Words that indicate portions
With words that indicate portions, e.g. percent, fraction, part, majority, some, all, none, remainder, and so forth, look at the noun in the of phrase (the complement of the preposition) to determine whether to use a singular or a plural verb. If the complement of the preposition is singular, use a singular verb. If the complement of the preposition is plural, use a plural verb:
(1) [Fifty percent of the pie] has disappeared.The singular pie is the head word of the NP (the pie) functioning as the complement of the preposition of.
(2) [Fifty percent of the pies] have disappeared.The verb agrees with the plural pies, i.e. the head of the NP functioning as the complement of the preposition of.
(3) [One-third of the city] is unemployed.
(4) [One-third of the people] are unemployed.
(5) [All of the pie] is gone.
(6) [All of the pies] are gone.
(7) [Some of the pie] is missing.
(8) [Some of the pies] are missing.
(9) [None of the garbage] was picked up.
(10) [None of the sentences] were punctuated correctly.
(11) [Of all her books, none] have sold as well as the first one.Please note that the fact that we can say both
(12) [Some of the pie] is missing.and
(13) [Some of the pies] are missing.could be taken to show that pie has both an uncountable and a countable use. Garbage, on the other hand, can only be used as an uncountable, i.e. we cannot say (14), or anything like that.
(14) *[Some of the garbages] were picked up.Example (11) above, repeated here as (15), shows that the verb agrees with the head of the noun phrase functioning as the complement of the preposition of in these cases, even when the complement of the preposition has been fronted (i.e. when it does not follow the preposition to which it belongs, but appears at the very beginning of the clause or sentence):
(15) [Of all her books, none] have sold as well as the first one.