Among all fractions that have a positive integer numerator and denominator and satisfy \( \frac{9}{11} \le x \le \frac{11}{13}, \) which fraction has the smallest denominator?
I know this is on the website already but it didn't help.
Here is my "guess":
9/11 x (4 1/9 / 4) =37 / 44
I think: 14 / 17
Thank You
Quite a challenging problem.
By exhaustion of the denominator, it is found that \(\dfrac{5}{6}\) has the smallest denominator :)
Simplify, try all fractions with denominator 1, then try all fractions with denominator 2, then 3 then 4, so on.
+209 
