das Drittel
third
One of three equal parts of a whole.
Ein Drittel der Befragten war mit dem Vorschlag nicht einverstanden.
One third of the respondents did not agree with the proposal.

third
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third
One of three equal parts of a whole.
Ein Drittel der Befragten war mit dem Vorschlag nicht einverstanden.
One third of the respondents did not agree with the proposal.

The word 'Drittel' (third) is derived from the ordinal number 'dritte' (third). The ending '-el' is often used in German to form fractions, for example also in 'Viertel' (quarter) or 'Achtel' (eighth).
Für den Kuchen brauchen wir nur ein Drittel der Zuckermenge.
For the cake, we only need one third of the amount of sugar.
When 'Drittel' (third) describes a share of something, the quantity is usually followed by the genitive (more formal) or connected with 'von' + dative (more common in spoken language).
Ein Drittel der Studierenden kommt aus dem Ausland.
One third of the students come from abroad.
The meaning 'Spielabschnitt' (period/section of play) is clearly recognizable from context. When words like 'Eishockey' (ice hockey), 'Spiel' (game), 'Tor' (goal), or phrases like 'im letzten Drittel' (in the final period) appear, this sports-related meaning is intended.
Die Mannschaft konnte das Spiel im letzten Drittel noch drehen.
The team was still able to turn the game around in the final period.
three
'drei' and 'das Drittel' are both connected to the number 3, but they do not mean the same thing. 'drei' counts whole things or people. 'das Drittel' means one of three equal parts of a whole. So you can have three pieces of cake, but 'ein Drittel' of a cake is only one part of it. In some sports, 'Drittel' can also mean a period of play. The words are easy to confuse because both are connected to 3. Ask yourself: Am I counting whole things? Then use 'drei'. Am I talking about a part of a whole? Then use 'ein Drittel'.

Vor der Reise sparen wir ein Drittel unseres Geldes für das Hotel.
Before the trip, we save one third of our money for the hotel.
Für die Feier kauft sie drei Flaschen Wasser.
She is buying three bottles of water for the party.