7's and — . 22. 24 is — 7's and — . Copy and multiply: 44 46 ^2 ^2 26 2i times and and - times and and - times and and - times and and - times and and times and and times and and - times and and - - over, times. over. times. over. times. over. times. over. times. over. times. over. times. over. - times. - times and ■ — - over. - and times. 22 is — 4's and — . 21 is — 2's and — . 23 is — 3's and — . 24 is — 8's. 64 n 24 2i PART II. 109 1. 20 ft. + 17 ft., means . 20 ft. and IT ft. - 2. 20 ft. - 17 ft., means . 20 ft. less ITft. = 3. 20 ft. X 2, means . 2 times . 4. 20 ft. X 2^, means . 2^ times . 5. 20 ft. -^ 4 ft., means . 4 ft. are contained . 6. 20 ft. -^ 4, means . i of . 7. 4^ ft. + 4- ft., means . i^ ft. and ^ ft. 8. ^ it. — ^ ft., means . ^ ft. less ^ ft. 9. 2 J- ft. X 4, means . 4 times 10. 4- ft. X 24-, means . 24 times 11. |- ft. -=- f ft., means . f ft. are contained 12. 64 ft. ^ 3, means . ^ of — . 13. .8 in. + .4 in., means .8 in. and .4 in. = 14. 1.2 in. — .5 in., means 1.2 in. less .5 in. = 15. 1.2 in. X 3, means ■. 3 times — 16. 1.2 in. X 24, means . 2^ times 17. 1.6 in. ^ .4 in., means . .4 in. are contained — 18 1.6 in. ~ 4, means . 4- of . Copy and divide: $5)$525 $5)$515 $5)$1025 $5)$1015 110 ELEMENTARY AIUTHMETIC. Thirty days liatli September, April, June, and November. Each of the other months has 31 days, except February. February has 29 days in a leap-year and 28 days in all other years. THIS YEAR. 1. In January there are — weeks and — days. 2. In February there are — weeks and — . 3. In March there are — weeks and — days. 4. In April there are — weeks and — days. 5. In May there are — weeks and — days. 6. In June there are — weeks and — days. 7. In July there are — weeks and — days. 8. In August there are — weeks and — days. 9. In September there are — weeks and — days. 10. In October there are — - weeks and — days. 11. In November there are — weeks and — days. 12. In December there are — weeks and — days. Can you read the 12 statements given above, filling each blank correctly, in 40 seconds? Can you do it if they are put ujoon the blackboard in some other order? Try it. 13. In February, 1896, there were — weeks and — day. Copy and divide : 5)$525 5)$515 5)$1025 5)$1015 PART II. Ill 4 sevens are 28 7 f oui-s are 28 4 eights are 32 5 sixes are 30 6 fives are 30 8 fours are 32 1. Thirty-two pecks are — 2. Twenty-four quarts are 3. Twenty-eight days are bushels. — pecks. — weeks. — wholes. 4. Twenty-eight fourths are — 5. Thirty fifths are wholes. 6. 7 bushels are pecks. 6 bushels = 7. 4 weeks are days. 3 weeks = 8. 10 yards are feet. 9 yards = 9. Thirty inches are feet and inches. 10. Thirty days are weeks and days. gallons and . dollars and . bushels and 1 1 . Thirty-one quarts are — 12. Thirty-two dimes are — 13. Thirty-three pecks are 14. Thirty-four quarts are pecks and 15. Four weeks and 3 days are 16. Ten yards and 2 feet are — — days. - feet. 17. Seven bushels and 3 pecks are pecks 18. Two feet and 8 inches are inches. 19. Four pecks and 1 quart are quarts. 20. Six gallons and 3 quarts are quarts Copy and add: 24| 345 138 224 27.3 33 226 304 246 30.2 25A 216 225 108 35.9 112 ELEMENTARY ARITHMETIC. 1. The sum of $12 and $4 is — — dollars. (a) Find the sum of $84 and $43.* 2. The difference of $12 and $4 is dollars. (b) Find the difference of $85 and $42. There can he no product of $8 and $^. 3. The product of $8 and 4 is dollars. (c) Find the product of $82 and 4. 4. The quotient of $28 divided by $7 is , (d) Find the quotient of $628 divided by $2. 5. The quotient of $28 divided by 7 is . (e) Find the quotient of $628 divided by 2. 6. A lady bought 4 yards of gingham at 8^ a yard; she gave the salesman half a dollar; she should receive in change cents. 7. A man paid $8 for a watch; he paid $4 for repairing it; he then sold the watch for $15; he gained dollars. 8. Alice paid 8^ for pens, 5^ for a pencil and 5^ for paper. If she gave the salesman 1 fourth of a dollar, how much change should she receive? She should receive . 9 . Peter had half a dollar ; he spent 1 tenth of a dollar; he had cents left. Copy and subtract: 53| 504 603 705 70.5 21t-V 268 377 489 48.9 * Problems designated by letters are for the slate. PART II. 113 1. If I should draw an oblong 4 inches wide and 8 inches long and then divide it into 1-inch squares, there Avould be rows of squares and in each row there would be squares. 2. The area of an oblong 4 inches by 8 inches is square inches. 3. The perimeter of an oblong 8 inches by 4 inches is inches. 4. The first day of August, 1895, was Thurs- day; the next Thursday was the th; the ninth was ; the seventh was . 5. Eight 4-cent stamps cost cents. 6. At 5^ a quart, 6 quarts of milk cost cents; 5 quarts cost cents. 7. At 4^ a quart, 7 quarts of milk cost cents; 8^ quarts cost cents. 8. A man agreed to pay $4 a day for keeping his family at a hotel. One week's board will cost dollars. 9. It takes 5 minutes for Alice to go home from school ; Mary lives farther away, and it takes her six times as long ; it takes Mary • minutes to go home from school. Alice and Mary started for home at 3:15 ; Alice reached home at : Mary reached home at — ■. Copy and multiply : 56 74 98 58 76 2i 2i 2i 2i 2i 114 ELEMENTARY ARITHMETIC. 1. 3 bu. 2 pk. + 4 bu. 1 pk. = 3i + 4]. 2. 4 bu. 3 pk. - 2 bu. 2 pk. = 4| - 2-^ 3. 5 biT. 1 pk. X 3 = 51x3 4. 2 bu. 2 pk. X 2, L _ 2^x2^ 5. 2 bu. 2 pk. - 2 pk. — 2i^ i 6. 2 pk. - 4 = 1^4 7. $2.4 + $3.1 =r 2i+3/„ 8. $6.8- $3.1=. H - 3tV 9. $5.2 X 4 = 51x4 10. $4.2 X 2\^ 41x2^ 11. $3.6- $.6 = 3|^ 1 12. $3.6-3 = 3f-3 13. The long hand of a clock moves from X to XII in mmutes; from YI to X in minutes. 14. The short hand of a clock moves from IX to XI in ; from IV to VIII in 15. The best trains go from Waukegan to Chi- cago in 50 minutes ; such a train leaving Wauke- gan at 10:30 should arrive in Chicago at . 16. A train from Aurora was due in Chicago at 2:15; it arrived at 2:45; it was minutes late. 17. From 1:30 to 2:45 it is hour and minutes. Copy and divide: $5)$630 . $5)$620 ■ $5)$610 $5)|640 PART II, 115 1. One third is 2. One sixth is — - 3. Two thirds are - 4. Two sixths are - 5. Tliree sixths are twelfths, twelfths. — twelfths. — twelfths. twelfths. 6. 7. 8. 9. 10. One third and 1 twelfth are One third less 1 twelfth are One sixth and 1 twelfth are One sixth less 1 twelfth is - Five sixths and 1 twelfth are 1 1 . Five sixths less 1 twelfth are 1 2 . Seven twelfths and 1 sixth are 1 3 . Seven twelfths and 1 third are 14. Two times 5 twelfths are — 15. Three times 5 twelfths are — — twelfths. — ■ twelfths. — twelfths, twelfth. — twelfths. — twelfths. — twelfths. — twelfths, twelfths. 16. Two twelfths are contained in 1 half times. 17. Two twelfths are contained in 1 whole 18. One half of 1 sixth is — 19. One fourth of 1 third is Copy and divide : 5)$6P>0 5)$62Q 5)$610 5)$640 116 ELEMENTARY ARITHMETIC. 1. One inch is of a foot. 2. Two inches are of a foot. 3. Three inches are of a foot. 4. Four inches are of a foot. 5. Five inches are of a foot. 6. Six inches are of a foot. 7. Seven inches are of a foot. 8. Eight inches are — of a foot. 9. Nine inches are of a foot. 10. Ten inches are of a foot. 11. I of a ft. + tV of a ft. = 3| + 3yV -= 12. 4 of a ft. - yV of a ft. = 4| - 2^V = 13. ^\ of a ft. X 2 = 6-j-V X 2 =: 14. Hft.-|ofaft.= 1|^tV- 15. 6|ft. -2= 61-4-2 = 16. Draw a line 3^ ft. long; draw another line 4y^^ ft. long ; together the lines are and — — feet long. 3|-f 4^^ = 17. Draw a line 3 ft. long; erase from it ly^-g- feet; the line that is left is and feet long. 3 — lyV — 18. Henry drew a 1^-foot square. The perim- eter of the square was 240 175 Copy and add: 35| 352 23 143 35A 262 l|x4 = 302 45.3 184 30.1 231 25.2 PART II. 117 12 sevens are 84 11 sevens are 77 7 twelves are 84 7 elevens are 77 1. Can you add column (a) in fifteen seconds, beginning at the top? 2. Can you add column (a) ^ o a n ^ in fifteen seconds, beginning at 7 7 7 7 2 the bottom? 7 7 7 7 1 3 . Practice until you can do 7 7 7 7 4 this with each cohimn. 7 7 7 7 6 7 7 7 7 3 4. Ten sevens are . 7 7 7 7 4 5. Eleven sevens are . 7 7 7 7 2 6. Twelve sevens are . 7 7 7 7 5 7. Twenty sevens are . ( 1 ( 7 o ^ 11111 8. 27 + 7 = 17 + 7 = 7 7 7 7 G 9. 37 + 7= 57 + 7= 7 7 7 7 1 7 7 7 7 4 10. 46 + 7 = 16 + 7 = J: J _^ _I ^ 11. 26 + 7 = 56 + 7 = 2 12. 38 + 7 = 18 + 7 = '> 13. 48 + 7 = 28 + 7 = "^ 4 14. 25 + 7 = 15 + 7 = 35 + 7 = 6 15. 65 + 7 = 45 + 7 = 75 + 7 = A Copy and subtract; 65 1 640 560 470 38 32^V 236 345 134 14.6 118 ELEMENTARY ARITHMETIC. 1. 5 is contained in 11 times and 2. 5 is contained in 11 — - and - 3. 5 is contained in 12 times and 4. 5 is contained in 12 — - and - 5. 5 is contained in 13 - 6. 5 is contained in 13 - 7. 5 is contained in 14 - 8. 5 is contained in 23 - times and and - and - and - 9. 5 is contained in 28 — - and 10. 5 is contained in 33 and 11. 5 is contained in 37 and 12. 5 is contained in 41 and 13. 5 is contained in 48 and - over, times. over. times. over. times, times, times. times, times, times, times, times. 14. When milk costs 2^ a pint, for 7^ I can buy — and pints. 7^ ^ 2^ — 15. When ribbon costs 3^ a yard, for 10^ I can buy and yards. 10^ -^ 3^ = 16. When milk is 4^ a quart, for 10^ I can buy — — and ■ quarts. 10^ -^ 4^ = 30 is 17. 18. 19. 32 is 30 is 7's and 4's and 5's and 30 is 31 is 32 is 9's and - — . G's and — . 3's and — . Copy and multiply 28 38 91 ^2 2i 48 2i 68 78 24 PART II. 119 1. 30 mill. + 15 mill., means 30 min. and 15 min. 2. 30 min. — 15 min., means 30 min. less 15 min. = 3. 12 min. x 2, means . 2 times — 4. 12 min. x 2 J, means . 2h times 5. 30 min. -^ 5 min., means . 5 min. are contained 6. 30 min. ^ 5, means . 4- of 7. 4- ft. + -f'Y ft., means . -I- ft. and -iV ft. = 8. |- ft. — -j^ ft., means . ^ I ft. less 3-V ft- = 9. 3y^-2- ft. X 5, means . 5 times — 10. 6 ft. X 2-|-, means . 2|- times — 11 . 2yV ft. -^ 3^ ft., means . yV ft. is 12. 8| ft. ^ 2, means . I of 13. $.7 + $.5, means • . $.7 and $.5 = " 14. $1.5 - $.8, means . $1.5 less $.8 = 15. $1.2 X 4, means . 4 times . 16. $.6 X 2|, means ■ . 2h times — . 17. $2.4 - $.6, means -. $.6 are . 18. $2.4 - 6, means . | of . 19. From 9:10 to 9:35 it is minutes. 20. From 9:50 to 10:10 it is minutes. Copy and divide: 21b.)451b. 21b.)631b. 21b.)871b. 21b.)291b. 120 ELEMENTARY ARITHMETIC. 1. What day of the week is it? To-day is . Two weeks from to-day will be . Four weeks from to-day will be Four weeks and 1 day from to-day will be . Twenty-nine days from to-day will be . Thirty days from to-day will be . Four weeks and three days from to-day will be . Thirty-one days from to-day will be . 2. From January 1st to February 1st it is days. From February 1st to March 1st it is days. From March 1st to April 1st it is days. From April 1st to May 1st it is days. From May 1st to June 1st it is days. 3. The year 1896 Avas a leap-year. February, 1896, had days. 4. January 1st, 1896, was Wednesday; Febru- ary 1st, 1896, was . 5. August 1st, 1896, was Saturday; September 1st, 1896, was . 6. February 1st, 1896, w^as Saturday; March 1st, 1896, was . 7. September 1st, 1896, was Tuesday; October 1st, 1896, was . Copy and divide: 2)45 lb. 2)63 lb. 2)87 lb. 2)29 lb. PART II. 121 5 sevens are 35 4 nines are 36 7 fives are 35 9 fours are 36 6 sixes are 36 1. Thirty-six pecks are 2. Thirty-five days are 3. Thirty-six spoons are 4. Thirty-five fifths are 5. Thirty-six ninths are 6. 9 gallons are quarts. 7. 5 weeks are days. 8. Thirty-seven inches are — 9. Thirty-eight days are 10. Thirty-nine quarts are - bushels, weeks. - sets. wholes, wholes. 8 gallons 4 weeks = — feet and - weeks and - 11. Five weeks and 2 days are - 12. Three feet and 3 inches are 13. Nine bushels and 1 peck are gallons and days, inches. - pecks. 14. 2| are 15. 2|- are 16. 2f are 17. 2|- are 18. li are 19. 41 are thirds. fourths. fifths. fifths. thirds, 3 1 are 3|- are 31- are 3|- are 4| are tiiirus. '±f ctru fourths. 4|- are thirds. fourths. fifths. fifths. thirds. fourths. Copy and add: 304 240 32| 23 158 425 106 232 356 114 205 24.T 10.2 33.4 122 ELEMENTARY ARITHMETIC. 1. Add 6 bu., 4 bu., 2 bu., and 1 bu. (a) Add 344 bu., 46 bu., and 35 bu. 2. From 19 bushels subtract 6 bushels. (b) From 472 bushels subtract 146 bushels. 3. Multiply 9 bushels by 4. (c) Multiply 292 bushels by 3. 4. Divide 35 bushels by 5 bushels. (d) Divide 525 bushels by 5 bushels. 5. Divide 35 bushels by 5. (e) Divide 525 bushels by 5. 6. At $3 a barrel, 8 barrels of apples cost . (f) At $236 an acre, 2 acres of land cost . 7. Two thirds of 12 dollars are dollars. (g) Two thirds of 99 dollars are ■ dollars. (h) Two thirds of 96 dollars are dollars. 8. Twelve dollars are f of dollars. (i) Forty-four dollars are f of dollars. (j) Forty-six dollars are f of dollars. 9. A lady bought 8 yards of lace at $2 a yard; she gave the salesman two ten-dollar bills; she o±xijLi±*^ icv^cxvv::; xxx v^jlxc Aji-l^K. K.\.KJ±±(Aji.O. Copy and subtract: 461 475 565 455 35.5 23^^ 235 236 237 12.8 PART II. 123 1. Tliink of an oblong 5 inches by 7 inches. Think of it divided into 1-inch squares. The area of the oblong is square inches. 2. The perimeter of an oblong 5 inches by 7 inches is inches. 3. The first day of September, 1895, was Sun- day ; the second Sunday was the th ; the third Sunday was the ; the fourth Sunday was the ; the fifth Sunday was the . 4. The first Sunday of August, 1895, was the fourth day of the month; the second Sunday was the th; the third Sunday was the th; the fourth Sunday was the th. 5. The Saturdays of August, 1895, were the 3d, , , , and . 6. A passenger train runs from Waukegan to Lake Forest in 15 minutes. If the train leaves Waukegan at 9:50 it should reach Lake Forest at 7. John rode 32 miles in 4 hours; he rode at the rate of miles an hour. 32 miles -^ 4 = 8. Henry rode 33 miles in 4 hours; he rode at the rate of miles an hour. 33 miles -^- 4 = Copy and multiply : 45 65 85 25 47 2i 2i 24 2i 24 124 ELEMENTARY ARITHMETIC. 1. 3 ft. 6. in. + 3 ft. 7 in. = 3| + 3^^-^ = 2. 3 ft. 6 in. - 1 ft. 4 in. = ^ - 1^ = 3. 4 ft. 8 in. X 4 == 4| x 4 = 4. 4 ft. 6 in. -f- 6 in. = 4| - I = 5. 4 ft. 6 in. - 2 = 4| - 2 = 6. The letters A.M. stand for the words ante meridiem. These words mean before noon. 7. The letters P.M. stand for the words post meridiem. These words mean after noon. 8. From 10 o'clock A.M. to 2 o'clock P.M. it is hours. 9. From 9 o'clock P.M. to 4 o'clock A.M. it is hours. 10. From 4:30 P.M. to 6:30 P.M. it is . 11. Mr. Smith begins work at 7 o'clock A.M.; he has one hour for dinner and rest at noon, and then works until 6 o'clock P.M. Each day he works hours. 12. A train from Chicago was due in Waukegan at 10:45; it arrived at 11:10; it was minutes late. 13. A tram moved 30 miles in 1 hour; this was at the rate of 1 mile in minutes. 14. A train moved at the rate of 40 miles an hour for 2 hours and 30 minutes; it moved miles. Copy and divide : 31b.)671b. 3 lb.)97 lb. 31b .)371b. 3 lb. )38 lb. PART II. 125 1. One third is 2. One fourth is 3. Two thirds are — 4. Three fourths are twelfths. - twelfths. - twelfths. twelfths. 5. Add 1 fourth and 1 third. 1 fourth is twelfths. 1 third is twelfths. — twelfths and twelfths are twelfths. 6. Add 2 thirds and 1 fourth. 2 thirds are twelfths. 1 fourth is twelfths. — twelfths and twelfths are twelfths. 7. From 3 fourths subtract 1 third. 3 fourths are twelfths. 1 third is twelfths. twelfths less twelfths are — 8. One fourth of a foot and are twelfths of a foot. twelfths. 1 third of a foot Copy and divide: 3 )67 lb. 3 )97 lb. — lb. 3)37 lb. 3)38 lb. 1 "3 + 1 _ 1 T — 1 _ 1 X 6 = 1 "3 X 6i = 1 "5 -^ 1 _ 1 2 - 1 3 -^ 4 = 126 ELEMENTARY ARITHMETIC. 1 . 4 of a dozen + 4- of a dozen = 2. 1^ of a dozen — 4- of a dozen = 3. ^ of a dozen x 6 = 4. I of a dozen x 6^^ = 5 . I of a dozen -^ -j^ of a dozen := 6. \ oi 2i dozen -=- 4 = 7. Draw a line 2| feet long; draw another line 2^ feet long ; together the lines are and feet long. 2| + 2| = 8. Draw a line 4 feet long; erase from it IfV f eet ; the line that is left is and feet long. 4 — 1^^ = 9. James drew a square. Each side of it was 1^ feet long. We might call it a ly-^-foot square. The perimeter of the square was and feet. lyV X 4 = 10. Peter had a piece of copper wire \\ feet long. He divided it into j^ieces, each of which was -f of a foot long. There were pieces. 1-^ X — 6 ~ 11. Harry had a piece of silver wire 1| feet long. He divided it into 2 equal pieces. Each piece was ■ of a foot long. \l ^2 = 12. l|feet-- 1 of a foot = 1| feet -f 2 = 13. 14- feet - 1 T of a foot — 14- feet -f -2 = Copy and add: 43|- 414 524 335 31.6 22 306 207 407 41.6 31A 412 623 502 51 .6 PART II. 127 12 eights are 96 11 eights are 88 8 tAvelves are 96 8 elevens are 88 1. Can you add column (a) in fifteen seconds, beginning at the toj)? a b c d e 2. Can you add column (a) o o a n o in fifteen seconds, beginning at 8 8 8 8 2 the bottom? 8 8 8 8 7 8 8 8 8 6 3 . Practice until you can do 8 8 8 8 3 this with each column. 8 8 8 8 5 8 8 8 8 1 4. Ten eights are . 8 8 8 8 4 5. Eleven eights are . 8 8 8 8 8 6. Twelve eights are . 8 8 8 8 6 7. Twenty eights are . 8 8 8 8 2 8 8 8 8 7 8. 27 + 8 = 17 + 8 = 8 8 8 8 3 9. 37 + 8 = 57 + 8 = 13 5 7 4 5 10. 46 + 8 = 16 + 8 = 2 11. 26 + 8= 56 + 8= 1 8 12. 38 + 8= 18 + 8= 58 + 8= 2 13. 48 + 8 = 28 + 8 =- 78 + 8 = 6 7 14. 25 + 8 = 15 + 8 = 35 + 8 = _5 15. 65 + 8 = 55 + 8 = 75 + 8 = Copy and subtract: 48 1- 444 554 464 47.4 26^V 125 126 127 12.8 128 ELEMENTARY ARITHMETIC. 1. 6 is contained in 13 times and 2. 6 is contained in 13 — - and - 3. 6 is contained in 14 times and 4. 6 is contained in 14 and - - over, times. over. 5. 6 is contained in 15 6. 6 is contained in 15 7. 6 is contained in 1 6 8. 6 is contained in 16 9. 6 is contained in 17 10. 6 is contained in IT times and and - times and and - times and and - times. over. times. over times. over. 11. 6 is contained in 25 and 12. 6 is contained in 20 and 13. 6 is contained in 34 and times. times, times, times. 14. When milk costs 6^ a quart, for 27^ I can buy and quarts. 27^ ^ 6^ = 15. If books cost 6^ each, with 27^ I can buy — — books and have cents left. 27^ -^ 6^ = 16. When milk costs 6^ a quart, for 33^ I can buy and quarts. 33^ -^ 6^ = 17. If books cost 6^ each, with 33^ I can buy books and have cents left. 33^ -^ 6^ = Copy and multiply : 36 39 33 63 66 2i 2i 2i 2i 24 PART II. 129 1. $.8 + $.6, means . $.8 and $.6 =: 2. $1.6 - $.9, means . $1.6 less $.9 -= 3. $1.5 X 4, means . 4 times $1.5 = 4. $.8 X 21, means . 24- times . 5. $2.4 - $.8, means . $.8 are -. 6. $2.4 - 8, means . | of 7. I can change fourths to 8ths, to , to 8. One fourth is twentieths. -^ is twenty-fourths. 4- is thirty-seconds. 9. I can change fifths to lOths, to , to ? 10. One fifth is twenty-fifths. 4" i^ thirtieths, f are twenty-fifths. 11. George had a quarter of a dollar; he spent 1 tenth of a dollar; he had cents left. 12. Richard played ball half an hour, and he played "hide and seek" 10 minutes; in all he played minutes. 13. Helen practiced her music lesson from 7:30 to 8:45; she practiced hour and min- utes. 14. 34 are halves. 44 are . 2" ctxc ixciavco. -i^ 15. 3| are thirds. ' 4^ are . 16. 3|- are fourths. 4| are . 17. 3i are fifths. 4|- are . Copy and divide: 3qt.)64qt. 3 qt.)65 qt. 3 qt.)94 qt. 3 qt.)95 qt. 130 ELEMENTARY ARITHMETIC, 1. What day of the week is it? To-day is Fourteen days from to-day will be Fifteen days from to-day will be . Thirteen days from to-day will be . 2. January 1st, 1898, was Saturday; February 1st was ; March 1st was ; April 1st was . 3. John lives 2 miles from the schoolhouse; Peter lives 1 and 3 tenths miles from the school- house. How much farther is John's home from the schoolhouse than Peter's? It is . 4. Harvey rode on his bicycle 2 and 3 tenths miles: Ernest rode 3 times as far; Ernest rode 5. One fourth of 12.8 miles is . 6. Three fourths of 12.8 miles are ^ . 7. Twelve and 4 tenths miles are two thirds of miles. 8. Twelve and 4 tenths miles are one half of miles. 9. I am thinking of an oblong whose area is 12 square inches. It is 6 inches long. It is inches wide. 10. I am thinking- of an oblong whose area is 15 square inches. It is 5 inches long. It is inches wide. Copy and divide : 3)64 qt. 3 )65 qt. 3 )94 qt. 3 )95 qt. PART II. 131 5 eights are 40 6 sevens are 42 8 fives are 40 7 sixes are 42 5 nines are 45 9 fives are 45 1. Forty quarts are pecks. 2. Forty-two days are weeks. 3. Forty-two spoons are sets. 4. Forty-five ninths are wholes. 5. 10 gallons are quarts. 9 gallons = 6. 6 weeks are days. 5 weeks = 7. Forty inches are feet and . 8. Forty-five days are weeks and . 9. Forty-six quarts are gallons and 10. Six weeks and 4 days are days. 11. Three feet and 7 inches are inches. 12. Eleven bushels and 1 peck are pecks. 13. 2| are sixths. 3| are sixths. 14. 4| are sixths. 5| are sixths. Read first by column, then by line. 3 2's are . 3 3's are . 3 4's are 3 5's are . 3 6's are . 3. 7's are 3 8's are . 3 9's are . 3 lO's are Copy and add: 53i 522 431 353 48.2 21 643 603 505 30.3 521 281 294 661 42.1 132 ELEMENTARY ARITHMETIC. 1. Add 2 ft. 10 in. and 4 ft. 5 in. (a) Add 146 ft. 10 in. and 83 ft. 6 in. 2. From 16 subtract the sum of 4 and 8. (b) From 256 subtract the sum of 47 and 38. 3. Multiply 2 ft. 3 in. by 5. (c) Multiply 53 ft. 4 in. by 5. 4. Divide 42 feet by 6 feet. (d) Divide 444 feet by 6 feet. 5. Divide 42 feet by 6. (e) Divide 444 feet by 6. 6. At $5 a ton, 9 tons of coal cost . (f) At $125 each J 3 horses cost . 7. Three fourths of 12 dollars are dollars. (g) Three fourths of 120 dollars are dollars. 8. Twelve dollars are | of dollars. (h) One hundred and twenty dollars are f of dollars. 9. A lady bought 9 curtains at $5 eachj she gave the salesman 5 ten-dollar bills; she should receive in change . (i) A gentleman bought 4 horses at $120 each; he gave in payment 5 one-hundred-dollar bills ; he should receive in change dollars. Copy and subtract: 87i 436 526 636 34.6 24f 208 319 117 12.8 PART II. 133 1. Think of an oblong 3 feet by 10 feet. Tliink of it divided into 1-foot squares. The area of the oblong is square feet. 2. The perimeter of an oblong 3 feet by 10 feet is feet. 3. Think of a floor 6 ft. by 7 ft. Think of it divided into 1-foot squares. The area of a floor 6 ft. by 7 ft. is square feet. 4. The perimeter of a floor 6 ft. by 7 ft. is feet. 5. The first day of October, 1895, was Tuesday; the second Tuesday of October was the th day of the month; the third Tuesday was the th; the fourth Tuesday was the ; the fifth Tuesday was the . 6. The Mondays of September, 1895, were the 2nd, , , , and . 7. Harry rode 45 miles in 5 hours; he rode at the rate of miles an hour. 45 ^ 5 = 8. James rode 46 miles in 5 hours; he rode at the rate of miles an hour. 46 -^ 5 = 9. Richard rode 48 miles in 5 hours; he rode at the rate of miles an hour. 48 -^ 5 = 10. At 20^ a peck, 3 pecks of apples cost cents; 8^ pecks cost ■. Copy and multiply : 63i 521 741 831 92^ 2 2 2 2 2 134 ELEMENTARY ARITHMETIC. 1. A year that is not a leap-year is sometimes called a common year. In a common year there are 365 days. 365 days -^ 7 days = . In a common year there are weeks and day. 2. If the first day of a common year is Monday, the first day of the next year will be . 3. We may think of a year as beginning at any time and ending on the same day of the same month of the next year; tlms, it is a year from April 10, 1894, to April 10, 1895; it is a year from May 4, 1895, to May 4, 1896. 4. Any year in which there is a February 29th contains 366 days; all other years contain . 5. From February 10th of a leap-year to Feb- ruary 10th of the next year it is days. 366 days -^ 7 days = 6. If February 10th of a common year is Wednesday, February 10th of the next year will be . 7. If February 10th of a leap-year is Wednes- day, February 10th of the next year will be 8. From March Isfc of a leap-year to March 1st of the next year it is days. If March 1st of a leap-year is Monday, March 1st of the next year will be . Copy and divide : 4^)56^ 4^)96^ 4^)64^ 4^)104^ TART II 135 1. One half is 2. One fifth is 3. Three fifths are 4. Two fifths are - 5. Four fifths are tenths, tenths. tenths. — tenths. — tenths. 6. Acid 1 half and 1 fifth. 1 half is tenths. 1 fifth is tenths. — tenths and tenths are 7. Add 2 fifths and 1 half. 2 fifths are tenths. 1 half is tenths. — tenths and tenths are 8. From 4 fifths subtract 1 half. 4 fifths are tenths. 1 half is tenths. — tenths less tenths are tenths. tenths. tenths. 9. are One fifth of a dollar and 1 half of a dollar — tenths of a dollar. Copy and divide : 4 )56^ 4 )96^ 4)64^ 4)104^ 136 ELEMENTARY ARITHMETIC. E I I I I I I I I I I I I I r 'T 1 . -^ of an inch + I- of an inch = ^ -|- -^ _ 2 . 4^ of an inch — ^ of an inch = ^ — -i- = 3. I of an inch x 2 = -^ X 2 = 4. ^ of an inch x 2^ = i- X 2| = 5. 5 inches ^ 4^ of an inch = 5 -^ -|^ = 6. 4- of ai^ inch ^ 5 — ^ -^ 5 = 7. Draw a line 3^ inches long; erase from it inches; the line that is left is and inches long. S^ — 2^ = 8. Draw a line 34 inches long; erase from it 1| inches; the line that is left is and inches long. 3^ — 1-5 = 9. Harry drew an oblong; it was 1^ inches wide and l^^ inches long; its perimeter was and inches. 10. Arthur had a piece of silver wire; it was 14 inches long; he wished to divide into pieces 4- of an inch long; he could make such pieces and have of an inch left. 11. James had a piece of copper wire; it was 1.5 inches long; he divided it into three equal pieces; each piece was Copy and add: 24^ 324 32 163 m 245 long. 136 252 20.5 252 347 34.2 344 142 61.6 PART II. 137 12 nines are 108 11 nines are 99 9 twelves are 108 9 elevens are 99 1. Can you add column (a) in fifteen seconds, beginning at the top? 2. Can you add column (a) in fifteen seconds, beginning at a 9 9 b 2 9 c 4 9 d 6 9 e 9 6 the bottom? 9 9 9 9 9 3. Practice until I you can do 9 9 9 9 9 9 9 9 9 this with each column. 9 9 9 9 8 4. Ten nines are » 9 9 9 9 9 9 9 9 9 1 5. Eleven nines are . 9 9 9 9 9 6. Twelve nines are . 9 9 9 9 2 7. Twenty nines ! are . 9 9 9 9 9 9 9 9 9 8. 27 + 9 = 17 + 9 = 1 3 5 7 9 9. 37 + 9 = 57 + 9 = 4 9 10. 46 + 9 = 16 + 9 = 85 + 9 — 5 11. 26 + 9 =. 56 + 9 = 73 + 9 = 9 6 12. 38 + 9 =. 18 + 9 = 47 + 9 9 13. 48 + 9 = 28 + 9 = 64 + 9 = 14. 25 + 9 - 15 + 9 = 35 + 9 = 15. 65 + 9 = 45 + 9 = 75 + 9 = Copy and subtract: 754- 370 640 750 84 321 128 239 34' 7 31.6 138 ELEMENTARY ARITHMETIC . 1. 7 is contained in 15 times and over. 2. 7 is contained in 15 and times. 3. 7 is contained in 16 times and over. 4. 7 is contained in 16 — — and times. 5. 7 is contained in 18 times and over= 6. 7 is contained in 18 and times. 7. 7 is contained in 23 times and over. 8. 7 is contained in 23 and times. 9. 7 is contained in 30 times and over. 10. 7 is contained in 30 and — - times. 11. 7 is contained in 38 and times. . 12. 7 is contained in 43 and times. 13. 7 is contained in 45 and times. 14. 7 is contained in 40 and times. 15. 7 is contained in 50 and times. 16. Wiien milk is 7^ a quart, for 18^ I can buy and quarts. 18^ -^ 7^ = Read first by column, then by line. 4 2's are . 4 5's are . 4 8's are . 4 3's are . 4 6's are . 4 9's are ■. 4 4's are . 4 7's are . 4 lO's are . Copy and multiply : 43i 54i 72h 61i 92^ 3 3 3 3 3 PART II. 139 1. If a man's wages are $40 for 5 weeks, in one week he earns dollars. (a) If a man's wages are $215 for 5 months, how much does he earn in one month? 2. If 6 barrels of flour are worth $30, 2 barrels are worth dollars. (b) If 6 acres of land are Avorth $264, how much are 2 acres worth? 3. At 4^ each, for 32^ I can buy pencils. (c) At 4^ each, how many pencils can be bought for $8.24? 4. Forty-eight quarts are gallons. (d) How many gallons are 572 quarts? 5. Eighty pints are gallons. (e) How many gallons are 440 pints? 6. A grocer sold 2 barrels of apples at $2.30 each; he received for them . (f ) A farmer sold 8 barrels of apples at $2.30 each. How much should he receive for them? Read first by column, then by line. 5 2's are . 5 5's are — -. 5 8's are . 5 3's are . 5 6's are . 5 9's are . 5 4's are -. 5 7's are . 5 lO's are . Copy and divide: 5^ )65^ 5^ )115^ 5^)75^ 5^ )125^ — times 140 ELEMENTARY ARITHMETIC. 1. January 1st, 1897, was Friday. January 1st, 1898, was . January 1st, 1899, was . 2. July 4th, 1897, was Sunday. July 4tli, 1898, was . July 4tli, 1899, was . 3. December 25tli, 1897, was Saturday. De- cember 25tli, 1898, was . December 25th, 1899, was . 4. A man paid 6 hundred dollars for a piece of land; he spent 1 hundred dollars in improving it, and sold it for 9 hundred dollars; he gained — ■■ — hundred dollars. (a) A man paid 614 dollars for a piece of land; he spent 136 dollars in improving it, and sold it for 975 dollars; he gained . 5 . A man paid 5 hundred dollars for a house ; he paid 1 hundred dollars for repairing it; he sold the house for 8 hundred dollars; he gained hundred dollars. 6. Mary bought 5^ worth of pens, 10^ worth of paper, and 3^ worth of gum; if she gave the salesman a quarter of a dollar, how much change should she receive? 7. Peter rode 36 miles in 4 hours; he rode at the rate of miles per hour. 36 -^ 4 = 8. Paul rode 37 miles in 4 hours; he rode at the rate of miles per hour. 37 ^ 4 = Copy and divide: 5)65(^ 5)115^ 5)75^ 5)125^ PART II 141 6 eights are 48 6 nines are 54 8 sixes are 48 9 sixes are 54 7 eights are 56 8 sevens are 56 7 sevens are 49 1. Forty-eight quarts are 2. Forty-nine days are — 3. Fifty-four spoons are 4. Fifty-six days are — 5. 7 pecks are — 6. 8 Aveeks are — — pecks, weeks. - sets. weeks. 7. Fifty inches are 8. Fifty days are - 9. Fifty quarts are 10. Seven weeks and 3 days are 11. Four feet and 5 inches are - quarts. 6 pecks = days. 7 weeks = — feet and inches. — weeks and day. — pecks and quarts. days. — inches. 12. Twelve bushels and 3 pecks are pecks. 13. 2f are 14. 4| are sevenths. 3^ are sevenths. 5f are sevenths, sevenths. Read first by column, then by line. 6 2's are . 6 5's are . 6 8's are 6 3's are . 6 6's are . 6 9's are 6 4's are . 6 7's are . 6 lO's are Copy and add: 33-1- 526 628 731 83.6 25 234 204 229 21.4 41|- 312 325 402 23.5 142 ELEMENTARY ARITHMETIC. 1. Add 5 gal. 2 qt. and 5 gal. 3 qt. (a) Add 124 gal. 2 qt. and 31 gal. 3 qt. 2. From tlie sum of 9 and 5, subtract 10. (b) From the sum of 236 and 72, subtract 104. 3. Multiply 6 by 3 and to the product add 6. (c) Multiply 125 by 3 and to the product add 125. 4. Divide 12 by 2 and multiply the quotient by3. _ (d) Divide 256 by 2 and multiply the quotient by 3. 5. Two thirds of 18 inches are inches. (e) Two thirds of 126 inches are inches. 6. Eighteen inches are f of inches. (f ) One hundred and twenty-six inches are f of inches. 7. A man paid 8 hundred dollars for a house; he repaired it at a cost of 4 hundred dollars, and sold it for 10 hundred dollars; he lost hun- dred dollars. (g) A man paid 836 dollars for a house; he repaired it at a cost of 124 dollars and sold it for Copy lXcXIDj lie J.UC5U and subtract: 671 408 509 706 80.4 34| 240 360 450 55 PART II. 143 1. Observe the diagram given below. It is an oblong 2 inches by 3^ inches. Think of it as made up of two rows of 1-inch squares with a piece of another square at one end of each row. The piece is of a square inch. In each row there are and square inches. 3| sq. in. X 2 = . The area of an oblong 2 inches by 3^ inches is . M ill T— t liu. lin. 1 in. d • r-l 2. Draw an oblong 4^ inches by 2 inches. Divide it as far as possible into 1-inch squares. It contains two rows of figures. In each row there are and square inches. The area of an oblong 4^ inches by 2 inches is . Copy and multiply: 31i 41^ 4 4 5U 611 4 71i 4 144 ELEMENTARY ARITHMETIC. 1. February 1st, 1897, was Monday. February 1st, 1898, was . February 1st, 1899, was 2. April 1st, 1897, was Thursday. April 1st, 1898, was . April 1st, 1899, was -. 3. May 1st, 1897, was Saturday. June 1st, 1897, was . 4. Two thirds of 12 are one half of . 5. One half of 16 is two thirds of . 6. Two thirds of 15 are one half of 7. One half of 20 is two thirds of - 8. Peter rode 56 miles in 7 hours; he rode at the rate of miles an hour. 9. Harris rode 57 miles in 7 hours; he rode at the rate of miles an hour. 10. Adam rode 59 miles in 7 hours; he rode at the rate of miles an hour. 11. 22 thirds are . 22 fourths are 12. 22 fifths are . 22 sixths are - 13. 24 fifths are . 25 sixths are - 14. I am thinking of a triangle, each side of. which is 9 inches. The perimeter of this triangle is inches. Copy and divide: |6)$126 $6)$186 $6)$192 $6)$204 PART II. 145 1. One fourth is 2. One sixth is - twelfths. — twelfths. 3. Three fourths are twelfths. 4. Five sixths are twelfths. 5. Add 1 fourth and 1 sixth. 1 fourth is twelfths. 1 sixth is twelfths. — twelfths and twelfths are twelfths. 6. Add 3 fourths and 1 sixth. 3 fourths are twelfths. 1 sixth is twelfths. — twelfths and twelfths are — twelfths. 7. From 5 sixths subtract 1 fourth. 5 sixths are twelfths. 1 fourth is twelfths. — twelfths less twelfths are — — twelfths. 8. One sixth of a foot and 1 fourth of a foot are twelfths of a foot. 9. Three fourths of a foot less 1 sixth of a foot are twelfths of a foot. Copy and divide : 6)$126 6)$186 6 )$192 6 )$204 146 ELEMENTARY ARITHMETIC. 1. 2. 3. 4. 5. 6. I- of a foot + ^ of a foot = I- of a foot — |- of a foot = 4 of a foot X 3 = 4- of a foot X ^ 1 o4 = 2 feet ^ I of a foot of a foot 1 -I- 1 1 T |x3 = TT X O-o- 1 T 7. Draw a line 4^ feet long; feet long; together the Imes are feet long. 4| + 2| = draw another 2- — and 41 — 21 8. Draw a Ime 4|- feet long; erase from it 2|^ feet; the line that is left is and feet long. 4|- - 2| = 4|- + 2| == 9. The perimeter of a l-|^-foot square is feet. U + U + U+U= U x 4 =. 10. Richard had a piece of silver wire 2|- feet long ; he wished to divide it into pieces -g- of a foot — such pieces and have long; he could make — of a foot left. 11. Ned had a piece of rope 11^ feet long; he divided it into 2 equal parts ; each part was and feet long. lli-^2= ^ of lU - 12. 12 ft. 13. 14 ft. 14. 12 ft. 2= 13 ft. - 2 15 ft. 1 '^ hit. 2 2 = 2 = 151 ft. - 2 == 13 ft. - 3 = 131 ft. Copy and add: 482 31 214 22| 224 24| 346 252 172 425 370 125 34.3 25.3 12.4 PART II. 147 REVIEW. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. ' + "2" + 1 _ T — jL _ 6 ~ i 1 _ To" ~ 1 _ T^ - + i = 1 T 1 I 1 _ T ' T — 1 I 1 _ ■S" I TY - 111 — T ^ ¥ — 1 I 1 _ T r i-g- - "5" + T^ 1 _ + 1 _ 1 1 2 1 a 1 1 3 1 3 1, 3 1 1 T 1 T 1 5 1 1 _ T — X — 6 ~~ 1 — 8 ~ 1 _ TTT - 1 _ TW ~ 1 _ T ~ X — 9 ~ 1 _ 1 2 - 1 _ 8 ~ 1 _ 1 _ TTT - 1 _ y^ - 1 1 2 1 2 1 "2" 1 2 1 T 1 T 5 1 X 4::= X 5 = X 3 = X G = X 7- 4x6 4 x 4: = i X o X 8 = X 5 = X 10:. X 18::: 13. Can you read the first 12 lines on this page, completing each statement correctly, in 2 minutes? Try to do this. 14. I can change halves to 4ths, to — , to , to , to . 15. One half is twentieths. fortieths. 16. One half is — dredths. 1 "2" IS fiftieths. 4- is hun- Copy and subtract: 37 518 416 25| 240 150 617 460 71.8 36. 148 ELEMENTARY ARITHMETIC. 1. 6- 1 2 2. 5 1 3. 4- 1 4. 4 1 3 5. 3 3 4, means 6, means ■I, means 5, means ^, means 4 J means I, means 4, means I, means 3, means -^ IS con -^ IS con iof — 6. One half of -j^ is 7. One half of ^ is -. loi 2 ^-^ Y'ff 1^ h of yV is 8. 4- is contained in 2 9. |- is contained in 2 10. ^ is contained in 2 11. -i^ is contained in 2 12. ^ is contained in 3 times, times, times, times, times. 1 T X 5 J_ 6 J_ 9 1 13. 14. 15. 16. 2| 1 3 1 T 1 5 6 - ^ 2| 1 _ 3 ~ 1 _ T — J_ _ 5 ~ X — 6 ~ 34 -^ Ri «->-/(- *> 1 ^1 3| ^ 3 Or Q5 Copy and multiply : 324 22-^- 424- 42|- 421 5 PART II. 149 REVIEW. 12_|_1_ 2_1_ 2 ^ A — 2.| + i= i-i= |x5 = 3.| + A= |-A= Ix6 = 4.34_1_ 3_1_ 3v/2 — K3il_ 3_1_ 3v^ — C 2 \ 1 — 2_1_ 2w4._ 721 3 _ 2_3_ 2 Ky a — '•"51 TO"— 5" TIJ— 5-^^ — 8. 1 + I = (Change to 6tlis.) i + I = 9. 4- - I = (Change to .) | - | = 10. I + ^ = (Change to .) | + i - 11. I - I = (Change to .) | - i = TESTS. If pupils have mastered the work up to this point, they will have no difficulty with the following. The real test is the pupil's power to do that which he has not done before. (a) Can you add ^ and i? (Change to .) (b) Can you subtract ^ from | ? (Change to .) (c) Can you add f and ^2 (Change to .) (d) Can you add i and -^2 ^ and -^-^2 (e) Multiply I by^7. | by 12. | by 6^. (f) Multiply 8 1 by 6. | by 60. 4 by 7|. (g) Multiply 6| by 8. | by 20. | by 40. Copy and divide : $3)$127 $3)$154 $3)$217 S3)$184 150 ELEMENTARY ARITHMETIC. 1. Divide 2 thirds by 1 fourth. 2 thirds are twelfths. 1 fourth is twelfths. 12ths in 12ths and times. 2. Divide 3 fourths by 1 third. 3 fourths are 12ths. 1 third is twelfths. 12ths in 12ths and - — times. 3. Divide 1 half by 1 fifth. 1 half is tenths. 1 fifth is tenths. tenths in tenths and — times. 4. Divide ^ by ^3. (Change to sixths.) 5. Divide -f- by \. (Change to eighths.) 6. Divide -| by -f- (Change to ninths.) 7. Divide -|- by -^. (Change to tenths.) 8. -I -^- YQ- = Yjj oi £1 dollar is contained in f of a dollar times. 9- T "^ TT — tV of ^ foot is contained in | of a foot times. 10. i ^ -J- = |- of a pie is contained in 1^ of a pie times. 11. |. ^ |- = ^ of a foot are contained in 3^ of a foot and times. Copy and divide : 4)$129 4)^169 4 )$2Q9 4)$210 PART II. 151 7 nines are 63 9 eights are 72 9 sevens are 63 8 nines are 72 8 eights are 64 9 nines are 81 '■&■' 1. Sixty-three days are weeks. 2. Sixty-four quarts are pecks. 3. Seventy-two pints are gallons. 4. Eighty-one ninths are Avholes. 5. Ninety inches are feet and inches. 6. Ninety days are weeks and days. 7. Nine weeks and 2 days are days. 8. Seven feet and 5 inches are inches. Read first by column, then by line. 7 2's are . 7 5's are . 7 8's are 7 3's are . 7 6's are . 7 9's are 7 4's aj^e . 7 7's are . 7 lO's are 8 2's are . 8 5's are . 8 8's are 8 3's are . 8 6's are . 8 9's are 8 4's are . 8 7's are . 8 lO's are 9 5's are . 9 8's are 9 6's are . 9 9's are 9 7's are . 9 lO's are 9 2's are - 9 3's are - . 9 4's Cop y and add: 26| 432 12 200 20i 148 546 342 36.2 84 108 31.3 225 705 32.6 152 ELEMENTARY ARITHMETIC. 2 times 2 3 times 2 4 times 2 5 times 2 6 times 2 7 times 2 8 times 2 9 times 2 2 times 5 3 times 5 4 times 5 5 times 5 6 times 5 7 times 5 8 times 5 9 times 5 2 times 8 3 times 8 4 times 8 5 times 8 6 times 8 7 times 8 8 times 8 9 times 8 are 4. are 6. are 8. are 10. are 12. are 14. are 16. are 18. are 10. are 15. are 20. are 25. are 30. are 35. are 40. are 45. are 16. are 24. are 32. are 40. are 48. are 56. are 64. are 72. TABLES. 2 times 3 are 6. 3 times 3 are 9. 4 times 3 are 12. 5 times 3 are 15. 6 times 3 are 18. 7 times 3 are 21. 8 times 3 are 24. 9 times 3 are 27. 2 times 6 3 times 6 4 times 6 5 times 6 6 times 6 7 times 6 8 times 6 9 times 6 2 times 9 3 times 9 4 times 9 5 times 9 6 times 9 7 times 9 8 times 9 9 times 9 are 12. are 18. are 24. are 30. are 36. are 42. are 48. are 54. are 18. are 27. are 36. are 45. are 54. are 63. are 72. are 81. 2 times 4 3 times 4 4 times 4 5 times 4 6 times 4 7 times 4 8 times 4 9 times 4 are 8. are 12. are 16. are 20. are 24. are 28. are 32. are 36. 2 times 3 times 4 times 5 times 6 times 7 times 8 times 9 times 9 and 4 8 and 5 7 and 6 9 and 5 9 and 6 8 and 7 9 and 7 9 and 8 7 are 14. 7 are 21. 7 are 28. 7 are 35. 7 are 42. 7 are 49. 7 are 56. 7 are 63. are 13. are 13. are 13. are 14. are 15. are 15. are 16. are 1 7. PART III. DECIMALS TENTHS. 1. 6^ and 2^ are cents. 2. .6 and .2 are tenths. 3. 6^ less 2^ are cents. 4. .6 less .2 are tenths. 5. 4^ X 2, means, ^ times Jf(^; 2 times 4^ are 6. .4x2, means, 2 times .Jf; 2 times .4 are 7. 6^ -^ 2^, means, y^nt^ Aoi'; ma?i?/ /zmes 2(^ are contained in 6^; 2^ are contained in 6^ times. 8. .6 -h .2, means, find Jioiv many times .2 are contained in .6 ; .2 are contained in .6 times. 9. 6^ -^ 2, means, ^?icZ one half of .6^; one half of 6^ is cents. 10. .6^2, means, find one half of .6 ; one half of .G is ■ tenths. Copy and multiply : 244- 23.6 24.8 34.9 231 4 2 2 2 G 153 154 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. One tenth of a dollar = dime. $.2 2. One tenth of a dollar = cents. $.3 3. Three tenths of a dollar = dhnes. $.5 4. Four tenths of a dollar = cents. $.6 5. Fifty cents = dimes. Seventy cents 6. Sixty cents = tenths of a dollar. 7. Eight dimes = tenths of a dollar. 8. $.8 = dimes. $.8 = cents. 9. %.d = cents. $.9 = dimes. 10. $1.2 = dollar and dimes. $1.4 11. $1.2 := dimes. $1.4 = dimes. 12. $1.2 == dollar and cents. $1.5 13. Mary had $.4 in her pocket and $.3 in her bank ; in both she had . 14. Jane had $.9; she spent $.3; she then had . 15. Sarah jwd $.4 for each of three books; for all she paid . 16. Alice had $.8 with which to buy tea at $.4 a pound ; she 'could buy pounds. 17. Maude paid $.6 for two pounds of coffee; one pound cost . Copy and divide : $.3 )$24.6^ $.4 )$25.2 $.5 )$27.5 times *Observe that the puijil is required to find how many times 3 tenths are contained in 216 tenths — 3 dimes in 246 dimes. PART III. 155 DECIMALS TENTHS. 1 , .5 + 'S. (To be read, 5 tenths plus 3 tenths.) .5 --h .3, means, .5 and .3. .5 and .3 are tenths. Arthur earned .5 of a dollar Monday and .3 of a dollar Tuesday; in both days he earned 2. .9 — .4. (To be read, .9 tenths minus 4 tenths.) .9 — .4, means, .9 less .4. .9 less .4 are tenths. Harry had .9 of a dollar; he spent .4 of a dollar; he then had . 3. .4x3. (To be read, 4 tenths multiplied by 3.) .4x3, means, S times .Jf, 3 times .4 are tenths. If one yard of ribbon is worth .4 of a dollar, 3 yards are worth tenths, or and tenths dollars. 4. 1.2 -^ .4. (To be read, 12 tenths divided by 4 tenths.) 1.2 ^ .4, means, find how many times .Jf are con- tained in 1.2, A are contained in 1.2 . James had 1.2 dollars with which to buy tea at .4 of a dollar a pound ; he could buy pounds. 5. 1.2 -^ 4. (To be read, 12 tenths divided by 4.) 1.2 H- 4, means, find one fourth of 1.2. One fourth of 1.2 is tenths. William jDaid 1.2 dollars for 4 pounds of coffee; one pound cost tenths of a dollar. Copy and divide : 3)$24.6 4)$25.2 5)$27.5 156 ELEMENTARY ARITHMETIC. DECIMALS TEXTHS. 1. The sum of 5.2 and 4.3 ls . 3.5 + 3.5 = 2. The sum of 4.6 and 4.6 is . 5.Q + 5.6 = 3. The sum of 3.6 and 4.6 is . 3.7 + 3.7 = 4. The sum of 4.7 and 5.7 is . 4.8 + 5.8 ^ 5. 10.2 + 10.2= 10.8 + 10.8 = 6. 10.2 + 12.2 = 20.3 + 20.3 = 7. 20.9 + 20.9 = 20.6 + 20.7 = 8. 23.4 + 20.4 = 23.5 + 22.4 = 9. 23.6 + 22.6 = 23.7 + 32.7 = 10. The sum of two and six tenths, and four and three tenths is — . 11. Tlie sum of eight and three tenths, and four and two tenths is . 12. Joseph paid $6.5 for a suit of clothes and $2.2 for a hat; for both he paid — . 13. In the month of September the rainfall in Chicago was 3.4 inches; in October it was 2.6 inches; in both months it was . (a) Find the sum of 25.3, 34, and 24.2. (b) Find the sum of 31.3, 25, and 32.2. (c) Find the sum of 26.4, 35, and 12.6". (d) Find the sum of 25.5, 37, and 23.4. (e) Find the sum of 31.2, 44, and 20.5. (f ) Find the sum of 42.5, 36, and 22.2. (g) Find the sum of 35.3, 28, and 32.4. (h) Find the sum of 34.2, 34, and 34.3. PART III. 157 DECIMALS TENTHS. 1. The difference of 8.6 and 4.3 is . 2. The difference of 8.2 and .6 is . 3. The difference of 8 and 4.2 is . 4. The difference of 8.5 and 1.6 is . 5. 20.6 - 10.2 = 20.6 + 10.2 = 6. 15.5 - 10.3 = 15.5 + 10.3 = 7. 20.2 - 10.6 = 20.2 + 10.6 = 8. 23.8 - 10.5= 23.8 + 10.5 = 9. Cyrus had $4.6; he paid $2.5 for a book; he then had . 6 = dollars and cents. $2.5 = dollars and cents. $2.1 = - — - dollars and cents. 10. A farmer received $4.7 for a sheep and $3.5 for a pig; for both he received and — — tenths dollars. $4.7 = dollars and cents. $3.5 = dollars and cents. .2 = dollars and cents. (a) From forty -three and eight tenths dollars take one and four tenths dollars. (b) From twenty-five and three tenths dollars take twelve and two tenths dollars. (c) From 75.3 subtract 28.1. (d) From 36.2 subtract 12.4. (e) From 84.7 subtract 2.9. 158 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. The product of 8.3 and 2 is 2. The product of 3.5 and 2 is 3. The product of 2.4 and 3 is 4. The product of 1.5 and 4 is 5. 3.2 X 3= 3.2 + 3= 3.2-3 = 6. 2.1 X 4 = 2.1 f .4 = 2.1 - A = 7. 2.3 X 4= 2.3 + 4= 2.3- .4 = 8. 2.5 X 5= 2.5 + .5= 2.5 - .5 = 9. At $4.5 a cord, 3 cords of wood will cost . $6.5x3 = 10. A man had $5.3 in one pocket and $3.9 in another ; in both he had . 11. Chester had $6.3; Elmer had $5.1; Chester had dollars more than Elmer. 12. 15 tenth-dollars = and tenths dollars. 13. 2 and 5 tenths dollars = tenth-dollars. 14. 35 tenth-dollars = and tenths dollars. 15. 1 and 8 tenths dollars = tenth-dollars. (a) Multiply twenty-four and 5 tenths dollars by 5. (b) Multiply thirty-six and 4 tenths dollars by 3. (c) Multiply forty-two and 3 tenths dollars by 4. (d) Find the product of 37.4 and 2. (e) Find the product of 25.3 and 3. PART III. 159 DECIMALS TEISTTHS. 1. The quotient of $4.5 divided by $.5 is 2. The quotient of $4.5 divided by 5 is — 3. The quotient of $3.2 divided by $.8 is 4. The quotient of $3.2 divided by 8 is — 5. The quotient of $4.8 divided by $.6 is 6. The quotient of $4.8 divided by 6 is — 7. The quotient of $3.0 divided by $.5 is 8. The quotient of $3.0 divided by 5 is - 9. The sum of two numbers is 15; one of the numbers is 10 ; the other number is . 10. The sum of two numbers is 7.5; one of the numbers is 3.2; the other number is . 11. The difference of two numbers is 4; the greater number is 12 ; the less number is . 12. The difference of two numbers is 3.4; the greater number is 12.8; the less number is . 13. The difference of two numbers is 5; the less number is 8 ; the greater number is . 14. The difference of two numbers is 5.3; the less number is 8.3; the greater number is . (a) Divide sixty-four and two tenths by two tenths. (b) Divide 48 and three tenths by three tenths, (c) Divide 36 and eight tenths by four tenths. (d) Divide 73 and five tenths by five tenths. 160 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. Eead the first ten lines twice; the first time read 1.2, twelve tenths ; the second time read it, one and two tenths, etc 1. One half of 1.2 is 2. One third of 1.2 is — 3. Two thirds of 1.2 are 4. One fourth of 1.2 is - 5. Three fourths of 1.2 are 6. .8 is what part of 1.2? 7. .9 is what part of 1.2? 8. .3 is what part of 1.2? 9. 1.2 is what part of 1.6? 10. 1.2 is what part of 3.6? 1.2 1.2 1.2 1.2 1.2 = iof — ¥ 1 2 i^of f of iof iof A of 1.2? .6 of 1.2? 1.2 of 2.4? 1.2 of 1.8? 1.2 of 4.8? 11. One fourth of 2 (2.0) is 1 2 . Three fourths of 2 are — 13. One fifth of 2 (2.0) is - 14. Three fifths of 2 are — 15. .4 is of 2. .5 is 16. .8 is of 2. — tenths. and tenths. — tenths. and tenths. of 2. Lois of 2. (a) Divide forty-six and four tenths by 2. (b) Divide fifty-two and six tenths by 2. (c) Divide forty-five and four tenths by 2. (d) Divide sixty-three and nine tenths by 3. (e) Divide seventy-two and six tenths by 3. (f) Divide eighty-four and four tenths by 4. (g) Divide ninety-six and fiYQ tenths by 5. PART III. 161 DECIMALS TEXTHS. 1. One tenth of 20 is . 2. One tenth of 30 is . 3. One tenth of 40 is . 4. One tenth of 50 is 5. Three tenths of 20 are 6. Three tenths of 30 are 7. Three tenths of 40 are 8. Seven tenths of 20 are .2 of 20 =: .2 of 30 = .2 of 40 = .2 of 50 = .4 of 20 = .4 of 30 = .4 of 40 = .6 of 20 = 9. .1 of 24 is - 10. .1 of 32 is 11. .1 of 43 is - 12. .1 of 23 = 13. .1 of 12 = 14. .1 of 33 = 15. .1 of 42 = and — and — and — .2 of 23 .2 of 12 .2 of 33 .2 of 42 tenths, tenths, tenths. .2 of 24 .2 of 32 .2 of 43 .3 of 23 .3 of 12 .3 of 33 .3 of 42 16. 1 tenth of 240 = 17.1 tenth of 250 = 18. 1 tenth of 225 = 19. 1 tenth of 235 = (a) Find .2 of 240. (b) Find .2 of 250. (c) Find .2 of 225. (d) Find .2 of 235c (e) Add $324.2, $123.1, and $231.3. (f) Add $140.4, $203.2, and $132.2. (g) Add $222.2, $101.1, and $303.3. ■(h) Add $158.2, $300.2, and $121.3. (i) Add $325.8, $234.3, and $286.6. (j) Add $165.5, $248.4, and $244.4. ?^ -^r >>rrv T%i£T' x^rrgfyim nr^ -3V - 5» 2? :ci- :! if t:^ .f $^ ^ if SiS 5? . — '~2t %> — _ ^ * it- '-iL ^ » — (r _-^ 45^ 3 'C'f 2 in,. — 13- Six Ter^5 :f f^ = .7 :z f i: = 14- SixT.Ti- : T-= .7'j^2i:i = 7-i i^ f To. mil _ :z ^- G£ lo. _ . > GE :fr5- 16? JL^ TEJTTME. 1. .? 2. ^. 3. V — 4. 5. ?2r' 6. jd ' 7. ?:^ 8. -$_- feid .1 •'"£ ?f5--" . ' ' ^ i j^ ^^ ^-xTt, 9. $6 X J- "-_^-. fni : -.-Til ^Gii $^. 10. ?' 11. t^ 12. $S A ,-;^ iS>.= 13. > = ^ ^ = f 14. >_. 1 = ^:1 X J = |1Z 15. .?- ..: -2 = #7 * .5 ^ f 14 . _.»j- JJ^ -7--:,7!T m 16. |2 - ^ - 18. i:. - _ _. 11^ X ±. - -S12 X 2,4 = » e » 1- ^ - - T 4. : ^ - _4 X -4. 164 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. Multiply $275 by 2.3. This means, >i6^ tioo times $27 5 lolus three tenths of $27S. Operation No. 1. Explanation. ^275 Two times $275 are $550. 2.3 One tenth of $275 is $27.5. Three tenths of $275 are $82.5. $550. (2 times $275.) $550 + $82.5 = $632.5. 1.5 (.3 of $275.) $632.5 (2.3 times $275.) Operation No. 2. Explanation. 1275^ One tenth of $275 is $27.5. Three tenths of $275 are $82.5. Two times $275 are $550. 2.3 $82.5 (.3 of $275.) 1550 + $82.5 :::. $632.5. $550. (2 times $275.) $632.5 (2.3 times $275.) SUGGESTED NUMBER STORY. If one acre of land is worth $275, 1 tenth of an acre is worth — 3 tenths of an acre are worth 2 acres are worth . 2.3 acres are worth . (a) Multiply $245 by 2.3. (b) $146 x 2.3 = (c) Multiply $234 by 3.2. (d) $156 x 3.2 = (e) Divide 25.8 by .2. (f ) Divide 37.6 by .2. (g) Divide 36.5 by .5. (h) Divide 48.5 by .5. PART III. 165 DECIMALS TENTHS. 1. Victor lives 3.4 miles north of the Court House; Harry lives 2.3 miles south of the Court House ; from Victor's home to Harry's home it is miles. (a) William lives 27.4 miles north of Wauke- gan; Henry lives 46.5 miles south of Waukegan. How far is it from William's home to Henry's home ? 2. Mr. Dow lives 2.4 miles west of Chicago; Mr. Just lives 5.6 miles west of Chicago; from Mr. Dow's home to Mr. Just's home it is miles. (b) Mr. Jones lives 24.3 miles west of Chicago; Mr. Adams lives 51.7 miles west of Chicago. How far is it from Mr. Jones's home to Mr. Adams's home ? 3. Jane lives 2.4 miles south of the Chicago post-office; Helen lives 3.5 miles south of Jane's home; from the Chicago post-office to Helen's home it is miles. (c) Mrs. Smith lives 17.3 miles south of the Chicago post-office; Mrs. Brown lives 24.5 miles south of Mrs. Smith's home. How far is it from the Chicago post-office to Mrs. Brown's home? (d) Divide 75.8 by 2. (e) Divide 85.6 by 2. (f ) Divide 46.5 by 5. (g) Divide 94.5 by 5. (h) Divide 61.5 by 5. (i) Divide 56.5 by 5. 166 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. Sarah paid $1.2 for some books that cost $.3 each; there were books. I found the number of books that Sarah bought by finding how many times $.3 is contained in $1.2. $.3 is con- tained in $1.2 times. Show upon the black- board how this would appear as an example in division. $.4 )$1.6 $.2 )$2.4 $.2 )$4.6 $.5 )$7.5 (a) Sarah's mother paid $27.6 for some chick- ens that cost $.3 each. How many chickens did she buy? I can find the number of chickens by finding how many times — . 2. John paid $1.2 for 3 second readers; each reader cost . I found the cost of 1 reader by finding 1 of $1.2. ^ of $1.2 is . Show upon the blackboard how this would appear as an example in division. 4 )$1.6 2 )$2.4 2)$4.6 5 )$7.5 (b) John's father paid $34.5 for 3 tons of hay. How much did one ton cost? I can find the cost of one ton by finding — -. (c) Add 421.6, 135.3, and 264.5. (d) Add 142.6, 25.4, and 391.5. (e) Add 204.6, 48.3, and 162.7. PART III. 167 DECIMALS TENTHS. 1. Henry paid $4 for some young clucks at $.2 each ; there were ducks. I found the num- ber of ducks that Henry bought by finding how many times . Show upon tlie black- board how this woukl appear as an example in division. $.2 )$6.Q $.4 )$8.Q $.2 )$10. $.5 )$1Q. $.2)$8. (a) Henry's father paid $48 for some fence posts that cost $.2 each. How many posts? 2. Jane paid $6 for 4 yards of velvet; each yard cost . I found the cost of one yard by finding J of . Show upon the black- board how this would appear as an example in division. 2 )$5.Q 4 )$1Q.Q 2 )$7. 2 )$9. 4 )$2. (b) Jane's mother paid $26 for 4 curtains. How much did one curtain cost? (c) Mr. Curtis paid $17 for 5 barrels of flour. How much did one barrel cost? (d) If two acres of land are worth $175, how much is one acre worth? (e) From 124.2 subtract 18.5. (f) From 135| subtract 112.1. (g) From 1641 subtract 122.4. (h) From 298f subtract 175.7. 168 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. William paid $2.3 for a pair of shoes; at the same rate 3 pairs of shoes would cost . I found the cost of 3 pairs by multiplying . Show upon the blackboard how this would appear as an example in multiplication. $2.3 $3.4 $2.5 $3.5 $6.2 2 2 2 2 3 (a) William's father paid $36.5 for a cow. At the same rate, how much would 3 cows cost ? 2. Mary paid $1.5 for 3 dozen oranges; one dozen oranges cost . I found the cost of one dozen by finding . Show upon the blackboard how this would appear as an example in division. 5 )$2.5 4 )$1.6 3 )$1.8 2 )$6.4 2)$5.4 (b) Mary's mother paid $27.5 for 5 chairs. How much did one chair cost ? (c) Multiply $325 by 2.2. (d) Multiply $124 by 1.3. (e) Multiply $426 by 3.4. (f) Multiply $321 by 3.4. (g) Multiply $347 by 4.3. (h) Multiply $252 by 4.3. (i) Multiply $212 by 1.5. (j) Multiply $140 by 2.1. PART III. 169 DECIMALS TENTHS. 1. Alice paid $2.5 for ribbon that cost $.5 a yard; she bought yards. I found the num- ber of yards by finding -. Show upon the blackboard how this would appear as an ex- ample in division. |.5 )$2.5 $.3 )$1.8 $.2 )$3.6 $.2 )$5.2 $.2 )$4.6 (a) Alice's mother paid $27.6 for a carpet that cost $.6 a yard. How many yards did she buy? 2. Peter paid $1.3 for a hat; at the same rate 3 hats would cost . I found the cost of of 3 hats by multiplying . I could find the cost of 4 hats by multiplying • . Show upon the blackboard how these would appear as examples in multiplication. $2.4 $2.5 $2.6 $2.7 $2.8 $2.9 2 2 2 2 2 2 (b) Peter's father paid $74.6 for a horse; at the same rate how much would 4 horses cost? (c) Divide 28.8 by .4. (d) Divide 29.6 by .4. (e) Divide 37.5 by .5. (f ) Divide 62.5 by .5. (g) Divide 25.2 by .6. (h) Divide 26.4 by .6. 170 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. Mr. Brown had 1.8 acres of land which he divided into lots, each containing .3 of an acre; there were lots. I found the number of lots by finding . Show upon the blackboard how this would appear as an example in division. .3 of an acre) 1.5 acres 5 of an acre) 3. 5 acres .4 of an acre) 2. 4 acres .6 of an acre) 4. 2 acres (a) Mr. Lyon had 46.8 acres of land which he divided into lots, each containing .3 of an acre. How many lots ? 2. Mr. Nichols had 1.8 acres of land which he divided into 3 equal parts ; each lot contained ^ . I found the amount of land in each lot by finding . Show upon the black- board how this would appear as an example in division. 3)1.5 acres 5)3.5 acres 4)8.4 acres 3)6.6 acres (b) Mr. Toll had 48.6 acres of land which he divided into three equal lots. How many acres in each lot ? (c) Divide 24.8 by 4. (d) Divide 25.2 by 4. (e) Divide 36.5 by 5. (f) Divide 38.5 by 5. (g) Divide 47.6 by 4. (h) Divide 51.2 by 4. (i) Divide 39.5 by 5. (j) Divide 42.5 by 5. PART III. 171 DECIMALS TENTHS. 1. Robert had $1.2; Peter liad ^ as much; Peter had . (a) Mr. Ford had $64.2; Mr. Davis had I as much. How much money did Mr. Davis have? 2. Mr. Frank's hat cost $1.2; this was 1 as much as his coat cost; his coat cost . They both cost . (b) A harness cost $24.5; this was 1 as much as a horse cost. How much did the horse cost? How much did both together cost? 3. Alice's hat cost $1.2; her gloves cost f as much; her gloves cost ; both together cost (c) Mr. Pratt's buggy cost $136.5; his horse cost f as much. How much did his horse cost? How much did both together cost? '&' 4. Verne's gloves cost $1.2; this was f as much as her hat cost; her hat cost ; both together cost . Mrs. Hill's new curtains cost $85.4; this was f as much as her carpets cost. (d) How much did the carpets cost? (e) How much did both together cost? (f) Add 27.4, 36.3, 25.7, and 13.2. (g) Add 12.5, 14.2, 15.3, and 10.2. (h) Add 22.2, 33.3, 44.4, and 55.5. 172 ELEMENTARY ARITHMETIC. DECIMALS TENTHS. 1. If 2 bushels of wheat are worth $1.6, 3 bushels of wheat are worth . (a) If 2 tons of bran are worth $28.8, how much are 3 tons of bran worth ? 2. If 3 bushels of apples are worth $1.8, 2 bushels of apples are worth . (b) If 3 tons of oil meal are worth $73.5, how much are 2 tons of oil meal worth ? 3. If 3 bushels of corn are worth $1.2, 4 bush- els of corn are worth . (c) If 3 tons of nails are worth $106.5, how much are 4 tons of nails worth? 4. $60 X .2 = (d) $740 X .2 = 5. $63 X .2 =- (e) $745 x .2 = 6. $5.4 X 2 := (f) $83.6 x 2 = 7. $50 X 2.2 = (g) $840 x 2.2 =: 8. $55 X 2.2 = (h) $635 x 4.2 = 9. $2.7 -$.9::= (i) $65.2 X $.4 = 10. If 4 lbs. of coffee are worth $1.6, 5 lbs. of coffee are worth . (j) If 4 acres of land are worth $97.2, how much are 7 acres worth? (k) If 5 tons of hay are worth $62.5, how much are 6^ tons worth? (1) From 641.3 subtract 238.1. (m) From 524.7 subtract 161.4. PART III. 173 SIMPLE NUMBERS. 1. At 2. At 3. At 4. At 5. At 6. At 7. At 8. At 9. At 10. At 11. At $23 each $25 each $28 each $27 each $23 each $24 each $25 each $23 each $25 each $27 each $24 each 45 23 135 90 1035 (a) (3 times 45.) (20 times 45.) (23 times 45.) 461 23 138 92 10694 2 cows 10 cows 10 cows 10 cows 20 cows 20 cows 20 cows 22 cows 23 cows 21 cows 24 cows cost cost cost cost cost cost cost cost cost cost cost dollars, dollars, dollars, dollars, dollars, dollars, dollars, dollars, dollars, dollars, dollars. (b) Multiply 48 by 24 (c) Multiply 37 by 46 (d)Multiply 58by 35 (e) Multiply 72 by 21 (f ) Multiply 86 by 24 (g) (23 times ^.) (3 times 46.) (20 times 46.) (23 times 46f) 46.5 23 139.5 930. 1069.5 (1^) (3 times 46.5.) (20 times 46.5.) (23 times 46.5.) (i) Multiply 47i by 25. (j) 47.5 by 25. (k) Multiply 38i by 23. (1) 38.5 by 23. 174 ELEMENTARY ARITHMETIC. DENOMINATE NUMBERS. 1. I can reduce (change) 6 quarts 1 pint to pints. 6 qt. 1 pt. = pints. (a) Reduce 36 qt. 1 pt. to pints. 2. I can reduce 3 gal. 2 qt. to quarts. 3 gaL 2 qt. = quarts. (b) Reduce 36 gal. 2 qt. to quarts. 3. I can reduce 2 ft. 5 in. to inches. 2 ft. 5 in. = inches. (c) Reduce 23 ft. 5 in. to inches. 4. I can reduce (change) 15 pints to quarts. 15 pints — (d) Reduce 85 pints to quarts. 2)85 5. I can reduce 15 quarts to gallons. 15 qt. = (e) Reduce 177 quarts to gallons. 4)177 6. I can reduce 21 pecks to bushels. 21 pk. = (f ) Reduce 230 pecks to bushels. 4 )230 7. I can reduce 18 days to weeks. 18 days = (g) Reduce 365 days to weeks. 8. I can reduce 2 hours 20 minutes to minutes. 2 hours 20 minutes = minutes. (h) Reduce 7 hours 20 minutes to minutes. (i) Divide $326 by $5. (j) Divide $427 by $5. (k) Divide $561 by $5. (1) Divide $472 by $5. (m)Divide $358 by $5. (n) Divide $629 by $5. PART III. 175 COMMON FRACTIONS. 1. One half is fourteenths. 2. One seventh is fourteenths. 3. Two sevenths are — fourteenths. 4. Three sevenths are fourteenths. 5. One half and 1 fourteenth are . 6. One half less 2 fourteenths are . 7. Two sevenths and 1 fourteenth are 8 . Two sevenths less 1 fourteenth are ■ 9 . Three sevenths and 1 fourteenth are 10. Three sevenths less 1 fourteenth are 11. -J- + -^\, means . ^ and -j\- = 12. 4" — fV? i^eans . -J- l^ss fV = 13. -f- X 5, means . 5 times |- = 14. 14 X -f, means . |^ of 14 = 15. 14 X 2f, means ■. 2f times 14 = 16. I- -=- -A , means . -A- is . 17. 2 18. 1 i, means — . ^ is 2, means . i of 4- 19. $1.4 is I of . I of 1.5 = (a) $36.8 is | of how many dollars? (b) I of 36.6 3^ (c) $54.2 is I of how many dollars? (d) I of 55.2 = (e) $17.4 is I of how many dollars? (f) I of 18.6 = (g) Divide $476 by 5. (h) Divide $397 by 5. (i) Divide $623 by 5. (j) Divide 532 by 5. 176 ELEMENTARY ARITHMETIC. COMMON FRACTIONS. 1 . Add I and |. (4 = ^^, | = ^^.) 2. Add I and |. (Change | to ^.) 3. From 4 subtract -|-. (i. = j^. ^ = j^.) 4. From ^ subtract -J-. (Change 1 to ^g.) 5. Multiply 6 by 5|. (5 times 6, plus | of 6.) 6. Multiply 84- by 6. (6 times J, plus 6 times 8.) 7. Divide ^ by 7. (Find \ of f ) 8. Divide 4 by f. (Find how many times, etc.) 9. Find the sum of 2.4 and 1|^. (} = ^^.) 10. Find the sum of S^- and 2^^. (^ = ^^.) 11. Find the difference of 3| and 1.3. (| - ^.) 12. Find the difference of 4| and 2yV' (^ = xr) 13. Find the product of 8 multiplied by 4|-. 14. Find the product of 4f multiplied by 8. 15. Find the quotient of |- divided by 2. 16. Find the quotient of 2 divided by f. 17. 1 4_ 1 1 1 _ ? (i — 6"- i- — G*) 18. 1 4_ 1 1 1 _ ? a- — T2- 4 — T3".) 19. 1 1 1 1 1 — ? -2 ^ "3 T^ T — • tt^ = T-^, etc.) 20. 1 1 1 1 1 _ ? ih- = 8, etc.) (a) Add 146|, 125|, and 136|. (b) Add 224.5, 126|, and 275. (c) Add 375, 246, 233, and 145. PART III. 177 MISCELLANEOUS PROBLEMS IN FRACTIONS. 1. 3 inches are contained in 7 inches and — times. 6-^3= 7-3= 8-3 = 2. 3 tenths are contained in 7 tenths — .6 -^ .3 = .7 - .3 = .8 - .3 = 3. 3 fourteenths are contained in 7 fourteenths 6.3_ 7.3_ 8^3_ TT ~ TT — TT • TT — XT * TT — 4. 4 inches are contained in 9 inches and times. 8^4= 9-4= 10-4= 11-4 = 5. 4 tenths are contained in 9 tenths .8 -.4= .9 -.4= 1.0 -.4= 1.1 -.4 = 6. 4 twelfths are contained in 9 twelfths 8.4— 9 _:^ 4 _ XQi _:_ _4_ — IJL ^ _4__ _ 1-2 ~ T2 ~ Tl^ • 1 2 — 12-12— 12-12 — 7. One half of 6 is 1 third of . 8. One third of 6 is 1 half of . 9. One fourth of 8 is 1 half of . 10. One fourth of 8 is 1 third of --, 11. One half of 8 is 1 third of , (a) From 432 subtract 271|. (b) From 536 subtract 362.4. (c) From 375 subtract 28|. (d) From 621 subtract 206.3. 178 ELEMENTARY ARITHMETIC. MEASUREMENTS. 1. A rectangle 1 inch wide and 1 foot long contains square inches. 2. A rectangle 2 inches wide and 1 foot long contains square inches. 3. A rectangle 3 inches wide and 1 foot long contains square inches. 4. A rectangle 8 inches wide and 1 foot long contains square inches. 5 . A 12-incli square contains square inches. 6. A 12-inch square is a square foot. 7. An oblong 2 feet by 3 feet contains . 8. An oblong 1 foot by 5 feet contains . 9. A square foot is what part of a 2-foot square ? 10. 2 square feet are what part of a 2-foot square ? 11 . 3 square feet are what part of a 2-foot square ? 12. 12 square inches are what part of a square foot? 13. 24 square inches are what part of a square foot? 14. An oblong 3 inches wide and 1 foot long is of a square foot. 15. An oblong 4 inches wide and 1 foot long is of a square foot. 16. An oblong 6 inches wide and 1 foot long is of a square foot. (a) Multiply $26 by 24. (d) $28 x 6.5. (b) Multiply $26 by 24i. (e) $34 x 25. (c) Multiply $28 by 6i. (f) $34 x 2.5. PART III. 179 ME AS UREMENTS . 1. A rectangle 1 ft. wide and 1 yd. long con- tains square feet. 2. An oblong 2 ft. wide and 1 yard long con- tains square feet. 3. A 3-foot square contains square feet. 4. A 3-foot square is a square ijard. 5. An oblong 1 yd. by 3 yd. contains . 6. An oblong 2 yd. by 3 yd. contains . 7. A square foot is of a sq. yd. 8. Two square feet are of a sq. yd. 9. Three square feet are of a sq. yd. 10. Six square feet are of a sq. yd. 11. A 2-foot square is of a sq. yd. 12. A 2-incli square is — •- — — of a 3-incli square. 13. A 2-incli square is — of a 4-inch square. 14. A 1-inch square is of a 2-inch square. 15. A 1-inch square is of a 3-mch square. 16. A 1-inch square is — '■ of a 4-inch square. 17. The area of an oblong 1 foot wide and 5 feet long is of a square yard. (a) Divide $342 by $6. (b) Divide $343 by $6. (c) Divide $276 by $6. (d) Divide $278 by $6. 180 ELEMENTARY ARITHMETIC. RATIO AND PKOPORTIOlSr. 5*7^ 10 cents. 1. If 3 apples are worth 5 cents, 6 apples are worth cents. 3. 4. [ 3 is 5 is 4 is 20 is ) is [12 is of 6. 6 is of 10. 10 is of 12. 12 is of 60. 60 is of 20. 20 is of 48. 48 is times 3. times 5. times 4. times 20. times 5. times 12 5. If 25^ pays for 7 lemons, 50^ pays for 6. If 10^ pays for 3 oranges, 30^ pays for 7. If $20 pays for 3 tons, $80 pays for - 8. If 50^ pays for 4 gallons, 25^ pays for 9. If 80^ pays for 12 tickets, 20^ pays for 10. If 75^ pays for 9 rides, 25^ pays for . 11. Mary has 10^; Jane has 20^; if Mary can buy 3 pencils, Jane can buy pencils. 12. Harry has 50^; Alice has 25^; if Harry can buy 6 tablets, Alice can buy tablets. (a) Divide $342 by 6. (b) Divide $344 by 6. (c) Divide $277 by 6. (d) Divide $279 by 6. (e) Divide $445 by 6. (f ) Divide $447 by 6. PART III. 181 RATIO AXD PROPORTION. 1. Twelve oranges are 'worth times as much as 6 oranges. If 6 oranges are worth 11^, 12 oranges are worth — cents. 2. Six Readers are worth times as much as 2 Eeaders. If 2 Readers are worth $1.20, 6 Readers are worth . 3. Five dozen eggs are w^ortli as much as 10 dozen eggs. If 10 dozen are worth $2.20, 5 dozen are worth . 4. Five yards of velvet are worth as much as 15 yards of velvet. If 15 yards are worth $12, 5 yards are worth dollars. 5. If 6 oranges are worth 9^, 2 oranges are Avorth cents. 6. If 3 tons of coal are worth $20, 6 tons are worth dollars. 7. John earns $7 in 2 weeks; in 6 weeks he earns dollars. 8. If 3 acres of land yield 5 tons of hay, at the same rate 9 acres will yield tons. 9. If 20 lbs. of salt cost 12^, at the same rate 40 lbs. will cost cents. 10. If 5 yards of ribbon cost I of a dollar, at the same rate 15 yards will cost . (a) Add 274|, 342, and 125^^- (b) Add 145fV, 231, and 273|. (c) Add 224, 375, 432, and 227. 182 ELEMENTARY ARITHMETIC. MISCELLANEOUS PROBLEMS. 1. In 1^ liours there are minutes. (a) How many minutes in T^- hours? 2. Henry earns $34^ each week; in 6 weeks he earns dollars. (b) How many dollars does Henry earn in 52 weeks ? 3. James spent ^ of the money his father gave him for a slate and |^ of it for a book, and had 10^ left. Before he spent any money he had cents. (c) A man spent -|- of l^is month's wages for fuel and ^ of it for groceries and had $12.5 left. How much was his wages? 4. At ^ of a dollar a yard, 10 yards of ribbon cost dollars. (d) At ^ of a dollar a yard, how much will 155 yards of ribbon cost? 5 . Alice spent i of her money and had 8^ left ; before spending any money she had cents; she spent cents. (e) Alice's mother spent |- of her money and had $73 left. How much money had she before spending any? How much did she spend? (f) From 1624 subtract 902-|-. (g) From 2436 subtract 814.3. PART III. 183 SIMPLE NUMBERS. (a) (b) (c) (d) 12 dollars 15 oranges 25^ 275 5 dollars 6 oranges 8^ 146 7 dollars 9 oranges 17^ 129 the 1. In problem (a) the minuend is subtrahend is ; the difference is — 2. In problem (b) the subtrahend is minuend is ; the difference is — — 3. In problem (c) the difference is minuend is ; the subtrahend is — 4. In problem (d) the minuend is difference is ; the subtrahend is — 5. In a problem the minuend is 8 dollars the the the the subtrahend is 5 dollars ; the difference is 6. When the difference is 5 inches and the sub- trahend is 4 inches, the minuend is — . 7. When the difference is 11 feet and the min- uend is 14 feet , the subtrahend is . 8. The sum of two numbers is 15; one of the .numbers is 6 ; the other number is . 9. The difference of two numbers is 9; the larger number is 20 ; the smaller number is . (e) Multiply $542 by 3. (f) $542 x .4. (g) Multiply $542 by 3.4. (h) $542 x 3.5. (i) Multiply $542 by 3^. (j) $542 x 2 J. 184 ELEMENTARY ARITHMETIC. DENOMINATE NUMBERS. 1. 2 gal. 1 qt. + 3 gal. 2 qt. are (a) Add 47 gal. 1 qt. and 35 gal. 2 qt. 2. 2 bu. 3 pk. -f 3 bu. 3 pk. are (b) Add 54 bu. 3 pk. and 29 bu. 3 pk. 3. 6 gal. 3 qt. — 3 gal. 1 qt. are (c) From 45 gal. 3 qt. subtract 37 gal. 1 qt. 4. 4 gal. 1 qt. — 1 gal. 3 qt. are (d) From 57 gal. 1 qt. subtract 24 gal. 3 qt. 5. 3 bu. 2 pk. X 4 equals . (e) Multiply 27 bu. 2 pk. by 6. 6. 3 bu. 2 pk. -^ 2 pk. equals — — . (f ) Divide 12 bu. 2 pk. by 2 pk. 7. 4 bu. 2 pk. -^ 2 equals (g) Divide 84 bu. 2 pk. by 2. 8. Six yards 2 feet equal feet. (h) Reduce 45 yards 1 foot to feet. 9. Two pecks 3 quarts equal quarts. (i) Reduce 23 pecks 3 quarts to quarts. 10. Twenty-seven feet equal yards. (j) Reduce 56 feet to yards. (k) Divide $245 by $7. (1) $246 - $7 : (m) Divide $252 by $7. (n) $254 - $7 : (o) Divide $364 by $7. (p) $367 - $7 : PART III. 185 COMMOX FRACTIONS. 1. One third is fifteenths. 2. One fifth is fifteenths. 3. Two fifths are fifteenths. 4. Three fifths are fifteenths. 5. One third and 1 fifteenth are . 6. One third less 1 fifteenth are . 7. Two fifths and 1 fifteenth are . 8. Two fifths less 1 fifteenth are — . 9. Three fifths and 2 fifteenths are . 10. Three fifths less 2 fifteenths are . 11- i + tV. means ^. i + yV = 12. I - ^\, means . | - A = 13. "I X 8, means . 8 times -| = 14. 10 X I, means . -| of 10 = 15. 10 X 2|, means ^^ . 2|- times 10 = 16- I -^ iV ? means . -^^ is . 17. 3 -^ f , means . f are — . 18. f ^ 3, means . ^ of f = 19. At $10 an acre, 21 acres of land cost . (a) At $65 an acre, how mnch will 2^ acres of land cost? 20. One half of the month of November plus one fifteenth of the month equals days. (b) Divide $364 by 7. (c) $365 - 7 = (d) Divide $161 by 7. (e) $165 - 7 = (f) Divide $455 by 7. (g) $459 - 7 - 186 ELEMENTARY ARITHMETIC. COMMON FRACTIONS. 1. Add f and 4. (1 = ^^. 1 = -^.) 2. Add I and -^. (Change | to ^^.) 3. From |^ subtract |. (f = t^. 1 = y^.) 4. From y^^ subtract \. (Change i to — .) 5. Multiply 8 by 3 J. (3 times 8, plus J of 8.) 6. Multiply 5|- by 6. (6 times i, plus 6 times 5.) 7. Divide | by 5. (Find 1 fifth of f.) 8. Divide 5 by |. (Find how many times, etc.) 9. Find the sum of 3.2 and If. (f = ^^.) 10. Find the sum of 2| and 2/^. (1 = y-^.) 11. Find the difference of Sf and 1.2. 12. Find the difference of 4 J- and 2^-^, 13. Find the product of 10 multiplied by 3f. 14. Find the product of 3|- multiplied by 10. 15. Find the quotient of 4 divided by 3. 16. Find the quotient of 3 divided by 5* 17. 1 4- i 4- 1 — ? (3^ = T^- 1 18. 1 1 1 4_ 1 — ? (i — T¥' 1 T 19. 1 J- 1 -U 1 — ? (i = To"* 1 20. 2 _l_ 2 1 1 _ ? 2 ■5 = T0-) = TT-) (a) Add 254|, 325, and 243J. (b) Add 324|, 271, and 442|-. (c) Add 462, 575, 834, 926. (d)Add378, 246, 575, 242. PART III. 187 MISCELLANEOUS PROBLEMS IN FRACTIONS. 1. Acid I, 4"? ^^cl yV- (Change f and i to ths.) 2. Add -J- and |-. (Change ^ and -| to ths.) 3. From 4 subtract 4-- (Change f and i to ths.) 4. From -f subtract 4-- (Change -f and i to ths.) 5. Multiply I by 3. (Three times .) 6. Multiply I by 5. (Five times -.) ■ 7. Multiply 12 by I . (Two thirds of .) 8. Multiply 15 by |. (Two fifths of .) 9. Multiply 6 by 2|. (Two times 6, plus J of 6.) 10. Multiply 41 by 2|. (Two times 4^, plus J of 4J.) 11. Divide 4 by f. (Change 4 to .) 12. Divide 5|- by |. (Change 5^ to .) 13. Divide ^^J h (Change i and i to .) 14. Divide |- by 2. (One half of .) 15. Divide | by 3. (One third of .) 16. Find tlie sum of ^ and |. | -[- ^ + 4 = 17. Find the difference of | and |. 4| — 1| = 18. Find the product of | and 4. | x 6 = 19. Find the product of 6 and 1|. 8 x 2^ = 20. Find the quotient of 5 divided by ^. 21. Find the quotient of ^ divided by 5. (a) From 2154 subtract 10T2f . (b) From 3275 subtract 843f . (c) From 4526 subtract 1283.4. 188 ELEMENTARY ARITHMETIC. MEASUREMENTS.* 2 in. 1. The area of a rectangle 1 inch wide and 6 — square inches. The area of a in. long is — rectangle ^ of an inch wide and 6 in. long is square inches. 2. The area of a rectangle 1 inch wide and 8 in. long is square inches. The area of a rectangle J of an inch wide and 8 in. long is square inches. 3. The area of a rectangle 1 in. wide and 5 in. long is square inches. The area of a rect- angle i of an inch wide and 5 in. long is square inches- 4. The area of an oblong 4 inches wide and 6 in. long is square inches. The area of an oblong 4 inches wide and 6^ in. long is square inches. (a) Multiply 60 minutes by 24. (b) Multiply 24 hours by 31. (c) Multiply 144 square inches by 8. * To THE Teacher. — Be sure that the pupil understands that by the expression square inch, we mean the equivalent of a 1-inch square. Then by paper cutting lead him to discover that the area of a piece of paper | in. by 2 in. is 1 square inch; that the area of a piece of paper \ in. by 4 in, is 1 square inch, etc. Remind the pujjil that a rectangle may be either a square or an oblong. PART III. 189 MEASUREMENTS. 1. The area of an oblong 1 ft. wide and 6 ft. long is square feet. The area of an oblong J of a foot wide and 6 ft. long is square feet. 2. The area of an oblong 1 ft. wide and 8 ft. long is square feet. The area of an oblong ^ of a foot wide and 8 ft. long is scjuare feet. 3. The area of an oblong 1 ft. wide and 5 feet long is square feet. The area of an oblong | of a foot wide and 5 feet long is square feet. 4. The area of an oblong 4 feet wide and 8 feet long is square feet. The area of an oblong 4 ft. wide and 8 J ft. long is square feet. The area of an oblong 4^ ft. wide and 8 ft. long is square feet. 5. A ^-foot square is of a square foot. 6. Draw upon the blackboard very carefully a 2|-foot square. Try to divide it so that you can see how many square feet it contains. 7. Draw upon the blackboard very carefully a l^-foot square. Try to divide it so that you can see how many square feet it contains. 8. In a 3J-foot square there are square feet. (a) Divide $176 by $8. (b) $177 - (c) Divide $264 by $8. (d) $267 (e) Divide $336 by $8. (f) $341 190 ELEMENTARY ARITHMETIC, RATIO AND PROPORTION. lO*? 15 cents. 1. If 4 lemons are worth 10^, 6 lemons are worth cents. 4 is — - of 6. 6 is — - of 4. 10 is —of 15. 15 is of 10. 8 is of 12. 12 is of 8. 12 is of 18. 18 is of 12. 2. 3. 4. 20^ pays for 6 lemons; 30^ pays for - 5. 10^ pays for 4 oranges; 15^ pays for 6. $4 pays for 12 yards; $6 pays for — 7. 75^ pays for 9 yards; 25^ pays for — 8. 15^ pays for 6 bananas; 10^ pays for 9. $40 pays for 12 tons; $10 pays for - 10. $30 pays for 9 tickets; $20 pays for . 11. Susan has 10^; Jane has 15^; if Susan can buy 4 pencils, Jane can buy pencils. 12. Henry has 20^; William has 30^; if Henry can buy 8 tablets, William can buy tablets. 13. If 4 horses consume 10 pecks of oats in a day, 6 horses will consume pecks. (a) Divide $176 by 8. (b) $178 - 8 = (c) Divide $264 by 8. (d) $269 - 8 = (e) Divide $336 by 8. (f ) $343 - 8 = PART III. 191 RATIO AND PROPORTIOX. 1. Twelve oranges are worth times as much as 8 oranges. If 8 oranges are Avorth 14^, 12 oranges are worth cents. 2. Fifteen dozen eggs are worth times as much as 10 dozen eggs. If 10 dozen eggs are worth $1.20, 15 dozen are worth . 3. Eight ponies consume as many oats in a day as 12 ponies. If 12 ponies consume 60 qt., 8 ponies consume quarts. 4. A man can earn times as much money in 6 days as he can earn in 2 days. If he earns $5 in 2 days, in 6 days he earns dollars. 5. If 10 lbs. of sugar are worth 40^, 15 lbs. are worth cents. 6 . If 4 acres of land yield 6 tons of hay, at the same rate 6 acres yield tons. 7. If 10 railroad tickets cost $4, at the same rate 15 tickets cost dollars. 8. If 4 bushels of beans are worth $7, 6 bush- els are Avorth . 9. If 6 bags of corn are worth $5, 9 bags of corn are worth . 10. If 8 yards of velvet are worth $11, 12 yards are worth . (a) Add 326|, 243, and 155i. (b) Add 276.2, 144.3, and 354.6. (c) Add 275, 436, 273, 244. 192 ELEMENTARY ARITHMETIC. MISCELLANEOUS PROBLEMS. (a) At $240 an acre, liow much will 3.2 acres of land cost ? (b) Find the cost of 9 sheep at $3.45 a head. (c) A lady paid $6.80 for a hat and | as much for shoes. Find the cost of both. (d) If 7 tons of coal cost $45.50, how much does one ton cost ? (e) A man bought two horses for $300; he sold one of them for $160, and the other for $180. How much did he gain ? (f) When cheese is worth $.08 a pound, how many pounds can be bought for $28.64. (g) At $.05 a pound, how many pounds of sugar will cost $24.50 ? (h) The lot upon which Mr. Smitli's new house stands cost $1300; the house cost 6 times as much as the lot. Find the cost of both. (i) Mr. Brown put into the bank on Monday, $24.30; on Tuesday, $11.50; on Wednesday, $13.45; on Thursday, $6.83; on Friday, $42; on Saturday, $13.75. How much in all? (j) Mr. Jones had $75.40 in the bank; he put in $15.20 and soon after drew out $42.30. How much did he then have in the bank ? (a) From 3246 subtract 1518. (b) From 4624 subtract 2481|. (c) From 2751 subtract 1480.4 PART IV. DECIMALS HUNDREDTHS. 1. 24^ and 8^ are cents. 2. .24 and .08 are lumdredtlis. 3. 24^ less 8^ are cents. 4. .24 less .08 are hundredths. 5. 24^ X 2, means, 2 times 2Jf<^; 2 thnes 24^ = 6. .24 X 2, means, f times .2Jf ', 2 times .24 = 7. 24^ -f- 4^, means, find how many times Jf<^ are contained in 2Jf(^; 4:^ are contained in 24^ times. 8. .24 -^ .04, means, find Jioiv many times .OJj. are contained in .2Jf', -04 are contained in .24 times. 9. 24^ ^ 4, means, ^;2<:? one fourth of 24^ ; one fourth of 24^ is cents. 10. .24 -^ 4, means, y^nc^ one fourth of .2Jfj one fourth of .24 is hundredths. (a) Multiply $224 by 2. (b) $2.24 x 2 = (c) Multiply $235 by 2. (d) $2.35 x 2 = (e) Multiply $346 by 2. (f) $3.46 x 2 := 193 194 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. One himdredtli of a dollar is cent. 2. Six hundredths of a dollar = cents. 3. 53 hundredths of a dollar = cents. 4. 46 hundredths = tenths and . 5. 52 hundredths = tenths and . 6. $.45 = tenths and hundredths of a dollar. 7. $.36 = tenths and hundredths of a dollar. 8. One half-dollar = hundredths of a dollar. 9. One fourth-dollar = hundredths of a dollar. 10. Mary had $.08 in her pocket and $.52 in her bank ; in both she had . 11. Jane had $.48; she spent $.11; she then had . 12. Sarah i^aid $.25 for each of 3 books; for all she paid . 13. Alice had $.50 with which to buy tea at $.25 a pound; she could by . 14. Maude paid $.80 for 4 pounds of coffee; one pound cost . (a) Divide $198 by $9. (b) $199 (c) Divide $297 by $9. (d) $299 - $9 = (e) Divide $306 by $9. (f ) $309 $9 $9 = PART IV. , 195 DECIMALS HUNDREDTHS. 1. .28 + .06. (To be read, 28 liimdredtlis plus 6 hundredths.) .28 + .06, means, .28 and .06 ; .28 and .06 = Arthur earned .28 of a dollar Monday and .06 of a dollar Tuesday ; in both days he earned . 2. .32 — .06. (To be read, 32 hundredths minus 6 hundredths.) .32 - .06, means, .32 less .06 ; .32 less .06 = Harry had .32 of a dollar; he spent .06 of a dollar; he then had . 3. .06x4, (To be read, 6 hundredths multiplied by 4.) .06 X 4, means, ^ times .06; 4 thnes .06 are If 1 yard of ribbon is wortli .06 of a dollar, 4 yards are worth 4. .48 -^ .06. (To be read, 48 hundredths divided by 6 hundredths.) .48 ^ .06, means, find how many times .06 are contained in .4-8; .06 are contained in .48 . James had .48 of a dollar with which to buy tablets at .06 of a dollar each; he could buy . 5. .48 ^ 6. (To be read, 48 hundredths divided by 6.) .48 -^ 6, means, find 1 sixth of .Jf8; 1 sixth of .48 is . William paid .48 of a dollar for 6 pounds of sugar; one pound cost . (a) Divide $198 by 9. (b) $1.98 by 9 = (c) Divide $297 by 9. (d) $2.97 by 9 = 196 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. The sum of $.2 and $.34 is — 2. The sum of $.43 and $.04 is - 3. The sum of $.30 and $.06 is - 4. The sum of $.40 and $.05 is - 5. The sum of $.08 and $.96 is - 6. The sum of $.25 and $.06 is - 7. The sum of $.09 and $.06 is - 8. The sum of $.35 and $.07 is - 9. The sum of $1.25 and $1.25 is 10. The sum of $1.35 and $.08 is - 11. The sum of $1.45 and $.4 is - 12. The sum of $1.55 and $.6 is - 13. The sum of two tenths and twenty-four hundredths is hundredths. (a) $26.2 + $84.24 = 14. The sum of eight tenths and six hundredths is hundredths, (b) $47.8 f $55.06 = 15. The sum of seven hundredths and ^xe hun- dredths is hundredths. (c) $36.07 + $45.05 = 16. The sum of fifty hundredths and fifty-five hundredths is hundredths. (d) $64.50 + $73.55 = (e) Add 26.24, 15.2, and 43.36. (f) Add 35.2, 47.34, and 48.24. (g) Add 84.25, 6.34, 2.58, and 31.21. PART IV. 197 DECIMALS HUNDREDTHS. 1. The difference of $.45 and $.25 is 2. The difference of $.6 and $.15 is - 3. The difference of $.40 and $.05 is 4. The difference of $.45 and $.2 is - 5. $2.30 - $1.25 = 2.30 - 1.28 6. $3.45 - $1.05 - 3.45 - 1.03 7. $4.55- $2.2 = 4.55 - 2.3 : 8. $5 - $.25 = 5 - .75 = (a) From 20 dollars and 45 cents subtract 14 dollars and 22 cents. (b) From 26 and 45 hundredths subtract 14 and 24 hundredths. (c) Add 35 dollars and 45 cents, and 27 dollars and 53 cents. (d) Add 35 and 24 hundredths, and 27 and 42 hundredths. (e) From 38 dollars and 52 cents subtract 21 dollars and 27 cents. (f) From 38 and 52 hundredths subtract 21 and 24 hundredths. (g) Add twenty-four dollars and forty-two cents and thirty-three dollars and twenty-seven cents. (h) From 37.24 subtract 12.18 (i) From 86.37 subtract 28.3. (j) From 97.8 subtract 34.25. 198 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. The product of $.12 multiplied by 2 - 2. The product of $1.04 multiplied by 5 3. The product of $2.25 multiplied by 3 4. The product of $1.50 multiplied by 2 5. $2.25 X 2= 1.25 X 3 = 6. $2.12 X 3= 2.12 X 4 = 7. $3.04 X 4= 3.04 x 5 = 8. $4.25 X 4= 4.25 x 5 = (a) Multiply 15 dollars and 26 cents by 5. (b) Multiply 15 and 27 hundredths by 5. (c) Multiply 24 dollars and 35 cents by 6. (d) Multiply 24 and 32 hundredths by 6. (e) Multij^ly 34 dollars and 3 dimes by 4. (f) Multiply 34 and 4 tenths by 4. (g) Multiply twenty-eight dollars and sixteen cents by three. (h) Multiply twenty-eight and sixteen hun- dredths by four. (i) Multiply forty-three dollars and twenty-five cents by four. (j) Multiply forty -three and twenty-five hun- dredths by three. (k) Multiply forty-six and three tenths by seven. (1) Multiply $245 by 5. (m) $2.45 x 5 =-- (n) Multiply $375 by 5. (o) $3.75 x 5 = (p) Multiply $237 by 5. (q) $2.37 x 5 - PART IV. 199 DECIMALS HUXDREDTHS. 1. The quotient of $.45 divided by $.05 is 3. The quotient of .55 divided by .05 is 4. The quotient of ,55 divided by 5 is . 5. $.36 - $.09 = .36 - .04 = 6. $.36- - 9 = .36 - -4 = 7. $.48- - $.06 = .48 - -.04 = 8. $.48- - 6 = .48 - -4 = 9. $.12- -$.02= .12- -.03 = 10. $.12- -2= .12- -3 = 11. $1.20- $.02 = 1.20- -.03 = 12. $1.20-2= 1.20- -3 = (a) Divide 24 dollars and 25 cents by 5^. (b) Divide 24 and 25 hundredths by .05. (c) Divide 37 dollars and 5 cents by 5 cents. (d) Divide 37 and 5 hundredths by 5 hundredths (e) Divide 37 dollars and 5 cents by 5. (f ) Divide 37 and 5 hundredths by 5. (g) Divide $2.25 by $.05. (h) $6.75 - $.05 = (i) Divide $3.45 by $.05. (j) $4.35- $.05= , (k) Divide $7.15 by $.05. (1) $8.55 - $.05 = 200 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. One half of .24 is . .24 is | of 2. One half of .16 is . ,16 is ^ of 3. One third of .12 is ■ -. . .12 is 4 of 4. Two thirds of .12 are . .12 is I of 5. Three fourths of .12 are 6. One half of 2.06 is .12 is I of 2.06 is 4- of . 7. .08 is what part of .12? .04 of .12? ' 8. .09 is what part of .12? .06 of .12? 9. .12 is what part of .16? .12 of .18? 10. .12 is what part of .36? .12 of .48? 11. .25 is what part of 1? .75 of 1? 12. One fourth of .2 (.20) is hundredths. 13. Three fourths of .2 (.20) are hun- dredths. 14. One fifth of .2 (.20) is hundredths. 15. Three fifths of .2 (.20) are hundredths. 16. .04 is of .2. .05 is of .2. 17. .08 is of .2. .12 is ^ of .2. 18. .15 is ^ of .2. .16 is of .2. (a) Divide $24.48 by 6. (b) $2449 (c) Divide $35.04 by 6. (d) $3505 (e) Divide $29.47 by 7. (f) $2949 (g) Divide $43.25 by 5. (h) $4326 PART ]V. 201 DECIMALS HUNDREDTHS. 1. One hundredth of 200 is . .02 of 200 = 02 of 300 2. One hundredth of 300 is 3. One hundredth of 400 is 4. Three hundredths of 200 are . .04 of 200 = 5. Three hundredths of 300 are . 02 of 400 = .04 of 300 = 6. .01 of 202 = .02 of 202 = .03 of 202 7. .01 of 302 = .02 of 302 = .03 of 302 8. .01 of 108 = .02 of 108 = .03 of 108 9. .01 of 212 = .02 of 212 = .03 of 212 10. .01 of 240 = (a) Find .02 of 240. 11. .01 of 243 = (b) Find .02 of 243. 12. .01 of 320 = (c) Find .03 of 320. 13. .01 of 324 = (d) Find .03 of 324. 14. .01 of 230 = (e) Find .05 of 230. 15. .01 of 236 :.= (f) Find .07 of 236. 16. .01 of 26 = (g) Find .08 of 26. 17. .01 of 45 = (h) Find .05 of 45. 18. .01 of 535 = (i) Find .03 of 535. (j) Add 3.05, 2.75, 25.3, and 346. (k) Add 45.03, 6.4, 325.2, and 240. (1) Add 6.21, 64.5, 146.2, and 150. 202 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. One hundredth of 6 is hundredths. 2. One hundredth of 3 is hundredths. 3. One hundredth of 5 is hundredths. 4. One hundredth of $8 is . .04 of 5. One hundredth of $6 is . .07 of $6 6. One hundredth of $9 is . .06 of $9 .03 of $25 = .02 of 7. One hundredth of $25 is - 8. One hundredth of $32 is - 9. One hundredth of $43 is . .02 of $43 = 10. One tenth of $3 is . .2 of $3 = 11. One hundredth of $3 is . .02 of $3 = 12. One tenth of $5 is . .3 of $5 = 13. One hundredth of $5 is . .03 of $5 = 14. One tenth of $12 is . .02 of $12 = 15. One hundredth of $12 is . .02 of $12 = 16. One tenth of $120 is . .2 of $120 = 17. One hundredth of $120 is . 02 of $120 = (a) From 24.4 subtract 12.27. (b) From 325.2 subtract 43.35. (c) From 146.25 subtract 84.82. PART IV. 203 DECIMALS HUXDREDTHS. 1. Harry paid $2 for 100 pencils; one pencil cost liundreclths of a dollar. 2. Arthur paid $4 for 10 First Readers; one First Reader cost tenths of a dollar. 3. Mr. Jones paid $26 for 100 watermelons; one watermelon cost . 4. Mr. Rice paid $45 for 10 cords of wood; one cord of wood cost . 5. If one pound of sugar is worth $.04, 100 pounds of sugar are worth . 6. If one ton of coal is worth $6.50, 10 tons of coal are worth . 7. One bushel of wheat weighs 60 pounds; 10 bushels of wheat weigh . 8. One bushel of oats weighs 32 pounds; 100 bushels of oats weigh . (a) Find 7 hundredths (.07) of 324. Operation. Explanation. 3 ''24 .01 of 324 = 3.24 .07 .07 of 324 = 22.68 22.68 (b) Find .06 of 437. (c) .5 of 437 := (d) Find .04 of 356. (e) .4 of 248 =. (f) Multiply $342 by 5. (g) $3.42 x 5. (h) Multidly $235 by 4. (i) $2.35 x 4. (j) Multiply $148 by 6. (k) $1.48 x 6. 204 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. 600 X .03, means 2. 400 X .03, means 3. 200 X .08, means 4. 500 X .07, means 5. 123 X .01, means 6. 123 X .02, means 7. 241 X .02, means 8. 222 X .03, means 9. $24 X .01, means 10. $24 X .02, means 11. $32 X .03, means 12. $62 X .03, means 13. $6 X .01, means - 14. $6 X .02, means - 15. $8 X .09, means - 16. $7 X .05, means - 12 X 3 = 23 X 3 17. 18. 19. $62 X 2 20. $26 X 2 $2 X $23 X $62 X $26 X .03 of 600 = .03 of 400 = .08 of 200 = .07 of 500 = .01 of 123 = .02 of 123 =. .02 of 241 = .03 of 222 = .01 of $24 = .02 of $24 = .03 of $32 =:= .03 of $62 = .01 of $6 = .02 of $6 = .09 of .05 of $2 X .03 = $23 X .03 = $62 X .02 = $26 X .02 = (a) Divide $4.36 by $.04. (b) 5.24 (c) Divide $6.24 by $.04. (d) 7.24 (e) Divide $5.44 by $.04. (f) 5.68 *600 X .03, means, find .03 of 600. .04 .04 .04 PART IV. 205 DECIMALS HUNDREDTHS. 1. When coal costs $4 per ton, — 2 tons cost . 3 tons cost .1 of a ton costs . .2 of a ton cost .3 of a ton cost . 2.1 tons cost — 2.2 tons cost . 2.3 tons cost — 2. When land costs $300 per acre, — 2 acres cost . 3 acres cost — .1 of an acre costs . .2 of an acre cost .3 of an acre cost . .4 of an acre cost .01 of an acre costs . .02 of an acre cost .03 of an acre cost . .04 of an acre cost 2.1 acres cost . 2.2 acres cost 2.01 acres cost . 2.02 acres cost 3. When coal costs $6 per ton, — 2 tons cost . 3 tons cost .1 of a ton costs . .2 of a ton cost 1.1 tons cost . 2.1 tons cost — 4. When corn meal costs $20 per ton, — 2 tons cost . 3 tons cost . .1 of a ton costs . .2 of a ton cost - .01 of a ton costs . .02 of a ton cost .3 of a ton cost . .03 of a ton cost 2.1 tons cost . 1.01 tons cost (a) Divide $4.36 by 4. (b) 5.25 - 4 = (c) Divide $6.24 by 4. (d) 7.33 - 4 = 206 ELEMENTARY ARITHMETIC o DECIMALS HUXDREDTIIS. (a) Multiply $234 by 3.25. This means, find three times $^SJf iilus two tenths of $2SJf i^ls five hundredths of $2oJf. Operation No. 1. Explanation. 1234. Three times $234 are $702. ' o*25 One tentli of $234 is $23.4. ^ Two tenths of $234 are $46.8. $702. (3 times $234.) One hundredth of $234 is $2.34. $46.8 (.2 of $234.) Five hundredths of $234 are $11.70 (.05 of $234.) $11.T0. $760:50 (3.25 times ^234.)*^^^+^^^-^+^^^-^^=^^^^-^^ Operation No. 2. • Explanation. ^234 One hundredth of $234 is $2.34. Q or Five hundredths of $234 are . ^:^ $11.70. $11.70 (.05 of $234.) One tenth of $234 is $23.4. $46.8 (.2 of $234.) Two tenths of $234 are $46.8. $702. (3 times $234.) Three times $234 are $702. $760:50 (3.25 times |234.)^^^-^^+^^^-^+^^^^=^^^^-^^ SUGGESTED NUMBER STORY. If one acre of land is worth $324, 1 hundredtli of an acre is worth . 5 hundredths of an acre are worth 1 tenth of an acre is worth . 2 tenths of an acre are worth 3 acres are worth . 3.25 acres are worth -. (b) Add 3.25, 24.6, 48, 375, and 42. PART lY. 207 DECIMALS HUNDREDTHS. 1. A farmer paid $4.2 for a sheep and $2.25 for a lamb ; for both he paid . (a) A farmer j)aid $125 for a horse, $95 for a buggy, and $24.50 for a harness. How much did he pay for all ? 2. A boy paid $4.65 for a coat and a pair of shoes; for the shoes he paid $2.2 ; for the coat he paid . (b) A man paid $346.5 for wood and coal ; for the wood he paid $38.25. How much for the coal ? 3. Harry had $5 ; he spent $2 for books and $2.55 for clothing; he then had . (c) Harry's father had $645.75; he spent $25.2 for groceries and $34.75 for fuel. How much money had he left ? 4. If one load of wood is worth $4.25, two loads are worth . (d) At $275.25 an acre, how much are four acres of land worth ? 5. William paid $.4 for oranges at $.05 each; he bought oranges. (e) William's father paid $19.6 for posts at $.08 each. How many posts did he buy ? (f) From 375.25 subtract 148.17. (g) From 464.2 subtract 238.46. (h) From 645.34 subtract 582.8. 208 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. At $300 a mile, how much will it cost to make 2.25 miles of road? 2 miles cost ; 2 tenths of a mile cost ; 5 hundredths of a mile cost ; 2.25 miles cost . (a) At $345 a mile, how much will it cost to make 3.25 miles of road? $345 x 3.25 = $345 X 3i = 2. Alice paid $1.26 for some tablets that cost $.06 each; there were tablets. $.05 )$. 60 $.05 )$.65 $.05)$2 $.05)$2.25 (b) Mr. Dunn paid $25.02 for paper that cost $.06 a pound. How many pounds were there? 3. Sarah paid $1.60 for 4 yards of ribbon; one yard cost . 4 )$1.2 4)$1.4 8)$1.6 8 )$1.2 (c) Mr. King paid $52.6t) for 4 tons of bran. How much did it cost per ton? 4. Charlie paid $.12 for 3 pencils; at the same rate 7 pencils would cost — — . (d) Mr. Johnson paid $26.50 for 2 tons of hay. At the same rate how much would 7 tons cost? (e) Multiply $521 by 4.25. (f ) $346 x 2.25 = (g) Multiply $435 by 6.25. (h) $164 x 5.25 = PART IV. 209 DECIMALS HUNDREDTHS. 1. Mr. Bliss had .72 of an acre of land which he divided into lots each containing .09 of an acre; there were lots. .09 of an acre)1.80 acres. .09 of anacre)2.79 acres. (a) Mr. Wheeler had 3.78 acres of land which he divided into lots each containing .09 of an acre. How many lots ? 2. Dr. Harris had 6.36 acres of land ; he divided it into 3 equal lots ; each lot contained . 2 )4.18 acres. 2 )6.06 acres. (b) Gen. Dow had 76.25 acres of land which he divided into 5 equal lots. How much in each lot? 3. Mr. Parker had 4 equal lots of land; each lot contained 1.05 acres; in all he had . 3.06 acres. 2.08 acres. 2.22 acres. 7.33 acres. 4 5 3 2 (c) Mr. Green had 4 equal lots of land; each lot contained 35.24 acres. How much land had he in all? (d) Divide 2.48 by .04. (f) Divide 6.72 by .06. (h) Divide 8.54 by .07. (e) 3.65 - .05 (g) 7.32 -. .06 (i) 1.20 - .08 210 ELEMENTARY ARITHMETIC. DECIMALS HUNDREDTHS. 1. Robert had $1.25; tliis is 4 as much as Peter had; Peter had — . (a) Mr. Hill had $24.45; this is | as much as Mr. Ford had. How much money did Mr. Ford have ? 2. Frank's book cost $1.20; his slate cost | as much ; his slate cost . (b) Mrs. Ford's carpet cost $54.78; her cur- tains cost I as much. How much did her curtains cost ? ^ 3. When apples are worth $.40 a bushel, ^ of a bushel is worth . f of a bushel are worth . (c) When meal is worth $18 per ton, how much is i of a ton worth ? f of a ton ? 4. James paid $.60 for f of a bushel of peaches ; at the same rate, a bushel would cost — . (d) Mr. Keen paid $6.45 for | of a ton of coal. At the same rate how much would :^ of a ton cost ? How much would 1 ton cost ? 5. If 2 yards of muslin are worth $.12, seven yards are worth . (e) If two barrels of apples are worth $6.50, how much are five barrels worth ? Seven barrels ? (f) Divide 3.56 by 4. (g) 2.75 (h) Divide 6.42 by 6. (i) 7.44 (j) Divide 9.24 by 7. (k) 1.36 - 8 = PART lY. DECIMALS— -HUNDREDTHS. 1. $300 X .2 = (a) $370 X .2 = 2. $320 X .2 = (b) $328 X .2 = 3. $300 X .02 = (c) $345 X .02 = 4. $300 X 2.2 = (d) $370 X 2.2 = 5. $300 X 2.02 = (e) $345 X 2.02 = 6. $300 X 2.22 = (f ) $234 X 2.22 = 7. $4 -$.2=: (g) $24 -$.2 = 8. $6 - $.02 = (h) $36 - $.02 = 9. $3.4- $.2 = (i) $43.4- $.2 = 10. $6.4.4- $.02 = (j) $56.38- $.02 11. $2.4- $.02 = (k) $34.4 - $.02 = 12. $4.8- $1.2 = (1) $52.8- $1.2 = 13. $2.50- $1.25 = (m)$7.50- $1.25 14. $3- $1.50 = (n) $27 - $1.50 = 15. $4.4-2 = (o) $46.8-2 = 16. $1.6-2 = (p) $47.8-2 = 17. $4.04-2 = (q) $74.04-2 = 18. $6.66-2 = (r) $56.38 - 2 = 19. $4.5-5 = (s) $37.5-5 = 20. $.35-5 = (t) $6.35-5 = 21. $5.35 ^ 5 = (u) $35.25 - 5 = 22. $8.88-4 = (v) $73.28-4 = 211 (w) Add 374.2, 46, 4.5, and 243.25. (x) Add 2454, 174|, and 328|. (y) Add 142^, 234.3, and 156.2. 212 ELEMENTARY ARITHMETIC. DECIMALS HUXDREDTHS. (a) Find the sum of $46, $275, and $342.27. (b) Find the difference of $467.2 and $275.38. (c) Find the product of $345.24 multiplied by 4. (d) Find the product of $2746 multiplied by .5. (e) Find the product of $35.62 multiplied by .05. (f ) Find the product of $624 multiplied by 2.5. (g) Find the product of $734 multiplied by 3.05. (h) Find the product of $476 multiplied by 2.35. (i) Find the quotient of 382.5 divided by .5. (j) Find the quotient of 382.5 divided by 5. (k) Find the quotient of $28.50 divided by $.05. (1) Find the quotient of $28.50 divided by 5. (m) Find the quotient of 74.4 divided by .4. (n) Find the quotient of 74.4 divided by 4. (o) Find the quotient of 85.2 divided by .6. (p) Find the quotient of 85.2 divided by 6. 1. Find f of $1.2. (q) Find f of $37.8. 2. $1.2 is J of what? (r) $37.8 is f of what? 3. Find I of $.18. (s) Find f of $4.74. 4. $.18 is I of what? (t) $4.74 is f of what? (u) From 564.7 subtract 146^. (v) From 352.75 subtract 234^. (w) From 634.32 subtract 247. 16, PAKT IV. SIMPLE NUMBERS. (a) 12 dollars 3 36 dollars 15 oranges 5 75 oranges 213 (c) 3 75^ 1. In problem (a) tlie multiplicand is ; the multiplier is ; the product is . 2. In j)roblem (b) the multij)lier is ; the product is ; the multiplicand is . 3. In problem (c) the product is ; the multiplier is ; the multiplicand is . 4. In a problem the product is 36 dollars; the multiplier is 4 ; the multiplicand is . 5. The product of two numbers is 45 ; one of the numbers is 5 ; the other number is . 6. N. B. — The multiplier can never be a num- ber of dollars or cents or oranges or books or feet or inches. It is always sbnphj a nmnher that tells how many times the multiplicand is to be taken. 7. Two cents multipUed hy tivo cents — nonsense. 8. If the multiplicand is bushels, the product is ; if the multiplicand is square inches, the product is square inches. (d) Multiply 144 square inches by 9. (e) Multiply 275 bushels by 23. (f) Multiply 348 dollars by 2.3. 214 ELEMENTARY ARITHMETIC. DENOMINATE NUMBERS. 16 ounces = 1 lb. 1. Two poimcls are ounces. 2. Three pounds are ounces. 3. One half of a pound is ounces. 4. One fourth of a pound is ounces. 5. One eighth of a pound is ounces. 6. Three fourths of a pound are ounces. 7. Three eighths of a pound are ounces. 8. One and ^ pounds are ounces. 9. When cheese costs 16^ a pound, 1 ounce costs cent; ^j lb. costs cents; 5 ounces cost ■ cents. 10. Henry bought 1 lb. 7 oz. of cheese at 16^ a pound; the cheese cost cents. 11. 2 lb. 8 oz. grapes at 10^ a pound cost . 12. lib. 4 oz. meat at 12^ a pound cost . 13. 1 lb. 8 oz. meat at 12^ a pound cost . 14. Mary gave a salesman 3 dimes in payment for 2 lb. 8 oz. maple sugar at 10^ a pound; she should receive in change cents. 15. Arthur gave a salesman i of a dollar in payment for 1 lb. 6 oz. cheese at 16^ a pound; he should receive in change cents. (a) Divide 34.5 by .3. (b) 34.6 - .3 = (c) Divide 53.2 by .4. (d) 53.5 - .4 =^ (e) Divide 62.5 by .5. (f ) 62.6 - .5 - PART IV. 215 COMMOX P^RACTIONS. 1. One half is sixteenths. 2. One fourth is sixteenths. 3. One eighth is sixteenths. 4. Three eighths are sixteenths. 5. One fourth and 1 sixteenth are 6. One fourth less 1 sixteenth are 7. Three eighths and 1 sixteenth are — 8. Three eighths less 1 sixteenth are - 4- -^^- I 1 6 3 g, means, j-g-, means, YT ^ ^? means, 3 9. 10. 11. 12. 12 X 13. 12 X 2|, means 14. I -^ y^y-, means, 15. 2^1, means, - 16 ^, means. 2, means, + 3 _ 3 _ IT — 1 6 o times Vtt = ^of 12 2|- times 12 = tV 1^ f are iof - 17. A rectangle 1^- inches wide and 10 inches long contains square inches. (a) A piece of land is 1^^ feet wide and 246 feet long. How many square feet does it contain? 18. Two thirds of 27 are one half of . 19. Three fourths of 36 are one half of . (b) Divide 34.8 by 3. (c) 34.5 - - 3 (d) Divide 53.6 by 4. (e) 51.2 - - 4 (f) Divide 61.5 by 5. (g) 63.5 . -5 216 ELEMENTARY ARITHMETIC. COMMON FRACTIONS. 1. Add I and y^. (Change | to Yg-- 2. Add |- and |. (Change | to -g. 3. From j%- subtract |-. (| = y-g.) 4. From |- subtract ^. (| = -j.) 5. Multiply 10 by 2|. (2 times 10, plus | of 10.) 6. Multiply 6| by 4. (4 times |, plus 4 times 6.) 7. Divide | by 2. (Find 1 half of f.) 8. Divide 2 by 4- (Find how many times, etc.) 9. Find the sum of 5-g- and 5yV- 10. Find the sum of 3|- and Oy^- 11. Find the difference of 8f and 4:^^. 12. Find the difference of 6 and 2y^. 13. Find the ^^roduct of 8 multiplied by 2 3 14. Find the product of 2| multiplied by 8. 15. Find the quotient of |- divided by 4. 16. Find the quotient of 4 divided by |. 17. A surface is 8 inches long and 5^ inches wide ; it contains square inches. (a) A surface is 46 feet long and 6|- feet wide. How many square feet is it ? (b) Add 256.4, 25.34, 52, and 1.75. (c) Add 624|, 346, and 138yV. (d) Add 150], 275, and 234.25. PART IV. 217 MISCELLANEOUS PROBLEMS. 1. Thomas sells oranges for 20^ a dozen; this is 6^ a dozen more than he paid for them ; he paid a dozen. (a) A man sold a farm for $9675; this was $1465 more than he paid for it. How much did he pay for the farm? 2. Bertha sold a chicken and a duck; for the chicken she received 25^; for the duck she re- ceived 10^ more than she did for the chicken; for both she received . (b) A man sold a cow and a horse; for the cow he received $37.50; for the horse he received $24.50 more than he received for the cow. How much did he receive for both? 3. Helen spent 8^ for paper, 4^ for a pencil, and had 13^ remaining. Before she bought the paper and pencil she had . (c) Mr. Lewis spent $124.50 for clothing, $275.40 for groceries, and had $134.10 remaining. How much had he before he purchased the cloth- ing and groceries? (d)At $2.75 a ]3air, how much will 9 pairs of shoes cost? (e) From 379.4 subtract 143.25. (f ) From 536.74 subtract 272|. (g)From 472.37 subtract 148.19. 218 ELEMENTARY ARITHMETIC. MEASUREMENTS. 1. A cube has square faces. The area of each face of a two-inch cube is square inches. The area of all the faces of a two-inch cube is square inches. 2. The area of each face of a three-inch cube is square inches. The area of all the faces of a three-inch cube is square inches. 3. Can you take your pencil and find the area of all the faces of a 4-inch cube? of a 5-inch cube? of a 6-inch cube? 4. Henry has a box that is 5 inches long, 3 inches wide, and 2 inches high. ( 1 ) The area of the top of the box is square inches. (2) The area oi tne bottom of the box is -. (3) The area of the top and bottom is . (4) The area of one side of the box is . (5) The area of both sides of the box is . (6) The area of one end of the box is . (7) The area of both ends of the box is . (8) Can you tell without your pencil the area of the entire outside of the box? (a) Multiply 246^ by T. (b) 436 x 2| == (c) Multiply 243 by 32. (d) 243 - 3.2 = (e) Multiply $8.75 by 5. (f) $3.62 -^7 = (g) Multiply 525 by 24. (h) 525 x 2.4 - (i) Multiply 144 cubic inches by 5. PART IV. 219 MEASUREMENTS. 1. Imagine a 1-foot cube. It has faces. Each face is a 1-foot . The area of the entire surface of the cube is square feet. 2. Imagine a 2-foot cube. It has faces. Each face is a square. The area of each face is square feet. The area of the entire surface of the cube is square feet. 3. The top of a desk is 3 feet wide and 4 feet long; its area is square feet. 4. A bLackboard is 4 feet wide and 10 feet long ; its area is square feet. 5. A rug is 6 feet wide and 8 feet long; its area is square feet. (a) (b) (c) 553 times 1825 times 1544 times ;5)$2765 $.3)$54T.5 25 3 26~ 24 25 24 15 7 15 6 1.5 1.5 1)$61.T6 4 21 20 1.7 1.6 .16 .16 (d) Divide $4735 by $5. (e) $346.5 - $.5: (f) Divide $56.25 by $.05. (g) $785 - $.5 .- (h) Divide $86 by $.05. (i) $57 - $.5 = 220 ELEMENTARY ARITHMETIC. RATIO AND PROPORTION. 9^ 12 CGDtS. 1. If 6 pears are worth 9^, 8 pears are worth - cents. 9 is of 12. 2. 6 is - 15 is 18 is of 8. - of 20. - of 24. 12 is 8 is 20 is 24 is of 9. of 6. of 15. of 18. 4. 30^ pays for 12 lemons; 40^ pays for 5. 15^ pays for 6 oranges; 20^ pays for (a) $553 5)$2765 25 26 25 15 15 (b) $182.5 3)$547.5 o O 24 7 6_ 1.5 1.5 $15.44 4)$61.76 _4 "21 20 1.7 1.6 .16 .16 (d) Divide $3265 by 5. (f) $4722 - 3 : (e) Divide $184.8 by 4. (g) $573.2 - 2 PART IV. 221 RATIO AXD PROPORTION. 1. Helen has 75^; Bertha has 50^; if Helen can buy 12 yards of ribbon, Bertha can buy . 2. Roy has 15^; David has 20^; if Roy can buy 12 oranges, David can buy . 3. If 3 horses consume 60 ears of corn in a day, 4 horses will consume . 4. If Willie can earn 24 cents in 3 hours, in 4 hours he can earn . 5. If a man can earn $15 in 6 days, in 8 days he can earn . 6. If 12 lb. of nails cost 30^, at the same rate 16 lb. will cost cents. 7. If 20 eggs are worth 18^, 30 eggs are worth cents. 8. Six ponies consume as many oats in a day as 8 ponies. If 8 ponies consume 20 quarts, 6 ponies consume quarts. 9. A man can earn times as much money in eight days as he can in 6 days. If he can earn $21 in 6 days, in 8 days he can earn ■ — — . 10. If 15 lbs. of sugar are worth 60^, 20 lbs. ^t^ti wuiLii ADDITION. (a) (b) (c) (d) 346| 478| 3511- 1361 175^ 243 246 241 242 187A 184A 826f| 222 ELEMENTARY ARITHMETIC. MISCELLANEOUS PROBLEMS. 1 . A pencil cost 5^ ; a book cost 6 times as much ; both together cost ■. (a) A harness cost $17.25 ; a carriage cost 5 times as much. Find the cost of both. 2. If 5 sheep cost $21, at the same rate 10 sheep will cost dollars. (b) If 5 tons of bran cost $62.50, at the same rate how much will 10 tons cost ? 3. If 5 bushels of apples cost $2.20, at the same rate 15 bushels Avill cost . (c) If 5 tons of flour cost $140.25, how much will 15 tons cost at the same rate ? (d) Find the sum of six thousand two hundred forty-two, one thousand eighty four, and seven hundred ninety-four. 4. Arthur's book cost 25^; his slate cost 10^ less than his book cost ; his slate and book together cost . (e) A man paid $5650 for a house ; for a piece of land he paid $1000 less than he paid for the house. How^ much did the land and house to- gether cost? SUBTRA CTION. (a) (b) (c) (d) 4325 2371 4628 3626 1816 1528 2819 1819 PART IV. 223 SIMPLE NUMBERS. (a) (b) (c) (d) (e) $3)$36 3)$36 7^)35^ 7)35^ i)8 12 times $12 5 times 5^ 16 1. In problem (a) the dividend is -, the quotient is ; the divisor is . 2. In problem (b) the quotient is ; the dividend is ; the divisor is . 3. In problem (c) the divisor is ; the quotient is ; the dividend is . 4. In problem (d) the and the are like numbers. 5. In problem (c) the and the are like numbers. 6. In a problem, the divisor is $3 and the quotient, 10; the dividend is . 7. In a problem, the dividend is $36 and the quotient, $9 ; the divisor is . 8. If the divisor is 1, the quotient number is the same as the dividend number. If the divisor is more than 1, the quotient number is than the dividend number. If the divisor is less than 1 the quotient number is than the dividend number. MULTIPLICATIOX. (f) (g) (10 (i) 326 143 234 245 24 23 32 42 224 ELEMENTARY ARITHMETIC. DENOMINATE NUMBERS. 1. From a can containing 15 qt. of milk, a dealer sold 5 qt. 1 pt. ; there remained . (a) From 425 qt., subtract 127 qt. 1 pt. 2. A milk dealer sold 2 qt. 1 pt. to his first cus- tomer, 3 qt. 1 pt. to his second customer, and 1 qt. 1 pt. to his third customer; to all he sold . (b) Add 25 qt. 1 pt., 15 qt. 1 pt., and 22 qt. 1 pt. 3. From a string 5 yd. long, George cut off 2 yd. 2 ft.; there remained . (c) From 345 yd., subtract 82 yd. and 2 ft. 4. From a piece of cheese weighing 6 lb. a, grocer cut off 1 lb. 12 oz.; there remained , (d) From 89 lbs. subtract 17 lbs. 5 oz. (e) (f) (g) 258 times 215 times 317 t's. ;25)$6450 $2.5)$537.5 $.25)$79.25 50 50 75 145 37 I^ 125 25 2.5 200 12.5 1.75 200 12.5 1.75 (h) Divide $6125 by $25. (i) $2875- $25 = (j) Divide $337.5 by $2.5. (k) $712.5-$2.5 = (1) Divide $84.50 by $.25. (m) $55.50- $.25 = PART IV. 225 COMMON FRACTIONS. thirds sixths ninths eighteenths 1. One third is eighteenths. 2. One sixth is eighteenths. 3. One ninth is eighteenths. 4. Two ninths are eighteenths. 5. One sixth and 1 eiorhteenth are . 6. One sixth less 1 eighteenth are - 7. Five ninths and 1 eighteenth are 8. Five ninths less 1 eighteenth are Q5_l3_ 5_3_ 10. 11 X 2 = 12 X I = 11. 12x2|= |-^A = 12. 2-1- 1-2 = (a) (b) (c) 1258 $21.5 $3.17 25)16450 25)$537.5 25)$79.25 50 50 75 145 37 4.2 125 25 2.5 200" 12.5 1.75 200 12.5 1.75 (d) Divide $3250 by 25. (e) $8125 -^ 25 : (f) Divide $572.5 by 25. (g) $547.5 - 25 (h) Divide $61.75 by 25. (i) $83.50 - 25 226 ELEMENTARY ARITHMETIC. COMMON FRACTIONS. 1. Add 4 and -^. (Eeduce 2. Add -^ and |-. (Eeduce 3. From |- subtract -^-^. (Eeduce 4. From |- subtract 4- (Eeduce 5. Multiply 12 by 2|. (2 times 6. Multiply 51 by 6. (6 times 7. Divide 8| by 2. (|- of .) 8. Divide 2| by |. (Find how many times, etc.) 9. Find the sum of 7^- and 7^. 10. Find the sum of 4^"^^^ and 3|. 11. Find the difference of 8 and 2|-. 12. Find the diiference of 9^ and 4y^^. 13. Find the product of 9 mi>lti]3lied by 2|. 14. Find the product of 2| multiplied by 9. 15. Find the quotient of f divided by 6. 16. Find the quotient of 6| divided by f . (a) (b) ADDITION. (d) (e) 24 35 46 56 24 32 24 21 46 34 41 31 38 36 44 55 42 20 26 84 47 56 34 16 24 38 38 47 66 74 PART IV. 22 .u^^ i MISCELLANEOUS PROBLEMS. 1. A dealer sold 6 bushels of oats for $1.80; tlie price per bushel was . (a) A farmer sold 25 bushels of wheat for $18.75. What was the price per bushel ? 2. Eight bushels of beans are worth times as much as 6 bushels. If 6 bushels are worth $7, 8 bushels are worth dollars. 3. Eight bags of salt are worth — — times as much as 6 bags. If 6 bags are worth $5, 8 bags are worth dollars. 4. Twelve bushels of corn are worth times as much as 8 bushels. If 8 bushels are worth $3, 12 bushels are worth dollars. 5. Henry's father is 6 feet 1 inch in height; Henry is 4 feet 9 inches ; Henry's father is taller than Henry. (b) From 75 ft. 2 in. subtract 43 ft. 8 in. 6. Alice has a picture that is 1 ft. 6 in. wide and 2 ft. 4 in. long ; its perimeter is . (c) What is the perimeter of the floor of a room that is 14 ft. 6 in. wide and 16 ft. 8 in. long ? SUBTRACTION. (d) (e) (f) (g) (li) 828| 954 425.2 48.75 38.1 182tV 1821-1- 131.8 29.08 19.6 228 ELEMENTARY ARITHMETIC. MEASUREMENTS. 1. A rectangle -^ of an inch wide and 10 inches long contains square inches. (a) A rectangular piece of land is 4^ of a foot wide and 238 feet long. How many square feet does it contain? 2. A rectangle 2 feet wide and 2 yards long contains square feet. (b) A rectangular piece of land 2 feet wide and 35 yards long contains how many square feet? 3. A rectangle contains 18 square inches; it is 6 inches long; it is inches wide. (c) A rectangular piece of land contains 726 square feet; it is 6 feet wide. How long is it? 4. Think of a room that is 12 feet long, 10 ft. wide, and 8 feet high. Is it a large or a small room? Could your teacher standing on the floor of such a room, reach the ceiling? (1) The area of the ceiling is square feet. (2) The area of the floor is square feet. (3) The area of one end wall is . (4) The area of one side wall is . MULTIPLICATIOJN "• (d) (e) (f) (g) (h) 372A 575 326 47.05 26.2 6 H 32 3 n PART IV. 229 ME AS U RE MEN TS . 1. An oblong 1 inch wide and 12 inches long contains square inches. It is of a square foot. 2. An oblong 3 inches wide and 12 inches long contains square inches. It is of a square foot. 3. Twenty -four square inches are of a square foot. 4. Forty-eight square inches are of a square foot. 5. An oblong 6 inches wide and 12 inches long contains square inches. It is of a square foot. 6. A rectangle 6 in. by 6 in. contains sq. inches. It is of a sq. foot. 7. Sixty square inches are of a square foot. 8. Eighty-four square inches are of a sq. foot. 9. An oblong 3 inches wide and 4 inches long contams square mches. It is - of a square foot. DIVISION. (a) (b) (c) (d) 30168* |.06)$8.34 6)$8.34 |0.4)$11. (e) Divide seventy-five and forty-five hundredths by five hundredths. *Change 3i and 168 to halves- 230 ELEMENTARY ARITHMETIC. ADDITION. (a) (b) (c) (d) (e) 734| 674> 74.3 24.35 65.2 48 132 156 6.07 74.8 35H 356] 17 21.4 53.5 123 47 842.5 8.25 87.6 246A 1874 7.2 '36.36 95.3 75 84 155 5.5 42.7 (f ) Add twenty-four and seven tenths, and eight and forty-three hundredths. SUBTRACTION. (g) (10 (i) (J) (k) 6431 954 725 34.76 89.1 171| 3281 186.2 18.29 42.8 (1) From twenty-five and eiglit tentlis, take twelve and five lumdredths. MULTIPLICATIO: N-. (m) (n) (0) (P) (q) 324A 482 534 6.25 2.75 6 71 231 5 8 (r) Multiply nine and four hundredths by six. (s) Divide 246.25 by 25. (t) Divide 14568 by 12. (u) Divide 32750 by 25. PART IV. 231 ADDITION. (a) (b) (c) (d) 308| 506| 75.4 25 bu. 2 pk. 64| 871 31.8 34 bu. 2 pk. SUBTRACTION. (a) (b) (c) (d) 187| 274-1- 35.6 54 bu. 38^V 146 f 20.8 31 bu. 3 pk. MULTIPLICATION. (a) Multiply 54 by 32. (b) 54 x 3.2 = (c) Multiply 53 by 35. . (d) 53.5 x 35 = (e) Multiply 53| by 35. (f ) 54.3 x 35 = (g) Multiply 454 by 24. (h) 45.5 x 24 = (i) Multiply 48 by 25-^. (j) 48 x 25.5 = (k) Multiply 56 by 23|.^ (1) 56 x 23.2 = (m)Multiply 64 by 18|. (n) 64 x 18.7 = (o) Multiply 86 by 21|. (p) 86 x 21.5 - DIVISION. (a) Divide 2106 by 26. (b) 220.8 - 24 (c) Divide 1272 by 24. (d) 687.5 - 25 (e) Divide 4150 by 25. (f ) 57.46 - 26 (g) Divide 8372 by 26. (h) 31.75 - 25 (i) Divide 5842 by 23. (j) 637.2 - 27 (k) Divide 8235 by 27. (1) 820.8 - 27 (m) Divide 6345 by 27. (n) 63.18 - 27 (o) Divide 8475 by 25. (p) 94.25 - 25 23^ ELEMENTARY ARITHMETIC. For dictation exercises in addition, subtraction, multiplication, and division.* (a) (b) (c) (d) ^ (6240 * t 3760 3675 5272 3852 6325 4728 6148 2 l^^2^ ' 14680 . 4354 3904 4266 5646 6096 5734 3 P4^^ ■ ' [2540 7532 7384 5058 2468 2616 4942 f4020 ' (5980 5831 3272 6282 4169 6728 3718 (1960 ■ 1 8040 6202 4352 7506 3798 5648 2494 a |2520 1 7480 2947 5376 3528 7053 4624 6472 7 i'3740 ' [6260 8274 4200 2358 1726 5800 7642 8 1^^^^ ' 1 1480 7385 6736 8172 2615 3264 1828 [5520 ' 1 4480 5467 8296 3726 4533 1704 6274 ^^ (7660 12340 4445 2776 5544 5555 7224 4456 * See " Suggestions to Teachers," pp. 247 and 248. DEFINITIONS AND EXPLANATIONS.^^ A unit is one. A number is one or it is composed of ones. Notation is tlie art of expressing numbers by figures or other characters. ARABIC NOTATION. In the Arabic Notation figures are employed. The figures are: 1, 2, 3, 4, 5, 6, 7, S, 9, 0. In the number 29, the figure 9 is said to stand in the first place and the figure 2 in the second place. In the number 437, the figure 7 is said to stand in the first place, the figure 3 in the second place, and the figure 4 in the third place. In the number 8156, the figure 6 is said to stand in the first place, the figure 5 in the second place, the figure 1 in the third place, and the figure 8 in the fourth place. A figure in the first place expresses units. A figure in the second place expresses tens. A figure in the third place expresses hundreds. A figure in the fourth place expresses thousands. A figure in the fifth place expresses tens of thousands. In the number 4.65, the figure 6 is said to be in the first decimal place, the figure 5 in the second decimal place. A figure in the first decimal place expresses tenths. A figure in the second decimal place expresses hundredths. Tell what each figure expresses in the following combination : 2764.35. *See that the pupil can read the following pages intelligentl>' before he is asked to commit to memory any part of them. 233 234 ELEMENTARY ARITHMETIC. ADDITION. Addition is the process of uniting two or more numbers into one number. The sum is the number obtained by 26 adding. Z^ 75 (Sum.) SUBTRACTION. Subtraction is the process of taking one number from (out of) another number. The minuend is the number from which another number is taken. The subtrahend is the number $75 (Minuend.) taken from another number. $38 (Subtrahend.) The difference is the number $37 (Difference.) obtained by subtracting. Observe that the sum of the subtrahend and difference equals the minuend.* MULTIPLICATION. Multiplication is the process of taking one number as many times as there are units in another number. $36 (Multiplicand.) The multiplicand is the num- 25 (Multiplier.) ber taken, or repeated. $180 The multiplier is the number ^72 that shows how many times $900 (Product.) the multiplicand is to be taken, or repeated. * Teach pupils to "prove" their problems in subtraction. DEFINITIONS AND EXPLANATIONS. 235 The product is the number obtained by multij)ly- ing. In the example given, $180 and $720 ai-e called the partial (part) products. $180 is the product of $36 and 5; $720 is the product of $36 and 20. Observe that dividing the product by the multiplier gives the multiplicand.* DIVISION. Division is one of tioo processes. I. It is finding how many times one number is contained in another number; $18 -^ $2 = 9. II. It is finding one of the equal parts of a number; $18 -- 2 = $9. To divide $18 by $2 means to separate $18 into groups of $2 each and count the groups. To divide $18 by 2 means to separate $18 into 2 equal groups, and count the dollars in one group; that is, find one half of $18. In Case I. the quotient tells how many times the divisor is contained in the dividend. In Case II. the quotient is a part of the dividend. To THE Teacher. — The second case is often very properly called partition. But both processes are evidently cases of division, since in both instances we separate (divide) the given number into equal parts. In Case I. we count the parts (groups). In Case II. we count the units in each part (gxoup). The dividend is the number divided or separated. The divisor is the number by which we divide. The quotient is the number obtained by dividing, * Teach pupils to " prove " their problems in multiplication. 236 ELEMENTARY ARITHMETIC. Observe that in either case the product of the divisor and quotient equals the dividend.* To THE Teacher. — There can be no remainder in a com- plete division. Therefore, the product of the quotient and divisor is ahvays equal to the dividend. We may have a remainder when the process of dividing is incom- plete. In such a case the quotient is incomplete and the remainder is the undivided part of the dividend. To the product of the incomplete quotient and divisor add the remainder, and the sum thus obtained will be equal to the dividend. An even number is the number two, or a number that can be separated into twos ; as, 4, 6, 20, 40, 44, etc. A number that cannot be exactly separated into twos is called an odd number : as, 3, 5, 7, 21, 71, etc. FRACTIONS. A fraction is one or more of the equal parts of a unit. A fraction is usually expressed by two numbers, one of them being written above a short horizontal line and the other below it; thus, |^, |, fV- The number above the line is called the numerator. The number below the line is called the denomi- nator. The denominator shows the number of equal parts into which the unit is divided. * Teach the pupils to " prove" their problems in divlBion. DEFINITIONS AND EXPLANATIONS. 237 The numerator shows the number of parts taken. The denominators of some fractions are not usually expressed by figures; thus, 5 tenths is usually written, .5; 27 hundredths is usually writ- ten, .27. Of the fraction |, 7 is the numerator and 8 is the denominator. Of the fraction .5, 5 is the numerator and 10 is the denominator. Of the fraction .27, 27 is the numerator and 100 is the denominator. If the numerator and the denominator of a frac- tion are the same number, as -|, ^l? w? ^^^•:> ^^^^ fraction is equal to one unit. If the numerator of a fraction is greater than the denominator, as f, l^, \^-, etc., the fraction is equal to more than one unit. A fraction whose numerator is equal to or greater than its denominator is called an improper fraction. A fraction whose numerator is less than its denominator is called a proper fraction. Two thirds, f, |-, |-^, are proper fractions. Five fourths, |^, |, ff, are improper fractions. 238 ELEMENTARY ARITHMETIC DRY MEASURE. 2 pints (pt.) = 1 quart (qt.). 8 quarts = 1 peck (pk.). 4 pecks = 1 bushel (bu.). LIQUID MEASURE. 2 pints (pt.) = 1 quart (qt.). 4 quarts = 1 gallon (gal.). MEASURE OF TIME. 60 seconds (sec.) = 1 minute (niin.)o 60 minutes = 1 hour (hr.). 24 hours = 1 day (da.). 7 days = 1 week (wk.). 28 to 31 days = 1 month (mo.). 12 months = 1 year (yr.). 365 days = 1 common year. 366 days = 1 leap year. 52 weeks and 1 day = 1 common yeaFo 52 weeks and 2 days = 1 leap year. LINEAR MEASURE. 12 inches (in.) =. 1 foot (ft.). 3 feet = 1 yard (yd.). DEFINITIONS AND EXPLANATIONS. 239 AVOIRDUPOIS WEIGHT. 16 ounces (oz.) = 1 pound (lb.). 2,000 pounds = 1 ton(T.). SQUARE MEASURE. 144 square inches (sq. in.) = l square foot (sq. ft.), 9 square feet (sq. ft.) = 1 square yard (sq. yd.). ROMAN NOTATION. In the Roman Notation seven capital letters are emj)loyed. The letters are — I, V, X, L, C, D, M. I. = 1, V. = 5, X. = 10, L. = 50, C. - 100, D. = 500, M. = 1000. PRINCIPLES. When a letter is repeated its value is repeated. XX. = 20. II. = 2. When a letter is placed before one of greater value, the difference of their values must be taken. IX. = ( 10 — 1 ) = 9. When a letter is placed betAveen two letters each of greater value, its value is taken from the last letter. XIX. =3 10 -f 10 - 1 = 19. Placing a short horizontal line over a letter multiplies its value by 1000. X. = 10,000. Sometimes small letters are employed instead of capitals ; thus, ii. = 2, iv. = 4, etc. 240 ELEMENTARY ARITHMETIC. ROMAN NOTATIOX TABLE. II. = 2. III. =: 3. IV. = 4 V.=:5. VI. := 6. VII. = 7. VIII. = 8. IX. =9. X.= 10. XL =11. XII. = 12. XIII. = 13. XIV. = 14. XV. = 15. XVI. = 16. XVII. = 17. XVIII. = 18. XIX. = 19. XX. = 20. XXX. = 30. XL. = 40. L.= 50. LX.= 60. LXX. = 70. LXXX. = 80. XC.= 90. C.= 100. CO. = 200. CCC.= 300. CCCC. = 400. D.= 500. DC. = 600. DCC.= 700. DCCC. = 800. DCCCC.= 900. M.= 1000. MM. = 2000, V.= 5000. XXXVIIL = XLVI. = MDCC. = XCIX. = CCCVL = DXLV. = XXIV. = LXXXIV. = LXXVI. = XL VII. = XXXII. = XCVII. = LVIIL = CCXIX. = DXIX. = MXIX. = LXXXI. = LXIV. = MDCCC. = MDCCCXCVL = The author of this book was born Feb. IX., in the year of our Lord MDCCCXLI. The Roman notation is now chiefly employed in num- bering chapters or lessons, in dates, and upon the dials of time-pieces. How is the number four represented upon the face of a clock ? *A period is usually placed after each completed Roman numeral. SUGGESTIONS TO TEACHERS. Read the preface of this book. Read pages 5 and 6, and see that pupils are familiar with the number facts there presented before they are required to bring the book to the schoolroom. But even after the book is in the hands of the pupil, he should not, as a rule, be asked to read a page until the teacher has assured herself that he is thoroughly prepared for it. The pupil cannot prepare himself. It is the business of the teacher not simply to "hear recitations," but to teach. The teaching to be done in connection with a page of this book, should be done mainly before the pupil attempts to read it. This teaching is the leading of the pupil to perceive those magnitude relations and to memorize those primary number facts which are necessary to be perceived and memorized in order that the pupil may be able to read the pages. Until the teacher can devise a better plan for herself, she should adhere strictly to the following order of procedure: STEP I. The teacher takes the book. The pupils are without books and give their undivided attention to the teacher. The teacher reads one of the statements, pausing at the blank for the pupils to supply the necessary word or w^ords. Pupils signify their readi- ness to answer by raising their right hands. The teacher names the pupil who is to give the words to be supplied. (Occasionally, especially if the problems seem difficult, a pupil may come for- ward briskly and whisper his answer to the teacher. Another and another may follow rapidly until all who are prepared to do so have given answers. This promotes independence and enables the teacher better to judge of individual work). If the teacher discovers that there are primary number facts introduced on the page w^hich have not been memorized by the pupil, this should be attended to at once. Do not proceed until this has been thoroughly accomplished. Better spend several days, if neces- sary, in the preparation for reading a single page, than to attempt to read it without proper preparation. STEP II. See that each pupil is familiar with the written forms of all words appearing upon the page under consideration. Use the blackboard for this purpose and, as a rule, show new words in the connection in which they appear in the book. 241 242 ELEMENTARY ARITHMETIC. STEP III. Put the book into the hands of the pupils and let them read silently the page for which preparation has been made. STEP IV. The pupils may now read aloud the page which has been read silently. If the work of preparation has been thoroughly done there will be but little hesitation on the part of the pupils in reading the page. STEP V. The pupils may copy (filling the blanks) sorne designated part of the page that has been read. Allow no careless written work. In examining the papers make but two classes; those that are "perfect" and those that are "imperfect." The teacher is at fault if more than half the papers are "imperfect," In a well taught class often 90 per cent, of the papers will be "perfect." In this examination of papers, spelling, capital letters, punctuation, and accuracy of result are to be considered. If there be a single mis- spelled word, or one figure or punctuation mark be wrong, the paper must be excluded from the "perfect paper" class. If the teacher finds it seemingly impossible to secure 50 to 75 per cent, of "perfect papers," more time should be spent in preparation and the amount of work required of the pupil should be diminished. Better a single statement accurately written than a half page with many errors. The work of the teacher should be not mainly the correction but the prevention of errors. Page 9. — If the pupil is prepared to read in a Third Reader, and if the number facts given on pages 5 and 6 have been mastered, he will read this page without much hesitation. If he finds difficulty in calling the words, lay the book aside and teach him to read. If he cannot readily fill the blanks, teach him orally the necessary number facts. Page 10. — During the first reading of this page by the teacher (the pupils filling the blanks) each pupil should have a foot ruler in his hand. After this, it should be read a second time, the ruler being hidden from view. Before reading statements 11 and 13, the pupils may "draw a square in the air" if such a procedure is necessary to assist the imaginative power. They must be trained in every possible way to image magnitude. Page 11. — Observe that there are problems in addition at the bottom of this page, also on pages 16, 21, 26, 31, 36, etc., through- out the book. So far as practicable, require pupils to make these additions ^?^s^ ivithout, then with, the aid of a pencil. The pupil SUGGESTIONS TO TEACHERS. 243 should perceive the fact that 28 and 2 are 30, before he is allowed to use his pencil to secure this result. He should use his pencil as a preparation for more difficult additions in which the pencil will be a convenience. Page 12. — Observe that there are problems in subtraction at the bottom of this page, also on pages 17, 22, 27, 32, 37, 42, etc., throughout the book. This work should be done in the same order as suggested for the work at the bottom of page 11. Page 13. — If the pupil cannot image the squares and oblongs described on this page the pencil or the crayon must be used; but sometime he must learn to image such figures without draw- ing them. The strength of the pupil depends very largely upon his skill in making accurate mental pictures from oral and written descriptions. This xooiver must he cultivated from the first. Observe that there are problems in multiplication at the bot- tom of this page, also on pages 18, 23, 28, 33, 38, etc., throughout the book. So far as practicable, require pupils to make these multiplications first ivithout, then with, the aid of a pencil. The pupil should perceive the fact that two 35's are 70, before he is allowed to use his pencil and "carry " to secure this result. Page 14. — Here the pupil should be made somewhat familiar with the meaning and the use of the expression, are contained in. Observe that in the problems at the bottom of this page as well as in those on pages 19, 24, 29, 34, 39, 44, 49, etc., the pupil is required to find hoiu many times one number of things is con- tained in another number of things. Page 15.— Observe that in the problems at the bottom of this page as well as in those on pages 20, 25, 30, 35, 40, 45, etc., the pupil is required to find one of the equal parts of a number of things; thus, to divide 12"? by 2 is to find | of 12*?. The pupil should solve these problems "mentally" before using the pencil in their solution. Page 16.— During the first reading of this page by the teacher (the pupils filling the blanks) the pint and quart measure may be before the pupils. The page should then be read again, the measures being hidden from view. Page 17.— See note under "Pacts of Partition and Multipli- cation," page 6. Page 19.— This page should not be attempted until the pupil is familiar with the thermometer and its use. In many schools 244 ELEMENTARY ARITHMETIC. the subject of temperature is presented in the lower grades. Even primary pupils will take great interest in a temperature record, and will, with little effort on the part of the teacher, become familiar with this class of problems. Page 30. — This page is designed to impress upon pupils the double nature of abstract problems in division. 6 divided by 2, may mean, find how Tiiany times 2 (apples, dollars, cents) are con- tained in 6 (apples, dollars, cents), or it may mQanfind ^ of 6 (apples, dollars, cents.) Page 31. — The pupil who has done the work thoroughly to this point will be able to read this 'page, filling all the blanks correctly, in two minutes or less. Page 32.^ — Before proceeding further, see that each pupil has so perfectly memorized the thirty-three addition problems that he can recite the answers to them in 33 seconds or less. Do not require him to name the figures, but to give sums only. Page 35. — Do not at first use a digit to represent the number of parts into which a unit is divided. Instead of i, write one^ fourth or 1 fou7^th. Pages 35, 36, 37, 38.— Observe that in solving the problems on page 35, the pupil thinks of surface magnitude; page 36, linear magnitude; page 37, value magnitude; while on page 38, all these are presented. Page 41. — The three number facts here given mustbeper- fectly memorized. Pupils cannot easily and quickly perceive magnitude relation without the mastery of the primary number facts. The more important of these are given on pages 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, and reviewed on page 152. See that these facts are mastered when presented. Do not allow it to he truthfully said of your fourth grade pupil that he ''does not knoiD the niidtiplication table." Page 45. — Teach orally the facts given on this page before the pupil is asked to read it. Put diagrams on the blackboard and continue the oral work, if need be, for several days, until the pupil can easily think one half, one fourth, one sixth of some thing when the words that should suggest these are spoken. Success here, as everywhere in mathematics, depends upon the ability of the pupil to b^ing imaged magnitude into consciousness. The suggestions given for page 45 will apply to pages 55, 65, 75, 85, 95, 105, 115, 125, 135, 145. If the pupil is unable to fill the SUGGESTIONS TO TEACHERS. 245 blanks on any one of these pages promptly, review all similar pages preceding it. If this does not enable the teacher to secure satisfactory results, more oral work should be done with the dia- grams on the blackboard confronting the pupil. The learner must perceive that \ and ^ are |; that \ and |- are f, etc. Observe that each of these pages provides problems in addition, subtraction, multiplication, division, and " partition" of fractions. Page 48. — Regard the problems on this page, particularly those near the top of the page, as a test of the quality of the work of the teacher and pupil while passing over the preceding pages of the book. Indeed the same may be said with reference to almost any page in the book after the first; but this thought is especially ai^plicable to pages 48, 58, 68, 78, 88, 98. Page 53. — Teach orally the meaning and use of the word perimeter. Do the same with other terms introduced on pages 63 and 73. Perfect familiarity with these terms and the ability to image such figures as are mentioned, are the necessary prepara- tion for the work on pages 83, 93, 103, 113, 123, 133, 143. Page 64. — Lead pupils to distinguish sharply between the two kinds of problems given in the first four examples. Ask, again and again, when a problem like one of these is presented, What does it mean 9'^ See pages 74, 84, 94. Page 67. — The drill suggested on this page is invaluable. The other steps of this drill will be found on pages 77, 87, 97, 107, 117, 127, 137. Require pupils to add numbers represented by figures in a column, without naming each number; thus, in adding column (a) page 67, the pupils will say, tico, four, six, eight, etc. Put columns similar to these upon the blackboard and continue the drill until the pupils can add a column made up of 2's and I's, or of 3's, 2's, and I's, almost as readily, as they can add a column of 2's or of 3's. Page 70. — On this page tenths are presented for the first time without the written denominator. If the pupil clearly understands that .4 is another way of writing j%, and that 2.7 is another way of writing f ^ or 2 j\, he will readily do work sug- gested on this page and similar work found on pages 80 and 90. Page 89. — If pupils are taught the meaning of the different problems on this page they will find no very great difficulty in their solution. The same may be said of the same class of prob- lems found on pages 96, 99, 106, 109, 116, 119, 126, 136, 146. 246 ELEMENTARY ARITHMETIC. Page 104. — Be sure that the pupil understands the meaning of the work on this page. Before he attempts to multiply by a fraction, what it means to do this, must be made clear to him. He must not be allowed to proceed mechanically to obtain an ansiver while he knows nothing of the magnitude relation in- volved. To multiply by \ is to take once | of a magnitude, that is, ^ of it; to multiply by | is to take three times | of a magnitude, that is, I of it. Page 109, Prob. 10.— To multiply | ft. by 2|, take 2 times | of a foot and to this add | of |- of a foot. Prob. 16. — To multiply 1.2 in. by 2|, take 2 times 1.2 in. (12 tenths), to which add | of 1.2 in. (12 tenths). Page 114, Problems 4 and 10.— Remind the pupil that to multiply by 2|, he must take 2 times the multiplicand and to this add ^ of the multiplicand. The multiplying of 2| by 2\ becomes a very simple problem when the pupil understands ivhat it means. Page 152. — Do not allow a pupil to begin the work in Part III of this book until he has memorized every number fact given on this page. Pages 153 to 172. — Observe that these 20 pages are devoted to the solution of problems involving whole numbers and tenths. The usual " spiral " appears on pages 153, 154, 155. Another " spiral " covers pages 156 to 159. Pages 161 to 161 are for the purpose of teaching the multiplication of any integral number (of things) by tenths. See that each step in this work is made clear to the pupil. Review many times if necessary. Pages 166 to 170 are for the purpose of making clear the distinction between (1) dividing a number cf tenths (of things) by a number of tenths (of things) and (2) finding one of the equal parts of a number of tenths (of things). If this work is done as here suggested it will go a long way in guarding the pupil against errors in " pointing off " in division of decimals. Pages 171 and 172. — Note the similarity of the numbered or "figure problems " to the corresponding " letter problems." Pupils who have solved the figure problems in class, should be able to solve the letter problems without assistance, at their seats. Page 173. — See that the pupil understands that to multiply 15 by 23, he may take 3 times 45, and 20 times 45, and find their sum. Page 182. — Pupils should solve the figure problems in class; the letter problems without assistance at their seats. SUGGESTIONS TO TEACHERS. 247 Page 188. — Pupils should be reminded, if necessary, that a square inch is a 1-inch square or its equivalent. Pages 193 to 212. — Observe that these pages are devoted to the solution of problems involving whole numbers, tenths, and hundredths. Review, if necessary, pages 153 to 172. Compare the following: Pages 153 and 193; 154 and 194; 155 and 195, etc. Pages 230 and 231.— The pupil should be expected to do this work, and to solve such problems as may be dictated from page 240, luith '' xmrfect accuracy." Nothing short of this should be commended in mechanical processes. To have one figure- ivrong in one problem of every ten is failure. " Ninety j^er cent " in such work is neither ^' excellent" nor "good,'' it is ivorthless. Careless work must not be tolerated. The accurate habit must be established. Page 232.— Hundreds of problems may be given by dictation from this page, and the teacher may know the answer to each problem with very little effort. ADDITION. Give any integral number represented by four figures, as 2461, and with this give all the numbers in any three groups on the page; their sum is 32461. The same number with any four groups will give 42461 ; with any five groups, 52461, etc. In giving the numbers in the groups, give first, one from each group; then, the remaining one of each group. Of course it is not neces- sary that the number supplied by the teacher should always be given first. SUBTRACTION. Take any number greater than 10000; from this subtract first one number of a group; from the remainder subtract the other number of the group; the last result should be the given number less 10000. Take the number 15246 ; subtracting a& directed, the last result will be 5246. Subtract either number of any group from 10000, and the result will be the other number of the group. Subtract either number of any group from a number that is 2 or 5 or 25 or 100 or 1000 more than 10000. and the result will be 2 or 5 or 25 or 100 or 1000 more than the other number of the group. MULTIPLICATION. Multiply any number by 3 and by 7, or by 4 and by 6, or by 2 248 ELEMENTARY ARITHMETIC. and by 8, and the sum of the two products equals 10 times the number. Multiply any number by 7 and by 8 and the sum of the two products equals 15 times the number, or 10 times the number plus |- of 10 times the number. Multiply any number by 12 and by 58, or by 17 and by 53, or by 36 and by 61, and the sum of the two products equals 100 times the number. DIVISION. Divide any number by 1 and by 5 and by 20, and the sum of the three quotients equals | of the number. Divide any number by 3 and by 6, and the sum of the two quotients equals ^ of the number. Divide the numbers in any group on the page by 7, and the sum of the two quotients is 1428^. Divide the numbers in any group on the page by 8, and the sum of the two quotients is 1250. Divide the numbers in any group on the page by 9, and the sum of the two quotients is 1111^. Each number in column (a) is exactly divisible by 2, by 4, by 5, by 10, and by 20. The first number of each group in column (b) is exactly divis- ible by 7. The first number of each group in column (c) is exactly divis- ible by 8. The first number of each group in column (d) is exactly divis- ible by 3, by 6, and by 9, If the teacher will make herself thoroughly familiar with the foregoing statements, she will be able to dictate an unlimited amount of practice work, and to test the accuracy of the pupils, without actually solving the problems herself. REVIEW. If, after the book has been completed, the pupils are found inaccurate and unskilled in mechanical processes, review the work found at the bottom of each page from page 9 to page 229. Insist upon absolute accuracy- ID d:DO^d h4t440 UNIVERSITY OF CAUFORNIA LIBRARY ^■HHi^HP ' ■iili liP i iiiP I ..ill Ji !! I if ii, : ,. nmm mnmUm lUif ll-tHH !! .'f i'ii!' ;.-;lh!Ui .*ilf!Hi! ilillPiUliifii, illll . j ■^' -" iiiff^^^^^^^^^^^