Fractions

Introduction

German fractions (die Bruchzahlen) allow us to talk about partial quantities. We can find fractions not only in mathematics, but also in recipes, for example (½ litre of water).

Read on to learn how to say fractions in German, then put your knowledge to the test in the exercises.

How to write fractions in German

To write fractions in German, we use a cardinal number for the numerator (der Zähler). To form the denominator (der Nenner), we take the word-stem of the ordinal number and add the ending el. The endings don’t change. (Exception: halb)

1/2 ein halb 1/10 ein zehntel
1/3 ein drittel 1/20 ein zwanzigstel
1/4 ein viertel 1/100 ein hundertstel
1/5 ein fünftel 1/1000 ein tausendstel

Do we decline German fractions?

The numerator eins and the denominator halb are the only words that are declined in fractions.

Examples:
Ich trinke jeden Tag einen halben Liter Kaffee.I drink half a litre of coffee every day.
Er hat einen viertel Liter Wein bestellt.He ordered a quarter of a litre of wine.

The word halb is declined like a normal adjective: its ending agrees with the grammatical number and gender of the noun/pronoun it is describing. The word eins is treated like an indefinite article.

Example:
ein halbes Kilo Mehlhalf a kilo of flour (masculine noun, nominative case)
für einen halben Tagfor half a day (masculine noun, accusative case)
in einer halbe Stundein half an hour (feminine noun, dative case)
trotz eines halben Liters Abweichungdespite half a litre of deviation (masculine noun, genitive case)

Writing fractions in German

Capitals or not?

If the fraction is referring to a specific noun (e.g. a unit of measurement), then we write both parts without a capital letter.

Example:
zwei drittel Liter Milchtwo-thirds of a litre of milk

If the fraction stands alone, however, it is treated like a noun and written with a capital letter.

Example:
Ich habe erst zwei Drittel von dem, was ich wollte, geschafft.I’ve only managed to get two-thirds of the work done that I wanted to finish.

Separate or compound words?

Normally, the fraction is written as a separate word when it comes before a unit of measurement.

Example:
ein viertel Liter Wassera quarter-litre of water
drei achtel Kilo Mehlthree-eighths of a kilo of flour

If the fraction and the unit of measurement are considered a single item, however, they are written together as a single word.

Example:
eine Dreiviertelstundethree-quarters of an hour
der Sechsachteltakt6/8 time
ein Viertellitera quarter-litre

The word halb

As a noun, halb becomes Hälfte.

Example:
Ich habe den halben Kuchen gegessen. → Ich habe die Hälfte des Kuchens gegessen.I’ve eaten half of the cake.

When halb is part of a compound word, it loses the adjective ending.

Example:
ein halbes Jahr → ein Halbjahr

If ein halb follows a whole number, they are written together as one word.

Examples:
1 ½ → eineinhalb/anderthalb
2 ½ → zweieinhalb
3 ½ → dreieinhalb
Ich wohne seit fünfeinhalb Jahren hier.I’ve lived here for five and a half years.

Fractions without a numerator

In some contexts, we use the denominator part of the fraction without a numerator. This is the case for the words halb, drittel, viertel and achtel.

Examples:
Die Mannschaft ist im Achtelfinale. Um das Viertelfinale zu erreichen, müssen die Spieler schon in der ersten Halbzeit Druck machen und verstärkt im Angriffsdrittel agieren.The team is in the final 16. To reach the quarterfinals, the players have to put the pressure on in the first half and act more up front.