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(1/3) +(1/2)(1/3) = 1/2
Math checks out from this end.
"a half is one-third more than a third" should mean either
1/3 + 1/3 = 1/2
Or
1/3 + (1/3 × 1/3) = 1/2
Neither of which is true.
I feel like 'a half is one-third more than a third' is ambiguous and same as in 'X is N% more than Y' one may use X or Y as 100%
I'm sure that one interpretation is more common, but I don't think that it is exclusively correct
Basically, "X is one-third more than Y" means either X = (4/3) × Y or X = Y + 1/3. I'm fine with either interpretation.
The problem is that with the values of X and Y in this example, neither interpretation produces a valid equation.
1/3 more than 1/3 is 4/9. What you wrote is 1/2 more than 1/3, not 1/3 more of it.