The main part of this talk will aim to answer the question, what is the expected value of the smallest denominator of a rational number in a randomly chosen interval of fixed radius? Along the way, we will provide a cautionary tale to explain classical results that demonstrate how similar "easy" questions about the distribution of reduced rationals end up being extremely difficult to solve. For the adventurous, we will give an "easy" reformulation of the Riemann hypothesis. For the sober-minded, we will also present several other open problems.