Order of Operations
What do you do first? Every sum here has a different answer depending on how you read it — which is exactly why there are rules about the order.
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Why 4 + 3 × 2 is not 14
Reading left to right gives 7 × 2 = 14. The answer is 10, because the 3 × 2 is one thing — three twos — and the 4 is added to it. Until now, every sum you have met could safely be read straight along the line. This is the first one that cannot, and that is the whole lesson.
The order
- Brackets. Whatever is inside them, first.
- Powers — squares and cubes.
- Times and divide, working left to right between them.
- Add and take away, working left to right between them.
Times and divide are on the same step as each other, and so are add and take away. That is the part the mnemonics get wrong: 12 ÷ 3 × 2 is 8, not 2, because you take the divide and the times in the order they are written.
Brackets are how you say what you meant
Once a sum can be read two ways, you need a way of writing down which one you meant — and that is all a bracket is. 4 + 3 × 2 is 10; (4 + 3) × 2 is 14. Both are perfectly good sums. The brackets are not a rule to remember, they are punctuation.
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.