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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

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.

Paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities

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===