Rational numbers/Comparing/573 by -1234 and -2007 by 4322/Exercise/Solution

Multiplication yields

$573\cdot 4322=2476506{\text{ and }}1234\cdot 2007=2476638.$

Therefore

${}{\frac {573}{1234}}\leq {\frac {2007}{4322}}\,$

and so

${}p={\frac {573}{-1234}}={\frac {-573}{1234}}\geq {\frac {-2007}{4322}}=q\,.$

To the exercise