Changing a ratio

Objective. Update a ratio when quantities are added or removed.

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2. Worked example
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Learn: the key idea

Changing a ratio means recalculating the relationship between quantities after some amount is added to or removed from one or both groups, rather than simply scaling the original ratio. Work out the actual quantities first using the original ratio, apply the change, then form and simplify the new ratio from the updated amounts. If a bag has sweets in ratio 3:2 totalling 20, that's 12 and 8; removing 4 from the first group gives 8:8, which simplifies to 1:1. Always convert back to actual amounts before comparing the new ratio.

Worked example

A classroom has boys and girls in the ratio 4:5, totalling 36 pupils. If 6 more girls join, find the new ratio of boys to girls in simplest form.

1 $Find one part: 36 \div (4 + 5) = 4$
2 $Find actual numbers: boys = 16, girls = 20$
3 $Add 6 girls: girls = 26$
4 $New ratio 16:26 simplifies to 8:13$

Answer: 8:13

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Common mistake. Pupils often add or subtract the change directly from the ratio numbers themselves, turning 3:2 minus 4 into −1:2 instead of working with real quantities first. Always find true quantities from the ratio before applying any change.

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