I think this just adds to the confusion. Is "adding" ratios really the same as averaging them? (I would just say that adding ratios is simply not defined.) Can you only average things by moving from fractions to ratios and then back again?

I think better to address the problem directly in fractions by saying that they're two different ways of combining them, addition and averaging, like the parent comment says. Feel free to make up a different symbol for the averaging operator, just let the kids know that it's not standard.