Chapter 2 - Multiplying and Dividing Fractions - 2.1 Basics of Fractions - 2.1 Exercises - Page 117: 19

$\frac{303}{520}$

First, you must subtract the number of rooms reserved for nonsmokers from the total number of rooms. $520-217=303$, so 303 rooms are for smokers out of the 520 rooms total. That means that the numerator--the number of rooms for smokers--is 303, and the denominator--the total number of rooms--is 520. The final answer is $\frac{303}{520}$.