Subring $R=\left\{\frac{m}{2^a3^b}|m\in \mathbb{Z},a,b\in\mathbb{N}\right\}$

Question

Show that $R=\left\{\frac{m}{2^a3^b}|m\in \mathbb{Z},a,b\in\mathbb{N}\right\}$ is a subring of $\mathbb{Q}$. Show that $\frac{1}{5}\notin R$. Is $\mathbb{Z}$ in $R$?

I have already shown, that the product, the sum and the difference of two Elements from $R$ are in $R$.

Answer 1

Hint: $$ \frac{1}{5}\in R \iff \frac{1}{5}=\frac{m}{2^a3^b} \iff {2^a3^b}= {5m} $$