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Prove that a/(b/c) = ac/b

  1. Sep 11, 2014 #1
    I know that by definition, a/(b/c)= a x 1(b/c)....but from there I am lost. Help please!
     
  2. jcsd
  3. Sep 11, 2014 #2
    Well, I'm terrible at formal proofs, but consider:

    a/(b/c)

    multiply numerator and denominator by c, so that we get b by itself as the denominator (nobody likes pesky fractions in their denominator):

    (c/c)*[a*(b/c)]

    You can do this because c/c = 1.

    now you have:

    (c*a) / [c*(b/c)]

    which equals:

    (c*a) / b
     
  4. Sep 11, 2014 #3
    Nevermind I got it!
     
  5. Sep 11, 2014 #4
    Ah, king you posted that just as I got it. Thanks though!
     
  6. Sep 13, 2014 #5

    CKH

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    a/(b/c) = ac/b

    Just a note that you have to be careful. The above is only true when both b and c are not 0. The reason is that division by 0 is undefined. In the above proof (c/c) is used which is 0/0 when c=0. 0/0 is undefined.

    I just got shut out of physics thread by a Mentor poster who believed that:

    ab = ac implies b = c for all values a. That is not correct when a is 0.
     
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