Ratio and Proportion
“For every 2, there are 3.” Make equal ratios, cancel them down, share an amount out in a given ratio, and scale a recipe up.
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2 : 3 is not two thirds
This is the mistake that costs marks, and it is an easy one to make. In the ratio 2 : 3 the 2 and the 3 are two parts, so there are five parts altogether — and the first share is two fifths, not two thirds.
The bar drawn above each sharing question is there for exactly this. Count the parts in it before you divide anything, and the mistake stops being available.
Sharing, in three steps
- Add the parts. 2 : 3 means 5 parts.
- Find one part. Divide the amount by 5.
- Take as many as you need. The first share is 2 of them, the second is 3.
Ratios scale by multiplying
2 : 3 and 8 : 12 are the same ratio, because both sides were multiplied by 4. They are not the same as 8 : 9 — adding 6 to each side changes the relationship completely. It is the same rule as equivalent fractions, which is not a coincidence: a ratio and a fraction are two ways of writing the same comparison.
School levels
School levels are a guide only. They show where a skill is usually taught in each country and are not taken from, aligned to, or endorsed by any curriculum authority. Your school may cover it earlier or later.