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Writing fractions

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

What is a fraction (der Bruch)? You learn the numerator (der Zähler), the denominator (der Nenner) and the fraction bar (der Bruchstrich). Then you can read and write fractions.
📄 Open worksheet (PDF, German)

The video

In the video we divide circles and a pizza into equal parts. Watch the colours: the counted pieces are orange, the division and the denominator are blue.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:23 One part of a circle
  3. 1:00 Several parts
  4. 1:36 How to write it
  5. 2:13 The pizza
  6. 2:44 Numerator and denominator
  7. 3:09 Try it yourself

The most important points

We divide a whole into parts of equal size. One part or several parts of it are a fraction (der Bruch). Very important: all parts are the same size.

One half, one third, one quarter, one fifth: the more parts, the smaller each piece.
One half, one third, one quarter, one fifth: the more parts, the smaller each piece.

The fraction (der Bruch)

\( \dfrac{3}{4} \)   The denominator (der Nenner, at the bottom) tells you: into how many equal parts is the whole divided? The numerator (der Zähler, at the top) counts: how many parts do we have? In between is the fraction bar (der Bruchstrich).

Three quarters: the circle has 4 equal parts, 3 of them are orange.
Three quarters: the circle has 4 equal parts, 3 of them are orange.

How to read fractions in German: \( \frac{1}{2} \) ein Halb, \( \frac{1}{3} \) ein Drittel, \( \frac{1}{4} \) ein Viertel, \( \frac{1}{5} \) ein Fünftel, \( \frac{3}{4} \) drei Viertel. Drei becomes Drittel, vier becomes Viertel. Only for two we say: ein Halb.

A pizza in 6 equal slices, 5 are still there: five sixths. The denominator names. The numerator counts.
A pizza in 6 equal slices, 5 are still there: five sixths. The denominator names. The numerator counts.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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The worksheet – Page 4
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The worksheet – Page 5
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Show the worksheet solutions
The worksheet – Page 6
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Try it yourself

Task

A cake has 8 equal pieces. You eat 3 pieces. What fraction of the cake is that? What fraction is left?

Show solution

You eat \( \frac{3}{8} \) (drei Achtel, three eighths). \( \frac{5}{8} \) (fünf Achtel, five eighths) is left.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: writing and reading fractions (numerator, denominator, fraction bar). Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Write in simple German and put an English translation in brackets after each sentence.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.