Which operation comes first
Maths · Key Stage 2 · The School
Two readings, two answers
Work out 2 + 3 × 4. Left to right gives 20. Doing the multiplication first gives 14. Both are defensible readings of the same marks on paper, which is exactly the problem: a calculation that means two things means nothing. The order of operations is the agreement that settles it.
The agreed order
Brackets first, then powers, then multiplication and division together, then addition and subtraction together. So 2 + 3 × 4 is 14. The pairs really are equal in rank: in 12 ÷ 4 × 3 you go left to right and get 9, not 1, because division does not outrank multiplication.
Brackets are how you overrule it
If you actually want the addition first, say so: (2 + 3) × 4 = 20. Brackets are not decoration, they are an instruction, and they are the only honest way to make a calculation mean what you intended. When in doubt, add them — nobody ever lost a mark for a bracket that was not strictly needed.
The convention is a choice, not a law of nature
There is no deep reason multiplication must beat addition; mathematicians agreed on it because it makes algebra tidy. 3x + 2 means three lots of x, then add two, with no brackets needed — which is the common case, so it got the shorter spelling. Knowing it is a convention makes it easier to remember that brackets override it.
Where the order actually bites
The rule looks academic until a calculation has money in it. A shop sells pens at 3 for £2 and you buy 12: writing 12 ÷ 3 × 2 gives £8, and reading it left to right is what you want here. But 5 + 3 × 2 for a £5 delivery plus three items at £2 is £11, and anyone reading left to right pays £16. Calculators mostly apply the convention and phone calculators mostly do not — the plain one on a phone often works strictly left to right, which is why the same keystrokes give different answers on different devices. Knowing the rule is what lets you tell which of them is lying to you.