Order of Operations

≈ 20 min

When a calculation mixes operations, we cannot just work left to right. Everyone must agree on an order, or the same sum would give different answers. The rule:

Brackets first.
Then × and ÷, working left to right.
Then + and −, working left to right.

Worked example. $4 + 3 \times 5$ . Multiplication comes before addition, so $3 \times 5 = 15$ first, then $4 + 15 = 19$ . (Working blindly left to right would give the wrong answer $35$ .)

Brackets let you override the order: $2 \times (7 + 3) = 2 \times 10 = 20$ .

Calculate $4 + 3 \times 5$ .

$19$

$35$

$23$

$32$

Calculate $2 \times (7 + 3)$ .

Which calculation equals $6 \times (10 - 4)$ ?

$36$

$56$

$60$

$26$

Calculate $20 - 12 \div 4 + 1$ .