For those of you who may be math nuts, here are some basic multiplication rules for The Trachtenberg Method of Speed Mathematics.
TO MULTIPLY BY A PARTICULAR NUMBER,
THE PROCEDURE IS THIS:
To Multiply By 11 Add the neighbor. (the # to the right)
To Multiply By 12 Double the number and add the neighbor.(The # to the right)
To Multiply By 6 Add 5 to the number if the number is odd; add nothing if it is even. Add "half" the neighbor (dropping fractions, if any).
To Multiply By 7 Double the number and add 5 if the number is odd, and add "half" the neighbor.
To Multiply By 5 Use "half" the neighbor, plus 5 if the number is odd.
To Multiply By 9 First step: subtract from 10.
Middle steps: subtract from 9 and add the neighbor.
Last step: reduce left-hand digit of multiplicand by 1.
To Multiply By 8 First step: subtract from 10 and double.
Middle steps: subtract from 9, double, and add the neighbor.
Last step: reduce left-hand digit of multiplicand by 2.
To Multiply By 4 First step: subtract from 10, and add 5 if the number is odd.
Middle steps: subtract from 9 and add "half" the neighbor, plus 5 if the number is odd.
Last step: take "half" the left-hand of the multiplicand and reduce by 1.
To Multiply By 3 First step: subtract from 10 and double, and add 5 if the number is odd.
Middle steps: subtract from 9 and double, add 5 if the number is odd, and add "half" the neighbor.
Last step: take "half" the left-hand digit of the multiplicand and reduce by 2.
To Multiply By 2 Double each digit of the multiplicand without using the neighbor at all.
To Multiply By 1 Copy down the multiplicand unchanged.
To Multiply By 0 Zero times any number at all, is zero.
TO MULTIPLY BY A PARTICULAR NUMBER,
THE PROCEDURE IS THIS:
To Multiply By 11 Add the neighbor. (the # to the right)
To Multiply By 12 Double the number and add the neighbor.(The # to the right)
To Multiply By 6 Add 5 to the number if the number is odd; add nothing if it is even. Add "half" the neighbor (dropping fractions, if any).
To Multiply By 7 Double the number and add 5 if the number is odd, and add "half" the neighbor.
To Multiply By 5 Use "half" the neighbor, plus 5 if the number is odd.
To Multiply By 9 First step: subtract from 10.
Middle steps: subtract from 9 and add the neighbor.
Last step: reduce left-hand digit of multiplicand by 1.
To Multiply By 8 First step: subtract from 10 and double.
Middle steps: subtract from 9, double, and add the neighbor.
Last step: reduce left-hand digit of multiplicand by 2.
To Multiply By 4 First step: subtract from 10, and add 5 if the number is odd.
Middle steps: subtract from 9 and add "half" the neighbor, plus 5 if the number is odd.
Last step: take "half" the left-hand of the multiplicand and reduce by 1.
To Multiply By 3 First step: subtract from 10 and double, and add 5 if the number is odd.
Middle steps: subtract from 9 and double, add 5 if the number is odd, and add "half" the neighbor.
Last step: take "half" the left-hand digit of the multiplicand and reduce by 2.
To Multiply By 2 Double each digit of the multiplicand without using the neighbor at all.
To Multiply By 1 Copy down the multiplicand unchanged.
To Multiply By 0 Zero times any number at all, is zero.