imc

Cross-multiplying gives $MN=36.$ We write $36$ as a product of two positive integers: $$\begin{array}{rl}36& =1\cdot 36\\ & =2\cdot 18\\ & =3\cdot 12\\ & =4\cdot 9\\ & =6\cdot 6.\end{array}$$ The products $1\cdot 36,2\cdot 18,3\cdot 12,$ and $4\cdot 9$ each produce $2$ ordered pairs $(M,N),$ as we can switch the order of the factors. The product $6\cdot 6$ produces $1$ ordered pair $(M,N).$ Together, we have $4\cdot 2+1=\boxed{9}$ ordered pairs $(M,N).$