1. ## fractions

Hiya,
Need some help in proving something..

if we consider fractions like xy/yx

for example 43/34 it is equal to

43/34 = 473/374 = 4773/3774 = 47773/37774 etc

Basically the number in between is the addition of the 2 numbers 4 and 3 whcih is 7.

how can i prove that for any number of 7's inbetween ,the value of the fraction remains the same..

any help??

2. Originally Posted by lunatic
Hiya,
Need some help in proving something..
if we consider fractions like xy/yx

for example 43/34 it is equal to

43/34 = 473/374 = 4773/3774 = 47773/37774 etc

Basically the number in between is the addition of the 2 numbers 4 and 3 whcih is 7.
how can i prove that for any number of 7's inbetween ,the value of the fraction remains the same..
any help??
Hello,

I don't know much about number theory (wait until TPH has spotted this post ), but while playing with your fractions, I noticed:

$\frac{473}{374}=\frac{43}{34} \cdot \frac{11}{11}$

$\frac{4773}{3774}=\frac{43}{34} \cdot \frac{111}{111}$

$\frac{47773}{37774}=\frac{43}{34} \cdot \frac{1111}{1111}$

and so on...

Thus you only have to show that the product is allways:

$43 \cdot \underbrace{111111.....}_{n\ digits \ 1}=4\underbrace{777777...}_{n\ digits \ 7}3$

I haven't got a clue how to prove this. So sorry!

EB

3. Hello,

it's me again. I'm going to try to prove what I've suggested in my previous post:

Code:
11111.....1111 * 43
-------------------
44444.....4444
33333....33333
-------------------
47777.....77773
Maybe this helps a little bit further.

EB