EVALUATING ALGEBRAIC EXPRESSIONS WORKSHEET

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

Concepts to be known :

Example 1 :

a3 - [(b2 + c)/a] + (ab + c), if a = 4, b = -3 and c = 7

Solution :

= a3 - [(b2 + c)/a] + (ab + c)

When a = 4, b = -3 and c =-7

= 43 - [((-3)2 + 7)/4] + [(4)(-3) + 7]

= 64 - [(9 + 7)/4] + [-12 + 7]

= 64 - (16/4) + (-5)

= 64 - 4 - 5

= 55

Example 2 :

What is the value of

(2c/a)2 - 10 x (b +a)/c

if a = -2, b = 3 and c = 5 ?

Solution :

= (2c/a)2 - 10 x (b +a)/c

= [2(5)/-2]2 - 10 x (3 - 2)/5

= (-5)2 - 10 x (1/5)

= 25 - 2

= 23

Example 3 :

What is the value of

9 - 2x ÷ (z - y)3

if x = 4, y = -1 and z = -3 ?

Solution :

= 9 - 2x ÷ (z - y)3

= 9 - 2(4) ÷ (-3 + 1)3

= 9 - 8 ÷ (-2)3

= 9 - 8 ÷ (-8)

= 9 + 1

= 10

Example 4 :

If x = 10, what is the value of x/2 + x/20 + x/200 ?

Solution :

= x/2 + x/20 + x/200

When x = 10

= 10/2 + 10/20 + 10/200

= 5 + 1/2 + 1/20

= (100+10+1)/20

= 111/20

= 5.55

Example 5 :

If a = 3, b = -1 and c = -2, what is the value of

7 - [(a - 12) ÷ (2 - b)]/(c+ 3) ?

Solution :

= 7 - [(a - 12) ÷ (2 - b)]/(c+ 3)

= 7 - [(3 - 12) ÷ (2 +1)]/(-2+ 3)

= 7 - (-9 ÷ 3)/(-2+ 3)

= 7 - (-3)/1

= 7 + 3

= 10

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