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Calculating the percentage value

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

A jacket costs 80 €. Today there is a \(25\,\%\) discount. How many euros do you save? You calculate the part of the whole.
📄 Open worksheet (PDF, German)

The video

In the video a percentage bar shows the three quantities. Then we calculate with the rule of three and with the formula.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:16 Three quantities
  3. 0:37 With the rule of three
  4. 0:59 With the formula
  5. 1:25 Careful, mistake!
  6. 1:45 Try it yourself

The most important points

The three quantities

Base value (der Grundwert) \(G\): the whole, always \(100\,\%\). Percentage rate (der Prozentsatz) \(p\,\%\): the share in percent. Percentage value (der Prozentwert) \(W\): the part.

G = 80 €, p\,\% = 25\,\%, W is unknown.
\(G = 80\) €, \(p\,\% = 25\,\%\), \(W\) is unknown.

With the rule of three (der Dreisatz)

\(100\,\% \mathrel{\widehat{=}} 80\) €, \(1\,\% \mathrel{\widehat{=}} 0{,}80\) €, \(25\,\% \mathrel{\widehat{=}} 20\) €.

First divide by 100, then multiply by 25.
First divide by 100, then multiply by 25.

With the formula

\(W = G \cdot p : 100\). Faster with a decimal: \(80 \cdot 0{,}25 = 20\). You save 20 €.

25\,\% = 0{,}25
\(25\,\% = 0{,}25\)

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

Calculate: a) \(30\,\%\) of 150 € b) \(15\,\%\) of 40 kg

Show solution

a) \(150 \cdot 0{,}3 = 45\), so 45 € b) \(40 \cdot 0{,}15 = 6\), so 6 kg

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: den Prozentwert berechnen (Dreisatz und Formel W = G · p : 100). 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.