Ratio: notation and simplification
A high-frequency Edexcel topic. Foundation tests reading and simplifying ratios; Higher tests ratio in algebraic and geometric contexts.
Ratio notation
Ratio compares two or more quantities of the same kind.
- 3 : 2 (read "three to two")
- 5 : 3 : 4 (three-part ratio)
Simplifying a ratio
Divide all parts by their HCF.
12 : 18 → divide both by 6 → 2 : 3. 20 : 25 → divide by 5 → 4 : 5. 8 : 12 : 16 → divide by 4 → 2 : 3 : 4.
Ratios with units
Convert to the same units before simplifying.
50 cm : 1 m → 50 cm : 100 cm = 1 : 2. £3 : 75p → 300p : 75p = 4 : 1.
Ratios with decimals or fractions
Multiply through to clear decimals/fractions.
0.4 : 0.6 → multiply by 10 → 4 : 6 = 2 : 3. 1/2 : 2/3 → multiply by 6 → 3 : 4.
Ratio in the form 1 : n
Divide both parts by the first part.
5 : 12 → 1 : 12/5 = 1 : 2.4. 8 : 3 → 1 : 3/8 = 1 : 0.375.
Ratio in the form n : 1
Divide both parts by the second.
5 : 12 → 5/12 : 1 ≈ 0.417 : 1. 8 : 3 → 8/3 : 1 ≈ 2.667 : 1.
Edexcel exam tip
A ratio in "1 : n" form is often required for currency exchange and map scales. e.g. "Express in the form 1 : n" — divide both by the first quantity.
⚠Common mistakes— Common errors
- Trying to simplify ratios with different units (e.g. 50 cm : 1 m).
- Treating 3 : 6 and 1 : 2 as different (they're equivalent — same ratio).
- Using a ratio as if it were a fraction directly: girls : boys = 3 : 5 means 3/8 of the total are girls (not 3/5).
- Computing "1 : n" by inverting (giving 1 : 1/n) — actually, divide both parts by the first.
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