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Maths proof for fractions

  1. Sep 18, 2012 #1
    Could someone show me the proof to why we use the reciprocal in fractions division. I ask this because it seem we are taught the how in math but never the why. Algebra proof would be best thanks.
  2. jcsd
  3. Sep 18, 2012 #2
    It's not a proof, it's a definition. Division is the inverse operation of multiplication, and so dividing by a fraction is the same as multiplying by the inverse of that fraction, which is its reciprocal.
  4. Sep 18, 2012 #3
    My LaTeX always looks so ugly.

    [tex]n = \frac{(\frac{a}{b})}{(\frac{c}{d})}[/tex]
    [tex]n\left(\frac{c}{d}\right) = \frac{a}{b}[/tex]
    [tex]nc = \frac{ad}{b}[/tex]
    [tex]n = \frac{ad}{bc} = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)[/tex]
  5. Sep 19, 2012 #4
    Thanks for the proof abacus, well appreciated makes things clearer for me.
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