Subjects arithmetic

Ratios And Time C96948

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Question: a. 12 b. 11 c. 10 d. 9 position_hint=top-left: Text question asking “Nine men can repair a house in 12 days?” with answer choices 12, 11, 10, 9. a. 15:40 b. 16:45 c. 18:40 d. 20:45 position_hint=center: Text question asking “Express the ratio of 64 minutes to three hours.” with answer choices 15:40, 16:45, 18:40, 20:45. position_hint=bottom-left: Text question asking “Express the ratio of 300 g to 2 kg.”
1. **Problem 1:** Nine men can repair a house in 12 days. The question is to confirm or understand this statement. Since the problem states "Nine men can repair a house in 12 days," this is a direct statement, so the answer is $12$ days. --- 2. **Problem 2:** Express the ratio of 64 minutes to three hours. - First, convert three hours to minutes: $$3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}.$$ - The ratio is then $$\frac{64}{180}.$$ - Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 4: $$\frac{64}{180} = \frac{\cancel{4} \times 16}{\cancel{4} \times 45} = \frac{16}{45}.$$ - So the ratio is $16:45$. --- 3. **Problem 3:** Express the ratio of 300 g to 2 kg. - Convert 2 kg to grams: $$2 \text{ kg} = 2 \times 1000 = 2000 \text{ g}.$$ - The ratio is $$\frac{300}{2000}.$$ - Simplify by dividing numerator and denominator by 100: $$\frac{300}{2000} = \frac{\cancel{100} \times 3}{\cancel{100} \times 20} = \frac{3}{20}.$$ - So the ratio is $3:20$. --- **Final answers:** 1. $12$ 2. $16:45$ 3. $3:20$