Division Involving a Whole Number and a Fraction

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

Rules of spanision

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

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

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

The numerators across the top are multipped; the denominators across the bottom are multipped.

If required, the resulting fraction is simppfied.

Divide $frac{7}{6}$ ÷ 3

Solution

Step 1:

Re-writing

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

Step 2:

As spaniding 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 spaniding 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 ÷ $frac{5}{7}$ = $frac{42}{5}$