How To Multiply Numbers And Algebra Equations By Drawing Lines

[@drakono82]

3:37 "The reason it works..." is never revisited. It works because the concept is identical to the method taught in elementary school. Multiply each digit in one number by all of the digits in the other, line them up by powers of tens, add and carry. Only this method involves drawing a lot of lines and counting, or learning tricks and managing more numbers. I really can see this as being any simpler than learning the multiplication tables up to 9x9.

[@elektra01]

drakono82 in my curriculum we have to learn our multiplication table up to 12x12 by 3rd-4th grade

[@nattaphatpanyasang266]

That's normal curriculum. At least, at my place.

[@Anklejbiter]

I was gonna say. Seems quite similar to lattice multiplication

[@Chalisque]

The difference is that using digits and multiplication tables for single digits saves you from having to count a large number of intersections as you might have if you use this method for e.g. 78*89 -- basically if you speed this lines method up by learning that when 7 lines meets 8 lines then there are 56 intersection points, rather than counting them, you get our current elementary school method.

[@crochetmom5]

I am older (55) and we didn't have calculators when I was in elem. school in the 60s in England. When we did get them we were NOT allowed to use them, we actually had to develop brain cells, memorize times tables, and figure things out on paper, so I love this! I am a visual learner and math rarely made sense to me... except for geometry which was drawing!. This is wonderful... thank you for taking the time to share it and help me keep my brain active!

[@aka5]

math isn't all about arithmetic. That's just a very tiny part, that's overblown by the population since it's as far as most people get.

[@Madpencildust22]

The schools here in the US are very sad....kids don't learn without a calculator

[@salumtummundi9462]

Well us we didn't have calcu in elem and it was easy.

[@MindYourDecisions]

Someone asked how to do 59x98 using this method. You have to be clever to avoid drawing a lot of lines. Here is an illustration with an explanation: imgur.com/KuU4IY0

[@Alexrose12345678910]

Or you go: 59 x 98 ------ 472 5310 ------- 5782 Which takes, what, 20 seconds?

[@JavMuyx]

Alexrose12345678910 That's what i was thinking the throughout the whole vid. It's faster to just actually do the math.

[@Alexrose12345678910]

Rudy Vang Yep, it's literally primary school maths, I don't understand why you would sit around drawing a tonne of lines, and then on top of that you STILL have to carry the numbers and do the addition at the end of it. Completely pointless. Every 8 year old is taught long multiplication, if you don't know it, don't do this shit, just learn how to do it, it's basic.

[@bridgecross]

Rudy Vang Agreed it's faster to do the math. You might want to show this method at the elementary school level, so kids can visualize what's going on with the multiplication.

[@osamu_90]

Alexrose12345678910 This is just how some groups of people do their math *long* ago. It's just a neat trivia to know, but no one in their right mind would use this over the basic modern calculation method and I believe the uploader knows that as well.

[@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): en.wikipedia.org/wiki/Multiplication_algorithm 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 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 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: kzbin.info/www/bejne/l17IaZmwpttmeac Original video Metacafe www.metacafe.com/watch/296904/easy_graphical_multiplication_trick/ Akahad

[@simonlevett4776]

Who cares about cr*ppy wikipedia.

[@weaveroll]

This is absoluty mindblowing for me. Ive always had a really Hard time doing math and this technique and the way you present it was a real eye opener. I thank you sir!

[@truejustice2012]

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

[@chinmoypal3397]

Fantastic

[@colerobison6916]

I'm curious- could you multiply 3 numbers together using planes in a 3 dimensional space? The first two planes are perpendicular like your lines, and then the third plane would lie perpendicular to those as well-like 3 sides of a cube. I'm gonna try it out. I expect finding out how to group the dots will be difficult in 3D space.

[@ukayy002]

Got any clue? Im working on it so just want to know if u have found something.

[@globnomulous]

Couldn't you multiply two of the three numbers and then multiply the product and the third?

[@ukayy002]

@@globnomulous i thought of that but its boring. Bringing up a 3d can be fun + will help in understanding 4d shapes as well

[@manguy01]

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

[@nargarex2390]

Everybody gangsta till variables appear

[@rykerduquette6783]

It's easy to draw a distinct line to represent 5. This way when counting the connecting dots, it saves time not only with drawing lines, but counting in 5s is simple and fast

[@VENOM-tx6gp]

@@rykerduquette6783 just like abacus!it made it easy

[@ThatTacoBoi]

The answer is 51,552 ( fifty one thousand five hundred and fifty two)

[@d.-_-.b]

You're right, though I managed it on the back of a napkin using a wavy line to represent 5 lines: 2, 22, 82, 128, 72 then 2+2 is 4, 2+8 is 10, 2+12 is 14,8+7 is 15, 2 then 4+1 is 5, 0+1 is 1, 4+1 is 5, 5, 2 = 51552

[@copsnrobed]

this man is single handedly teaching me more math than i have ever learned in my entire 14 years of being on this earth.

[@ERMSlNDE]

That would be great ten years ago.

[@zilla-king5647]

I my condolence.

[@thekohzyfam4499]

It would 8

[@pranjalpathak4498]

Your comment is 10 years ago

[@TiagoSilva-sd7yr]

Getting old 😁

[@pranjalpathak4498]

@@TiagoSilva-sd7yr woah.. You both have same display picture

[@swapnil3060]

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...

[@Thuyngle]

The method becomes cumbersome when involving digits higher than 5. To alleviate , may I suggest that we identify the line by the digit it represents. For example for 29x19 we draw the first line and identify it by 2, then further away another line calling it 9, then we draw the cross lines and do the same for 19 , then using basic table of multiplication to count the points in each grouping, for example when 2 crosses 9 we count 18, when 9 cross 9 we count 81 etc. But then I realize that it's basically the traditional method but presented in a visual way. In the end the traditional method is neater and take less space!

[@artgoddess50]

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.

[@kkbmath007]

kzbin.info/www/bejne/j5C1kn-JfpieapY

[@Keiththegoober]

You retired now?

[@smallpcgaming7279]

@@Keiththegoober lmao

[@SleepStarvedNerd]

For all the negative comments, I would just like to say that I personally don't get math at all. My mind kind of just shuts down with anything over basic addition, especially when you start putting letters into an equation. I lean way more toward grammar, literature, biology, and art. This method actually gave me a little bit of hope for being able to do math. I would just like to say thank you.

[@KrishnabrodDWD]

This is brilliant method for me and my students Salute for you sir

[@hrvad]

Thanks - awesome video. Tried it out and it really works. Then my daughter age 11 came home and I ask her if she wants to see something cool? Just two two-digit numbers... She then picked 43 and 54 ... took a sec to get the carrying to work. Of course, kids being kids, she just dryly commented: "I should have asked you to do it on 99 x 99" :)

[@kryptonaut_]

Why the hell wasn't I taught this in school? Damn this could've helped me in soooo many situations...

[@Slinx92OLD]

because teachers are bad

[@ALIXXMUSIC]

Because the American School system has failed all of us for generations

[@thastayapongsak4422]

This line multiplication, is just a graphical interpretation of the numerical method taught in school.

[@danburch9989]

"Show how how you got your answer" as the teacher would say. This would turn the teacher's brain into jell-o.

[@brittanyofferman5581]

I'm the type of person who would love this method, granted that I could figure it out with larger 4 digits multiplied by 3 digit numbers. Can you help me figure out the groupings for 1234 X 333? This method would really help me out if I could just figure out the groupings.

[@priyankag1145]

I know it's late, thought this might help someone. Just have to add a zero line at the beginning for the second number and do the mapping as we would for four digit numbers. I tried and it works.

[@rathore9980]

@@priyankag1145 i know it's late... Though it helped me :) Thanks

[@priyankag1145]

@@rathore9980 I'm glad that it helped! :)

[@ancillareshma3979]

Oki lol

[@agnidiptahomroy8656]

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

[@souljaboytellem4474]

How do you determine the sections? That is the only part that bemuses me. By the way, thank you, MindYourDecisions for this neat video!

[@jasonhendrick1271]

Cut triangles that point left and right out of your math square. Make sure to include all dots around the triangle and adjust it's border accordingly. Using a curved line helps the sections stand out from the math lines. I hope this helps!

[@ErikBoesen]

This is the most brilliant thing I've ever heard of. Thanks ***** for showing me!

[@ErikBoesen]

I think you were wondering about this, KENNETH UDUT.

[@BrandonLaDuke]

You're welcome. :)

[@KENNETHUDUT]

***** Erik Boesen Oh! Chinese stick! jwilson.coe.uga.edu/EMAT6680Fa2012/Faircloth/Essay1alf/ChineseStickMultiplication.html yes - it's awesome! They have a few really neat tricks they use in China.

[@1.allantan785]

May not be easy for very big numbers, but the idea is very very good and interesting. If u invented it, then I will say u are a genius.

[@alexandery8508]

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

[@TechnoAtHeart]

What if in the algebra example it was a negative? (x-2y)(x-3y)

[@marygracepascua9966]

Ikr

[@Liam-bx5no]

Id imagine it would be the same answer but instead with negative in front so. X² -5xy -6y²

[@mithunanaik5284]

@@Liam-bx5no x^2-5xy + 6y^2

[@krazystacy84]

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

[@ChuckBakerc]

I appreciate bringing the algebraic expression example at the end, but how would you keep negative/positive straight in an expression that was not all positive coefficients?

[@OzventureTime]

WHHHYYY DID WE NOT LEARN THIS IN SCHOOL!?!? This is amazing mate, impressive stuff!

[@4YUNZ]

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

[@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.

[@BurrritoYT]

how was this not invented 3000 years ago

[@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!

[@oscarmendez4825]

Thank you so much I'm going to show this to my friends you don't know how much I needed this.

[@ooloncolluphid7904]

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

[@Arcterion]

So as a highschool dropout I've never really touched algebra, but with this method I'm actually kinda understanding it... Nifty! :D

[@tokyg795]

Also how do u decide where to group the curve lines to decide where to count

[@gamerofclashofclans8732]

Isne tho dear sir ka chaappa hai...dear sir ne bhi asse hi bataya hai..achhe dung se...

[@KrystalNCMA]

I truly wish that I had learned this while I was still in school. Would've been so helpful.

[@corvo_queso]

Thanks for showing this method, I usually do multiplications quite slow but this method looks like can speed it up massively.

[@victorvalenzuela7626]

+Corvo “Cheese Puffington” Conors what if the last digits are 9 or 8? damn! it gets very annoying to do it this way.

[@corvo_queso]

+Victor Valenzuela You will have to draw 9/8 lines but at least it gives you a result.

[@JnaArt]

How do you measure or decide to group the connecting dots between crossed lines to get number for answer? I can see you do it grouping dots "vertically" but the curved line dunirg example doesn't clarify it to me. How about dots connecting in-between groups? Most lines be at 45° angle? Thank you for sharing this method & im looking foward to be clarify from my doubt.

[@mikeyoung3870]

I’m wondering is the spacing of the lines because of the base 10? Could we do something similar with base 2?

[@mowafaqakkawi5066]

this man is a genius You earned a sub buddy keep it up

[@teresamuriel8676]

This is genius!

[@MrSidhujatt11]

thanks for slowing down process of multiplication.

[@want-diversecontent3887]

Just lattice it. Lattice method, not this one.

[@asifali4698]

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 ☺️

[@uxuaecheverria1523]

does this only work for symmetric (or equal in positions) numbers ? such as : 123 x 234 , how do you make groups with numbers such as : 2543 x 231 ?

[@imba.hjaltalin]

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...

[@adityaprasaddhal2462]

can u please explain this trick

[@hamiltonianpathondodecahed5236]

@@adityaprasaddhal2462 it is only an application of distributive property

[@HeavenlyEx]

Its awesome and very usefull for my faculty exams where calculator is prohibited

[@mach037]

It is much slower with large numbers than learning multiplication tables.

[@mrmike198619861986]

i wonder what kind of faculty is this.. where a simple elementary math require u to draw !!!!

[@HeavenlyEx]

Abakos calculator in prohibited in non mathematical subjects like electromagnetism, elecrical circuits, control and systems etc. The point is, sometimes you start solving a problem using a non usual or alternate method and that makes you work with high and difficult numbers. Thats where this way of doing maths is usefull

[@maxbored]

Very good system as long as you are multiplying numbers that start with 1 or have 1 in them. 37 X 53 makes a mess and it's actually faster by the old method.

[@EnchantedAmbienceSoundscapes]

That is so cool! Nice for those of us who are visual thinkers.

[@randomguy8461]

Does this work with a three digit number times a two digit number?

[@JohnLee-me3vg]

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

[@fotoldyify]

I love this method. It takes the memorizing out of multiplication. Wish they taught this when I was growing up.

[@Chalisque]

Try this method to multiply 78*89 and you'll soon see the point of memorizing the multiplication table for single digits.

[@jerryeubanks491]

Been 10 years since you put this out so I don't know if you'll ever see this comment my only question is when you got out to timestamp 1 52 is there a trick where you draw your arcs when you multiply two digits by two digits you had two parts but when you did three digits by three digits you had four arcs is there a trick to it and how many arcs would there be if you had a two-digit time of three-digit I don't know and I liked your factoring out at the end

[@javedansari-nb2pk]

But for digits greater than 5, counting lines becomes tedious, is there an easy for them too?

[@kattelinen]

Great! But how does it work with ex. 132*41?

[@JoeJoeTater]

It's interesting how everyone in the comments is debating whether or not this is a practical method for multiplication, when it's really more of a video about a clever application of algebra and geometry.

[@lunoxmain4737]

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 😂

[@mohammadmahidulalamaraf8888]

Is this technique universal? Applicable for all bytes numbers?

[@panagiotischristo]

Is there a dividing method with lines?

[@crislorie3339]

Can you pls show more examples on algebraic expression. Pls

[@minamishail_Tech2024]

I see you are calculating only same length two numbers but what if we have two numbers with different lengths such as 105 X 23 ??

[@seth2kplays547]

In this case you would just put a zero in the hundreds place as a placeholder and ignore the intersections with the “zero line”

[@RichardWadeUK]

A great alternative method... nicely done :)

[@toniokettner4821]

this is not an alternative method. this is just the worse version of the traditional method you learn in elementary school

[@RichardWadeUK]

@@toniokettner4821 Its a good alternative method... I wonder if it will be another 6years before the next comment 🤔

[@deleon7271]

Im In 3rd Grade When Summer Ends And This Will Be Very Useful Thx 😝

[@covalencedust2603]

Does this work for someone hing like (2x+y) (x+3) (y+4)?

[@budosfasz]

how it is working with zero end? like 10x6 or 10x10 we have to count zero....how we know when we need to count zero?

[@alancouto1905]

Nice job! But can you explain me what's the trick on this method? I mean how and why does it work?? Thanks!

[@koopiedoobie1416]

Can this method be used to multiply in Base 6? I got that question on my assignment and I'm not sure how to answer it.

[@gaurangagarwal3243]

Really innovative way of multiplication

[@insuklee5419]

How did you figure out this clever strategy

[@butterybiscuitss277]

How do you know where to section the lines?

[@kaorukokazusumi]

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

[@CareerGoneBad]

We have been trying to use this to multiply 81 x 114 BUT, we can not seem to figure out the correct location to group it correctly to get the exact answer. Can this be used for calculations with mis-matched amount of numerals in the equation?

[@venkatanirmalavemula2]

If there is a minus in between

[@neerajgupta6855]

Kudos............Brilliantly explained... thanks sir

[@david-yt4oo]

I find this trick to be... amazing. but how do you know what to group and what not to?

[@prof.dalmar6989]

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.

[@yahelben-zvi7290]

could you do multiplication with each number having different amount of digits (for example, 8 x 749, or 24 x 954, etc.)?

[@MindYourDecisions]

Yes, this is covered in the book ;) I recommend the paperback because the image formatting is better amzn.to/1vLazID. There is also an eBook version: amzn.to/1ColhXi

[@rickwhite4137]

Just put zeros in front: 008 x 749, or 024 x 954, etc

[@danburch9989]

In school, we were told to show our work (how we got the answer). This would turn the brains of all of my math teachers into jell-o.

[@RB-tt2bw]

How is this handled: (x+3y)(x-5y)?

[@leafs98]

Very interesting video! But why do you divide the lines into 4 areas when multiplying bigger number ( ie. 103 x 221, and 123 x 321)? How do you know when to subtract numbers when multiplying numbers like 59 by 98? How do you know which intersections are for the zero lines? Thank You & Best Regards :-)

[@MindYourDecisions]

To give a shameless plug, everything is explained in my forthcoming book on this topic, so please stay tuned and check it out when it's released! The short answers are: 4 areas = placeholders of 10, the 59x98 was a fun diagram but there's a way without negative numbers, and the zero lines you can mark in another color or with a dashed line.

[@imeemi8850]

I don`t understand how you decide to group the lines?

[@manishanikalje7743]

can use same trik for (x-2y) (x+3y)

[@aymenrajaa]

what about decimals (45.5*13.7)? it possible with this method? if yes would you please demonstrate? thanks

[@scdividad6312]

this isn't really the answer, but you could just use this method with 455*137 and put in the decimal two spaces from the right.

[@guerreroin]

hey, what happens if you need to multiply only with one digit, f.e. 9x9. I think it need another method. Thanks

[@farche2]

***** Make sure you don't miscount.

[@ismailhehehe]

Just learned a new way to maintain my swag Expect atleast 1k likes

[@sonicbrewonline]

99 x 99, I can do this the old fashioned long way in about 10 secs. After 10 mins of trying it with lines I gave up. Is there a way to get it to work using the line method?

[@Lisa42002]

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

[@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

[@proximityclockworkx1572]

Does this work for this 6,78*4,98?

[@seatbelttruck]

This is interesting. I'll have to play around with it. It sounds like a good way to check work, if nothing else. Doing a problem two different ways can help a lot. Where to draw the lines is a tad confusing, though.

[@SerenityLoman]

Can you divide using lines?

[@noraidasua4546]

how do u know where to put the curved line

[@lacraysha1]

How do you know where to draw your lines?

[@sheikhabrahim3463]

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.

[@BananaKing.]

Amazing ! luv it ! How about numbers that are not whole? i mean 123.3x101.7 ?

[@the_real_amir_shady]

it would work for that too. just imagine you kept drawing lines after the line which represents units. it gets much harder in my opinion for larger multiplications, but a fun trick nonetheless.

[@tabibmohameddhia1659]

123.3x101.7=(1233x1017)/100

[@JoeGP]

Dhia Tabib isn't that divided by 10 ?

[@JoeGP]

***** you're right, i shouldn't do math at 1 AM any more

[@Psylent]

Ignore the decimals until you get your answer. Then follow math laws and an appropriate number of decimals at the end

[@mehakmalhotra6397]

I love you trick. But how do you know that how many groups you have to make:O Can u plz tell me

[@christianwacay]

How about if 231 x 564 ? I cant solve if the number is greatest 4 up to 10

[@AdityaSharma-qi8nu]

This only works neatly for some small examples, I can't see how this is in anyway easier than the regular technique.

[@rasheedbankole3615]

can you please demonstrate 25x4 for me. Thanks.

[@GregorianMG]

I just found this and this absolute method!!! I will use it and thanks to upload it!!!

[@christianpintado4464]

Wow i didn't know you can do that, never seen that before. I want to learn to try that!