Addition works because like all mathmatics as long as you know 1/2 of the equation, answer, and type of equation (addition,subtraction,multiplication, or division) there is only 1 answer.
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Associative works for addition and multiplication. Commutative works for addition and multiplication Distributive works for addition, multiplication and subtraction as well as some combinations of them, but not for division. Nothing works for division.
Is the set of negative interferes a group under addition? Explain,
The commutative property of addition is a fact that proves an answer is the same even if you switch the 2 numbers in the addition problem around. This only works with addition.
(4+5) +2 = 9 + 2? Explain
It works for some operations, for others it doesn't. Specifically, both addition and multiplication of real numbers are commutative.