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Calculating beyond one

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

\( \frac{5}{4} \) is more than a whole pizza. You learn proper and improper fractions and mixed numbers – and you add and subtract with them.
📄 Open worksheet (PDF, German)

The video

In the video we put the pieces on several pizzas: first one pizza is filled, then the rest goes on the next one.

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

Contents of the video

  1. 0:00 Lots of pizza
  2. 0:27 More than one pizza
  3. 0:54 Proper and improper
  4. 1:27 Finding whole pizzas
  5. 2:05 Back to the fraction
  6. 2:30 Plus beyond one
  7. 3:03 Different denominators
  8. 3:36 Adding mixed numbers
  9. 4:11 Minus
  10. 4:45 Cutting up a pizza
  11. 5:14 One more example
  12. 5:34 The strategy
  13. 6:02 Practice
  14. 6:30 More practice
  15. 6:57 Summary

The most important points

Three new words

Proper fraction (echter Bruch): numerator smaller than denominator, less than 1, e.g. \( \frac{3}{4} \). Improper fraction (unechter Bruch): numerator bigger than denominator, more than 1, e.g. \( \frac{5}{4} \). Mixed number (gemischte Zahl): wholes and a fraction, e.g. \( 1\frac{1}{4} \) – in German you say „eins und ein Viertel“.

Proper fraction, a whole pizza, improper fraction.
Proper fraction, a whole pizza, improper fraction.

Improper fraction → mixed number: divide the numerator by the denominator. \( 7 : 4 = 1 \) remainder \( 3 \), so \( \frac{7}{4} = 1\frac{3}{4} \). The way back: cut up the whole pizzas. \( 1\frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3} \).

How many whole pizzas are in the fraction?
How many whole pizzas are in the fraction?

If the fraction is not enough for minus, you cut up a whole pizza: \( 1\frac{1}{4} - \frac{3}{4} = \frac{5}{4} - \frac{3}{4} = \frac{2}{4} = \frac{1}{2} \). The safe way: turn all mixed numbers into improper fractions.

Cutting a whole pizza into quarters.
Cutting a whole pizza into quarters.

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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The worksheet – Page 6
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Show the worksheet solutions
The worksheet – Page 7
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Try it yourself

Task

a) Write \( \frac{11}{5} \) as a mixed number. b) \( \frac{3}{4} + \frac{1}{2} \) c) \( 2\frac{1}{3} - \frac{2}{3} \)

Show solution

a) \( 2\frac{1}{5} \) b) \( \frac{5}{4} = 1\frac{1}{4} \) c) \( \frac{7}{3} - \frac{2}{3} = \frac{5}{3} = 1\frac{2}{3} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: calculating beyond one (improper fractions, mixed numbers, plus and minus). 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.