1. **State the problem:** Calculate the value of $5 \frac{1}{6} - 2 \frac{1}{3} + 1 \frac{1}{8}$. 2. **Convert mixed numbers to improper fractions:** $$5 \frac{1}{6} = \frac{5 \times 6 + 1}{6} = \frac{31}{6}$$ $$2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ $$1 \frac{1}{8} = \frac{1 \times 8 + 1}{8} = \frac{9}{8}$$ 3. **Rewrite the expression with improper fractions:** $$\frac{31}{6} - \frac{7}{3} + \frac{9}{8}$$ 4. **Find the least common denominator (LCD):** Denominators are 6, 3, and 8. Prime factors: - 6 = 2 \times 3 - 3 = 3 - 8 = 2^3 LCD = $2^3 \times 3 = 8 \times 3 = 24$ 5. **Convert each fraction to have denominator 24:** $$\frac{31}{6} = \frac{31 \times 4}{6 \times 4} = \frac{124}{24}$$ $$\frac{7}{3} = \frac{7 \times 8}{3 \times 8} = \frac{56}{24}$$ $$\frac{9}{8} = \frac{9 \times 3}{8 \times 3} = \frac{27}{24}$$ 6. **Perform the operations:** $$\frac{124}{24} - \frac{56}{24} + \frac{27}{24} = \frac{124 - 56 + 27}{24} = \frac{95}{24}$$ 7. **Simplify or convert back to mixed number:** $$\frac{95}{24} = 3 \frac{23}{24}$$ **Final answer:** $3 \frac{23}{24}$