# Algebra 1 Chapter 2 Properties

a+(-a)=0 and (-a)+a=0 Property of Opposites
ab=ba Communicative Property of Multiplication
(ab)c=a(bc) Associative Property of Multiplication
a=a Reflexive Property of Equality
a=b, then b=a Symmetric Property of Equality
a=b and b=c, then a=c Transitive Property of Equality
a+0=a and 0+a=a Identity Property of Addition
-(a+b)=(-a)+(-b) Property of the Opposite of a Sum
a-b=a+(-b) Definition of Subtraction
a(b+c)=ab+ac and (b=c)a=ba+ca Distributive Property(of multiplication with respect to Addition
a(-c)=ab-ac and (b-c)a+ba-ca Distributive Property(of Multiplication with respect to subtraction
a x 1=a Identity Property of Multiplication
a x 0=0 Multiplicative Property of Zero
a(-1)=-a and (-1)a=-a Multiplicative Property of -1
(-a)(b)=-ab a(-b)=-ab (-a)(-b)=ab Property of Opposites in Products
1/-a=-1/a Property of the Reciprocals of the opposite of a Number
a x 1/a=1 and 1/a x =1 Property of Reciprocals
1/ab=1/a x 1/b Property of the Reciprocals of a Product
a/b=a x 1/b Definition of Division