p and q

If a is rational then there exist integers p and q such that a = p/q where q>0.

Similarly, b = r/s for some integers r and s (s>0)

Then a*b = p/q * r/s = (p*r)/(q*s)

Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0

Thus a*b can be expressed as x/y where

p and r are integers implies that x = p*r is an integer

q and s are positive integers implies that y = q*s is a positive integer.

That is, a*b is rational.

Possible.

int cmp;

cmp= strcmp (p, q);

if (cmp<0) printf ("%s < %s\n", p, q);

else if (cmp>0) printf ("%s > %s\n", p, q);

else printf ("%s == %s\n", p, q);

p/q * r/s = (p*r)/(q*s)