How To Multiply Numbers And Algebra Equations By Drawing Lines

Some people say this is "how the Japanese multiply." Others say this is "Vedic Math." I'm not sure of the origin, but this is a visual way to multiply two numbers and it does work. The video also shows how to use the same method to multiply algebraic expressions like (x + 2)(x + 3).

I've made a few follow-up videos you might like.

Multiply by lines (advanced examples)

Multiply by lines (why it works)

Multiply by lines (the rotation trick)

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[manguy]

Cool visualization, but it gets ugly with numbers like 288 x 179

[truejustice]

This is how Japanese youngsters learn to multiply in school. Thanks for sharing, whomever you are.

[artgoddess]

Nice.  Although I'm an art teacher, I'll share this with my younger students.  I think I may even make it into an art project somehow.  Very cool.

[MindYourDecisions]

1. From my extensive research, line multiplication dates to Nov 16th 2006 from a Chinese teacher (see links below). If you know of an earlier source, please let us all know with proper proof.

2. To people who say this method is well-known, so why isn't line multiplication mentioned on Wikipedia? It's really, really important that research meet certain standards to be part of academic literature. I would love to see the history of the method, and its uses, as part of the multiplication algorithm--just like lattice multiplication is listed as a method. I think line multiplication merits an entry and mention, but the active community of Wikipedia can let be the experts. These are the closest examples of pages where I think the method could be mentioned (or have its own page too):



3. To my knowledge, I am the only person's who has published this method in a book Multiply Numbers By Drawing Lines

Of course I'm interested in other sources. I've been searching for 5 years and no one has yet sent me anything.

Sources for 1
What is the origin of line multiplication? Math StackExchange post authored by me July 2014

Bill Hart:
"Vi, you might be interested to know this method seems to have originated with a school teacher in China. It was first taught to a school girl in China. She taught it to her boyfriend, Akahad, who made a video on MetaCafe on Nov 16th 2006. Akahad was criticised for the fact that it is inefficient for numbers with large digits. However he claimed it was not intended to be an actually efficient method, but only "meant to be a little trick to show to friends and kids who hate maths". The video was so popular it made $2000 in 4 days. The school teacher who introduced it apparently did so to get kids interested in maths and the criss-cross pattern was used because it reminded the school children of the stools they sat on. It is commonly referred to as the Vedic or Mayan or Japanese method. But perhaps we should be calling it a Chinese method (though there are other Chinese methods perhaps more worthy of the appellation)!?"

Original video Metacafe
Akahad

[MsHojat]

This is really good. I wish I was taught this much earlier. I never really had any significant problem with math except for as a kid memorizing my multiplication table or doing math quickly though, but still *It really helps to visualize things*, and probably would have helped to learn quicker.
I feel like it would be really useful tool to figure out shortcuts or tricks, or possibly to figure out mental math techniques.

 It also makes it unnecessary (*in a sense*) to even have had to ever memorize any multiplication table, since this method uses only addition (although one still kind of needs to recognize simple multiplications such as 4x3 grids, or if one used a line to represent 5 lines, what multiples of 5 are).

I guess I wasn't taught it because seemingly it wasn't even known or widely-known at the time? It seems absurd to me that people wouldn't have figured this out like 1000 years ago though. Hell, I feel like it'd be guaranteed that I would have figured this out if I spent my life working on silly math tricks rather than other things.

[asifali]

Let it's be
ab × cd
Now
ac×100 + (bc+ad)×10 + bd
And here's the answer

35 × 28
ac×100 + (bc+ad)×10 + bd
3×2×100 + (2×5 + 3×8)×10 + 5×8
600+340+40
980 ☺️

[carrieandglenn]

I wonder what kind of tool could be used to do this. Kinda like rekenreks, etc. I think this is a great way to visually see the problem and fun!

[prof.dalmar]

Grt thanks sir am mathematician mostly focus in differential geometry and number theory thanks again i wish to contribute new theorems in math may within 2-3 years because iwas doing research in some un solved math problems.

Thanks.

[faljap]

This is nice and works if you are using numbers such as 1, 2, or 3, or even 5, like in the video.
Try to use this trick for 548 x 96 and you´ll see it´s nightmarish.

[Grimmysiw]

This is great. Prefer this over the Common Core Math that is being pushed.

Wish I would of learned this when I was young

[currysteph]

cool...i'll show my class this tomorrow

[IT-zxjc]

This looked really good until I realized how much slower in fact it is. The classical western method is much easier and with less risk of making a visual mistake, as in counting the dots wrong or making a wrong number of lines (I did that myself). Plus learning to use you mind is better for the easier ones, like the first one (12 x 13) you can just do 10 times 13=130 and then add 2:13=26 in your head and not bother writing it up, better yet we should know 12 x 12 is 144 and then plus 12...

[kaorukokazusumi]

Math is now way easier for me because of u thank u very much

[lunoxmain]

I lab it soooo matcha 🍵 😋 many thanks you so mucho haha






Geez it was so simple this whole time and I'm stressing myself for nothing 😂

[RichardtRadekLarsen]

If you dont have different colors of pen, make the 0-line a oval instead. 
Also works for x and y problems.

[terry]

this makes more sense than common core...

[lima]

Muito bom,  raciocinio de forma organizada.

[JohnLee-mevg]

Could you make a video explaining the mathematics behind why this works??

[molaybiswas]

At first, I reckoned you are Indian: thought I heard your name, Paresh:D. So, watched the video with helluava elation n' enthusiasm. Having finished, when I read the description, the silly disappointment of you not being an Indian was offset by the awe at the true prodigy out here.

[cverde]

First time I saw algebraic equations solved this way🤯