Whole numbers - EdexcelOrder of operations

Numbers can be written in words. Both positive and negative numbers can be added, subtracted, multiplied and divided using rules. These rules must be applied in a specific order.

Part of MathsNumber

Order of operations

BO/IDMAS
BracketsPowers/IndicesDivide and Multiply - work from left to rightAdd and Subtract - work from left to right
BBrackets
O/IPowers/Indices
DMDivide and Multiply - work from left to right
ASAdd and Subtract - work from left to right

Example

Calculate the value of \(3 + 4^2 - 10 \div 2\).

  1. There are no brackets (B), so calculate the or first (O or I). \(4^2 = 16\) so the calculation becomes \(3 + 16 - 10 \div 2\).
  2. Do any divisions or multiplications (DM), working from left to right: \(10 \div 2 = 5\) so the calculation becomes \(3 + 16 - 5\).
  3. Then, do any additions or subtractions (AS), working from left to right: first do the addition, \(3 + 16 = 19\) so the calculation becomes \(19 - 5\).Then do the subtraction to give the answer 14.

Question

Calculate the value of \(2^2 \times 5 - 6 \div 3\).

Calculations involving brackets

To solve calculations involving brackets, always calculate the value inside the brackets first. If there are brackets inside other brackets, calculate the inside brackets first.

Example

Calculate the value of \([40 - (2 + 4^2)] \times 2\).

  1. Using the BODMAS/BIDMAS rule, first calculate the inside brackets (B). Work out the power or index in order to do this (O or I): \(2 + 4^2 = 2 + 16 = 18\), giving \([40 - 18] \times 2\).
  2. Next, do the outer brackets: \(40 - 18 = 22\) giving \(22 \times 2\).
  3. Once the brackets have been calculated, finish with the multiplication: \(22 \times 2\) to give 44.

Question

Calculate the value of \([3 \times (6 - 4)^2] + 1\).

Question

Use one pair of brackets to make the statement \(17 - 5 \times 2 + 4 = 28\) correct.