The operation $\dagger$ is defined as $\frac{m}{n}\dagger\frac{p}{q} = (m)(p)(\frac{q}{n}).$  What is the simplified value of $\frac{7}{12}\dagger\frac{8}{3}$?
So, $\frac{7}{12}\dagger\frac{8}{3} = (7)(8)(\frac{3}{12})$. Now, I can cancel out the common factors of 3 and 12, leaving $\frac{7}{12}\dagger\frac{8}{3} = (7)(8)(\frac{1}{4})$. Finally, I can multiply 7 by 8 and divide by 4, getting $\frac{7}{12}\dagger\frac{8}{3} = (56)(\frac{1}{4}) = 14$. 