Simplifiable fractions?

Boggis, the class clown, is told to simplify the fraction $\frac{16}{64}$ . He cancels the 6's and writes $\frac{1}{4}$ , but that happens to be the correct answer!

How many such fractions are there which can be cancelled correctly like this (by cancelling any two digits which are equal, one in the numerator and one in the denominator), but not necessarily into its simplest form?

NOTE- the numerator and denominator are distinct, and both contain two non-zero digits. The numerator is not necessarily smaller than the denominator.