1. **Problem 6:** At a certain school, \(\frac{1}{4}\) of the teachers are women. Find the ratio of the number of male teachers to female teachers. - Total teachers = 1 (consider as whole) - Female teachers = \(\frac{1}{4}\) - Male teachers = \(1 - \frac{1}{4} = \frac{3}{4}\) - Ratio male to female = \(\frac{3}{4} : \frac{1}{4} = 3 : 1\) 2. **Problem 7:** Sana cleaned \(4 \frac{1}{6}\) of her house, and her sister cleaned \(5 \frac{1}{5}\) of the remaining. Find the ratio of clean to unclean. - Convert mixed numbers to improper fractions: - Sana cleaned: \(4 \frac{1}{6} = \frac{25}{6}\) - Sister cleaned: \(5 \frac{1}{5} = \frac{26}{5}\) - Total cleaned = Sana + Sister = \(\frac{25}{6} + \frac{26}{5} = \frac{125}{30} + \frac{156}{30} = \frac{281}{30}\) - Since total house is 1, unclean = \(1 - \frac{281}{30} = \frac{30}{30} - \frac{281}{30} = -\frac{251}{30}\) (negative means problem data inconsistent or interpreted incorrectly; assuming question means parts cleaned out of total 10 parts, ratio clean to unclean = \(\frac{25}{6} + \frac{26}{5} : \text{remaining}\) is ambiguous, so we skip this or clarify.) 3. **Problem 8:** Two sums of money are in the ratio 5 : 8. The smaller amount is 65. Find the larger amount. - Ratio: 5 : 8 - Smaller amount corresponds to 5 parts = 65 - One part = \(\frac{65}{5} = 13\) - Larger amount = 8 parts = \(8 \times 13 = 104\) 4. **Problem 9:** The weight of 15 feet of wire is 6 pounds. How many pounds will 25 feet of the same wire weigh? - Weight per foot = \(\frac{6}{15} = 0.4\) pounds - Weight of 25 feet = \(25 \times 0.4 = 10\) pounds 5. **Problem 10:** 16 boys can dig a ditch in 8 hours. How many hours would it take 10 boys working at the same rate? - Work done = boys \(\times\) hours = constant - For 16 boys: \(16 \times 8 = 128\) boy-hours - For 10 boys: hours = \(\frac{128}{10} = 12.8\) hours Final answers: - Problem 6: Ratio male to female = \(3 : 1\) - Problem 8: Larger amount = 104 - Problem 9: Weight of 25 feet = 10 pounds - Problem 10: Time for 10 boys = 12.8 hours Note: Problem 7 data is ambiguous and skipped.