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 Amazon.com

99 comments

  • diego ricardo

    uhs pues la verdad no entiendo mucho por el idioma pero excelente técnica

    Reply
  • lisa muslimah

    thank you soooo much I can't wait to tell my teacher what i found out

    Reply
  • aung oo

    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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    Reply
  • Adithya Krishnan

    wow this works

    Reply
  • xtine u

    how about if the zero is the last digit, let's say 320×412?

    Reply
  • 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.

    Reply
  • CL H

    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!

    Reply
  • InSuk LEE

    How did you figure out this clever strategy

    Reply
  • Sheikh Abrahim

    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.

    Reply
  • Richard Bersaky

    27×98 anyone ?

    Reply
  • ABK MHD

    how do u group the lines

    Reply
  • Hamid S

    excellent

    Reply
  • NS R

    this is vedic maths great india

    Reply
  • vinod kumar

    best explanation ???

    Reply
  • Hector Athan

    that's brilliant

    Reply
  • oolon colluphid

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

    Reply
  • ElectroLlama

    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.

    Reply
  • Neeraj Gupta

    Kudos…………Brilliantly explained… thanks sir

    Reply
  • vishal chavda

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

    Reply
  • angelhelp

    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.

    Reply
  • aniket sagar

    123×12=?

    Reply
  • Eric

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

    Reply
  • Offprestyra

    FUCK ME why do i see this only now

    Reply
  • whattup chiatos

    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

    Reply
  • Ebi Fornale

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

    Reply
  • SoldierSide77

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

    Reply
  • Karolina Czarnecka

    You are too smart 🙂

    Reply
  • Braxtyn Hendricks

    its not helpful

    Reply
  • Mat North

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

    Reply
  • Sophia S

    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

    Reply
  • Waylyn Amolar

    Amazing

    Reply
  • krazystacy84

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

    Reply
  • krazystacy84

    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

    Reply
  • krazystacy84

    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

    Reply
  • krazystacy84

    OH PFFFFFFT I GET IT LOL thanks ;-;

    Reply
  • Kierra Rose8

    I don't get it

    Reply
  • 茅简

    很有趣的方法,但是不符合四则运算交换律,有点矩阵的意思了

    Reply
  • Angel Caban

    Awsome content.

    Reply
  • DeShong Tattoo Studio

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

    Reply
  • Jesse Sinclair

    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

    Reply
  • Thomas Parker

    It’s cool but also just a waste of time and space

    Reply
  • Chloe Hinton

    Wtf I’m so mad nobody never taught me this

    Reply
  • lily lily

    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

    Reply
  • lily lily

    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

    Reply
  • lily lily

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

    Reply
  • Maxine Kristi Morris

    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

    Reply
  • LaCray Francis

    How do you know where to draw your lines?

    Reply
  • Keyli Salazar

    This is called Chinese multiplication

    Reply
  • Sister Rosie

    I am only 11 and i understand it is so easy

    Reply
  • Agnidipta Hom Roy

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

    Reply
  • JoshieFlay's Outdoor's

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

    What am I missing ?

    Reply
  • Gaurang Agarwal

    Really innovative way of multiplication

    Reply
  • Hanna Koriem

    Is this Chinese

    Reply
  • Swapnil

    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…

    Reply
  • Swapnil

    Sir how can i contact you personally ?

    Reply
  • Glad you seen

    Any limitations??

    Reply
  • Ayush Arora

    So awesome

    Reply
  • Prithviraj Patil

    Very nice techniques

    Reply
  • cooking queen

    Good trick

    Reply
  • Kishore Kishore

    Great

    Reply
  • App Arte

    i didnt ask for this video

    Reply
  • SundaloAko PangKalawakan

    I dont know why have dislike

    Reply
  • Oscar Archila

    nice

    Reply
  • srikant nayak

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

    Reply
  • m k dada

    I love these tricks… Thank you very much sir.

    Reply
  • m k dada

    You are great

    Reply
  • Joseph John

    In grouping together different lines, I wrongly group lines, plz tell more detail for grouping lines

    Reply
  • GUPTA SIDDARTH

    Awsome alternative way for multiply .

    Reply
  • Marc Bartolabac

    u know what, THE SCHOOL SYSTEM IS BROKEN!!!!!

    Reply
  • Keon's Corner

    ____+____=56.7

    Reply
  • Papope Mueanpaopong

    try 9987 x 7887

    Reply
  • Molay Biswas

    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.

    Reply
  • Roblock gamer !

    I did this for school it helped

    Reply
  • Indic gamer

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

    Reply
  • EB 3000

    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.

    Reply
  • Trash Bad

    I think this way of multiplying comes from the Mayans

    Reply
  • Sushil Devkota

    Wow

    Reply
  • GAMEPLAY GAMR

    You are a legend
    Thanks for the video……..
    Thankful to u ????????????????????

    Reply
  • Nate Burnside

    That’s really cool I’ll have to try using it in my brain sometime

    Reply
  • Shandy Verdyo

    How if multiplication like 100×20?
    What is the representation of "0"?

    Reply
  • Alexander Y

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

    Reply
  • Asif Ali

    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 ☺️

    Reply
  • Crazy4Hitman

    Or you can just calculate it normally

    Reply
  • JayJay

    I searched in utube:
    How was i born
    Thats not, how i was borned

    Reply
  • Vijay Kumar

    not understand in algebraic multiplication

    Reply
  • 500 subs with only 1 scamming vids challenge

    Mulply number by drawing dots now..

    Reply
  • Vishesh Agrawal

    Very good

    Reply
  • 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):

    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

    Reply
  • Peter Christo

    Is there a dividing method with lines?

    Reply
  • Ange Samuel

    WoW… That's all I have to say… WOW

    Reply
  • Biswajit Dhar

    Nice video

    Reply
  • DarkCube

    Mind blown

    Reply
  • Mary Grace Pascua

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

    Reply
  • Abhishek N

    Sir can you please tell your email id

    Reply
  • Koushik Bannu

    Tq brother I'm from india

    Reply
  • Jeewan Kumar

    Calculate 100*300

    Reply
  • kunal sawant

    how to calculate 324 * 27 please tell us

    Reply
  • Venkata Nirmala Vemula

    If there is a minus in between

    Reply
  • Amit Jadhav

    How to calculate 98×99

    Reply

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