Let $R$ be an integral domain and $M$ a finitely generated $R$-module. Show that $rank(M/Tor(M))$=$rank(M)$

I only need item b).  Full question:

Let $R$ be an integral domain and $M$ a finitely generated $R$-module.

• a) Show that $M/Tor(M)$ is free of torsion. (ALREADY PROVEN) ?
• b) Show that $rank(M/Tor(M))$=$rank(M)$.
Again, I've already shown item a). Just announced it in case it's needed.

• Note that "less than" and "largen than" are to be understood as $\leq$ and $\geq$.