# Division Involving a Whole Number and a Fraction

The division involving a whole number and a fraction is done as follows.

Rules of division

• The whole number, at first, is written as a fraction. The division then becomes division of two fractions.

• Dividing by a number is same as multiplying with its reciprocal.

• The multiplication of the fractions follows the same procedure as learnt in previous lessons.

• The numerators across the top are multiplied; the denominators across the bottom are multiplied.

• If required, the resulting fraction is simplified.

Divide $\frac{7}{6}$ ÷ 3

### Solution

Step 1:

Re-writing

$\frac{7}{6}$ ÷ 3 = $\frac{7}{6}$ ÷ $\frac{3}{1}$

Step 2:

As dividing by a number is same as multiplying by its reciprocal

$\frac{7}{6}$ ÷ $\frac{3}{1}$ = $\frac{7}{6}$ × $\frac{1}{3}$ = $\frac{7}{18}$

Step 3:

So, $\frac{7}{6}$ ÷ 3 = $\frac{7}{18}$

Divide 6 ÷ $\frac{5}{7}$

### Solution

Step 1:

Re-writing

6 ÷ $\frac{5}{7}$ = $\frac{6}{1}$ ÷ $\frac{5}{7}$

Step 2:

As dividing by a number is same as multiplying by its reciprocal

$\frac{6}{1}$ ÷ $\frac{5}{7}$ = $\frac{6}{1}$ × $\frac{7}{5}$ = $\frac{(6×7)}{(1×5)}$ = $\frac{42}{5}$

Step 3:

So, 6 ÷ $\frac{5}{7}$ = $\frac{42}{5}$ 