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6. From of an acre take of a rod.

Ans. IR. 17p. 22yd. 2ft. 108in.

7. From of a cord take of a cord.

Ans. 91ft. 1602 in.

8. From of a hhd. of wine there leaked out of it; what remained? Ans. 6gal. 3qt. Opt. 17gi. 9. From Boston to Concord, N. H., the distance is 72 miles; of this distance, how much remains ? Ans. 30m. 6fur. 34rd. 4ft. 8in. 11⁄2bar. of a week.

having travelled

10. From of a year take

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Ans. 101da. 5h. 54m. 174sec. of a foot.

Ans. 1R 18p. 5yd. 4ft. Oin.

SECTION XIX.

MULTIPLICATION OF VULGAR FRACTIONS.

CASE I.

To multiply a simple fraction by a simple fraction. 1. Multiply by %.

OPERATION.

This process may be understood by sup× Ans. posing a man to have found of a dollar, and that he gave of it to his wife, and that he wished to ascertain what part of a dollar his wife received. If of a dollar be divided into 5 equal parts, one of these parts will be of a dollar. And, if of of a dollar be of a dollar, of will be 7 times as much, and 7 times are If then, of be, of will be 3 times as much, and 3 times are. The wife will therefore receive 23 of a dollar.

RULE. Multiply the numerators together for a new numerator, and the denominators for a new denominator. The fraction should then be

reduced to its lowest terms.

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The operation of the following questions may be abridged by

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To multiply a whole number by a fraction, or a fraction by

a whole number.

1. If a man earn of a dollar in one day, how much will he earn u.

days?

OPERATION.

}× =3= $77 Ans.

much, and 9 times 7 eighths

To analyze this question, we say, if he earn 7 eighths of a dollar in 1 day, in 9 days he will earn 9 times as are 63 eighths = 63=$77 Ans. Multiply the whole number by the numerator of the fraction, and divide the product by the denominator, and the quotient is the answer required.

RULE.

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NOTE. If any of the fractions are compound, they must be reduced to simple fractions by Case VI., Sect. XVI.

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Ans. $161.

+16. At of a dollar per foot, what cost 7 cords of wood?

CASE III.

Ans. $35.

To multiply a mixed number by a whole number, or a whole number by a mixed number.

1. Multiply 7 by 9.

7

OPERATION. In performing this question, we say 9 times 5 eighths are 45 eighths, and 45 eighths are equal to 5. We write down the and carry the 5 to the product of 9 times 7 68.

9

68-59

=

RULE. Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction, and as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, let it be a numerator and the divisor a denominator to a frac tion to be affixed to the product.

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11. What will 237 pounds of lead cost, at 8 cents a pound?

12. What will 15

pound?

13. What will 29

Ans. $1.91. pounds of sugar cost, at 12 cents a Ans. $1.881.

cwt. of hay cost, at $ 1.12 per cwt.? Ans. $32.94.

14. What will 97 yards of broadcloth cost, at $8 per yard? Ans. $79.00.

16

15. What will 17 tons of potash cost, at $97 per ton? Ans. $1703.561.

16. What will 3 per ton?

17. What will 17

18. What will 273 pound?

19. What will 29 dozen ?

tons of plaster of Paris cost, at $12.75 Ans. $40.1859.

dozen candles cost, at 16 cents a dozen? Ans. $2.783.

pounds of bar soap cost, at 7 cents a

Ans. $1.91§.

dozen of axes cost, at $11.62 per Ans. $343.75§.

20. Bought 28 bales of cotton cloth, each bale containing 313 yards; what will be the cost, at 16 cents per yard?

Ans. $140.56.

NOTE. If both numbers be mixed, or either of them be a complex fraction, they must first be reduced to simple ones.

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29. Multiply 8 by 7.

30. Multiply 12 by .

31. Multiply 15 by f

32. A merchant owns of a ship, he sells

A. What part is that of the whole ship? 33. Multiply 37 by 104.

34. Multiply of 74 by 7 of 11.

35. Multiply of 9 by

of 17.

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Ans. 6337.

Ans. 788.

Ans. 4031.

Ans. 261.
Ans. 63.
Ans. 84.
Ans. 82.
of his share to
Ans. zz.
Ans. 39.
Ans. 49183.

33

Ans. 263. Ans. 25

Ans. 299.

Ans. 380
Ans..

per barrel ?

Ans. $39.

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41. What cost 83 bushels of apples, at $14 per bushel? Ans. $11.

42. Bought 117 bushels of corn, at $13 per bushel, and sold of it for $1 per bushel, and the remainder at $17 per bushel; what is gained on the sale of the corn? Ans. $32. 43. What is the continued product of the following numbers: 27 878 Ans. 374' 98' 247

81

and

?

128

SECTION XX.

DIVISION OF VULGAR FRACTIONS.

CASE I.

To divide a fraction by an integer or whole number. 1. How many times will contain 8?

OPERATION.

To illustrate this question we will sup× = Ans. pose of an orange to be divided equally among 8 persons. Now, if we divide of an orange into 8 equal parts, one of these parts will be equal to of a whole orange, but as there are to be divided among 8 persons, each will receive 5 times person

RULE.

Ans.

- Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Or, divide the numerator of the fraction by the whole number, if it can be done without a remainder, and write the quotient over the denominator.

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To divide a whole number by a fraction.

1. How many times will 17 contain

?

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