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Bodmas in Math,
Order of Operations

On this Page:
  Intro
  BODMAS
  Examples

When doing sums in Math, there are specific rules of arithmetic that give operations different rank in order in which they are to be performed.

These rules are also commonly referred to as the ‘order of operations’ in arithmetic.



Rules of Arithmetic Intro:


Let’s look at a standard sum we could encounter.

    42 + 3 × 2

What order do we perform the operations in?


Two possibilities are:
42 + 3 × 2   =   16 + 3 × 2   =   19 × 2   =   38

42 + 3 × 2   =   16 + 3 × 2   =   16 + 6   =   22


Which is correct though?
We want to be sure that we perform each operation in the correct order, according to the rules of arithmetic.

The standard operations in arithmetic sums are addition and subtraction, multiplication and division, along with powers/exponents.
There can also be the presence of brackets at times which can influence a sum.

Fortunately, there is a handy way of remembering the correct order of operations to perform.



BODMAS


The word ‘BODMAS’ is an effective way of remembering how to solve sums.

The letters are ordered in the same way as to perform operations in a sum as they appear.

1)   B   Brackets
2)   O   Order / Exponent
3)   DM   Division AND Multiplication
4)   AS   Addition AND Subtraction


As can be seen, Multiplication and Division are ranked together, as is also the case with Addition and Subtraction.

If these operations appear together in a sum. The order to perform each operation is just from left to right as they are positioned in the sum.


So for the first example shown, the correct order and answer is:

42 + 3 × 2  =  16 + 3 × 2  =  16 + 6  =  22.







BODMAS in Math, Order of Operations Examples



(1.1) 
14 − 32

The  3;2  is taken care of first, then the minus comes after.
14 − 32  =  14 − 9  =  5



(1.2) 
2 × 42 + 6

The  42  comes first, followed by the multiplication then addition.
2 × 42 + 6  =  2 × 16 + 6  =  32 + 6  =  38



(1.3) 
( 2 + 2 ) × 3

Multiplication does come before addition usually, but as the addition is inside brackets, we deal with the addition first to eliminate the brackets.

( 2 + 2 ) × 3  =  4 × 3  =  12



(1.4) 

10 ÷ 2 × 6 ÷ 3

As the operations have the same rank, they are carried out in order from the left.

10 ÷ 2 × 6 ÷ 3  =  5 × 6 ÷ 3  =  30 ÷ 3  =  10





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