Properties of Real Numbers

Table of PropertiesLet a, b, and c be real numbers, variables, or algebraic expressions.(These are properties you need to know.)

	Property	Example
1.	Commutative Property of Addition a + b = b + a	2 + 3 = 3 + 2
2.	Commutative Property of Multiplication a • b = b • a	2 • ( 3 ) = 3 • ( 2 )
3.	Associative Property of Addition a + ( b + c ) = ( a + b ) + c	2 + ( 3 + 4 ) = ( 2 + 3 ) + 4
4.	Associative Property of Multiplication a • ( b • c ) = ( a • b ) • c	2 • ( 3 • 4 ) = ( 2 • 3 ) • 4
5.	Distributive Property a • ( b + c ) = a • b + a • c	2 • ( 3 + 4 ) = 2 •  3 + 2 • 4
6.	Additive Identity Property a + 0 = a	3 + 0 = 3
7.	Multiplicative Identity Property a •  1 = a	3 • 1  = 3
8.	Additive Inverse Property a + ( -a ) = 0	3 + (-3) = 0
9.	Multiplicative Inverse Property Note: a cannot = 0
10.	Zero Property a • 0 = 0	5 • 0 = 0