We all know that there’s a stereotype that people of Asian descent are better at maths. We also know it’s not necessarily true, but, of course, stereotypes are born from at least a seed of truth. Perhaps there is a reason that this seed exists: the Japanese, at least, have more awesome ways of figuring out multiplication.

The picture above doesn’t really make much sense on first glance, but when you find out how it works – your mind will be blown.

Basically, you take your first number and draw a group of lines corresponding to each number parallel to each other – so if it’s 21, for example, you draw a group of two lines and then further along, but still parallel, you draw one line. Then you take the second number and do the same thing, but crossing the other group. You then count up the intersections in each group and voila – you get your answer.

Here’s a nifty video that shows you how it works – and how it works for higher numbers as well.

This is way better than the long multiplication I was taught in high school. And University. Now can we make this work for division?

[Via Mad Ryan]

http://www.youtube.com/watch?v=a-e8fzqv3CE&list=UUOGeU-1Fig3rrDjhm9Zs_wg&index=40

It’s just a visual binomial expansion. I still think it’s not a good way to learn multiplication. For instance, it breaks down (to my thinking) for 3 digit numbers.

Yeah, looks good with numbers smaller than 4. Try multiplying 78 x 969 this way.

Becomes a bit tougher when numbers have higher digits. Think of 89 x 98. You’d be counting 72 intersections or learning your 10x tables first. Zeros also require you to keep track of columns.

Having said that, at higher numbers the method approaches the way we learn multiplication and is a good way to visualise the maths.

if you like number puzzles like sudoku – using this method to deduce a division could be a real challenge!

After a certain threshold just switch to http://en.wikipedia.org/wiki/Lattice_multiplication

This isn’t just the way Japanese kids learn, I have also been taught in this way at my school in England. It’s a great way of doing multiplication, and once you start using the technique for a while, you can visualise the lines without needing to draw them.

You didn’t learn how to multiply until high school? We started multiplying double and triple digit numbers in 4th grade. (I assume the writer learned this in elementary school as well, I just couldn’t help but react to the sentence “This is way better than the long multiplication I was taught in high school.”)

I wouldn’t have noticed it if jachim hadn’t pointed it out, but it IS just a visual representation of binomial expansion. I do remember realizing that the FOIL method worked for numbers and having my mind momentarily blown, before realizing of course it does or it wouldn’t work for algebraic expressions.

Using FOIL:

13 x 12 = (10 + 3)(10 + 2)

= First (10*10) + Outer (10*2) + Inner (3*10) + Last (3*2)

= 100 + 20 + 30 + 6 = 156.

This isn’t a good way to learn though as it skips over a fair few basics that are required for understanding what is going on.

This is simply a nicely visualised method of solving (Ax+By)*(Cx+Dy)=ACx^2+(AD+BC)xy+BDy^2 where x=10 and y=1 (so x^2 = 100, xy=10 and y^2 = 100) and I really can’t see the benefits of skipping over the stages between single digit times tables and solving algebraic equations.

Still I think that standard methids are faster, than counting dots.