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Subtracting fractions

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

Subtracting (subtrahieren) means doing minus. It is the way back from adding – the strategy is the same.
📄 Open worksheet (PDF, German)

The video

There is \( \frac{5}{6} \) of a pizza on the plate. Your friend eats \( \frac{1}{3} \). How much is left? In the video the piece that is taken away is pink.

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

Contents of the video

  1. 0:00 Who else is eating pizza?
  2. 0:33 Taking pieces away
  3. 1:02 Like fractions
  4. 1:37 Examples
  5. 2:03 A whole pizza
  6. 2:41 Different denominators
  7. 3:23 The result
  8. 3:55 The strategy
  9. 4:30 Expanding one fraction
  10. 4:56 Simplifying cleverly
  11. 5:28 Expanding both
  12. 6:01 Practice
  13. 6:33 Summary

The most important points

Same denominators

You only subtract the numerators. The denominator stays: \( \frac{5}{8} - \frac{2}{8} = \frac{3}{8} \). Never subtract the denominators – you cannot cut a pizza into 0 pieces.

Subtracting like fractions.
Subtracting like fractions.

A whole pizza has as many pieces as the denominator says: \( 1 - \frac{3}{8} = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \).

Different denominators: first make them the same. \( \frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \). Before, we had \( \frac{1}{2} + \frac{1}{3} = \frac{5}{6} \). Minus undoes plus.

Minus undoes plus.
Minus undoes plus.
The strategy is the same as for adding.
The strategy is the same as for adding.

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

Calculate: a) \( 1 - \frac{2}{5} \) b) \( \frac{3}{4} - \frac{1}{2} \) c) \( \frac{2}{3} - \frac{1}{4} \)

Show solution

a) \( \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \) b) \( \frac{3}{4} - \frac{2}{4} = \frac{1}{4} \) c) \( \frac{8}{12} - \frac{3}{12} = \frac{5}{12} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: subtracting fractions (make them gleichnamig, subtract the numerators, the denominator stays, simplify at the end). Give me five tasks, one after the other, without negative results. 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.