## Thursday, February 16, 2006

### HOWTO: What are the small multiples of 9?

This is a mathematical "trick" or shortcut I learned in grade school. Its purpose was to learn an algorithmic trick to multiply a single-digit integer by nine (9), and ostensibly the child would eventually memorize the multiplication table (for 9's, at least). Recently one close to me told me they had never heard of this trick, which shocked me! After I learned the trick, I never bothered to actually memorize the table. (oh, i know them all if i think about it, but i can actually do this calculation faster than i can remember the answer, so this is kinda "how" i memorized them) If this reaches one other person that doesn't already know this, typing it in has been worthwhile!

Anyway, it's really simple. If X is the single-digit integer multiplied by 9, the quotient's answer, represented in double-digits, is (D1=X-1)(D2=9-D1).

E.g. 5*9 = (d1=5-1=4)(d2=9-4=5)=45.

My brain even kicks this up a notch by, instead of thinking "what is 9-D1?", thinks "what, when added to D1 equals 9?". For some reason I find the latter slightly faster, mentally.

Burton MacKenzie
http://www.burtonmackenzie.com