Solve the expression: $$\left(1\frac{17}{15} - 1\frac{1}{12}\right) \cdot 2\frac{20}{33} =$$

Let's solve the expression step by step: 1. First, convert the mixed numbers to improper fractions: $$1\frac{17}{15} = \frac{1 \cdot 15 + 17}{15} = \frac{15 + 17}{15} = \frac{32}{15}$$ $$1\frac{1}{12} = \frac{1 \cdot 12 + 1}{12} = \frac{12 + 1}{12} = \frac{13}{12}$$ $$2\frac{20}{33} = \frac{2 \cdot 33 + 20}{33} = \frac{66 + 20}{33} = \frac{86}{33}$$ 2. Now, subtract the first two fractions: $$\frac{32}{15} - \frac{13}{12}$$ To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 12 is 60. $$\frac{32}{15} = \frac{32 \cdot 4}{15 \cdot 4} = \frac{128}{60}$$ $$\frac{13}{12} = \frac{13 \cdot 5}{12 \cdot 5} = \frac{65}{60}$$ $$\frac{128}{60} - \frac{65}{60} = \frac{128 - 65}{60} = \frac{63}{60}$$ Simplify the fraction: $$\frac{63}{60} = \frac{21}{20}$$ 3. Multiply the result by the third fraction: $$\frac{21}{20} \cdot \frac{86}{33}$$ $$\frac{21 \cdot 86}{20 \cdot 33} = \frac{1806}{660}$$ 4. Simplify the fraction: $$\frac{1806}{660} = \frac{903}{330} = \frac{301}{110}$$ 5. Convert the improper fraction to a mixed number: $$\frac{301}{110} = 2\frac{81}{110}$$ So, the final answer is: $$\left(1\frac{17}{15} - 1\frac{1}{12}\right) \cdot 2\frac{20}{33} = 2\frac{81}{110}$$ Answer: $$2\frac{81}{110}$$