Hi this is Presh Talwalkar and today I am going to explain a math trick of how you can multiply numbers just by

drawing lines. Let’s say you want to multiply 12 by 13 For this one we will draw one line and for the two we will leave a little bit of space and we will draw two lines. For the other number, we will draw lines in the other direction. Now we will group together different lines and we will count the dots. Here we have six different dots. In the middle we have five different dots. And on the other side we have one dot. And that’s the answer 156. We will do another example. For 15 by 21, we start out by drawing one line. Then we’ll leave a little bit space and draw five lines. For the other number we draw lines in the other direction. We draw two lines here and one line here. We will again group the different lines Here we have five dots. In the middle we have eleven dots. And the other end we have two dots. We will need to make one adjustment

because we have 11. We will need to carry this one over which will make 3. And our answer is 315. We can even do this for bigger numbers. For 123 we start out with one line and with some space two lines. And with some more space three lines. And we draw the other lines for the other number in the other direction. We again group the lines. We have three dots here, eight dots here, fourteen, eight, and three. Once again we’re going to have to carry

this one over (from the 14). So that’s our answer. It’ll be 39,483. You can even use this trick when a number includes 0. But one thing is when you draw this line

you should still draw the line, but put it in a different color or different

marking. And the trick will be that we don’t count any of the dots for that line So when we make the grouping, we have three dots here. For the second arrangement, we’re only going to count the dots for

the non-zero lines. So we have six dots here. We don’t

count any of the intersections for the zero line. In the middle, we again ignore the zero line, which makes seven. Here we have two dots. And two dots here. So you can even use this method when you have a number that includes zero. The reason it works is you can even use it

for algebraic equations. Let’s say you have x plus 2y times x plus 3y. We will draw one line for the x, and we will draw two lines for the 2y

and we will draw the lines in blue. We will put all the x lines in black and all the y lines in blue. The other number we draw the lines in the other direction And again we make groupings. So here we have six dots and because both of the lines are blue that means it’s y-squared. In the middle we have five dots, and these are the intersections of a black and blue line, which means it will be an x and a y. On the end we just have one dot and

that’s for two black lines so it’s x-squared. So that’s the answer. I hope you enjoyed this trick. Please subscribe to my channel. I make videos on math and game theory. You can follow me on Twitter @preshtalwalkar, and get my ebooks on Amazon.com

## 100 thoughts on “How To Multiply Numbers And Algebra Equations By Drawing Lines”

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!

How did you figure out this clever strategy

How do you doย 'completing ย the square' usingย these 'tricks'? I have to teach this concept of completing the square and is somewhat tuff for the students I'm currently teaching. Hence, I really need your help. Thanks and keep up the good work.

27×98 anyone ?

how do u group the lines

excellent

this is vedic maths great india

best explanation ๐๐๐

that's brilliant

Fascinating! I'm going to start using this trick with shop math. I'm always closer to a pencil than a calculator! Thank you!

This is dumb. Instead of memorizing 5×7 = 35, you're counting the 35 elements in a 5×7 grid. The addition step is also counting. This method is incredibly slow.

Kudos…………Brilliantly explained… thanks sir

What about when we want to multiply 123 x 21??? Please Ans

For numbers in the teens and twenties, it's an interesting trick. However, I must be doing something VERY wrong because it most definitely doesn't work (for me!) with larger numbers. Maybe I'm not correctly walling off each set of intersections from the others. Math tricks generally haven't worked for me; I'd rather just do the math than try to retain so-called tricks.Where the trick IS the method for solving, such as using FOIL, I tend to do fine. The line thing, the finger multiplication trick, and lots of others waste more time (for me) than they could possibly save.

123ร12=?

Who the hell came up with this?! Awesome!!!

FUCK ME why do i see this only now

I tried doing 46ร78 but I couldn't figure out why I was wrong. my answer was 35455 and the actual answer was 3588

When there're 3 sets of numbers in a multiplication, you'll need to draw a cube

Presh Talwalkar, you have a very unusual name. What is your ethnic background or the origin of your name?

You are too smart ๐

its not helpful

I'm curious as an American do people who have learned this way think about math in more of a physical form?

This trick is super awesome ..it can be helpful for those who needs a easy trick to solve any problem in math.. Just like me whose having a hard time to solve any math problem

Amazing

Omg your the best yet, the other videos are so confusing, I was like "you know what forget it"

Just kidding, I don't get it, you said the middle was five, how is I think five I don't see any dots, think smarter and put dots

Ok, I'm really confused, your got 14 when it was 9, and in the middle you said there was five when I saw no dots

OH PFFFFFFT I GET IT LOL thanks ;-;

I don't get it

ๅพๆ่ถฃ็ๆนๆณ๏ผไฝๆฏไธ็ฌฆๅๅๅ่ฟ็ฎไบคๆขๅพ๏ผๆ็น็ฉ้ต็ๆๆไบ

Awsome content.

Best Ever….my mind is blown…thank you for sharing…I am gonna show my kids this trick!!!

Excellent maths trick, mind blown, however I bet you can't answer why the hell majority of tertiary education in Western countries haven't adopted this into the studies of they're curriculum… Unbelievable! Evident the powers that be only want you to know "just" enough to complete your selected occupation out of predetermined roles aka the "*world of potential" that's paraded infront of you as if it is the be all and end all when you approach university

Itโs cool but also just a waste of time and space

Wtf Iโm so mad nobody never taught me this

please not use this stupid way. it is slow and illogical. ! please use chinese way : http://www.mers.hk/resource/bulletin/content/96/images/8.2.jpg

this video will make a clever students to be a stupid one. it really do not make sense at all ! also waste the time to draw the line , then to count the dots, it totally waste the time ! please see how chinese calculate. this mutiple, a 10 years old chinese child can get the result in 20s. this is chinese way : http://www.mers.hk/resource/bulletin/content/96/images/8.2.jpg

this is chinese calculate devide way : http://chowkafat.net/Picture/calculation6.jpg

Omg I'm like a math idiot all my life! Specially with multiplications! This is the first time maths actually made sense to me because it's all visual! Why didn't they teach this method in primary school here in Germany? Ever time we had a maths teacher we had to learn new ways of calculating and then I just gave up and concentrated more on art and biology

How do you know where to draw your lines?

This is called Chinese multiplication

I am only 11 and i understand it is so easy

This trick is absolutely outstanding, hats off. Perfectly explained.

I tried for 16×25 and could not get the result of 400

What am I missing ?

Really innovative way of multiplication

Is this Chinese

You explains very good sir, I am a teacher and I like the way you explains everything slowly…

thanks for being such a great inspiration for me…

Sir how can i contact you personally ?

Any limitations??

So awesome

Very nice techniques

Good trick

Great

i didnt ask for this video

I dont know why have dislike

Sir how to multiply 123 with 144. Please send me the solution.

I love these tricks…

Thank you very much sir.You are greatIn grouping together different lines, I wrongly group lines, plz tell more detail for grouping lines

Awsome alternative way for multiply .

u know what,

THE SCHOOL SYSTEM IS BROKEN!!!!!____+____=56.7

try 9987 x 7887

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.

I did this for school it helped

It's vedic maths that I have learned when I was 10

So what if it's 34ร18?

I end up with 3 ) 20 ( 32.

How does that workout to 612?

I hope somebody answers this because it's driving me nuts.

I think this way of multiplying comes from the Mayans

Wow

You are a legend

Thanks for the video……..

Thankful to u ๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐๐

Thatโs really cool Iโll have to try using it in my brain sometime

How if multiplication like 100ร20?

What is the representation of "0"?

This method chocked me when i found out that it really works. Thank you!

Let it's be

ab ร cd

Now

acร100 + (bc+ad)ร10 + bd

And here's the answer

35 ร 28

acร100 + (bc+ad)ร10 + bd

3ร2ร100 + (2ร5 + 3ร8)ร10 + 5ร8

600+340+40

980 โบ๏ธ

Or you can just calculate it normally

I searched in utube:

How was i born

Thats not, how i was borned

not understand in algebraic multiplication

Mulply number by drawing dots now..

Very good

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):

https://en.wikipedia.org/wiki/Multiplication_algorithm

https://en.wikipedia.org/wiki/Lattice_multiplication

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

https://www.amazon.com/gp/product/B00N85DCTU

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

https://math.stackexchange.com/questions/877120/what-is-the-origin-of-how-the-japanese-multiply-line-multiplication

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)!?"

From ViHart video: https://youtu.be/a-e8fzqv3CE

Original video Metacafe

http://www.metacafe.com/watch/296904/easy_graphical_multiplication_trick/

Akahad

Is there a dividing method with lines?

WoW… That's all I have to say… WOW

Nice video

Mind blown

Cool but the hard part 8s doin this at ur head

Sir can you please tell your email id

Tq brother I'm from india

Calculate 100*300

how to calculate 324 * 27 please tell us

If there is a minus in between

How to calculate 98ร99

Spece com down process,

Where did he get his inspired??

Easy

superrr

this is very easy tricks for multiplication so thank u sir…

When I was multiplying with the three number, I was confused that two lines are to be fixed, just like you said, but if you want to apply the lines of the third figure, and where to put the dots.plz make video of three lines multiply . I was confused in this question . . . . . . 16 m 16 m 16

How can we say this is correct. How can we say this is correct

thank you,sir!!