This method is ideal for multiplication in doing arithmetic with number systems having a base other than 10 where the memorized multiplication facts for base 10 are invalid. To avoid more than one auxiliary multiple above the multiplicand (as the 2-multiple in this example) you might occasionally find it quicker to use subtraction. For example when filling in the 9-multiple when none of the previous multiples add to the 9-multiple, you can subtract the multiplicand from its 10-Multple in place (without actually appending the zero) by subtracting each digit from the one to its right assuming a zero on each end. Likewise, if there are no previously created multiples that add to the 5-multiple you might find it quicker to divide the 10-Multiple by 2 by assuming an appended zero such that if the multiplicand is odd the remainder of one will give a final 5 rather than zero. (In base 12 these "subterfuges" could be used for 11 and 6 rather than 9 and 5.)

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue