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.
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 =6 |
Operation Parenthesis Exponent 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 |
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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