I’m sorry, but I believe the accepted answer is wrong. The “half
(of) a NUMBER” construct works like “a lot of SOMETHING” or “a
few of SOMETHING” does, in that the verb should agree with the
number of the noun that follows those constructs, not with
something like half or lot or few, even though each of those is
by itself nominally singular. This is what is called a
predeterminer, and it does not affect the grammatical
concordance of the noun it modifies with that noun’s verb. In
works like an adjectival phrase, if you would. From Cognitive
English Grammar, by Günter Radden and René Dirven: More rarely,
a quantifier occurs before a determiner; in this function
quantifiers are usually described as predeterminers. . . . More
rarely, a quantifier may precede an indefinite determiner as in
half a dozen or half a million, where the quantifier half
describes a clear subset of a well-defined set. You can find no
end of examples in examples of such things retaining their
plural number in printed literature, and none