Question 8
The fraction $\frac{21}{22}$ is split as $\frac ab+\frac cd$, where $\frac ab$, $\frac cd$ and $\frac bd$ are all in lowest terms and $a,b,c,d$ are nonzero. Practice clarification: take $a,b,c,d$ to be positive integers. How many different splits are there? Reversing the two terms counts as the same split; for example, $\frac{21}{22}=\frac12+\frac5{11}=\frac5{11}+\frac12$ counts once.
