Originally Posted by

**MathCrusader** Find a fraction between 97/36 and 96/35 which has the smallest denominator. Since 97/36 > 96/35, I formed the following inequality

$\displaystyle \frac {97}{36} < \frac pq < \frac{96}{35} \, .$

Now, appropriately so, we could write the given fractions with common denominators and thusly yield

$\displaystyle \frac {3395}{1260} < \frac pq < \frac{3456}{1260} \, .$

Now this is where I am stuck. The correct answer is p = 19 and q = 7, which corresponds to the fraction 3420/1260.

Anyone got any idea?