Order of Operations
Shows the order step by step: brackets → indices → multiplication and division → addition and subtraction.
Practice examples
How to use it
Order of operations: when an expression has several operations, you carry them out in a fixed order — not simply left to right.
- Brackets — always first, working from the innermost out.
- Indices and roots — after brackets.
- Multiplication and division — left to right, at equal rank.
- Addition and subtraction — last, also left to right.
Example 1: 2 + 3 × 4 = 2 + 12 = 14 (multiplication before addition).
Example 2: (2 + 3) × 4 = 5 × 4 = 20 (brackets first).
Example 3: 2 + 3² = 2 + 9 = 11 (index before addition).
Common mistake: 3 + 4 × 2 — not 14, but 11. Because multiplication comes first! First 4 × 2 = 8, then 3 + 8 = 11.
💼 Tip:whenever an expression looks complicated, adding brackets makes it easier to see what to work out first. Don't be afraid to add brackets even when they are not strictly needed.
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✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specifications