jmc

The fraction halfway between $\frac{1}{5}$ and $\frac{1}{3}$ is simply their average, which is $$\begin{array}{rl}\frac{\frac{1}{5}+\frac{1}{3}}{2}& =\frac{\frac{3}{15}+\frac{5}{15}}{2}\\ & =\frac{\frac{8}{15}}{2}\\ & =\frac{4}{15}\end{array}$$ $\boxed{\text{C}}$ For any two fractions that have the property $\frac{a}{b}$ and $\frac{a}{c}$ where a is equal for both fractions; Set aside the a. Take the average of b and c. For this example, the average of 3 and 5 is 4. Then multiply those numbers. 35=15. The number that is exactly in between $\frac{a}{b}$ and $\frac{a}{c}$ will be $\frac{a\ast ((b+c)/2)}{b\ast c}$. In this example, it would be $\frac{1((3+5)/2)}{3\ast 5}$, which simplifies to $\frac{4}{15}$. Therefore, the answer is $\boxed{\frac{4}{15}}$ Edit by mathmagical~