Splitting Hard Numbers

Investors size up deals with quick napkin math: capture X% of a Y-dollar market at Z% margins, and the multiplication runs in their head using the distributive property.

Example: 47 x 63. Split it as (50-3)(60+3) = 50x60 + 50x3 - 3x60 - 3x3 = 3000 + 150 - 180 - 9 = 2,961. Or use the simpler route: 47x63 = 45x63 + 2x63 = 2835 + 126 = 2,961. Both break one hard multiplication into a few easy ones.

The Trachtenberg system grew out of the same idea: Jakow Trachtenberg, a Jewish engineer imprisoned in a Nazi camp during WWII, worked the shortcuts out in his head and turned them into a complete mental arithmetic method.