Foundations Summary

Algebra 1 · Axiom Academy

SUMMARY Foundations of Algebra Let's review the core rules for working with variables and expressions. Algebra replaces specific numbers with variables — letters like x that stand for values that change or are unknown. An expression combines variables, numbers, and operations; evaluating it means substituting values and computing. PEMDAS fixes the order of operations, so every expression has exactly one correct value. The commutative, associative, and distributive properties are the legal moves for rearranging and simplifying expressions. Core Concept Variables: The Language of Algebra A variable is a letter or symbol (like x or t ) that acts as a placeholder for a number that can change or is unknown. An algebraic expression combines variables, numbers, and operations into one mathematical phrase. Evaluating: replace each variable with its number and calculate the result — this process is called substitution . Watch out for: a number written next to a letter means multiplication — 3x is . Core Concept The Rules of the Road Two kinds of rules keep algebra consistent: the order of operations (PEMDAS) sets the sequence to compute in, and the properties of numbers — Commutative, Associative, and Distributive — say which rewrites are legal. Simplifying: use the properties to combine like terms and shorten expressions — for example, 3(x + 2) simplifies to 3x + 6 .

This is the written version of the interactive lesson above. See the full Algebra 1 course.