| A | B |
| (-6)(1) = -6 | identity property of multiplication |
| b + 0 = b | identity property of addition |
| x + 5 = 1x + 5 | identity property of multiplication |
| 5 + (2m + 3x ) = 5 + ( 3x + 2m ) | commutative property of addition |
| 9(3 * 2) = (3 * 2)9 | commutative property of multiplication |
| -4 (-5 * 6) = -4 ( 6 * -5) | commutative property of multiplication |
| 8x + -8x = 0 | identity property of addition |
| 3x + 9 + -8x = 3x + -8x + 9 | commutative property of addition |
| Definition of Identity Property of Addition | Adding 0 does not change the value of a # |
| Definition of Identity Property of Multiplication | Multiplying by 1 does not change the value of a # |
| Definition of Zero Property of Multiplication | Multiplying by 0 results in a product of 0 |
| Definition of Commutative Property of Addition | Changing the order of the numbers does not change the sum |
| Definition of Commutative Property of Multiplication | Changing the order of the factors does not change the product |