Looks like a different representation of what we do: multiply every digit of the first number with every digit of the second. But the way it makes it so visual is pretty neat indeed.

I prefer long division and long multiplication when doing things by hand it`s easier/quicker for me to double check. In my head I prefer weird approximations or dealing with fractions.

I tried it the japanese way. Perhaps once you are very familiar with the system its fast. But it took me longer to sit and count and add than it took the way I was taught.

996 * 693 = 690228 Less than a minute to do by "old fashion" hand calculation. This is slow aswell I suppose.

About 2 minutes with the japanese system. Id love to see a japanese person do this, I presume the drawing of the system becomes less needed once you get used to it.

They count the number of times lines cross eachother. They go left to right, counting diagonally. So 1, 5, 6. Means that top left the lines cross 1 time. middle diagonal they cross a total of 5 times and bottom right cross 6 times.

The numbers represent digits and 1`s, 10`s, 100`s and so on. going from high to low. The 1 represent 100, 5 represent 50 and the 6 representy 6.

If the lines add up to say 12. Then, given the lines location, it represents 12, 120, 1200 and/or so on. Try to apply it to the slightly larger calculation. It makes sense, in a japanese kind of way.

This is called Vedic maths. Its actually from India.as a kid I could use this method before I learned the western method. My teachers actually graded my work as an F once because even though my answers were correct, I could not show them my working out.

To be honest, this is good for teaching the concepts behind multiplication of multi-digit numbers in a way that naturally leads to polynomial multiplication. It`s just pointing out that the first one, 13*12, is equivalent to (10+3)*(10+2), then you distribute it to 10*10+10*3+10*2+3*2 which equals 156. Same for anything larger. 123*456 = (100+20+3)*(400*50*6)=(100*400 + 100*50 + 100*6 + 20*400 + 20*50 + 20*6 + 3*400 + 3*50 + 3*6)= 40000 + 5000 + 600 + 8000 + 1000 + 120 + 1200 + 150 + 18 = 56088. The concept expands to polynomial multiplication since everything so far has just been polynomial multiplication with single digit coefficients and with x=10. So if x=10, then (327*151) = (3x^2+2x+7)*(x^2+5x+1)= (3x^4 + 15x^3 + 3x^2 + 2x^3 + 10x^2 + 2x + 7x^2 + 35x + 7) = 3x^4+17x^3+20x^2+37x+7. Plugging 10 back in for x, 30000+17000+2000+370+7 = 49377.

- Japan: Where even the math is weird.
In my head I prefer weird approximations or dealing with fractions.

I cant...I dont even...what?

553 * 352 = 194656

I tried it the japanese way. Perhaps once you are very familiar with the system its fast. But it took me longer to sit and count and add than it took the way I was taught.

996 * 693 = 690228

Less than a minute to do by "old fashion" hand calculation. This is slow aswell I suppose.

About 2 minutes with the japanese system.

Id love to see a japanese person do this, I presume the drawing of the system becomes less needed once you get used to it.

No one I always hated mathS.

They count the number of times lines cross eachother. They go left to right, counting diagonally. So 1, 5, 6. Means that top left the lines cross 1 time. middle diagonal they cross a total of 5 times and bottom right cross 6 times.

The numbers represent digits and 1`s, 10`s, 100`s and so on. going from high to low. The 1 represent 100, 5 represent 50 and the 6 representy 6.

If the lines add up to say 12. Then, given the lines location, it represents 12, 120, 1200 and/or so on.

Try to apply it to the slightly larger calculation. It makes sense, in a japanese kind of way.

Its actually from India.as a kid I could use this method before I learned the western method.

My teachers actually graded my work as an F once because even though my answers were correct, I could not show them my working out.

Imagine quantum physics or simple integral methods.

I doubt I would come up with this by my self, but this appears quite "simple".

I got stuck at `5`