Basic Fractions (Edexcel GCSE Maths)

Revision Note

Written by: Naomi C

Reviewed by: Dan Finlay

A fraction is part of a whole
A fraction is written as $\frac{a}{b}$ 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, $\frac{2}{3}$ means that the whole is divided into 3 parts and you have 2 of these parts

Method 1
Divide by the denominator and multiply by the numerator
- To find $\frac{2}{5}$ of $60$ , divide it by 5 then multiply it by 2
  - $60 \div 5 = 12$ , then $12 \times 2 = 24$
Method 2
Change the fraction into a decimal, then multiply
- To find $\frac{9}{10}$ of $15$ , turn $\frac{9}{10}$ into $0.9$ then multiply
  - $0.9 \times 15 = 13.5$
Method 3
Write both numbers as fractions and multiply the two fractions together
- To find $\frac{5}{6}$ of $8$ , turn $8$ into $\frac{8}{1}$
  - Work out $\frac{5}{6} \times \frac{8}{1} = \frac{40}{6} = \frac{20}{3}$

Equivalent fractions are two fractions that represent the same amount
- They are different ways of writing the same thing
- For example, $\frac{1}{2}$ and $\frac{6}{12}$ are equivalent fractions

To find an equivalent fraction, multiply the top and bottom of a fraction by the same number
- $\frac{5}{6}$ is equivalent to $\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ and $\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ and $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$ etc.
- For each fraction, there are an infinite number of equivalent fractions

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

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

Last updated: 1 July 2024

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