PEMDAS Rule :
In this section, we are going to learn PEMDAS rule.
This rule can be used to simplify or evaluate complicated numerical expressions with more than one binary operation easily.
Very simply way to remember PEMDAS rule :
P -----> Parenthesis
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 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 :
16 ÷ 4 x 3 = 4 x 3 = 12
18 - 3 + 6 = 15 + 6 = 21
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 practice problems.
Problem 1 :
Evaluate :
6 + 7 x 8
Solution :
Expression 6 + 7 x 8 |
Evaluation = 6 + 7 x 8 = 6 + 56 = 62 |
Operation Multiplication Addition Result |
Problem 2 :
Evaluate :
(25 + 11) x 2
Solution :
Expression (25 + 11) x 2 |
Evaluation = (25 + 11) x 2 = 36 x 2 = 72 |
Operation Parenthesis Multiplication Result |
Problem 3 :
Evaluate :
10² - 16 ÷ 8
Solution :
Expression 10² - 16 ÷ 8 |
Evaluation = 10² - 16 ÷ 8 = 100 - 16 ÷ 8 = 100 - 2 = 98 |
Operation Power Division Subtraction Result |
Problem 4 :
Evaluate :
3 + 6 x (5 + 4) ÷ 3 -7
Solution :
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 |
Problem 5 :
Evaluate :
36 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10
Solution :
Problem 6 :
Evaluate :
6 + [(16 - 4) ÷ (2² + 2)] - 2
Solution :
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 |
Problem 7 :
Evaluate :
(96 ÷ 12) + 14 x (12 + 8) ÷ 2
Solution :
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 |
Problem 8 :
Evaluate :
(93 + 15) ÷ (3 x 4) - 24 + 8
Solution :
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 |
Problem 9 :
Evaluate :
55 ÷ 11 + (18 - 6) x 9
Solution :
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 |
Problem 10 :
Evaluate :
(7 + 18) x 3 ÷ (2 + 13) - 28
Solution :
Expression (7+18)x3÷(2+13)- 28 |
Evaluation = (7+18)x3÷(2+13)-28 = 25 x 3 ÷ 15 - 28 = 75 ÷ 15 - 28 = 5 - 28 = -23 |
Operation Parentheses Multiplication Division Subtraction Result |
After having gone through the stuff given above, we hope that the students would have understood, "Pemdas rule"
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WORD PROBLEMS
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Word problems on simple equations
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Word problems on average speed
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L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
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