To add these fractions together, we need to find a common denominator. In this case, the least common multiple of 24, 330, and 220 is 2640.

Now we can rewrite each fraction with a denominator of 2640:

3/16 = 495/2640
5/24 = 275/2640
13/330 = 104/2640
9/220 = 99/2640

Now we can add the fractions together:

495/2640 + 275/2640 + 104/2640 + 99/2640 = (495 + 275 + 104 + 99)/2640
= 973/2640

Therefore, the sum of the fractions 3/16, 5/24, 13/330, and 9/220 is 973/2640.