Rational Multiplication is Associative

Theorem
The operation of multiplication on the set of rational numbers $\Q$ is associative:


 * $\forall x, y, z \in \Q: x \times \left({y \times z}\right) = \left({x \times y}\right) \times z$

Proof
Follows directly from the definition of rational numbers as the quotient field of the integral domain $\left({\Z, +, \times}\right)$ of integers.

So $\left({\Q, +, \times}\right)$ is a field, and therefore a priori $\times$ is associative on $\Q$.