Calculation Shortcuts

[Anonymous No.9480264]

Post your favorite calculation shortcuts. Any subject or difficulty level.
>inb4 just use a cuckulator XDDD

[Anonymous No.9480268]

https://math.stackexchange.com/questions/175561/is-the-following-matrix-invertible

[Anonymous No.9480277]

if an integers added numbers add up to something divisible by 3 the number itself is divisible by 3
ex
[math] 222 = 2 + 2 + 2 = 6 [/math]

222 is evenly divisible by 3

[Anonymous No.9480285]

>>9480268
Brilliant!

[Anonymous No.9480308]

Every composite number other than 6 has non trivial dubs in some base.

[Anonymous No.9480426]

>>9480264
if a^b = c
then b = log c / log a

used this all the time in high school to be quick as fuck

[Anonymous No.9480458]

>>9480277
Also works for 9.
Any number divisible by nine has digits that sum to a multiple of nine.

[Anonymous No.9480473]

To multiply two numbers between 10 and 20 (let's note them in decimal notation ab and cd)

First add ab and d
Then multiply by ten
Finally add to b*d the result

Example :

16*18 = ?
24
240
288

It is easy to prove but makes life easier on many cases especially if you work with hexadecimal notations

[Anonymous No.9480482]

>>9480277
The same trick exists with 11

Can 94578132 be divided by 11 ?

2-3+1-8+7-5+4 - 9 = -11
The answer is yes

[Anonymous No.9480505]

>>9480482
>same trick
same? you're subtracting every other digit.
neat trick, but not the same.

And it doesn't seem to work for me.
Can 22 be divided by 11?
2-2 = 0

Can 121 be divided by 11?
1-2+1 = 0

3,861?
1-6+8-3 = 0

What are you trying to pull here?

[Anonymous No.9480519]

>>9480277
Same with 9 my 9ger

[Anonymous No.9480521]

>>9480505
>11*0=/=0
(Different anon but still)

[Anonymous No.9480533]

>>9480521
>>11*0=/=0
I'm more confused than ever.
Anon (>>9480482) shows adding and subtracting backwards digits in a number adds up to -11 in his example: "therefore big number is divisible by 11".

When I try smaller numbers, trick seems to work except they all add up to zero, not -11.

I have NO idea what you're trying to say with "11 * 0".

[Anonymous No.9480797]

>>9480264
You can compute almost any squared root using this little iterative method

[math]x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}, \in \mathbb{N}[/math]

where [math]x_{0}[/math] is your initial guess, I suggest something like [math]x_{0} = \frac{x_{n}}{2}[/math] in order to achieve a fast convergence in most cases.

[Anonymous No.9480863]

Is there any formal approach to this? I want to get my hands on books that teach this.
I've gone through most advanced maths you can get in Engineering but thanks to calculators I'm a disgusting arithmetic idiot. Please help, even some basic stuff like bigger multiplications is hard for me.

[Anonymous No.9480871]

>>9480264
newton raphson

[Anonymous No.9480872]

>>9480863
Your employer doesn't want you doing headmath.

[Anonymous No.9480894]

>>9480871
stop copying my comment

[math]\mathbb{R}^{eeeeeeeeeeeeeeeeeeeeeeeeeeeeeee}[/math]

[Anonymous No.9480906]

>>9480894
I didn't even read the thread.

[Anonymous No.9481325]

bump

[Anonymous No.9481355]

Currently reading through this at work, figured it’s pretty relevant. Enjoy.

https://archive.org/details/SecretsOfMentalMath

[Anonymous No.9481422]

1/x = 1/y + 1/z => x = yz/(y+z)