Use the equivalents ...
... 1/3 = 2/6
... 9/18 = 3/6
... 1 = 6/6
First we split the mixed numbers into integer parts and fractional parts, adding each separately.
(5 1/3) + (-3 9/18) = (5 +(-3)) +(1/3 +(-9/18))
... = 2 + (2/6 - 3/6) . . . . . . use the equivalents for 1/3 and 9/18 to have a common denominator (6)
... = 2 - 1/6 . . . . . . . . . . . . the sum of the fractional parts is negative
... = (1 + 1) - 1/6 . . . . . . . . here's how we subtract it from the integer part
... = 1 + (6/6 - 1/6)
... = 1 5/6
