Multiplying & Dividing Fractions (Edexcel GCSE Maths: Foundation)

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Naomi C

Last updated

16 February 2024

Multiplying Fractions

How do I multiply two fractions?

Cancel any factors that are common to both the numerator and the denominator
- The common factors could be in either of the fractions
- $\frac{3}{25} \times \frac{10}{11} = \frac{3}{25^{5}} \times \frac{10^{2}}{11} = \frac{3}{5} \times \frac{2}{11}$
Multiply
- Multiply the numerators
- Multiply the denominators
- $\frac{3}{5} \times \frac{2}{11} = \frac{3 \times 2}{5 \times 11} = \frac{6}{55}$
Cancel any common factors again if possible

How do I multiply two fractions if one is a mixed number?

Always convert mixed numbers into top heavy fractions before multiplying
- Convert top heavy fractions back into mixed numbers at the end if required

Worked example

Find $\frac{4}{15} \times \frac{25}{11}$ .

The 15 and 25 can be cancelled before multiplying

$\frac{4}{3 \times 5} \times \frac{5 \times 5}{11} = \frac{4}{3 \times 5} \times \frac{5 \times 5}{11} = \frac{4}{3} \times \frac{5}{11}$

Multiply the numerators together and the denominators together

$\frac{4 \times 5}{3 \times 11} = \frac{20}{33}$

There is no further cancelling that can be done
Write down the fraction

$\frac{20}{33}$

Dividing Fractions

How do I divide two fractions?

Flip the second fraction and change ÷ into × ”
- $\frac{1}{3} \div \frac{4}{5}$ becomes $\frac{1}{3} \times \frac{5}{4}$
- The 'flipped' fraction is called a reciprocal fraction
Cancel any factors that are common to both the numerator and the denominator
Multiply the fractions
- Multiply the numerators
- Multiply the denominators
Cancel any common factors again if possible

How do I divide two fractions when one of them is a mixed number?

Always convert mixed numbers into top heavy fractions before dividing
- Convert top heavy fractions back into mixed numbers at the end if required

Examiner Tip

Remember “flip’n’times'.
- When dividing fractions you end up multiplying!

Worked example

Divide $3 \frac{1}{4}$ by $\frac{3}{8}$ , giving your answer as a mixed number.

Rewrite $3 \frac{1}{4}$ as a top heavy fraction

$3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4}$

Turn the division into a multiplication
'Flip' the second fraction and turn ÷ into ×

$\frac{13}{4} \div \frac{3}{8} = \frac{13}{4} \times \frac{8}{3}$

Cancel a factor of 4 from the numerators and denominators

$\frac{13}{4} \times \frac{8}{3} = \frac{13}{4} \times \frac{4 \times 2}{3} = \frac{13}{1} \times \frac{2}{3}$

Multiply the fractions

$\frac{13 \times 2}{1 \times 3} = \frac{26}{3}$

Rewrite as a mixed number

$\frac{26}{3} = \frac{24}{3} + \frac{2}{3} = 8 \frac{2}{3}$

$8 \frac{2}{3}$

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