Activities/Abacus/Worksheet/Answersheet: Difference between revisions
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Ways to make 1/2 with more than one string | Ways to make 1/2 with more than one string | ||
1/3 + 1/6 | 1/3 + 1/6 = (2+1)/6 = 3/6 = 1/2 | ||
1/3 + 2/12 | 1/3 + 2/12 = (4+2)/12 = 6/12 = 1/2 | ||
1/4 + 1/6 + 1/12 | 1/4 + 1/6 + 1/12 = (3+2+1)/12 = 6/12 = 1/2 | ||
1/4 + 2/8 | 1/4 + 2/8 = (2+2)/8 = 4/8 = 1/2 | ||
1/4 + 3/12 | 1/4 + 3/12 = (3+3)/12 = 6/12 = 1/2 | ||
3/9 + 2/12 | 3/9 + 2/12 = (12+6)/36 = 18/36 = 1/2 | ||
2/8 + 3/12 | 2/8 + 3/12 = 1/4 + 1/4 = 1/2 | ||
1/6 + 4/12 | 1/6 + 4/12 = (2+4)/12 = 6/12 = 1/2 | ||
1/6 + 3/9 | 1/6 + 3/9 = (3+6)/18 = 9/18 = 1/2 | ||
1/6 + 2/8 + 1/12 | 1/6 + 2/8 + 1/12 = (4+6+2)/24 = 12/24 = 1/2 | ||
2/6 + 2/12 | 2/6 + 2/12 = (2+1)/6 = 3/6 = 1/2 | ||
1/5 + 3/10 | 1/5 + 3/10 = (2+3)/10 = 5/10 =1/2 | ||
2/5 + 1/10 | 2/5 + 1/10 = (4+1)/10 = 5/10 =1/2 | ||
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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. | 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. | ||
You can paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities | |||
===Ways to make 1/3=== | ===Ways to make 1/3=== | ||