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Multiplying fractions

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

How big is a tile that is \( \frac{4}{5} \) m wide and \( \frac{3}{4} \) m high? You learn the rule for fraction times fraction.
📄 Open worksheet (PDF, German)

The video

In the video we put the tile into a square metre with small boxes. We count: all the boxes and the boxes of the tile.

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

Contents of the video

  1. 0:00 The tile
  2. 0:37 One square metre
  3. 1:01 The tile in the square
  4. 1:37 The rule
  5. 1:58 Another tile
  6. 2:33 Examples
  7. 3:12 Times means of
  8. 3:52 More examples
  9. 4:26 Practice
  10. 4:45 More practice
  11. 5:06 Summary

The most important points

The square metre has \( 5 \cdot 4 = 20 \) boxes. The tile has \( 4 \cdot 3 = 12 \) boxes. So the tile is \( \frac{12}{20} = \frac{3}{5} \) m² big.

The tile in the square metre: 12 of 20 boxes.
The tile in the square metre: 12 of 20 boxes.

Multiplying fractions

Numerator times numerator and denominator times denominator: \( \frac{4}{5} \cdot \frac{3}{4} = \frac{4 \cdot 3}{5 \cdot 4} = \frac{12}{20} = \frac{3}{5} \). You do not need a common denominator. At the end you simplify if you can.

The rule.
The rule.

Times means „of“ here: \( \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} \) is half of one half. You write a whole number as a fraction with the denominator 1: \( 3 \cdot \frac{2}{5} = \frac{3}{1} \cdot \frac{2}{5} = \frac{6}{5} = 1\frac{1}{5} \).

Times means of. Whole number = number over 1.
Times means of. Whole number = number over 1.

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
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The worksheet – Page 4
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The worksheet – Page 5
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Show the worksheet solutions
The worksheet – Page 6
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Try it yourself

Task

Calculate and simplify: a) \( \frac{2}{3} \cdot \frac{3}{4} \) b) \( \frac{1}{2} \cdot \frac{3}{4} \) c) \( 3 \cdot \frac{3}{4} \)

Show solution

a) \( \frac{6}{12} = \frac{1}{2} \) b) \( \frac{3}{8} \) c) \( \frac{9}{4} = 2\frac{1}{4} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: multiplying fractions (numerator times numerator, denominator times denominator, simplify at the end). 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.