Equivalent Fractions (Cambridge O Level Maths)

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Last updated

23 October 2023

“Splitting into 2 parts, then taking 1 part” is the same as “splitting into 4 parts, then taking 2 parts”
- $\frac{1}{2}$ is the same as $\frac{2}{4}$
- Similarly, $\frac{2}{4}$ is the same as $\frac{4}{8}$ , or $\frac{8}{16}$ , or $\frac{3}{6}$ etc
Equivalent fractions are two fractions that represent the same amount (they are different ways of writing the same thing)
To make equivalent fractions, 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!

Using equivalent fractions can help with shading parts of diagrams questions as well as adding and subtracting fractions without a calculator

If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified (made easier)
To simplify the fraction, divide the top and bottom by the common factor

- $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
- $\frac{25}{45} = \frac{25 \div 5}{45 \div 5} = \frac{5}{9}$
- This process is also called cancelling a fraction
- The simplified fraction is an equivalent fraction
A fully simplified fraction is the simplest equivalent fraction that can be made using whole numbers on top and bottom

Make use of your calculator in the exam if it is available to you
- typing any fraction into it and pressing equals will automatically simplify the fraction for you
If you do not have a calculator check your fraction is simplified by looking for any common factors on the numerator and denominator