问题


There is a single choice question about elementary mathematics. Answer the question by replying A, B, C or D.
Question: Write the ratio of 96 runners to 216 swimmers in simplest form.
A. 96 over 216
B. 16 over 36
C. 4 over 9
D. 9 over 4
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

C. 4 over 9		 C
deepseekr1

To simplify the ratio of 96 runners to 216 swimmers, first express it as \( \frac{96}{216} \). Finding the greatest common divisor (GCD) of 96 and 216 using prime factorization:

- **96** factors into \( 2^5 \times 3 \).
- **216** factors into \( 2^3 \times 3^3 \).

The GCD is \( 2^3 \times 3 = 24 \). Dividing both numbers by 24:

\[
\frac{96 \div 24}{216 \div 24} = \frac{4}{9}.
\]

Option **B** (\( \frac{16}{36} \)) is an intermediate step but not fully simplified. Option **D** (\( \frac{9}{4} \)) inverts the ratio. Thus, the simplest form is **C**.

Answer: C		 C
gpto1 C C
GPT-4o The correct answer is C. 4 over 9. C
llama3.1-70B-Instruct

C		 C
llama3.1-405B-Instruct

C. 4 over 9		 C
DeepSeek-Coder-V2 C. 4 over 9 C
Qwen2-72B-Instruct C. 4 over 9 C
baichuan4 C C
doubao C. 4 over 9

To simplify the ratio 96:216, divide both numbers by their greatest common divisor, which is 24. 96÷24 = 4 and 216÷24 = 9, so the simplest form is 4:9, which is 4 over 9.		 C
minimax To simplify the ratio of 96 runners to 216 swimmers, we need to divide both numbers by their greatest common divisor (GCD). The GCD of 96 and 216 is 48.

Dividing both numbers by 48 gives us:

96 ÷ 48 = 2
216 ÷ 48 = 4.5

However, ratios are typically expressed as whole numbers, so we can multiply both parts of the ratio by 2 to eliminate the decimal:

2 × 2 = 4
4.5 × 2 = 9

So the simplified ratio of runners to swimmers is 4 to 9.

The correct answer is:

C. 4 over 9		 C
kimi To find the ratio of 96 runners to 216 swimmers in simplest form, you need to divide both numbers by their greatest common divisor (GCD).

The GCD of 96 and 216 is 48.

So, you divide both numbers by 48:

96 ÷ 48 = 2
216 ÷ 48 = 4.5

Now, simplify the ratio 2:4.5 by multiplying both numbers by 2 to get rid of the decimal:

2 × 2 = 4
4.5 × 2 = 9

The simplest form of the ratio is 4:9.

Answer: C. 4 over 9		 C
wenxinyiyan C C
zhipu To simplify the ratio of 96 runners to 216 swimmers, we need to find the greatest common divisor (GCD) of 96 and 216 and then divide both numbers by this GCD.

First, let's find the GCD of 96 and 216.

1. The prime factorization of 96 is \( 2^5 \times 3 \).
2. The prime factorization of 216 is \( 2^3 \times 3^3 \).

The common factors are \( 2^3 \) and \( 3 \), so the GCD is \( 2^3 \times 3 = 8 \times 3 = 24 \).

Now, divide both 96 and 216 by 24:
\[ \frac{96}{24} = 4 \]
\[ \frac{216}{24} = 9 \]

Therefore, the simplified ratio is \( \frac{4}{9} \).

So the answer is:
C. 4 over 9		 C
gpto1 C C
deepseekv3 To simplify the ratio of 96 runners to 216 swimmers, follow these steps:

1. Write the ratio as a fraction:
\[
\frac{96}{216}
\]

2. Find the greatest common divisor (GCD) of 96 and 216. The GCD of 96 and 216 is 24.

3. Divide both the numerator and the denominator by the GCD:
\[
\frac{96 \div 24}{216 \div 24} = \frac{4}{9}
\]

Thus, the simplified ratio is **4 over 9**.

**Answer:** C. 4 over 9		 C