GEMDAS ORDER OF OPERATIONS

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 :

---> Grouping (Parentheses)

----> Exponent

----> Multiply

----> Divide

----> 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.

Practice Problems

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 :

102 - 16 ÷ 8

Solution :

Evaluation

102 - 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) ÷ (22 + 2)] - 2

Solution :

Evaluation

= 6 + [(16 - 4) ÷ (2+ 2)] - 2

= 6 + [12 ÷ (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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