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Calculating the base value

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

Lina has saved 60 €. That is \(40\,\%\) of the price of a bike. How much does the bike cost? You know the part and look for the whole.
📄 Open worksheet (PDF, German)

The video

In the video the part is known on the percentage bar. We calculate back to \(100\,\%\).

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 The base value is missing
  3. 0:36 With the rule of three
  4. 0:57 With the formula
  5. 1:24 Careful, mistake!
  6. 1:46 Try it yourself

The most important points

Looking for the whole

The base value \(G\) is always \(100\,\%\). Here we know \(W = 60\) € and \(p\,\% = 40\,\%\).

40\,\% \mathrel{\widehat{=}} 60 €. What is 100\,\%?
\(40\,\% \mathrel{\widehat{=}} 60\) €. What is \(100\,\%\)?

With the rule of three

\(40\,\% \mathrel{\widehat{=}} 60\) €, \(1\,\% \mathrel{\widehat{=}} 1{,}50\) €, \(100\,\% \mathrel{\widehat{=}} 150\) €.

First divide by 40, then multiply by 100.
First divide by 40, then multiply by 100.

With the formula

\(G = W \cdot 100 : p\). Faster: \(60 : 0{,}4 = 150\). The bike costs 150 €.

Check: 150 · 0{,}4 = 60 ✓
Check: \(150 \cdot 0{,}4 = 60\) ✓

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) \(25\,\%\) of a class are 12 children. How many children does the class have? b) \(20\,\%\) are 30 €. How much is \(100\,\%\)?

Show solution

a) \(12 : 0{,}25 = 48\) children b) \(30 : 0{,}2 = 150\), so 150 €

Keep learning with a language model

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