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| ==Answers to the Abacus Worksheet== | | == Abacus/Worksheet/Answersheet == |
| ===Ways to make 1/2===
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| Ways to make 1/2 just using one string
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| [[File:Abacus1of2.jpg]][[File:Abacus2of4.jpg]] [[File:Abacus3of6.jpg]] [[File:Abacus4of8.jpg]] [[File:Abacus5of10.jpg]] [[File:Abacus6of12.jpg]]
| | Read at https://help.sugarlabs.org/abacus_worksheet_answers.html |
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| 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
| | The source file has been moved to [https://github.com/godiard/help-activity/blob/master/source/abacus_worksheet_answers.rst GitHub] |
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| Ways to make 1/2 with more than one string
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| 1/3 + 1/6 = (2+1)/6 = 3/6 = 1/2
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| 1/3 + 2/12 = (4+2)/12 = 6/12 = 1/2
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| 1/4 + 1/6 + 1/12 = (3+2+1)/12 = 6/12 = 1/2
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| 1/4 + 2/8 = (2+2)/8 = 4/8 = 1/2
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| 1/4 + 3/12 = (3+3)/12 = 6/12 = 1/2
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| 3/9 + 2/12 = (12+6)/36 = 18/36 = 1/2
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| 2/8 + 3/12 = 1/4 + 1/4 = 1/2
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| 1/6 + 4/12 = (2+4)/12 = 6/12 = 1/2
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| 1/6 + 3/9 = (3+6)/18 = 9/18 = 1/2
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| 1/6 + 2/8 + 1/12 = (4+6+2)/24 = 12/24 = 1/2
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| 2/6 + 2/12 = (2+1)/6 = 3/6 = 1/2
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| 1/5 + 3/10 = (2+3)/10 = 5/10 =1/2
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| 2/5 + 1/10 = (4+1)/10 = 5/10 =1/2
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| Is this all of the possibilities?
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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.
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| You can paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities
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| ===Ways to make 1/3===
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| This program can be modified for 1/3 and 2/3 (and with more work it could be used for the Caacupé abacus). Circled below, the program above has 0.5 replaced with 1/3 to find the ways of making 1/3
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| 4/12
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| 3/9
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| 2/8 + 1/12
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| 1/6 + 2/12
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| 2/6
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| 1/4 + 1/12
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| 1/3
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| ===Other representations of fraction addition===
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| ====Paint====
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| You need to guess the centre of the circle and angles of the pie slice lines. The full circle or 360 degrees represents '1' so the 1/3 and 1/6 pie slices are
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| 360/3 =120 degrees
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| 360/6 = 60 degrees
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| You can use either the Ruler [[File:Polarruler.jpg]] or TurtleArt [[File:Polarturtle.jpg]] to help visualise the angles
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| ====Turtle Art====
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| Copy [[File:Turtle Art Activity pie.ta | this code]] into TurtleArt to generate the pie for 1/3 + 1/6
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| [[File:Fractionpieturtle.jpg]]
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| ====Socialcalc====
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| Spreadsheets are powerful tools for representing numbers. The Socialcalc Activity (V5) is a little buggy, the menu bars are very cramped. If you have access to Gnumeric in Gnome, it is recommended
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| Enter the data 1/3, 1/6 and 1/2 into 3 cells, select (grey highlight) the 3 cells
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| [[File:Soccalcpieentry.jpg]]
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| Click the graph tab, select 'Pie Chart'
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| [[File:Fractionpiesocialcalc.jpg]]
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| ===The Caacupé abacus===
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| We have not given answers here for the Caacupé abacus. There are a lot more solutions. Trial and error could take a long time. The TurtleArt program above could be modified to generate solutions.
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