I got the common denominator, which was 27, I came up with 39/27, and then I divided 39 by 27 which I got 1.44, I'm having a problem estimating,

The LCM of the denominators 3 and 9 is 9 itself. Hence the 2nd fraction can be represented as 6/9.
Thus the sum would be 7+6/9 = 13/9 = 1 + 4/9 = 1.44
Similarly, the difference would be 7-6/9 = 1/9 = 0.11...