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Are you asking for an explanation of the Associative, Distributive, and Commutative Properties? The answer is a little long. The first link is a simpler explanation, the second one is more detailed:
The associative property states that the result of an addition or multiplication sentence will be the same no matter the grouping of the terms. Associative: (a + b) + c = a + (b + c) (a × b) × c = a × (b × c)
yes it does work for subtraction
it depends wht kind (multiplication, addition)
There is no synonym for the associative properties.