A6. How many fractions between $\frac{1}{6}$ and $\frac{1}{3}$ inclusive can be written with a denominator of 15 ?
SolUtion
3

First note that $\frac{1}{6}=\frac{5}{30}$ and $\frac{1}{3}=\frac{10}{30}$. Any fraction of the form $\frac{k}{30}$ between (and including) these two values, where $k$ is an even number, will simplify to have a denominator of 15 . Therefore, $k=6,8$ or 10 and so there are three fractions.