Algebraic Explanation for Wrist Multiplication
Date: 09/10/2004 at 22:01:14 From: Heidi Subject: Why does wrist multiplication work? I am learning wrist multiplication and am curious as to why and how it works for the numbers 11-15. It is easier and quicker to use this application but I don't understand how it works. For example, 12 x 13. Your wrists count as 50 each, each finger is 10. Hold up 2 fingers on one hand and 3 fingers on the other. Touch your wrists together and count this as 100. You should have 5 fingers showing and this counts as 50 (10 per finger). Then multiply 2 fingers by 3 fingers and count this as 6. Add 100 + 50 + 6 and it equals 156!!! Why and how??!!
Date: 09/11/2004 at 06:40:43 From: Doctor Luis Subject: Re: Why does wrist multiplication work? Hi Heidi, If you think about it, you can write the numbers 11,12,13,14,15 as 10 + x, where x is between 1 and 5 (the number of fingers in a typical hand). Then, to multiply two such numbers, you get: (10 + x)(10 + y) = 10*10 + x*10 + 10*y + x*y = 100 + 10(x+y) + x*y So, the first 100 can be accounted for with the two wrists (50 each). The x+y weighed by 10 is the value you gave to the total number of fingers, which do add up according to our algebraic formula above. Of course, the product of x and y is just the product of the actual number of fingers we're holding up in each hand, which was 2*3 = 6 in your example. This is a nifty mnemonic way of multiplying two numbers that I hadn't seen until now. Please note that the formula itself holds no matter what x and y are, since it's an algebraic identity. The reason we restrict them to the values 1 thru 5 is simply that we find it difficult to hold up six fingers in a single hand, much less the 28 extra fingers that would be required to multiply 13 x 42 using this method. The sixty-fingered creatures that live in Alpha Proxima Centauri can probably have better luck with that last multiplication. I hope this helped! Let us know if you have any more questions. - Doctor Luis, The Math Forum http://mathforum.org/dr.math/
Date: 09/11/2004 at 23:18:27 From: Heidi Subject: Thank you (Why does wrist multiplication work?) Thank you so much for your help. The formula really helps to understand the concept.
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