Activities/Abacus/Worksheet/Answersheet

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Answers to the Abacus Worksheet

Ways to make 1/2

Ways to make 1/2 just using one string

Abacus1of2.jpgAbacus2of4.jpg Abacus3of6.jpg Abacus4of8.jpg Abacus5of10.jpg 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

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 Diophantine equations, computer programs including ones written in TurtleArt can find all the solutions by trial and error.

Paste File:Turtle Art Activity fraction diophantine.ta 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.


4/12

3/9

2/8 + 1/12

1/6 + 2/12

2/6

1/4 + 1/12

1/3