> Sorry, but I do not understand why adding Fraction.as_integer_ratio() prevents adding math.as_integer_ratio().

I also support a public function for that. It seems that we're planning this "as_integer_ratio" thing to become public API, so why not have a function as Serhiy proposes?

I consider the situation with as_integer_ratio() very analogous to __index__ where we have operator.index(), so I would actually suggest operator.as_integer_ratio() but that's bikeshedding territory.