Order of Operations (BIDMAS/BODMAS)

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Order of operations (BIDMAS/BODMAS)

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 BIDMAS or BODMAS can help you remember the order of operations

Fractions mean division in calculations (BIDMAS/BODMAS)
There may be "invisible brackets" around the numerator and around the denominator
- e.g. $\frac{2 + 5}{7 - 2}$ means $(2 + 5) \div (7 - 2)$
- 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 (BIDMAS/BODMAS)
There may be "invisible brackets" under the root
- e.g. $\sqrt{9 + 16}$ means $\sqrt{(9 + 16)}$
- Instead of brackets we extend the top line on the root symbol to show everything that is to be rooted

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

Worked example

Work out $(5 - 3) + 2 \times 7^{2}$ .

Answer:

Use BODMAS

First calculate anything inside brackets, $5 - 3 = 2$ , so the question becomes

$2 + 2 \times 7^{2}$

Then any powers, $7^{2} = 49$

$2 + 2 \times 49$

followed by any divisions and multiplications, $2 \times 49 = 98$

$2 + 98$

and finally any additions and subtractions, $2 + 98 = 100$

$(5 - 3) + 2 \times 7^{2} = 100$

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