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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.

 Jun 15, 2019
edited by NoobGuest  Jun 15, 2019
 #1
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Here is my "guess":

9/11  x  (4 1/9 / 4) =37 / 44

 Jun 15, 2019
edited by Guest  Jun 15, 2019
 #2
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I think: 14 / 17

 Jun 15, 2019
 #3
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Thank You

NoobGuest  Jun 15, 2019
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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.

 Jun 22, 2019

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