PEMDAS RULE

About "PEMDAS rule"

What is PEMDAS rule ?

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

Very simply way to remember PEMDAS rule!

P -----> Parentheses

E -----> Exponents

M -----> Multiplication

D -----> Division

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. Multiplication does not always come before division. We have to do one by one 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 PEMDAS rule, let us look at some more examples problems.

Some more 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

Exponent

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

Operation

Parenthesis

Exponent

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

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

After having gone through the example problems explained on PEMDAS rule, we hope that students would have understood "How to do problems on PEMDAS rule"

Apart from the example problems explained above, if you want to know more about PEMDAS rule, please click here.

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