A LITTLE PRACTICE, EVERY DAY·GCSE MATHS
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Number · Foundation & Higher

Order of operations (BIDMAS)

BIDMAS tells you the order in which to do operations: Brackets, Indices, Division and Multiplication (left to right), then Addition and Subtraction (left to right).

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Revising order of operations (bidmas) the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Order of operations (BIDMAS) GCSE” on the site for the complete guide.

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Key facts to remember

  • 1B – Brackets first.
  • 2I – Indices (powers and roots).
  • 3DM – Division and Multiplication, left to right.
  • 4AS – Addition and Subtraction, left to right.
  • 5Division and multiplication have equal priority (same for + and −).
  • 6A fraction bar acts like brackets over both the numerator and denominator.
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Worked examples

Example 1

Work out 3 + 4 × (5 − 2)².

Working

  1. Brackets: 5 − 2 = 3
  2. Indices: 3² = 9
  3. Multiplication: 4 × 9 = 36
  4. Addition: 3 + 36 = 39
Answer39
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Common mistakes

✗Doing addition before multiplication.
✗Applying powers to the wrong part of an expression, e.g. treating −3² as 9 instead of −9.
✗Forgetting brackets imposed by a fraction bar.
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Exam tips

✓Rewrite the calculation step by step, showing each BIDMAS stage.
✓Use brackets generously in your working to avoid ambiguity.
✓On a calculator, always use brackets for complex expressions.

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