0

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?

Air Mike
  • 3,804
  • 1
    All the definitions of "relatively prime" that I can find say that "Two integers are relatively prime if they do not share any factors, other than 1". The terns "prime"' and "relatively prime" apply only to integers. – user247327 Sep 18 '20 at 21:29
  • 2
    I don't believe there is any universally recognized notion of relative primality for rationals. I agree with the people you link to that it makes some sense to define $\gcd\left(\frac aq\frac bq\right)$ to be $\frac {\gcd (a,b)}q$. But other notions are possible. Looking at the set of primes which divide either numerator or denominator makes sense too. In context, I'd expect any writer to clearly define the notion they had in mind. – lulu Sep 18 '20 at 21:32

0 Answers0