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Very simple fraction simplification

  1. Aug 19, 2013 #1
    I feel stupid asking this, but I just can't see it. I need to simply this and I already know the answer, but I don't know why this is the answer.

    simplify

    3p-3q
    5p-5q

    My first reaction was to remove a factor of p-q but that would leave

    p-q(3-3)
    p-q(5-5)

    Which would be 0/0. I know the answer is 3/5 but I just can't see why.
     
  2. jcsd
  3. Aug 19, 2013 #2

    CAF123

    User Avatar
    Gold Member

    You can factor out p-q top and bottom, but your end result is not quite right. If you try to use the distributive law here, that is a(b+c) = ab + ac, this might help you see your error.
     
  4. Aug 19, 2013 #3

    Mark44

    Staff: Mentor

    The above is incorrect, and simplifies to 1, assuming p ≠ 0. This is based on what you wrote, which might not be what you intended.

    The simplest way to go would be to notice that 3 is a factor of the terms in the numerator, and that 5 is a factor of the terms in the denominator. The original expression can be written like so:
    $$ \frac {3(p - q)}{5(p - q)}$$
    Of course, this can be simplified further.
     
  5. Aug 19, 2013 #4
    That makes perfect sense now. Thanks for explaining it.
     
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