Maths

BODMAS – The Order Of Mathematical Operations | Maths | Tutorial

You may come across a simple maths questions with a mixture of brackets, orders (powers), division, multiplication, addition and subtraction all at once. You may think to yourself where do I start, this is where BODMAS is a useful acronym to use. BODMAS provides us with the order the mathematical operations need to be carried out.

This tutorial will illustrate how to apply the order of operation using BODMAS to an equation.

Order of Operation

  1. Brackets
  2. Orders/Power
  3. Division
  4. Multiplication
  5. Addition
  6. Subtraction

Example

45 – 2 (25 + 16 ÷ 4 x 3 – 5 x 5) + 8 =

Solution

Step 1 – Brackets

First, we will apply BODMAS within the brackets

45 – 2 (25 + 16 ÷ 4 x 3 – 5 x 5) + 8

Step 2 – Orders/ Power

There are no powers or square root (√) in this question therefore this step is n/a

Step 3 – Division

45 – 2 (25 + 16 ÷ 4 x 3 – 5 x 5) + 8

45 – 2 (25 + 4 x 3 – 5 x 5) + 8

Step 4 – Multiplication

45 – 2 (25 + 4 x 35 x 5) + 8

45 – 2 (25 + 1225) + 8

Step 5 – Addition

45 – 2 (25 + 12 – 25) + 8

45 – 2 (37 – 25) + 8

Step 6 – Subtraction

45 – 2 (37 – 25) + 8

45 – 2 (12) + 8

Once Step 6 has been Completed inside the bracket, we need to follow BODMAS again for the rest of the equation.

Step 1 – Brackets

The bracket no longer has a function within it so we can remove it as follows

45 – 2 x 12 + 8

Step 2 – Orders/ Power

There are no powers or routes in this question therefore this step is n/a

Step 3 – Division

There are division in this equation therefore this step is n/an

Step 4 – Multiplication

45 – 2 x 12 + 8

45 – 24 + 8

Step 5 – Addition

45 24 + 8

45 24 + 8

Step 6 – Subtraction

45 – 16

29

Answer

29

Note: There are many ways to calculate the answer to this question incorrectly, but if you follow BODMAS you will never go wrong.

10 thoughts on “BODMAS – The Order Of Mathematical Operations | Maths | Tutorial”

    1. Yes you are correct, of is used as well but it still means orders (indices). In my school days it was ‘other’. BIDMAS is also another acronym that is used.

      Liked by 1 person

  1. Correct answer. However I think you could clarify the final steps a little bit. I was taught that Division/Multiplication are done together as one step, as are Addition/ Subtraction.
    Subtraction is really just adding a negative number. If we take them as two steps it’s very easy to ignore the minus sign in the next to last step and add 24+8= 32 before we subtract from 45, giving an incorrect answer of 13.

    Liked by 1 person

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