GEMDAS 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 GEMDAS rule :
G ---> Grouping (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 :
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.
Problem 1 :
Evaluate :
5 + 6 x 7
Solution :
Evaluation = 5 + 6 x 7 = 5 + 42 = 47 |
Operation Multiplication Addition Result |
Problem 2 :
Evaluate :
(25 + 11) x 2
Solution :
Evaluation = (25 + 11) x 2 = 36 x 2 = 72 |
Operation Grouping Multiplication Result |
Problem 3 :
Evaluate :
10^{2} - 16 ÷ 8
Solution :
Evaluation = 10^{2} - 16 ÷ 8 = 100 - 16 ÷ 8 = 100 - 2 = 98 |
Operation Exponent Divide Subtract 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 Grouping 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 Grouping 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 Grouping Power Parenthesis Parenthesis Addition Subtraction 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 Grouping Multiplication Division Addition 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 Grouping Division Subtraction Subtraction 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 Grouping Division Multiplication Addition 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 Grouping Multiplication Division Subtraction Result |
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