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Multiplying & Dividing Fractions (Cambridge (CIE) IGCSE Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Cambridge (CIE) Maths: CoreEdexcel Maths A (Modular): Higher Unit 1Edexcel Maths A: HigherCambridge (CIE) International Maths: ExtendedCambridge (CIE) International Maths: CoreCambridge (CIE) Maths: Extended

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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.

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

bold 20 over bold 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.

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

bold 8 bold 2 over bold 3

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    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    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

    Author: Dan Finlay

    Expertise: Maths 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.