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Mathematics · Numbers

Order of operations

Is 2 + 3 × 4 equal to 20 or 14 — and who decides?

Why we need an agreed order, the DMAS / BODMAS rule, brackets, and how the distributive property explains it all.

5 depths≈ 200 min of reading75 practice questions

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  1. Discoverabout 30 minOne line of maths, one answerMeet the puzzle 2 + 3 × 4 through a shopping bill, learn why everyone needs one agreed order, and practise the three rules: brackets first, then × and ÷, then + and −, with partners going left to right.Owner-accepted · not line-by-line reviewed
  2. Understandabout 40 minThe rule, preciselyMake the order of operations precise: split expressions into terms, see why DMAS, BODMAS and PEMDAS all mean one rule, handle nested brackets and "of", write expressions from word problems and find mistakes in working.Owner-accepted · not line-by-line reviewed
  3. Investigateabout 40 minBrackets under the microscopeExperiment with the order of operations: count how many values brackets can make, find when brackets change nothing, test always/sometimes/never statements, fill in missing signs, compare calculators and hit targets.Owner-accepted · not line-by-line reviewed
  4. Go deeperabout 45 minWhy the rule is the ruleJustify the order of operations: why × comes before + (repeated addition, the distributive property), why partners go left to right (negatives and reciprocals), where powers fit, the vinculum and history of brackets, expression trees, RPN and edge cases.Owner-accepted · not line-by-line reviewed
  5. Extendabout 45 minPuzzles, arguments and the wider worldTake the order of operations further: why 8 ÷ 2(2 + 2) starts arguments, the four fours and 24 puzzles, olympiad problems, how code and spreadsheets differ, other notations, projects and open questions.Owner-accepted · not line-by-line reviewed

Practise and apply

Question bank · 75 questions

8 sections from Foundation to Challenge, each with hints and a worked solution — or play a 10-question round for points and stars.

Foundation 19Core 31Stretch 17Challenge 8

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The web

Connected ideas

Follow a connection when you’re curious — some lead into completely different areas.

Order of operations

  • Builds on

    Properties of numbers

    The distributive property explains why multiplication is done before addition and how brackets change a result.

  • Builds on

    Four operations

    Once each operation is reliable, the next question is which one to do first when several appear together.

  • Related to

    Number and shape patterns

    A pattern rule such as 3 × n + 1 is an expression — you need the order of operations to use it.

Words to know

53 words are explained in these lessons

All vocabulary →

OperationExpressionValueSimplifyOrder of operationsBracketsDMASBODMASLeft to rightConventionArithmetic expressionTerm+41 more