# ORDER OF OPERATIONS IN MATHS

## About "Order of operations in maths"

Order of operations in maths :

"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 in matths 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

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 in maths", let us look at some more examples problems.

## Order of operations in maths - Examples

Example 1 :

Evaluate : 6 + 7 x 8

 Expression6 + 7 x 8 Evaluation=  6 + 7 x 8=  6 + 56 =  62 OperationMultiplicationAdditionResult

Example 2 :

Evaluate : 10² - 16 ÷ 8

 Expression10² - 16 ÷ 8 Evaluation=  10² - 16 ÷ 8=  100 - 16 ÷ 8=  100 - 2=  98 OperationPowerDivisionSubtractionResult

Example 3 :

Evaluate : (25 + 11) x 2

 Expression(25 + 11) x 2 Evaluation=  (25 + 11) x 2=  36 x 2=  72 OperationParenthesisMultiplicationResult

Example 4 :

Evaluate : 3 + 6 x (5+4) ÷ 3 -7

 Expression3 + 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 OperationParenthesisMultiplicationDivisionAdditionSubtractionResult

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 OperationParenthesisPowerParenthesisParenthesisAdditionSubtractionResult

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 OperationParenthesesMultiplicationDivisionAdditionResult

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 OperationParenthesisDivisionSubtractionSubtractionResult

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 OperationParenthesisDivisionMultiplicationAdditionResult

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 OperationParenthesesMultiplicationDivisionSubtractionResult

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