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There are two properties of addition.

The COMMUTATIVE property states that the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a

The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c.

That is IT. No more!

The DISTRIBUTIVE property is a property of multiplication over addition (OR subtraction), not a property of addition.

The existence of of an IDENTITY and an ADDITIVE INVERSE are properties of the set over which addition is defined; again not a property of addition. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.

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Q: What are properties of addition?

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Because addition properties allow you to add them in the first place and without them, you couldn't add!

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