Fraction Division

Introduction

Dividing a fraction by a fraction is fraction division.

To divide, we convert the fraction division process into fraction multiplication process by using following steps

We change the '÷' (division sign) into '×' (multiplication sign) and write the reciprocal of number to right of the sign.
We multiply the numerators.
We multiply the denominators.
We simplify and re-write the fraction, if required, in simplest form.

Problem 1:

Divide $\frac{3}{8}$ ÷ $\frac{5}{12}$

Step 1:

Since dividing by a fraction is same as multiplying by its reciprocal

$\frac{3}{8}$ ÷ $\frac{5}{12}$ = $\frac{3}{8}$ × $\frac{12}{5}$ = $\frac{(3 × 3)}{(2 × 5)}$ = $\frac{9}{10}$

Step 2:

So, $\frac{3}{8}$ ÷ $\frac{5}{12}$ = $\frac{9}{10}$

Problem 2:

Divide $\frac{5}{6}$ ÷ $\frac{7}{9}$

Step 1:

Since dividing by a fraction is same as multiplying by its reciprocal

$\frac{5}{6}$ ÷ $\frac{7}{9}$ = $\frac{5}{6}$ × $\frac{9}{7}$ = $\frac{(5 × 3)}{(2 × 7)}$ = $\frac{15}{14}$

Step 2:

So, $\frac{5}{6}$ ÷ $\frac{7}{9}$ = $\frac{15}{14}$