# 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 ÷ $\frac{5}{7}$ = $\frac{42}{5}$