Multiplying with lines math trick: how it works

A friend sent me a video about a multiplication trick.

The person draws out a certain number of lines for each number, and then counts out points to determine the answer.

It’s a bit hard to explain, so watch this video to see the method:

Video: how to Japanese multiply?

The trick looks impressive, but the way it works is by visually representing placeholders of powers of 10.

For example, take a look at this picture.

For the number 21, the person drew a set of 2 lines and then a bit further away a just 1 line. For the number 13, the person drew just 1 line followed by a set of 3 lines.

What do the lines represent? You can note the lines are really placeholders for the following multiplication:

21 x 13 = (2x10 + 1)(1x10 + 3)

So rather than writing out the numbers like above, the person in the video drew lines.

Computing the result is then a matter of grouping the powers of 10 and then counting.

(2x10 + 1)(1x10 + 3)= 2*10² + (2×3 +1)x10 + 3 = 273

The answer of 273 was obtained by finding out there are 2 units of 10², then 7 units of 10, and finally 3 units of 1. In the video the person counted the dots to find the exact same answer.

If you really want to multiply quickly, you might consider an alternate decomposition that seems more natural to me:

21 x 13 = 21(10 + 3) = 210 + 63 = 273

So in conclusion, while the method of using lines and dots is visually more pleasing, I’m ultimately not convinced it’s any faster or less error prone than the old-fashioned way of multiplying. But of course, to each his own.