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Line 1: − + − ===Ways to make 1/2=== − 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]]+ − 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+ − − − Ways to make 1/2 with more than one string − − 1/3 + 1/6 = (2+1)/6 = 3/6 = 1/2 − − 1/3 + 2/12 = (4+2)/12 = 6/12 = 1/2 − − 1/4 + 1/6 + 1/12 = (3+2+1)/12 = 6/12 = 1/2 − − 1/4 + 2/8 = (2+2)/8 = 4/8 = 1/2 − − 1/4 + 3/12 = (3+3)/12 = 6/12 = 1/2 − − 3/9 + 2/12 = (12+6)/36 = 18/36 = 1/2 − − 2/8 + 3/12 = 1/4 + 1/4 = 1/2 − − 1/6 + 4/12 = (2+4)/12 = 6/12 = 1/2 − − 1/6 + 3/9 = (3+6)/18 = 9/18 = 1/2 − − 1/6 + 2/8 + 1/12 = (4+6+2)/24 = 12/24 = 1/2 − − 2/6 + 2/12 = (2+1)/6 = 3/6 = 1/2 − − 1/5 + 3/10 = (2+3)/10 = 5/10 =1/2 − − 2/5 + 1/10 = (4+1)/10 = 5/10 =1/2 − − − 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. − − 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=== − 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 − − − 4/12 − − 3/9 − − 2/8 + 1/12 − − 1/6 + 2/12 − − 2/6 − − 1/4 + 1/12 − − 1/3 − − ===Other representations of fraction addition=== − ====Paint==== − 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 − 360/3 =120 degrees − 360/6 = 60 degrees − − You can use either the polar grids of Ruler [[File:Polarruler.jpg]] or TurtleArt [[File:Polarturtle.jpg]] to help visualise the angles − − ====Turtle Art==== − Copy [[File:Turtle Art Activity pie.ta | this code]] into TurtleArt to generate the pie for 1/3 + 1/6 − − [[File:Fractionpieturtle.jpg]] − − It can be modified for other pie slice sizes. The fill command does not work on line arcs, so the pies are not coloured. Here is another solution for coloured pie slices [[File:Turtle_Art_Activity_pie_chart.ta]] − − ====Socialcalc==== − 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 − − Enter the data 1/3, 1/6 and 1/2 into 3 cells, select (grey highlight) the 3 cells − − [[File:Soccalcpieentry.jpg]] − − Click the graph tab, select 'Pie Chart' − − [[File:Fractionpiesocialcalc.jpg]] − − − ===The Caacupé abacus=== − 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.
Activities/Abacus/Worksheet/Answersheet (view source)
Revision as of 00:54, 27 March 2018
, 00:54, 27 March 2018Migrate to GitHub
==Answers to the Abacus Worksheet==
Wiki Page Status: <span style="color:#ff0000"> DEPRECATED </span>
Read at https://help.sugarlabs.org/abacus_worksheet_answers.html
The source file has been moved to [https://github.com/godiard/help-activity/blob/master/source/abacus_worksheet_answers.rst GitHub]