Lesson 2: Evaluate, Simplify, and Translate Expressions

New Concept

This lesson builds a bridge from arithmetic to algebra. You'll work with algebraic expressions by finding their value, simplifying them by combining like terms, and translating word phrases into the language of algebra.

What’s next

Get ready to apply these concepts! Next up are practice cards for evaluating expressions, followed by interactive examples on combining like terms.

Property

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.

Examples

• To evaluate $8y - 5$ when $y=3$, substitute $3$ for $y$: $8(3) - 5 = 24 - 5 = 19$.

• To evaluate $a^2 + 5$ when $a=4$, substitute $4$ for $a$: $4^2 + 5 = 16 + 5 = 21$.

Property

A term is a constant or the product of a constant and one or more variables. The constant that multiplies the variable(s) in a term is called the coefficient. Like terms are terms that are either constants or have the same variables with the same exponents.

Examples

• In the expression $4x^2 + 7y - 3$, the terms are $4x^2$, $7y$, and $-3$. The coefficient of $4x^2$ is $4$, and the coefficient of $7y$ is $7$.

• Identify like terms in the list: $2a, 5b^2, 6, 9a, 3b^2$. The like terms are $2a$ and $9a$ (both have the variable $a$) and $5b^2$ and $3b^2$ (both have $b^2$).

Property

To simplify an expression, combine the like terms.

Step 1. Identify like terms.

Step 2. Rearrange the expression so like terms are together.

Property

Translating word phrases into algebraic expressions involves identifying keywords that signify mathematical operations.

• Addition: sum, more than, plus, increased by
• Subtraction: difference, less than, minus, decreased by
• Multiplication: product, times, twice
• Division: quotient, divided by

Examples

• Translate "the product of 4 and a number x" into an expression. The keyword "product" means multiplication, so the expression is $4x$.