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Unusual fractions

  1. Sep 16, 2010 #1
    16/64 is an unusual fraction such that when you cancel 6's from the top and bottom youre left with correct answer of 1/4.
    I need to Find a way for finding all other unusal fractions for a fraction n/m such that n>=11 , and m <=99.

    I have tried writing it as (10a+b)/(10b+c)=a/c ,but stuck
    Thanks for any help

    NB:this is not a homework question to the mods
     
  2. jcsd
  3. Sep 16, 2010 #2

    Mentallic

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    Homework Helper

    Here's a start:

    [tex]\frac{10a+b}{10b+c}=\frac{a}{c}[/tex]

    [tex]10ac+bc=10ab+ac[/tex] ...Multiply through.

    [tex]10a(c-b)=c(a-b)[/tex] ...Factorize

    [tex]\frac{a}{c}=\frac{a-b}{10(c-b)}[/tex] ...Solve for a/c

    [tex]\frac{10a+b}{10b+c}=\frac{a-b}{10(c-b)}[/tex] ...Substitute from the original equation for a/c

    [tex]10ab+ac-10b^2-bc=100ac+10bc-100ab-10b^2[/tex] ...multiply through and expand

    [tex]10ab=9ac+bc[/tex] ...simplify

    Maybe you can work a bit with this equality.
     
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