Order of operations and negative numbers

The order

When a sum has several steps, everyone works it out in the same order, so everyone gets the same answer:

1. Brackets first.
2. Then powers, like 3².
3. Then × and ÷, from left to right.
4. Then + and −, from left to right.

Example: 8 − 2 × 3 = 8 − 6 = 2, not 6 × 3 = 18.

Example: 12 ÷ (2 + 4) × 3. Brackets give 6. Then from left to right: 12 ÷ 6 = 2, and 2 × 3 = 6.

Negative numbers

Think of a number line. Adding moves right; subtracting moves left. So 3 − 7 = −4, and −2 + 5 = 3.

Subtracting a negative is the same as adding: 5 − (−2) = 5 + 2 = 7.

When multiplying or dividing:

same signs give a positive, different signs give a negative

So (−4) × (−5) = 20, and (−12) ÷ 3 = −4.

A trap with powers

(−3)² means (−3) × (−3) = 9. But −3² means −(3²) = −9, because the power comes before the minus.

Guided practice

Work out 20 − 4 × (1 − 3). Brackets: 1 − 3 = −2. Multiply: 4 × (−2) = −8. Subtract: 20 − (−8) = 20 + 8 = 28.