Order of operations

When a calculation has more than one operation, there’s an agreed order so everyone gets the same answer: Brackets, Indices (powers), Division and Multiplication, then Addition and Subtraction. That’s BIDMAS (or BODMAS, or PEMDAS in the US).

Key facts

  • Brackets first, then powers and roots.
  • × and ÷ have the same rank: work left to right.
  • + and − have the same rank: work left to right.
  • A fraction bar acts like brackets around the top and the bottom.

Worked examples

Example 1

Work out 3 + 4 × 5.

  1. There are no brackets or powers. Multiply first. 4 × 5 = 20
  2. Then add. 3 + 20 = 23

Answer: 23

Example 2

Work out (8 − 2)² ÷ 3 + 1.

  1. Brackets first. 8 − 2 = 6
  2. Then the power. 6² = 36
  3. Then divide. 36 ÷ 3 = 12
  4. Then add. 12 + 1 = 13

Answer: 13

Example 3

Amira works out 20 − 6 ÷ 2 and gets 7. Is she right?

  1. Amira did 20 − 6 first, then halved it. 14 ÷ 2 = 7
  2. Division comes before subtraction. 6 ÷ 2 = 3
  3. So the right answer is 20 − 3 = 17

Answer: 17