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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 slics are − 360/3 =120 degrees − 360/6 = 60 degrees − − You can use either the Ruler or TurtleArt 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]] − − ====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'
Activities/Abacus/Worksheet/Answersheet (view source)
Revision as of 23:49, 14 June 2018
, 23:49, 14 June 2018Add header
==Answers to the Abacus Worksheet==
== Abacus/Worksheet/Answersheet ==
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]