Question 904009
To start, I would recommend dividing by -1 for both numerator and denominator. This gets rid of the negative signs nicely. Then I would turn the mixed number numerator into an improper fraction. Let's work it out below:

(- 1 2/3 ) / -10

=  (1 2/3) 10  (here, the negative signs are gone as we have divided by -1)
=  (5/3) /10   (here, the mixed number numerator is now an improper fraction)
=   5/3 *1/10  (the reciprocal of 10 is 1/10 )      
=   1/6

 -28 5/36 + 16 7/30 (turn these into improper fractions as well)
=   - 1013/36  + 487/30
Uh oh.. now we have a problem. Some big numbers here ; don't let it worry you. We need to find the LCM of both the denominators, 36 and 30. This is the lowest common multiple; it's just a fancy term to mean the smallest number that is a multiple of both 36 and 30. The LCM makes the denominator the same so that you can work the problem.

To find LCM, we need to do some prime factorization:

36 : 12 * 3 = 4 * 3 * 3 = 2 * 2 * 3 * 3
30 :  6 * 5 = 2 *3 * 5

Let's arrange the prime factors :

36 :  2  2  3   3 
30 :  2     3      5    

Note: Please put it into columns on your own scratch paper as it won't show up here very clearly. You should have '2's' in the 2 column and '3's' in the 3 column and '5' will be by itself. I will try to upload an illustration if anyone requests it.
To find the LCM, we use the number in each column; no matter how many times it is repeated, we only use it once. In this case, it would be
2 * 2 * 3 * 3 * 5 = 180

Now we can finish the problem:

- 1013 /36 + 487 / 30
= - 5065/180 + 2922/ 180
= - 2143/ 180

And that's your answer.  2143 is a prime number , so you can't really simplify any more than that.