The Internet’s Guide to…Algebra Properties

By Ethan SutherlandIf a+(-a)=0

Then (-a)+a=0?

Additive Identify Property

a+0=a

+0=

Additive Inverse Property

a+(-a)=0

+(-

)=0

Multiplicative Identity Property

a·1=a

·1=

Multiplicative Property of Zero

a·0=0

·0=0

Multiplicative Property of -1

a·-1=-a -a·-1=a

·-1=- - ·-1=

Multiplicative Inverse Property

a/b·b/a=1

__ __· =1

Commutative Property

a+b=b+a ab=ba

+ = + =

Associative Property

(a+b)+c=a+(b+c)(ab)c=a(bc)

( + )+ = +( + )

( ) = ( )

Distributive Property

a(b+c)=ab+aca(b-c)=ab-ac

+(

=

=

(

+)

- ) -

Symmetric Property

a=b, b=c, a=c

= = =,,

Reflexive Property

a=a

=

Transitive Property

a=b, b=a

= =

Addition Property of Equality

a+c=b+c

= ++

Subtraction Property of Equality

a-c=b-c

- = -

Multiplication Property of Equality

ac=bc

=

Division Property of Equality

a/c=b/c c≠0

__ __= ≠0