1. **State the problem:** Subtract and simplify the expression $$17 \frac{1}{6} - \frac{18}{30}$$. 2. **Convert mixed number to improper fraction:** $$17 \frac{1}{6} = \frac{17 \times 6 + 1}{6} = \frac{102 + 1}{6} = \frac{103}{6}$$. 3. **Simplify the second fraction:** $$\frac{18}{30} = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}$$. 4. **Find common denominator:** The denominators are 6 and 5. The least common denominator (LCD) is 30. 5. **Convert both fractions to have denominator 30:** $$\frac{103}{6} = \frac{103 \times 5}{6 \times 5} = \frac{515}{30}$$ $$\frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30}$$ 6. **Subtract the fractions:** $$\frac{515}{30} - \frac{18}{30} = \frac{515 - 18}{30} = \frac{497}{30}$$ 7. **Convert improper fraction back to mixed number:** Divide 497 by 30: $$497 \div 30 = 16 \text{ remainder } 17$$ So, $$\frac{497}{30} = 16 \frac{17}{30}$$ **Final answer:** $$16 \frac{17}{30}$$