To divide by a fraction, multiply by its reciprocal.
Examples of reciprocal of a number:
1. reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$ or 2
2. reciprocal of $\frac{5}{13}$ is $\frac{13}{5}$
Let us divide whole number by a fraction:
$1$ ÷ $ \frac{7}{8}$ = $1$ x $ \frac{8}{7}$ = $\frac{8}{7}$ or $1 \ \frac{1}{7}$
$6$ ÷ $ \frac{3}{5}$ = $6$ x $ \frac{5}{3}$ = $\frac{2 \ x \ 5}{1}$ = $10$
$18$ ÷ $ \frac{2}{7}$ = $18$ x $ \frac{7}{2}$ = $\frac{9 \ x \ 7}{1}$ = $63$
From the examples,we use the reverse of division which is multiplication and write the reciprocal of the divisor, then multiply.
Remember that any number divided by zero does not exist. Also 0 has no reciprocal.
Now let us divide fractions:
$ \frac{3}{4}$ ÷ $ \frac{15}{16}$ = $\frac{3}{4}$ x $ \frac{16}{15}$ = $\frac{1 \ x \ 4}{1 \ x \ 5}$ = $\frac{4}{5}$
The reciprocal of the divisor $ \frac{15}{16}$ was used. We apply cancellation method then multiply.
