Ratio notation and simplification

WJEC tests ratio every paper at every tier. Foundation expects basic notation; Higher integrates ratio with similar shapes, currency conversion and best-buy reasoning.

Notation

a : b "a to b" — same units; order matters.

A ratio of 3 : 5 means for every 3 parts of one quantity there are 5 parts of the other. Total parts = 8.

Same units first

If a recipe uses 200g flour to 1kg sugar, convert to common units before forming the ratio.

200g : 1000g = 200 : 1000 = 1 : 5 (after dividing both by 200).

Simplifying ratios

Divide all parts by their HCF.

• 12 : 18. HCF = 6. Simplified: 2 : 3.
• 4 : 6 : 10. HCF = 2. Simplified: 2 : 3 : 5.

Ratios containing fractions or decimals

Multiply through to clear them.

• 1/2 : 1/3 → multiply by 6 → 3 : 2.
• 0.4 : 1.2 → multiply by 10 → 4 : 12 → 1 : 3.

Unitary form (1 : n)

Divide both sides by the smaller term. Useful for comparison.

• 5 : 12 → 1 : 12/5 = 1 : 2.4.

Sharing in a ratio

Total parts = sum of ratio numbers. Each share = (its ratio number ÷ total parts) × total quantity.

Example: share £56 in ratio 3 : 5.

• Total parts = 8.
• One part = £56 ÷ 8 = £7.
• Shares: 3 × £7 = £21 and 5 × £7 = £35. Check: 21 + 35 = 56 ✓.

WJEC exam tip

When asked "give your answer in the form 1 : n", divide both sides by the smaller term — don't leave the answer as 5 : 12 thinking it's already simplified.