Math

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Show that z/pq = 1/pr + 1/qr, where r = (p + q)/z

Finding decmpositions of a fraction into 2 units as indicated on a paprus written in Greek.

  • Math -

    rz/pqr = q/pqr + p/pqr
    rz = q + p
    r = (p+q)/z

  • Math -

    RS = 1/(pr) + 1/(qr) , if r = (p+q)/z
    = 1/( p(p+q)/z) + 1/( q(p+q)/z)
    = z/(p(p+q)) + z/(q(p+q))
    = (zq + zp)/( pq(p+q))
    = z(p+q)/(pq(p+q))
    = z/(p+q)
    = LS

    This allows you to express any fraction , which has a factorable denominator , into two fraction each with a numerator of 1

    e.g.
    suppose we have 5/12

    5/12 = 5/(3x4)
    so using the above formula
    z = 5
    p = 3
    q=4
    then r = 7/5

    so 5/12 = 1/(3(7/5)) + 1/4(7/5))
    = 1/(21/5) + 1/(28/5)
    = 5/21 + 5/28
    = 5( 1/21 + 1/28)

  • Math -

    Thank you so much!!

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