Basic Fractions (Cambridge (CIE) IGCSE International Maths)

Revision Note

Basic Fractions

What is a fraction?

  • A fraction is part of a whole

  • A fraction is written as a over b where a and b are integers

    • The number on the top, a, is called the numerator

    • The number on the bottom, b, is called the denominator

  • The values of the numerator and denominator tell us about the size of the fraction 

    • The denominator is how many parts the whole is split into 

    • The numerator is how many parts you have

      • For example, 2 over 3 means that the whole is divided into 3 parts and you have 2 of these parts

How do I find a fraction of an amount?

  • Method 1
    Divide by the denominator and multiply by the numerator

    • To find 2 over 5 of 60, divide it by 5 then multiply it by 2

      • 60 divided by 5 equals 12, then 12 cross times 2 equals 24

  • Method 2
    Change the fraction into a decimal, then multiply

    • To find 9 over 10 of 15, turn 9 over 10 into 0.9 then multiply

      •  0.9 cross times 15 equals 13.5

  • Method 3
    Write both numbers as fractions and multiply the two fractions together

    • To find 5 over 6 of 8, turn 8 into 8 over 1

      • Work out 5 over 6 cross times 8 over 1 equals 40 over 6 equals 20 over 3

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

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 Tips and Tricks

  • Make use of your calculator 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.

Dan Finlay

Author: Dan Finlay

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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.