Thursday, September 13, 2012

Multiplying by Nine on Your Fingers

I mentioned finger-counting in a recent comment as a cognitive activity that was not all 'in the brain'. We tend to think of finger-counting as a pretty elementary thing, but this is simply a matter of what you do with them. It put me in mind of a handy trick for multiplying single-digit numbers by nine on your fingers.

(1) Put both hands in front of you, fingers stretched out.
(2) Counting from the left, bend down the finger you want to multiply by nine. For instance, if you want to multiply by 2, bend down the second finger of your left hand. If you want to multiply by 6, bend down the thumb of your right hand.
(3) The number of fingers to the left of the bent finger is the tens-place digit and the number of fingers to the right of the bent-finger is the ones-place digit of your answer.

Pretty neat. And, of course, you can do much more. For instance, you can do many numbers with more than one digits in exactly the same way -- the rules get more complicated because you have to start reserving fingers for a hundreds-place, but they can still be done. For instance, to multiply nine by thirteen, you hold out your hands, bend the third finger of your left hand, read your left pinky finger as a 100, the next finger as a 10, and the rest of your fingers as 1's, giving you 117. And you can do it in reverse (I asked myself, which number is it again that gives you 117 when you multiply it by 9, put 117 on the fingers and read it right off). You can also do the same thing with number systems of a lower base than ten. For instance, you can multiply things times 7 in base-8 arithmetic by ignoring a finger on each hand. And there are other tricks for other numbers.

Basically what you are doing is taking advantage of some basic number theory in order to use your fingers as a crude abacus, which is the underlying principle of things like the Chisanbop calculation method, which had some popularity a couple of decades ago. Even if you, like most people, remember your multiplication table, such things can be ways of keeping track of calculations or avoiding simple arithmetic mistakes.

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