Properties and Operations Vocabulary

Flashcards covering the fundamental algebraic properties including Commutative, Associative, Identity, and Distributive properties.

Commutative Property

The property stating that the order in which 2 numbers are added or multiplied does not change the sum or product; depicted as $a+b=b+a$ for addition and $ab=ba$ for multiplication.

Associative Property

The property stating that the order in which 3 numbers are added or multiplied does not change the sum or product; depicted as $(a+b)+c=a+(b+c)$ for addition and $(ab)c=a(bc)$ for multiplication.

Identity Property

The property establishing that zero is the additive identity ($a+0=a$) and one is the multiplicative identity ($a \times 1=a$).

Additive Identity

The number zero, which when added to any number $a$, results in the sum being the original number $a$.

Multiplicative Identity

The number one, which when multiplied by any number $a$, results in the product being the original number $a$.

Distributive Property

The process of multiplying a term to ALL values inside parentheses; depicted as $a(b+c)=ab+ac$ for addition and $a(b-c)=ab-ac$ for subtraction.