|
|
| (17 intermediate revisions by 2 users not shown) |
| Line 1: |
Line 1: |
| ==Answers to the Abacus Worksheet== | | == Abacus/Worksheet/Answersheet == |
| ===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]]
| | Read at https://help.sugarlabs.org/abacus_worksheet_answers.html |
|
| |
|
| 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] |
| | |
| | |
| Ways to make 1/2 with more than one string
| |
| | |
| 1/3 + 1/6
| |
| | |
| 1/3 + 2/12
| |
| | |
| 1/4 + 1/6 + 1/12
| |
| | |
| 1/4 + 2/8
| |
| | |
| 1/4 + 3/12
| |
| | |
| 3/9 + 2/12
| |
| | |
| 2/8 + 3/12
| |
| | |
| 1/6 + 4/12
| |
| | |
| 1/6 + 3/9
| |
| | |
| 1/6 + 2/8 + 1/12
| |
| | |
| 2/6 + 2/12
| |
| | |
| 1/5 + 3/10
| |
| | |
| 2/5 + 1/10
| |
| | |
| | |
| 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.
| |
| | |
| Paste [[File:Turtle Art Activity fraction diophantine.ta |this code]] into Turtle Art to calculate all the possibilities
| |
| | |
| This program can be modified for 1/3 and 2/3 and with more work it could be used for the Caacupé abacus.
| |
| | |
| ===Ways to make 1/3===
| |
| 4/12
| |
| | |
| 3/9
| |
| | |
| 2/8 + 1/12
| |
| | |
| 1/6 + 2/12
| |
| | |
| 2/6
| |
| | |
| 1/4 + 1/12
| |
| | |
| 1/3
| |