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Mixed numbers: multiplying and dividing

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

Three children eat \( 1\frac{1}{2} \) pizzas each. You learn to multiply and divide mixed numbers: first improper fractions (unechte Brüche), then calculate.
📄 Open worksheet (PDF, German)

The video

In the video you calculate step by step. The fractions are shown big on the board.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:17 Multiplying
  3. 0:59 Cancel first
  4. 1:25 Dividing
  5. 1:57 Careful, mistake!
  6. 2:25 Try it yourself

The most important points

Multiplying

Turn both numbers into improper fractions, then numerator times numerator and denominator times denominator: \( 1\frac{1}{2} \cdot 2\frac{1}{4} = \frac{3}{2} \cdot \frac{9}{4} = \frac{27}{8} = 3\frac{3}{8} \).

First improper fractions, then multiply.
First improper fractions, then multiply.

Cancel first

\( 2\frac{2}{3} \cdot 1\frac{1}{2} = \frac{8}{3} \cdot \frac{3}{2} \). Cancel the 3 with the 3, and the 8 and the 2 by 2: the result is \( 4 \).

Cancel crosswise before multiplying.
Cancel crosswise before multiplying.

Dividing

Divided by a fraction means: times the reciprocal (der Kehrbruch). \( 3\frac{1}{2} : 1\frac{3}{4} = \frac{7}{2} : \frac{7}{4} = \frac{7}{2} \cdot \frac{4}{7} = 2 \).

Times the reciprocal.
Times the reciprocal.

Careful: do not multiply the wholes and the fractions separately. \( 2\frac{1}{2} \cdot 2\frac{1}{2} = \frac{5}{2} \cdot \frac{5}{2} = \frac{25}{4} = 6\frac{1}{4} \), not \( 4\frac{1}{4} \).

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

Try it yourself

Task

Calculate: a) \( 1\frac{1}{2} \cdot 3 \) b) \( 2\frac{1}{2} \cdot 1\frac{1}{5} \) c) \( 4\frac{1}{2} : 1\frac{1}{2} \)

Show solution

a) \( 4\frac{1}{2} \) b) \( 3 \) c) \( 3 \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: multiplying and dividing mixed numbers (gemischte Zahlen: improper fractions, cancelling, reciprocal). 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.