# Multiplying and dividing fractions

## Multiplying fractions

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

### Example 1

Work out .

can be simplified to (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 .

( ) and ( )

is the same as .

which can be to (take out a common factor of 3) which should be converted to a mixed number as the question contains mixed numbers. (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 .

This is the same as (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: