Using the meaning of a number we show three novel and simpler ways to do ordinary or carry type multiplication. It is assumed that one knows the multiplication table by heart. Let p = ab where a and b are positive integers. Write a = a_{1} + a_{2} where a_{1} contain a’s even powers of ten and a_{2} contains a’s odd powers of ten. Form p_{1} = a_{1}b, p_{2} = a_{2}b via ordinary multiplication. Then p = p_{1}+p_{2}. The subproducts of p_{1}, p_{2} will not have any carries and can be written down by rote. Alternatively, each row of p_{1} and p_{2} can be paired as two rows and then p can be computed directly. This second way is another way to do box multiplication. Furthermore, if one now adds each pair of rows together producing a single row again one would obtain carry type multiplication done another way. We also expand our approach to handle doing these new algorithms in base 100 and base 1000.

By:* Fred G. Gustavson*

Published in: RC24726 in 2009

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