| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B |
A |
| deepseekr1 | The ratio 8/18 simplifies to 4/9. To determine which option does not form a proportion with 8/18, we check if each simplifies to 4/9 or has equivalent cross products. - **Option A (46/108)**: Simplifies to 23/54, which is not 4/9. Cross products: \(8 \times 108 = 864\) and \(18 \times 46 = 828\), which are unequal. - **Option B (12/27)**: Simplifies to 4/9. Cross products: \(8 \times 27 = 216\) and \(18 \times 12 = 216\), equal. - **Option C (60/135)**: Simplifies to 4/9. Cross products: \(8 \times 135 = 1080\) and \(18 \times 60 = 1080\), equal. - **Option D (4/9)**: Already matches 4/9. Cross products: \(8 \times 9 = 72\) and \(18 \times 4 = 72\), equal. Only **A** does not form a proportion. **Answer: A** |
A |
| gpto1 | A | A |
| GPT-4o | A. 46 over 108 | A |
| llama3.1-70B-Instruct | B |
A |
| llama3.1-405B-Instruct | B |
A |
| DeepSeek-Coder-V2 | B. 12 over 27 | A |
| Qwen2-72B-Instruct | D. 4 over 9 | A |
| baichuan4 | D | A |
| doubao | D. 8/18 = 4/9, so 4/9 can form a proportion with 8/18. 46/108 = 23/54 ≠ 8/18; 12/27 = 4/9 ≠ 8/18; 60/135 = 4/9 ≠ 8/18. So A, B, C cannot form a proportion with 8/18. |
A |
| minimax | To determine which ratio cannot form a proportion with 8 over 18, we need to simplify each option and compare it to the simplified form of 8/18. First, let's simplify 8/18 by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 8 ÷ 2 = 4 18 ÷ 2 = 9 So, 8/18 simplifies to 4/9. Now let's simplify each of the options: A. 46 over 108 Divide both numerator and denominator by 2: 46 ÷ 2 = 23 108 ÷ 2 = 54 So, option A simplifies to 23/54, which cannot be further simplified. B. 12 over 27 Divide both numerator and denominator by 3: 12 ÷ 3 = 4 27 ÷ 3 = 9 So, option B simplifies to 4/9, which is the same as the simplified form of 8/18. C. 60 over 135 Divide both numerator and denominator by 15: 60 ÷ 15 = 4 135 ÷ 15 = 9 So, option C simplifies to 4/9, which is the same as the simplified form of 8/18. D. 4 over 9 This option is already in its simplest form and is the same as the simplified form of 8/18. Since options B, C, and D all simplify to 4/9, they can all form a proportion with 8/18. Option A simplifies to 23/54, which is not equivalent to 4/9, so it cannot form a proportion with 8/18. Therefore, the correct answer is: A. 46 over 108 |
A |
| kimi | To determine which ratio cannot form a proportion with 8 over 18, we need to find the ratios that are equivalent to 8/18. First, let's simplify 8/18: 8/18 = 4/9 (dividing both numerator and denominator by 2) Now, let's simplify each of the given ratios: A. 46/108 = 23/54 = 1/2.45 (dividing both numerator and denominator by 2) B. 12/27 = 4/9 (dividing both numerator and denominator by 3) C. 60/135 = 4/9 (dividing both numerator and denominator by 15) D. 4/9 (already simplified) Now, we compare each simplified ratio to 4/9: A. 1/2.45 is not equivalent to 4/9. B. 4/9 is equivalent to 4/9. C. 4/9 is equivalent to 4/9. D. 4/9 is equivalent to 4/9. The ratio that cannot form a proportion with 8 over 18 is A. 46 over 108. |
A |
| wenxinyiyan | D Explanation: Proportions are equality relationships between two ratios. To determine whether a given ratio can form a proportion with 8/18, we need to check if they are equal when simplified. A. 46/108 = 23/54 (simplified) and 8/18 = 4/9 (simplified). These two ratios are not equal, but that doesn't mean they can't form a proportion with other numbers. Since we are looking for ratios that CANNOT form a proportion with 8/18, we need to compare each option directly to 8/18 in its original or simplified form. B. 12/27 simplifies to 4/9, which is the same as 8/18 simplified. So, they can form a proportion. C. 60/135 simplifies to 4/9, which is also the same as 8/18 simplified. Again, they can form a proportion. D. 4/9 is already simplified and is not equal to 8/18 (which simplifies to 4/9 but is not the same ratio before simplification). Therefore, 4/9 cannot form a proportion with 8/18 because there are no numbers that you can multiply both numerator and denominator of 4/9 by to get 8/18. Since the question asks which ratio CANNOT form a proportion with 8 over 18, the answer is D (4 over 9). |
A |
| zhipu | To determine which ratio cannot form a proportion with \( \frac{8}{18} \), we need to compare each given ratio to \( \frac{8}{18} \) and see if they are equivalent. First, simplify \( \frac{8}{18} \): \[ \frac{8}{18} = \frac{4}{9} \] Now, let's simplify each of the given ratios: A. \( \frac{46}{108} \): \[ \frac{46}{108} = \frac{23}{54} \] (This is not equivalent to \( \frac{4}{9} \)) B. \( \frac{12}{27} \): \[ \frac{12}{27} = \frac{4}{9} \] (This is equivalent to \( \frac{4}{9} \)) C. \( \frac{60}{135} \): \[ \frac{60}{135} = \frac{4}{9} \] (This is equivalent to \( \frac{4}{9} \)) D. \( \frac{4}{9} \): \[ \frac{4}{9} \] (This is already \( \frac{4}{9} \)) The ratio that cannot form a proportion with \( \frac{8}{18} \) (or \( \frac{4}{9} \)) is: A. \( \frac{46}{108} \) So, the answer is: A |
A |
| gpto1 | A | A |
| deepseekv3 | To determine which ratio **CANNOT** form a proportion with \(\frac{8}{18}\), we simplify \(\frac{8}{18}\) and compare it with each option. \[ \frac{8}{18} = \frac{4}{9} \quad \text{(dividing numerator and denominator by 2)} \] Now, check each option: **A. \(\frac{46}{108}\)** Simplify: \[ \frac{46}{108} = \frac{23}{54} \quad \text{(dividing numerator and denominator by 2)} \] This is **not** equal to \(\frac{4}{9}\). **B. \(\frac{12}{27}\)** Simplify: \[ \frac{12}{27} = \frac{4}{9} \quad \text{(dividing numerator and denominator by 3)} \] This **is** equal to \(\frac{4}{9}\). **C. \(\frac{60}{135}\)** Simplify: \[ \frac{60}{135} = \frac{4}{9} \quad \text{(dividing numerator and denominator by 15)} \] This **is** equal to \(\frac{4}{9}\). **D. \(\frac{4}{9}\)** This is already equal to \(\frac{4}{9}\). Only **option A** does **not** form a proportion with \(\frac{8}{18}\). \boxed{A} |
A |