Order of operations

The order of operations for whole numbers: brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.

The rules

Example 1●

Evaluate $5 + 3 \times 4$.

$3 \times 4 = 12$

Multiply before adding.

$5 + 12 = 17$

Equal priority: left to right

Example 2●●

Evaluate $48 \div 6 \times 2$ and $20 - 8 + 3$.

$48 \div 6 \times 2 = 8 \times 2 = 16$

÷ and × have equal priority, so go left to right.

$20 - 8 + 3 = 12 + 3 = 15$

Example 3: brackets●●

Evaluate $3 \times [20 - (4 + 2) \times 3]$.

Inner brackets: $4 + 2 = 6$.

Square brackets: $20 - 6 \times 3 = 20 - 18 = 2$.

$3 \times 2 = 6$

Flashcards

Order of operations

Brackets, then × and ÷ (left to right), then + and − (left to right).

$10 - 4 + 2$

$8$ (left to right)

A fraction bar acts like...

brackets around the top and the bottom.

Practice

Evaluate $5 + 3 \times 4$.
Evaluate $48 \div 6 \times 2$.
Evaluate $20 - 8 + 3$.
Evaluate $3 \times [20 - (4 + 2) \times 3]$.
Evaluate $\dfrac{12 + 8}{4}$.
Evaluate $18 - 4 \times 4$.
Where do brackets go to make $2 + 6 \times 3 = 24$ true?
Evaluate $100 \div (5 \times 4) + 2$.