Fractions, Ratios, and Roots / essentials (PDF)

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 1^st 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 done primarily 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.

The contents

The target groups

• Lecturers and students of mathematics or students who want to repeat basic knowledge of fractions for their statistics lectures
• People interested in mathematics, who want to refresh and expand their knowledge from fractions to hypothesis testing from school

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 professionaltraining of future mathematics teachers at various types of schools.