The National Arithmetic on the Inductive System

16. What will 3 tons of plaster of Paris cost, at $12.75 per ton? Ans. $40.1859.

17. What will 17 dozen candles cost, at 16 cents a dozen? Ans. $2.783.

18. What will 273 pound? 19. What will 29 dozen ?

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 31 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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31. Multiply 15 by ft.

32. A merchant owns of a ship, he sells

A. What part is that of the whole ship? 33. Multiply 37 by 10.

34. Multiply of 7 by 7 of 11. 35. Multiply of 9 by of 17. 36. Multiply of 8 by 4 of 91. 37. Multiply 183 by 159.

38. Multiply of by of 114

Ans. 63. Ans. 84. Ans. 8.

of his share to

Ans. Ans. 39 Ans. 49133. Ans. 263.

Ans. 25245.

Ans. 29911

39. What cost 73 barrels of flour, at $5 per barrel?

Ans. $39.

40. What cost 9 acres of land, at $273 per acre?

Ans. $2564.

41. What cost 87 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 $13 per bushel; what is gained on the sale of the corn? Ans. $333. 43. What is the continued product of the following numbers: 27 870 6 Ans. 33. 374' 981' 21'

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 person will receive 5 times Ans.

RULE.-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.

To divide a whole number by a fraction.

1. How many times will 17 contain ‡ ?

==223 Ans.

It is evident that 17 will contain

as many times as there are fourths in 17, which are 4 X 17

68 times. Again, if 17 contain 1 fourth 68 times, it will contain 3 fourths as many times as 68 will contain 3=223 Ans.

RULE. Multiply the whole number by the denominator of the frac tion, and divide the product by the numerator.

To divide a mixed number by an integer or whole number. 1. Divide 27g by 6.

OPERATION.

6)273 41843 Ans.

We divide 27 by 6, and find that it is contained 4 times, which we write under the 27, and we have 3 remaining, which we multiply by 5, the denominator of the fraction, and to the product we add the numerator 3, and the amount is 18. This we write over the product of 6, the divisor, multiplied by the denominator, 5, 6 × 5=30. We then reduce the fraction.

RULE. ·Divide the integers as in whole numbers, and if any thing remains multiply it by the denominator of the fraction, and to the product add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator.

9. Divide of a prize, valued at $1723, equally between 12 seamen. Ans. $125.6317.

10. What will a barrel of flour cost, if 19 barrels can be purchased for $107 ? Ans. $5.65g. 11. If 15 pounds of raisins can be obtained for $32, what will 1 pound cost? Ans. $0.211. 12. If 12 quarts of wine cost $3.75, what will a quart cost? Ans. $0.31.

13. If $19 will buy 375 acres of land, how much can be bought for $1? Ans. 1933 acres.

CASE IV.

To divide one fraction by another, whether the fractions be simple, compound, mixed, or complex.

1. Divide by §.

OPERATION.

Ans. 11.

To understand the rationale of this process, we find the two factors of, which are and; multiplied by make, as is evident from a preceding rule. We now divide by †, which by Case I. of this section will be x. Again, we wish to divide by . It is evident that will contain eight times as often as it will a unit, and it contains an unit times, therefore it contains eight times A=X=1 Ans. It will be perceived, that in performing this question the numerator of the dividend has been multiplied by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor.

RULE.-Invert the divisor, and proceed as in multiplication. If, however, there be mixed numbers in the question, they must first be reduced to improper fractions, and compound and complex fractions must be reduced to simple fractions.