Direction of map between tensor products 
Suppose $A$ and $B$ are commutative rings, $A\to B$ is a ring map, and $M, N$ are $B$-modules. Is there a map $M\otimes_A N \to M\otimes_B N$, or in the other direction?

This should be very simple but for some reason I'm confused.
Thanks for your help.

There is a natural map $M\otimes_AN\to M\otimes_BN$, which maps $m\otimes n$ to $m\otimes n$.
