Why does the associative property work?

Answer 1

With binary operations, the associative property means that you can perform the operation on any adjacent pair before moving to further pairs.

Thus: a + b + c = (a + b) + c = a + (b + c).

This also applies to multiplication but not to subtraction nor division.

5 - (3 - 2) = 5 - 1 = 4

(5 - 3) - 2 = 2 - 2 = 0

Also, associativity does not imply commutativity so the order of the operands (numbers) cannot be changed unless the operation is also commutative.