Solution
= Solution
Interpret membership as having a representation with denominator <coprime> to $30$, equivalently having this property in lowest terms. Clearly $0,1\in R$. If $a/b,c/d\in R$ with admissible denominators, then
$$
\frac ab-\frac cd=\frac{ad-bc}{bd},\qquad\frac ab\frac cd=\frac{ac}{bd}.
$$
The product $bd$ is still <coprime> to $30$. These are elements of $R$, proving that $\boxed{R\text{ is a subring of }\mathbb Q}$.