How the japanese multiply

by javier on 16/12/2010

It may be an old one but I just found out at reaction [beta] and man, I’m still in shock:

There are 18 comments in this article:

16/12/2010Tweets that mention How the japanese multiply - THE COSMONAUTS -- Topsy.com says:

[...] This post was mentioned on Twitter by Juanjo Bernabeu, Karina Ibarra, Javier Cañada, sergiors_rss, Javier Cañada and others. Javier Cañada said: how the japanese mltiply (SHOCKING!) http://www.vostok.es/blog/how-the-japanese-multiply [...]
16/12/2010Tzek says:

Pero funciona sólo con números 1, 2 y 3, no es así?
17/12/2010dan says:

So 24×42 = 8208?
17/12/2010r says:

Tried 45*89

and it works

4005

Not sure it saves any knowledge of basic mathematics though
17/12/2010Ed says:

It is the lattice method. Many high school teach this method, although this seems less tedious the making exact lines.
17/12/2010Tyler says:

Dan,

24×42 = 1008

The technique to get this is explained in the video.

If you follow the second example you will see that it shows what to do when any particular step results in a digit greater than 9. In your example the you end up with 8 20 8. You take the 2 from the 20 and add it to 8 resulting in 10 you then have 10 0 8 = 1008.
18/12/2010Visuelle Multiplikation | freakcommander.de says:

[...] The Cosmonauts] window.fbAsyncInit = function() { FB.init({appId: "188021156289", status: true, cookie: true, [...]
18/12/2010iq4sale says:

I hadn’t seen this. A child can do it. I don’t know if it saves any time, without the line drawing the concept could.
18/12/2010Hoe The Japanese Multiply-Video | eWallstreeter says:

[...] Click here for video [...]
19/12/2010Marty says:

Awesome.
19/12/2010OMG says:

OMG – it is working!!!!!

I tryed it with ALOT of numbers – and it’s working!!!!!!!!

Try to do 100% the same as the video says (just with diffrent numbers)!

WOW!
19/12/2010Daniel says:

Well it obviously works. Just think about what you are doing by drawing the lines according to the method.

Consider a simple single-digit one like 2 * 3:
It is obvious why it works in this case, you intersect 3 lines twice, so you got 6 intersections ( 3 + 3 ). This is how integer multiplication is done by adding.

Now lets look at the first example in the video: 21 * 13
What is done mathmatically here is the following: you look at this product in a special way, i.e.
21 * 13 = (2*10 + 1*1)* (1*10+3*1)
This is based on our usage of the decimal system (base-10).
then you expand this product.
21 * 13 = (2*10) * (1*10) + (2*10) * (3*1) + (1*1) * (1*10) + (1*1) * (3*1)
then you go ahead and order them by the number of 10s they contain and factorize them.
21 * 13 = (2*1) * (10*10) + (2*3 + 1*1) * (10) + (3*1) * (1)
Then calculate the terms in the parenthesis:
21 * 13 = 2*100 + 7*10 + 4*1
Add, and you get the result:
21 * 13 = 2*100 + 7*10 + 4*1 = 273

This is exactly what you do by drawing the lines and counting the intersections.
Rewriting the product and expanding it is basically the same as drawing the lines.
Looking at the columns of the intersections is the same as ordering by number of occurencies of the 10s. Counting the intersections (as shown with the 2*3 example) is simply the single digit multiplication.

So this system of multiplication is just a visual way of using normal math. It even is the same way you would normally calculate a product (at least the way i learned in school) only the order is slightly changed.

The clear advantage of this system shows when you do the calculation in your head rather than writing it down. As our brain is way better in conjuring and remembering images than it is in remembering a lot of numbers, you can actually do fairly big multiplications in your head (gets a little difficult with higher digits (everything greater than 5 usually is hard to do)).
Additional advantage here is that you can use the right half of your brain (im only 70% sure its the right half. might be the other way around) which is responsible for spatial reasoning for looking at the question and simplifiing it for your left half of your brain which does the nesseccary calculations that are left over (left half being responsible for “linear” processing such as logic, language and so on).

Hope this clarifies things a bit.

(Sorry for mediocre english, haven’t written in this language for some time)
19/12/2010Latita's Life » » Multiplizieren mal anders says:

[...] Awesome, oder? Wie kommt man auf diese Idee? via vostok.es [...]
23/12/2010petri says:

Try 9876 X 6789… it will take you a full A4 to do it this way… now thats not VERY green, nor efficient!
25/12/2010goopah says:

Aha! So my computer is actually counting DOTS in there, not ones and zeroes!
27/12/2010Matias Kreder says:

interesting.. I have never read about this way.. I know about this way:

http://es.wikipedia.org/wiki/Multiplicaci%C3%B3n_por_duplicaci%C3%B3n

I don’t know how to translate that.
29/12/2010Life » Blog Archive » How the japanese multiply – THE COSMONAUTS says:

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9/01/2011Stretching Cow › Breakfasts, APs and Misconceptions says:

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How the japanese multiply

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