To add these mixed numbers, first convert them all to improper fractions.

9 7/8 = 89 + 7 = 79/8
5 2/7 = 75 + 2 = 37/7
1 1/8 = 81 + 1 = 9/8
4 5/7 = 74 + 5 = 33/7

Now add the fractions:

79/8 + 37/7 + 9/8 + 33/7

To add fractions, they must have the same denominator. The least common multiple of 8 and 7 is 56:

79/8 7/7 = 553/56
37/7 8/8 = 296/56
9/8 7/7 = 63/56
33/7 8/8 = 264/56

Now add the fractions:

553/56 + 296/56 + 63/56 + 264/56 = 1176/56

Now simplify the fraction:

1176/56 = 21

So, 9 7/8 + 5 2/7 + 1 1/8 + 4 5/7 = 21.