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Calculating the percentage rate

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

The test has 40 points. Ali has 30 points. What percentage is that? You know the whole and the part and look for the share in percent.
📄 Open worksheet (PDF, German)

The video

In the video we calculate with the rule of three and with the formula: part divided by whole.

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 The percentage rate is missing
  3. 0:37 With the rule of three
  4. 0:59 With the formula
  5. 1:24 Careful, mistake!
  6. 1:45 Try it yourself

The most important points

Looking for the share

\(G = 40\) points (\(100\,\%\)), \(W = 30\) points. We are looking for the percentage rate \(p\,\%\).

30 of 40 points: less than 100\,\%.
30 of 40 points: less than \(100\,\%\).

With the rule of three

40 points \(\mathrel{\widehat{=}} 100\,\%\), 1 point \(\mathrel{\widehat{=}} 2{,}5\,\%\), 30 points \(\mathrel{\widehat{=}} 75\,\%\).

First divide by 40, then multiply by 30.
First divide by 40, then multiply by 30.

With the formula

\(p\,\% = W : G\), so part divided by whole: \(30 : 40 = 0{,}75 = 75\,\%\).

30/40 = 3/4 = 75\,\%
\(\frac{30}{40} = \frac{3}{4} = 75\,\%\)

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

What percentage is it? a) 12 of 15 questions b) 6 € of 24 €

Show solution

a) \(12 : 15 = 0{,}8 = 80\,\%\) b) \(6 : 24 = 0{,}25 = 25\,\%\)

Keep learning with a language model

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