[math-fun] Mediant question

The mediant of any 2 positive rational numbers p/q and r/s is med(p/q, r/s) = (p+q)/(r+s). This can be thought of as a mapping med: Q+ x Q+ —> R from the cartesian product of the positive rationals with itself to the reals. Question: --------- Is med the restriction to Q+ x Q+ of some continuous function Med: R x R —> R ???