| Term | Definition |
| Absolute Value | if n is positive, |n| = n
if n is negative |n| = -n |
| The Addition Property of Equality | for all rational numbers if a = b then a + c = b + c |
| The Addition Property of Inequalities | for all rational numbers a, b and c
if a < b then a + c < b + c
if a > b then a + c > b + c
similar statements can be made for ≤ and |
| Additive Inverses | two rational numbers whose sum is 0. |
| Associative Property of Addition | a + (b + c) = (a + b) + c |
| Associative Property of Multiplication | a(bc) = (ab)c |
| The Closure Property of Addition | if a and b are real numbers a + b is a real number. |
| The Closure Property of Multiplication | if a and b are real numbers ab is a real number. |
| Commutative Property of Addition | a + b = b + a |
| Commutative Property of Multiplication | ab = ba |
| Density Property | between any two rational numbers, there is another rational number. |
| Distributive Property of Multiplication Over Addition | a(b + c) = ab + ac
and
(b+c)a = ba + ca |
| Distributive Property of Multiplication over Subtraction | a(b - c) = ab =ac
and
(b-c)a = ba -ca |
| Dividing a number by itself | when a≠0, a/a =1 |
