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Percentage change

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

A bike costs 200 €. The price goes up by \(10\,\%\), later it goes down by \(10\,\%\). Does it cost 200 € again? You get to know the growth factor (der Wachstumsfaktor).
📄 Open worksheet (PDF, German)

The video

In the video the percentage bar first gets longer and then shorter.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:19 Increase
  3. 0:41 Decrease
  4. 1:04 The growth factor
  5. 1:33 Careful, mistake!
  6. 2:00 Try it yourself

The most important points

Increase (die Erhöhung)

\(100\,\% + 10\,\% = 110\,\% = 1{,}1\). So \(200 \cdot 1{,}1 = 220\): the bike costs 220 €.

The bar gets 10\,\% longer.
The bar gets \(10\,\%\) longer.

Decrease (die Verminderung)

Now 220 € is the whole. \(100\,\% - 10\,\% = 90\,\% = 0{,}9\). So \(220 \cdot 0{,}9 = 198\): 198 €, not 200 €.

10\,\% of 220 € are taken away.
\(10\,\%\) of 220 € are taken away.

The growth factor

new value = old value · factor. \(+10\,\% \to 1{,}10\), \(+25\,\% \to 1{,}25\), \(-10\,\% \to 0{,}90\), \(-20\,\% \to 0{,}80\).

Factor bigger than 1: more. Smaller than 1: less.
Factor bigger than 1: more. Smaller than 1: less.

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 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

a) 50 € become \(20\,\%\) more expensive. b) 80 € become \(25\,\%\) cheaper. What is the new price?

Show solution

a) \(50 \cdot 1{,}2 = 60\), so 60 € b) \(80 \cdot 0{,}75 = 60\), so 60 €

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: prozentuale Veränderung (Erhöhung, Verminderung, Wachstumsfaktor). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

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.