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First teaching 2021

Last exams 2024

Multiplying & Dividing Fractions (CIE IGCSE Maths: Core)

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Author

Mark

Last updated

4 March 2023

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Multiplying Fractions

Dealing with mixed numbers

Always turn mixed numbers into top heavy fractions before multiplying

Multiplying fractions

Cancel any numbers on the tops of the fractions with numbers on the bottoms of the fractions (either fraction)
Multiply the tops
Multiply the bottoms
Cancel again if possible
Turn top heavy fractions back into mixed numbers (if necessary / asked for)

Worked example

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

The 15 and 25 can be cancelled before multiplying (to make the next step easier)

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

Multiply the numerators together and the denominators together

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

There is no further cancelling that can be done

$\frac{20}{33}$

Dividing Fractions

Dealing with mixed numbers

Always turn mixed numbers into top heavy fractions before dividing

Dividing fractions

Never try to divide fractions
Instead “flip’n’times” (flip the second fraction and change ÷ into ×)
So $\div \frac{a}{b}$ becomes $\times \frac{b}{a}$ (flipping a fraction creates a reciprocal fraction)
Then multiply the fractions (multiply tops and multiply bottoms)
Cancel the final answer (if possible)

Worked example

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

Rewrite $3 \frac{1}{4}$ as an improper fraction

$3 \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}$

Turn the division into a multiplication, using the fact that dividing by a fraction is the same as multiplying by its reciprocal

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

Multiply the fractions

$\frac{13}{4} \times \frac{8}{3} = \frac{13 \times 8}{4 \times 3} = \frac{104}{12}$

Simplify the fraction, by dividing the numerator and denominator by 4

$\frac{104}{12} = \frac{26}{3}$

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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Previous:Adding & Subtracting FractionsNext:Basic Percentages

Multiplying & Dividing Fractions (CIE IGCSE Maths: Core)

Revision Note

Dealing with mixed numbers

Multiplying fractions

Dealing with mixed numbers

Dividing fractions

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Author: Mark