Definition:Addition/Rational Numbers

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

Let:
 * $a = \dfrac p q, b = \dfrac r s$

where:
 * $p, q \in \Z$
 * $r, s \in \Z_{\ne 0}$

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

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 an example.

Also see

 * Rational Addition is Well-Defined


 * Rational Addition is Commutative
 * Rational Addition is Associative


 * Rational Addition Identity is Zero
 * Inverses for Rational Addition