Ratio

What is a ratio?

A ratio compares two or more quantities of the same type. The ratio 3:5 means for every 3 parts of the first quantity, there are 5 parts of the second.

Edexcel 1MA1 uses ratio heavily in functional/contextual problems on Papers 2 and 3: mixing paints, sharing profits, unit pricing, recipes.

Simplifying ratios

Divide both parts by the HCF (highest common factor). Example: 24:36 → HCF is 12 → 2:3.

For ratios involving different units, convert to the same unit first. Example: 80p : £2 → 80p : 200p → 4:10 → 2:5.

Dividing a quantity in a given ratio

Step 1: add the parts of the ratio to find the total number of shares. Step 2: divide the quantity by the total to find one share. Step 3: multiply each part of the ratio by one share.

Example: Share £360 in the ratio 3:5. Total shares = 8. One share = £360 ÷ 8 = £45. First part = 3 × £45 = £135. Second part = 5 × £45 = £225. Check: 135 + 225 = 360 ✓.

Three-part ratios

Example: A:B:C = 2:5:3. Share 200 g in this ratio. Total = 10. One share = 20 g. A = 40 g, B = 100 g, C = 60 g.

Ratio and fractions

A ratio of a:b means the first quantity is a/(a+b) of the total. Example: in a ratio 3:7, the first part is 3/10 of the whole.

Unequal sharing with more information

"Tom and Anya share prize money in the ratio 5:3. Tom receives £240 more than Anya. How much does each receive?" Tom's share − Anya's share corresponds to 5 − 3 = 2 parts = £240. One part = £120. Tom = 5 × £120 = £600. Anya = 3 × £120 = £360. Check: 600 − 360 = 240 ✓.

Unit pricing / best value (Edexcel functional)

Edexcel Papers 2/3 regularly ask: "Which offer gives better value?" Method: calculate price per unit (e.g. per gram, per litre) for each offer and compare.

Example: 500 g for £2.80 vs 750 g for £3.90. Price per g: £2.80/500 = 0.56p; £3.90/750 = 0.52p. → 750 g offer is better value.