Algebraic Proofs Properties

Addition Property of Equality

IF a=b THEN a+c=b+c

Additive Identity Property

a+0=a

Additive Inverse Property

a+(-a)=0

Associative Property of Addition

(a+b)+c=a+(b+c)

Associative Property of Multiplication

(a
b)
c=a
(b
c)

Commutative Property of Addition

a+b=b+a

Commutative Property of Multiplication

a
b=b
a

Distributive Property of Multiplication over Addition/Subtraction

a(b+c)=a
b+a
c AND a(b-c)=a
b=a
c

Division Property of Equality

a/c=b/c IF a=b

Multiplication Property of Equality

IF a=b THEN a
c=b
c

Multiplicative Identity Property

1*a=a

Multiplicative Inverse Property

a*1/a=1

Substitution Property

IF a=b THEN EITHER ONE CAN BE SUBSTITUTED FOR THE OTHER

Subtraction Property of Equality

IF a=b THEN a-c=b-c

Transitive Property of Equality

IF a=b AND b=c THEN a=c

Zero Product Property

IF a*b=0 THEN a=0, b=0, OR BOTH EQUAL ZERO.