I recently learned group completion in K-theory. I feel it is very similar to field of fractions of integral domain. Recall the definitions:
Group completion: For an abelian monoid $M$, we define its group completion $M^{-1} M$ as free abelian group, each element $[m]$ satisfying $m \in M$. The group completion needs to quotient subgroup generated by $[m+n] - [m] - [n]$.
Field of fractions: For an integral domain $M$, we define its field of fractions $M^{-1} M$ as product $M \times M^*$ quotient equivalence relation $(a, b) \sim (c, d) $ if $ad = bc$.
I think field of fractions is just group completion of multiplicative structure of a ring. Is it correct?