I would avoid multiplication entirely and say that if you are combining tables, you need to update the bottom with the new number of total students. So something like:

  (T1 girls) + (T2 girls)   1 + 1
  _______________________ = _____
  (T1 total) + (T2 total)   3 + 3

I think that's more intuitive than averages, and would still work if the tables were of different sizes.

This is definitely a good explanatory strategy (and one that I'd use). I might label the units of the right side as well. Would you attempt to explain the abstract rules of fraction arithmetic as an system?