| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | C. 24 over 64 |
C |
| deepseekr1 | The question asks which ratio is equivalent to 3/8. To determine this, we check if cross products are equal. For each option: - **A (18/40)**: \(3 \times 40 = 120\), \(8 \times 18 = 144\). Not equal. ❌ - **B (18/56)**: \(3 \times 56 = 168\), \(8 \times 18 = 144\). Not equal. ❌ - **C (24/64)**: \(3 \times 64 = 192\), \(8 \times 24 = 192\). Equal. Simplifying \(24/64\) by dividing numerator and denominator by 8 also gives \(3/8\). ✅ - **D (15/48)**: \(3 \times 48 = 144\), \(8 \times 15 = 120\). Not equal. ❌ Only **C** forms a proportion with \(3/8\). Answer: C |
C |
| gpto1 | C | C |
| GPT-4o | To determine which ratio can form a proportion with \( \frac{3}{8} \), we need to find the ratio that is equivalent to \( \frac{3}{8} \). Let's check each option: A. \( \frac{18}{40} \) \[ \frac{18}{40} = \frac{18 \div 2}{40 \div 2} = \frac{9}{20} \] B. \( \frac{18}{56} \) \[ \frac{18}{56} = \frac{18 \div 2}{56 \div 2} = \frac{9}{28} \] C. \( \frac{24}{64} \) \[ \frac{24}{64} = \frac{24 \div 8}{64 \div 8} = \frac{3}{8} \] D. \( \frac{15}{48} \) \[ \frac{15}{48} = \frac{15 \div 3}{48 \div 3} = \frac{5}{16} \] The correct answer is C. \( \frac{24}{64} \). Answer: C |
C |
| llama3.1-70B-Instruct | To form a proportion with 3 over 8, the ratio must be equivalent to 3/8. Let's analyze each option: A. 18 over 40 = 9/20 (not equivalent to 3/8) B. 18 over 56 = 9/28 (not equivalent to 3/8) C. 24 over 64 = 3/8 (equivalent to 3/8) D. 15 over 48 = 5/16 (not equivalent to 3/8) So, the correct answer is C. 24 over 64. |
C |
| llama3.1-405B-Instruct | C. 24 over 64 |
C |
| DeepSeek-Coder-V2 | To determine which ratio can form a proportion with 3 over 8, we need to check if the ratios given in options A, B, C, and D are equivalent to 3/8. This can be done by simplifying each ratio to see if it matches 3/8. Let's simplify each option: A. 18 over 40: Simplify 18/40 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 18 ÷ 2 = 9 40 ÷ 2 = 20 So, 18/40 simplifies to 9/20, which is not equal to 3/8. B. 18 over 56: Simplify 18/56 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 18 ÷ 2 = 9 56 ÷ 2 = 28 So, 18/56 simplifies to 9/28, which is not equal to 3/8. C. 24 over 64: Simplify 24/64 by dividing both the numerator and the denominator by their greatest common divisor, which is 8: 24 ÷ 8 = 3 64 ÷ 8 = 8 So, 24/64 simplifies to 3/8, which is equal to 3/8. D. 15 over 48: Simplify 15/48 by dividing both the numerator and the denominator by their greatest common divisor, which is 3: 15 ÷ 3 = 5 48 ÷ 3 = 16 So, 15/48 simplifies to 5/16, which is not equal to 3/8. Based on the simplifications, the correct answer is C. 24 over 64. Answer: C |
C |
| Qwen2-72B-Instruct | B. 18 over 56 | C |
| baichuan4 | A. 18 over 40 | C |
| doubao | C. 24 over 64. To determine if two ratios form a proportion, we can cross-multiply. For 3/8 and 24/64, 3×64 = 192 and 8×24 = 192, so they form a proportion. | C |
| minimax | To determine which ratio can form a proportion with 3 over 8, we need to find a ratio that is equivalent when both ratios are simplified. First, let's simplify the given ratio 3 over 8 by dividing both the numerator and the denominator by their greatest common divisor, which is 1 in this case. So, the ratio 3/8 is already in its simplest form. Now, we need to check each option to see if any of them can be simplified to the same ratio as 3/8: A. 18 over 40 can be simplified by dividing both the numerator and the denominator by 2: 18 ÷ 2 = 9 40 ÷ 2 = 20 So, 18/40 simplifies to 9/20, which is not equivalent to 3/8. B. 18 over 56 can be simplified by dividing both the numerator and the denominator by 2: 18 ÷ 2 = 9 56 ÷ 2 = 28 So, 18/56 simplifies to 9/28, which is not equivalent to 3/8. C. 24 over 64 can be simplified by dividing both the numerator and the denominator by 8: 24 ÷ 8 = 3 64 ÷ 8 = 8 So, 24/64 simplifies to 3/8, which is equivalent to the given ratio. D. 15 over 48 can be simplified by dividing both the numerator and the denominator by 3: 15 ÷ 3 = 5 48 ÷ 3 = 16 So, 15/48 simplifies to 5/16, which is not equivalent to 3/8. The correct answer is the one that simplifies to 3/8, which is option C. |
C |
| kimi | To determine which ratio can form a proportion with 3 over 8, we need to find which of the given ratios is equivalent to 3/8. A proportion is formed when two ratios are equal. First, let's simplify the ratio 3/8. The greatest common divisor (GCD) of 3 and 8 is 1, so the ratio is already in its simplest form. Now, let's simplify each of the given options: A. 18/40: The GCD of 18 and 40 is 2, so the simplified ratio is (18/2) / (40/2) = 9/20. B. 18/56: The GCD of 18 and 56 is 2, so the simplified ratio is (18/2) / (56/2) = 9/28. C. 24/64: The GCD of 24 and 64 is 8, so the simplified ratio is (24/8) / (64/8) = 3/8. D. 15/48: The GCD of 15 and 48 is 3, so the simplified ratio is (15/3) / (48/3) = 5/16. Now, we compare each simplified ratio to 3/8: A. 9/20 is not equal to 3/8. B. 9/28 is not equal to 3/8. C. 3/8 is equal to 3/8. D. 5/16 is not equal to 3/8. The ratio that can form a proportion with 3/8 is 3/8. Answer: C. 24 over 64 |
C |
| wenxinyiyan | C Explanation: Two ratios are said to be in proportion if their cross products are equal. That means, if a/b = c/d, then a*d = b*c. Given ratio is 3/8. We need to find which option can form a proportion with 3/8. A. 18/40 Cross product: 3*40 = 120 and 8*18 = 144. Since 120 ≠ 144, this ratio does not form a proportion with 3/8. B. 18/56 Cross product: 3*56 = 168 and 8*18 = 144. Since 168 ≠ 144, this ratio does not form a proportion with 3/8. C. 24/64 Cross product: 3*64 = 192 and 8*24 = 192. Since both cross products are equal, this ratio forms a proportion with 3/8. D. 15/48 Cross product: 3*48 = 144 and 8*15 = 120. Since 144 ≠ 120, this ratio does not form a proportion with 3/8. Therefore, the correct answer is C. 24/64. |
C |
| zhipu | To determine which ratio can form a proportion with \( \frac{3}{8} \), we need to find a ratio that is equivalent to \( \frac{3}{8} \). This means that the cross products of the two ratios should be equal. Let's check each option: A. \( \frac{18}{40} \) \[ 3 \times 40 = 120 \] \[ 8 \times 18 = 144 \] Since \( 120 \neq 144 \), \( \frac{18}{40} \) is not equivalent to \( \frac{3}{8} \). B. \( \frac{18}{56} \) \[ 3 \times 56 = 168 \] \[ 8 \times 18 = 144 \] Since \( 168 \neq 144 \), \( \frac{18}{56} \) is not equivalent to \( \frac{3}{8} \). C. \( \frac{24}{64} \) \[ 3 \times 64 = 192 \] \[ 8 \times 24 = 192 \] Since \( 192 = 192 \), \( \frac{24}{64} \) is equivalent to \( \frac{3}{8} \). D. \( \frac{15}{48} \) \[ 3 \times 48 = 144 \] \[ 8 \times 15 = 120 \] Since \( 144 \neq 120 \), \( \frac{15}{48} \) is not equivalent to \( \frac{3}{8} \). Therefore, the correct answer is: C. \( \frac{24}{64} \) |
C |
| gpto1 | C | C |
| deepseekv3 | To determine which ratio can form a proportion with \( \frac{3}{8} \), we need to check if the cross-products of the ratios are equal. Let's evaluate each option: **Option A: \( \frac{18}{40} \)** \[ 3 \times 40 = 120 \quad \text{and} \quad 8 \times 18 = 144 \] Since \( 120 \neq 144 \), this is not a proportion. **Option B: \( \frac{18}{56} \)** \[ 3 \times 56 = 168 \quad \text{and} \quad 8 \times 18 = 144 \] Since \( 168 \neq 144 \), this is not a proportion. **Option C: \( \frac{24}{64} \)** \[ 3 \times 64 = 192 \quad \text{and} \quad 8 \times 24 = 192 \] Since \( 192 = 192 \), this is a proportion. **Option D: \( \frac{15}{48} \)** \[ 3 \times 48 = 144 \quad \text{and} \quad 8 \times 15 = 120 \] Since \( 144 \neq 120 \), this is not a proportion. Therefore, the correct answer is: **C** |
C |