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Math Help - fractions

  1. #1
    lunatic
    Guest

    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??
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by lunatic View Post
    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
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  3. #3
    Super Member
    earboth's Avatar
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    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
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