Properties of Math
Commutative Property of Addition
a b b a
Commutative Property of Multiplication
a b b a
Associative Property of Addition
a (b c)
Associative Property of Multiplication
a (b c)
Distributive Property
a (b c) ab ac
(b c) a ba ca
Additive Inverse
a ( a)
Multiplicative Inverse
a
Identity
a 0 0 a a
a1 1a a
1
a
(a b) c
( a b) c
0
1
Rules for Zeroes
a
a
a
0
a
Rule for Ones
1a a
a 1 a
0 a
0 a
0 0
a 0, a 0
0 undefined
Negative of a Negative
( a)
Absolute Value
a
a
a, a
0
Addition Property of Inequality
If a b,
then a c b c
Multiplication Property of Inequality
If a b, and c is positive,
then a c b c
If a b, and c is negative,
then a c b c
LSC-Montgomery Learning Center: Properties of Math
Updated April 7, 2011