Order of Operations (BIDMAS/BODMAS) (Cambridge International IGCSE Mathematics)

Order of operations (BIDMAS/BODMAS)

What is the 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

In what order should fractions and roots be dealt with?

• 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)÷(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 √((9+16))
  • 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

Exam Hint Make sure that you always check that your answer seems sensible!

Worked Example Work out $(5--3)+2\times7^{2}$.

Answer:

Use BODMAS

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

$2+2\times7^{2}$

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

$2+2\times49$

followed by any divisions and multiplications, $2\times49=98$

$2+98$

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

$(5--3)+2\times7^{2}=100$