Equations and Functions

Evaluating Expressions
An arithmetic expression consists of numbers and operations using parentheses, exponents, multiplication, division, addition, and subtraction. An algebraic expressionis like an arithmetic expression, but contains at least one variable. A variable is a letter that represents a number.

When evaluating the expressions in this chapter, students are told to first evaluate within the parentheses and then complete the evaluation from left to right. Students also use the Commutative, Associative, Distributive, Identity, and Zero properties when evaluating expressions. A review of these properties is necessary as students progress through this chapter. The summary below provides a verbal statement of each property followed by an arithmetic example and an algebraic example.

Using the Commutative, Associative, and Distributive properties may simplify the process of evaluating expressions or make it possible to complete the evaluation mentally.

Examples:

5 + 87 + 3 = 92 + 3 = 95
Work from left to right
5 + 87 + 3 = 5 + (87 + 3)
= 5 + 90 = 95
Use the Associative Property.
76 × 97 + 3 × 76 = 7,372 + 228
= 7,600
76 × 97 + 3 × 76 = 76 × 97 + 76 × 3
Use the Commutative Property.
= 76 × (97 + 3)
Use the Distributive Property.
= 76 × 100 = 7,600
(This may look longer, but can be done mentally.)

Equations
The equality of two expressions gives an equation. To solve an equation means to find the value of the variable that will make the equation true. The equations in this chapter are simple enough to be solved by inspection or by using a guess-and-check strategy. Explain to students that not all equations are as simple as the equations in this chapter, so it is necessary to learn to use inverse operations to solve simple equations before learning to solve more difficult ones.

Examples:

4p = 24
p = 24 ÷ 4
p = 6

← Use inverse operations. →

x ÷ 3 = 9
x = 9 × 3
x = 27