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Ratio and proportion questions are a favourite on the SET 11+ maths papers. They test your ability to compare quantities, scale recipes, share amounts fairly, and solve problems involving maps and models. On Stage 2, you will need to show clear working for every step. This lesson covers everything you need to know.
A ratio compares two or more quantities. It tells you how much of one thing there is compared to another.
| Example | Ratio | Meaning |
|---|---|---|
| 3 red balls and 5 blue balls | 3 : 5 | For every 3 red, there are 5 blue |
| £10 shared between Amy and Ben as 2 : 3 | 2 : 3 | Amy gets 2 parts, Ben gets 3 parts |
Important: Ratios do not tell you the actual amounts — they tell you the relative amounts.
Simplify a ratio by dividing both sides by their highest common factor (HCF).
Example: Simplify 18 : 24
This is one of the most common ratio questions on the SET.
Share £72 in the ratio 4 : 5.
Step 1: Find the total number of parts: 4 + 5 = 9 parts.
Step 2: Find the value of one part: £72 ÷ 9 = £8.
Step 3: Multiply:
Check: £32 + £40 = £72. Correct!
Proportion means that two ratios are equal. It is used when you need to scale up or down.
A recipe for 6 people uses 450 g of flour. How much flour is needed for 10 people?
Step 1: Find the amount for 1 person: 450 ÷ 6 = 75 g.
Step 2: Multiply for 10 people: 75 × 10 = 750 g.
SET Tip: The "find one, then find many" method works for almost every proportion question. Write each step clearly on Stage 2.
These questions ask you to compare prices by finding the unit cost (cost per item or cost per gram).
Shop A sells 6 pencils for £1.50. Shop B sells 8 pencils for £1.84. Which shop offers better value?
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