I think you mean, what are the 3 properties of addition? Well, addition, like everything else, has infinitely many properties. But I am guessing you mean the 3 properties of addition that are described in the axioms of algebra. Namely,
1. The commutative law. This says that you can add 2 numbers in either order and get the same answer. In symbols, x+y equals y+x.
2. The associative law. This says that if you add 3 numbers, you can group them either way without changing the answer. In symbols, (x+y)+z equals x+(y+z)
3. The distributive law of addition over multiplication. I will not try to describe this in words, which would be long and confusing. It is most clearly described in symbols: x*(y+z) equals x*y + x*z
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An excellent attempt at answering a flawed question. There are only two properties of addition, so trying to describe 3 is not really possible. The third one, above, is a property of multiplication over addition - not of the operation of addition.
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Addition and multiplication: yes
The DISTRIBUTIVE (not distributed) property is a property of multiplication over addition (OR subtraction). In its simplest form, if x, y and z are three numbers then, according to the distributive property of multiplication over addition, x*(y + z) = x*y + x*z
There is no property of addition that uses parentheses.
The reflexive property of relations is not the same as the addition property of equality.
Addition, by itself, does not have a distributive property. Multiplication has a distributive property over addition, according to which: a*(b + c) = a*b + a*c