Simplify ratios

Objective. Write ratios in their simplest whole-number form.

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2. Worked example
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Learn: the key idea

Simplifying a ratio means writing it using the smallest possible whole numbers while keeping the same proportion between the quantities, much like simplifying a fraction. You divide every part of the ratio by their highest common factor. For example, the ratio 20:15 has HCF 5, so dividing both parts gives 4:3, which cannot be simplified further. If a ratio contains decimals or fractions, first multiply every part by the same number to clear them before simplifying, such as turning 0.5:2 into 1:4 by doubling both parts.

Worked example

Simplify the ratio 36:24 fully.

1 $Find the HCF of 36 and 24, which is 12.$
2 $Divide the first part by 12: 36\div12=3.$
3 $Divide the second part by 12: 24\div12=2.$
4 $Check 3 and 2 share no common factor, so the ratio is fully simplified.$

Answer: 3:2

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Common mistake. Pupils sometimes simplify only one part of a ratio, turning 10:15 into 10:3 instead of 2:3. Always divide every part of the ratio by the same common factor.

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