(Quickly) finding the smallest fraction

All fractions are greater than $1/4$ except for $\frac{53}{216}$

Reciprocate/flip them, divide (long division), and see which of these is the biggest. The biggest reciprocal should correspond to the smallest number.

If you have $\frac{a}{b}$ and $\frac cd$ then $\frac ab > \frac cd \iff ad> bc$. Multiplication isn't too slow.

Now pick your favourite fraction, compare it against another, discarding the larger. To ensure you are working with smaller numbers, you can discard any common factors between $ab$ and $cd$. You need 4 comparisons to check which is smallest. Each comparison requires 2 multiplications. I understand that 7.5 seconds is not enough to do a multiplication, but it does not seem too bad sometimes.

As both @lulu and @roddy point out, there are more tricks for these specific fractions, which speed up the process quite a bit. Practicing your multiplication as well as exploiting these tricks should make this problem easy.