In order to convert a rational number into its standard form, why do we need to make the denominator positive?
A rational number a/b is said to be in the standard form if b is positive, and the integers a and b have no common divisor other than 1.
ie,the positive denominator is one of the conditions for a rational number to be a standard one because the standard is defined like that.
So,making denominator positive is one step to making it a standard rational number.
I think it is so for the ease of claculations with rational numbers.