Among all fractions x that have a positive integer numerator and denominator and satisfy 9/11 ≤ x ≤ 11/13 which fraction has the smallest denominator?
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We want to find a fraction a/b such that

This is true if and only if

We can choose a value for a only if the two extremes include at least one integer, i.e. if

Solving for b, we have

So, the smallest fraction is given for . We have

Solving for a, we have a=30.

The fraction 30/36 can be simplified to 5/6. So, we have

and this is the smallest possible denominator.

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