Why is the word associative used to represent the concept of the associative property? For the commutative property ... According to wikipedia: > The word "commutative" is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." Therefore the choice of the word commutative to represent the concept of commutative property makes sense. if you switch the order of the operands, you get the same result a * b = b * a What is the corresponding story for the associative property?

In French, _associer_ means making links and connections. Therefore, _associative_ literally means tending to make links and connections. If $\star$ is an associative law, one has: $$(a\star b)\star c=a\star(b\star c).$$ With an associative law, you get the same result regardless of the pairwise associations.