Fractions

Introduction

We use fractions when we’re talking about partial quantities. We can find fractions not only in mathematics, but also in recipes, for example (½ litre of water).

Construction

To construct fractions, we take the word-stem of the ordinal number and add the ending el. The form of fractions doesn’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

Exceptions for halb

The word halb is treated just like a normal adjective. Its ending matches the corresponding noun/pronoun and is declined.

Example:
der halbe Liter Wasserthe half-litre of water (masculine, nominative, definite article)
ein halbes Kilo Mehlhalf a kilo of flour (neuter, nominative, indefinite article)
in einer halben Stundein half an hour (feminine, dative)

Writing Fractions

Capitals Or Not?

If the fraction is referring to something specific (e.g. a unit of measurement), then we write the number 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 of a unit of measurement is written as a separate word.

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 also written together as a single word.

Example:
eine Dreiviertelstundethree-quarters of an hour
der Sechsachteltaktsix-eight time
ein Viertelliterglasa quarter-litre glass

Note the difference:

ein Viertelliterglas gefüllt mit Wasser
(The glass can hold a quarter-litre and is full.)

ein viertel Literglas gefüllt mit Wasser
(The glass can hold a litre, and is only a quarter full.)