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Comparing fractions

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

Which fraction is bigger? You learn three ways: same denominators, same numerators, and making the denominators the same (gleichnamig machen).
📄 Open worksheet (PDF, German)

The video

The question in the video: do you get more pizza with \( \frac{3}{8} \) or with \( \frac{1}{3} \)? Three pieces are more than one piece – but the pieces have different sizes.

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

Contents of the video

  1. 0:00 Which pizza?
  2. 0:30 Same denominators
  3. 1:06 Examples: same denominators
  4. 1:34 The denominator and the size of the pieces
  5. 1:57 Same numerators
  6. 2:30 Expanding
  7. 3:16 Two ways
  8. 3:43 Summary

The most important points

Same denominators

Fractions with the same denominator are called gleichnamig (like fractions). All pieces have the same size. You only compare the numerators: \( \frac{3}{8} < \frac{5}{8} \). The point of the sign points to the smaller fraction.

Same denominators: the bigger numerator wins.
Same denominators: the bigger numerator wins.

Same numerators

The bigger the denominator, the smaller the pieces. With the same numerators, the smaller denominator wins: \( \frac{3}{4} > \frac{3}{8} \).

Same numerators: the smaller denominator has the bigger pieces.
Same numerators: the smaller denominator has the bigger pieces.

If nothing is the same, you expand (erweitern) the fractions: numerator and denominator times the same number. \( \frac{3}{8} = \frac{9}{24} \) and \( \frac{1}{3} = \frac{8}{24} \). So \( \frac{3}{8} > \frac{1}{3} \). It is best to make the denominators the same – you will need this later for plus and minus too.

The three ways at a glance.
The three ways at a glance.

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

Put in \( < \) or \( > \): a) \( \frac{4}{9} \;\square\; \frac{7}{9} \) b) \( \frac{2}{3} \;\square\; \frac{2}{5} \) c) \( \frac{2}{3} \;\square\; \frac{3}{4} \)

Show solution

a) \( \frac{4}{9} < \frac{7}{9} \) (same denominators) b) \( \frac{2}{3} > \frac{2}{5} \) (same numerators) c) \( \frac{8}{12} < \frac{9}{12} \), so \( \frac{2}{3} < \frac{3}{4} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: comparing fractions (same denominators, same numerators, making them gleichnamig). Give me five pairs of fractions, one after the other. I say which one is bigger. 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.