  In this work we will introduce the concept of ratio-covariety, as a nonempty
family $\mathscr{R}$ of numerical semigroups verifying certain properties. This
concept will allow us to:
  \begin{enumerate}
  \item Describe an algorithmic process to compute $\mathscr{R}.$
  \item Prove the existence of the smallest element of $\sR$ that contains a
set of positive integers.
  \item Talk about the smallest ratio-covariety that contains a finite set of
numerical semigroups.
  \end{enumerate}
  In addition, in this paper we will apply the previous results to the study of
the ratio-covariety $\mathscr{R}(F,m)=\{S\mid S \mbox{ is a numerical semigroup
with Fro-}
  \mbox {benius number }F \mbox{ and multiplicity }m\}.$
