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I'm wondering why, it is

Die Familie hat die Koffer gepackt.

and not

Die Familie haben die Koffer gepackt.

Die Familie is a plural, so they are many people "They have packed the luggage "=" Sie haben die koffer gepackt."

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    Please note the difference between grammar and common sense here: No, "Familie" is not plural, "Familien" would be the plural form. Please compare the Duden entry. This way your question can be answered easily: "Die Familie [Sg.] hat [Sg.] die Koffer [sic!] gepackt." would be correct. If many families are travelling it would be "Die Familien [Pl.] haben [Pl.] die Koffer gepackt." – pbx Dec 10 '16 at 16:16
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    Even from common sense, I would not expect Familie to be plural. – user1583209 Dec 10 '16 at 16:49
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»Die Familie« is not plural. It is singular, and it is feminine. You are talking about one family, not about many families.

Plural is »die Familien«:

Die Familien haben die Koffer gepackt.

I give you examples:

Singular:

Walter and Doris have a son, Michael. Together they are one family. This one family packed its suitcases.
Walter und Doris haben einen Sohn, Michael. Zusammen sind sie eine Familie. Diese eine Familie hat ihre Koffer gepackt.

Plural:

Eugen and Petra have a daughter, Christa. They are also one family. This one family packed its suitcases at the same time when Walter, Doris and Michael packed their suitcases. So all together we have two families. This two families packed their suitcases.
Eugen and Petra haben eine Tochter, Christa. Sie sind also eine Familie. Diese eine Familie packte ihre Koffer zur selben Zeit als Walter, Doris und Michael ihre Koffer packten. Daher haben wir, alles zusammen, zwei Familien. Diese zwei Familien haben ihre Koffer gepackt.

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True a family is a group of people and thus is considered plural in some languages. However, German is not one of those languages. Plural and singular are grammatical categories and nouns referring to collections of individuals refer to one or many collections, not to the individuals they are composed of.

Hence, die Familie is singular, as it refers to a single collection - one family.

I've always found the idea of such collections automatically being plural strange. It also generally is used inconsistently in English - e.g. a political party is treated as singular, even if it has millions of members..

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