Fractions inside ratio problems

This is the conceptual bridge between ratio (R-strand) and number (N-strand). Edexcel tests it at both tiers; Higher questions on Paper 1H or 2H typically combine ratio with fraction arithmetic.

Fraction-to-ratio conversion

If 3/5 of a class are girls, the ratio of girls to boys is 3:2 (because girls = 3 parts, boys = 5 − 3 = 2 parts). Always check that the parts add to the original whole.

Ratio-to-fraction conversion

If A:B = 3:7, then A is 3/10 of the total and B is 7/10 of the total.

Multi-stage problems

A common Edexcel item: "After spending 2/5 of his money, he gives 3/4 of the remainder to charity. He has £30 left. How much did he start with?"

Strategy: work backwards from the £30.

• £30 = 1/4 of the remainder (after he gave 3/4 away).
• Remainder = £30 × 4 = £120.
• £120 = 3/5 of the original (he had 3/5 left after spending 2/5).
• Original = £120 × (5/3) = £200.

When ratios change (Higher focus)

If A:B = 3:5 and 4 is added to A so the new ratio becomes 7:10, find original A:

• Let A = 3k, B = 5k.
• (3k + 4)/5k = 7/10.
• 10(3k + 4) = 35k → 30k + 40 = 35k → k = 8.
• Original A = 24.

Edexcel paper alignment

• Paper 1F/1H: simple fraction-to-ratio conversion, sharing in a ratio.
• Paper 2H/3H: multi-stage word problems and ratio-change problems.

Common Edexcel exam tip

In multi-stage problems, define a variable (like k) for "one part" or write "let original = T". Mark schemes give M1 for setting up the variable and the equation; A1 for the correct value.