Algebra Properties

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x = x

Reflexive property

If x = y, then y = x

Symmetric property

If x = y and y = z then z = x

Transitive property

If x = y then x + z = y + z

Addition property of equality

If x = y then xz = yz

Multiplication property of equality

x + y = y + x

Commutative Property (Addition)

xy = yx

Commutative Property (Multiplication)

(x + y) + z = x + (y + z)

Associative Property (Addition)

(x*y) * z = x * (y*z)

Associative Property (Multiplication)

x + 0 = x

Identity Property (Additon)

x * 1 = x

Identity Property (Multiplication)

x + (-x) = 0

Inverse Property (Addition)

x * 1/x = 1

Inverse Property (Multiplication)

x * (y + z) = xy + xz

Distributive property

x ÷ y = x * 1/y

Definition of division

x - y = x + (-y)

Definition of subtraction

If you perform an operation (+, -, x) on numbers in a set, the answer is also in the set

Closure