Algebraic Properties

Vocabulary flashcards covering core algebraic and mathematical properties.

commutative property of addition

The property stating that changing the order of addends does not change the sum: $a + b = b + a$.

commutative property of multiplication

The property stating that changing the order of factors does not change the product: $a \times b = b \times a$.

associative property of addition

The property stating that changing the grouping of addends does not change the sum: $(a + b) + c = a + (b + c)$.

associative property of multiplication

The property stating that changing the grouping of factors does not change the product: $(a \times b) \times c = a \times (b \times c)$.

multiplicative property of zero

The property stating that the product of any number and zero is zero: $a \times 0 = 0$.

multiplicative identity property

The property stating that the product of any number and one is that number: $a \times 1 = a$.

multiplicative inverse property

The property stating that the product of a non-zero number and its reciprocal is one: $a \times \frac{1}{a} = 1$.

additive identity property

The property stating that the sum of any number and zero is that number: $a + 0 = a$.

additive inverse property

The property stating that the sum of a number and its opposite is zero: $a + (-a) = 0$.

symmetric property

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

transitive property

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

substitution property

The property stating that if $a = b$, then $a$ may be substituted for $b$ in any expression or equation.

distributive property

The property stating that multiplying a sum by a number is equal to multiplying each addend individually by the number: $a(b + c) = ab + ac$.

reflexive property

The property stating that any quantity is equal to itself: $a = a$.