| A | B |
|---|
| closure | Under a binary operation [=, - or X, divide], when every pair of elements from the set results in an element from that set |
| commutative of addition | the order in which two numbers are added can be changed without changing the sum |
| commutative of multiplication | the order in which two numbers are multiplied can be changed without changing the product |
| associative of addition | the way in which we group numbers to be added does not change the sum |
| associative of multiplication | the way in which we group numbers to be multiplies does not change the product |
| distributive property | the product of one number times the sum of a second and a third equals the product of the first and second numbers plus the product of the first and third numbers |
| identity element of addition | when zero is added to any real number, that number is returned |
| identity element of multiplication | when one is multiplied by any real number that number is returned |
| additive inverse | when two opposites are added, the result is the identity element [zero] |
| multiplicative inverse [reciprical] | when two recipricals are multiplies the result is the identity element [1] |
| multiplicative property of zero | any number multiplied by zero is always zero |
