I think this one of those situations where you do a bunch of working out and get to the end and see that, mathematically, the problem is fixed, but in your heart it still feels like the original problem is still there. (1/2) * (1/3) + (1/2) * (2/3) might seem like a small calculation to us, but if you've just encountered fractions for the first time I think that is a huge amount of abstract notation.
Instead, I think it's better to follow CydeWeys's suggestion of saying that both are correct results of combining 1/3 with 1/3, but they're two different ways of combining them. Say that when you combine two fractions within the same group we call it "addition" and use a plus, but when we combine two fractions from different groups we call it "averaging" (and maybe make up your own symbol for it).
Once you've talking about averaging a bit you can move on to multiplication, which in some ways is a more basic concept but, for fractions, is actually a bit less intuitive.
Instead, I think it's better to follow CydeWeys's suggestion of saying that both are correct results of combining 1/3 with 1/3, but they're two different ways of combining them. Say that when you combine two fractions within the same group we call it "addition" and use a plus, but when we combine two fractions from different groups we call it "averaging" (and maybe make up your own symbol for it).
Once you've talking about averaging a bit you can move on to multiplication, which in some ways is a more basic concept but, for fractions, is actually a bit less intuitive.