11. John Jones owns

Ans..

Ans.

Ans. 132

Ans.

Ans..

Ans. g.

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Ans. Tog

of a share in a railroad, valued at $117; this he bequeaths to his five children. What part of a share will each receive?

Ans..

Ans. 15 Ans..

14. James Page's estate is valued at $10,000, and he has given of it to the Seamen's Society; of the remainder he gave to his good minister; and the remainder he divided equally among his 4 sons and 3 daughters. What sum will each of his children receive? Ans. $68047.

160. To divide a whole number by a fraction.

Ex. 1. How many times will 13 contain ?

Ans. 30.

13 will contain as many times as there are sevenths in 13, equal 91 sevenths. Now, if 13 contain 1 seventh 91 times, it will contain as many times as 91 will contain 3, or 30.

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

160. The rule for dividing a whole number by a fraction? the rule?

The reason for

9. I have 50 square yards of cloth; how many yards, g of a yard wide, will be sufficient to line it?

Ans. 83 yards.

10. A. Poor can walk 37 miles in 60 minutes; Benjamin can walk as fast as Poor. How long will it take Benjamin to walk the same distance? Ans. 73 minutes.

161. To divide a mixed number by a whole number.

Having divided the whole number as in simple division, we have a remainder of 5%, which we reduce to an improper fraction, and divide it by the divisor, as in Art. 159. Annexing this That is, we

result to the quotient 2, we obtain 248 for the answer.

Divide the integral part of the mixed number; and the remainder, reduced if necessary to a simple fraction, divide as is in Art. 159.

12. Divide $1077 among 4 boys and 3 girls, and give each

of the girls twice as much as each of the boys?

Ans. Boy's share, $ 1042; Girl's share, 213g. 13. If $14 will purchase of a ton of copperas, what quan tity will $1 purchase? Ans. 1cwt.

161. How do you divide a mixed number by a whole number?

162. To divide a whole number by a mixed number. Ans. 51.

Ex. 1. Divide 25 by 4g.

OPERATION.

43 25

5 5

We first reduce the divisor and dividend to fifths, and then divide as in whole numbers.

The divisor and dividend were both multiplied 23) 125 (519 by the same number, 5; therefore their relation to each other is the same as before, and the quotient is not changed. (Art. 115, Note.) Hence,

115

10

Reduce the divisor and dividend to the same fractional parts as are denoted by the denominator of the fraction in the divisor, and then divide as in whole numbers.

6. There is a board 19 feet in length, which I wish to saw into pieces 23 feet long; what will be the number of pieces?

163. To divide a fraction by a fraction.

Ex. 1. Divide by

FIRST OPERATION.

Ans. 714 pieces.

Ans. 13.

SECOND OPERATION.

Since 1 is contained in 7,7 times, is contained in 7 9 times 7 times, or 3 times; and is contained in, of a times, which is , or 1, times.

That is, we have multiplied the denominator of the dividend by the number denoting the numerator of the divisor, and the numerator of the dividend by the number denoting the denominator of the divisor; hence, for convenience, as in the second operation, we can simply invert the terms of the divisor and proceed as in Art. 156.

How does it

162. How do you divide a whole by a mixed number? appear that this process does not alter the quotient?-163. How do you divide a fraction by a fraction? Give the reason why this process divides the fraction of the dividend.

RULE. Invert the divisor, and then proceed as in multiplication of fractions.

NOTE 1. Factors common to numerator and denominator should be canceled.

NOTE 2. When the divisor and dividend have a common denominator their denominations cancel each other, and the division may be performed by simply dividing the numerator of the dividend by that of the divisor.

164. To divide a mixed number by a mixed number.

Reduce them to improper fractions, and proceed as in Art. 163.

163 The rule for dividing one fraction by another? How may fractions be divided when they have a common denominator? Does this process differ in principle from the other? 164. How do you divide a mixed number by

a mixed number?

to a simple fraction.

Ans.

Since the numerator of a fraction is the dividend, and the denominator the divisor (Art. 132), we simply divide the numerator, , by the denominator, g, as in division of

fractions. (Art. 163.)

RULE. — Reduce the terms of the complex fraction, if necessary, to the form of a simple fraction. Then divide the numerator of the complex fraction by its denominator.

NOTE. Another method is to multiply both terms of the complex fraction by a common multiple of their denominators.

165. The rule for reducing complex to simple fractions? How does this process differ from division of fractions?

Ans. 1.