GENERATING EQUIVALENT NUMERICAL EXPRESSIONS 

numerical expression is a mathematical sentence involving only numbers with some operations like addition, subtraction, multiplication division etc.,

Let us consider the numerical expression which is given below.

 92 + 19

In this numerical expression, two operations are used. One is exponent and other one is addition.

To generate the equivalent numerical expression, we have to simplify. 

Then, we have

92 + 19  =  81 + 19  =  100

100 is the equivalent numerical expression  to 92 + 19.

To get equal numerical expression to  92 + 19,  first we apply the operation "exponent", then we apply "addition"

Sometimes, we may get confused in the order of taking operations.

To know the order of operations, we have to be aware of "Bodmas rule" 

What is BODMAS rule ?

The rule or order that we use to simplify expressions in math is called "BODMAS" rule.

Very simply way to remember  BODMAS rule! 

 B -----> Brackets

       O -----> Of (orders :Powers and radicals) 

       D -----> Division

       M -----> Multiplication

       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. 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.

To have better understanding on BODMAS rule, let us look at some more examples.

Practice Problems

Problem 1 :

Evaluate :

6 + 7 x 8

Solution :

Expression

6 + 7 x 8



Evaluation

=  6 + 7 x 8

=  6 + 56

=  62

Operation

Multiplication

Addition

Result

Problem 2 :

Evaluate :

102 - 16 ÷ 8

Solution :

Expression

102 - 16 ÷ 8

Evaluation

102 - 16 ÷ 8

100 - 16 ÷ 8

=  100 - 2

=  98

Operation

Power

Division

Subtraction

Result

Problem 3 :

Evaluate :

(25 + 11) x 2

Solution :

Expression

(25 + 11) x 2

Evaluation

(25 + 11) x 2

=  36 x 2

=  72

Operation

Bracket

Multiplication

Result

Problem 4 :

Evaluate :

3 + 6 x (5 + 4) ÷ 3 -7

Solution :

Expression

3 + 6 x (5+4) ÷ 3 -7

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

Bracket

Multiplication

Division

Addition

Subtraction

Result

Problem 5 :

Evaluate :

36 - 2(20 + 12 ÷ 4 x 3 - 2 x 2) + 10

Solution :

Problem 6 :

Evaluate :

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

Bracket

Power

Parenthesis

Parenthesis

Addition

Subtraction

Result

Problem 7 :

Evaluate :

(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

Bracket

Multiplication

Division

Addition

Result

Problem 8 :

Evaluate :

(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

Bracket

Division

Subtraction

Subtraction

Result

Problem 9 :

Evaluate :

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

Bracket

Division

Multiplication

Addition

Result

Problem 10 :

Evaluate :

(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

Bracket

Multiplication

Division

Subtraction

Result

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