This is exactly like long division, except each digit is drawn into dots. Connecting dots can be seen as subtracting the dividend by the divisor. Which also explains why this works for polynomial division as well.
Which way do you connect the dots? Why are u going north vertically in some and south vertically in others? Left or right? You skip a ton of info . Then finally u have a Y shape. Why didn't u start with a Y shape? This is very confusing. What do you mean there's no figures started in the column? What is a figure? I can see a horizontal line , so why isn't that a figure? It looks exactly like the one on the left, i see no difference
Man, you are a master of deception. Selling the good old division algorithm under the guise of dots is brilliant. For the rest of you, this is the the same division algorithm that you learn in school. Just instead of digits you use dots. Instead of subtracting you connect the dots.
i figured it out in the first problem the first shape has 1 in the 1st 2 in the 2nd and 3 in the third so you draw them based on the number you are dividing so the first number in the divisor is how many dots you put in the figure in the first column and so on
@Xander Michels No worries,pal. Here's how he's doing it,& the info won't cost you a cent. thescienceexplorer.com/universe/use-quick-trick-speed-long-division
This method is efficient only if the digits in the divisor are all small numbers. Let's consider 392 / 98 as an example, where the divisor digits are large enough. In this case we should see the 3 dots in the first line as 30 dots in the second line and do the similar thing to the second and the third lines, and this process is quite complicated.
Because it doesn't work for all situations. It's common core where this comes up and one of the biggest reasons i refuse to teach it. Kids can learn it the way it's been taught for centuries, and even millennia. It's not hard and it works for all situations.
This is really coolest method I have seen I really like that method it is better than any division method this is the greatest and simplest method than other
This method is very good. I dont know why a bunch of idiots are pissed off in the comment section. It worked, a good tool to have in an arsenal. Some people just looked in for a minute and tried not to understand anything.
I think I will like this method WHEN I learn to use it. Right now, I can't get past your explanation of of how the answer is calculated, so I'll have to look elsewhere for clearer instructions. Thanks for getting me interested, though. Hey, there were NO other explanations, so I had to come back here. Finally, on about the tenth view, I understood how you counted the dots. Funny, that I had no such problem with your other method. Maybe that's why I liked it more.
But this means that it's not possible for a divided number to have a digit higher than any of it's original digits. 100 / 25 is 4, but 4 shapes can't be created from the single dot that 100 draws.
You have first. 1|0|0 dots, but you cant have 2 connectet dots in one dot. You transfer the one dot to the 0 dots, but than these are 10 dots. Now you have 0|10|0 dots. But you cant connet 5 dots in the third dot line. You transfer 2 dots from the second to the third. Now you have 0|8|20. Now you can connect these right. 4 times 2 dots in the second and 4 times 5 dots in the third.
@Sebastian Henkins The problem is, people are not taught (at least int the US) what the long division algorithm means. They are taught to manipulate numbers in a certain pattern they have memorized. If you learn that you can regroup the numbers to the next place over, then there's a chance you will actually understand our place value system. I teach children who can divide huge numbers, but when put into context, cannot tell what the remainder is. They can tell me it's "2" but not 2 what. Is it two students? Two buses? What do we do with it? Is it appropriate to make it a fraction or a decimal? Does the remainder answer the question? Do we ignore the remainder? Does the remainder tell us to increase the quotient by one? A memorized algorithm does not teach number sense, which at least American students, do not have. Regrouping dots or disks isn't meant to be a faster way to divide. It's meant to show something interesting that can work in our base 10 number system.
@Sebastian Henkins : Yes. Notice he uses small digits. It looks very tedious if you have a lot of 8's and 9's in your divisor or dividend, both of which terms he avoided, entirely. Also, I'm wondering how he handles remainders, since they are important.
if you do it vertically, that second one can also be 1/2/0, which is X+2, so...... , so there's gotta be more to it that's not explained, or else it falls apart pretty quickly
I think the idea is that you're supposed to connect one dot in one column to one dot in the next column. Connecting two dots in the first column, vertically, (and none in the second) would correspond to dividing by 2x.
It looks like this method only works when no carrying is required in the multiplication. This wouldn't work if I were to divide 21 by 7 - I don't even have 7 dots to connect!
And it's no surprise that this method works for algebraic expressions. Where as dividing numbers means you are working in base 10, dividing algebraic expressions means you are working in base x.
if you divided a number with 0s in it... for example, 1001/7... you would put 10 dots because this works with 1-10 digits. It's kind of complicated, but true
It is really not. It works well in this well tailored example. Try dividing 23714/29 the way you were taught and then with dots. See which one will take longer.
Seems cool !!! I a lot of details are missed. ¿From where I start connecting dots and where I go? ¿Just straigh lines? I proof will also be very interesting to see. Good vid!!!
Great vid but maybe explain the rules for connecting dots, how to choose left, down, or right. Otherwise there are several ways to connect the dots starting from the right to create different figures that will be incorrect.
It doesn't matter how you connect the dots. Just connect the proper number of dots from each column. I personally would prefer always starting from the top. Makes things simple in complicated cases.
Thanks for this video. i don't anderstand a lot, because i don't anderstand a lot English, but this video seems be a good one . I hope someone explain this in french. Have a nice day ! 15/04/20
This only works well i some rare situations, usually this method causes problems. You might run out of dots or end up having extra dots that can't be used, but these cases can be solved by ruling out one dot in one column and then drawing 10 dots in the next column (because dots in the last column represent ones, dots in the second last column tens etc.) With x, it will be a hard time though and I don't know how to solve it for polynomials. So this method is quite impractical, but it's nice to see a fun and different way for dividing numbers.
Like the multiplication by drawing lines trick, it works well for illustrating multiplying and dividing graphically, which can aid intuition, but when the digits are all large (like 7,8,9), it gets tricky. For example, try this trick dividing 96497093 by 979.
+Dr J. Chalisque D. E. Allsup Nice example. I am familiar with the method, and know about the technique for carrying dots over to the column on the right but you picked one mother of a problem there. Given a choice of methods, for your example I would choose chunking - no need to deal with the 979 times table then!
+Andy Wright Just tried to do chunking with that calculation - hey man you chose well with that problem. I think just normal straightforward long division with the 979 times table going down the side of the paper is best
J'ai essayé avec 234*543=127062 puis 127 062 / 234 pour voir si la méthode fonctionne... Le premier "1" n'est pas "suffisant" pour commencer ma division alors je le barre et transforme en 10 points dans la colonne suivante, etc. Ça marche ! Mais c'est TRÈS long et je me suis arrêté au deux premiers "résultats" : 54. ma feuille n'était plus assez haute 🙄 Donc amusant, mais pas utilisable pour un enfant, contrairement à la multiplication avec lignes et points.
I think I’d have trouble with the divisor drawings. Are there any more examples on how to draw the connected dots? Do you always use the first dot to link connections?
This trick only works when the sum of the digits of the divisor is greater than or equal to the sum of the dividend. In order to solve that, you would have to draw 12 dots and connect 4
You have to borrow, like in regular long division. For example: 4746/42 Place the dots as shown in video. Connect 4 dots from first column to 2 dots in second column. We are done with first column. Connect 4 dots in second column to 2 dots in third column. We now have 1 dot left in second column. Since we cannot form a figure with 1 dot in this column, take the 1 dot from second column and change it into 10 dots in third column. We now have 12 dots in third column and 6 dots in fourth column. We can now form 3 groups of 4 and 2 dots from these 2 columns. So we have 1 group starting in first column, 1 group starting in second column, 3 groups starting in third column. 4746/42 = 113 For 12 divided by 4, the 1 dot in left column is changed into 10 dots in right column for a total of 12 dots in right column. Connect dots in groups of 4 to get 3 groups, and answer is 3.
That I relate to. When young I devise several methods to mental calculate, specially if a number is a multiple of any other chosen one. It wasn't exactly as decribe here because I never make / figure out the last step but it is close to the first steps. Let illustrate by an example. I want to know if 8358 is a multiple of 7. I first substract an already known multiple of 7 (multiplied by 10, 100, 1000...) from the number studied. Here it gives 8358-350 = 8008. I repeat that process with the rest for 8008-7000 = 1008 and then 1008-700 = 308, 308-280 = 28 and finally 28-28=0. If there is no rest, it is a multiple. The idea is to keep it easy to remember while doing something else. I was first in that exercise when I learnt about factors in grade 4 or 5 (about 9 to 10 y.o.) while walking to school when I had nothing to read. The numbers tested were on car plates along the sidewalk I walked on. Now being 55 years older I still do that when I walk or drive. That method was design to be versatile and can take different approach like this one for the same numbers, 8358 and 7 : 8358-7000 = 1358, 1400-1358 = 42 and 42-42 = 0; no rest hence 7 is a factor. The twist here was to see 1358 as an easy number to compare with a multiple of 7 but higher. When looking at the method in the video I see what I was applying develop in my mind. The goal wasn't not the same but the processes are close one to the other.
I have had more luck designing the dot covering graph first and then obtaining the numbers from that. Kind of reveals what numbers are permitted by this method. This must be why you called it a 'trick' :)
Great video/method, although there are 2 things that i can't quite understand: 1) the pattern you choose/ chose to connect the dots in the first example and 2) the column at which you stop when taking the answer (i mean it's obvious that the result will be a 4 digit number in the first example and a first degree polynomial in the second but, more details please?)
We write numbers in base ten as sums of products of integers and the base, ten, to the power of its place value (with ones place being 0, tens place being 1, and so forth). So 231 would be written as 2*10^2 + 3*10^1 + 1*10^0. If we let the base be arbitrary, say x. 231 in base x is 2*x^2 + 3*x^1 + 1*x^0. If x is zero, then every number is equivalent to zero, so base zero doesn't make sense. But what this means is that any polynomial is just a number of base x. When we set the number equal to it, we are solving for in what base that number is equivalent to the right hand side. The solution to 1*x^2 + 0*x^1 + 1*x^0 = 5 => x^2 - 4 = 0 => x = 2 (we want positive x because it makes more sense.) So the number 101 in base 2 is equal to 5.
+Rawesomeguy Rawesome Well, you should check that you're dividing for a reasonable bynomial. Also, to be honest, when you have 17s and 9s as arguments in your polynomial you're better off with long division rather than drawing 19 dots and making a mess of aalmost vertical lines. Long division is not really that long.
interesting way of visualising the process... but some things are very unclear. What if there is a zero in one of the numbers? And extending from that, what if the resunlt is not integer? Is there a way to apply this method in those cases?
I did it in my head, got 1,102. Then you did the dots and now I don’t think I can divide anymore because you confused me so much lol. An abacus is interesting, doesn’t mean it’s replacing the calculator.
There seems to be so much that's not explored by this video. What happens when the numbers are not carefully selected to work out perfectly? What if there's no number in the second column where you need to connect to 2 dot? What if you divide by a large number and there are not enough dots to match to? What about remainders? So many more questions to explore to see if this works beyond the two examples shown.
In the words of Jim Carrey “I just learned this radical new move in karate! But ya gotta come at me like THIS! “ (puts his arm up swinging down straight in front of him). While this is intriguing I am unclear on : How the dots connect with a different dividend geometrically and what to do for numbers that convert to dots that are highly asymmetrical.
You created a geometric long division, but you forget to specify one point on the video and forget to manage when it's 11/2, =) You can make a pro version of your algorithm pretty easy. Nice job.
Did the first problem in my head... 1,102. I saw that 121 went into 133 once with 12 left over, this is how I got 1000. So then I put 12 before the 3 to make it 123 and 121 also goes into that once with 2 left over now, thats how I got the 100. I saw that 121 wouldn't go into 24, which is how I got 0 for the tens place. Then I moved the 24 to the end so that it would be 242, which 121 can go into twice, and thats how I got 2. I find this much simpler than drawing out a whole system of dots, even if i did do it in my head (which I probably would do, I am very good at visualizing these things).
hey i tried yo way i like it way better tried myself on a problem came up with a 4 digit number answer. But when i checked my ans. with cal. that 4 digit number answer was correct which was 1101 but the actual ans in the cal. was 1101.00754678 r sum sht my question to u is any way to know the remainder with yo method. can i get the full cal ans with yo method
How do you know when to stop? I guess you could say when there are no dots left, but in that case what if the answer is 10 or 100 or any 10^x (x >=1). Great trick BTW.
It's confusing. Can you answer me these questions? 1. What do you do if there is a zero in the number you are trying to divide by? 2. Is it that the number of dots connected in one shot is the number your trying to divide with adding up all of its digits? 3. It's confusing, but amazing.
divide 18 by 6... it does not work. in fact, the "10" has to disappear to make 10 "1". you forgot to say that. this method is better to see how it works. but it is not a better algorithm (I mean it's quadratic)
It does not work for all cases. If A ÷ B where sum of digits of B exceeds sum of digits of A, it won't be possible to conduct division using dot method.
It's more complicated, but you can. You just have to move dots from one column to the next. Remember that 1 dot in hundreds column is the same as 10 dots in tens column. For example: *1127/49* Place dots as shown in video. We don't have enough dots in first column, so we remove that dot from 1st column and add 10 dots to 2nd column. The number of dots in each column is now: 0 - 11- 2 - 7 We have enough dots in 2nd column, but not enough in 3rd column. So we remove 1 dot from 2nd column and add 10 dots to 3rd column. We now have: 0 - 10 - 12 - 7 *_Connect 4 dots from 2nd column to 9 columns from 3rd column._* Number of unused dots in each column: 0 - 6 - 3 - 7 Again, we don't have enough in 3rd column. So we remove 1 dot from 2nd column and add 10 dots to 3rd column. We now have: 0 - 5 - 13 - 7 *_Connect 4 dots from 2nd column to 9 columns from 3rd column._* Number of unused dots in each column: 0 - 1 - 4 - 7 We no longer have enough dots in 2nd column, so we remove that dot from 2nd column and add 10 dots to 3rd column. The number of unused dots in each column is now: 0 - 0 - 14 - 7 But we still don't have enough dots in 4th column, so remove 1 dot from 3rd column and add 10 dots to 4th column: 0 - 0 - 13 - 17 *_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column: 0 - 0 - 9 - 8 Again, we remove 1 dot from 3rd column and add 10 dots to 4th column: 0 - 0 - 8 - 18 *_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column: 0 - 0 - 4 - 9 *_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column: 0 - 0 - 0 - 0 So we have 0 groups starting in 1st column, 2 groups starting in 2nd column, 3 groups starting in 3rd column. *1127/49 = 23*
There are a couple of limitations to this trick. First each digit in the divisor must be less than any digit in the dividend. Also the number of digits it the divisor must be a factor of the number of digits in the dividend. These are 2 of the limitations I found and I don't want to check for every detail but I'm getting the list isn't very short. This method is helpful In a few good cases but I don't think it is worth it to check for every mathematical equation.
What if you run out of dots in a column? Like, if the first digit of the number you are dividing by is larger than the first digit of the number dividing from?
Please explain in general terms first. Then, show examples. What do you mean "connect" - left, right, diagonal - which direction ?? This is not clear enough, please help - this seems very promising / interesting !
Or you just take the good old fashioned method of multiplying the denominator with 10^x where x is the length of the numerator -denominator. In this case 121*10^(6-3) subtract that from the numerator and repeat until you got an answer. This works because a Division is multiplicative Subtraction.
Can anyone provide a source for proof that this method works on the two methods of division described in the video? I'm very intrigued. I would also like to know how you know not to go passed a certain point on the dots. For example, you only had 4 numbers but 6 columns in the first problem. Then the second problem had 2 numbers and 3 columns. How did you know to stop at 4 and 2, not 6 and 3?
What happens if you run out of dots in a column using this method? Example: (I just thought of this today) 952/2 would leave exactly 1 dot in the hundreds column. What do you do then?
Some background infos to this method. This is the same procedure like long division with pen and paper. The examples in this video are "easy" in two senses. 1) no remainder 2) (more important) no carry! How is this stuff working? Imagine you have 10 dots and you ask, how many groups of 2 dots are there? * * * * * * * * * * 10 dots (**)(**)(**)(**)(**) 5 groups of 2 dots. -> 10/2 = 5 What is here going on is the following. Imagine the first step: 133342 : 121 = ... * * * * * * * * * * * * * * * * Here you have the same like saying: 1 * 10^6, 3 * 10^5 , 3*10^4 , and so on. What would you now do with pen and paper? You would ask: I take the 1. Does 121 fit in 1? No. I take 13. Does 121 fit in 13? No. I take 133. Dos 121 fit in 13? Yes! 1 times: So you take 1 from the 10^6 position. You take 2 from the 10^5 position. You take 1 from 10^4 position. We get after subtracting! (delete all connected points and shift the rest to the top!) * * * * * * * * * * * * This explains, why the t-shape can flip or get an Y-Shape. So far so good. No we play the game again! So there is nothing special about this. It gets tricky, when you have a carry! Imagine 402 : 3. * .. * * .. * * * Since 3 is from the form 10^0, we connect only verticaly. In the first column we can connect 3 points 1 time. * .. * * So far: 402 : 3 = 1.... and we left with 102. But what to do now, if we are only allowed to connect verticaly? Hm, the remaining 1*10^2 = 10 * 10^1 ! * * * * * * * * * * * * So we can connect 3-times a group of 3 vertical dots. This is exactly what you would do with pen and paper. 102 : 3 3 doesn´t fit in 1. 3 does fit in 10! So we are left with * * * or 402 : 3 = 13... or the remaining 12:3 And again here. We have 1 * 10^1 and we cannot connect 3 dots vertically. Therefore: 1*10^1 = 10*10^0. We are left with 12 dots * ... ... * (12 dots) Here we can group 4 time a size of 3. (12 : 3, like it was mentioned a couple of lines earlier.) Therefore: 402 : 3 = 134 Summary! Dots method is isomorphic to pen and paper method. This method shows very nice the connection from doing stuff with pen and paper because we do it since 30 years and the deeper understanding of number systems.
This is interesting. Obviously you can't do just any numbers, because you run out of dots. ...or can you? If you don't have enough dots, simply carry over one dot from a column to the next column to the right, creating 10 dots there. Also, I found it less messy (still extremely messy, though) to, rather than connecting the dots, simply cross out dots one at a time. But the very first dot you cross out (any in the left-most column involved) in one full round of subtraction, circle it instead. Then count the circled dots in each column. Of course, this works to find the decimal expansion too, or just a remainder after the whole.
looks like common core. Also it can be shown this method doesn't work using the first method if I decide to connect the first dot in the first column to the middle dot in the second column then decide the connect that second dot to the dots above and below. It will produce a 10__ not a 11__. Sorry, but this method only works based on specific rules and in the end it's so much easier to just do this the old fashioned way.
I'm so happy this isn't how I was taught to divide.
This is an interesting way of dividing. It's hard to learn but saving time for explaining long division to lot of non thinking ones.
Hahahahahaha
Pls do more example of this kind
This is the division algorithm how you´ve learned it. Just another notation.
@@another_august It ISN'T hard to learn at all! It is absolutely instant.
Next lesson: How to divide numbers using sweet potatoes.
use potatos as dots same logic
@@NerdBryant64 r/wooosh
This is exactly like long division, except each digit is drawn into dots.
Connecting dots can be seen as subtracting the dividend by the divisor.
Which also explains why this works for polynomial division as well.
Which way do you connect the dots? Why are u going north vertically in some and south vertically in others? Left or right? You skip a ton of info . Then finally u have a Y shape. Why didn't u start with a Y shape? This is very confusing.
What do you mean there's no figures started in the column? What is a figure? I can see a horizontal line , so why isn't that a figure? It looks exactly like the one on the left, i see no difference
Even I too have these doubts pls reply
I agree this is more complicated than u Make it look
Pause the video. ;)
it's the same way you have learn in school he just change number into dot try to make it easier(but it isn't)
Tanmoy Dutta ]
Try dividing 1001 by 7 this way. >:)
LOL
Eden's Aquaponics
The answer is143
ពីដេីម: ប្រុស I know
Rrriiiiiight... good point. This is reminding me how they did division with an abacus.
Man, you are a master of deception. Selling the good old division algorithm under the guise of dots is brilliant.
For the rest of you, this is the the same division algorithm that you learn in school. Just instead of digits you use dots. Instead of subtracting you connect the dots.
Thank you. Free the reality.
yeah
Depends on your country
@@SekaiNoGaijin yeah in my country i don't remember learning anything similar to thia
He is right.
This is exactly the same procedure.
There is nothing special about this.
i see there seems to be a problem of knowing which dots to connect
ikr
i figured it out in the first problem the first shape has 1 in the 1st 2 in the 2nd and 3 in the third so you draw them based on the number you are dividing so the first number in the divisor is how many dots you put in the figure in the first column and so on
@Xander Michels No worries,pal. Here's how he's doing it,& the info won't cost you a cent.
thescienceexplorer.com/universe/use-quick-trick-speed-long-division
Other problems
This only seems to work if all of the digits in the divisor are less than or equal to each of the digits in the dividend.
This method is efficient only if the digits in the divisor are all small numbers. Let's consider 392 / 98 as an example, where the divisor digits are large enough. In this case we should see the 3 dots in the first line as 30 dots in the second line and do the similar thing to the second and the third lines, and this process is quite complicated.
Never thought I would say this
School taught me better then that
Looked at comments and _everybody’s been stumped by this for 5 years-_
It’s 2019 I don’t get it, don’t think anyone else will
Because it doesn't work for all situations. It's common core where this comes up and one of the biggest reasons i refuse to teach it. Kids can learn it the way it's been taught for centuries, and even millennia. It's not hard and it works for all situations.
each colums corrosponse to a digit from the dividend
13 would be
..
.
.
the rest is not so hard right :p
@@fuseteam It still is clunky and doesn't work unless you are specific. Many ways to make errors.
I was a little confused at first but after the second time I got it and it's made everything so much easier.
This is really coolest method I have seen I really like that method it is better than any division method this is the greatest and simplest method than other
This method is very good. I dont know why a bunch of idiots are pissed off in the comment section. It worked, a good tool to have in an arsenal. Some people just looked in for a minute and tried not to understand anything.
I think I will like this method WHEN I learn to use it. Right now, I can't get past your explanation of of how the answer is calculated, so I'll have to look elsewhere for clearer instructions. Thanks for getting me interested, though. Hey, there were NO other explanations, so I had to come back here. Finally, on about the tenth view, I understood how you counted the dots. Funny, that I had no such problem with your other method. Maybe that's why I liked it more.
But this means that it's not possible for a divided number to have a digit higher than any of it's original digits.
100 / 25 is 4, but 4 shapes can't be created from the single dot that 100 draws.
You have first. 1|0|0 dots, but you cant have 2 connectet dots in one dot. You transfer the one dot to the 0 dots, but than these are 10 dots. Now you have 0|10|0 dots. But you cant connet 5 dots in the third dot line. You transfer 2 dots from the second to the third. Now you have 0|8|20. Now you can connect these right. 4 times 2 dots in the second and 4 times 5 dots in the third.
Iyoda Immortas so is this like common core math?
@@darthtorus9341 No this is the basic background of number systems. The same thing you would do with pen and paper.
@Sebastian Henkins The problem is, people are not taught (at least int the US) what the long division algorithm means. They are taught to manipulate numbers in a certain pattern they have memorized. If you learn that you can regroup the numbers to the next place over, then there's a chance you will actually understand our place value system. I teach children who can divide huge numbers, but when put into context, cannot tell what the remainder is. They can tell me it's "2" but not 2 what. Is it two students? Two buses? What do we do with it? Is it appropriate to make it a fraction or a decimal? Does the remainder answer the question? Do we ignore the remainder? Does the remainder tell us to increase the quotient by one? A memorized algorithm does not teach number sense, which at least American students, do not have. Regrouping dots or disks isn't meant to be a faster way to divide. It's meant to show something interesting that can work in our base 10 number system.
@Sebastian Henkins : Yes. Notice he uses small digits. It looks very tedious if you have a lot of 8's and 9's in your divisor or dividend, both of which terms he avoided, entirely.
Also, I'm wondering how he handles remainders, since they are important.
What a method ! Thank you for sharing with us such an interesting trick
This is beautiful thank you so much. It's like abstract algebra.
WHAT SORCERY IS THIS
Lol 😂😂😂
it just appears he is doing a visual representation of long division
+jesusthroughmary lol
In the video he just does following visually:
133342 - 121000 = 12342, 12342 - 12100 = 242, 242 - 121 = 121, 121 - 121 = 0 which implies that 133342 = 121 * (1000 + 100 + 1 + 1) = 121 * 1102. Thus 133342/121 = 1102.
I just asked my dad something along those lines lol
if you do it vertically, that second one can also be 1/2/0, which is X+2, so...... , so there's gotta be more to it that's not explained, or else it falls apart pretty quickly
Yeah...it took me two seconds to realize that
I think the idea is that you're supposed to connect one dot in one column to one dot in the next column. Connecting two dots in the first column, vertically, (and none in the second) would correspond to dividing by 2x.
Noticed that immediately, but I think the dude who commented above me might have the right idea
It looks like this method only works when no carrying is required in the multiplication. This wouldn't work if I were to divide 21 by 7 - I don't even have 7 dots to connect!
+Drake Thomas connect what you do havs if you run out of dots
carry them on to next line drawing 10 for every unused one
Aonodensetsu *draws 100 dots*
i have red that this is only applicable if the sum of the digits of the dividend is greater or equal to the sum of digits of the divisor
omg... this is so confusing and does not apply to call cases. Definitely not stitching any dot.
@Tanmoy Dutta video is unavailable, got any up to date link?
It does apply to all cases, but it will become rather confusing for bigger digits. Imagine doing 1648295996÷597 like this ...
2:29 why do you stop there ??? and giving the answer 1102 ? should you not proceed for the other dots ??
It seems like you stop after all figures have been covered
the polynomial thing at the end proves it works in all bases
And it's no surprise that this method works for algebraic expressions. Where as dividing numbers means you are working in base 10, dividing algebraic expressions means you are working in base x.
if you divided a number with 0s in it...
for example, 1001/7...
you would put 10 dots because this works with 1-10 digits. It's kind of complicated, but true
I don't know why this isn't taught in school. It's actually useful.
It is really not. It works well in this well tailored example. Try dividing 23714/29 the way you were taught and then with dots. See which one will take longer.
Well it doesnt always work but i used the method in my head and i divided 120 by 12 and sure i got 10
Hahahaha lol lol
What the duck? You can use this for Algebra?! Mother of God why didn't I find this earlier!
Seems cool !!! I a lot of details are missed. ¿From where I start connecting dots and where I go? ¿Just straigh lines? I proof will also be very interesting to see. Good vid!!!
Great vid but maybe explain the rules for connecting dots, how to choose left, down, or right. Otherwise there are several ways to connect the dots starting from the right to create different figures that will be incorrect.
It doesn't matter how you connect the dots. Just connect the proper number of dots from each column. I personally would prefer always starting from the top. Makes things simple in complicated cases.
Thanks for this video.
i don't anderstand a lot, because i don't anderstand a lot English, but this video seems be a good one . I hope someone explain this in french. Have a nice day ! 15/04/20
This only works well i some rare situations, usually this method causes problems. You might run out of dots or end up having extra dots that can't be used, but these cases can be solved by ruling out one dot in one column and then drawing 10 dots in the next column (because dots in the last column represent ones, dots in the second last column tens etc.) With x, it will be a hard time though and I don't know how to solve it for polynomials. So this method is quite impractical, but it's nice to see a fun and different way for dividing numbers.
You didn't explain the general method.
@Joshua Diocares i agree with u, he must explain multiplication then division, did u see Gday Math by James Tanton?
Like the multiplication by drawing lines trick, it works well for illustrating multiplying and dividing graphically, which can aid intuition, but when the digits are all large (like 7,8,9), it gets tricky. For example, try this trick dividing 96497093 by 979.
+Dr J. Chalisque D. E. Allsup Nice example. I am familiar with the method, and know about the technique for carrying dots over to the column on the right but you picked one mother of a problem there. Given a choice of methods, for your example I would choose chunking - no need to deal with the 979 times table then!
+Andy Wright Just tried to do chunking with that calculation - hey man you chose well with that problem. I think just normal straightforward long division with the 979 times table going down the side of the paper is best
+Andy Wright There we go, 98567 sweet as a nut. You can't beat some of these old-school methods
J'ai essayé avec 234*543=127062 puis 127 062 / 234 pour voir si la méthode fonctionne... Le premier "1" n'est pas "suffisant" pour commencer ma division alors je le barre et transforme en 10 points dans la colonne suivante, etc. Ça marche ! Mais c'est TRÈS long et je me suis arrêté au deux premiers "résultats" : 54. ma feuille n'était plus assez haute 🙄 Donc amusant, mais pas utilisable pour un enfant, contrairement à la multiplication avec lignes et points.
I think I’d have trouble with the divisor drawings. Are there any more examples on how to draw the connected dots? Do you always use the first dot to link connections?
Wow amazing... Alien method... Thanks for sharing... ☺️👍👍👍👍
how do you do 12 divided by 4. it looks like . .
. so ?
This trick only works when the sum of the digits of the divisor is greater than or equal to the sum of the dividend. In order to solve that, you would have to draw 12 dots and connect 4
The Ninja Eevee the question is very good i also raise the same question
noooop
,3
You have to borrow, like in regular long division.
For example: 4746/42
Place the dots as shown in video.
Connect 4 dots from first column to 2 dots in second column. We are done with first column.
Connect 4 dots in second column to 2 dots in third column. We now have 1 dot left in second column.
Since we cannot form a figure with 1 dot in this column, take the 1 dot from second column and change it into 10 dots in third column. We now have 12 dots in third column and 6 dots in fourth column. We can now form 3 groups of 4 and 2 dots from these 2 columns.
So we have 1 group starting in first column, 1 group starting in second column, 3 groups starting in third column.
4746/42 = 113
For 12 divided by 4, the 1 dot in left column is changed into 10 dots in right column for a total of 12 dots in right column. Connect dots in groups of 4 to get 3 groups, and answer is 3.
That I relate to. When young I devise several methods to mental calculate, specially if a number is a multiple of any other chosen one. It wasn't exactly as decribe here because I never make / figure out the last step but it is close to the first steps. Let illustrate by an example. I want to know if 8358 is a multiple of 7. I first substract an already known multiple of 7 (multiplied by 10, 100, 1000...) from the number studied. Here it gives 8358-350 = 8008. I repeat that process with the rest for 8008-7000 = 1008 and then 1008-700 = 308, 308-280 = 28 and finally 28-28=0. If there is no rest, it is a multiple. The idea is to keep it easy to remember while doing something else. I was first in that exercise when I learnt about factors in grade 4 or 5 (about 9 to 10 y.o.) while walking to school when I had nothing to read. The numbers tested were on car plates along the sidewalk I walked on. Now being 55 years older I still do that when I walk or drive. That method was design to be versatile and can take different approach like this one for the same numbers, 8358 and 7 : 8358-7000 = 1358, 1400-1358 = 42 and 42-42 = 0; no rest hence 7 is a factor. The twist here was to see 1358 as an easy number to compare with a multiple of 7 but higher. When looking at the method in the video I see what I was applying develop in my mind. The goal wasn't not the same but the processes are close one to the other.
I have had more luck designing the dot covering graph first and then obtaining the numbers from that. Kind of reveals what numbers are permitted by this method.
This must be why you called it a 'trick' :)
Great video/method, although there are 2 things that i can't quite understand: 1) the pattern you choose/ chose to connect the dots in the first example and 2) the column at which you stop when taking the answer (i mean it's obvious that the result will be a 4 digit number in the first example and a first degree polynomial in the second but, more details please?)
We write numbers in base ten as sums of products of integers and the base, ten, to the power of its place value (with ones place being 0, tens place being 1, and so forth). So 231 would be written as 2*10^2 + 3*10^1 + 1*10^0. If we let the base be arbitrary, say x. 231 in base x is 2*x^2 + 3*x^1 + 1*x^0. If x is zero, then every number is equivalent to zero, so base zero doesn't make sense. But what this means is that any polynomial is just a number of base x. When we set the number equal to it, we are solving for in what base that number is equivalent to the right hand side. The solution to 1*x^2 + 0*x^1 + 1*x^0 = 5 => x^2 - 4 = 0 => x = 2 (we want positive x because it makes more sense.) So the number 101 in base 2 is equal to 5.
Hi you are the bestest person ever
do a book about this trick! love your channel!
AWESOME VIDEO😀😀😀😀
What a great way to divide. Connecting the dots. I could try that myself. But you know, I love long division.
How is this so simple. Does it work all the time
for the algebraic expression, how do u decide which figures get multiplied to x or powers of x?
it's a quadratic expression divided by a linear, so the first term is x, and you go one power of x down each time
You know the answer and you are just making your own method and showing us. In life don't make anyone fool.
If you look closely it's like normal division only. But interesting. Thanks a lot. I love this.
I'll use this for competive exams, I love how I wont need to use long polynomial division anymore. Like this comment if you agree
+Rawesomeguy Rawesome Well, you should check that you're dividing for a reasonable bynomial. Also, to be honest, when you have 17s and 9s as arguments in your polynomial you're better off with long division rather than drawing 19 dots and making a mess of aalmost vertical lines.
Long division is not really that long.
interesting way of visualising the process... but some things are very unclear. What if there is a zero in one of the numbers? And extending from that, what if the resunlt is not integer? Is there a way to apply this method in those cases?
I did it in my head, got 1,102. Then you did the dots and now I don’t think I can divide anymore because you confused me so much lol. An abacus is interesting, doesn’t mean it’s replacing the calculator.
There seems to be so much that's not explored by this video.
What happens when the numbers are not carefully selected to work out perfectly?
What if there's no number in the second column where you need to connect to 2 dot?
What if you divide by a large number and there are not enough dots to match to?
What about remainders?
So many more questions to explore to see if this works beyond the two examples shown.
is this applicable if the dividend is not divisible by your divisor?
Nice one sir....I have used this in my lessons too.. :)
i dont get it!!!!
SAME
A good way looks awesome..!
In the words of Jim Carrey “I just learned this radical new move in karate! But ya gotta come at me like THIS! “ (puts his arm up swinging down straight in front of him).
While this is intriguing I am unclear on :
How the dots connect with a different dividend geometrically and what to do for numbers that convert to dots that are highly asymmetrical.
th-cam.com/play/PLjGnVzD4rvf3XeeXLzySD4MpniMuub-5e.html
Very simple Short trick of Typical questions of maths in 1 second for all latest govt.exam
Well I got the answer in my head by the time you drew the first dot, but still, this should be interesting.
You created a geometric long division, but you forget to specify one point on the video and forget to manage when it's 11/2, =)
You can make a pro version of your algorithm pretty easy. Nice job.
If somebody don't understand it. First of all learn multiplication using dots. It's a japanese method.
OMG it actually works!!!!😱😱😱
But is was not for any number, only if you made a dot into ten, and put it to another digit
Thanku you so much for providing such videos 🙏
Did the first problem in my head... 1,102. I saw that 121 went into 133 once with 12 left over, this is how I got 1000. So then I put 12 before the 3 to make it 123 and 121 also goes into that once with 2 left over now, thats how I got the 100. I saw that 121 wouldn't go into 24, which is how I got 0 for the tens place. Then I moved the 24 to the end so that it would be 242, which 121 can go into twice, and thats how I got 2. I find this much simpler than drawing out a whole system of dots, even if i did do it in my head (which I probably would do, I am very good at visualizing these things).
hey i tried yo way i like it way better tried myself on a problem came up with a 4 digit number answer. But when i checked my ans. with cal. that 4 digit number answer was correct which was 1101 but the actual ans in the cal. was 1101.00754678 r sum sht my question to u is any way to know the remainder with yo method. can i get the full cal ans with yo method
#knoll question for you black maj
Better Explaining a Bit More
Illustrate with More Examples and the rule to Connect the Dots
This didn’t work for me when I used different dot configurations than the example.
How do you know when to stop? I guess you could say when there are no dots left, but in that case what if the answer is 10 or 100 or any 10^x (x >=1). Great trick BTW.
It's confusing. Can you answer me these questions? 1. What do you do if there is a zero in the number you are trying to divide by? 2. Is it that the number of dots connected in one shot is the number your trying to divide with adding up all of its digits? 3. It's confusing, but amazing.
divide 18 by 6... it does not work.
in fact, the "10" has to disappear to make 10 "1".
you forgot to say that.
this method is better to see how it works.
but it is not a better algorithm (I mean it's quadratic)
It does not work for all cases.
If A ÷ B where sum of digits of B exceeds sum of digits of A, it won't be possible to conduct division using dot method.
It's more complicated, but you can. You just have to move dots from one column to the next.
Remember that 1 dot in hundreds column is the same as 10 dots in tens column.
For example: *1127/49*
Place dots as shown in video.
We don't have enough dots in first column, so we remove that dot from 1st column and add 10 dots to 2nd column. The number of dots in each column is now:
0 - 11- 2 - 7
We have enough dots in 2nd column, but not enough in 3rd column. So we remove 1 dot from 2nd column and add 10 dots to 3rd column. We now have:
0 - 10 - 12 - 7
*_Connect 4 dots from 2nd column to 9 columns from 3rd column._* Number of unused dots in each column:
0 - 6 - 3 - 7
Again, we don't have enough in 3rd column. So we remove 1 dot from 2nd column and add 10 dots to 3rd column. We now have:
0 - 5 - 13 - 7
*_Connect 4 dots from 2nd column to 9 columns from 3rd column._* Number of unused dots in each column:
0 - 1 - 4 - 7
We no longer have enough dots in 2nd column, so we remove that dot from 2nd column and add 10 dots to 3rd column. The number of unused dots in each column is now:
0 - 0 - 14 - 7
But we still don't have enough dots in 4th column, so remove 1 dot from 3rd column and add 10 dots to 4th column:
0 - 0 - 13 - 17
*_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column:
0 - 0 - 9 - 8
Again, we remove 1 dot from 3rd column and add 10 dots to 4th column:
0 - 0 - 8 - 18
*_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column:
0 - 0 - 4 - 9
*_Connect 4 dots from 3rd column to 9 dots from 4th column._* Number of unused dots in each column:
0 - 0 - 0 - 0
So we have 0 groups starting in 1st column, 2 groups starting in 2nd column, 3 groups starting in 3rd column.
*1127/49 = 23*
How to divide any no which contains 0 in it like 2098 or 500
There are a couple of limitations to this trick. First each digit in the divisor must be less than any digit in the dividend. Also the number of digits it the divisor must be a factor of the number of digits in the dividend. These are 2 of the limitations I found and I don't want to check for every detail but I'm getting the list isn't very short. This method is helpful In a few good cases but I don't think it is worth it to check for every mathematical equation.
Wow, great video, thanks so much
What if you run out of dots in a column?
Like, if the first digit of the number you are dividing by is larger than the first digit of the number dividing from?
You carry, you remove 1 dot and add 10 dots to the next column
Please explain with more examples..
What about 9801÷99??
Please explain in general terms first. Then, show examples. What do you mean "connect" - left, right, diagonal - which direction ?? This is not clear enough, please help - this seems very promising / interesting !
My life would have been so much easier if I had known this before....
thank you so much ive been havin troubles with division😛😛
@Ash Xi how can you say that?
do you know me?
@Ash Xi whats your real name?
@Ash Xi and if you know me give one name of my classmates
@Ash Xi ha your talking to the wrong person
If you connect the dots vertically, this doesn't work. You should specify the lines must be horizontal. Just a thought... I really enjoy your posts!
doing it straight up by long division method is faster,easier and less confusing
Lot of questions than answers #LOQTA
Me: Wait, everything is just dots...
Presh: 🌎👨🚀🔫👨🚀
I guess it doesn't work for polynomials with negative terms and for division of a number by a number less than 10, right?
+Rodrigo Appendino LOL, I think this is only applicable for natural numbers XD it doesn't apply to polynomials with rational coefficients either.
Or you just take the good old fashioned method of multiplying the denominator with 10^x where x is the length of the numerator -denominator. In this case 121*10^(6-3) subtract that from the numerator and repeat until you got an answer.
This works because a Division is multiplicative Subtraction.
awesome trick everyone must watch this video...
Wow thats interesting thankyou very much 👍🎉🎉
You must mention the limitation of this method. ...
Can anyone provide a source for proof that this method works on the two methods of division described in the video? I'm very intrigued.
I would also like to know how you know not to go passed a certain point on the dots.
For example, you only had 4 numbers but 6 columns in the first problem.
Then the second problem had 2 numbers and 3 columns.
How did you know to stop at 4 and 2, not 6 and 3?
Will it work on any long division
What happens if you run out of dots in a column using this method?
Example: (I just thought of this today) 952/2 would leave exactly 1 dot in the hundreds column. What do you do then?
Oh I get it. Just like that time Cartman got the Underpants Gnomes’ 3 phase plan
Thanks bro helps a lot
What if you divide 1111 by 121?
Neermind
that's will leave the answer in decimal
What about 133,343...How would something like that be handled?
Some background infos to this method.
This is the same procedure like long division with pen and paper.
The examples in this video are "easy" in two senses.
1) no remainder
2) (more important) no carry!
How is this stuff working?
Imagine you have 10 dots and you ask, how many groups of 2 dots are there?
* * * * * * * * * * 10 dots
(**)(**)(**)(**)(**) 5 groups of 2 dots. -> 10/2 = 5
What is here going on is the following. Imagine the first step:
133342 : 121 = ...
* * * * * *
* * * * *
* * * *
*
Here you have the same like saying: 1 * 10^6, 3 * 10^5 , 3*10^4 , and so on.
What would you now do with pen and paper? You would ask:
I take the 1. Does 121 fit in 1? No.
I take 13. Does 121 fit in 13? No.
I take 133. Dos 121 fit in 13? Yes! 1 times:
So you take 1 from the 10^6 position. You take 2 from the 10^5 position. You take 1 from 10^4 position.
We get after subtracting! (delete all connected points and shift the rest to the top!)
* * * * *
* * * *
* *
*
This explains, why the t-shape can flip or get an Y-Shape. So far so good.
No we play the game again!
So there is nothing special about this.
It gets tricky, when you have a carry!
Imagine 402 : 3.
* .. *
* .. *
*
*
Since 3 is from the form 10^0, we connect only verticaly.
In the first column we can connect 3 points 1 time.
* .. *
*
So far: 402 : 3 = 1....
and we left with 102.
But what to do now, if we are only allowed to connect verticaly?
Hm, the remaining 1*10^2 = 10 * 10^1 !
* *
* *
*
*
*
*
*
*
*
*
So we can connect 3-times a group of 3 vertical dots.
This is exactly what you would do with pen and paper.
102 : 3
3 doesn´t fit in 1.
3 does fit in 10!
So we are left with
* *
*
or 402 : 3 = 13...
or the remaining 12:3
And again here.
We have 1 * 10^1 and we cannot connect 3 dots vertically.
Therefore: 1*10^1 = 10*10^0.
We are left with 12 dots
*
...
...
* (12 dots)
Here we can group 4 time a size of 3. (12 : 3, like it was mentioned a couple of lines earlier.)
Therefore: 402 : 3 = 134
Summary! Dots method is isomorphic to pen and paper method.
This method shows very nice the connection from doing stuff with pen and paper because we do it since 30 years and the deeper understanding of number systems.
love it! Proff
Tq so much for this method
This is interesting. Obviously you can't do just any numbers, because you run out of dots. ...or can you? If you don't have enough dots, simply carry over one dot from a column to the next column to the right, creating 10 dots there. Also, I found it less messy (still extremely messy, though) to, rather than connecting the dots, simply cross out dots one at a time. But the very first dot you cross out (any in the left-most column involved) in one full round of subtraction, circle it instead. Then count the circled dots in each column. Of course, this works to find the decimal expansion too, or just a remainder after the whole.
looks like common core. Also it can be shown this method doesn't work using the first method if I decide to connect the first dot in the first column to the middle dot in the second column then decide the connect that second dot to the dots above and below. It will produce a 10__ not a 11__. Sorry, but this method only works based on specific rules and in the end it's so much easier to just do this the old fashioned way.