# EVALUATING ALGEBRAIC EXPRESSIONS

Evaluating algebraic expressions :

Recall that an algebraic expression contains one or more variables. We can substitute a number for each variable and then find the value of the expression.

This process is called evaluating the expression.

For example, to evaluate 2m for m = 5, we would plug 5 for m.

2m  =  2(5)  =  10

Parentheses are another way to show multiplication.

2(5)  =  2 × 5  =  10

## Evaluating algebraic expressions - Examples

Example 1 :

Evaluate the expression for the given value of the variable.

x - 9; x  =  15

Solution :

15 - 9  =  6

Therefore, when x  =  15, x - 9  =  6

Example 2 :

Evaluate the expression for the given value of the variable.

16 / n; n  =  8

Solution :

16 / 8  =  2

Therefore, when n  =  8, 16 / n  =  2

Example 3 :

Evaluate the given expression for x = 3  and y = 5.

3x + 2y

Plug x = 3 and y = 5 in the given expression

3(3) + 2(5)  =  9 + 10  =  19

Therefore, 3x + 2y  =  19

Example 4 :

Evaluate the given expression for y = 1.4.

0.5y

Plug y  =  1.4 in the given expression

0.5(1.4)  =  0.5 x 1.4  =  0.7

Therefore, 0.5y  =  0.7

Example 5 :

Evaluate the given expression for s = 5.

s² + 7s - 2

Plug s = 5 in the given expression

5² + 7(5) - 2  =  25 + 35 - 2  =  58

Therefore, s² + 7s - 2  =  58

Example 6 :

Evaluate the given expression for m = 1/3.

18m² + 3m + 7

Plug m = 1/3 in the given expression

18(1/3)² + 3(1/3) + 7  =  2 + 1 + 7  =  10

Therefore, 18m² + 3m + 7  =  10

Example 7 :

Evaluate the given expression for m = 13.

m² + m - 54

Plug m = 13 in the given expression

13² + 13 -54  =  169 + 13 - 54  =  128

Therefore, m² + m - 54  =  128

Example 8 :

Evaluate the given expression for x = 3  and y = 5.

x² + y²

Plug x = 3 and y = 5 in the given expression

3² + 5²  =  9 + 25  =  34

Therefore, x² + y²  =  34

Example 9 :

Evaluate the given expression for m = 5  and n = 2.

5m² + 2m²n

Plug m = 5 and n = 2 in the given expression

5(5)² + 2(5)²(2)  =  125 + 100  =  225

Therefore, 5m² + 2m²n  =  225

Example 10 :

Evaluate the given expression for m = 3.

(2m² + 5m - 7) / 2

Plug m = 3 in the given expression

[2(3)² + 5(3) - 7] / 2  =  [18 + 15 - 7 ] / 2  =  26 / 2  =  13

Therefore, (2m² + 5m - 7) / 2  =  13

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