$\bf{Z}$-module homomorphism and $\bf{Q}$-module homorphism

Question

$R$-modules are also $\bf{Z}$-modules and $R$-module homomorphisms are also $\bf{Z}$-module homomorphisms. If $M$ and $N$ are $\bf{Q}$-modules and $f : M \rightarrow N$ is a $\bf{Z}$-module homomorphism, must it also be a $\bf{Q}$-module homomorphism?

Answer 1

Hint: For any $x/y \in \mathbb{Q}$ $$ y\cdot f\left(\frac x y m\right) = x\cdot f(m). $$