We don't know how this multiplication trick works, but it's never failed us yet.   Take any two numbers: say, 116 ahd 3,011.   Halve the first number again and again, discarding any fractional remainder, until you reach the number 1.   Thus: 116, 58, 29, 14, 7, 3, 1.   Double the second as many times as you halved the first.   Thus: 3,011; 6,022; 12,044; 24,088; 48, 176; 96,352; 192,704.   Write these series alongside each other, and cross out every even number in the halves column and its partner in the dou- bles column.   Thus, as shown in the following columns, the even numbers in the halves column (116, 58, and 14) are crossed out along with their companions in the doubles column (3,011; 6,022; and 24,088), regardless of whether these are even or odd.

Add the numbers that remain in the doubles column only. The resulting sum will be equal to the product of the two numbers you started with.
Thus: 12,044 + 48,176 + 96,352 + 192,704 = 349,276 = 116 X 3,011.