What is the origin or author of the method 1 shown in the following image?
Notes
- Also known as Japanese Multiplication Method for Kids.
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1Uhm... Japan...? – JohnWO Oct 24 '14 at 14:37
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2To me it's just a visual expression of the distribution property $$(10a+b)(10c+d)=100ac+10(bc+ad)+bd.$$ But of course it's a lot more impressive by pictures that way. – Quang Hoang Oct 24 '14 at 14:40
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3It's much less impressive if you're not dealing with small digits (1, 2, 3, 5) or two-digit numbers. – anomaly Oct 24 '14 at 14:45
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Are you asking why it works? – GFauxPas Nov 02 '14 at 14:00
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@GFauxPas I looking for the author of this method. – Paul Vargas Nov 03 '14 at 00:02
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According to Wikipedia, "It is not known where it arose first, nor whether it developed independently within more than one region of the world".
GFauxPas
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This method is just breaking up the numbers into their tens, hundreds, and so on so that you can keep track of place values when multiplying. In this example, $$15*23=(10+5)*(20+3)=20*10 + 5*20 + 10*3 + 5*3=200 + 130 + 15$$ So the first digits of each number 1 and 2 correspond to 10 and 20 which when multiply to give the largest place value, the mixed terms are in between and the last digits 5 and 3 give the smallest contribution. So basically, the method is using distributivity and is not very different from other methods. It does nicely keep track of powers of 10.
ET93
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