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To solve this problem, we need to subtract the amount of paint used from the total amount of paint.
First, we need to convert the fractions to a common denominator. The common denominator of 3 and 9 is 9.
15 1/3 gallons = 15 + 1/3 = 15 + 3/9 = 15 + 3/9 = 15 3/9 gallons
11 5/9 gallons = 11 + 5/9 = 11 + 5/9 = 11 + 5/9 = 11 5/9 gallons
Now, subtract the amount of paint used from the total amount of paint:
15 3/9 - 11 5/9 = 15 - 11 + 3/9 - 5/9 = 4 + 3/9 - 5/9 = 4 3/9 - 5/9 = 4 3/9 - 5/9 = 4 2/9 gallons
Therefore, the lady has 4 2/9 gallons of paint left.