Just Move The 4 #shorts

The best way to divide a certain class of numbers is to use absolutely no math at all. WHAT?!

It’s true -- you can get the job done simply by transposing the first digit to the end of the number. 410,256 is a small, accessible number to try it. Just slide the 4 from the first digit to the last digit and you’re all set… and it works with some much larger numbers, too.

In terms of mathematical value, these quirky numbers probably don’t lay the foundation for a groundbreaking Fields Medal-worthy discovery. But this is what recreational mathematics is all about: pushing and pulling on numbers to recognize patterns and curiosities that facilitate your ability to handle heavier-duty work, sort of like how poetry plays with words to express thoughts that *could* be written much more simply. It’s beautiful. And it’s just plain interesting.

#vsauce #education #maths

[Sphinxinator]

Instructions unclear:
16 ÷ 1 = 61

I got kicked out of math class

[espumosoYT]

"Can I have the wifi password?"
"Its in the back of the router"
The back of the router:

[szhzs]

i'm going to pretend with absolute certainty that this works for every single number and will refuse any evidence to the contrary

[omkarprabhu]

( as many digits you want ) divided by 1 works the exact same way 🤯

[squeaksquawk]

I will now go high-five a koala, as I definitely have koalas in my back garden, like a normal person.

[shygamer]

This only work with specific number dont use this on test or quiz related!!

[HiNerd]

People who realised him and micheal are both left handed

[ericeaton]

Immensely disappointed that you didn’t even mention the name of this type of number, much less tell us how to know which ones they are.

[Wiwi_]

I’ll definitely start using this trick from now on

[danielyuan]

Fun fact: if you take 0.102564102564... repeating and multiply it by 4, you'll get the same number as when adding 4 and dividing by 10, this fact follows directly from the property mentioned in the video.

This means you can use the equation 4x=(x+4)/10, to solve for x, so here you get x=4/39, which is the fractional representation of 0.102564... repeating


Can use this to get any number that works from 2 to 9.

210526315789473684 divided by 2, is the same number but with the 2 moved to the front. This is generated from 2/19.

For 3 it's 3103448275862068965517241379, and it's generated by 3/29

You've already seen 4

For 5 it's 510204081632653061224489795918367346938775, generated by 5/49

You've already seen 6

7: 7101449275362318840579

8: 8101265822784

9:

You can also do this with other bases, and you don't have to move the same digit as the number you are dividing.

[soccerdogboy]

What class of numbers does this work with

[tjfjt]

Any number with 1 as it's first digit is also really easy to divide by it's first digit

[noobofnoobs]

fact that makes things less fun: this doesn’t work with all numbers. For example: 200, 000 divided by 2 does not equal 2.

[prathamchadha]

Every odd number with an even number in the beginning, and infinitely many others: _My goals are beyond your understanding._

[goodsocksproductions]

What's the name of this "class of numbers...?"

[hhhhhh]

there are 9 classes of number for which this works, one for each digit other than 0
in these formulas, j can be any integer
dividing by 1: n = (10^j - 1) / 9 (the repdigits e.g. 1111) (these are the only ones you can do multiple times)
dividing by 2: n = 4 * (10^(18j) - 1) / 19
dividing by 3: n = 9 * (10^(28j) - 1) / 29
dividing by 4: n = 16 * (10^(6j) - 1) / 39
dividing by 5: n = 25 * (10^(42j) - 1) / 49
dividing by 6: n = 36 * (10^(58j) - 1) / 59
dividing by 7: n = 49 * (10^(22j) - 1) / 69
dividing by 8: n = 64 * (10^(13j) - 1) / 79
dividing by 9: n = 81 * (10^(44j) - 1) / 89
these formulas list all possible examples for base 10. you can prove this with some basic number theory

[ltcolthorin]

Is there a way to recognize the numbers in that class?

[ckq]

It's kinda easy.

The first one is the decimal expansion of the solution to

10x-4=x/4
Which is 16/39

16 ÷ 39 = 0.410256410256....

Every fraction repeats

For the second one it's
10x-6 = 1/6x

so the decimal expansion of 36/59 which has 58 digits

[jellymunoz]

Ok imma remember it for the probability my teacher puts it in a test

[Sireaquired]

If anyone's curious, that number is 61 octodecilion, 169 septendecillion, 491 sedecillion, 152 quindecillion, 542 quattourdecillion, 372 tredecillion, 881 duodecillion, 355 undecillion, 932 decillion, 203 nonillion, 389 octillion, 830 septillion, 50 sextillion, 847 quintillion, 457 quadrillion, 627 trillion, 118 billion, 644 million, 67 thousand, 796