| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | D |
D |
| deepseekr1 | To determine which pair of ratios forms a proportion, check if the cross-products are equal: - **Option A**: \( \frac{2}{5} \) vs. \( \frac{8}{10} \) \( 2 \times 10 = 20 \), \( 5 \times 8 = 40 \). Not equal. ❌ - **Option B**: \( \frac{2}{5} \) vs. \( \frac{10}{15} \) (simplifies to \( \frac{2}{3} \)) \( 2 \times 15 = 30 \), \( 5 \times 10 = 50 \). Not equal. ❌ - **Option C**: \( \frac{2}{5} \) vs. \( \frac{4}{25} \) \( 2 \times 25 = 50 \), \( 5 \times 4 = 20 \). Not equal. ❌ - **Option D**: \( \frac{2}{5} \) vs. \( \frac{6}{15} \) (simplifies to \( \frac{2}{5} \)) \( 2 \times 15 = 30 \), \( 5 \times 6 = 30 \). Equal. ✅ **Answer: D** |
D |
| gpto1 | D | D |
| GPT-4o | D. 2 over 5 and 6 over 15 | D |
| llama3.1-70B-Instruct | B |
D |
| llama3.1-405B-Instruct | D |
D |
| DeepSeek-Coder-V2 | D | D |
| Qwen2-72B-Instruct | A. 2 over 5 and 8 over 10 | D |
| baichuan4 | A. 2 over 5 and 8 over 10 | D |
| doubao | D. To determine if two ratios form a proportion, we check if their cross-products are equal. For 2/5 and 6/15, 2×15 = 30 and 5×6 = 30, so they form a proportion. |
D |
| minimax | To determine which pair of ratios can form a proportion, we need to check if the cross products are equal. For two ratios a/b and c/d to be in proportion, the following must be true: a/b = c/d => a*d = b*c Let's check each option: A. 2/5 and 8/10 Cross products: 2*10 = 5*8 20 ≠ 40 (Not a proportion) B. 2/5 and 10/15 Cross products: 2*15 = 5*10 30 = 50 (Not a proportion) C. 2/5 and 4/25 Cross products: 2*25 = 5*4 50 ≠ 20 (Not a proportion) D. 2/5 and 6/15 Cross products: 2*15 = 5*6 30 = 30 (This is a proportion) Therefore, the correct answer is: D. 2 over 5 and 6 over 15 |
D |
| kimi | A. 2 over 5 and 8 over 10 To form a proportion, the ratios must be equivalent. This means that when you simplify both ratios, they should have the same value. Let's simplify each option: A. \( \frac{2}{5} \) and \( \frac{8}{10} \) simplifies to \( \frac{2}{5} \) and \( \frac{4}{5} \) (since \( \frac{8}{10} \) is the same as \( \frac{4}{5} \) when reduced to its simplest form). These are not equivalent. B. \( \frac{2}{5} \) and \( \frac{10}{15} \) simplifies to \( \frac{2}{5} \) and \( \frac{2}{3} \) (since \( \frac{10}{15} \) is the same as \( \frac{2}{3} \) when reduced to its simplest form). These are not equivalent. C. \( \frac{2}{5} \) and \( \frac{4}{25} \) simplifies to \( \frac{2}{5} \) and \( \frac{2}{25} \) (since \( \frac{4}{25} \) is the same as \( \frac{2}{25} \) when reduced to its simplest form). These are not equivalent. D. \( \frac{2}{5} \) and \( \frac{6}{15} \) simplifies to \( \frac{2}{5} \) and \( \frac{2}{5} \) (since \( \frac{6}{15} \) is the same as \( \frac{2}{5} \) when reduced to its simplest form). These are equivalent. So, the correct answer is D. 2 over 5 and 6 over 15. |
D |
| wenxinyiyan | D Explanation: Two ratios can form a proportion if they are equal. To check this, we can compare the cross products of the ratios. A. 2/5 and 8/10 Cross product: 2 × 10 ≠ 5 × 8, so they are not equal and do not form a proportion. B. 2/5 and 10/15 Reducing 10/15 to lowest terms gives 2/3. Cross product: 2 × 3 ≠ 5 × 2, so they are not equal and do not form a proportion. C. 2/5 and 4/25 Cross product: 2 × 25 ≠ 5 × 4, so they are not equal and do not form a proportion. D. 2/5 and 6/15 Reducing 6/15 to lowest terms gives 2/5. Cross product: 2 × 5 = 5 × 2, so they are equal and form a proportion. |
D |
| zhipu | To determine which pair of ratios can form a proportion, we need to check if the two ratios are equivalent. This means that the cross-products of the ratios should be equal. Let's analyze each option: A. \( \frac{2}{5} \) and \( \frac{8}{10} \) Cross-multiplying: \( 2 \times 10 = 20 \) and \( 5 \times 8 = 40 \) Since \( 20 \neq 40 \), these ratios do not form a proportion. B. \( \frac{2}{5} \) and \( \frac{10}{15} \) Cross-multiplying: \( 2 \times 15 = 30 \) and \( 5 \times 10 = 50 \) Since \( 30 \neq 50 \), these ratios do not form a proportion. C. \( \frac{2}{5} \) and \( \frac{4}{25} \) Cross-multiplying: \( 2 \times 25 = 50 \) and \( 5 \times 4 = 20 \) Since \( 50 \neq 20 \), these ratios do not form a proportion. D. \( \frac{2}{5} \) and \( \frac{6}{15} \) Cross-multiplying: \( 2 \times 15 = 30 \) and \( 5 \times 6 = 30 \) Since \( 30 = 30 \), these ratios do form a proportion. Therefore, the correct answer is: D |
D |
| gpto1 | D | D |
| deepseekv3 | To determine which pair of ratios forms a proportion, we need to check if the two ratios are equal. This can be done by cross-multiplying and seeing if the products are equal. Let's examine each option: **A. \( \frac{2}{5} \) and \( \frac{8}{10} \)** - Cross-multiplying: \( 2 \times 10 = 20 \) and \( 5 \times 8 = 40 \) - \( 20 \neq 40 \), so these ratios do not form a proportion. **B. \( \frac{2}{5} \) and \( \frac{10}{15} \)** - Cross-multiplying: \( 2 \times 15 = 30 \) and \( 5 \times 10 = 50 \) - \( 30 \neq 50 \), so these ratios do not form a proportion. **C. \( \frac{2}{5} \) and \( \frac{4}{25} \)** - Cross-multiplying: \( 2 \times 25 = 50 \) and \( 5 \times 4 = 20 \) - \( 50 \neq 20 \), so these ratios do not form a proportion. **D. \( \frac{2}{5} \) and \( \frac{6}{15} \)** - Cross-multiplying: \( 2 \times 15 = 30 \) and \( 5 \times 6 = 30 \) - \( 30 = 30 \), so these ratios form a proportion. Therefore, the correct answer is: **D** |
D |