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Mixed numbers: number line and comparing

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

The recipe says \( 1\frac{1}{2} \) cups of flour. You place mixed numbers (gemischte Zahlen) on the number line, convert improper fractions (unechte Brüche) and compare mixed numbers.
📄 Open worksheet (PDF, German)

The video

In the video the numbers lie on a number line from 0 to 3, divided into quarters.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:16 Number line
  3. 0:44 Improper fractions
  4. 1:03 Comparing
  5. 1:38 Careful, mistake!
  6. 1:59 Try it yourself

The most important points

Mixed number

A mixed number has wholes and a fraction: \( 2\frac{1}{4} = 2 + \frac{1}{4} \). Between the wholes and the fraction there is an invisible plus.

Mixed numbers lie between the whole numbers: 11/4 , 13/4 , 21/2 .
Mixed numbers lie between the whole numbers: \( 1\frac{1}{4} \), \( 1\frac{3}{4} \), \( 2\frac{1}{2} \).

Improper fraction and mixed number

\( \frac{7}{4} = 1\frac{3}{4} \) and \( \frac{5}{2} = 2\frac{1}{2} \): the same point on the number line, two ways to write it.

7/4 and 5/2 on the number line.
\( \frac{7}{4} \) and \( \frac{5}{2} \) on the number line.

Comparing

First compare the wholes: \( 2\frac{1}{4} > 1\frac{3}{4} \), because \( 2 > 1 \). If the wholes are equal, compare the fractions. Give them the same denominator first: \( 1\frac{1}{2} < 1\frac{2}{3} \), because \( \frac{3}{6} < \frac{4}{6} \).

First compare the wholes, then the fractions.
First compare the wholes, then the fractions.

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
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Try it yourself

Task

a) Write \( \frac{11}{4} \) as a mixed number. b) Which is bigger: \( 3\frac{2}{5} \) or \( 3\frac{1}{3} \)?

Show solution

a) \( 2\frac{3}{4} \) b) \( 3\frac{2}{5} \), because \( \frac{6}{15} > \frac{5}{15} \)

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: mixed numbers (gemischte Zahlen: number line, improper fractions, comparing). 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.