7. If a barrel of flour is worth $93, how much are 2 barrels worth? 3 barrels? W. 11 barrels? 223 barrels ?

8. 2 loaves of bread will last 1 man 2 days: at the same rate how much will 3 men require? 5 men? W. 68 men? 125 men?

96. TO MULTIPLY AN INTEGER BY A FRACTION, OR TO TAKE THE FRACTIONAL PART OF A NUMBER.

ORAL EXERCISES.

1. What is of an apple? ANS. One of the two equal parts into which an apple is divided.

2. What is of an orange? of a pound? of an inch?

3. What is of a lemon? ANS. Two of the three equal parts into which a lemon is divided. What is of a gallon? of an ounce ?

4. Multiply $2 by 2, or, what is of $2?

NOTE. -The word "of" is used instead of "times" when the multiplier is a fraction.

66

We say "3 of 2," instead of " times 2."

$2 X 3 ÷ 4.

of 1 dollar

of 3 times 2 dollars; or, $2 × 3÷4 $11.

RULE. To multiply by a fraction, multiply by the numerator, and divide by the denominator of the fraction. NOTE. Whenever it is possible, the equal factors of the dividend and divisor should be canceled.

5. Multiply $7 by 5, by 2, by . 6. Multiply 8 by 4, by 3, by 3.

7. Multiply 9 by 5, by 3, by .

REVIEW. - Define a composite number. (70.) What is a prime number. (71.) What is a factor, or divisor? (72.) What is a greatest common divisor? (74.) What is a common multiple? (75.)

5

5. Multiply 8 by 3. 7 by 4. 9 by 12 by §.

By Cancellation.

2

FORMULA. 8×3=8×3÷4=8×3÷4=6.

6. What is of 14? of 16? of 21?5 of 22?

2

9. If 1 bushel of potatoes is worth $1.25, what are bushels worth? W. of a bushel? g of a bushel? 25 bushels?

10. If a bushel of wheat costs $2.10, what must be given for 2 bushels? W. For of a bushel? For 52

bushels?

11. W. An acre of land is valued at $314.27: what are 2 acres of such land worth? of an acre? 57

- acres?

I

12. W. If I pay $4.37 for a cord of wood, what must for 3 cords of such wood? For 43 cords? For 78 cords? For of a cord?

pay

13. What will of a pound of indigo cost, at $4 per pound? W. At $3.40? At $8.96 ?

14. W. What will 13 bushels clover-seed cost, at 8 dollars per bushel? At $9.70? At $11.23?

REVIEW. When is a fraction said to be proper? (82.) Illustrate by an object. Describe an improper fraction. (83.) Illustrate by an object. What is a mixed number? (84.)

ANALYSIS. — 1. If ¦ is divided into 4 equal parts, each part is

of as there are 3 thirds in a
unit, each of which may be divided
into 4 such parts, the unit contains
12 such parts, and each part is
2. Since of is, of 12.
3. Since of is, of
2 3=12.

12

RULE. Multiply the numerators together for a new numerator, and the denominators for a new denominator. NOTE. Mixed numbers may be changed to improper fractions when more convenient, or when the operation can be shortened by cancellation. Fractions with the word "of" between them are sometimes called "compound fractions." The word "of "is equivalent to the word "times," or the sign of multiplication; thus, of 3 = times; or, X.

ORAL EXERCISES.

1. Multiply by 2; or, what is of ?

4. If of a pie be cut into 2 equal pieces, what part of the whole pie is 1 piece? If cut into 3 equal pieces? 5. A girl, having of an orange, gave of it to her brother what part of the orange did she give him.

ANALYSIS. — of an orange is equal to : } of of an orange is Hence she gave him of an orange.

VI.
VII. What is V of 1? W of 2? X of 3?

Prefix 3 to X, and multiply by 7.

By 8.

By 9.

VIII.

W of X?

.

By 2.

By 1.

By 19.

XI.

XII.

By.44.

- What is V of W? V of X? IX. — Prefix 1 to V, and multiply by

X.- Prefix 2 to W, and multiply by.

Prefix 3 to X, and multiply by 2. By 83.
1-V+W+2 × X=what?

ORAL AND WRITTEN EXERCISES.

15. If a pound of rice is worth $3, what is of a pound worth? W. 63 pounds? 9 pounds? 93

16. W. How much grain can be put into 71 bags, if each bag holds 21 bushels? 22 bushels?

17. W. What will 4 pounds of sugar cost, at 83 cents per pound? At 94 cents? At 115 cents?

10

18. What will 114 pounds of tea cost, at $1 per pound? At $1 per pound? W. At $? At $? At $13? 19. What will 228 bushels of corn cost, at 1 dollar a bushel? At $11 per bushel? At $11?

Change mixed numbers to improper fractions, and cancel when possible.

WRITTEN EXERCISES.

20. What will of a pound of sugar cost at 191

21. What will of a bushel of corn weigh, if 1 bushel weighs 56 pounds?

22. If a box of starch weighs 283 pounds, how many pounds in 3 boxes? In of a box? In 13 boxes? 23. How many yards in g of 176 yards? In ‡ of 3435 yards? In 5 of 1134 yards?

24. If 1 yard of lace is worth 884 cents, what are 16 yards worth?

2. Find value 16 yards. (1.) of $881=$588.

=

(2.) 16 times $.884 $14.12; the sum of $.585 and $14.12- $14.70%.

25. If in 1 pane of glass there are 201 square inches, how many square inches in 43 such panes?

26. Find the weight of 34 boxes of raisins, if 1 box weighs 67 pounds?

27. If there are 901 quarts of milk in a can, how many quarts in of the can?

* Either expression may be used at the option of the teacher.