Hello, esteemed 4chaners. Do you have any math shortcuts that you would like to share?
For instance:
To multiply a 2-digit number by 11, take the sum of its digits. If it's a single digit number, just write it between the two digits. If the sum is 10 or more, do not forget to carry 1 over.
For example, 34x11=374 since 3+4=7. 47x11=517 since 4+7=11.
Divisible by 7 test:
1. Remove the last digit, double it, and subtract it from the remaining digits.
2. If the result is negative and there are 2 or more digits, drop the negative sign.
3. Repeat until you end up with a multiple of 7. (-7, 0, or +7)
If a number ends in an even number, it is divisible by 2.
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Anonymous2006-07-07 5:47
>>7
You can modify this test for any prime number. The factor of -2 is what varies from prime to prime; for example for 3 it's 1 (hence the sum the digits for divisibility by 3 rule), for 7 it's -2, for 13 it's 4, etc.
I actually calculated this for many primes back in the days when my nerd friends and I used to play prime/notprime. You say a number, they have to figure out whether it's prime or not. I don't remember many of them off the top of my head; after a while you just sortof remember the multiples of everything and you can tell whether or not a number is prime by 'intuition' or whatever.
your mother is divisible by seven and nine. (really, i performed both tests)
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Anonymous2006-07-08 1:58
to find the square of a number n, take the square of n-1, add 2 times n-1, and add unity. while not _really_ obvious, this follows from the binomial theorem: (n)^2 =
((n-1)+1)^2 =
(n-1)^2+2(n-1)(1)+1
This fact is particularly useful for math competitions where calculators are not allowed.
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Anonymous2006-07-08 3:05
10x= x with the decimal place moved on blip to the right 8)
9x = 10x-x
367473586*9=3674735860-367473586=3307262274
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Anonymous2006-07-08 3:23
>>7 >>9
More specifically, represent the number as N = 10*a+b (mod p). For primes other than 2 and 5 (they divide 10), N = 10*a+b = a+(10)^(-1)*b (mod p). Thus the multiplier for the last digit is (10)^(-1) (mod p).
This modular inverse can easily by calculated via the extended Euclidean algorithm. For example, for a divisibility test by 37:
proceeding forward with the normal Euclidean algorithm,
Thus, (10)^(-1) = -11 (mod 37). So a rule for 37 is remove the last digit and subtract it 11 times from the remaining digits.
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Anonymous2006-07-08 3:56
When multiplying a numver by 5, multiply it by 10 and then divide it by 2.
Or, and this is easier, first divide it by 2, then move the decimal point over one (multiply by 10). This is the quickest way to do it in your head
236 * 5 = 118 * 10 = 1180
I know this is pretty simple, but I figured it out in 4th grade, but my math teacher wouldn't believe me and totally discredited it. Since then I've always used it, constantly.
Nice shortcut. Most math teachers are too by-the-book. I like those that teach shortcuts. Afterall, if the answer is the same, why teach to long, drawn out one.
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Anonymous2006-07-10 13:07 (sage)
but my math teacher wouldn't believe me
Your teacher wouldn't believe that 5x=10x/2? WTF!?
Well, at the time I was saying that 5x = x/2, then with the decimal moved to the right. But yeah.
It's not like I had a long debate with him, he just brushed me off as not being worth listening too because I was a kid and didn't bother to think about it. And in his defense, it's probably pretty rare a kid that age has something important to say. But yeah, pretty pathetic
if your half decent at being able to remember a list of numbers in your head and gd at mental arithmatic there is a shotcut on long multiplication
break up each part of the sum into its units, tens, 100's, etc then multiply that by all of the others.
347*134= (300*100)+(300*30)+(300*4)+(40*100)+(40*30)+(40*4)+(7*100)+(7*30)+(7*4)
=30,000+9,000+1,200+4,000+1,200+160+700+210+28
=46,498
ok that may look horrid but i can add that in my head without having to write anything down
might not be shorter if you have pen and paper but if you got a gd memory then you can do it without.
a temp maths teacher taught this when i was 10, then i used to confuse the crap out of the highschool teachers.
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Anonymous2006-07-15 21:23
>>24
Yeah, I've used that system a lot, it works nicely, exp. to impress people.
Also, never abbreviate 'good' as 'gd' again. Ever.
it's pretty important to know the underlying concepts to the math you're doing
if you don't know why you're doing what you're doing you'll eventually fuck up
proven science right there
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Anonymous2006-07-18 23:09
When multiplying two numbers in my head, I'll factor the numbers and use the property (ab == (a/c)(bc)) until i can get it into an easier form.
then i'll do essentially what >>24 does to get the answer.
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Anonymous2006-07-19 5:45
Yeah, >>24 is a waste of work to do directly; with practice you can factor of even 4-digit numbers in your head in a split second. Then just add up the primes and multiply it back out. Much less work, much quicker answer.
I dunno. I'll have to try what you are saying, but I can do what >>24
does very fast as well, with very little hesitation. Once you have a pattern for it, it's nothing more than multiplying a bunch of one-digit numbers together, and not even so many at that. And it works on any numbers. Factoring? Seems like that could get nasty with certain numbers.
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Ouzo2006-07-19 20:00
true, that it is quite possibly a long way round of doing it. If you are adept at factorising then you could do it that way. I am not which is why i stick to my way.
Also its something that 10year olds can do....factorising would be hard to teach to a kid of that age.
Actually, that's not how the brain works. It's the connections between neurons that defines what you know. Since there are basically unlimited potential connections, there is really no limit to how much you can know. It's not like a neuron has "solving multiplication with factoring" assigned to it. A single neuron can have many thousands of uses.
Maybe if you had been using your "neurons" you might have figured that out.
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Anonymous2006-07-20 3:21
CAN YOU TELL ME HOW TO CALCULATE A DEA NUMBER
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Anonymous2006-07-20 9:47
Since there are basically unlimited potential connections,
Fail. You don't have unlimited space, nor unlimited energy. Also, this is not about stored knowledge, but about processing. Neurons are just as involved as connections (signal thresholding, etc).
acutally....
you do have close to unlimited space. It's not just the connection between 2 neurons that defines something. It's whole layout of connections. So one neuron can literally be part of millions of different neuron firing patterns with only having a dozen connections. That's why the brain has such apparently huge potential. There are close to unlimited combinations of neuron firing patterns (although granted not all are useful, you still have more then you could ever have use for). Taking into account how different chemicals can alter the use of firing patterns even further, and you have an even larger threshold of potential firing patterns.
As for energy, while it is true that using neurons requires energy, having connections between neurons doesn't (besides their construction, which is basically nothing). It's the use of these connections that uses energy. And since we have access to as much food as we desire, you won't just run out of energy. True, you could tire yourself out more if you have problems with staying up for a full day. But for normal people, it would take a large and constant use of neurons to affect their lives. And seeing as how you are browsing 4chan, I don't think constant mental strain is a problem for you.
Point being, anyone who doesn't learn how to solve a math problem faster simply because they "don't want to waste neurons" is either stupid or lazy, or more likely both.
However, I admit to the slim chance that even though they are browsing 4chan, they really spend every bit of their time thinking about something vitally important, and breaking away from that thought for even a few minutes would be terrible. In that case I admit defeat.
P.S. processing? All that is saying is you don't feel like solving math problems mentally because you would rather think about other things (like typing it out on your calculator). If that's the case, then say that instead of bringing in 'neurons' which you obviously don't fully understand.
Autistic people have complete control over their minds. However it takes enormous mental discipline for them to use their minds effectively. Conversely it takes enormous mental discipline for non-autistic people to have complete control over their minds.
Some form of intensive indoctrination from infancy would give a non-autistic person the same calculating and memory abilities as an autistic person.
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Anonymous2006-07-25 1:46
>>complete control over their minds
wut, like mind control except to the self?
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Anonymous2006-07-25 11:16
>>41 Autistic people have complete control over their minds.
Hmmm, sounds like a lie.
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Anonymous2006-07-28 2:59
I'm an aspie; from my own personal experience, I have to do a lot of stuff 'manually'; to make small talk, I have to actively think about it. Same thing with a lot of other activities - it doesn't just "flow", it comes from conscious effort.
It's far from "complete control over my mind", though.
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Anonymous2006-07-28 14:08
>>44
I hate small talk so it also takes a lot of effort from me...
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Anonymous2006-07-28 15:21
Maths is about finding relationships between numbers.
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Anonymous2006-08-01 16:18
this is important! what if nigga does steals your calculator of a size of a gaping spider?