+0

Hi can you pls help?

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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
+208
-1

Thank You

NoobGuest  Jun 15, 2019
#4
+7683
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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