Let $A$ be a commutative ring with $1$ and let $M,N$ be $A$-modules. Let $I$ be an ideal of $A$.
How do we show the following isomorphism?
$(M \otimes_{A} N)/(I \cdot (M \otimes_{A} N)) \cong M/(IM) \otimes_{A/I} N/(IN)$
What confuses me is how to pass from tensoring with respect $A$ to tensoring with respect $A/I$.