Order of Operations
One sum, one answer. BIDMAS is the agreed order every calculator and every examiner uses: Brackets, Indices, Divide and Multiply, Add and Subtract. The tie-break rule — equal ranks go left to right — is where the marks hide.
National curriculum KS3: use conventional notation for the priority of operations, including brackets, powers and roots1 · Why order matters
What is 3 + 4 × 2? If you read left to right you get 14. A calculator says 11. Maths needs one agreed order, or every sum would have many answers.
= 7 × 2
= 14 ✗
= 3 + 8
= 11 ✓
2 · The order: BIDMAS
Work down this list. Each level beats the ones below it.
| Order | Letters | Means |
|---|---|---|
| 1 | B | Brackets first, always |
| 2 | I | Indices (powers and roots): 3² before anything else outside brackets |
| 3 | D M | Divide and Multiply — equal rank, do them left to right |
| 4 | A S | Add and Subtract — equal rank, do them left to right |
The common trap: D does not beat M, and A does not beat S. They are ties, settled left to right. 10 − 4 + 2 is 6 + 2 = 8, not 10 − 6 = 4.
3 · Step through it
Pick an expression, then press Do next step. The highlighted part is the one BIDMAS says to do next.
4 · Brackets change everything
Brackets say "me first", whatever is inside. The same numbers can give very different answers.
20 − 6 ÷ 2 = 20 − 3 = 17
(20 − 6) ÷ 2 = 14 ÷ 2 = 7
Worked examples
Work out 5 + 3 × 2²
Work out (10 − 4)² ÷ 9
Work out 24 ÷ 6 × 2
Quick check
What you've learned
Brackets first. Indices next. Divide and multiply are a tie, done left to right; so are add and subtract. Writing one step per line keeps the order honest and makes mistakes easy to spot. If you want a different order, you must add brackets — that is what they are for.