PEMDAS is the rule that can be used to simplify or evaluate complicated numerical expressions with more than one binary operation.
Very simply way to remember PEMDAS rule!
P ----> Parentheses
E ----> Exponent
M ----> Multiply
D ----> Divide
A ----> Add
S ----> Subtract
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. Division does not always come before multiplication. 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.
Problem 1 :
Evaluate :
6 + 7 x 8
Solution :
Evaluation = 6 + 7 x 8 = 6 + 56 = 62 |
Operation Multiply Add Result |
Problem 2 :
Evaluate :
10^{2} - 16 ÷ 8
Solution :
Evaluation = 10^{2} - 16 ÷ 8 = 100 - 16 ÷ 8 = 100 - 2 = 98 |
Operation Exponent Divide Subtract Result |
Problem 3 :
Evaluate :
(25 + 11) x 2
Solution :
Evaluation = (25 + 11) x 2 = 36 x 2 = 72 |
Operation Parentheses Multiply Result |
Problem 4 :
Evaluate :
3 + 6 x (5 + 4) ÷ 3 -7
Solution :
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 Parentheses Multiply Divide Add Subtract Result |
Problem 5 :
Evaluate :
56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10
Solution :
Evaluation = 56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10 = 56 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10 = 56 - 2(20 + 3 x 3 - 2 x 2) + 10 = 56 - 2(20 + 9 - 4) + 10 = 56 - 2(29 - 4) + 10 = 56 - 2(25) + 10 = 56 - 50 + 10 = 6 + 10 = 16 |
Operation Parentheses Divide Multiply Add Subtract Multiply Subtract Add Result |
Problem 6 :
Evaluate :
6 + [(16 - 4) ÷ (2^{2} + 2)] - 2
Solution :
Evaluation = 6 + [(16 - 4) ÷ (2^{2 }+ 2)] - 2 = 6 + [12 ÷ (2^{2 }+ 2)] - 2 = 6 + [12 ÷ (4 + 2)] - 2 = 6 + [12 ÷ 6] - 2 = 6 + 2 - 2 = 8 - 2 = 6 |
Operation Square Bracket Exponent Parentheses Square Bracket Add Subtract Result |
Problem 7 :
Evaluate :
(96 ÷ 12) + 14 x (12 + 8) ÷ 2
Solution :
Evaluation = (96 ÷ 12) + 14 x (12 + 8) ÷ 2 = 8 + 14 x 20 ÷ 2 = 8 + 280 ÷ 2 = 8 + 140 = 148 |
Operation Parentheses Multiply Divide Add Result |
Problem 8 :
Evaluate :
(93 + 15) ÷ (3 x 4) - 24 + 8
Solution :
Evaluation = (93 + 15) ÷ (3 x 4) - 24 + 8 = 108 ÷ 12 - 24 + 8 = 9 - 24 + 8 = -15 + 8 = -7 |
Operation Parentheses Divide Subtract Subtract Result |
Problem 9 :
Evaluate :
55 ÷ 11 + (18 - 6) x 9
Solution :
Evaluation = 55 ÷ 11 + (18 - 6) x 9 = 55 ÷ 11 + 12 x 9 = 5 + 12 x 9 = 5 + 108 = 113 |
Operation Parentheses Divide Multiply Add Result |
Problem 10 :
Evaluate :
(7 + 18) x 3 ÷ (2 + 13) - 28
Solution :
Evaluation = (7 + 18) x 3 ÷ (2 + 13) - 28 = 25 x 3 ÷ 15 - 28 = 75 ÷ 15 - 28 = 5 - 28 = -23 |
Operation Parentheses Multiply Divide Subtract Result |
Problem 11 :
Evaluate :
[11 - 20 ÷ (5^{2} - 13) ÷ 3 + 8] x 2
Solution :
Evaluation = [11 - 20 + (5^{2} - 13) ÷ 3 x 8] x 2 = [11 - 20 + (5^{2} - 13) ÷ 3 x 8] x 2 = [11 - 20 + (5^{2} - 13) ÷ 3 x 8] x 2. = [11 - 20 + (25 - 13) ÷ 3 x 8] x 2 = [11 - 20 + 12 ÷ 3 x 8] x 2 = [11 - 20 + 4 x 8] x 2 = [11 - 20 + 32] x 2 = [-9 + 32] x 2 = 23 x 2 = 46 |
Operation Bracket^{2} Parentheses^{2} Exponent^{2} Parentheses Division Multiplication Subtraction Bracket Multiplication Result |
Problem 12 :
Evaluate :
a^{3 }- (b^{2} + c) ÷ a + (ab + c)
if a = 4, b = -3 and c = 7.
Solution :
a^{3 }- (b^{2} + c) ÷ a + (ab + c)
Substitute a = 4, b = -3 and c = 7.
4^{3 }- ((-3)^{2} + 7) ÷ 4 + (4(-3) + 7)
Evaluation = 4^{3 }- ((-3)^{2} + 7) ÷ 4 + (4(-3) + 7) = 4^{3 }- ((-3)^{2} + 7) ÷ 4 + (4(-3) + 7) = 4^{3 }- (9 + 7) ÷ 4 + (4(-3) + 7) = 4^{3 }- 16 ÷ 4 + (-12 + 7) = 4^{3 }- 16 ÷ 4 - 5 = 64 - 16 ÷ 4 - 5 = 64 - 4 - 5 = 60 - 5 = 55 |
Operation Parentheses^{2} Exponent^{2} Parentheses^{2} Parentheses^{2} Exponent^{2} Division Subtraction Subtraction Result |
Problem 13 :
Evaluate the following expression for x = -1 and y = 2 :
x^{2 }+ 3y^{3}
Solution :
= x^{2 }+ 3y^{3}
Substitute x = -1 and y = 2.
= (-1)^{2 }+ 3(2)^{2}
= (-1)^{2 }+ 3(2)^{2} = 1^{ }+ 3(4) = 1 + 12 = 13 |
Exponent Multiplication Addition Result |
Problem 14 :
Evaluate the following expression for x = 1 and y = 1.
(y^{3} + x) ÷ 2 + x
Solution :
= (y^{3} + x) ÷ 2 + x
Substitute x = 1 and y = 1.
= (1^{3} + 1) ÷ 2 + 1
= (1^{3} + 1) ÷ 2 + 1 = (1^{3} + 1) ÷ 2 + 1 = (1 + 1) ÷ 2 + 1 = 2 ÷ 2 + 1 = 1 + 1 = 2 |
Parentheses ^{1}Exponent Parentheses Division Addition Result |
Problem 15 :
Evaluate the following expression for y = 3 and z = 7.
z^{3} - (y ÷ 3 - 1)
Solution :
= z^{3} - (y ÷ 3 - 1)
Substitute y = 3 and z = 7.
= 7^{3} - (3 ÷ 3 - 1)
= 7^{3} - (3 ÷ 3 - 1) = 7^{3} - (3 ÷ 3 - 1) = 7^{3} - (1 - 1) = 7^{3} - 0 = 243 |
^{1}Parentheses ^{1}Division ^{1}Subtraction ^{1}Exponent Result |
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