How to Apply BODMAS (Order of Operations) Principle / Rule

In a problem where more than two operations ('operations' mean add, subtract, multiply and divide etc) are involved, the BODMAS rule is followed. Do you know what each of these letters stands for ?

Look at this

• B - brackets
• O - of (multiplication)
• D - division
• M - multiplication
• A - addition
• S - subtraction

This order should be followed while solving problems with more than one mathematical operation.

Example 1 : Simplify 3 of 4 X 5 % 6

Solution : Three operations need to be done here. According to the BODMAS rule, we begin with 'of', then 'multiplication' and finally we perform 'division'

3 x 4 x 5 % 6  = 12 x 5 % 6 = 60 % 6 = 10

You should remember that if 'BODMAS' rule is not followed in case of one mathematical operation each method may give a different result.

Look at the following example, subtraction is followed by multiplication.

6 - 3 X 2

(6-3) x 2 = 3x 2  = 6

Alternate method (multiplication is followed by subtraction)

6 - 3 x 2

6 - 6 = 0

Although both methods seem correct, there cannot be two different answers to the same problem. There has to be one standard method. Hence the "BODMAS" rule is followed.

Example 2 : Simplify 4 + 5 x 12 - 6

Solution :

Applying the BODMAS rule, we get the following result

4 + 60 - 6

64 - 6 = 58

Example 3 : Simplify 5 + 7 x 15 % 5

Solution : According to the BODMAS rule, we first perform multiplication followed by addition.

5 + 7 x 3

5 + 21 = 26

Example 4 : simplify 5 of 4 + 2 x 2 % 2

Solution : Here, the first operation to be performed is 'of'

20 + 2 x 2 % 2

20 + 2 x 1

20 + 2 = 22

Example 5 : 30 - (2 x 6 + 15 % 3) + 8 x 3 % 6

Solution : Here,

let us remove the brackets first,

so (2 x 6 + 15 % 3) becomes (12 + 5 ) = 17

Now, 30 - 17 + 8 x 3 % 6

= 30 - 17 + 8 x 1/2

= 30 - 17 + 4 = 17

Some important points to remember about BODMAS rule :

1. If an expression contains brackets, you should solve the expression within brackets first.
2. If the expression involves 'of' (as we have mentioned in one of the above examples), multiplication (or division), addition and subtraction, then 'of' should be performed first, followed by multiplication or division. Then proceeding from the left to the right, addition and subtraction are carried out in the order in which the sign of addition and subtraction are given. It should be noted that if the expression contains 'of' and 'division' always do 'of' first and then do 'division' in order to get the correct answer.
3. Some problems may have certain numbers written in brackets or may contain more than one bracket. Such problems are solved with the help of following rule.
• Let us look at the sequence of brackets to be removed
• First bracket to be removed is the line "_______" bracket or the vinculum.
• Second bracket to be removed is the simple ( ) bracket.
• Third bracket to be removed is the curly { } bracket
• Fourth bracket to be removed is the square [ ] bracket

Example 6 : 

   





Solution : '5+2' is the first operation here followed by other bracketed operations.

= [4 x {7 +(9-7)} + 3 ]

= [ 4 x {7+2} + 3]

= [ 4 x 9 + 3 ]

= 36 + 3 = 39 



Example 7 : 1 + {1 % [1+1 % (1+ (1%4))]}



Solution : 



= 1 + { 1 % [1 + 1 % (1 +  % 4) ] }

= 1 + {1 % [ 1 + 1 %  1 + 1/4)]}

= 1 + { 1 % [ 1 + 1 % (5/4) ] }

= 1 + { 1 % [ 1 + 4/5]}

= 1 + 1 % 9/5}

= 1 + { 5/9}

=  14/9