Question 34439
Try this: Let x = the numerator and y = the denominator.

{{{x/y = 1/2}}} Rewrite this as: {{{y = 2x}}} and substitute below.
{{{x*y = 72}}}

{{{x(2x) = 72}}} Solve for x.
{{{2x^2 = 72}}} Divide both sides buy 2.
{{{x^2 = 36}}} Take the square root of both sides.
x = +or-6
y = 2x
y = +or-12

There are two answers:

{{{6/12 = 1/2}}}
{{{(-6)/(-12) = 1/2}}}

In both of these fractions, the product of the numerator (6 or -6) and the denominator (12 or -12) = 72