Order of operations

curriculum-key-fact
Mathematical operations must be carried out in the correct order. BODMAS and BIDMAS are ways of remembering this order.
BO/IDMAS
BracketsPowers/IndicesDivide and Multiply - work from left to rightAdd 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 power or index number 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.

  1. There are no brackets (B), so calculate the power or index number first (O or I), giving 4 \times 5 - 6 \div 3.
  2. Do any divisions or multiplications (DM), working left to right: 4 \times 5 = 20 and 6 \div 3 = 2, giving 20 - 2.
  3. And, finally, do any additions or subtractions (AS): 20 – 2 gives 18.

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.

  1. Calculate the brackets:
    • internal brackets first, giving [3 \times 2^2] + 1
    • then the other brackets, indices first, giving [3 \times 4] + 1
    • then finish the brackets with the multiplication, giving 12 + 1
  2. Finally, the addition, giving 13.
Question

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

Using the rules of BIDMAS, the value of 17 – 5 \times 2 + 4 is 11, because the multiplication is done before the addition and subtraction. Consider what would happen if you did the – or the + first:

  • doing the - first would give 12 \times 2 + 4
  • then the \times as usual would give 24 + 4
  • this gives the required answer, 28

Brackets are used to show that the subtraction needs to happen first. Therefore the answer (17 - 5) \times 2 + 4 = 28.