1. **State the problem:** Calculate the value of $17 \frac{1}{18} - 8 \frac{2}{3}$. 2. **Convert mixed numbers to improper fractions:** $17 \frac{1}{18} = \frac{17 \times 18 + 1}{18} = \frac{306 + 1}{18} = \frac{307}{18}$ $8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3}$ 3. **Find a common denominator to subtract:** The denominators are 18 and 3. The least common denominator (LCD) is 18. 4. **Convert $\frac{26}{3}$ to denominator 18:** $\frac{26}{3} = \frac{26 \times 6}{3 \times 6} = \frac{156}{18}$ 5. **Subtract the fractions:** $$\frac{307}{18} - \frac{156}{18} = \frac{307 - 156}{18} = \frac{151}{18}$$ 6. **Convert the improper fraction back to a mixed number:** Divide 151 by 18: $151 \div 18 = 8$ remainder $7$, so $$\frac{151}{18} = 8 \frac{7}{18}$$ **Final answer:** $8 \frac{7}{18}$