Algebra 1: Properties of Numbers

Vocabulary flashcards covering the properties of equality, identity, and operations from the 1.3 Properties of Numbers lecture notes.

Reflexive Property

For any real number $a$, $a = a$.

Symmetric Property

If $a = b$, then $b = a$.

Transitive Property

If $a = b$ and $b = c$, then $a = c$.

Substitution Property

If $a = b$, then $a$ can be substituted for $b$ in any equation or expression.

Additive Identity

For any number $a$, $a + 0 = a$.

Additive Inverse

For any number $a$, $a + (-a) = 0$.

Multiplicative Identity

For any number $a$, $a \times 1 = a$.

Multiplicative Property of Zero

For any number $a$, $a \times 0 = 0$.

Multiplicative Inverse

For any number $\frac{a}{b}$, where $a, b \neq 0$, the inverse is $\frac{b}{a}$ such that $\frac{a}{b} \times \frac{b}{a} = 1$.

Commutative Property

For any numbers $a$ and $b$, $a + b = b + a$ and $a \times b = b \times a$.

Associative Property

For any numbers $a$, $b$, and $c$, $(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$.