1. **State the problem:** Find the mean of the mixed numbers $1 \frac{1}{2}$, $2 \frac{2}{3}$, $3 \frac{3}{4}$, $4 \frac{4}{5}$, and $5 \frac{5}{6}$, and round the answer to two decimal places. 2. **Convert mixed numbers to improper fractions:** - $1 \frac{1}{2} = \frac{3}{2}$ - $2 \frac{2}{3} = \frac{8}{3}$ - $3 \frac{3}{4} = \frac{15}{4}$ - $4 \frac{4}{5} = \frac{24}{5}$ - $5 \frac{5}{6} = \frac{35}{6}$ 3. **Find a common denominator to add fractions:** The denominators are 2, 3, 4, 5, and 6. The least common denominator (LCD) is 60. 4. **Convert each fraction to have denominator 60:** - $\frac{3}{2} = \frac{3 \times 30}{2 \times 30} = \frac{90}{60}$ - $\frac{8}{3} = \frac{8 \times 20}{3 \times 20} = \frac{160}{60}$ - $\frac{15}{4} = \frac{15 \times 15}{4 \times 15} = \frac{225}{60}$ - $\frac{24}{5} = \frac{24 \times 12}{5 \times 12} = \frac{288}{60}$ - $\frac{35}{6} = \frac{35 \times 10}{6 \times 10} = \frac{350}{60}$ 5. **Add the fractions:** $$\frac{90}{60} + \frac{160}{60} + \frac{225}{60} + \frac{288}{60} + \frac{350}{60} = \frac{90 + 160 + 225 + 288 + 350}{60} = \frac{1113}{60}$$ 6. **Calculate the mean:** $$\text{Mean} = \frac{\frac{1113}{60}}{5} = \frac{1113}{60} \times \frac{1}{5} = \frac{1113}{300}$$ 7. **Simplify the fraction:** $$\frac{1113}{300} = \frac{\cancel{1113}}{\cancel{300}} \text{ (no common factors to cancel)}$$ 8. **Convert to decimal:** $$\frac{1113}{300} = 3.71$$ 9. **Round to two decimal places:** The mean is $3.71$. **Final answer:** (a) 3.71