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.
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
Addition and multiplication: yes
Addition identity.
There is no such thing. The distributive property involves at least three numbers, and two operations (usually multiplication and addition).
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
There are two concepts here that are often confused. If you mean that the order of the operation of addition can be carried out in any order then it is the property of associativity. If you mean that the numbers can be written in any order then the property is commutativity.
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
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.
It is the associative property as well as the commutative property.
The commutative property of addition can be stated as: a+b = b+a