Year 9 · Rates
Work out speed, distance or time
Definition
A ratio compares two or more amounts, like 2 : 3. Proportion is about keeping that relationship the same when you scale up or down, doubling a recipe keeps the ratio of ingredients unchanged.
Why Do I Have to Learn This?
Ratios compare amounts, like squash to water or flour to butter. Getting proportions right is how recipes, maps and models work.
Key Rules:
- 1. Simplify a ratio by dividing every part by the same number (like a fraction).
- 2. To share in a ratio, add the parts to find how many shares there are, then size one share.
- 3. Direct proportion: if one amount doubles, the other doubles too.
Remember:
- •2 : 3 is not the same as 23, the second part (3) is not the whole; the whole is 5.
- •Keep the order of a ratio consistent with what each number describes.
- •Scale every quantity by the same factor, not just one of them.
Direct proportion
Two quantities that change together: double one and the other doubles too. y = kx for a fixed number k.
If 1 apple costs 30p, then 4 apples cost 120p.
Animated Example:
Free Work out speed, distance or time Worksheet
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Before this: Proportion and scale (Year 8) · Next: Ratio and proportion (Year 11 Foundation)
Let’s Practise the Concept
Step 1 of 3
Change the unit
176 cm is how many metres?