Excellent explanation. This so-called "trick" is just a pictorial representation of exactly how we do multiplication, except it's inefficient and cumbersome. Anyone who thinks otherwise, do something simple like 67 X 88 both ways.
@numbcore That's actually a great idea. A few people have had questions about how to deal with "empty" spaces in the figure, and I think the dotted line would work very nicely as a placeholder.
I thought the base 6 part was the best part of the video, precisely for that reason mentioned, that it is hard to forget your base 10 multiplication facts.
Why don't we use this method to multiply numbers in processors? To the best of my understanding the "mult" function is repeated addition, why not use this configuration of wires and put "and" gates at the junctions and connect the outputs to full adders with the carry out's connected?
@FreshPrinceness The nice thing about this method (or the partial products algorithm, for that matter), is that it makes absolutely no difference where you start. Just pick a place value and count the intersections. The numbers will line up, regardless.
Nice lesson delivery. Really well presented. Its a very weird method. Would be good for some situations but not for others. depends how your brain works. thanks
Nice work, thanks for the clear explanation, this process has interested me for a while. By the way, what did you use in order to create this video? It's gorgeous.
In base 10 arithmetics, all natural numbers can be written as sums of powers of 10. Consider: 21 x 13 = (2*10^1 + 1*10^0) x (1*10^1 + 3*10^0) All those intersections actually represent all the possible products of powers of 10 that can be found in the parentheses. 2 terms in the 1st multiplied by 2 terms in the second, total 4 which is the number of the "corners" of that rectangle. The number of intersections at each corner is the coefficient product. So it appears different but it is not.
@3der3 You'd just put a single line in the hundreds place, just like "100" has a single 1 in the hundreds place. The problem with the visual method is that it lacks a placeholder (like the zeros in 100), so you really have to be careful lining things up.
In fact a combination of values and number of values e.g 2 x 3 H for 2 ones x 3 hundreds where it appears shall make the abstract method become tangible hence more understandable by the new learner.
@MrHn9296 You would just have to leave an empty space where the "zero line" would be, since that multiplication must result in 0 intersections. It's pretty much the same way we deal with that in numerals, except we have this nifty 0 symbol to use as a placeholder. If you want to improve this process, you could invent a placeholder symbol of your own for Vedic multiplication. Actually, that's a pretty good idea.
I think the ten to the power technique at 4min in might just confuse a beginner, seems easier to start right to left with counting up, also mentioning the rotation of the grid would make it clearer about how the alignment of the intersections adds up.
This method is so awesome for small kids but I won't let my son watch you do it. Dude, you made my head swim for a minute there. I know your doing place value but you make it sound sooo much harder than what it is. The point is it's as easy as literally counting dots. Common Core sucks so bad!
And there is also a mistake in base 6 that makes it confusing: The second column does not correspond to 10^1 in base six it corresponds to the 6^1 column, and then the 6²... and so on. So the given answer - which is correct - is equal to: 1133=1*6³+1*6²+3*6+3=(base 10) 216+36+18+3=273
I've had just seen the original video and my comment was they are teaching a trick not a skill, but the way you explain it may help understand the math facts behind the method.
Federico Robledo this. I don't know about other countries but the technique is pretty much exactly how Math was taught in my school (just without the lines which is the same when it comes to calculating using only your head). It's just divide & conquer which is a basic trick to master difficult tasks without much effort.
completely agree. This is only useful if you don't know how to multiply at all and only know how to add. And even then only for relatively small digits (try this with 9879, you'll be drawing and counting all day). If you know simple one-digit calculation, just do what most learn in (western) schools: 123 x 321 = ... 369 _246 __123 ------------- (addition per column, bring "1" of 14 one column left) 39483
I don't know the indian number system but the Japanese number system is founded on this method. Like how we say 1 hundred, 1 thousand, 1 million; they say 1 thousand, 1 ten-thousand, 1 hundred-million; except their words for ten-thousand and hundred-million don't contain the words for ten, hundred, thousand, million; they are their own word/unit. As you can see with this method, as you increase the number of digits being multiplied, the far left unit goes from ones -> tens -> hundreds -> thousands -> ten-thousands -> and a fourth digit would make it hundred-millions which matches up with their number system.
I made it easier by just adding up the cross sections and putting the values in from how they should look... eg 21x 18 = somewhere around 300 and y0u work the digits around there to get 378
Talking about place values may help some kids understand this strategy. I call it hashtag maths as kids are used to # things. Sometimes it is a good way of looking at number relationships.
Vedic multiplication actually comes from India. The Vedas are a very integrals part fo the country's culture, tradition, foundations of religion and also education
I don't necessarily grasp that either (and maybe it is just me) but I do not understand how you divide out each intersection and count "only" those in those intersections? How you set up the intersections and then count them is understood, it is just how you are partioning those out is fuzzy. Thank you
I literally Forgot Maths after Japanese way of multiplication .Lol what's the answer you get If you multiply 39X43 it's 1677 not your weird answer . There are thousand ways and methods to calculate a problem but the solution we get should be same ..
There just wouldn't be any lines there. You'd just know that the huge space you leave is meant to be blank. So, it's be a set of four lines, a large space, and a set of seven lines; and across them at the left side would be a set of three lines.
It is in fact Chinese. The original video on the web was uploaded in Nov 2006. It had been taught to the guy by his Chinese girlfriend. The criss-cross reminded the students of the stools they sat on in class.
I love this. Made perfect sense to me. Everyone learns differently. Some people are more visual. Both methods should be taught in schools so that both kinds of learning can be fully utilized and understood :) This can bring the "fun" back into math for the visual types. Nice work!
Both, for 321 x 123, red and green is still 100's x 1's which = hundreds, and yellow and yellow is still 10's x 10's which is also hundreds. So, it is a combination of both, but still easier than how I learned my multiplications in school. I'm more of a visual learner, so this would have been very helpful to visual learners. And I was pretty good at maths, so this should be really helpful for everyone.
I was messing around with it before i learned anything about it and actually thought up all of these things on my own. I'm quite proud. Lol
Excellent explanation. This so-called "trick" is just a pictorial representation of exactly how we do multiplication, except it's inefficient and cumbersome. Anyone who thinks otherwise, do something simple like 67 X 88 both ways.
Thank you for making this video, I really enjoyed it!
TRANSPARENT, THANK YOU PROF. CHRIS LUSTO.
@numbcore That's actually a great idea. A few people have had questions about how to deal with "empty" spaces in the figure, and I think the dotted line would work very nicely as a placeholder.
That makes so much sense Thank you
Thanks so much - great explanation!
Very clean video, well done!
THIS. IS. BRILLIANT!!
I thought the base 6 part was the best part of the video, precisely for that reason mentioned, that it is hard to forget your base 10 multiplication facts.
This is awesome, should totally use this for any exams/tests I may have....
Its pretty tricky though!
DarkWarrioR Well at first it was to me but, as it went on and the numbers got bigger, I somehow understand how it went XD
Good stuff Chris.
Why don't we use this method to multiply numbers in processors? To the best of my understanding the "mult" function is repeated addition, why not use this configuration of wires and put "and" gates at the junctions and connect the outputs to full adders with the carry out's connected?
@bruinburns13 Thanks. It just uses builds and transitions in Keynote. Nothing fancy.
Thanks, Chris!
thanks for the video!
you explain maths quite clearly, have you considered doing any other videos?
This is awesome! :)
@FreshPrinceness The nice thing about this method (or the partial products algorithm, for that matter), is that it makes absolutely no difference where you start. Just pick a place value and count the intersections. The numbers will line up, regardless.
Great up to the base 6 calculations. That has more potential to confuse than help the matter. It should be taken out to a follow up video.
clever. Thanks for sharing
Thank you for this video
Nice lesson delivery. Really well presented. Its a very weird method. Would be good for some situations but not for others. depends how your brain works. thanks
This is incredible and perfectly explained. Great job
Nice work, thanks for the clear explanation, this process has interested me for a while. By the way, what did you use in order to create this video? It's gorgeous.
In base 10 arithmetics, all natural numbers can be written as sums of powers of 10.
Consider: 21 x 13 = (2*10^1 + 1*10^0) x (1*10^1 + 3*10^0)
All those intersections actually represent all the possible products of powers of 10 that can be found in the parentheses. 2 terms in the 1st multiplied by 2 terms in the second, total 4 which is the number of the "corners" of that rectangle.
The number of intersections at each corner is the coefficient product. So it appears different but it is not.
@3der3 You'd just put a single line in the hundreds place, just like "100" has a single 1 in the hundreds place. The problem with the visual method is that it lacks a placeholder (like the zeros in 100), so you really have to be careful lining things up.
Thanks!
I like the style of that video. Wondering which software has been used to create it...
In fact a combination of values and number of values e.g 2 x 3 H for 2 ones x 3 hundreds where it appears shall make the abstract method become tangible hence more understandable by the new learner.
@MrHn9296 You would just have to leave an empty space where the "zero line" would be, since that multiplication must result in 0 intersections. It's pretty much the same way we deal with that in numerals, except we have this nifty 0 symbol to use as a placeholder. If you want to improve this process, you could invent a placeholder symbol of your own for Vedic multiplication. Actually, that's a pretty good idea.
Nice Job dude
just wow ,amazing so much easier this way
should do a side by side comparison between that method and the normal method
I think the ten to the power technique at 4min in might just confuse a beginner, seems easier to start right to left with counting up, also mentioning the rotation of the grid would make it clearer about how the alignment of the intersections adds up.
This method is so awesome for small kids but I won't let my son watch you do it. Dude, you made my head swim for a minute there. I know your doing place value but you make it sound sooo much harder than what it is. The point is it's as easy as literally counting dots. Common Core sucks so bad!
Wow. You took something really simple and made it really complex for no reason. Great method but it's over explained.
+TheRainbowDragoness Knowing what to do versus know WHY to do something. I will choose knowing WHY.
It can, just add a zero before 2 (02) to multiply is by ten, and use numbcore's idea to place a dotted line to represent the zero.
Is it a copy of "Vedic Mathematics - Ancient Indian Mathematics" in You Tube"?
Makes much more sense now.
Geweldig!
this is good!!!
And there is also a mistake in base 6 that makes it confusing: The second column does not correspond to 10^1 in base six it corresponds to the 6^1 column, and then the 6²... and so on. So the given answer - which is correct - is equal to: 1133=1*6³+1*6²+3*6+3=(base 10) 216+36+18+3=273
I've had just seen the original video and my comment was they are teaching a trick not a skill, but the way you explain it may help understand the math facts behind the method.
Federico Robledo this. I don't know about other countries but the technique is pretty much exactly how Math was taught in my school (just without the lines which is the same when it comes to calculating using only your head). It's just divide & conquer which is a basic trick to master difficult tasks without much effort.
THIS makes sense to me...
completely agree. This is only useful if you don't know how to multiply at all and only know how to add. And even then only for relatively small digits (try this with 9879, you'll be drawing and counting all day).
If you know simple one-digit calculation, just do what most learn in (western) schools:
123 x 321 = ...
369
_246
__123
------------- (addition per column, bring "1" of 14 one column left)
39483
that's nice and easy with small number digits... try it with a couple of 7, 8 or 9 and you'll count forever
I don't know the indian number system but the Japanese number system is founded on this method. Like how we say 1 hundred, 1 thousand, 1 million; they say 1 thousand, 1 ten-thousand, 1 hundred-million; except their words for ten-thousand and hundred-million don't contain the words for ten, hundred, thousand, million; they are their own word/unit. As you can see with this method, as you increase the number of digits being multiplied, the far left unit goes from ones -> tens -> hundreds -> thousands -> ten-thousands -> and a fourth digit would make it hundred-millions which matches up with their number system.
I made it easier by just adding up the cross sections and putting the values in from how they should look... eg 21x 18 = somewhere around 300 and y0u work the digits around there to get 378
I need to try this with Banylonian math!
dude nice chalkboard, where/what program or image is that?
it is just a more confusing picture the bigger the numbers get, but the same method applies.
Talking about place values may help some kids understand this strategy. I call it hashtag maths as kids are used to # things. Sometimes it is a good way of looking at number relationships.
it seems like when you get to higher numbers, like example 3 (123x321) it seems like it is more difficult and confusing than multiplying in your head!
How to I multiply for example 12x3 with this method? I've been trying and can't seem to get the right number.
I learned this in elementry 5th year using just pencil and scrap paper to calculate.
Is that base 6 stuff related to logarithms? Simone please help.
This is a good method but for the purpose of understanding multiplication values needed to be included.
And if the 0 is in the midle? like 1024x305 ? I tryed the dotted line but is not working
Cool
i have a question , how to represent the Zero in the lines ??
Gosh, I feel dumb. :(
None of the examples involve a carry, which I believe makes this more complex than it initially appears.
how do you multiply 302*4001=?
I think the lines have to create a square for this method to work. What if you tried diagramming 1024 x 0305?
I pulled out my iphone, and used the calculator, and came up with the answer about 50 times faster.
Vedic multiplication actually comes from India. The Vedas are a very integrals part fo the country's culture, tradition, foundations of religion and also education
I don't necessarily grasp that either (and maybe it is just me) but I do not understand how you divide out each intersection and count "only" those in those intersections? How you set up the intersections and then count them is understood, it is just how you are partioning those out is fuzzy. Thank you
I am Japanese, but I have never used such way to multiply.
Japanese people do multiplication like this:
39
x 43
--------
117
147
--------
1587
I literally Forgot Maths after Japanese way of multiplication .Lol what's the answer you get If you multiply 39X43 it's 1677 not your weird answer . There are thousand ways and methods to calculate a problem but the solution we get should be same ..
Sorry, the fourth roe must be 39X4 so 156. It is my mistake.
No Worries ....
We do so in Sweden im almost 13 years old
not accurate
Hey Chris, What software did you use to create the video?
what do you do if the number is 30 or 407 ? im not quite sure what to do with the zeros
There just wouldn't be any lines there. You'd just know that the huge space you leave is meant to be blank. So, it's be a set of four lines, a large space, and a set of seven lines; and across them at the left side would be a set of three lines.
do a zero line (looking different 2 the others) and any dots made by it don't count.
But how do i make it with a 100?
No line for the 0?
Short answer: no. Long answer: no, how could you?
this would really help you make a bamboo basket
Is this also possible with four digits?
I hope u'll gonna be responce to my question. Thank you.
cool
It is in fact Chinese. The original video on the web was uploaded in Nov 2006. It had been taught to the guy by his Chinese girlfriend. The criss-cross reminded the students of the stools they sat on in class.
why didn't they teach me this in the third grade?
If you google "vedic", the first result tells you immediately that it's of Indian origin. Nicely researched Chris Lusto.
wait im still confused....where would that go? say its 12 X 100, how would that work?
This seems similar to how the abacus is used
if you have 301 x 301 .. for example..what do you do ? :D
I still don't get how do you choose the correct intersections for every unit. LOL.
hello can we make division whit this technic
Wait, oh my gosh this is bothering me! Can you please explain why it's 20x10 becomes 200. Where did that come from? The 20 and 10! Thanks!
Chris, Why is called "Vedic"? Did it originate there?
Let's stick to the basis.
5:12 10^0 = 1. .true you dont have any 0's but u end up with a 1 instead
I got 224 no problem using this method
This is the calculation method of India.
日本でも話題にはなりましたけど・・・
I love this. Made perfect sense to me. Everyone learns differently. Some people are more visual. Both methods should be taught in schools so that both kinds of learning can be fully utilized and understood :) This can bring the "fun" back into math for the visual types. Nice work!
Wow
I am a Japanese, but I did not know how to calculate. :-(
I didn't understand last part but whatever,pretty interesting
OP Maths
Don't know how ya got that. There's 24 lines intersecting just on the right side. 1 on the left and 10 in the center.
so are we using visual , not mathematical thinking ?
Both, for 321 x 123, red and green is still 100's x 1's which = hundreds, and yellow and yellow is still 10's x 10's which is also hundreds. So, it is a combination of both, but still easier than how I learned my multiplications in school. I'm more of a visual learner, so this would have been very helpful to visual learners. And I was pretty good at maths, so this should be really helpful for everyone.
Could you over complicate this for me a little further please?
if so calculates Japanese how many sheets of notebook spoiled :)))
explain 18x18 please