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First teaching 2023

First exams 2025

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Equivalent Fractions (CIE IGCSE Maths: Core)

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Naomi C

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Naomi C

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Equivalent Fractions

What are equivalent fractions?

  • Equivalent fractions are two fractions that represent the same amount
    • They are different ways of writing the same thing
    • For example, 1 half and 6 over 12 are equivalent fractions

How do I find an equivalent fraction?

  • To find an equivalent fraction, multiply the top and bottom of a fraction by the same number
    • 5 over 6 is equivalent to fraction numerator 5 cross times 2 over denominator 6 cross times 2 end fraction equals 10 over 12 and fraction numerator 5 cross times 3 over denominator 6 cross times 3 end fraction equals 15 over 18 and fraction numerator 5 cross times 4 over denominator 6 cross times 4 end fraction equals 20 over 24etc.
    • For each fraction, there are an infinite number of equivalent fractions

Examiner Tip

  • Using equivalent fractions can help with shading parts of diagrams questions as well as adding and subtracting fractions without a calculator
    • Remember that if you have your calculator in the exam you can use it to check your work

Simplifying Fractions

What is a simplified fraction?

  • A simplified fraction is a fraction that is written using the smallest possible integer values
    • Simplifying turns a fraction into an 'easier' equivalent fraction
  • If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified
  • Simplifying is also called cancelling a fraction

How do I simplify fractions?

  • To simplify the fraction, divide the top and bottom by the common factor
    • 12 over 18 equals fraction numerator 12 divided by 6 over denominator 18 divided by 6 end fraction equals 2 over 3
    • 25 over 45 equals fraction numerator 25 divided by 5 over denominator 45 divided by 5 end fraction equals 5 over 9

Examiner Tip

  • Make use of your calculator if you have it in your exam
    • Type any fraction into it and pressing equals will automatically simplify the fraction for you
    • If the question asks you to show your working, you must show which number you divided by

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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.