Definition:Addition/Rational Numbers

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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


Sources