How To Multiply Numbers And Algebra Equations By Drawing Lines

How To Multiply Numbers And Algebra Equations By Drawing Lines

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

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

  1. does not work!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!I got a 0% on my test and a failed my grade,thanks a lot!!!!!!!!!!!: (it is your falt that i failed not mine!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  2. 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.


  3. 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!

  4. How do you do 'completing  the square' using 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.

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

  6. 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.

  7. 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.

  8. I tried doing 46×78 but I couldn't figure out why I was wrong. my answer was 35455 and the actual answer was 3588

  9. This trick is super awesome 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

  10. 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

  11. 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

  12. please not use this stupid way. it is slow and illogical. ! please use chinese way :

  13. 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 :

  14. 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

  15. 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…

  16. 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.

  17. So what if it's 34×18?
    I end up with 3 ) 20 ( 32.
    How does that workout to 612?
    I hope somebody answers this because it's driving me nuts.

  18. You are a legend
    Thanks for the video……..
    Thankful to u 👍👍👍👍👍👍👍😇😇😇😇😇😇😇😊😊😊😊😊😊

  19. Let it's be
    ab × cd
    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
    980 ☺️

  20. 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)!?"

    From ViHart video:

    Original video Metacafe


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