I often see the fraction 2/3 written with a hyphen, but I never see 1/2 written with one. Is it correct to have the hyphen in "two-thirds", and if so why don't we write "one-half"?
The Chicago Manual of Style has these guidelines:
So "1/2" should always be written out as one-half. (Unless it's in a sentence like "one half of a perfect pair," in which case it's not a fraction.)
It is correct to have the hyphen. I am not quite sure why the people that you see write "one half" do not write "one-half" but they should!
Searching for "one half" at dictionary.reference.com does not return any results, but searching for "one-half" does.
This is the same for "two-thirds".