1.1.1 Variables and Expressions
Key Objectives • Translate between words and algebraic expressions. • Evaluate algebraic expressions. • Write algebraic expressions. Key Terms • A variable is a letter or symbol that represents a quantity that can change. • A constant is a quantity that does not change. • An algebraic expression contains one or more variables and may contain operation symbols. • To evaluate an expression means to find its value. Expressions are math statements that can include constants (numbers), variables, and operations. Operations in expressions are represented symbolically. Four operations commonly used in expressions are addition ( + ), subtraction ( − ), multiplication ( × or ·), and division ( ÷ or /). Note that multiplication is the understood operation when a number is written next to a variable, with no symbol between them. For example, 2 n means “2 times n .” Example 1 Translating from Algebra to Words To express a mathematical statement (expression) as words, first translate the meaning of each operation. Because operations can be described using many different phrases, there are often multiple correct ways to write an expression as words. For example, the operation addition ( + ) can be described using the words “increased by”, “added to”, or with “sum of”.
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