# Multiplying and dividing fractions

## Multiplying fractions

To multiply two fractions together, multiply the together and multiply the together.

### Example 1

Work out $$\frac{3}{5} \times \frac{2}{3}$$.

$\frac{3}{5} \times \frac{2}{3} = \frac{3 \times 2}{5 \times 3} = \frac{6}{15}$

$$\frac{6}{15}$$ can be simplified to $$\frac{2}{5}$$ (take out a of 3).

If the fractions to be multiplied contain mixed numbers, first convert them to and then multiply the numerators together and multiply the denominators together.

### Example 2

Work out $$2 \frac{1}{3} \times 1 \frac{1}{2}$$.

$$2 \frac{1}{3} = \frac{7}{3}$$ ($$\frac{2 \times 3 + 1}{3}$$) and $$1 \frac{1}{2} = \frac{3}{2}$$ ($$\frac{1 \times 2 + 1}{2}$$)

$$2 \frac{1}{3} \times 1 \frac{1}{2}$$ is the same as $$\frac{7}{3} \times \frac{3}{2}$$.

$$\frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{21}{6}$$ which can be to $$\frac{7}{2}$$ (take out a common factor of 3) which should be converted to a mixed number as the question contains mixed numbers. $$\frac{7}{2} = 3 \frac{1}{2}$$ (divide the numerator by the denominator).

This fraction cannot be simplified any further, so this is the final answer.

## Dividing fractions

To divide two fractions, multiply the first fraction by the of the second fraction. This means simply that the divide sign is swapped for a multiply sign, and the second fraction is flipped upside down.

### Example

Work out $$\frac{3}{5} \div \frac{2}{3}$$.

This is the same as $$\frac{3}{5} \times \frac{3}{2}$$ (keep the first fraction the same, change the divide sign to a multiply and write the second fraction as a reciprocal - flip it upside down).

The sum is now:

$\frac{3}{5} \times \frac{3}{2} = \frac{3 \times 3}{5 \times 2} = \frac{9}{10}$