# Thread: A neat trick with the number 9

1. A neat trick with the number 9:

Multiply 9 by any number you wish.

Lets say 9 * 36 = 324

Now add 3 + 2 + 4 = 9 !!!!!!

(Doesnt even have to be an integer)......

9 * 528.336 = 4755.024

Then add 2+7 = 9 !!!!!!!!!!!!!!

How COOOOOOL is that !!

2.

3. Originally Posted by leohopkins
A neat trick with the number 9:

Multiply 9 by any number you wish.

Lets say 9 * 36 = 324

Now add 3 + 2 + 4 = 9 !!!!!!

(Doesnt even have to be an integer)......

9 * 528.336 = 4755.024

Then add 2+7 = 9 !!!!!!!!!!!!!!

How COOOOOOL is that !!

You know... someone always has to be a smart-ass... might as well be me this time...

9*0 = 0
...still equals zero.

(-2)*9=-18
what do I do with the negative?

But it is a really cool trick. Thanks Leo. I think it only works for the positive reals though...?

Cheers

4. i've known that works with simple numbers since about 4th grade, but i didn't know it worked with decimals too. Interesting.

5. Originally Posted by william
Originally Posted by leohopkins
A neat trick with the number 9:

Multiply 9 by any number you wish.

Lets say 9 * 36 = 324

Now add 3 + 2 + 4 = 9 !!!!!!

(Doesnt even have to be an integer)......

9 * 528.336 = 4755.024

Then add 2+7 = 9 !!!!!!!!!!!!!!

How COOOOOOL is that !!

You know... someone always has to be a smart-ass... might as well be me this time...

9*0 = 0
...still equals zero.

(-2)*9=-18
what do I do with the negative?

But it is a really cool trick. Thanks Leo. I think it only works for the positive reals though...?

Cheers
Other than the zero it works. take -18 and just do 1+8 = 9. or -1 + -8 = -9

(Its still a 9 whether its a pos or neg)

But, you got me on the Zero !!!

6. cool trick? not really

how about if we change base? lets say to octan?
11=9 here

50*11=550

5+5+0=10 wich is 8 in our base. well there did that trick go

7. Originally Posted by Zelos
cool trick? not really

how about if we change base? lets say to octan?
11=9 here

50*11=550

5+5+0=10 wich is 8 in our base. well there did that trick go
EH ??????

8. Originally Posted by Zelos
cool trick? not really

how about if we change base? lets say to octan?
11=9 here
The correct term is 11d = 9o !

When mixing bases you must at least specify any non-decimal, or preferably all bases!
Originally Posted by Zelos
50*11=550
WOW! did you use a calculator for that one!
Originally Posted by Zelos
5+5+0=10 wich is 8 in our base. well there did that trick go
Actually 10 = 2

9. The correct term is 11d = 9o !
no cause octanian dont have 9
so it should be 11o=9d

When mixing bases you must at least specify any non-decimal, or preferably all bases!
yes, but i didnt feel for it im so evil

WOW! did you use a calculator for that one!
WHO TOLD YOU

Actually 10 = 2
binary yes

10. If you must count in '8's the term is octal in English. Octanian was an 8 legged Roman....

11. Hey this property has a neat little proof (not my proof btw, the guys on mathforum i think)

The trick is to realise that if a natural number is a multiple of 9 then adding up its decimal expansion still gives you a multiple of 9. To see this consider the number

9n = a + 10b + 100c + ... = a + (b + 9b) + (c + 99c) + ... = (a + b + c + ...) + 9 * (b + 11c + ...) = (a + b + c + ...) + 9k

where k is a natural number. This implies that (a + b + c + ... ) = 9 * (n - k)

i.e. (a + b + c + ...) is a multiple of 9

Now its easy to see that the sequence you get from the operation is decreasing and it stops when you arrive at a number less then 10. Now the only natural number (here im excluding 0 from the naturals, dont you love convention) which is a multiple of 9 and is less then 10 happens to be 9 itself. So you always arrive at 9 QED

PS - There is a formula for the result of this trick on any number in any base, all you do is work out n mod (B-1)

12. Here's another one for you leo,

Take any number ending with a 5 and square it. say 75*75
The quick mental way to do this is multiply the 7 by 8 = 56 then just place 5*5 (25) on the end ie 75*75 = 5625.

Just take all the digits befor the last and multiply itself by itself + 1 so 125 *125 becomes (12*13) and add on the 25 ie 15625!

Proof: 75*75 = 7*8*100 +25 = 5625

(a+5)^2 = a^2 + 10a + 25 = ( (a/10 * (A+10)/10 ) * 100 )+25

Drop the 25's from each side and simplify a/10 * (A+10)/10

down to ((a^2 + 10a)/100) then Mult by the 100 gives

a^2+10a = a^^+10a

I am sure there are othre proofs for this, but this one I worked out some time ago.

So now when you are asked what 205 times 205 is Leo you'll know it is 42025!

And for 206 * 206 it's just 42025 + 205 + 206 or 42436!

13. I wonder if there is any other number with this property (of 9, that is)? I suspect not, but don't know.

Here's another. The sum of digits in the solution to 11x = 2x, for all x (it's easy to see why) In fact, I'd place a (small) bet on the fact that one could come up with more-or-less exotic similar relations for any fixed n and all x.

This is the sort of stuff that makes number theorists go all gooey. Well, whatever rings your bell I guess.........

14. are you saying that the sum of the digits of 11x = the sum of the digits of 2x guitarist (with that i agree) or that 2x = The sum of digits in the solution to 11x?

15. Originally Posted by river_rat
are you saying that the sum of the digits of 11x = the sum of the digits of 2x guitarist (with that i agree) or that 2x = The sum of digits in the solution to 11x?
Yes, the former, I mis-spoke, or, if you prefer, mis-thought. I am crap with numbers, and I don't even posses a calculator.

What little I've seen of number theory leaves me completely cold.

16. I wonder if there is any other number with this property (of 9, that is)? I suspect not, but don't know.
every that is only 9s in, 9,99,999 and so on have the same ability the only differens is that you have to put toghater the same amount of digits as there is in 9s
for exempel, 9 do we already know

but 99
50x99 = 4950
49+50=99

same thing just need to add them 2 and 2 there instead of everyone alone

999 then:
50x999 = 49950
049+950 = 999
here we have to add them 3 and 3 starting the count of 3 from the back, why it seems only to get 2 there with 49 is cause ýou can think of a invisible 0 infront of it

and if we take 7 in octan base, instead of our 9
7o*11o=77o
7o+7o = 16o
1o+6o = 7o

where o just tells its octan base. as you can see its the same thing there

id suspect its so with every base for the number n-1 where n is the base number

17. Originally Posted by Guitarist
I wonder if there is any other number with this property (of 9, that is)? I suspect not, but don't know.

Here's another. The sum of digits in the solution to 11x = 2x, for all x (it's easy to see why) In fact, I'd place a (small) bet on the fact that one could come up with more-or-less exotic similar relations for any fixed n and all x.

This is the sort of stuff that makes number theorists go all gooey. Well, whatever rings your bell I guess.........
if you work in base p, p-1 has this property.

18. Looks to me like these tricks only work for the field of rational numbers. Take, for example, 9*pi or 9*e. Doesn't look like the trick works for irrational numbers I wonder if this idea could be extended to the field of complex numbers, assuming the real and imaginary parts are rational? Should be interesting to see.

19. Originally Posted by Vroomfondel
Looks to me like these tricks only work for the field of rational numbers. Take, for example, 9*pi or 9*e. Doesn't look like the trick works for irrational numbers I wonder if this idea could be extended to the field of complex numbers, assuming the real and imaginary parts are rational? Should be interesting to see.
Um, how do you get that this works for rational numbers? For example how do you work out the sum of the digits of 9*1/27?

20. Oops, thought wrong. I was thinking "terminating decimals" but i typed rational. That was late, give me a break

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