EVALUATING NUMERICAL EXPRESSIONS
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PEMDAS 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 ----> Parentheses (or Brackets)
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.
Examples :
16 ÷ 4 x 3 = 4 x 3 = 12
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.
Problem 1 :
Evaluate the following numerical expression.
29 - 5 x 3
Solution :
|
Expression 29 - 5 x 3 |
Evaluation = 29 - 5 x 3 = 29 - 15 = 14 |
Operation Multiplication Subtraction Result |
Problem 2 :
Evaluate the following numerical expression.
(14 + 12) x 3
Solution :
|
Expression (14 + 12) x 3 |
Evaluation = (14 + 12) x 3 = 26 x 3 = 78 |
Operation Parentheses Multiplication Result |
Problem 3 :
Evaluate the following numerical expression.
92 - 15 ÷ 3
Solution :
|
Expression 92 - 15 ÷ 3 |
Evaluation = 92 - 15 ÷ 3 = 81 - 15 ÷ 3 = 81 - 5 = 76 |
Operation Power Division Subtraction Result |
Problem 4 :
Evaluate the following numerical expression.
5 + 5 x (5 + 7) ÷ 4 - 6
Solution :
|
Expression 5 + 5 x (5+7) ÷ 4 -6 |
Evaluation = 5 + 5 x (5+7) ÷ 4 -6 = 5 + 5 x 12 ÷ 4 -6 = 5 + 60 ÷ 4 -6 = 5 + 15 -6 = 20 - 6 = 14 |
Operation Parentheses Multiplication Division Addition Subtraction Result |
Problem 5 :
Evaluate the following numerical expression.
-2(12 ÷ 4 x 3) + 10
Solution :
|
Expression -2(12 ÷ 4 x 3) + 10 |
Evaluation = -2(12 ÷ 4 x 3) + 10 = -2(12 ÷ 4 x 3) + 10 = -2(3 x 3) + 10 = -2(9) + 10 = -18 + 10 = -8 |
Operation Parentheses Division Multiplication Multiplication Subtraction Result |
Problem 6 :
Evaluate the following numerical expression.
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 Parentheses Power Parentheses Parenthesis Addition Subtraction Result |
Problem 7 :
Evaluate the following numerical expression.
(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 the following numerical expression.
(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 Parentheses Division Subtraction Subtraction Result |
Problem 9 :
Evaluate the following numerical expression.
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 Parentheses Division Multiplication Addition Result |
Problem 10 :
Evaluate the following numerical expression.
(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 |
Problem 11 :
19 - {(3 x 7) - (9 ÷ 3)} + 14
Solution :
= 19 - {(3 x 7) - (9 ÷ 3)} + 14
= 19 - (21 - 3) + 14
= 19 - 18 + 14
= 1 + 14
= 15
So, the answer is 15.
Problem 12 :
[2 x 3 + (11 - 5)] ÷ 3
Solution :
= [2 x 3 + (11 - 5)] ÷ 3
= [2 x 3 + 6] ÷ 3
= [6 + 6] ÷ 3
= 12 ÷ 3
= 4
So, the answer is 4.
Problem 13 :
{4 x (4 x 3) ÷ 2} x 7
Solution :
= {4 x (4 x 3) ÷ 2} x 7
= {4 x 12 ÷ 2} x 7
= {4 x 6} x 7
= 24 x 7
= 168
So, the answer is 168.
Problem 14 :
5 + [13 - (8 ÷ 4)]
Solution :
= 5 + [13 - (8 ÷ 4)]
= 5 + [13 - 2]
= 5 + 11
= 16
So, the answer is 16.
Problem 15 :
[25 - (16 - 11)] ÷ [12 ÷ 4 + 2]
Solution :
= [25 - (16 - 11)] ÷ [12 ÷ 4 + 2]
= [25 - 5] ÷ [3 + 2]
= 20 ÷ 5
= 4
So, the answer is 4.
Replace * with either +, -, x or ÷ to make a true statement :
Problem 16 :
3 + 15 * 3 = 8
Solution :
3 + 15 * 3 = 8
When * is replaced with +, we get
= 3 + 15 + 3
= 21
It is not equal to 8. So, + is not the replacement.
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