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

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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Polar Form of a Complex Number

    Apr 16, 24 09:28 AM

    polarform1.png
    Polar Form of a Complex Number

    Read More

  2. Conjugate of a Complex Number

    Apr 15, 24 11:17 PM

    conjugateofcomplexnumber1.png
    Conjugate of a Complex Number

    Read More

  3. Complex Plane

    Apr 14, 24 07:56 AM

    complexplane1.png
    Complex Plane

    Read More