Question 15
Split $\frac{21}{22}$ as $\frac{a}{b}+\frac{c}{d}$, where $\frac{a}{b}$, $\frac{c}{d}$ and $\frac{b}{d}$ are all in lowest terms, and $a,b,c,d$ are nonzero natural numbers. How many different splits are there? Reversing the summands counts as the same split; for example, $\frac{21}{22}=\frac12+\frac5{11}=\frac5{11}+\frac12$ is one split.
