Activities/Abacus/Worksheet/Answersheet

Answers to the Abacus Worksheet

Ways to make 1/2

Ways to make 1/2 just using one string

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). 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