Integers have special properties for addition and multiplication. Understanding and using these properties, correctly, can make problems involving integers easier.
| Property | Addition | Multiplication |
| Closure Property | a + b is an integer | ab is an integer |
| Commutative Property (changes order of integers) |
a + b = b + a | ab = ba |
| Associative Property (changes grouping of integers) |
(a + b) + c = a + (b + c) | (ab)c = a(bc) |
| Identity Property | a + 0 = a | 1(a) = a |
| Inverse Property | a + -a = 0 | a( 1/a ) = 1 |
| Property of Zero (Multiplication only) |
0(a) = 0 | |
| Distributive Property | a(b + c) = ab + ac |
Where a, b, and c are integers.