BIDMAS (Order of operations) — easy step-by-step guide

BIDMAS tells you the order to do parts of a calculation so you get the correct answer. BIDMAS stands for:

• B — Brackets (do these first)
• I — Indices (powers or exponents, e.g. squared)
• D — Division
• M — Multiplication
• A — Addition
• S — Subtraction

Important note: Division and Multiplication are the same level — do whichever comes first from left to right. The same goes for Addition and Subtraction.

Step-by-step method

1. Resolve anything inside brackets first. If there are brackets inside brackets, do the inner ones first.
2. Calculate indices (powers), e.g. 3^2 = 9.
3. Work left to right doing divisions and multiplications as they appear.
4. Finally, work left to right doing additions and subtractions.
5. Write down each step when you work — Functional Skills will usually expect clear working.

Worked examples

1. 3 + 4 × 2

   Do multiplication first: 4 × 2 = 8. Then add: 3 + 8 = 11.

2. (5 + 3) × 2

   Brackets first: 5 + 3 = 8. Then 8 × 2 = 16.

3. 16 ÷ 4 × 2

   Division and multiplication are same level, so go left to right:

   16 ÷ 4 = 4, then 4 × 2 = 8. (Wrong to do 4 × 2 first.)

4. 10 - 3 + 2

   Addition and subtraction are same level, go left to right: 10 - 3 = 7, then 7 + 2 = 9.

5. 2 + 3^2 × 4

   Indices first: 3^2 = 9. Then multiplication: 9 × 4 = 36. Finally add: 2 + 36 = 38.

6. Nested example: (2 + (3 + 1) × 2)^2

   Inner bracket: (3 + 1) = 4. Then 4 × 2 = 8. Now (2 + 8) = 10. Finally 10^2 = 100.

Special note about negative numbers and indices

-3^2 equals -(3^2) = -9 because the minus is not inside brackets. But (-3)^2 = 9 because the negative is inside the brackets. Always watch where the minus sign sits.

Tips and common mistakes

• Remember: B, then I, then D/M (left to right), then A/S (left to right).
• Don’t assume multiplication always comes before division — check left to right.
• Write each step down. Examiners want to see working for Functional Skills.
• When using a calculator, enter steps carefully or use brackets on the calculator to avoid mistakes.
• Be careful with negative numbers and powers: use brackets when necessary.

Practice questions (try them first, then check answers below)

1. 7 + 6 × (5 - 2)
2. 18 ÷ 3 × 2 + 5
3. (4 + 2)^2 ÷ 3
4. 5 - 2^2 × 3
5. -2^2 + 3^2
6. (3 + 5)/(2 + 1) × 4

Answers

1. 7 + 6 × (5 - 2) = 7 + 6 × 3 = 7 + 18 = 25
2. 18 ÷ 3 × 2 + 5 = (18 ÷ 3) × 2 + 5 = 6 × 2 + 5 = 12 + 5 = 17
3. (4 + 2)^2 ÷ 3 = 6^2 ÷ 3 = 36 ÷ 3 = 12
4. 5 - 2^2 × 3 = 5 - (4 × 3) = 5 - 12 = -7
5. -2^2 + 3^2 = -(2^2) + 9 = -4 + 9 = 5 (note: (-2)^2 would be 4)
6. (3 + 5)/(2 + 1) × 4 = 8/3 × 4 = 32/3 ≈ 10.666...

If you want, I can give a short worksheet with more practice questions at the right level and a step-by-step marking guide. Tell me how many questions you want and whether you prefer fractions, decimals or a mix.