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Equivalent & Simplified Fractions (Cambridge (CIE) IGCSE International Maths)

Revision Note

Naomi C

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Expertise

Maths

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, $\frac{1}{2}$ and $\frac{6}{12}$ 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
- $\frac{5}{6}$ 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

Exam 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

$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
$\frac{25}{45} = \frac{25 \div 5}{45 \div 5} = \frac{5}{9}$

Exam 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

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.