Arithmetic properties
| Commutative | Addition 3+5 = 5+3 Multiplication 3 x 5 = 3 x 5 | Changing the order of addends does not change, the change the Sum Changing the order of the factors Doesn’t change the product. |
| Associative | Addition 3+(4+5) = (3+4) +5 Multiplication 3x (4×5) = (3×4) x5 | Change in grouping of addends does not change the Sum Change in the grouping of factors doesn’t change the product |
| Distributive Property | 3(4+5) = 3×4 + 3×5 | Multiplying a number and sum of addends is equal to sum of product of each addend and the number |
| Identity property | Addition 4 + 0 = 0 + 4 = 4 Multiplication 2 x 1 = 1 x 2 = 2 | Adding 0 to any number doesn’t change the value of the number Multiplying 1 and a number doesn’t change the value of the number |
| Inverse property | Addition 2 + (-2) = 0 Multiplication 2 x ½ = 1 | If sum of two numbers is 0 then one number is additive inverse of the other. If the product of two numbers is 1 then one number is multiplicative inverse(reciprocal) of the other. |