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Adding fractions

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

Adding (addieren) means doing plus. You learn how to add fractions with the same and with different denominators.
📄 Open worksheet (PDF, German)

The video

After a party, \( \frac{1}{2} \) and \( \frac{1}{3} \) of a pizza are on the plate. How much is that altogether? In the video the second fraction is pink.

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

Contents of the video

  1. 0:00 After the party
  2. 0:35 Same pieces
  3. 1:05 Like fractions
  4. 1:42 Examples
  5. 2:09 A whole pizza
  6. 2:42 Different denominators
  7. 3:30 The result
  8. 3:52 The strategy
  9. 4:22 Expanding one fraction
  10. 4:50 Simplifying cleverly
  11. 5:22 Expanding both
  12. 5:57 Practice
  13. 6:28 Summary

The most important points

Same denominators

You only add the numerators. The denominator stays: \( \frac{3}{8} + \frac{2}{8} = \frac{5}{8} \). Never add the denominators! \( \frac{5}{16} \) is even less than \( \frac{3}{8} \).

The denominator tells you how big the pieces are. The pieces stay the same size.
The denominator tells you how big the pieces are. The pieces stay the same size.

If the denominators are different, you first need pieces of the same size: a common denominator (gemeinsamer Nenner). You find it in the times tables. 6 is in the two times table and in the three times table: \( \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \).

Different denominators: cut both pizzas into sixths.
Different denominators: cut both pizzas into sixths.

How to calculate

1. Same denominators? Then add the numerators. 2. Different denominators? Find a common denominator. 3. Make them the same: expand or simplify. 4. Add the numerators, the denominator stays. 5. Simplify the result if you can.

The strategy in five steps.
The strategy in five steps.

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: a) \( \frac{2}{7} + \frac{3}{7} \) b) \( \frac{3}{8} + \frac{1}{4} \) c) \( \frac{1}{3} + \frac{1}{4} \)

Show solution

a) \( \frac{5}{7} \) b) \( \frac{3}{8} + \frac{2}{8} = \frac{5}{8} \) c) \( \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: adding fractions (make them gleichnamig, add the numerators, the denominator stays, simplify at the end). Give me five tasks, one after the other; the result is at most 1. 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.