theorem Th39: :: RING_3:39

for p, q being Rational
for m, n being Nat
for i, j being Integer st m = denominator p & n = denominator q & i = numerator p & j = numerator q holds
( denominator (p * q) = (m * n) div ((i * j) gcd (m * n)) & numerator (p * q) = (i * j) div ((i * j) gcd (m * n)) )