\begin{definition}[Definition:Rational Number/Formal Definition]
The field $\struct {\Q, +, \times}$ of rational numbers is the field of quotients of the integral domain $\struct {\Z, +, \times}$ of integers.
This is shown to exist in Existence of Field of Quotients.
In view of Field of Quotients is Unique, we construct the field of quotients of $\Z$, give it a label $\Q$ and call its elements '''rational numbers'''.
\end{definition}