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Order of Operations

FoundationChallengeAQAEdexcelOCR

Order of Operations is a key number topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on using BIDMAS / order of operations, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Follow BIDMAS: Brackets, Indices, Division/Multiplication, then Addition/Subtraction.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Challenge / Extension

Stretch yourself beyond the basics.

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Topic overview

Order of operations tells you which part of a calculation to do first when several operations appear together. Without an agreed order, \(2 + 3 \times 4\) could mean \(20\) or \(14\), so the order removes the ambiguity.

The order is brackets first, then indices (powers and roots), then multiplication and division, and finally addition and subtraction. Many students remember it as BIDMAS, though the important detail is what the letters hide.

Multiplication and division rank equally, and so do addition and subtraction. Where two operations of the same rank appear, you work from left to right rather than doing all the multiplication first. This is where most marks are lost.

Revision notes

The order in full

Work through in this order: brackets, then indices, then multiplication and division, then addition and subtraction.

So in \(2 + 3 \times 4\) the multiplication is done first, giving \(2 + 12 = 14\). In \((2 + 3) \times 4\) the bracket forces the addition first, giving \(5 \times 4 = 20\).

Equal ranks and working left to right

Multiplication and division share a rank, and addition and subtraction share a rank. When two operations of equal rank meet, work from left to right.

So \(12 \div 3 \times 2\) is \(4 \times 2 = 8\), not \(12 \div 6 = 2\). Doing the multiplication first because it appears in BIDMAS is a common and costly error.

Hidden brackets

A fraction line acts as a bracket around the whole numerator and the whole denominator, so \(\frac{4 + 8}{3}\) means \((4 + 8) \div 3 = 4\).

A square root sign does the same, so you must simplify everything underneath it before taking the root.

Key points

  • Order: brackets, indices, multiplication and division, addition and subtraction.
  • Multiplication and division rank equally; work left to right.
  • Addition and subtraction rank equally; work left to right.
  • A fraction line acts as a bracket around the top and the bottom.
  • Brackets can be used to change the order deliberately.
  • Indices include both powers and roots.

Worked examples

Example 1

Work out \(5 + 2 \times 3^2\).

Working

\[3^2 = 9\]indices come before multiplication
\[2 \times 9 = 18\]then do the multiplication
\[5 + 18 = 23\]finally the addition

Example 2

Work out \(20 \div 4 \times 5\).

Working

\[20 \div 4 = 5\]division and multiplication rank equally, so work from left to right
\[5 \times 5 = 25\]then multiply by 5

Example 3

Work out \(\frac{6 + 14}{2 + 3}\).

Working

\[6 + 14 = 20\]the fraction line acts as a bracket, so simplify the numerator first
\[2 + 3 = 5\]then simplify the denominator
\[20 \div 5 = 4\]finally divide

Common mistakes

  • Doing all the multiplication before any division.

    They rank equally, so 12 ÷ 3 × 2 is 8, not 2. Work left to right when ranks are equal.

  • Ignoring a power attached to only one term.

    In 2 × 3², only the 3 is squared, giving 18. Squaring the whole product would give 36.

  • Dividing only part of the numerator.

    In (6 + 14) ÷ 5, the whole numerator must be simplified first. Dividing just the 14 gives the wrong answer.

  • Typing a long calculation into a calculator without brackets.

    The calculator applies the correct order to what you actually typed, which may not be what you meant.

Exam tips

  • Write out each stage on a new line rather than doing several steps at once.
  • Use brackets in your own working to make the intended order clear.
  • When ranks are equal, always move left to right.
  • Check a calculator answer against a rough mental estimate.

Key terms

BIDMAS
A way of remembering the order: brackets, indices, division and multiplication, addition and subtraction.
Index
A power, such as the 2 in \(3^2\), showing how many times a number multiplies itself.
Operation
A mathematical process such as adding, subtracting, multiplying or dividing.
Numerator
The expression on the top of a fraction.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.