Activities/Abacus/Worksheet/Answersheet

Answers to the Abacus Worksheet

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


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.