Order of Operations

Use BIDMAS to work out calculations with more than one operation and get the same answer every time.

About 3 min read
  • State the order of operations
  • Work out calculations with brackets and powers
  • Use brackets to change the value of a calculation
Before you start

You can already add, subtract, multiply and divide. You also know that 3² means 3 × 3.

Why we need an order

Look at 2 + 3 × 4. If you add first you get 20, but if you multiply first you get 14. Both cannot be right, so mathematicians agreed on one order. The correct answer is 14 because multiplication comes before addition.

Definition: BIDMAS

The order of operations: Brackets, Indices, Division and Multiplication, then Addition and Subtraction.

Using BIDMAS

Division and multiplication have equal priority, so work them from left to right. Addition and subtraction also have equal priority, so work them from left to right as well. This means 24 ÷ 4 × 2 is 6 × 2, which equals 12.

Brackets, a power and subtraction

Work out (4 + 3)² − 5.

Maths
(4 + 3)² − 5
7² − 5        brackets first
49 − 5        then the power
44            then the subtraction

Answer: 44

Equal priority

Multiplication does not always come before division. When they appear together, work from left to right.

Exam focus
Say it like this“20 − 6 ÷ 2 = 20 − 3 = 17”
Not like this“20 − 6 ÷ 2 = 14 ÷ 2 = 7” — Division comes before subtraction, so 6 ÷ 2 is worked out first.
Common mistakeWorking from left to right through the whole calculation instead of following BIDMAS.

Practice

Work out 8 + 2 × 5.
2 × 5 = 10, then 8 + 10 = 18.
Work out 3 × (6 − 2)².
6 − 2 = 4, then 4² = 16, then 3 × 16 = 48.
Work out 24 ÷ 4 × 2.
Work left to right: 24 ÷ 4 = 6, then 6 × 2 = 12.
Going further
Work out 2 + 3 × (8 − 2)² ÷ 4.
8 − 2 = 6, then 6² = 36. 3 × 36 = 108, then 108 ÷ 4 = 27. Finally 2 + 27 = 29.

Quick check

Order of operations quick check

What is 6 + 4 × 2?

Multiply 4 by 2 first to get 8, then add 6.

What is (6 + 4) × 2?

Brackets come first, so add to get 10, then multiply by 2.

Which step comes first in 5 + 2³ × 3?

Indices come before multiplication and addition, so find the power first.
Key takeaways
  • Follow BIDMAS so everyone gets the same answer.
  • Work division and multiplication from left to right.
  • Work addition and subtraction from left to right.
  • Use brackets to change the order.
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