# Dividing Fractions

We will discuss here about dividing fractions by a whole number, by a fractional number or by another mixed fractional number.

First let us recall how to find reciprocal of a fraction, we interchange the numerator and the denominator.

 For example, the reciprocal of ¾ is 4/3.

Find the reciprocal of 3 ¾

 The reciprocal of 3 ¾ is 4/15.

I. Division of a fraction by a whole number:

For example:

(i) Divide 3/5 by 12

 Solution:3/5 ÷ 12 = 3/5 ÷ 12/1 = 3/5 × 1/12 = (3 × 1)/(5 × 12) = 3/60 = 1/20 Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual. Step II: Express the product in its lowest terms.

(ii)  Solve: 5/7 ÷ 10

 = 5/7 ÷ 10/1 = 5/7 × 1/10 = (5 × 1)/(7 × 10) = 5/70 Step I: Find the reciprocal of the whole number and multiply with the fractional number as usual. Step II: Express the product in its lowest terms.

II. Division of a fractional number by a fractional number:

For example:

(i) Divide 7/8 by 1/5

 Solution:7/8 ÷ 1/5 = 7/8 × 5/1 = (7 × 5)/(8 × 1) = 35/8 = 4 3/8 Step I: Find reciprocal of 1/5. Step II: Multiply 7/8 by it. Step III: Express the product in its simplest form.

(ii) Divide: 5/9 ÷ 10/18

 Solution:5/9 ÷ 10/18 = 5/9 × 18/10 = (5 × 18)/(9 × 10) = 90/90 = 1 Step I: Find reciprocal of 1/5. Step II: Multiply 7/8 by it. Step III: Express the product in its simplest form.

III. Division of a mixed number by another mixed number:

For example:

(i) Divide 2 ¾ by 1 2/3

 Solution:2 ¾ ÷ 1 2/3 = 11/4 ÷ 5/3 = 11/4 × 3/5 = (11 × 3)/(4 × 5) = 33/20 = 1 13/20 Express the mixed numbers as improper fractions and multiply as usual.

(ii) Divide: 2  4/17 ÷ 1  4/17

 Solution:2  4/17 ÷ 1  4/17 = 38/17 ÷ 21/17 = 38/17 × 17/21 = (38 × 17)/(17 × 21) = 646/357 = 38/21 = 1 17/21 Express the mixed numbers as improper fractions and multiply as usual.
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