Rational Additive Inverses

Why

What is the additive inverse of $[(a, b)]$ in the rationals?

The additive inverse of

[(a, b)] \in Q

[(- a, b)]

We denote the additive inverse of $q \in Q$ by $- q$ . We denote $a + (- b)$ by $a - b$ .

We call the operation $(a, b) \mapsto a - b$ subtraction.