Multiplying and dividing fractions

Multiplying fractions

To multiply two fractions together, multiply the numerators together and multiply the denominators 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 common factor of 3).

If the fractions to be multiplied contain mixed numbers, first convert them to improper fractions 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 simplified 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 reciprocal 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}