金声玉亮2.0模型评测报告

There is a single choice question about elementary mathematics. Answer the question by replying A, B, C or D.
Question: Write 60 over 72 in simplest form.
A. 4 over 6
B. 10 over 12
C. 15 over 17
D. 5 over 6
Answer:

答案

模型	模型答案	正确答案
金声玉亮2.0	D. 5 over 6	D
deepseekr1	To simplify \( \frac{60}{72} \), find the greatest common divisor (GCD) of 60 and 72. The prime factorization of 60 is \( 2^2 \times 3 \times 5 \), and for 72 it is \( 2^3 \times 3^2 \). The GCD is \( 2^2 \times 3 = 12 \). Dividing both numerator and denominator by 12: \[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6}. \] Options A (\( \frac{4}{6} \)) and B (\( \frac{10}{12} \)) are not fully simplified. Option C (\( \frac{15}{17} \)) is incorrect. The correct answer is D. \( \frac{5}{6} \). Answer: D	D
gpto1	To simplify the fraction \( \frac{60}{72} \), follow these steps: 1. Find the Greatest Common Divisor (GCD) of 60 and 72: - Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 - Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 - The common factors are 1, 2, 3, 4, and 6, with 6 being the largest common factor. - Actually, 12 is a common factor as well (12 times 5 = 60, 12 times 6 = 72), so the GCD is 12. 2. Divide both the numerator and the denominator by the GCD: - \( \frac{60 ÷ 12}{72 ÷ 12} = \frac{5}{6} \) So, \( \frac{60}{72} \) simplified is \( \frac{5}{6} \). Now, compare this result with the options provided to determine the correct answer.	D
GPT-4o	To simplify the fraction 60 over 72, we need to find the greatest common divisor (GCD) of 60 and 72 and then divide both the numerator and the denominator by that number. The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The greatest common divisor of 60 and 72 is 12. Now, divide both the numerator and the denominator by 12: 60 ÷ 12 = 5 72 ÷ 12 = 6 So, 60 over 72 in simplest form is 5 over 6. Answer: D	D
llama3.1-70B-Instruct	B	D
llama3.1-405B-Instruct	D. 5 over 6	D
DeepSeek-Coder-V2	D. 5 over 6	D
Qwen2-72B-Instruct	D. 5 over 6	D
baichuan4	D	D
doubao	D. 5 over 6. 60/72 = (60÷12)/(72÷12) = 5/6.	D
minimax	To simplify the fraction 60/72, we need to find the greatest common divisor (GCD) of the numerator (60) and the denominator (72) and then divide both by that number. The GCD of 60 and 72 is 12. Dividing both the numerator and the denominator by 12 gives us: 60 ÷ 12 = 5 72 ÷ 12 = 6 So, 60/72 in simplest form is 5/6. The correct answer is: D. 5 over 6	D
kimi	To simplify the fraction \( \frac{60}{72} \), we need to find the greatest common divisor (GCD) of 60 and 72 and then divide both the numerator and the denominator by that number. The GCD of 60 and 72 is 12. Now, divide both the numerator and the denominator by 12: \[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \] So the simplest form of \( \frac{60}{72} \) is \( \frac{5}{6} \). Answer: D. 5 over 6	D
wenxinyiyan	D	D
zhipu	D. 5 over 6 To simplify the fraction \( \frac{60}{72} \), we need to find the greatest common divisor (GCD) of 60 and 72. The GCD of 60 and 72 is 12. Dividing both the numerator and the denominator by 12, we get: \[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \] So, the simplest form of \( \frac{60}{72} \) is \( \frac{5}{6} \). Thus, the correct answer is D.	D
gpto1	To simplify the fraction \( \frac{60}{72} \), follow these steps: 1. Find the Greatest Common Divisor (GCD) of 60 and 72: - Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 - Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 - The common factors are 1, 2, 3, 4, and 6, with 6 being the largest common factor. - Actually, 12 is a common factor as well (12 times 5 = 60, 12 times 6 = 72), so the GCD is 12. 2. Divide both the numerator and the denominator by the GCD: - \( \frac{60 ÷ 12}{72 ÷ 12} = \frac{5}{6} \) So, \( \frac{60}{72} \) simplified is \( \frac{5}{6} \). Now, compare this result with the options provided to determine the correct answer.	D
deepseekv3	To simplify the fraction \( \frac{60}{72} \), follow these steps: 1. Find the greatest common divisor (GCD) of 60 and 72. - The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. - The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. - The greatest common factor is 12. 2. Divide both the numerator and the denominator by the GCD (12). \[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \] So, the simplified form of \( \frac{60}{72} \) is \( \frac{5}{6} \). The correct answer is: D. 5 over 6.	D

模型

模型答案

正确答案

金声玉亮2.0

D. 5 over 6

deepseekr1

To simplify \( \frac{60}{72} \), find the greatest common divisor (GCD) of 60 and 72. The prime factorization of 60 is \( 2^2 \times 3 \times 5 \), and for 72 it is \( 2^3 \times 3^2 \). The GCD is \( 2^2 \times 3 = 12 \). Dividing both numerator and denominator by 12:

\[
\frac{60 \div 12}{72 \div 12} = \frac{5}{6}.
\]

Options A (\( \frac{4}{6} \)) and B (\( \frac{10}{12} \)) are not fully simplified. Option C (\( \frac{15}{17} \)) is incorrect. The correct answer is **D. \( \frac{5}{6} \)**.

Answer: D

gpto1

To simplify the fraction \( \frac{60}{72} \), follow these steps:

1. **Find the Greatest Common Divisor (GCD) of 60 and 72**:
- **Factors of 60**: 1, 2, 3, 4, 5, **6**, 10, 12, **15**, 20, 30, 60
- **Factors of 72**: 1, 2, 3, 4, **6**, 8, 9, 12, 18, 24, 36, 72
- The common factors are 1, 2, 3, 4, and **6**, with 6 being the largest common factor.
- Actually, 12 is a common factor as well (**12** times 5 = 60, **12** times 6 = 72), so the GCD is **12**.

2. **Divide both the numerator and the denominator by the GCD**:
- \( \frac{60 ÷ 12}{72 ÷ 12} = \frac{5}{6} \)

So, \( \frac{60}{72} \) simplified is \( \frac{5}{6} \).

Now, compare this result with the options provided to determine the correct answer.

GPT-4o

To simplify the fraction 60 over 72, we need to find the greatest common divisor (GCD) of 60 and 72 and then divide both the numerator and the denominator by that number.

The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

The greatest common divisor of 60 and 72 is 12.

Now, divide both the numerator and the denominator by 12:

60 ÷ 12 = 5
72 ÷ 12 = 6

So, 60 over 72 in simplest form is 5 over 6.

Answer: D

llama3.1-70B-Instruct

llama3.1-405B-Instruct

D. 5 over 6

DeepSeek-Coder-V2

D. 5 over 6

Qwen2-72B-Instruct

D. 5 over 6

baichuan4

doubao

D. 5 over 6.

60/72 = (60÷12)/(72÷12) = 5/6.

minimax

To simplify the fraction 60/72, we need to find the greatest common divisor (GCD) of the numerator (60) and the denominator (72) and then divide both by that number.

The GCD of 60 and 72 is 12.

Dividing both the numerator and the denominator by 12 gives us:

60 ÷ 12 = 5
72 ÷ 12 = 6

So, 60/72 in simplest form is 5/6.

The correct answer is:

D. 5 over 6

kimi

To simplify the fraction \( \frac{60}{72} \), we need to find the greatest common divisor (GCD) of 60 and 72 and then divide both the numerator and the denominator by that number.

The GCD of 60 and 72 is 12.

Now, divide both the numerator and the denominator by 12:
\[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \]

So the simplest form of \( \frac{60}{72} \) is \( \frac{5}{6} \).

Answer: D. 5 over 6

wenxinyiyan

zhipu

D. 5 over 6

To simplify the fraction \( \frac{60}{72} \), we need to find the greatest common divisor (GCD) of 60 and 72. The GCD of 60 and 72 is 12.

Dividing both the numerator and the denominator by 12, we get:
\[ \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \]

So, the simplest form of \( \frac{60}{72} \) is \( \frac{5}{6} \). Thus, the correct answer is D.

gpto1

deepseekv3

To simplify the fraction \( \frac{60}{72} \), follow these steps:

1. **Find the greatest common divisor (GCD) of 60 and 72.**
- The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
- The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
- The greatest common factor is **12**.

2. **Divide both the numerator and the denominator by the GCD (12).**
\[
\frac{60 \div 12}{72 \div 12} = \frac{5}{6}
\]

So, the simplified form of \( \frac{60}{72} \) is \( \frac{5}{6} \).

The correct answer is: **D. 5 over 6**.

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