Visualize Math Problems With the Japanese Multiplication Method

In the age of smartphones, calculators and voice assistants, multiplying large numbers by hand can seem like a strange and completely unnecessary skill. However, you never know when you will need to do quick calculations, and the Japanese multiplication method (also called multiplication by rows) can help you figure out the answer simply by counting. All you need is a piece of paper and a pen. (Three different ink colors can be used, but this is not required.)

This is how the trick works.

First, select the multiplication problem. YouTuber MindYourDecisions has a great explanatory video , so to follow their lead, we’ll choose the 12 x 13 format .

Then draw your lines. You will need one line to represent each position of the tens and a parallel set of separate lines to represent the numbers in the ones place. This will give you a box shape formed by one line + one line + two lines + three lines. Tens are always on the left, and the rectangle is rotated 45 degrees.

(If you want to color-code your lines to make it easier to understand, the colored pens will come in handy here. However, again, this is not necessary for this method.)

Once you’ve laid out the lines, all that’s left to do is draw points wherever the lines intersect, and then count all of your points.

In the right corner of the 12 x 13 box, you have six points (intersection of two lines representing black 2 and three lines representing blue 3). This gives you 6 for your “ones” in your final number.

In the lower corner, you have two points representing the intersection of 10 of 13 and black 2. In the upper corner, you have three points representing the intersection of 10 of 12 and blue 3. Put them together, and the result is 5 (representing 50 actual intersections) gives you the place of “ten” in your final number.

Finally, the left corner represents one dot (1), but it represents 10 times 10 or 100. That 1 gives you the place of “hundreds” in your final number.

It may be helpful to draw curved vertical lines to separate each digit, but from here it is as easy as dropping each digit in its correct place: 12 x 13 = 156 .

Of course, this trick also works with large numbers with a lot of digits. Here’s ahandy sketch of how to solve 213 x 13.

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