Commutative Property for Addition
a+b=b+a
Commutative Property for Multiplication
a(b)=b(a)
Associative Property for Addition
a+(b+c)=(a+b)+c
Associative Property for Multiplication
[(a)(b)]c=a[(b)(c)]
Distributive Property
a(b+c)=ab+ac
Identity Property for Addition
a+0=a
Identity Property for Multiplication
a=1(a)
Additive Inverse Property
a+(-a)=0
Multiplicative Inverse Property
a(1/a)=1;a does not equal 0
Closure Property for Addition
a+b is a real number
Closure Property for Multiplication
a(b) is a real number
Reflexive Property of Equality
a+b=a+b
Symmetric Property of Equality
If a=b+c, then b+c=a
Transitive Property of Equality
If a=b+c and b+c=d, then a=d
Addition Property of Equality
If a=b, then a+c=b+c
Multiplication Property of Equality
If a=b, then ac=bc
Cancellation Property of Addition
If a+c=b+c, then a=b
Cancellation Property of Multiplication
If ab=ac, then b=c
Cancellation Property of Additive Inverse
-(-a)=a
Multiplication Property of -1
-1b=-b
Multiplication Property of 0
0(a)=0
Property of the Opposite of a Sum
-(a+b)=-a+(-b)
Property of the Reciprocals of a Product
1/ab=1/a(1/b)
Substitution Principle
If x=8-5, then x=3
Property of Opposites in a Product
x(-y)=-xy
Absolute Value Property
IaI x IbI = IaxbI