The Language of Algebra

You may not realize it, but you already use algebra every day — working out a tip at a restaurant, figuring the change you are owed, or comparing the batting averages of your favorite players. Algebra begins in earnest when we use letters to stand for numbers. That small move lets us state rules that hold for every number at once, and to describe relationships whose values we do not yet know.

This chapter introduces the words, symbols, and notation used to describe algebra, and starts you on the path to solving algebraic problems with confidence.

Sections

• Use the Language of Algebra — variables and constants, the symbols for the four operations, equality and inequality, expressions versus equations, exponential notation, and the order of operations.
• Evaluate, Simplify, and Translate Expressions — evaluating an expression for a given value, identifying terms, coefficients, and like terms, combining like terms, and translating word phrases into algebraic expressions.
• Solve Equations Using the Subtraction and Addition Properties of Equality — determining whether a number is a solution of an equation, solving equations by adding or subtracting the same quantity from both sides, and translating word sentences into equations and solving them.
• Find Multiples and Factors — identifying multiples of a number, using divisibility tests, finding all the factors of a number, and identifying prime and composite numbers.
• Prime Factorization and the Least Common Multiple — writing composite numbers as products of primes and finding least common multiples from prime factorizations.

This chapter overview is adapted from Prealgebra 2e, Chapter 2 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.