The "Zero Property" is actually called the Additive Identity Property. The additive identity is the unique number which, when added to any other number returns a sum which is the other number. 0 is the additive identity.
The Additive Inverse Property is that each nonzero number has a unique number which, when added to the number will return a sum of zero. (A more mathematical way to say this is that it will return a sum which is the additive identity.)
Examples: 23 + (23) = 0 (3/4) + (3/4) = 0 √3 +(√3) = 0  x^{2} + x^{2} = 0
The Commutative Property of Addition is that when two numbers are added together they will produce the same sum, regardless of the order of the two numbers.
Examples: 28.3 + (12.7) = 15.6, 12.7 + 28.3 = 15.6
(1/3) + (3/4) = (13/12), (3/4) + (1/3) = (13/12)
What you are calling the 1 Property is the Multiplicative Property of Identity. It is not a property of addition. 1 is the identity for multiplication, just like 0 is the identity for addtion.
6/11/2013

Jason T.
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