Algebraic Expressions and Properties of Real Numbers

Vocabulary flashcards defining key real number properties and variable concepts from the lecture notes.

Variables

Representations of numbers, allowing the properties of real numbers to be used in simplifying algebraic expressions.

Closure Property

A property stating that for any real numbers $a$ and $b$, $a + b$ is a unique real number and $ab$ is a unique real number.

Commutative Property

A property stating that for any real numbers $a$ and $b$, $a + b = b + a$ and $ab = ba$.

Associative Property

A property stating that for any real numbers $a$, $b$, and $c$, $(a + b) + c = a + (b + c)$ and $(ab)c = a(bc)$.

Distributive Property

A property stating that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$ and $a(b - c) = ab - ac$.

Additive Identity Element

The element $0$, which satisfies $a + 0 = a$ or $0 + a = a$ for any real number $a$.

Multiplicative Identity Element

The element $1$, which satisfies $a \cdot 1 = a$ or $1 \cdot a = a$ for any real number $a$.

Additive Inverse Element

Elements $a$ and $-a$ that satisfy $a + (-a) = 0$.

Multiplicative Inverse Element

Elements $a$ and $\frac{1}{a}$ (where $a \neq 0$) that satisfy $a \cdot \frac{1}{a} = 1$ or $\frac{1}{a} \cdot a = 1$.

Zero Property for Multiplication

A property stating that $a \cdot 0 = 0$ for any real number $a$.