Sunday, September 30, 2018

[dptrkenh] Base-10 versus base-5 abacus

Most abacuses are base 5, or more precisely mixed radix (5,2,5,2,...).  However simple base-10 abacuses with 10 beads per pole, typically marketed toward children, are very intuitive and easy to learn how to use.

Base 10: adding 8 is equivalent to adding 10 and subtracting 2.  Just have a chart of complements base 10.

Base 5: adding 8 is equivalent to adding 5 and adding 3.  Adding 5 is equivalent to adding 10 and subtracting 5.  Adding 3 is equivalent to adding 5 and subtracting 2.

Color the beads on a base-10 abacus in a way that it's easy to count how many you are moving and how many are left.  I have used one that had just the 5th and 6th beads differently colored.

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