Order of Operations

Stage 6 of 23 Strand 1 of 7 3 lessons

3 illustrated lessons, each teaching the why before the how.

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Brackets First #

Brackets say which part to work out first.

Whatever sits inside brackets is worked out first

3 + 4 × 2 could read as 14 or 11. Brackets remove the doubt: (3 + 4) × 2 is 14.

Move the brackets and the meaning moves: 3 + (4 × 2) is 3 + 8, which is 11.

Now you

(6 + 6) × 5

3 × (8 − 6)

No brackets? Do × and ÷ first, left to right.

Without brackets, multiplying and dividing happen before adding and subtracting

No brackets, so the × acts first: 4 × 2 is 8, and 3 + 8 makes 11.

Dividing acts first too: 12 ÷ 4 becomes 3, so 20 − 12 ÷ 4 is 20 − 3, which is 17.

Plus and minus share a rank, so work left to right: 10 − 4 is 6, then 6 + 3 is 9.

Now you

6 × 3 + 5

15 − 6 ÷ 3

Brackets, then × and ÷, then + and −.

Brackets first, then multiply and divide, then add and subtract — the order of operations

With brackets: 5 + 3 makes 8 first, then 8 × 2 makes 16.

Take the brackets away and the × acts first: 5 + 3 × 2 is 5 + 6, which is 11.

All four at once: the bracket gives 6, dividing gives 3, adding gives 4.

Now you

(21 − 12) ÷ 3

(10 − 8) ÷ 2