Isn't this why you end up seeing these "silly" units like kg/kg in chemistry? So that, while the value is technically dimensionless, it doesn't get added to another dimensionless value (e.g. l/l) that's a ratio of values of a different dimension?

This hits the nail on the head:

1 (person at table A) / 3 (people at table A) can't be added to 1 (person at table B) / 3 (people at table B) without conversion of units.

And then it's easy to make them see how her answer was right in its own way by adding another unit, (person at table a+b and people at table a+b) and show why it may be harder to works like that for now.

I heard so many people complains that each year in maths they would essentially learn that everything they learned the year before was wrong... can we fix that please?!

Why? Each is a pure number without units. Since the units cancel in each term.

Another way of labeling this:

  : = Out Of
  A = Table A
  B = Table B
  E = Every Table Added (A + B)
  
  1:3 * A + 1:3 * B = (1:3 + 1:3) * E
  2 out of 6 among Every Table Added

Somewhat aside, but in grade school I recall learning that ratios were written [group-A]:[group-B], not [group-A]:[total]. So the girl-boy ratio at the table would be 1:2. Different for you?

It really depends on the two things being compared. The ratio of boys to girls is 1:2, but the ratio of boys (implicitly: to the total) is 1:3.