Order of Operations (BIDMAS/BODMAS) (OCR GCSE Maths) : Revision Note

Order of Operations (BIDMAS/BODMAS)

What is the order of operations (BODMAS/BIDMAS)?

  • If there is more than one operation in a calculation then they should be done in the following order

    • Brackets: ( )

      • Perform any calculation(s) inside brackets first

    • pOwers or Indices (sometimes Order):  2, 3, √ and similar

      • These include powers, roots, reciprocals

    • Divisions or Multiplications: × or ÷

      • If there are more than one of these then work them out left to right

      • Division includes fractions

    • Additions or Subtractions: + or -

      • If there are more than one of these then work them out left to right

  • The acronym BODMAS or BIDMAS can help you remember the order of operations

In what order should fractions and roots be dealt with?

  • Fractions mean division in calculations (BODMAS/BIDMAS)

  • There may be "invisible brackets" around the numerator and around the denominator

    • e.g.  fraction numerator 2 plus 5 over denominator 7 minus 2 end fraction means open parentheses 2 plus 5 close parentheses divided by open parentheses 7 minus 2 close parentheses

    • Instead of brackets we extend the fraction line to show exactly what is on the top and what is on the bottom

  • Roots are pOwers (BODMAS/BIDMAS)

  • There may be "invisible brackets" under the root

    • e.g.  square root of 9 plus 16 end root means square root of open parentheses 9 plus 16 close parentheses end root

    • Instead of brackets we extend the top line on the root symbol to show everything that is to be rooted

How do I use a calculator for BIDMAS/BODMAS questions?

  • Ensure that you enter a long or complicated calculation carefully

    • For most modern calculators, the calculation can be typed in exactly as it is written on paper 

    • You may need to use additional brackets on older calculators

Examiner Tips and Tricks

  • Make sure that you always check that your answer seems sensible!

Worked Example

Work out left parenthesis 5 space – space 3 right parenthesis space plus space 2 space cross times space 7 squared.

Use BODMAS

First calculate anything inside "B"rackets, 5 minus 3 equals 2, so the question becomes      

2 space plus space 2 space cross times space 7 squared

Then any p"O"wers, 7 squared equals 49                

2 space plus space 2 space cross times space 49

followed by any "M"ultiplications and "D"ivisions, 2 cross times 49 equals 98

2 plus 98

and finally any "A"dditions and "S"ubtractions, 2 plus 98 equals 100

bold left parenthesis bold 5 bold space bold – bold space bold 3 bold right parenthesis bold plus bold 2 bold cross times bold 7 to the power of bold 2 bold equals bold 100

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Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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