Notes

To evaluate means to "find the value of." You have been evaluating numerical expressions since the time you began learning addition facts. Because a variable represents an "unknown," it is impossible to evaluate algebraic expressions unless values for the variables are provided. You cannot find the value of x + 3 without knowing what "x" is. When you use a formula, for example, A = lw (Area = length × width), you must evaluate an expression.

OBJECTIVES

Evaluate algebraic expressions for given values of the variables.
VOCABULARY

algebraic expression a mathematical expression containing one or more variables
evaluate to find the numerical value of
substitution replacing a quantity with its equal
variable a letter or symbol used to represent an unknown
Vocab Arcade
Evaluating Expressions
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Example:
Evaluate the expression A + 4 for A = 10 and A = 75.

Solution:
If A = 10, then A + 4 = 10 + 4 = 14.
If A = 75, then A + 4 = 75 + 4 = 79.

Any number can replace the variable A. Each replacement makes the expression A + 4 take on some new value.

The first step to evaluating an expression is to replace each variable with the equivalent numerical value. (Put the numbers in place of the letters.)

Once the substitution has been made, simplify by performing the operation. To evaluate expressions involving more than one operation, you are to follow the order of operations:

Calculate inside parentheses.
Deal with exponents.
Multiply and divide from left to right.
Add and subtract from left to right.
Example:
Evaluate 5x - 10 for x = 30.

Solution:

5x - 10
= 5(30) - 10
= 150 - 10
= 140
original expression
Substitution: replace x with 30.
Multiply.
Subtract.
Example:
Evaluate A2+ 2A + 5 for A = 4.

Solution:
A2 + 2A + 5
= (4)2 + 2(4) + 5
= 16 + 2(4) + 5
= 16 + 8 + 5
= 29
original expression
Substitution: replace A with 4.
Simplify the exponents.
Multiply.
Add.
Note that the value of the variable was substituted into the expression using parentheses. This is especially helpful when the value is a negative number. These parentheses do not have an operation within them, so they are not included as the first step in the order of operations.

Example:
Evaluate A2+ 2AB for A = 3 and B = 2.

Solution:

A2 + 2AB
= (3)2 + 2(3)(2)
= 9 + 2(3)(2)
= 9 + (6)(2)
= 9 + 12
= 21

original expression
Substitution: replace A with 3 and B with 2.
Simplify the exponents.
Multiply left to right.
Multiply.
Add.


LET'S REVIEW!

Before going on to the practice problems, make sure that you understand the main points of this lesson:

To evaluate means to find the numerical value of an expression.
Algebraic expressions can only be evaluated when the values of the variables are provided.
The given values are substituted in for the variables in the expression.
The order of operations is used to find the value of the expression.
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