What number is halfway between 1 and 3? You can probably pretty quickly say the answer is 2 without thinking about it. But how would you calculate it?
Well, what's the distance between 1 and 3? It's 3-1 = 2. What's half that distance? 2/1 = 1. So to go halfway to 3 from 1, we do 1 + 1 = 2.
Now just replace the 1 and 3 with your numbers, 1/2 and 7/8. What's the distance between 1/2 and 7/8? It's 7/8 - 1/2 = 7/8 - 4/8 = 3/8. Half that distance is 3/8 ÷ 2 = 3/16. To get the answer, we just add 3/16 to 1/2. 1/2 + 3/16 = 8/16 + 3/16 = 11/16.
(Note that you can get the same answer by just taking the average of 1/2 and 7/8. That is, add them up and divide by two: (1/2 + 7/8) ÷ 2 = (4/8 + 7/8) ÷ 2 = 11/8 ÷ 2 = 11/16.)