# GENERATING EQUIVALENT NUMERICAL EXPRESSIONS

## About "Generating equivalent numerical expressions"

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"

## 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! -----> Brackets first (Parentheses)

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

D -----> Division

-----> Multiplication

-----> 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 problems.

## Generating equivalent numerical expressions - Practice problems

Problem 1 :

Write equivalent numerical expression for

6 + 7 x 8

Solution :

 Expression6 + 7 x 8 Evaluation=  6 + 7 x 8=  6 + 56 =  62 OperationMultiplicationAdditionResult

Problem 2 :

Write equivalent numerical expression for

10² - 16 ÷ 8

Solution :

 Expression10² - 16 ÷ 8 Evaluation=  10² - 16 ÷ 8=  100 - 16 ÷ 8=  100 - 2=  98 OperationPowerDivisionSubtractionResult

Problem 3 :

Write equivalent numerical expression for

(25 + 11) x 2

 Expression(25 + 11) x 2 Evaluation=  (25 + 11) x 2=  36 x 2=  72 OperationParenthesisMultiplicationResult

Problem 4 :

Write equivalent numerical expression for

3 + 6 x (5+4) ÷ 3 -7

 Expression3 + 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 OperationParenthesisMultiplicationDivisionAdditionSubtractionResult

Problem 5 :

Write equivalent numerical expression for

36 - 2(20+12÷4x3-2x2) + 10

Solution : Problem 6 :

Write equivalent numerical expression for

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 OperationParenthesisPowerParenthesisParenthesisAdditionSubtractionResult

Problem 7 :

Write equivalent numerical expression for

(96÷12)+14x(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 :

Write equivalent numerical expression for

(93+15) ÷ (3x4) - 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 OperationParenthesisDivisionSubtractionSubtractionResult

Problem 9 :

Write equivalent numerical expression for

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 OperationParenthesisDivisionMultiplicationAdditionResult

Problem 10 :

Write equivalent numerical expression for

(7 + 18) x 3 ÷(2+13) - 28

Solution :

 Expression(7+18)x3÷(2+13)- 28 Evaluation= (7+18)x3÷(2+13)-28= 25x3 ÷ 15 - 28= 75 ÷ 15 - 28= 5 - 28= -23 OperationParenthesesMultiplicationDivisionSubtractionResult

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