Division of Fractions

To divide a whole number, a fraction, or a mixed number, by a fraction or a mixed number :

; 6 by 1; by ; 63 by ; 171 by 2 1.

When it may be readily seen by inspection how many times the divisor is contained in the dividend, no further process is necessary.is contained in 1 twice and in 4 eight times (a). 11⁄2 is contained in 6 four times (b).

2 fifths is contained in 4 fifths twice (c). is contained in 1 three times and in 6 nineteen times (d). 2 is contained in 5 twice, in 15

three times, and in 17 seven times (e).

Division of Fractions

1. Divide by 2; 53 by 11.

SECOND METHOD

1 ÷ 3 = 13 ÷ 18 = 18 or 9 or 13.

5} + 1} = ÷ } = 1 ÷ 2 = 1 or 37.

In all cases in which the quotient cannot be easily found by inspection, the mixed numbers may be fractions and the fractions made similar.

be divided by the other.

changed to the form of Then one numerator may

10 fifteenths is contained in 12 fifteenths as many times as 10 are contained in 12.

divided by 5 would be, but since we wish to divide only by

one ninth of 5, the quotient is nine times, or §.

Therefore, instead of making the fractions similar we may divide by the numerator of the divisor and then multiply by its denominator, or invert the divisor and proceed as in multiplication of fractions.

Miscellaneous Problems

1. Upon an ordinary leaf of an apple tree there are as many as 100,000 openings for the admission of air from which carbon is obtained for the growth of the tree. How many such openings are there upon all the leaves of a tree which has 10,000 leaves?

2. There are about 2 miles of silk fiber in the cocoon of a silkworm of the size of a robin's egg. How many of these cocoons would furnish silk enough to form a continuous line reaching twice around the earth?

3. How many times would the silk from one of these cocoons reach across a web of cloth which is of a yard wide?

4. If a ball is struck with two blows at the same instant, one of which would send it south 12 feet in a second, and the other west 16 feet in a second, in which direction and how far will it roll in the second?

Each blow is About how far

5. A ball is struck with two blows at the same instant in directions at right angles to each other. sufficient to send it 20 feet in a second. does it roll in the second?