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©2021 Compass Learning TechnologiesGXWeb Jigsaws and QuizzesGXWeb Fractured Fractions → GXWeb Fractured Fractions Jigsaw

GXWeb Fractured Fractions Jigsaw

Saltire Software, home of Geometry Expressions and GXWeb

Symbolic computations on this page use Nerdamer Symbolic JavaScript to complement the in-built CAS of GXWeb

Chaos in Numberland: The secret life of continued fractions by John D. Barrow

Explore Bill Gosper (1972): Continued Fraction Arithmetic

Calkin and Wilf (1999): Recounting the Rationals

Try the full Fractured Fractions Jigsaw

 
 

Welcome to the Fractured Fractions Jigsaw!

Begin with the JigSaw: Just rearrange the squares to fill the given rectangle, and then press INPUT (or the JIGSAW button again) to enter your answer.

Then go on and explore some of the wonderful connections between continued fractions and some surprising and important corners of mathematics. Did you know, for example, that fractions grow on trees?

 
 

With special thanks to Dr Keith Tognetti of the University of Wollongong for pointing me in the direction of these wonderful numbers and igniting in me a life-long passion.

 

 
 
 

Continue your fractured fractions journey...

Rearrange the squares to fill the given rectangle, and then press INPUT (or the JIGSAW button again) to enter your answer.
(The first one has the squares marked out for you - and try 1,2,3 as your first answer!)

This document requires an HTML5-compliant browser.

App generated by GXWeb

 

\[ \frac{10}{7} = [1,2,3]\]

\[ ⇒ 1 + \frac{1}{2 + \frac{1}{3}}\]

\[ \approx 1.4285714286\]

 

 

Introduction

If you have not come across continued fractions in your mathematical travels, then it is high time you did!

Every real number, rational and irrational, can be represented as a continued fraction. While normal fractions can only represent rational numbers, continued fractions are different - full of surprising patterns and relationships.

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Mathematical ToolBox

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Explore Further: Continued Fractions, Farey Numbers and Fraction Trees

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Share with Different Senses

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Construct your own Model with GXWeb

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Behind the Scenes

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©2021 Compass Learning TechnologiesGXWeb ShowcaseGXWeb Jigsaws and QuizzesGXWeb Fractured Fractions ← GXWeb Fractured Fractions Jigsaw