Rational Sums

Why

We want to add rationals.¹

Definition

Let $\eqc{(a, b)}, \eqc{(b, c)} \in \Q $. The rational sum of $\eqc{(a, b)}$ with $\eqc{(b, c)}$ is $\eqc{(ad + bc, bd)}$.²

Notation

We denote the rational sum of $q, r \in \Q $ by $q + r$.

1. Future editions will expand on this why. ↩︎
2. An account that this is well-defined will appear in future editions. ↩︎