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Dividing fractions

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

How many portions fit in? You learn the reciprocal (der Kehrwert) and the rule for dividing by a fraction.
📄 Open worksheet (PDF, German)

The video

In the video we share pizzas: each person gets \( \frac{1}{2} \) or \( \frac{1}{4} \) of a pizza. We count the portions. The reciprocal is purple in the video.

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

Contents of the video

  1. 0:00 How many people?
  2. 0:30 Smaller portions
  3. 0:55 The reciprocal
  4. 1:33 Counting portions
  5. 2:00 Big portions
  6. 2:24 A fraction divided by three
  7. 2:45 The strategy
  8. 3:08 Examples
  9. 3:47 Practice
  10. 4:09 More practice
  11. 4:30 Summary

The most important points

3 pizzas, each person gets half a pizza: 6 people have enough to eat. \( 3 : \frac{1}{2} = 6 \). The question is: how often does \( \frac{1}{2} \) fit into 3?

3 : 1/2 = 3 · 2 and 3 : 1/4 = 3 · 4 .
\( 3 : \frac{1}{2} = 3 \cdot 2 \) and \( 3 : \frac{1}{4} = 3 \cdot 4 \).

Reciprocal (der Kehrwert)

For the reciprocal, numerator and denominator swap places: \( \frac{3}{4} \to \frac{4}{3} \). You divide by a fraction by multiplying by its reciprocal. Careful: only turn the second fraction upside down.

The reciprocal.
The reciprocal.

Example: \( \frac{2}{3} : \frac{4}{5} = \frac{2}{3} \cdot \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \). By a whole number: \( \frac{1}{2} : 3 = \frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6} \).

How to divide by a fraction.
How to divide by a fraction.

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) Reciprocal of \( \frac{5}{7} \)? b) \( \frac{3}{4} : \frac{1}{2} \) c) \( 5 : \frac{2}{3} \)

Show solution

a) \( \frac{7}{5} \) b) \( \frac{3}{4} \cdot \frac{2}{1} = \frac{6}{4} = 1\frac{1}{2} \) c) \( \frac{5}{1} \cdot \frac{3}{2} = \frac{15}{2} = 7\frac{1}{2} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: dividing fractions (reciprocal, multiplying by the reciprocal). Give me five short tasks, one after the other. Always wait for my answer, then explain briefly. 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.