To add 7/15 and 2 8/3, we first need to convert the mixed number to an improper fraction.

2 8/3 = 2 * 3 + 8 = 6 + 8 = 14/3.

Now, we add 7/15 and 14/3:

7/15 + 14/3

To add fractions, we need a common denominator. In this case, the common denominator is 15:

7/15 + 14/3 = 7/15 + 70/15 = 77/15

Next, to subtract 17/20 and 2.7, we need to convert 2.7 to a fraction:

2.7 = 2 + 0.7 = 2 + 7/10 = 2 + 14/20 = 2 7/10.

Now, we can subtract 17/20 and 2 7/10:

17/20 - 2 7/10

We convert the mixed number to an improper fraction:

2 7/10 = 2 * 10 + 7 = 20 + 7 = 27/10

Now, subtract 17/20 from 27/10:

27/10 - 17/20

To subtract fractions, we need a common denominator. In this case, the common denominator is 20:

27/10 - 17/20 = 54/20 - 17/20 = 37/20

Therefore, the result of the addition and subtraction is:

7/15 + 2 8/3 = 77/15

17/20 - 2.7 = 37/20.