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Fractions of quantities

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

A pizza costs 12 €. You eat \( \frac{3}{4} \) of it. How much do you pay? You learn to calculate fractions of quantities and to find the whole backwards.
📄 Open worksheet (PDF, German)

The video

In the video we calculate with a pizza, the children in a class and grams. A strip shows the whole and its parts.

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

Contents of the video

  1. 0:00 What does my part cost?
  2. 0:22 The rule
  3. 0:43 Children and grams
  4. 1:12 Finding the whole
  5. 1:38 Finding the fraction
  6. 1:58 Careful, mistake!
  7. 2:20 Try it yourself
  8. 3:00 Summary

The most important points

A fraction of a quantity

First divide by the denominator (der Nenner), then multiply by the numerator (der Zähler): \( \frac{3}{4} \) of 12 €: \( 12 : 4 = 3 \), \( 3 \cdot 3 = 9 \). You pay 9 €.

2/3 of 24 children are 16 children, 3/4 of 200 g are 150 g.
\( \frac{2}{3} \) of 24 children are 16 children, \( \frac{3}{4} \) of 200 g are 150 g.

Finding the whole

\( \frac{2}{5} \) are 10 children. First divide by the numerator: \( 10 : 2 = 5 \). Then multiply by the denominator: \( 5 \cdot 5 = 25 \). The class has 25 children.

One fifth is 5 children, five fifths are 25.
One fifth is 5 children, five fifths are 25.

Finding the fraction

Part divided by whole: 6 of 24 children are \( \frac{6}{24} = \frac{1}{4} \). Careful: a proper fraction of a quantity is always less than the whole.

6 of 24 children: one quarter.
6 of 24 children: one quarter.

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
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The worksheet – Page 2
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The worksheet – Page 3
Page 3/4
Show the worksheet solutions
The worksheet – Page 4
Page 4/4

Try it yourself

Task

a) How many minutes are \( \frac{2}{3} \) of an hour? b) \( \frac{3}{4} \) of a distance are 600 m. How long is the whole distance?

Show solution

a) \( 60 : 3 \cdot 2 = 40 \), so 40 minutes b) \( 600 : 3 \cdot 4 = 800 \), so 800 m

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: fractions of quantities (Bruchteile von Größen: a fraction of a quantity, finding the whole, finding the fraction). 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.