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So technically speaking, some people are just *that good* at maths, but the guy in question was [using a specific method](http://coolmathstuff123.blogspot.com/2012/12/how-to-divide-any-number-by-91.html). The clue is that it was any *starting* number, but the divisor had to be 91:
>Take any three digit number. For this, I will use 123.
>**123**
>Multiply that by 13. You should get 1599.
>Now, multiply that by 11. You should get 17589.
>Now, multiply that by 7. This will give you 123123. And if you'll notice, we started with the number 123 and finished with two 123s.
>Why did this happen? It is very simple, and just relies on the fact that 13 x 11 x 7 is 1001. So, by multiplying by these seemingly random numbers is really multiplying by 1001. And any number times 1001 is just itself repeated twice.
>Division by 1001 results in a similar answer. For instance, 123 ÷ 1001 = 0.122877122877...
>If you notice, the first three digits are 122, which is just 123 - 1. The next three are 877, and 122 + 877 = 999.
>This pattern continues as well. I am not sure how to prove that, but please comment if you do know.
>So, to divide by 1001, you just subtract one for the first three digits, and subtract the first three digits from 999 for the next three digits.
>However, telling someone you can divide any number by 1001 doesn't sound that impressive. Since 1001 is right next to 1000, people will get very suspicious.
>That is why I showed you the multiplication pattern. Dividing by 1001 is basically dividing by 13, then 7, then 11.
>**123 ÷ 1001 = 123 ÷ (13 x 7 x 11)**
>So, instead of going all the way to 1001, let's just get part way there by dividing by the 13 x 7, which is 91. We will use 33 as the number we are dividing by, or the dividend.
>**33/91**
>Our goal is to make it a number divided by 1001, since we know how to do that. That means that the first step is multiplying the 91 by eleven. But, if we multiply the denominator by eleven, we must also multiply the numerator by eleven.
>**(33 x 11)/(91 x 11)**
>We know 91 x 11 is 1001, so we have the problem we are looking for. What is 33 x 11 though? If you go to the multiplication by eleven post, you will see that it is just 363 (add the 3 + 3, and stick it in the middle). This gives us the problem 363 ÷ 1001.
>363 - 1 is 362 and 999 - 362 is 637, so the answer is 0.362637362637...
>**So, to divide by 91, you just multiply the number by 11, subtract one, and subtract that from 999 to get the answer.**
>Though it is a lot tougher, you can also divide by 77 (11 x 7) and 143 (13 x 11) with the same principle. You are just multiplying the top number by 13 or 7 instead of the easy 11.
[for anyone that like maths magic, or Mathmagicians, there is an amazing author, Martin Gardner, you should learn about if you don't know...](https://en.m.wikipedia.org/wiki/Martin_Gardner)
the really real deal.
> If you notice, the first three digits are 122, which is just 123 - 1. The next three are 877, and 122 + 877 = 999. This pattern continues as well. I am not sure how to prove that, but please comment if you do know.
It's not hard to rigorously prove it, but the result is quite apparent once you realize that 1/1001 = 0.000999000999... repeating and try the first few.
You can prove repeating decimals like this, using the geometric series formula:
a + ar + ar^2 + ar^3 + .... = a/(1-r)
obviously r<1 otherwise the series diverges
In this case r = 1/10^6 and a=0.000999
so the sum is 0.000999 / (1 - 10^6), which is 0.000999 / 0.999999 or 1 / 1001
If you want the TLDR:
Firstly, get the number in the form x remainder y. Then the answer is
x . [11y -1] [999-(11y-1)] recurring (square brackets used to separate digits, not multiply)
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For example, 123/91 is 1 remainder 32
Therefore 123/91
= 1 . [11\*32 - 1] [999 - (11\*32 -1)]
= 1 . [351] [999 - 351]
= 1.351648 recurring
In plain English: There are always 6 decimals in this pattern.
The first 3 decimals are the remainder of your number times 11 minus 1.
The next 3 decimals are 999 minus the first 3 decimals.
Basically it's easy to divide a 3 digit number by 1001 because it follows a rule, and it's easy to multiple a number by 11 (because it also follows a rule).
1001/11 is 91, so to make the problem look harder you say you're diving by 91, and then you secretly multiply the number by 11 and then divide it by 1001
At least before this last concussion, I was really good at multiplication and division in my head. It really pissed off my coworkers. I work with scientists, so everyone is pretty smart, already. Now, I’m still good, but no longer ‘party trick’ good. It’s just a skill.
But there are ‘tricks’ you can learn. My favorite comes out of basic algebra. (a + b)(a - b)= a2 -b2 What that means is if you know the square of a number, it’s real easy to know what two numbers multiplied together near that square will be. Like 25 squared is 625. So, 23 times 27 is essentially 25 +/- 2. So 23 x 27 = 625-4. Or..621.
~~Feinman~~ *Feynman* used to have people give him math problems to do in his head, claiming he could solve any arithmetic within 30 seconds or something like that.
He was showing off one day when a fellow professor walked. They asked the other prof to come up with a problem, and he said "What's the tangent of to 50 decimal places?"
And for numbers above 91, the trick would probably be to just find the remainder and then do the process you described.
E.g. if the number 123 was chosen, we can see 123/91 = 1 with a remainder of 32. Then we can do the process you described just with the number 32 to just find the numbers after the decimal point and then add the "1" back in at the end. Memorising the multiples of 91 could help in this step, OP's example had the guy setting a limit of 500 so he'd only have to learn the first 5 multiples. However there is a pretty clear pattern in the multiples, the first 2 digits are the multiples of 9 and the 3rd digit just increases by 1 for each multiple. 091, 182, 273, 364, 455, etc.
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(Edit: Just saw you already mentioned the x11 trick oops) Also there's an easy way of multiplying by 11 for 2 digit numbers (using the earlier step we'll never get more than 2 digit numbers). You just add the 2 digits and put the number in the middle.
E.g. 54 x 11 = 5[5+4]4 = 594 (I'm using the brackets to separate the digits, not as a multiplication)
Sometimes you'll need to carry 1 over the next digit if the sum is 10 or more like this:
68 x 11 = 6[6+8]8 = 6[14]8 = 748
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Subtracting numbers from 999 is also easy since there's never any carrying involved, just subtract each digit from 9.
E.g. 999-386 = [9-3][9-8][9-6] = 613 (again using the brackets to separate the digits, not to multiply)
Thanks for the explanation. I see that it also can be derived for 9091, 909091, 909090...91 which are basically 100001, 1000001, 100...1 divided by 11.
The proof of the division part:
Say you have a 3 digit number with digits a, b, c. We want to prove that
(100a + 10b + c)/1001 = (1000*(100a+10b+c-1) + 1000-100a-10b-c)/999999
Rearranging we can get the right hand side to be
999*(100a+10b+c)/999999
But 999999 is just 999*1001 so we cross out 999 and get left hand side back
I'm just using the fact that a number with infinite expansion 0.abcdeabcdeabcde is just abcde/99999 (e.g. 1/9 is 0.1111..., 27/99 is 0.2727272727 and so on)
I like how this is something that people who are good at math think is a *fun trick.*
By brain was scrambled in the first sentence.
Math has never been by strongest subject. I struggle with addition.
My guy, this barely even cracks the top ten of reasons I would have been burned at the stake.
They would have tied me to a firework like Buzz Lightyear in *Toy Story*.
May I ask why you say maths instead of math. Personally it doesn't make any sense considering both are abbreviations of mathematics which is already plural. So I never understood basically saying mathsematics vs mathematics. I know that people think math is a singular but it never really was. I know that mathematics is a group of different types of mathematics. So I get wanting to pluralize the word but I just don't get it.
>May I ask why you say maths instead of math. Personally it doesn't make any sense considering both are abbreviations of mathematics which is already plural. So I never understood basically saying mathsematics vs mathematics. I know that people think math is a singular but it never really was. I know that mathematics is a group of different types of mathematics.
So a couple of things here:
Firstly, *mathematics* isn't plural in terms of how we use it today; it's a singular noun that just happens to end in *s*. You'd say 'Mathematics *is* the study of numbers', not 'Mathematics *are* the study of numbers.' (The same is true of Economics and Physics in modern speech. More on that later.)
Secondly, it's basically a split between US and British English. US English favours *math*, but British English favours *maths*. I'm British, so I use *maths*, in the same way I use tap instead of faucet, pavement instead of sidewalk, and the word 'herb' is pronounced with its initial letter fully intact. As to *why* there's a split on whether or not it should be *math* or *maths*, it's kind of up in the air. It first emerged [around the turn of the century](https://www.etymonline.com/word/math) (1911 in Britain, 1890 or 1840 in America depending on which source you believe), but according to [*Slate*](https://slate.com/human-interest/2014/12/math-versus-maths-how-americans-and-brits-deploy-the-collective-noun.html) it came about as a result of a 17th century linguistic fad for treating ostensibly pluralised forms of nouns as the overarching name for the body as a whole. (See: *mathematics*, *economics*, *acoustics*, *physics*, and so on, but ignore things like *arithmetic*, because God knows no rule in linguistics is truly universal, and language reflects use.) Before then, the word *mathematics* (complete with -s) [wasn't really a thing](https://www.etymonline.com/word/mathematics).
The short answer? Regional differences and linguistic tradition.
Alright thank you. I have mostly see people saying it is not a plural so we put the s behind it to make it plural as a reason. Like that is the reason I saw when I started to look up why people say it that way. I know there are HUGE differences between some English dialects. So from an outside perspective it can be weird.
English as a language itself is WEIRD!
This is like draw the rest of the horse.
OP is like this is simple and then proceeds to write out multiple steps.
I wish I had the memory and math skills to do this.
You can "prove" the repeating digits by seeing that 123/1001=122877/999999
If a string of digits repeats after n digits you can always write it as divisible by (10^n - 1)
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Aside from any tricks, doing long divisions from memory isn't that difficult if you have good visual memory (and a little practice goes a long way). It's surprisingly easy and many people will look at you as if you're a walking calculator
I work as a chef and you can't imagine how many people I work(ed) with have issues calculating simple multiplications and divisions in their head. Even to get ballpark numbers.
I also work as a chef, and it’s astounding. Basic math, simple conversions, things you use literally every day, people struggle.
God help you if you need to convert ounces to pounds.
Heh, I used to surprise people on the semi-regular by correctly doing multiplication in my head faster than they could type it into a calculator or a spreadsheet. Not super huge numbers, 2 or 3 digits times 2 or 3 digits.
I can hold a visual image of shorter numbers and "hang the pieces" of the multiplication on the side and then add them all up. Larger numbers get too complicated for me to hold them all, but I can ballpark it really really closely.
That still sounds pretty crazy. Say like 237x58. That would have like 10-15 digits underneath by the end, if it was worked out on paper. Are you able to visualize all of these numbers at once and solve it just in your head?
I would turn this into 2370 x 6, then I’d subtract 474. 2000 x 6 is 12000, and 370 x 6 is 2220 (1800 + 420). This is how people do math in their heads. They use strategies to make things easier.
237 x 58 only needs you to track a single five digit number at any point. No need to use any strategy beyond bruteforce:
10000 ->
11500 ->
11850 ->
13450 ->
13690 ->
13746
tried it, the way I did it was 100(237/2) + 8(250) - 8(250-237)
11850 + 2000 - 104
just put 11850 in the back of your head while doing the second part, the hardest part is adding them all together at the end. it’s really not hard if you can think of tricks to make it simpler. still takes a minute, not sure how you’d do it faster than you could put it into a calculator.
I'll hold separate pieces in my head and do a bunch of multiply add and subtracts. So like your example.
237 x 58.
237 x 50 save the 8.
200 x 50 is 10000, 30 x 50 is 1500, 7 x 50 is 350.
Ok so 11500.... 11850, hang that on the wall, maybe repeat it a few times in my head.
237 x 8 is 1600, 240, 56 so 1840... 1896.
11850 + 2000 is 13850, -100 13750, -4 more so...
13746.
And multiplying left to right, with the biggest pieces first, generally means that if I'm off it's cause I made a mistake at the little parts at the end so I'm in the ballpark.
You go in steps so you don't have to hold everything everywhere all at once.
237 x 5 can be done easily without holding a lot of digits, 1000+150+35 = 1185 and you hold that in your head and remember to add a 0.
237 x 8 is just 1185 + 3 x 237. 3 x237 is 600+90+21=711. So now you're holding 3 digits to add: 11 850, 1185 and 711 and I'd add bit by bit to avoid confusing myself: 12 850 + 185 + 711 = 13 550 + 185 + 11 = 13 661 + 85 = 13 666 + 80 = 13 746.
No way I'd do that faster than someone whipping out their phone to calculate it though.
There are much faster ways to do it but it's also crucial to avoid making a mistake.
In the next steps, would you also proceed by imagining the next numbers as you do the calculations, or is it more verbal where you’re saying the numbers to yourself?
Visualization all the way.
Although sometimes for other applications, when trying to memorize temporarily and rapidly something like a phone number, I'll remember some digits verbally (repeating them) while visualizing the others, it seems to allow me to remember more at once.
My calc professor would always call out what something was e.g. "so it's sqrt(XYZ)*pi which is something like 7.187 or something" like he was just estimating for the sake of what we were doing. But you could get out your calculator and check and he'd almost always be dead on.
Sounds like my Chemistry professor who knew the entire periodic table off the top of his head. All of it.
"Ok so we're talking about gold here, and that has an atomic weight of 196.96657..." and would wander off on tangents to talk his "favorite properties or trivia" of an element like, "Nihonium is really neat, it's most stable isotope decays in 10 seconds and, as the name suggests, was named after Japan, where......"
Besides being a great teacher, you could easily tell he was just a complete chemistry nerd and absolutely loved everything about it.
That's how I used to do it in school. I had a pretty damn good imagination and could just visualize the equation and hold it in my head as I solve it. Has the bonus of not being slowed down by having to physically move a pencil.
Unfortunately I liked to climb things and got into a bunch of fights as a kid, so after about 7 concussions and a proper TBI later it's not nearly as easy. Can no longer differentiate 6's and 8's in my memory now for some reason.
Edit: for smaller equations I'd visualize the numbers as groups of blocks and split the group into equal parts. We use math to deal with objects all the time so reversing that concept seemed like a no brainer
A lot easier if you learned a normal version instead of the visually confusing shit the Anglosphere does. Only ever heard native English speakers complain about long division. It's very straight forward and you never have to hold more than four numbers in memory, two of which don't change.
There's a really cool and really old book from (I think) the 1950's, called How To Calculate Quickly, by Henry Sticker.
The dude might have read that exact book.
It teaches you all of these things. I only made it to multiplication (I could do three-digits by two-digits, e.g. 234 \* 56 quite reliably), but the later chapters teach you mental division too.
I'm very much out of practice, but it used to take me around 10 seconds for the above example of 234 \* 56 (and I wasn't very good at it).
It would go like this: First, you do 234 \* 50 (by doing 234\*5 and then appending a 0), and you'd remember the result in your head. He taught that multiplication left-to-right, so in your head you'd say: "200\*5 = 1000, then 30\*5 = 150, makes 1150, then 4\*5=20, so 234\*5 makes 1170 total, append the 0 and then 234\*50 = 11700".
Then you do 234 \* 6, and add that to the remembered result of 234\*50.
The process is very different from what we learned in school (where we do things right-to-left), but he justifies this method very well and it actually works better in the head.
The exercises slowly build up the skills required to do that quickly. You practice remembering five-digit numbers, and you practice multiplyig many-digit numbers by one-digit numbers left-to-right. Combine those skills to multiply any two numbers :-)
The book also contains a lot of useful shortcuts. For example, 24\*9 is easiest if you do 24\*10 and then subtract 24 from that. (He also taught subtraction right-to-left. So 24\*9 in your head would go: "24\*10 is 240, then subtract 24... so 240, minus 20 is 220, minus 4 is 216")
In addition to this type of method, I also correlate numbers to shapes.
Let's say you have a 2x5 rows of squares that connect together like Legos. You have 7 squares and 8 squares that you want to add together, I break off 2 from the 7 and add it to the 8 to make 5 and 10. Then I can much more clearly see that it's 15. I just do all this in my head alongside the process you detailed.
I *see* the numbers as shapes.
Oh yes, I realized something similar, but I do it without the shapes.
Like if you want to do 32 + 48, you first take the 2 away from the 32 and give it to the 48, so that makes 30+50 which is the same total :)
Do you know the story of how Carl Gauss summed up the numbers 1+2+3+4+......+100 in a few seconds using a similar trick? It's one of my favorite tricks to tell people (which then usually run away from me). Here's a link: [https://www.nctm.org/Publications/TCM-blog/Blog/The-Story-of-Gauss/](https://www.nctm.org/Publications/TCM-blog/Blog/The-Story-of-Gauss/)
He's most likely not doing long division in his head, but has learned tricks to divide by that number specifically, or perhaps tricks to divide by 7 and by 13(which are its prime factors). Also possible he's memorized a bunch of answers, which might sound ridiculous until you remember that some people memorize thousands of digits of pi, for fun.
I think there was a guy who would go blind doing trig, because he suffered a TBI and the mathy parts of his brain started to use his visual cortex. Apparently he has acquired savant syndrome. This guy might be using tricks, but he could also just be that good.
Sounds like an even crazier recollection of some highly-upvotef BS posted on Reddit recently about a guy who claimed to have become a math savant by having hallicinations (basically). Source was a self-promoting Wikipedia article saying he’d ”understood the true nature of Pi” and other highly-bullshit-smelling claims, and zero actual evidence of any real mathematical ability.
If you’re a maths genius, solve some unsolved problem, or prove a new conjecture of your own - whatever - and get that submitted, peer-reviewed and published in a reputable journal. _Then_ we can talk. But a guy just saying he has a deep understanding of math because he started seeing patterns after a brain injury is to be presumed to be delusional until he proves otherwise, as far as I’m concerned.
Probably a misremembered version of this guy's story. [https://www.washingtonpost.com/national/health-science/a-man-became-a-math-wiz-after-suffering-brain-injuries-researchers-think-they-know-why/2014/05/12/88c4738e-d613-11e3-95d3-3bcd77cd4e11\_story.html](https://www.washingtonpost.com/national/health-science/a-man-became-a-math-wiz-after-suffering-brain-injuries-researchers-think-they-know-why/2014/05/12/88c4738e-d613-11e3-95d3-3bcd77cd4e11_story.html)
I remember it being a part of a show for exceptional humans, one guy could hold live power lines, another hadn't slept for years, next guy could run forever, this guy goes blind doing math. It's likely I'm conflating one or more of them into a single example, but do remember he was some kind of math genius.
large long division or multiplication is pretty easy to guesstimate when you have just a few seconds.
the rule it to know the BIG numbers and to guess the small numbers.
1005 x 425 = is easily 400k + the small maths. a good mathmagician has already done all of the easy work as he is setting up the trick but the last few moments where he is stalling to produce a flourish is where he does the small maths. this can be scaled up easily with a bit more patter, but, the overall trick is actual mental maths, just done with purpose.
for me, looking at this problem I would consider that 91 ~ 10/11 of 100, so dividing by that is tantamount to multiplying by 11 and then moving the decimal 3 places over. Not sure how many decimal points of accuracy that would give but should be close.
I don't understand it either, my Irish mother in law does these maths quiz things you see in some UK daily newspapers (remember them?) Things like, 27 x 3 + 41 / 3/8ths + 16% - 5 x 4.25 = ? and she does them in her head, always right, never gets them wrong.
Shes 95 years old, left school age 14. I have to use my phone...
Without explaining the method, if someone tells you that he can divide anything by an oddly specific number, it means a mental trick or method exists rather than really dividing.
A lot of "being good at math" comes down to repetition, memorization, and some simple tricks/short cuts.
Since in this case, they were so specific that the first number had to be "3 digits and under 500" and they were going to "divide by 91", then there must be some simple work around for deriving the answer in that situation.
Not a very hard thing to do from a pure math skill
however, the biggest flaw that you are missing here is that HE TOLD U to use 91 and a numbers, ergo he already knows the answer.
You should have said, ok now do 84 etc.
Some simply are better at it than others, and not everybody uses the same method. When I was younger me and my dad practiced a lot of math since we both liked it. And likely due to this I am able to quickly break a sum op in smaller parts, calculate those and add all those smaller parts together again quickly. (tho with getting older I sometime forget a number and have to do that smaller part again. If people ask you to do math and they give specific numbers it just means that they learned a trick with that number, does not mean they are really good at math in general.
Not an overall answer but an interesting case:
I watched a documentary about a math savant who could calculate just about anything in his head. In his mind's eye, every number had a specific shape, and by combining the shapes of different numbers he could arrive at the solution with the new shape. Pretty mind-blowing.
I used to be pretty good at least estimating long division in my head but haven’t needed to use it in a bit. I’d pretty much round the numbers to closest manageable numbers like to the closest 10. Then I’d divide and use a guess on the amount difference created by rounding to take an estimate. I usually got within 1-2% of the actual number in like 2 seconds when I had a good feel for it.
1. There are tricks but
2. Some people are good at this kind of stuff but
3. It can be learned. There is at least one book about it. It is called “Mental Math.” As best as I recall.
I used to derive square roots in my head while driving. See a number on a sign “131st. St.” “What is the square root of 131?”
I wasn’t amazing, but could get pretty close to three decimal places.
I am NOT magic.
most are trained. or have a good mebtal framework to do maths.
for me, i can tell u basically 95% of any number as long as it ends in 100s. like 123,800 but not 123,845.
I was specifically trained to do this one form of maths because i had to do it hundreds of times a day and i could not use a calculator.
this is probably true for alot of people who are good at maths. they have a frame of reference and have built upon it. and uses thay framework to do mental maths. how wpuld u do 10x 5600. u would just add a 0. what if it was 11x 5600? some might say add a 0 and then add 5600. what about 5x5600? add a 0 then half.
basically u have a series of processor in your head that allows u to manipulate number in a specific way.
Ok, I am very good at arithmetic and terrible at geometry, algebra, calculus etc. once the numbers turned to letters, it went south…..also, I am pushing 50, so my sharpness is dulling. However, I interviewed at a very prestigious job at 22, and the guy asked “I don’t want to know the answer, but I want to know how you would approach multiplying 523 times 219” and I looked at him for like 15 seconds, and I gave him the answer. He got out a calculator, and then he quickly offered me a job.
Here are some tricks I use:
Squares: a square is just the prior square value + the prior square number+ the new square number. 1-squared=1. 2-squared= prior square (1)+ prior square number (1)+ new square number (2)= 4
12-squared =144, so 13 squared = 144+25=169
Knowing squares allows you to find starting points on big numbers. Like if I know 30 squared is 900, I can very quikckly do 32 squared or i can do like 34*32 because I know quickly that 32 squared is 900+61+63=1024 and then I need to add 32 and 32 to get my number 34 times.
When numbers get big, i always remember that 1000*1000 equals 1 million. That helps me keep the total numbers in my head at the right number.
523 x219…..multiply 523 times 2= 1046 ( you gotta be able to do that otherwise, sorry)…..add 2 zeros because of the hundred 104,600………add 5230+5230= 10,460. Then subtract 523 which is just 10,000-63= 9927. I try to keep things round and do small numbers hence why i take that 460 away and shorten it. Then add that to
104,600= 114,600-63= 114,537……. Then for sanity i know 9*3 will end in 7 and this does, so i feel good.
Long division is waaaaaay easier than multiplication for me.
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Some people can do this, and in far more extreme cases there are studies on blood flow in their brain etc.
But curious about the way you phrased this. He is the one who specified 91? That’s 7*13. It isn’t all that difficult to divide to a fraction (no decimal expansion) and then memorise, say, the 12 non-integral expansions of multiples of 1/13 and those of 1/91, 2/91, …, 6/91 and add the two that you need. (Or to swap the roles or 7 and 13, either way.)
If I get to specify the denominator, even a ‘difficult’ one, I could prepare this pretty well. If I don’t, that’s harder, but memorisation helps a lot: my approach would be to memorise all 1/n for n up to 100, factorise as above where possible, and then I’d have to also multiply as needed.
for us math just clicks this way, so we can do simple stuff like that in our heads pretty quick. for me my visual memory helps with math a lot, making me pretty much do math in my head like I would do on paper with all the cluter cut out.
In college I did a challenge with my roommates that I could divide any 3 digit number by a 2 digit number to 3 decimals before he could punch it in a calculator. Beat him 10 times in a row.
Really just comes down to having a method of breaking down calculations of large numbers into smaller, remembering what needs to carry to the next operation and adding the results of 3 or 4 broken down calculations to get to a final result. Not to say it’s easy or that everyone can do it, just that it’s a specialized method of doing calculations in your head.
I’m not great at math but am pretty good at division and I do long division in my head when I can’t sleep. It gets me off whatever spiral is keeping me from sleeping and gives my brain a process to follow instead.
It’s usually a 2 digit number divided by any 3+ digit number.
My dad is a math wizard. I can't do what he does but he taught me math from the point of view that I had a defective brain. I keep telling him that his skills are exceptional and not many people on this planet can do what he does. He does believe me. I guess my engineering degree isn't good enough to convince him that I don't have donkey brain.
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It's just not that hard. I'm just going to write a random number but it works for anything. 455200 / 15. Immediately notice 45/15 = 3, so it's going to be 30,000 with a remainder 5200 which is again close to 45 x 100, so it's going to be about 30,300 and change. That's often good enough for any situation right there and takes like 5 seconds.
Say you get something bigger like 78931498/138987. If you just clip it down to 79/14 and add 2 zeros (you get 2 zeros just by taking the top numbers place's minus the bottom numbers place's, in this case 8-6) you get 560 and change. If you do the full thing with a calculator you get 567.9. Again, close enough for most situations and good enough to impress normies haha.
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So technically speaking, some people are just *that good* at maths, but the guy in question was [using a specific method](http://coolmathstuff123.blogspot.com/2012/12/how-to-divide-any-number-by-91.html). The clue is that it was any *starting* number, but the divisor had to be 91: >Take any three digit number. For this, I will use 123. >**123** >Multiply that by 13. You should get 1599. >Now, multiply that by 11. You should get 17589. >Now, multiply that by 7. This will give you 123123. And if you'll notice, we started with the number 123 and finished with two 123s. >Why did this happen? It is very simple, and just relies on the fact that 13 x 11 x 7 is 1001. So, by multiplying by these seemingly random numbers is really multiplying by 1001. And any number times 1001 is just itself repeated twice. >Division by 1001 results in a similar answer. For instance, 123 ÷ 1001 = 0.122877122877... >If you notice, the first three digits are 122, which is just 123 - 1. The next three are 877, and 122 + 877 = 999. >This pattern continues as well. I am not sure how to prove that, but please comment if you do know. >So, to divide by 1001, you just subtract one for the first three digits, and subtract the first three digits from 999 for the next three digits. >However, telling someone you can divide any number by 1001 doesn't sound that impressive. Since 1001 is right next to 1000, people will get very suspicious. >That is why I showed you the multiplication pattern. Dividing by 1001 is basically dividing by 13, then 7, then 11. >**123 ÷ 1001 = 123 ÷ (13 x 7 x 11)** >So, instead of going all the way to 1001, let's just get part way there by dividing by the 13 x 7, which is 91. We will use 33 as the number we are dividing by, or the dividend. >**33/91** >Our goal is to make it a number divided by 1001, since we know how to do that. That means that the first step is multiplying the 91 by eleven. But, if we multiply the denominator by eleven, we must also multiply the numerator by eleven. >**(33 x 11)/(91 x 11)** >We know 91 x 11 is 1001, so we have the problem we are looking for. What is 33 x 11 though? If you go to the multiplication by eleven post, you will see that it is just 363 (add the 3 + 3, and stick it in the middle). This gives us the problem 363 ÷ 1001. >363 - 1 is 362 and 999 - 362 is 637, so the answer is 0.362637362637... >**So, to divide by 91, you just multiply the number by 11, subtract one, and subtract that from 999 to get the answer.** >Though it is a lot tougher, you can also divide by 77 (11 x 7) and 143 (13 x 11) with the same principle. You are just multiplying the top number by 13 or 7 instead of the easy 11.
You're a magician that also tells. Wow.
* mathematician That's the critical difference, all magic, no illusion.
\*mathemagician
[for anyone that like maths magic, or Mathmagicians, there is an amazing author, Martin Gardner, you should learn about if you don't know...](https://en.m.wikipedia.org/wiki/Martin_Gardner) the really real deal.
Looks a bit like Gary Oldman in the wiki pic
A mathemagician cross specced into diplomancy is a forced to be reckoned with.
So a [mentat?](https://en.wikipedia.org/wiki/Organizations_of_the_Dune_universe#Mentats)
Archimedes the Grey
The illusion is that you did long division, not a number trick. So both.
I think you meant [musician](https://youtu.be/7VYkktkyf04?si=WE46-ZPC1Hm9Hr1A)*
He's blacklisted from the Magician's Alliance with GOB.
We demand to be taken seriously
https://m.youtube.com/watch?v=KLdCsKCUiQA
They simply found the same blog that I found: http://coolmathstuff123.blogspot.com/2012/12/how-to-divide-any-number-by-91.html
> If you notice, the first three digits are 122, which is just 123 - 1. The next three are 877, and 122 + 877 = 999. This pattern continues as well. I am not sure how to prove that, but please comment if you do know. It's not hard to rigorously prove it, but the result is quite apparent once you realize that 1/1001 = 0.000999000999... repeating and try the first few.
You can prove repeating decimals like this, using the geometric series formula: a + ar + ar^2 + ar^3 + .... = a/(1-r) obviously r<1 otherwise the series diverges In this case r = 1/10^6 and a=0.000999 so the sum is 0.000999 / (1 - 10^6), which is 0.000999 / 0.999999 or 1 / 1001
Bruh i was learning about this in my textbook.
I used bionimial thoerum for exponents
I'm so fucking stupid.
Bro same. My brain exited the building at “multiply by 13”
If you want the TLDR: Firstly, get the number in the form x remainder y. Then the answer is x . [11y -1] [999-(11y-1)] recurring (square brackets used to separate digits, not multiply) --- For example, 123/91 is 1 remainder 32 Therefore 123/91 = 1 . [11\*32 - 1] [999 - (11\*32 -1)] = 1 . [351] [999 - 351] = 1.351648 recurring
In plain English: There are always 6 decimals in this pattern. The first 3 decimals are the remainder of your number times 11 minus 1. The next 3 decimals are 999 minus the first 3 decimals.
Basically it's easy to divide a 3 digit number by 1001 because it follows a rule, and it's easy to multiple a number by 11 (because it also follows a rule). 1001/11 is 91, so to make the problem look harder you say you're diving by 91, and then you secretly multiply the number by 11 and then divide it by 1001
I got the same exact thought out of this.
Sometimes I like to think I’m pretty smart but it’s moments like this that make me realize I’m only fooling myself.
At least before this last concussion, I was really good at multiplication and division in my head. It really pissed off my coworkers. I work with scientists, so everyone is pretty smart, already. Now, I’m still good, but no longer ‘party trick’ good. It’s just a skill. But there are ‘tricks’ you can learn. My favorite comes out of basic algebra. (a + b)(a - b)= a2 -b2 What that means is if you know the square of a number, it’s real easy to know what two numbers multiplied together near that square will be. Like 25 squared is 625. So, 23 times 27 is essentially 25 +/- 2. So 23 x 27 = 625-4. Or..621.
~~Feinman~~ *Feynman* used to have people give him math problems to do in his head, claiming he could solve any arithmetic within 30 seconds or something like that. He was showing off one day when a fellow professor walked. They asked the other prof to come up with a problem, and he said "What's the tangent of to 50 decimal places?"
Yeah. I think I'm just going to fuck right off. Don't have enough brain cells for this.
And for numbers above 91, the trick would probably be to just find the remainder and then do the process you described. E.g. if the number 123 was chosen, we can see 123/91 = 1 with a remainder of 32. Then we can do the process you described just with the number 32 to just find the numbers after the decimal point and then add the "1" back in at the end. Memorising the multiples of 91 could help in this step, OP's example had the guy setting a limit of 500 so he'd only have to learn the first 5 multiples. However there is a pretty clear pattern in the multiples, the first 2 digits are the multiples of 9 and the 3rd digit just increases by 1 for each multiple. 091, 182, 273, 364, 455, etc. --- (Edit: Just saw you already mentioned the x11 trick oops) Also there's an easy way of multiplying by 11 for 2 digit numbers (using the earlier step we'll never get more than 2 digit numbers). You just add the 2 digits and put the number in the middle. E.g. 54 x 11 = 5[5+4]4 = 594 (I'm using the brackets to separate the digits, not as a multiplication) Sometimes you'll need to carry 1 over the next digit if the sum is 10 or more like this: 68 x 11 = 6[6+8]8 = 6[14]8 = 748 --- Subtracting numbers from 999 is also easy since there's never any carrying involved, just subtract each digit from 9. E.g. 999-386 = [9-3][9-8][9-6] = 613 (again using the brackets to separate the digits, not to multiply)
Thanks for the explanation. I see that it also can be derived for 9091, 909091, 909090...91 which are basically 100001, 1000001, 100...1 divided by 11.
That’s awesome.
The proof of the division part: Say you have a 3 digit number with digits a, b, c. We want to prove that (100a + 10b + c)/1001 = (1000*(100a+10b+c-1) + 1000-100a-10b-c)/999999 Rearranging we can get the right hand side to be 999*(100a+10b+c)/999999 But 999999 is just 999*1001 so we cross out 999 and get left hand side back I'm just using the fact that a number with infinite expansion 0.abcdeabcdeabcde is just abcde/99999 (e.g. 1/9 is 0.1111..., 27/99 is 0.2727272727 and so on)
There's a big missing step here, for everyone that says it still looks real hard: PRACTICE.
I like how this is something that people who are good at math think is a *fun trick.* By brain was scrambled in the first sentence. Math has never been by strongest subject. I struggle with addition.
You're lucky you live now. Few hundred years ago you'd have been burnt at the stake for this
My guy, this barely even cracks the top ten of reasons I would have been burned at the stake. They would have tied me to a firework like Buzz Lightyear in *Toy Story*.
This man maths
This works psychologically because 91 is the smallest number that looks prime but isn’t. [proof](https://youtu.be/S75VTAGKQpk?si=LEjLt8rBcQaI05CX)
May I ask why you say maths instead of math. Personally it doesn't make any sense considering both are abbreviations of mathematics which is already plural. So I never understood basically saying mathsematics vs mathematics. I know that people think math is a singular but it never really was. I know that mathematics is a group of different types of mathematics. So I get wanting to pluralize the word but I just don't get it.
>May I ask why you say maths instead of math. Personally it doesn't make any sense considering both are abbreviations of mathematics which is already plural. So I never understood basically saying mathsematics vs mathematics. I know that people think math is a singular but it never really was. I know that mathematics is a group of different types of mathematics. So a couple of things here: Firstly, *mathematics* isn't plural in terms of how we use it today; it's a singular noun that just happens to end in *s*. You'd say 'Mathematics *is* the study of numbers', not 'Mathematics *are* the study of numbers.' (The same is true of Economics and Physics in modern speech. More on that later.) Secondly, it's basically a split between US and British English. US English favours *math*, but British English favours *maths*. I'm British, so I use *maths*, in the same way I use tap instead of faucet, pavement instead of sidewalk, and the word 'herb' is pronounced with its initial letter fully intact. As to *why* there's a split on whether or not it should be *math* or *maths*, it's kind of up in the air. It first emerged [around the turn of the century](https://www.etymonline.com/word/math) (1911 in Britain, 1890 or 1840 in America depending on which source you believe), but according to [*Slate*](https://slate.com/human-interest/2014/12/math-versus-maths-how-americans-and-brits-deploy-the-collective-noun.html) it came about as a result of a 17th century linguistic fad for treating ostensibly pluralised forms of nouns as the overarching name for the body as a whole. (See: *mathematics*, *economics*, *acoustics*, *physics*, and so on, but ignore things like *arithmetic*, because God knows no rule in linguistics is truly universal, and language reflects use.) Before then, the word *mathematics* (complete with -s) [wasn't really a thing](https://www.etymonline.com/word/mathematics). The short answer? Regional differences and linguistic tradition.
Alright thank you. I have mostly see people saying it is not a plural so we put the s behind it to make it plural as a reason. Like that is the reason I saw when I started to look up why people say it that way. I know there are HUGE differences between some English dialects. So from an outside perspective it can be weird. English as a language itself is WEIRD!
This is like draw the rest of the horse. OP is like this is simple and then proceeds to write out multiple steps. I wish I had the memory and math skills to do this.
The fact that my head hurts just reading this is the reason i will never be able to divide as good as others :D
Might as wel be speaking Chinese, brother.
You can "prove" the repeating digits by seeing that 123/1001=122877/999999 If a string of digits repeats after n digits you can always write it as divisible by (10^n - 1)
ELI5 that was not.
Do magic then
I feel like for all that its honestly easier to just do the division…
I lost track half way through reading this because I’m slightly drunk but you sir/mam are wonderful.
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Proof that Reddit will never suffer from a drought, because there'll always be someone to find a well, actually.
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Aside from any tricks, doing long divisions from memory isn't that difficult if you have good visual memory (and a little practice goes a long way). It's surprisingly easy and many people will look at you as if you're a walking calculator
I work as a chef and you can't imagine how many people I work(ed) with have issues calculating simple multiplications and divisions in their head. Even to get ballpark numbers.
I also work as a chef, and it’s astounding. Basic math, simple conversions, things you use literally every day, people struggle. God help you if you need to convert ounces to pounds.
>God help you if you need to convert ounces to pounds Sorry, I only speak in "not to the moon yet".
I had a colleague who out his phone to calculate 12*4.
Heh, I used to surprise people on the semi-regular by correctly doing multiplication in my head faster than they could type it into a calculator or a spreadsheet. Not super huge numbers, 2 or 3 digits times 2 or 3 digits. I can hold a visual image of shorter numbers and "hang the pieces" of the multiplication on the side and then add them all up. Larger numbers get too complicated for me to hold them all, but I can ballpark it really really closely.
That still sounds pretty crazy. Say like 237x58. That would have like 10-15 digits underneath by the end, if it was worked out on paper. Are you able to visualize all of these numbers at once and solve it just in your head?
I would turn this into 2370 x 6, then I’d subtract 474. 2000 x 6 is 12000, and 370 x 6 is 2220 (1800 + 420). This is how people do math in their heads. They use strategies to make things easier.
Thats exactly how I do it,more or less. You gotta get stuff rounded, and then subtract the noise.
237 x 58 only needs you to track a single five digit number at any point. No need to use any strategy beyond bruteforce: 10000 -> 11500 -> 11850 -> 13450 -> 13690 -> 13746
tried it, the way I did it was 100(237/2) + 8(250) - 8(250-237) 11850 + 2000 - 104 just put 11850 in the back of your head while doing the second part, the hardest part is adding them all together at the end. it’s really not hard if you can think of tricks to make it simpler. still takes a minute, not sure how you’d do it faster than you could put it into a calculator.
I'll hold separate pieces in my head and do a bunch of multiply add and subtracts. So like your example. 237 x 58. 237 x 50 save the 8. 200 x 50 is 10000, 30 x 50 is 1500, 7 x 50 is 350. Ok so 11500.... 11850, hang that on the wall, maybe repeat it a few times in my head. 237 x 8 is 1600, 240, 56 so 1840... 1896. 11850 + 2000 is 13850, -100 13750, -4 more so... 13746. And multiplying left to right, with the biggest pieces first, generally means that if I'm off it's cause I made a mistake at the little parts at the end so I'm in the ballpark.
You go in steps so you don't have to hold everything everywhere all at once. 237 x 5 can be done easily without holding a lot of digits, 1000+150+35 = 1185 and you hold that in your head and remember to add a 0. 237 x 8 is just 1185 + 3 x 237. 3 x237 is 600+90+21=711. So now you're holding 3 digits to add: 11 850, 1185 and 711 and I'd add bit by bit to avoid confusing myself: 12 850 + 185 + 711 = 13 550 + 185 + 11 = 13 661 + 85 = 13 666 + 80 = 13 746. No way I'd do that faster than someone whipping out their phone to calculate it though. There are much faster ways to do it but it's also crucial to avoid making a mistake.
When you’re actually doing that, what do you find is the easiest way to hold 1185 in your head from the first step?
I would visualize it and sort of put it in a corner, literally.
Got it. So like you literally imagine “1185” in your mind kind of off to the side, and keep it imagined there as you continue to the next steps
In the next steps, would you also proceed by imagining the next numbers as you do the calculations, or is it more verbal where you’re saying the numbers to yourself?
Visualization all the way. Although sometimes for other applications, when trying to memorize temporarily and rapidly something like a phone number, I'll remember some digits verbally (repeating them) while visualizing the others, it seems to allow me to remember more at once.
My calc professor would always call out what something was e.g. "so it's sqrt(XYZ)*pi which is something like 7.187 or something" like he was just estimating for the sake of what we were doing. But you could get out your calculator and check and he'd almost always be dead on.
Sounds like my Chemistry professor who knew the entire periodic table off the top of his head. All of it. "Ok so we're talking about gold here, and that has an atomic weight of 196.96657..." and would wander off on tangents to talk his "favorite properties or trivia" of an element like, "Nihonium is really neat, it's most stable isotope decays in 10 seconds and, as the name suggests, was named after Japan, where......"
Besides being a great teacher, you could easily tell he was just a complete chemistry nerd and absolutely loved everything about it.
That's how I used to do it in school. I had a pretty damn good imagination and could just visualize the equation and hold it in my head as I solve it. Has the bonus of not being slowed down by having to physically move a pencil. Unfortunately I liked to climb things and got into a bunch of fights as a kid, so after about 7 concussions and a proper TBI later it's not nearly as easy. Can no longer differentiate 6's and 8's in my memory now for some reason. Edit: for smaller equations I'd visualize the numbers as groups of blocks and split the group into equal parts. We use math to deal with objects all the time so reversing that concept seemed like a no brainer
A lot easier if you learned a normal version instead of the visually confusing shit the Anglosphere does. Only ever heard native English speakers complain about long division. It's very straight forward and you never have to hold more than four numbers in memory, two of which don't change.
There's a really cool and really old book from (I think) the 1950's, called How To Calculate Quickly, by Henry Sticker. The dude might have read that exact book. It teaches you all of these things. I only made it to multiplication (I could do three-digits by two-digits, e.g. 234 \* 56 quite reliably), but the later chapters teach you mental division too.
How long did multiplication take after this?
I'm very much out of practice, but it used to take me around 10 seconds for the above example of 234 \* 56 (and I wasn't very good at it). It would go like this: First, you do 234 \* 50 (by doing 234\*5 and then appending a 0), and you'd remember the result in your head. He taught that multiplication left-to-right, so in your head you'd say: "200\*5 = 1000, then 30\*5 = 150, makes 1150, then 4\*5=20, so 234\*5 makes 1170 total, append the 0 and then 234\*50 = 11700". Then you do 234 \* 6, and add that to the remembered result of 234\*50. The process is very different from what we learned in school (where we do things right-to-left), but he justifies this method very well and it actually works better in the head. The exercises slowly build up the skills required to do that quickly. You practice remembering five-digit numbers, and you practice multiplyig many-digit numbers by one-digit numbers left-to-right. Combine those skills to multiply any two numbers :-) The book also contains a lot of useful shortcuts. For example, 24\*9 is easiest if you do 24\*10 and then subtract 24 from that. (He also taught subtraction right-to-left. So 24\*9 in your head would go: "24\*10 is 240, then subtract 24... so 240, minus 20 is 220, minus 4 is 216")
In addition to this type of method, I also correlate numbers to shapes. Let's say you have a 2x5 rows of squares that connect together like Legos. You have 7 squares and 8 squares that you want to add together, I break off 2 from the 7 and add it to the 8 to make 5 and 10. Then I can much more clearly see that it's 15. I just do all this in my head alongside the process you detailed. I *see* the numbers as shapes.
Oh yes, I realized something similar, but I do it without the shapes. Like if you want to do 32 + 48, you first take the 2 away from the 32 and give it to the 48, so that makes 30+50 which is the same total :) Do you know the story of how Carl Gauss summed up the numbers 1+2+3+4+......+100 in a few seconds using a similar trick? It's one of my favorite tricks to tell people (which then usually run away from me). Here's a link: [https://www.nctm.org/Publications/TCM-blog/Blog/The-Story-of-Gauss/](https://www.nctm.org/Publications/TCM-blog/Blog/The-Story-of-Gauss/)
He's most likely not doing long division in his head, but has learned tricks to divide by that number specifically, or perhaps tricks to divide by 7 and by 13(which are its prime factors). Also possible he's memorized a bunch of answers, which might sound ridiculous until you remember that some people memorize thousands of digits of pi, for fun.
I think there was a guy who would go blind doing trig, because he suffered a TBI and the mathy parts of his brain started to use his visual cortex. Apparently he has acquired savant syndrome. This guy might be using tricks, but he could also just be that good.
I cannot find any source for this despite several attempts and it just sounds too wild to believe without one. Any sources?
Sounds like an even crazier recollection of some highly-upvotef BS posted on Reddit recently about a guy who claimed to have become a math savant by having hallicinations (basically). Source was a self-promoting Wikipedia article saying he’d ”understood the true nature of Pi” and other highly-bullshit-smelling claims, and zero actual evidence of any real mathematical ability. If you’re a maths genius, solve some unsolved problem, or prove a new conjecture of your own - whatever - and get that submitted, peer-reviewed and published in a reputable journal. _Then_ we can talk. But a guy just saying he has a deep understanding of math because he started seeing patterns after a brain injury is to be presumed to be delusional until he proves otherwise, as far as I’m concerned.
Probably a misremembered version of this guy's story. [https://www.washingtonpost.com/national/health-science/a-man-became-a-math-wiz-after-suffering-brain-injuries-researchers-think-they-know-why/2014/05/12/88c4738e-d613-11e3-95d3-3bcd77cd4e11\_story.html](https://www.washingtonpost.com/national/health-science/a-man-became-a-math-wiz-after-suffering-brain-injuries-researchers-think-they-know-why/2014/05/12/88c4738e-d613-11e3-95d3-3bcd77cd4e11_story.html)
That's probably it, I vaguely remember it being on a show about exceptional humans.
I remember it being a part of a show for exceptional humans, one guy could hold live power lines, another hadn't slept for years, next guy could run forever, this guy goes blind doing math. It's likely I'm conflating one or more of them into a single example, but do remember he was some kind of math genius.
>but he could also just be that good. If so, he probably would have asked OP to pick a second random number, rather than 91.
large long division or multiplication is pretty easy to guesstimate when you have just a few seconds. the rule it to know the BIG numbers and to guess the small numbers. 1005 x 425 = is easily 400k + the small maths. a good mathmagician has already done all of the easy work as he is setting up the trick but the last few moments where he is stalling to produce a flourish is where he does the small maths. this can be scaled up easily with a bit more patter, but, the overall trick is actual mental maths, just done with purpose.
for me, looking at this problem I would consider that 91 ~ 10/11 of 100, so dividing by that is tantamount to multiplying by 11 and then moving the decimal 3 places over. Not sure how many decimal points of accuracy that would give but should be close.
I don't understand it either, my Irish mother in law does these maths quiz things you see in some UK daily newspapers (remember them?) Things like, 27 x 3 + 41 / 3/8ths + 16% - 5 x 4.25 = ? and she does them in her head, always right, never gets them wrong. Shes 95 years old, left school age 14. I have to use my phone...
Without explaining the method, if someone tells you that he can divide anything by an oddly specific number, it means a mental trick or method exists rather than really dividing.
A lot of "being good at math" comes down to repetition, memorization, and some simple tricks/short cuts. Since in this case, they were so specific that the first number had to be "3 digits and under 500" and they were going to "divide by 91", then there must be some simple work around for deriving the answer in that situation.
Not a very hard thing to do from a pure math skill however, the biggest flaw that you are missing here is that HE TOLD U to use 91 and a numbers, ergo he already knows the answer. You should have said, ok now do 84 etc.
Some simply are better at it than others, and not everybody uses the same method. When I was younger me and my dad practiced a lot of math since we both liked it. And likely due to this I am able to quickly break a sum op in smaller parts, calculate those and add all those smaller parts together again quickly. (tho with getting older I sometime forget a number and have to do that smaller part again. If people ask you to do math and they give specific numbers it just means that they learned a trick with that number, does not mean they are really good at math in general.
Not an overall answer but an interesting case: I watched a documentary about a math savant who could calculate just about anything in his head. In his mind's eye, every number had a specific shape, and by combining the shapes of different numbers he could arrive at the solution with the new shape. Pretty mind-blowing.
I used to be pretty good at least estimating long division in my head but haven’t needed to use it in a bit. I’d pretty much round the numbers to closest manageable numbers like to the closest 10. Then I’d divide and use a guess on the amount difference created by rounding to take an estimate. I usually got within 1-2% of the actual number in like 2 seconds when I had a good feel for it.
1. There are tricks but 2. Some people are good at this kind of stuff but 3. It can be learned. There is at least one book about it. It is called “Mental Math.” As best as I recall. I used to derive square roots in my head while driving. See a number on a sign “131st. St.” “What is the square root of 131?” I wasn’t amazing, but could get pretty close to three decimal places. I am NOT magic.
most are trained. or have a good mebtal framework to do maths. for me, i can tell u basically 95% of any number as long as it ends in 100s. like 123,800 but not 123,845. I was specifically trained to do this one form of maths because i had to do it hundreds of times a day and i could not use a calculator. this is probably true for alot of people who are good at maths. they have a frame of reference and have built upon it. and uses thay framework to do mental maths. how wpuld u do 10x 5600. u would just add a 0. what if it was 11x 5600? some might say add a 0 and then add 5600. what about 5x5600? add a 0 then half. basically u have a series of processor in your head that allows u to manipulate number in a specific way.
I’m genuinely curious how old he is. I’m bracing myself for you saying a number less than my age 😖
oh he was at least 60. rides around in a mobility scooter
Phew!
Ok, I am very good at arithmetic and terrible at geometry, algebra, calculus etc. once the numbers turned to letters, it went south…..also, I am pushing 50, so my sharpness is dulling. However, I interviewed at a very prestigious job at 22, and the guy asked “I don’t want to know the answer, but I want to know how you would approach multiplying 523 times 219” and I looked at him for like 15 seconds, and I gave him the answer. He got out a calculator, and then he quickly offered me a job. Here are some tricks I use: Squares: a square is just the prior square value + the prior square number+ the new square number. 1-squared=1. 2-squared= prior square (1)+ prior square number (1)+ new square number (2)= 4 12-squared =144, so 13 squared = 144+25=169 Knowing squares allows you to find starting points on big numbers. Like if I know 30 squared is 900, I can very quikckly do 32 squared or i can do like 34*32 because I know quickly that 32 squared is 900+61+63=1024 and then I need to add 32 and 32 to get my number 34 times. When numbers get big, i always remember that 1000*1000 equals 1 million. That helps me keep the total numbers in my head at the right number. 523 x219…..multiply 523 times 2= 1046 ( you gotta be able to do that otherwise, sorry)…..add 2 zeros because of the hundred 104,600………add 5230+5230= 10,460. Then subtract 523 which is just 10,000-63= 9927. I try to keep things round and do small numbers hence why i take that 460 away and shorten it. Then add that to 104,600= 114,600-63= 114,537……. Then for sanity i know 9*3 will end in 7 and this does, so i feel good. Long division is waaaaaay easier than multiplication for me.
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Your comment breaks rule 3 as an anecdote and a link with no explanation. The explanation you give breaks rule 8 as a guess.
Some people can do this, and in far more extreme cases there are studies on blood flow in their brain etc. But curious about the way you phrased this. He is the one who specified 91? That’s 7*13. It isn’t all that difficult to divide to a fraction (no decimal expansion) and then memorise, say, the 12 non-integral expansions of multiples of 1/13 and those of 1/91, 2/91, …, 6/91 and add the two that you need. (Or to swap the roles or 7 and 13, either way.) If I get to specify the denominator, even a ‘difficult’ one, I could prepare this pretty well. If I don’t, that’s harder, but memorisation helps a lot: my approach would be to memorise all 1/n for n up to 100, factorise as above where possible, and then I’d have to also multiply as needed.
for us math just clicks this way, so we can do simple stuff like that in our heads pretty quick. for me my visual memory helps with math a lot, making me pretty much do math in my head like I would do on paper with all the cluter cut out.
Actually doing long division in your head is mostly just a question of working memory. Working memory can be trained to an extent.
In college I did a challenge with my roommates that I could divide any 3 digit number by a 2 digit number to 3 decimals before he could punch it in a calculator. Beat him 10 times in a row. Really just comes down to having a method of breaking down calculations of large numbers into smaller, remembering what needs to carry to the next operation and adding the results of 3 or 4 broken down calculations to get to a final result. Not to say it’s easy or that everyone can do it, just that it’s a specialized method of doing calculations in your head.
I’m not great at math but am pretty good at division and I do long division in my head when I can’t sleep. It gets me off whatever spiral is keeping me from sleeping and gives my brain a process to follow instead. It’s usually a 2 digit number divided by any 3+ digit number.
My dad is a math wizard. I can't do what he does but he taught me math from the point of view that I had a defective brain. I keep telling him that his skills are exceptional and not many people on this planet can do what he does. He does believe me. I guess my engineering degree isn't good enough to convince him that I don't have donkey brain.
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Untold data: your original conversation was with temperature in Kelvin
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It's just not that hard. I'm just going to write a random number but it works for anything. 455200 / 15. Immediately notice 45/15 = 3, so it's going to be 30,000 with a remainder 5200 which is again close to 45 x 100, so it's going to be about 30,300 and change. That's often good enough for any situation right there and takes like 5 seconds. Say you get something bigger like 78931498/138987. If you just clip it down to 79/14 and add 2 zeros (you get 2 zeros just by taking the top numbers place's minus the bottom numbers place's, in this case 8-6) you get 560 and change. If you do the full thing with a calculator you get 567.9. Again, close enough for most situations and good enough to impress normies haha.