I have encountered a question in stackexchange. I am putting a link below:
Can fractions be relatively prime?
It is said that "Two numbers are relatively prime if they do not share any factors, other than $1$. Is it possible for fractions to be relatively prime?"
According to accepted answer $\frac{8}{35},\frac{11}{9}$ are relatively prime. It seems me correct in the first glance, but when I thought about it , I saw that it contradicts with the definition of being relatively prime.Because , to be relatively prime, $\gcd$ must be equal to $1.$
However , $\gcd(\frac{8}{35},\frac{11}{9}) = \frac{1}{315}$ by the formula for fractions.
I hesitated to accept the accepted question because of the definition. Can you enlighten me about it? How can I determine whether given fractions are relatively prime or not? Moreover, are the given fractions relatively prime?