Notation for subring of quotient ring

Question

Let $S$ be a subring and $I$ an ideal of the ring $R$. What is the appropriate notation for the subring of $R/I$ given by $\{ s + I: s \in S \}$? Is it appropriate to write $S/I$ even though $I$ is not necessarily an ideal in $S$ or should one stick to the more technically correct $(S + I)/I$ or $S/(S \cap I)$?