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Fractions, Ratios, and Roots

Rediscover the Basics and Learn About Interesting Applications

  • Book
  • © 2021

Overview

Authors:
  1. Renate Motzer

    1. Augsburg, Germany

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  • What fractions are and how to calculate with them
  • Why there are also numbers that cannot be expressed as fractions
  • Why it is so important for percentages to know what the basic value is

Part of the book series: essentials (ESSENT)

Part of the book sub series: Springer essentials (SE)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Renate Motzer
    Pages 1-1

  3. What Are (Common) Fractions?

    • Renate Motzer
    Pages 3-4

  4. Fractions as Parts of a Whole

    • Renate Motzer
    Pages 5-11

  5. Fractions as Ratios

    • Renate Motzer
    Pages 13-21

  6. Ordering Fractions

    • Renate Motzer
    Pages 23-24

  7. Decimal Fractions

    • Renate Motzer
    Pages 25-30

  8. Percentage Calculations

    • Renate Motzer
    Pages 31-33

  9. Irrational Numbers

    • Renate Motzer
    Pages 35-39

  10. Probabilities

    • Renate Motzer
    Pages 41-50

  11. Various Mean Values

    • Renate Motzer
    Pages 51-54

  12. Conclusion

    • Renate Motzer
    Pages 55-55

  13. Back Matter

    Pages 57-59
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Keywords

About this book

Renate Motzer introduces the world of fractions and connects them with decimal numbers. She clearly shows that fractions can be understood as parts of a whole, but also as ratios of two quantities. The author clearly shows why roots cannot be exactly indicated by fractions, how to find good approximations and why an unusual addition of fractions can lead to paradoxical results. Furthermore, she explains the use of fractions in percentage and probability calculations in a practical way and finally discusses different ways of forming mean values.

This Springer essential is a translation of the original German 1st edition essentials, Brüche, Verhältnisse und Wurzeln by Renate Motzer, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was doneprimarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Authors and Affiliations

  • Augsburg, Germany

    Renate Motzer

About the author

Dr. Renate Motzer is an academic senior councillor at the Chair for Didactics of Mathematics at the University of Augsburg. Her main focus is the didactic and professional training of future mathematics teachers at various types of schools.

Bibliographic Information

  • Book Title: Fractions, Ratios, and Roots

  • Book Subtitle: Rediscover the Basics and Learn About Interesting Applications

  • Authors: Renate Motzer

  • Series Title: essentials

  • DOI: https://doi.org/10.1007/978-3-658-32574-9

  • Publisher: Springer Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden GmbH, part of Springer Nature 2021

  • eBook ISBN: 978-3-658-32574-9Published: 25 June 2021

  • Series ISSN: 2197-6708

  • Series E-ISSN: 2197-6716

  • Edition Number: 1

  • Number of Pages: VIII, 59

  • Number of Illustrations: 28 b/w illustrations

  • Topics: Algebra, Mathematics Education, Arithmetic and Logic Structures

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