ORDER OF OPERATIONS

About "Order of operations"

Order of operations : 

"Operations" means things like add, subtract, multiply, divide, squaring, etc.

When we have two or more operations in the same expression, we may have question about which one has to be done first, which one has to be done next.   

But order of operations or bodmas rule or pemdas rule tells us in which order we have to do the operations one by one. 

What is BODMAS rule ?

The rule or order that we use to simplify expressions in math is called "BODMAS" rule.

Very simply way to remember  BODMAS rule!

B -----> Brackets first (Parentheses)

O -----> Of (orders :Powers and radicals)

D -----> Division

M -----> Multiplication

A -----> Addition

S -----> Subtraction

Important notes :

1. In a particular simplification, if you have both multiplication and division, do the operations one by one in the order from left to right.

2. Division does not always come before multiplication. We have to do one by one in the order from left to right. 

3. In a particular simplification, if you have both addition and subtraction, do the operations one by one in the order from left to right.

Examples : 

12 ÷ 3 x 5  =  4 x 5  =  20

13 - 5 + 9   =  8 + 9  =  17

In the above simplification, we have both division and multiplication. From left to right, we have division first and multiplication next. So we do division first and multiplication next.

To have better understanding on "Order of operations", let us look at some more examples problems. 

Order of operations - Examples

Example 1 :

Evaluate : 6 + 7 x 8

Expression

6 + 7 x 8



Evaluation

=  6 + 7 x 8

=  6 + 56

=  62

Operation

Multiplication

Addition

Result

Example 2 :

Evaluate : 10² - 16 ÷ 8

Expression

10² - 16 ÷ 8

Evaluation

10² - 16 ÷ 8

100 - 16 ÷ 8

=  100 - 2

=  98

Operation

Power

Division

Subtraction

Result

Example 3 :

Evaluate : (25 + 11) x 2

Expression

(25 + 11) x 2

Evaluation

(25 + 11) x 2

=  36 x 2

=  72

Operation

Parenthesis

Multiplication

Result

Example 4 :

Evaluate : 3 + 6 x (5+4) ÷ 3 -7

Expression

3 + 6 x (5+4) ÷ 3 -7

Evaluation

=  3 + 6 x (5+4) ÷ 3 -7

3 + 6 x 9 ÷ 3 -7

3 + 54 ÷ 3 -7

=   3 + 18 -7

=   21 - 7

=   14

Operation

Parenthesis

Multiplication

Division

Addition

Subtraction

Result

Example 5 :

Evaluate : 36 - 2(20+12÷4x3-2x2) + 10

Example 6 :

Evaluate : 6+[(16-4)÷(2²+2)]-2

Expression

6+[(16-4)÷(2²+2)]-2

Evaluation

= 6+[(16-4)÷(2²+2)]-2

= 6+[12÷(2²+2)]-2

= 6+[12÷(4+2)]-2

= 6+[12÷6]-2

= 6+2 - 2

= 8 - 2

=6

Operation

Parenthesis

Power

Parenthesis

Parenthesis

Addition

Subtraction

Result

Example 7 :

Evaluate :  (96÷12)+14x(12+8)÷2

Expression

(96÷12)+14x(12+8) ÷ 2

Evaluation

=(96÷12)+14x(12+8) ÷ 2

= 8 + 14x20 ÷ 2

= 8 + 280 ÷ 2

= 8 + 140

= 148

Operation

Parentheses

Multiplication

Division

Addition

Result

Example 8 :

Evaluate : (93+15) ÷ (3x4) - 24 + 8

Expression

(93+15)÷(3x4)-24+8

Evaluation

= (93+15)÷(3x4)-24+8

= 108 ÷ 12 - 24 + 8

9 - 24 + 8

= -15 + 8

-7

Operation

Parenthesis

Division

Subtraction

Subtraction

Result

Example 9 :

Evaluate : 55 ÷ 11 + (18 - 6) x 9

Expression

55÷11+(18-6)x9

Evaluation

= 55÷11+(18-6)x9

= 55÷11 + 12x9

= 5 + 12x9

= 5 + 108

= 113

Operation

Parenthesis

Division

Multiplication

Addition

Result

Example 10 :

Evaluate : (7 + 18) x 3 ÷(2+13) - 28

Expression

(7+18)x3÷(2+13)- 28

Evaluation

= (7+18)x3÷(2+13)-28

= 25x3 ÷ 15 - 28

= 75 ÷ 15 - 28

= 5 - 28

= -23

Operation

Parentheses

Multiplication

Division

Subtraction

Result

Related topics

We hope that the students would have understood the stuff given on "Order of operations".   

Apart from the example problems explained above, if you want to know more about "Order of operations", please click here.

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