Past exam of the algebra, analysis and differential equations II course of the University of Oxford / 2010 / Algebra / 3 / a / 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, thenThe product $bd$ is still coprime to $30$. These are elements of $R$, proving that $\boxed{R\text{ is a subring of }\mathbb{Q}}$.