Real numbers

Properties of Real Numbers

Let a, b, and c be real numbers, variables, or algebraic expressions.
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 can not = 0