das Fünftel
fifth
One of five equal parts of a whole; the fraction 1/5.
Ein Fünftel der Befragten war mit dem Vorschlag nicht einverstanden.
One fifth of the respondents did not agree with the proposal.

fifth
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fifth
One of five equal parts of a whole; the fraction 1/5.
Ein Fünftel der Befragten war mit dem Vorschlag nicht einverstanden.
One fifth of the respondents did not agree with the proposal.

Fractions like 'das Fünftel' (the fifth) are often derived from the corresponding ordinal number, here from 'fünfte' (fifth). It is treated like a noun and is therefore capitalized.
Für das Rezept benötigst du nur ein Fünftel der Packung.
For the recipe, you only need one fifth of the package.
When the fraction refers to a group or quantity, it is usually followed by the genitive or a 'von' construction with the dative. The genitive is somewhat more formal.
Ein Fünftel der Mitarbeiter war krank.
One fifth of the employees were sick.
Although it describes a part, 'Fünftel' (fifth) itself can be counted. So you can also say 'zwei Fünftel' (two fifths) or 'drei Fünftel' (three fifths).
Zwei Fünftel des Kuchens sind noch übrig.
Two fifths of the cake are still left.
half
'die Hälfte' and 'das Fünftel' both describe a part of a whole. The difference lies in the size of the part. 'die Hälfte' is one of two equal parts, so 1/2. 'das Fünftel' is one of five equal parts, so 1/5. They can be confused because both express fractions. A practical tip: with 'Hälfte', you divide by two; with 'Fünftel', you divide by five.

Ein Fünftel der Pizza bleibt für den nächsten Tag übrig.
One fifth of the pizza is left over for the next day.
Vor dem Termin esse ich zur Sicherheit nur die Hälfte des Kuchens.
Before the appointment, I eat only half of the cake to be on the safe side.