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My first introduction to short division was as a compromise between my 5th grade maths teacher (who really wanted me to show my work) and my 10-year-old self (who could do everything in her head just fine) XD
Yeah, I had the whole Daddy-Mommy-Sister-Brother (Divide-Multiply-Subtract-Bring down) pneumonic Though what happens in the video is way shorter than what was actually put into practice
Funnily enough, just like many of the comments here, I was taught short division instead of long division in school. However, Interestingly, I was taught long division when dividing Polynomials, mostly because it just works better, but I think that was beyond secondary school.
In the UK this is how division is taught and its called "The Bus Stop Method" since it looks like the dividend numbers are in a bus stop and the divisor is the bus
It is so interesting to see the way you divide. In Brazil, where I am from, we also use long and short division, although I am not certain if everybody learns short division, since I learned it at Kumon and when I think about learning division at school I remember being taught the long one. But the different thing is the way you organize the calculation, we place the dividend at the left side, and the "L" shaped line is upside down with the divisor on its right, and the quotient is placed below the line, under the divisor. Plus, we write the result of the subtraction under the original number and then we bring down the next number of the dividend.
With logs you can also determine the exact value of (2^4901)/11 with the slightly cheaty (2^4901)/2^(log2(11))=(2^4901)*2^-(log2(11))=2^(4901-log2(11))
For me the unusual thing wasn't only the line at the left, but also the zeros being added to the right of the numbers. I always just bring down the number as it was, no zeros to the right needed.
The idea of writing the remainder in the space above the numbers is cool but it’d be really hard to do when your dividing by a two digit number and get two digit remainders.
While true, I think doing this fully mentally with no writing is the point I think! Learn it by hand, and then transfer it to mental math and be able to do division mentally rapidly.
not really, you can just leave a little extra gap between each digit if you are expecting this. If you like, you can write the remainder below, it really doesn't matter. Whatever works for you.
"Short division" is the method I came up with on my own in elementary school because I couldn't be asked to do long division. Still don't know how to do it and this has been mindblowing to know that I wasn't the only one.
…I have, on several occasions, decided to pass the time by doing square roots of non-square numbers. Now I use a number system of my own design to attempt to use the same method to find the square root of complex numbers (in balanced base 3) *without* using algebra. I strongly suspect that I’m not normal in enjoying that.
@@NStripleseven which part? The square roots with pencil and paper, or the complex balanced ternary number system? Because one of those is significantly more complicated to describe using text alone.
@@Autoskip square roots with pencil and paper is something I can and have just Googled. What method you could possibly be using to make that work with not only complex numbers, but complex numbers written in balanced ternary of all things, is what I’m interested in.
I was taught the long division method in school, but after looking up the chunking method, I see that is what I use as an adult that is good with numbers. I imagine other kids that were good at math also stumble into using that method. Were you taught the chunking method as a part of common core in a US public school? Also, for the problem, we also know 2^10 = 1 (mod 11) from Fermat's little theorem, which with its generalization in Euler's Theorem, is usually the first thing one would try when faced with a big number modular problem.
Also I think we might have been taught chunking briefly in like 3rd grade but I don’t remember and I think if we did it was more of a way to understand what division is than how to do it.
I'm impressed by how I have never heard of that before! I'm a math teacher, I've explored many interesting and different ways for doing multiplication algorithms and what not. But it is the first time hearing about this. Great to see inovative content. I just started watching your channel from the recent binary chessboard calculator.
Appreciate it! I just linked you to that video in another comment, so forgive the redundancy. A lot of people have heard about short division but I was in the same boat, never heard of it despite all my time doing math and teaching it!
I briefly was taught short division in school while learning long division. I forgot how to do it, but remembered learning it from time to time. Nice to finally see how it was done! :)
I love modular math. The first time I saw it they called it CLOCK math. so like 13 mod 12 is 1 like what a hand on a clock would do if you sent it around 13 places past 12. Lots of uses for it in cryptology, like you said.
You have just explained the modular system in a 13 minute video better than my college teacher did in an entire semester. I finally understand it now. Thank you.
I was taught this "short division" at school as the one method, and we were taught to write the remainder of each of the steps under the dividend and "drag" the next digit to use down to it instead of writing it small in between the digits of the dividend, which, sure, makes it compact, but it makes it hard to write with divisors of two or more digits, so putting it underneath in a kind of ladder makes things easier
Intresting. I feel like that's like a medium division then? Since you still do the bring down rule, but instead of writing out the multiplication and subtraction like in long division, you just write the remainder and do the multiplication and subtraction in your head.
If you haven't done an episode about long square roots, that might be neat. I was writing an explanation of it, but tbh I think I might make my own video about it now
@jack002tuber back in college, I figured out why it worked and was able to create a way to do long cube roots. It's unwieldy and impractical, but it is possible, so I think the majority of the video will be on that process of figuring out how to go from one to the other
That just looks like an artist's glove - it's designed to let your hand slide over the page (or graphics tablet) without impeding your dexterity at holding a pen or pencil (or stylus).
6:40 I actually figured this one out way faster. I noticed it was 22 more than 560 (the next least multiple of 70 and thus also divisible by 7) and so I knew right away it wasn't divisible by 7, and also congruent to 1 mod 7.
My grandmother used to do short division, but instead of the L-shape going on the top and left of the number being divided, the L-shape went under and on the left side of the number being divided (which means it is a backwards L-shape)
This reminds me of when I made a division method in elementary school that was just multiplication, but you divided instead of multiplied. It wasn't very efficient or convenient, but it worked I guess
Knowing 2¹⁰ = 1024 by 2¹⁰ = (2⁵)² = 32² = 1024 is wild I just remember that 2 to the 10th is the power close to 1,000, which is 1,024. Being that close it's a handy one for rough mental estimation.
8 / 8 = 1 60 / 8 = 7 + 4 / 8 700 / 8 = 87 + 4 / 8 3000 / 8 = 375 20000 / 8 = 2500 2500 + 375 + 87 + 7 + 1 + 8 / 8 = 2971 No subtraction involved. We keep the fractional part rational until the end so we don't have to deal with nasty decimals from divisors like 3 or 7. Since our denominators will always be the same, no simplification is required and it's just like adding any integers.
Say two people are playing a game where they're given an integer between 1000 and 9999 and asked to take the square root. In front of both of them is a single cork board with a number line where they can stick a thumb tack, and whoever is closest to the actual value, wins. But the benefit of moving first is that you block out all the area under your tack, so if the correct answer is within half a radius of your approximation, you can't lose. How precise should you be before you make the leap and stick your thumb tack in the board? I don't get the hate for the metallic markers, unless you mean the smell. They do smell pretty bad. But they also tend to have nice, sharp lines, and the gold just fades to brown after a few seconds while remaining sharp, I don't really have any problem with them visually.
Lmao I was taught a hybrid of the two, as a Brazilian. For me, it is also written w the denominator and numerator switched, in long/short division, and the "L" is actually an L, which covers the bottom of the numerator and separates it from the denominator
To be fair I was using this method for decades already, nobody taught me it, I just came to doing it myself as long division is unneccesarilly tedious and has way to many steps you don't need if you are good at mental math... I use similar tricks for multiplication too...
5:23 lol I did with a reverse rule of multiplying by 11, the number being 1 x 2, and with 3 being able to get both 4 and 5, if for example the number was 4 and 6 you can instantly know that there's no x for which it would equal 1 + x = 4 and 2 + x = 6
This method is definitely superior to long division when the divisor is relatively small number, but once you get into higher two digits and beyond, squeezing the digits in that tiny space is just not practical, but then again, so is dividing on paper over simply using a calculator at that point 😅
I'm first time hearing the name of this method, but after looking it up I've got that in school I wasn't taught it, I came to it by myself and I was doing it on a subconscious level
You can know 1452 is divisible by 11 by the nature of numbers divisible by 11. 1+5=4+2. 2^1=2 mod 11 2^2=4 mod 11 2^3=8 mod 11 2^4=5 mod 11 2^5=10 mod 11 2^6=9 mod 11 2^7=7 mod 11 2^8=3 mod 11 2^9=6 mod 11 2^10=1 mod 11 So every 10 powers of 2 are brought back to the same value mod 11. 2^1=2 mod 11. 2^4901=2 mod 11.
@@Moonlite_Kitsune yeah but the "how many times does x go into y?" question completely disappears since the only nonzero digit is 1 so its even simpler in binary
It requires more of the practitioner insofar as mental math is concerned, but if you have the chops for it I love how quick it is! I never remember hearing about it in school.
@@WrathofMath we were all like “dividing 16 by 8 is much easier than dividing the entire 1647 by 8” Tbf we were such !mb3c!|es we!d manage to take more time with short division Or, at least me 😅
23768/8 =(23800-32)/8 Calculate from there. I am sometimes too lazy to calculate on paper, so i do that thing to ease myself the task. Doesnt work every time. Also dividing by simpler divisors almost always easier(instead of 12 use 3 then 4)
2:10 yeah, I know, that's the normal method. What's the new part? I'll always hide the subtracting part unless I'm dividing by a big number that I don't know the multiplication table by head Edit: 2:25 oh. New fancy notation. Ok makes sence
Not really? I feel like most people were taught a version of long division where you don't write as many zeros as what was shown here. It's just the divide, multiply, subtract, bring down, repeat algorithm. The biggest difference is that in short division, you do the multiply and subtract part in your head and write down the remainder as a pseudo-exponent, whereas in the long division we were taught, you write down basically everything but with the bring down rule instead of writing lots of zeros.
@moondust2365 yeah, I was never taught long division as an actual thing to do. It was told very briefly during primary school and then never touched again until polynomials in A-level where I relearned it because I hadn't used it for 7 years.
It's feedback for the division method. The way long division works, is you divide each group of digits as close as you can, without going over. Then, multiply to see how close you got. Subtract to find the error, and use that error as the starting point for your next cycle of the process. Append the next digit, and continue. The way I learned it, was with the mnemonic: Daddy, Mommy, Sister, Brother Daddy: Divide Mommy: multiply Sister: subtract Brother: bring down And finally, Rover the dog, for the remainder when applicable.
If your remainders while doing short division is more than one digit, do you still attatch it to the next number? For instance for a number like 56789 If after 56 you got a remainder of 23, would the next number to divide be 237?
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the only difference between this and long division is showing your work
The small numbers in between are proof of work, but it could be confused with the number if written badly enough and is also less didatic to learn
This channel is supposed to be introducing simple mathematical concepts to people.
My first introduction to short division was as a compromise between my 5th grade maths teacher (who really wanted me to show my work) and my 10-year-old self (who could do everything in her head just fine) XD
@@RedFoxtail26 I love this
"Short division" is literally just how I was taught long division.
Yeah, I had the whole Daddy-Mommy-Sister-Brother (Divide-Multiply-Subtract-Bring down) pneumonic
Though what happens in the video is way shorter than what was actually put into practice
@@_marshP Mnemonic, unless you were remembering it with your lungs :)
@@PerMortensenmy lungs are great with memory skills, personally speaking. how else do i remember to breathe?
Same, I'm confused why people decided to make it more difficult
@@_marshP I mean I've never heard of this and all I thought was "what the hell kinda symbol is called "bring down""
Funnily enough, just like many of the comments here, I was taught short division instead of long division in school. However, Interestingly, I was taught long division when dividing Polynomials, mostly because it just works better, but I think that was beyond secondary school.
Any place-valued number is a polynomial in its base.
@@mcgovemjyeah but you don’t get negative stuff
In the UK this is how division is taught and its called "The Bus Stop Method" since it looks like the dividend numbers are in a bus stop and the divisor is the bus
That's very adorably british
@@blanktester
sudden primary school memories
@@blanktester indeed
Yup so true
It is so interesting to see the way you divide. In Brazil, where I am from, we also use long and short division, although I am not certain if everybody learns short division, since I learned it at Kumon and when I think about learning division at school I remember being taught the long one. But the different thing is the way you organize the calculation, we place the dividend at the left side, and the "L" shaped line is upside down with the divisor on its right, and the quotient is placed below the line, under the divisor. Plus, we write the result of the subtraction under the original number and then we bring down the next number of the dividend.
With logs you can also determine the exact value of (2^4901)/11 with the slightly cheaty (2^4901)/2^(log2(11))=(2^4901)*2^-(log2(11))=2^(4901-log2(11))
haha nice one. in some sense that gives a hint of why modular arithmetic allows for powers to be replaced with their remainder.
This is interesting, I've never seen long division done the way you did it
Yeah, because of that long line on the right side
For me the unusual thing wasn't only the line at the left, but also the zeros being added to the right of the numbers. I always just bring down the number as it was, no zeros to the right needed.
The idea of writing the remainder in the space above the numbers is cool but it’d be really hard to do when your dividing by a two digit number and get two digit remainders.
While true, I think doing this fully mentally with no writing is the point I think! Learn it by hand, and then transfer it to mental math and be able to do division mentally rapidly.
not really, you can just leave a little extra gap between each digit if you are expecting this. If you like, you can write the remainder below, it really doesn't matter. Whatever works for you.
"Short division" is the method I came up with on my own in elementary school because I couldn't be asked to do long division. Still don't know how to do it and this has been mindblowing to know that I wasn't the only one.
They're both the same, only on one you show your work. If you can subtract in your head, you can do short division
@@jack002tuber yeah right it just mental math, nothing big
I was taught this in my NSW primary school! It made polynomial division into a real pain!
…I have, on several occasions, decided to pass the time by doing square roots of non-square numbers.
Now I use a number system of my own design to attempt to use the same method to find the square root of complex numbers (in balanced base 3) *without* using algebra.
I strongly suspect that I’m not normal in enjoying that.
That sounds genuinely fascinating, how does it work
@@NStripleseven which part? The square roots with pencil and paper, or the complex balanced ternary number system?
Because one of those is significantly more complicated to describe using text alone.
@@Autoskipexplain as much as you can, I’m interested too!
@@Autoskip square roots with pencil and paper is something I can and have just Googled. What method you could possibly be using to make that work with not only complex numbers, but complex numbers written in balanced ternary of all things, is what I’m interested in.
Teach me your sacred ways, wizard.
I was taught the long division method in school, but after looking up the chunking method, I see that is what I use as an adult that is good with numbers. I imagine other kids that were good at math also stumble into using that method. Were you taught the chunking method as a part of common core in a US public school?
Also, for the problem, we also know 2^10 = 1 (mod 11) from Fermat's little theorem, which with its generalization in Euler's Theorem, is usually the first thing one would try when faced with a big number modular problem.
Also I think we might have been taught chunking briefly in like 3rd grade but I don’t remember and I think if we did it was more of a way to understand what division is than how to do it.
Is it just me or is short division basically just long division with less writing because you do all the same steps?
This is blowing my mind. I'm 24, work in STEM, and have NEVER seen this method. Long division is the only thing I was ever taught.
For whatever reason my brain went back to synthetic division of polynomials.
I'm impressed by how I have never heard of that before! I'm a math teacher, I've explored many interesting and different ways for doing multiplication algorithms and what not. But it is the first time hearing about this. Great to see inovative content. I just started watching your channel from the recent binary chessboard calculator.
Appreciate it! I just linked you to that video in another comment, so forgive the redundancy. A lot of people have heard about short division but I was in the same boat, never heard of it despite all my time doing math and teaching it!
Everyone saying they were taught with short division, I was only taught the "long division" 😢
I briefly was taught short division in school while learning long division. I forgot how to do it, but remembered learning it from time to time. Nice to finally see how it was done! :)
This video has greatly assisted me when it comes to doing division in my head as I do not have to worry about 1 million variables to deal with.
I love modular math. The first time I saw it they called it CLOCK math. so like 13 mod 12 is 1 like what a hand on a clock would do if you sent it around 13 places past 12. Lots of uses for it in cryptology, like you said.
I'm glad he used modulo, I love using it.
Me too. It has many uses
3:29 oh my god this is nice
oh my god this method is actually amazing
bro is flabbergasted
I would have used Fermat's Little Theorem for the problem:
(2^4901)%11
Simplifies things slightly.
He used Fermat’s Little Theorem without calling it that. Euler’s totient of 11, φ(11), is 10.
a^(p-1)=1 mod p, for prime p. So 2^10=1 since 11 is prime.
You have just explained the modular system in a 13 minute video better than my college teacher did in an entire semester. I finally understand it now. Thank you.
I had been using this strategy unconsciously since 1st grade
I was taught this "short division" at school as the one method, and we were taught to write the remainder of each of the steps under the dividend and "drag" the next digit to use down to it instead of writing it small in between the digits of the dividend, which, sure, makes it compact, but it makes it hard to write with divisors of two or more digits, so putting it underneath in a kind of ladder makes things easier
Intresting. I feel like that's like a medium division then? Since you still do the bring down rule, but instead of writing out the multiplication and subtraction like in long division, you just write the remainder and do the multiplication and subtraction in your head.
If you haven't done an episode about long square roots, that might be neat.
I was writing an explanation of it, but tbh I think I might make my own video about it now
Do it. Make a reply here and I'll go watch it. 👍👍👍
@jack002tuber back in college, I figured out why it worked and was able to create a way to do long cube roots.
It's unwieldy and impractical, but it is possible, so I think the majority of the video will be on that process of figuring out how to go from one to the other
@@Elitekross Cool, just let me know. Your newest vid is like nine years old there. You need a new one ;-D
0:15 What happened to your hand?
That just looks like an artist's glove - it's designed to let your hand slide over the page (or graphics tablet) without impeding your dexterity at holding a pen or pencil (or stylus).
or without the pen ink brushing over your hand when you're still writing
@@mr.duckie._. …does it show that I've never even used one?
…or even owned one for that matter.
He divided it
short division is just basically doing mental math of division
I always use short division, except on very rare occasions. So much easier.
6:40 I actually figured this one out way faster. I noticed it was 22 more than 560 (the next least multiple of 70 and thus also divisible by 7) and so I knew right away it wasn't divisible by 7, and also congruent to 1 mod 7.
My grandmother used to do short division, but instead of the L-shape going on the top and left of the number being divided, the L-shape went under and on the left side of the number being divided (which means it is a backwards L-shape)
This is the exact moment that short division became long division. It’s over, I know. Bravo Vince.
For 11 you can just alternate digits + and - and if it =0 it will be divisible
This reminds me of when I made a division method in elementary school that was just multiplication, but you divided instead of multiplied. It wasn't very efficient or convenient, but it worked I guess
2:40 it's the bus stop method that's how I was taught to do division
ive always loved math but i never figured out how to do division until watching this video
this is how i was taught division in school we called it the 'bus stop' method
Short division is how I was taught at school. I was never shown long division
for 4:30 just use alternating sum to see if its divisible by 11
1-4+5-2 = 0 so it is divisible by 11
Knowing 2¹⁰ = 1024 by 2¹⁰ = (2⁵)² = 32² = 1024 is wild
I just remember that 2 to the 10th is the power close to 1,000, which is 1,024. Being that close it's a handy one for rough mental estimation.
8 / 8 = 1
60 / 8 = 7 + 4 / 8
700 / 8 = 87 + 4 / 8
3000 / 8 = 375
20000 / 8 = 2500
2500 + 375 + 87 + 7 + 1 + 8 / 8 = 2971
No subtraction involved. We keep the fractional part rational until the end so we don't have to deal with nasty decimals from divisors like 3 or 7. Since our denominators will always be the same, no simplification is required and it's just like adding any integers.
Has nobody else been doing this for ages??? I don't even write out the remainder, I just run through the digits super fast.
We have used the short method very soon after we learn long division, about 8 years old maybe.
Say two people are playing a game where they're given an integer between 1000 and 9999 and asked to take the square root. In front of both of them is a single cork board with a number line where they can stick a thumb tack, and whoever is closest to the actual value, wins. But the benefit of moving first is that you block out all the area under your tack, so if the correct answer is within half a radius of your approximation, you can't lose. How precise should you be before you make the leap and stick your thumb tack in the board?
I don't get the hate for the metallic markers, unless you mean the smell. They do smell pretty bad. But they also tend to have nice, sharp lines, and the gold just fades to brown after a few seconds while remaining sharp, I don't really have any problem with them visually.
This is bus stop division, in the UK we learn this in primary school, the British equivalent to elementary :)
Lmao I was taught a hybrid of the two, as a Brazilian. For me, it is also written w the denominator and numerator switched, in long/short division, and the "L" is actually an L, which covers the bottom of the numerator and separates it from the denominator
I’ll keep this in mind when I need to divide 4 digit numbers quickly
To be fair I was using this method for decades already, nobody taught me it, I just came to doing it myself as long division is unneccesarilly tedious and has way to many steps you don't need if you are good at mental math... I use similar tricks for multiplication too...
Thats absolutely outrageous!
Busting out the metallic sharpie?! Ooh you know this is a good one then!
Thanks for teaching me long long devision. What you call short devision is what I was taught as long devision.
5:23 lol I did with a reverse rule of multiplying by 11, the number being 1 x 2, and with 3 being able to get both 4 and 5, if for example the number was 4 and 6 you can instantly know that there's no x for which it would equal 1 + x = 4 and 2 + x = 6
I do short Division in my head when i have no calc or paper around.
i was taught long division then "medium" division where you still drop the remainders but none of those n-n parts
This method is definitely superior to long division when the divisor is relatively small number, but once you get into higher two digits and beyond, squeezing the digits in that tiny space is just not practical, but then again, so is dividing on paper over simply using a calculator at that point 😅
I’ve been doing this the entire time while racing with my friend at math, I didn’t know it was called that
In Russia I was taught this "Short Division", it was written something between long and short divisions, but basicly it's the same
Were you also taught the "halving and doubling" method of multiplication in Russia?
I'm first time hearing the name of this method, but after looking it up I've got that in school I wasn't taught it, I came to it by myself and I was doing it on a subconscious level
short division is also called Bus Stop
I dont know where i picked it up, but instead of saying i "mod out the 11s" i always say i "reduce mod 11". I swear it mustve been from a texbook
You can know 1452 is divisible by 11 by the nature of numbers divisible by 11. 1+5=4+2.
2^1=2 mod 11
2^2=4 mod 11
2^3=8 mod 11
2^4=5 mod 11
2^5=10 mod 11
2^6=9 mod 11
2^7=7 mod 11
2^8=3 mod 11
2^9=6 mod 11
2^10=1 mod 11
So every 10 powers of 2 are brought back to the same value mod 11. 2^1=2 mod 11. 2^4901=2 mod 11.
I learned short division at 6 years old!!!! (year 1)
"Short division" is what is taught as long division in the British school system
When i first learnt division i never used long division unless the divisor was too big aka 2658943/543
Thank you, get this man to 1 mill subs
I always use this method when simplifying fractions. Didn’t know it could be done like this tho
I learnt short division from my older sister, so I never used long division.
long division: can i survive pls
We.... don't even write the remainders all in head
mimics polynomial synthetic division because in both you dont have to write down the whole entire thing
6:41 no. But I used the 7 divisibility rule
short division only works with short divisors
i wonder how this would work in binary
to my knowledge exactly the same, theres no reason the base should affect the method
@@Moonlite_Kitsune yeah but the "how many times does x go into y?" question completely disappears since the only nonzero digit is 1
so its even simpler in binary
it is the same you just do not write them on paper
As 2⁵=32 =-1 (mod 11),
2⁴⁹⁰¹=2×2⁴⁹⁰⁰
=2×(2⁵)⁹⁸⁰
=2×(-1)⁹⁸⁰ (mod 11)
= 2.
I know only about "short" division never heard of "long" division
other way around for me
i dont even know what long division is
I hated showing my work for the steps that were trivial; It was just unnecessary bloat!
We were taught about the existence of short division, and no one did it, ever. Too difficult
It requires more of the practitioner insofar as mental math is concerned, but if you have the chops for it I love how quick it is! I never remember hearing about it in school.
@@WrathofMath we were all like “dividing 16 by 8 is much easier than dividing the entire 1647 by 8”
Tbf we were such !mb3c!|es we!d manage to take more time with short division
Or, at least me 😅
23768/8 =(23800-32)/8 Calculate from there. I am sometimes too lazy to calculate on paper, so i do that thing to ease myself the task. Doesnt work every time. Also dividing by simpler divisors almost always easier(instead of 12 use 3 then 4)
It’s just long division with shorthand. It’s still long division.
As someone from brazi, Im very confused. Why are your division upside-down?
é porque a estrutura do cálculo de divisão usada nos Estados Unidos é diferente da usada no Brasil
@a.a.1012 mas por que isso?
@@rennangandara7697 convenção histórica né
só acho sacanagem que as escolas nunca ensinaram esse método de divisão curta
@a.a.1012 só se for na sua, porque na minha ensinaram
soo is long division but you do it in a different way so is faster ti write and maybe slightly faster to do mentally
yeah... short division.
This is awesome.
Fermat’s little theorem!
2:10 yeah, I know, that's the normal method. What's the new part?
I'll always hide the subtracting part unless I'm dividing by a big number that I don't know the multiplication table by head
Edit: 2:25 oh. New fancy notation. Ok makes sence
8 divided by 23768?
Remove the 8s and the divided by, swap the 3 and the 7, and swap the 6 and the 3. What do you get?
So... this is just regular division. Long division is literally never used except for polynomials.
Not really? I feel like most people were taught a version of long division where you don't write as many zeros as what was shown here. It's just the divide, multiply, subtract, bring down, repeat algorithm. The biggest difference is that in short division, you do the multiply and subtract part in your head and write down the remainder as a pseudo-exponent, whereas in the long division we were taught, you write down basically everything but with the bring down rule instead of writing lots of zeros.
@moondust2365 yeah, I was never taught long division as an actual thing to do. It was told very briefly during primary school and then never touched again until polynomials in A-level where I relearned it because I hadn't used it for 7 years.
Even then, you can use synthetic division, which is much easier
That is more or less how i learnt it, but we didn't draw that angle.
Did anyone else's teacher flame you for not showing your work or am I just schizophrenic?
This is my long division!!!
short division is the norm to me
What is the subtraction underneath for, I never learned that way
It's feedback for the division method. The way long division works, is you divide each group of digits as close as you can, without going over. Then, multiply to see how close you got. Subtract to find the error, and use that error as the starting point for your next cycle of the process. Append the next digit, and continue.
The way I learned it, was with the mnemonic: Daddy, Mommy, Sister, Brother
Daddy: Divide
Mommy: multiply
Sister: subtract
Brother: bring down
And finally, Rover the dog, for the remainder when applicable.
@@carultch Wish I could send a picture of how I do it, but I don't know if UA-cam allows it
its literally the same but youre just not writing it out.
If your remainders while doing short division is more than one digit, do you still attatch it to the next number?
For instance for a number like 56789
If after 56 you got a remainder of 23, would the next number to divide be 237?
10:08 oh damn it is 2.
1024
102 = 99 + 3 (99 = 11 * 9)
34 = 33 + 1 (33 = 11 * 3)
1^490 = 1
2 * 1 = 2
2^4901 is congruent to 2 (mod 11)
Nine Hundred and Seventy Four
Plus five times half of a score
To the one over ten
And not altered again
Is two, at the end of our tour
It's a bit of a cheat, using 2^10 without explaining *why* you chose that number.
4:31 I did it by head in like 5 secounds and 1451 is congruent to 10 (mod 11)
Oh. That's technically a reading error, not a calculation error. 1452 is congruent to 0 (mod 11).
i only know short division and not the long one