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Working from scratch, following simplicity

The Japanese method: do multiplications with fun

You learn something new every day, indeed I discovered a new way to do multiplications with much fun: the Japanese method. The approach is pretty graphical but obviously the maths is the same used in the traditional method. I show you in a video four examples and a gallery with a comparison of the two techniques. Sure you will appreciate it and amazing your friends with awesome maths!

The Japanese method is an elegant and handful procedure to solve the multiplications reducing them to a sum of dots subdivided in horizontal and vertical lines.

The Japanese method: do multiplication with fun

An animation of the Japanese Multiplication MethodAs I explain in the animation on the right and in the gallery below it consists in four steps:

  1. transform the first factor in the equivalent number of horizontal lines leaving some empty space between every whole components and starting from the left, if a number is 0 draw a dotted line;
  2. draw the second factor in the same way but this time through vertical lines;
  3. once you a have obtained a lattice divide it in areas of influence and draw a dots wherever the lines intercept themselves (if the line is dotted don't make any dot);
  4. sum every single areas and write the corresponding results, then you will obtain the final result selecting the numbers in anticlockwise order starting from the top left-hand corner.

Below I made a video with four examples and a gallery in which I solve a multiplication step by step comparing side by side the Japanese and Traditional method.

I created the images of the gallery using LaTeX, as you can see online on my Overleaf1 account, it is available here.

  • 1Overleaf is the new collaborative writing and publishing system developed by the team behind the popular writeLaTeX editor. Overleaf is designed to make the whole process of writing, editing and producing scientific papers much quicker for both authors and publishers. Here is my referall link to Overleaf:


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Nicola Rainiero

A civil geotechnical engineer with the ambition to facilitate own work with free software for a knowledge and collective sharing. Also, I deal with green energy and in particular shallow geothermal energy. I have always been involved in web design and 3D modelling.