Add the opposite number of 1 1/5 to the sum of the numbers (−8 3/4 ) and (−2 5/6 ).

Start by finding the sum of (-8 3/4) and (-2 5/6).  Find the least common denominator (LCD).  12 is the first thing that both 4 and 6 will evenly divide into, so we convert both fractions to 12ths:

-8 3/4 = -8 9/12 (multiply 4 by 3 to get 12, so multiply the numerator, 3, by 3 as well)
-2 5/6 = -2 10/12 (multiply 6 by 2 to get 12, so multiply the numerator, 5, by 2 as well)
-8 9/12 + -2 10/12 = -10 19/12
We must convert the improper fraction.  12 goes into 19 1 time with 7 left over, so 19/12 = 1 7/12
This means that -10 19/12 = -11 7/12
The opposite of 1 1/5 is -1 1/5.  Add this to -11 7/12.  Again find the LCD; in this case it is 60.
-1 1/5 = -1 12/60
-11 7/12 = -11 35/60
Adding these two we get -12 47/60.