| A | B |
| Identity Property for Addition | For any real number n; n + 0 = n |
| Identity Property for Multiplication | For any real number n; n ( 1 ) = n |
| Inverse Property for Addition | For any real number n; n + -n = 0 |
| Inverse Property for Multiplication | For any real number n; n ( 1/n ) = 1 |
| Zero Property for Multiplication | For any real number n; n (0) = 0 |
| Commutative Property for Addition | For any real number a and b; a + b = b + a |
| Commutative Property for Multiplication | For any real number a and b; a ( b ) = b ( a ) |
| Closure Property for Real Numbers | If I add or multiply real numbers my answer will always be a real number. |
| Associative Property for Addition | For any real numbers a, b, and c; a + (b + c) = (a + b) + c |
| Associative Property for Multiplication | For any real numbers a, b, and c; a (b * c) = (a * b) c |
| Distributive Property of Multiplication over Addition | For any real numbers a, b, and c; a ( b + c) = a (b) + a (c) |