Order of operations

Work out calculations in the right order: brackets, powers, then multiplication and division, then addition and subtraction.

Also known as: BIDMAS, BODMAS, PEMDAS, order of operations rules.

GCSE Maths · Number IGCSE Maths · Number

Key ideas

Brackets first, then powers (indices or exponents), then multiplication and division, then addition and subtraction.
Multiplication and division have equal priority: work them from left to right. The same goes for addition and subtraction.
A fraction bar groups everything above it and everything below it: $\frac{6 + 4}{2} = 5$ , not $8$ .
$-3^2 = -9$ , but $(-3)^2 = 9$ : the power applies only to what it's attached to.

Why there's an order

Without an agreed order, $2 + 3 \times 4$ could mean $20$ or $14$ . Everyone uses the same convention, so it means $2 + 12 = 14$ : multiplication happens before addition.

The order goes by different names around the world:

Name	Used in	Stands for
BIDMAS	UK	Brackets, Indices, Division and Multiplication, Addition and Subtraction
BODMAS	UK, India, Australia and elsewhere	Brackets, Orders, Division and Multiplication, Addition and Subtraction
PEMDAS	US	Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

They all describe the same rules.

The left-to-right rule

The most common misunderstanding is thinking that multiplication always comes before division (because M comes before D in PEMDAS), or that addition always comes before subtraction. It doesn't: multiplication and division have the same priority, and so do addition and subtraction. When operations have the same priority, work from left to right.

$12 \div 3 \times 2 = 4 \times 2 = 8 \quad (\text{not } 12 \div 6 = 2)$ $10 - 4 + 3 = 6 + 3 = 9 \quad (\text{not } 10 - 7 = 3)$

Brackets, powers and fraction bars

Work out the innermost brackets first. Then powers: in $2 \times 3^2$ , square the $3$ first, giving $2 \times 9 = 18$ .

A fraction bar acts like brackets around the top and the bottom: $\frac{8 + 4}{2 \times 3} = \frac{12}{6} = 2.$

Be careful with negative numbers and powers: $-3^2$ means $-(3^2) = -9$ , while $(-3)^2 = 9$ . Calculators follow the same rule, so type the brackets if you mean $(-3)^2$ .

Worked examples

Example 1 · Mixed operations

Work out $8 + 6 \div 2 \times 3$ .

Step 1.Division and multiplication come before addition. Work them left to right: $6 \div 2 = 3$ , then $3 \times 3 = 9$ .
Step 2.Then add: $8 + 9 = 17$ .

Answer: $17$

Example 2 · Brackets and powers

Work out $20 - 3 \times (4 + 2)^2 \div 9$ .

Step 1.Brackets: $4 + 2 = 6$ .
Step 2.Power: $6^2 = 36$ .
Step 3.Multiplication and division, left to right: $3 \times 36 = 108$ , then $108 \div 9 = 12$ .
Step 4.Subtraction: $20 - 12 = 8$ .

Answer: $8$

Example 3 · A fraction bar

Work out $\dfrac{5 + 3 \times 5}{2^2 + 1}$ .

Step 1.Top: $3 \times 5 = 15$ , then $5 + 15 = 20$ .
Step 2.Bottom: $2^2 = 4$ , then $4 + 1 = 5$ .
Step 3. $20 \div 5 = 4$ .

Answer: $4$

Common mistakes

Always multiplying before dividing: $12 \div 3 \times 2$ is $8$ , not $2$ .
Always adding before subtracting: $10 - 4 + 3$ is $9$ , not $3$ .
Squaring a negative without brackets: $-3^2 = -9$ .
Working left to right through the whole calculation and ignoring the priorities.
Forgetting that a fraction bar groups the top and bottom.

Try it yourself

Original practice questions. Your answer is checked instantly.

Question 1Order of operationsEasier

Work out $2 + 3 \times 4$ .

Question 2Order of operationsEasier

Work out $(2 + 3) \times 4$ .