There are five major properties of addition in math: the commutative property, the associative property, the distributive property, the identity property and the additive inverse property.
The commutative property states that the order in which two values are summed does not affect the resulting sum. For example, 2 + 3 = 5 and 3 + 2 = 5.
The associative property states that when three or more numbers are being grouped before addition, the grouping order does not effect the sum. For example, (2 + 3) + 4 = 9 and 2 + (3 + 4) = 9.
The distributive property states that the sum of two numbers multiplied by another number is equal to each addend multiplied by that third number and then summed. For example, 6 x (2 + 1) = 18 and 6 x 2 + 6 x 1 = 18.
The identity property states that the sum of any value and zero is that same value. For example, 3 + 0 = 3.
The additive inverse property states that for any value, there is an equal, opposite value, such that, when the two are summed, they equal zero. For example, 2 + -2 = 0.
Moreover, since subtraction may be rewritten as addition with negative numbers, subtraction follows the same basic properties as addition once rewritten.