Order of Operations (BIDMAS) — Is 8÷2(2+2) 1 or 16? | KS3 Maths

$8 \div 2(2+2)$ is the calculation the internet cannot agree on. By the order of operations taught today the answer is 16 — division and multiplication share a rung of the ladder and run left to right. The genuinely interesting part is why so many people reach a different answer, and what that says about writing maths clearly.

The question everyone argues about

Worked example

Settle it: 8 ÷ 2(2 + 2)

Brackets first: $2 + 2 = 4$, so the expression becomes $8 \div 2 \times 4$ — because $2(4)$ just means $2 \times 4$.

Now we have a division and a multiplication. They're equal priority, so work left to right, like reading a sentence:

$8 \div 2 = 4, \qquad \text{then} \qquad 4 \times 4 = \mathbf{16}$

In UK schools — and in every exam you'll ever sit — the answer is 16.

So why do some people say 1?

They read $2(2+2)$ as one glued-together object — as if the 2 belongs to the brackets — and work it out first: $8 \div 8 = 1$. That gluing has a proper name, multiplication by juxtaposition, and the people who use it aren't making it up: around a hundred years ago many textbooks really did teach "do all the multiplications first, then divide", and some calculators (and even physics journals) still bind $2(4)$ tighter than $\div$ today. That's why two different calculators can give two different answers to the same buttons.

But the modern convention used in UK schools and exams is settled: equal priority, left to right — 16.

More trick questions

Worked example

The PhD who said 5! — work out 230 − 220 ÷ 2

This one comes with a famous caption: "I say 120 — my maths PhD friend says 5!"

No brackets, no indices, so division before subtraction: $220 \div 2 = 110$, then $230 - 110 = \mathbf{120}$.

So was the PhD wrong? Look closely: they said "5**!**" — and in maths an exclamation mark means factorial. $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. The PhD was right all along. Sneaky.

Practice questions

Try these yourself, then click to check each answer. Remember: brackets, indices, then divide/multiply left to right, then add/subtract left to right.