You should convert each fraction into an equivalent fraction so that you have common denominators:
1 1/2 = 3/2 = 24/16
5/8 = 10/16
1/16 = 1/16
Adding the equivalent fractions together:
24/16 + 10/16 + 1/16 = 35/16
35/16 reduces down to 2 3/16
So your answer is 2 3/16 inches.