Grammarbook.com gave the following rules that will help us learn the proper subject-verb agreement for portion indicators.
(a) With words that indicate portions—e.g., a lot, a majority, some, all—(A subject will come before a phrase beginning with of), and we are guided by the noun after of. If the noun after of is singular, use a singular verb. If it is plural, use a plural verb.
A lot of the pie has disappeared.
A third of the people are unemployed.
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