Ratio & Proportion
Calculators, worked examples and guides — from simplifying basic ratios through to direct proportion, best-value comparisons and map scales.
Learning about Ratio & Proportion
The key idea: a ratio compares quantities without giving individual amounts. "3:2" means for every 3 of the first thing, there are 2 of the second. It tells you the relationship — not the size.
Type 1 — Simplifying ratio
"Simplify 15:10"
Step 1: Find HCF of 15 and 10 → 5
Step 2: Divide both by 5: 15÷5 : 10÷5 = 3:2
Shortcut: Divide both sides by the HCF in one step
Type 2 — Sharing in a ratio
"Share £240 in the ratio 3:5"
Step 1: Total parts = 3 + 5 = 8
Step 2: Value of 1 part = £240 ÷ 8 = £30
Step 3: Shares: 3 × £30 = £90 and 5 × £30 = £150
Shortcut: Always find the value of one part first
Type 3 — Direct proportion
"If 6 eggs cost £1.80, how much do 10 eggs cost?"
Step 1: Cost of 1 egg = £1.80 ÷ 6 = £0.30
Step 2: Cost of 10 eggs = 10 × £0.30 = £3.00
Shortcut: Unitary method — find 1 unit first, then scale
Ratio & Proportion Formula Sheet & Rules
Need a printable revision sheet? Access rules for simplifying ratios, unitary form 1:n, sharing totals across parts, scale factors, direct and inverse proportion, and compound measures with step-by-step worked examples and custom print export.
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Ratio & Proportion Questions Answered
What is a ratio?
A ratio is a comparison of two or more quantities. 3:2 means for every 3 of the first quantity there are 2 of the second. Ratios do not give individual amounts — only the relationship between them.
How do I simplify a ratio?
Divide all parts by their highest common factor. For 15:10, the HCF is 5, so it simplifies to 3:2.
How do I share an amount in a ratio?
Add the ratio numbers to find total parts. Divide the amount by total parts to find one part. Multiply each ratio number by one part. For £240 in ratio 3:5: total parts = 8, one part = £30, shares are £90 and £150.
What is the difference between ratio and proportion?
A ratio compares quantities directly. A proportion is a statement that two ratios are equal — it is used when scaling one quantity relative to another.
What is direct proportion?
Two quantities are in direct proportion when one increases at exactly the same rate as the other. If 3 items cost £12, then 6 items cost £24 — doubling one doubles the other.