targas-edu.de
DE ☾ A+

Simplifying fractions

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

Simplifying (kürzen) is the way back from expanding. You learn when you can simplify and why you simplify as far as possible.
📄 Open worksheet (PDF, German)

The video

In the video we put pizza slices back together. The purple cuts disappear. There are fewer pieces, but the amount stays the same.

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

Contents of the video

  1. 0:00 Half a pizza
  2. 0:40 Putting pieces together
  3. 1:16 Simplifying
  4. 1:49 When can you simplify?
  5. 2:36 As far as possible
  6. 3:10 Examples
  7. 3:41 More examples
  8. 4:18 Careful: only divide!
  9. 4:51 Simplifying pizza
  10. 5:17 Practice
  11. 5:58 Summary

The most important points

Simplifying (kürzen)

When you simplify, you divide the numerator and the denominator by the same number. This number is called the Kürzungszahl. Fewer pieces, bigger pieces, same value: \( \frac{3}{6} = \frac{3 : 3}{6 : 3} = \frac{1}{2} \).

Simplifying by 3. Expanding multiplies, simplifying divides.
Simplifying by 3. Expanding multiplies, simplifying divides.

You can only simplify if a number goes into the numerator and into the denominator without a remainder. Look at the times tables: 4 and 6 are both in the two times table, so \( \frac{4}{6} = \frac{2}{3} \). For \( \frac{3}{4} \) no number fits – you cannot simplify. If both numbers are even, you can always divide by 2.

When can you simplify? The times tables help.
When can you simplify? The times tables help.

Always simplify as far as possible: \( \frac{8}{12} = \frac{2}{3} \) (by 4). And careful: when you simplify, you divide – never subtract.

Summary.
Summary.

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
Page 1/7
The worksheet – Page 2
Page 2/7
The worksheet – Page 3
Page 3/7
The worksheet – Page 4
Page 4/7
The worksheet – Page 5
Page 5/7
The worksheet – Page 6
Page 6/7
Show the worksheet solutions
The worksheet – Page 7
Page 7/7

Try it yourself

Task

Simplify as far as possible: a) \( \frac{6}{9} \) b) \( \frac{12}{16} \) c) \( \frac{10}{25} \) d) Can you simplify \( \frac{4}{9} \)?

Show solution

a) \( \frac{2}{3} \) (by 3) b) \( \frac{3}{4} \) (by 4) c) \( \frac{2}{5} \) (by 5) d) No: no number goes into both 4 and 9.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: simplifying fractions (numerator and denominator divided by the same number, as far as possible). 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.