In this paper, by  considering the notion of a $\wedge$-closed set
in $BCK$-algebras, we construct the fractions of $BCK$-algebras
and prove some related results. Moreover, we study the notion of a
$BCK$-module and prove that any $BCK$-algebra is a $BCK$-module on
itself. Finally, we construct the fractions of $BCK$-modules.