===========================
Explanation:
Let's focus on adding 8/9 to -5/6
To do this, we need the denominators to be the same. The LCD is often the best choice, but you could pick any common denominator.
LCM of 9 and 6 is 18
8/9 = 16/18 after multiplying top and bottom by 2
-5/6 = -15/18 after multiplying top and bottom by 3
So,
8/9 + (-5/6) = 16/18 - 15/18 = 1/18
The two fractions up top combine to 1/18
----------------
The original expression turns into (1/18) over (1/6)
This is the same as
(1/18)*(6/1)
since we flip the second fraction and multiply. Let's simplify that
(1/18)*(6/1)
(1*6)/(18*1)
(6*1)/(6*3)
1/3
