| A | B |
| commutative property | the order changed |
| associative property | parenthesis regrouped but order did not change |
| additive identity | adding zero did not change the number |
| multiplicative identity | multiplying by zero did not change the number |
| multiplicative property of zero | anything multiplied by zero equals zero |
| multiplicative inverse | flip the number (reciprocal) |
| additive inverse | the opposite of the number |