GCSEMathsAQAHigherRevision Notes1. NumberFractionsMultiplying & Dividing Fractions

Multiplying & Dividing Fractions (AQA GCSE Maths): Revision Note

Exam code: 8300

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

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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

    • 3 over 25 cross times 10 over 11 equals 3 over up diagonal strike 25 to the power of 5 cross times up diagonal strike 10 squared over 11 equals 3 over 5 cross times 2 over 11

  • Multiply

    • Multiply the numerators

    • Multiply the denominators

    • 3 over 5 cross times 2 over 11 equals fraction numerator 3 cross times 2 over denominator 5 cross times 11 end fraction equals 6 over 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 improper fractions before multiplying

    • Convert improper fractions back into mixed numbers at the end if required

Worked Example

Find 4 over 15 cross times 25 over 11.

Answer:

The 15 and 25 can be cancelled before multiplying

fraction numerator 4 over denominator 3 cross times 5 end fraction cross times fraction numerator 5 cross times 5 over denominator 11 end fraction equals fraction numerator 4 over denominator 3 cross times up diagonal strike 5 end fraction cross times fraction numerator up diagonal strike 5 cross times 5 over denominator 11 end fraction equals 4 over 3 cross times 5 over 11

Multiply the numerators together and the denominators together

 fraction numerator 4 cross times 5 over denominator 3 cross times 11 end fraction equals 20 over 33

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

20 over 33

Dividing fractions

How do I divide two fractions?

  • Flip the second fraction and change ÷ into × ”

    • 1 third divided by 4 over 5  becomes  1 third cross times 5 over 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 improper fractions before dividing

    • Convert improper fractions back into mixed numbers at the end if required

Examiner Tips and Tricks

Remember “flip’n’times":

When dividing fractions you are multiplying by the reciprocal.

Worked Example

Divide 3 1 fourth by 3 over 8, giving your answer as a mixed number.

Answer:

Rewrite 3 1 fourth as an improper fraction

3 1 fourth equals fraction numerator 3 cross times 4 plus 1 over denominator 4 end fraction equals 13 over 4

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

13 over 4 divided by 3 over 8 equals 13 over 4 cross times 8 over 3

Cancel a factor of 4 from the numerators and denominators

13 over 4 cross times 8 over 3 equals fraction numerator 13 over denominator up diagonal strike 4 end fraction cross times fraction numerator up diagonal strike 4 cross times 2 over denominator 3 end fraction equals 13 over 1 cross times 2 over 3

Multiply the fractions

fraction numerator 13 cross times 2 over denominator 1 cross times 3 end fraction equals 26 over 3

Rewrite as a mixed number

26 over 3 equals 24 over 3 plus 2 over 3 equals 8 2 over 3

8 2 over 3

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths Content Creator

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.