1. **State the problem:** Simplify the expression $2\frac{1}{2} - 1\frac{1}{5}$. 2. **Convert mixed numbers to improper fractions:** - $2\frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$ - $1\frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5}$ 3. **Rewrite the expression:** $$\frac{5}{2} - \frac{6}{5}$$ 4. **Find a common denominator:** The denominators are 2 and 5, so the least common denominator (LCD) is 10. 5. **Convert fractions to have the LCD:** - $\frac{5}{2} = \frac{5 \times 5}{2 \times 5} = \frac{25}{10}$ - $\frac{6}{5} = \frac{6 \times 2}{5 \times 2} = \frac{12}{10}$ 6. **Subtract the fractions:** $$\frac{25}{10} - \frac{12}{10} = \frac{25 - 12}{10} = \frac{13}{10}$$ 7. **Convert back to a mixed number:** $$\frac{13}{10} = 1 \frac{3}{10}$$ **Final answer:** $1 \frac{3}{10}$