Using the Associative Property in Algebra

The associative property allows you to break a problem up into sub-problem, and solve it with sub-solution. As long as you stay in the same type, when you concatenate them together, you concatenation as the associative property. Commutative means you can solve, you can do operations in any order. If I do F first and then G, it's the same as doing G first and then F. And that also has nice properties, or is it a nice property?