Definition:Addition/Rational Numbers

Definition
The addition operation in the domain of rational numbers $\Q$ is written $+$.

Let $\displaystyle a = \frac p q, b = \frac r s$ where $p, q \in \Z, r, s \in \Z - \left\{{0}\right\}$.

Then $a + b$ is defined as:
 * $\displaystyle \frac p q + \frac r s = \frac {p s + r q} {q s}$

This definition follows from the definition of and proof of existence of the quotient field of any integral domain, of which the set of integers is one.

Also see

 * Rational Addition is Well-Defined


 * Rational Addition is Commutative
 * Rational Addition is Associative


 * Rational Addition Identity is Zero
 * Inverses for Rational Addition