Unit 1A: Expressions and Properties Study Guide

Vocabulary terms, operational definitions, properties of equality, and algebraic translation rules covered in the Unit 1A: Expressions study guide.

Absolute Value

The distance of a number from 0 on a number line, meaning $|x| \ge 0$ for all real numbers.

Distributive Property

A property of operations represented by the key formulas $a(b + c) = ab + ac$ and $a(b - c) = ab - ac$.

Reflexive Property of Equality

The property stating that $a = a$, meaning a quantity is equal to itself.

Symmetric Property of Equality

The property stating that if $a = b$, then $b = a$.

Transitive Property of Equality

The property stating that if $a = b$ and $b = c$, then $a = c$.

"Less than" and "fewer than"

Key verbal subtraction phrases that flip the order of terms in an algebraic expression (for example, "5 less than x" becomes $x - 5$).

Verbal Keywords for Addition

Translational key words that indicate addition: sum, plus, added to, increased by, and more than.

Verbal Keywords for Subtraction

Translational key words that indicate subtraction: difference, minus, subtracted from, decreased by, fewer than, and less than.

Verbal Keywords for Multiplication

Translational key words that indicate multiplication: product, times, and multiplied by.

Verbal Keywords for Division

Translational key words that indicate division: quotient, divided by, and ratio of.

Order of Operations (PEMDAS / GEMDAS)

The four-step sequence for evaluating expressions: 1. Groups / Parentheses (innermost first), 2. Exponents & Radicals, 3. Multiplication & Division (left to right), and 4. Addition & Subtraction (left to right).

Like Terms

Terms that contain the exact same variables raised to the exact same powers, which are simplified by combining their coefficients.