Trachtenberg Multiplication

Trachtenberg Multiplication

1. always place one zero in front of the first multiplier for each digit of the second multiplier.

2. apply the rule acording to the second multiplier, working through the digits of the first multiplier from right to left

The rule will call for doubling or taking half. Taking half of even numbers presents no problem. Uneven numbers ("odd" numbers) are divided as: half of 1 is 0, half of 3 is 1, half of 5 is 2, half of 7 is 3, half of 9 is 4.
For odd numbers the rule will sometimes call for a special procedure.

Multiply by	Rule
11	Add the neighbor
12	Double, add the neighbor
6	Add half the neighbor plus 5 if number is odd
7	Double, add half the neighbor, add 5 if number is odd
5	Take half of the neighbor, add 5 if the number is odd
9	1. Last digit: subtract from 10    2. Middle digits: subtract from 9 and add the neighbor    3. First digit: (the leading zero) subtract 1 from the neighbor.
8	1. Last digit: subtract from 10 and double    2. Middle digits: subtract from 9 and double, add the neighbor    3. First digit: (the leading zero) subtract 2 from the neighbor.
4	1. Last digit: subtract from 10, add 5 if odd    2. Middle digits: subtract from 9, add half neighbor, +5 if odd    3. First digit: (the leading zero): half the neighbor less 1.
3	1. Last digit: subtract from 10, double, +5 if odd    2. Middle digits: subtract from 9, double, add half neighbor, +5 if odd.    3. First digit: (the leading zero) half the neighbor and subtract 2.