Posted by **Barb** on Thursday, January 31, 2013 at 10:54am.

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 -
**Steve**, Thursday, January 31, 2013 at 11:09am
rz/pqr = q/pqr + p/pqr

rz = q + p

r = (p+q)/z

- Math -
**Reiny**, Thursday, January 31, 2013 at 11:44am
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 -
**Barb**, Thursday, January 31, 2013 at 12:13pm
Thank you so much!!

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