1. **State the problem:** Sana cleaned $\frac{1}{4}$ of her house, and her sister cleaned $\frac{1}{5}$ of the remaining part. We need to find the ratio of the clean part to the unclean part of the house. 2. **Identify the total and parts cleaned:** - Total house = 1 (whole) - Sana cleaned $\frac{1}{4}$ - Remaining after Sana cleaned = $1 - \frac{1}{4} = \frac{3}{4}$ 3. **Calculate the part cleaned by sister:** - Sister cleaned $\frac{1}{5}$ of the remaining $\frac{3}{4}$ - So, sister cleaned $\frac{1}{5} \times \frac{3}{4} = \frac{3}{20}$ 4. **Calculate total cleaned:** - Total cleaned = Sana's part + Sister's part = $\frac{1}{4} + \frac{3}{20}$ - Find common denominator 20: $\frac{5}{20} + \frac{3}{20} = \frac{8}{20} = \frac{2}{5}$ 5. **Calculate unclean part:** - Unclean = Total - Cleaned = $1 - \frac{2}{5} = \frac{3}{5}$ 6. **Find ratio of clean to unclean:** - Ratio = Clean : Unclean = $\frac{2}{5} : \frac{3}{5}$ - Simplify by multiplying both sides by 5: $2 : 3$ **Final answer:** The ratio of clean to unclean parts of the house is $2 : 3$.