This is a great baseline for the units answer.
I think it then needs an addendum on things that are the same dimension but expressed in different units.
Like, "students at table A" and "students at table B" are both of the same dimension as "students", but are different units. Like meters and miles. You can add them together, but only if you know the factors needed to convert them to a common unit. In this case, the conversion factors are, how many students are at table A and how many at table B.
1+1=1
One shoe plus one shoe equals one pair of shoes.
Once they grasp that explaining the fraction issue should be easier.