Japanese multiplication method

There is a bunch of videos going around lately that seem to be very popular, which demonstrate a style of Japanese multiplication.  It is quite visual, and I would argue that more complicated products could require even more work than traditional (at least, what I consider traditional) methods.  In any case, it is a very interesting process that you could use to impress your friends and family, or even use it as a math trick.  Here's the gist of how the Japanese multiplication method works.

Let's try a simple example.  Find the product of 12 x 31.

Essentially, you denote the digits as groups of lines, and then you count the intersections to arrive at your result.  So, in this case, the 12 is represented by a group of 1 line and a group of 2 lines, and the 31 is represented by a group of 3 lines and a group of 1 line.  We'll draw the "12" lines slanting up in blue, and the "31" lines slanting down in orange.

Now, imagine that these lines and their intersections can be divided into columns.  You get the left point of the diamond in the first column, the top and bottom of the diamond together in the second column, and the right point of the diamond in the third column.  Now, to find the product of these two numbers, all you do is count the intersections in each column and write that number down.  These numbers will be the digits in the final answer.

Check with your calculator and you can verify that 12 x 31 = 372!  It takes a bit of work, but it's a pretty cool method of multiplying numbers together!  This works really easily when you are multiplying a pair of two digit numbers together.  When you have three digits numbers, or more, you simply add another group of lines, and then you will wind up with more columns to tally the intersections.  Also, in any one column, if you count more than 9 intersections, you simply carry the tens digit of your intersections over one column to the left and add to that total.  So, if you count 12 intersections in a column, the value you keep is the 2, and you add the 1 to whatever is in the column to the left.

If nothing else, I think this method is a really cool demonstration for a cool math trick, though I don't think that I would use it to replace the style of multiplication that I learned in school.  However, that's not to say that it won't be more appealing or useful to you!  Do you use this method in your studies?  Let me know in the comments, and don't forget to hit the Facebook Like button at the start of the post to support my site!

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