Difference between revisions of "Activities/Abacus/Worksheet/Answersheet"

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==Answers to the Abacus Worksheet==
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== Abacus/Worksheet/Answersheet ==
Ways to make 1/2 just using one string
 
  
[[File:Abacus1of2.jpg]][[File:Abacus2of4.jpg]] [[File:Abacus3of6.jpg]] [[File:Abacus4of8.jpg]] [[File:Abacus5of10.jpg]] [[File:Abacus6of12.jpg]]
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Read at https://help.sugarlabs.org/abacus_worksheet_answers.html
  
To make 1/2 just using one string, the fraction denominator must be divisible by 2. The string must contain an even number of beads, 2 4 6 8 10 12
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The source file has been moved to [https://github.com/godiard/help-activity/blob/master/source/abacus_worksheet_answers.rst GitHub]
 
 
 
 
Ways to make 1/2 with more than one string
 
 
 
1/3 + 1/6
 
 
 
1/3 + 2/12
 
 
 
1/4 + 1/6 + 1/12
 
 
 
1/4 + 2/8
 
 
 
1/4 + 3/12
 
 
 
3/9 + 2/12
 
 
 
2/8 + 3/12
 
 
 
1/6 + 4/12
 
 
 
1/6 + 3/9
 
 
 
1/6 + 2/8 + 1/12
 
 
 
2/6 + 2/12
 
 
 
1/5 + 3/10
 
 
 
2/5 + 1/10
 
 
 
 
 
Is this all of the possibilities?
 
 
 
See [http://en.wikipedia.org/wiki/Diophantine_equation Diophantine equations], computer programs [http://tonyforster.blogspot.com/2010/09/turtle-diophantine.html including ones written in TurtleArt] can find all the solutions by trial and error.
 
 
 
Paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities
 
 
 
This program can be modified for 1/3 and 2/3 and with more work it could be used for the Caacupé abacus.
 

Latest revision as of 22:49, 14 June 2018

Abacus/Worksheet/Answersheet

Read at https://help.sugarlabs.org/abacus_worksheet_answers.html

The source file has been moved to GitHub