Part or percentage of a group - singular or plural?


I keep struggling with sentences/clauses like these:

“part of the group is” vs. “part of the group are”
“20 percent of the people is” vs. “20 percent of the people are”
“half of the items is” vs. “half of the items are”

Please tell me which ones are correct and explain why. I would need a grammar rule or a “rule of thumb” that I can follow when encountering such a structure.


§ 20. collective noun
Some nouns, like committee, clergy, enemy, group, family, and team, refer to a group but are singular in form. These nouns are called collective nouns. In American usage, a collective noun takes a singular verb when it refers to the collection considered as a whole, as in The family was united on this question or The enemy is suing for peace. It takes a plural verb when it refers to the members of the group considered as individuals, as in My family are always fighting among themselves or The enemy were showing up in groups of three or four to turn in their weapons. In British usage, collective nouns are more often treated as plurals: The government have not announced a new policy. The team are playing in the test matches next week.

Thanks a lot. And how about the “half of the items is” vs. “half of the items are” question? “Item” is not a collective noun, I guess.

American version: “half of the items is” in a box (all of them); “half of the items are” broken (each one is broken). British: “half of the items are” in a box.
(According to my limited understanding.)