GCSE Maths · Topic guide
Ratio questions ask you to split an amount, scale a recipe or map, or connect ratio to fractions and percentages. Write ratios in simplest integer form unless told otherwise. ‘Divide £60 in the ratio 2:3’ means 2 + 3 = 5 parts; each part is £12. Map scales often combine with unit conversion — check metres vs centimetres. Show working so method marks are secure if arithmetic slips.
Worked examples & mini quiz
Add ratio parts to find total parts. Divide the quantity by total parts to find one share, then multiply by each ratio term. For 2:3 and £60: 5 parts → £12 per part → £24 and £36.
Example 1
Share £80 in ratio 3:5
8 parts total → £10 per part. 3 × £10 = £30; 5 × £10 = £50. Check: £30 + £50 = £80.
Example 2
Simplify 12:18
Divide by HCF 6 → 2:3.
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1. Divide 40 in the ratio 1:3
Correct: 10 and 304 parts → 10 each part; 1×10 and 3×10.
2. Ratio 2:3 as a fraction of the whole for the first part is:
Correct: 2/52 of 5 equal parts.
3. To compare 3:4 and 6:7 you might:
Correct: Convert to a common scale or use fractionsExpress as equivalent ratios or compare part sizes.
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