PEMDAS RULE
About "PEMDAS Rule"
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.
PEMDAS Rule - 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
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
