# EVALUATING NUMERICAL EXPRESSIONS

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 :

----> Parentheses (or Brackets)

E ----> Exponents

M ----> Multiplication

----> Division

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 :

 Expression29 - 5 x 3 Evaluation=  29 - 5 x 3=  29 - 15=  14 OperationMultiplicationSubtractionResult

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 OperationParenthesesMultiplicationResult

Problem 3 :

Evaluate the following numerical expression.

92 - 15 ÷ 3

Solution :

 Expression92 - 15 ÷ 3 Evaluation=  92 - 15 ÷ 3=  81 - 15 ÷ 3=  81 - 5=  76 OperationPowerDivisionSubtractionResult

Problem 4 :

Evaluate the following numerical expression.

5 + 5 x (5 + 7) ÷ 4 - 6

Solution :

 Expression5 + 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 OperationParenthesesMultiplicationDivisionAdditionSubtractionResult

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 OperationParenthesesDivisionMultiplicationMultiplicationSubtractionResult

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 OperationParenthesesPowerParenthesesParenthesisAdditionSubtractionResult

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 OperationParenthesesMultiplicationDivisionAdditionResult

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 OperationParenthesesDivisionSubtractionSubtractionResult

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 OperationParenthesesDivisionMultiplicationAdditionResult

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 OperationParenthesesMultiplicationDivisionSubtractionResult

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