To add these fractions, we need to find a common denominator.

The common denominator for 8, 16, 45 is 360.

Now, let's convert each fraction to have a denominator of 360:

9/8 = (9 * 45) / (8 * 45) = 405/360
5/16 = (5 * 22.5) / (16 * 22.5) = 90/360
39/45 = (39 * 8) / (45 * 8) = 312/360
13/45 = (13 * 8) / (45 * 8) = 104/360

Now, we can add the fractions:

405/360 + 90/360 + 312/360 + 104/360 = (405 + 90 + 312 + 104) / 360 = 911/360

Therefore, 9/8 + 5/16 + 39/45 + 13/45 = 911/360.