问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: What is $$\frac{-\frac{18}{7}}{-\frac{6}{5}}?$$
A. \frac{7}{15}
B. \frac{15}{7}
C. \frac{15}{8}
D. \frac{15}{11}
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

B. \frac{15}{7}
B
deepseekr1

The problem requires dividing two negative fractions: \(\frac{-\frac{18}{7}}{-\frac{6}{5}}\). Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of \(-\frac{6}{5}\) is \(-\frac{5}{6}\). Thus, the expression becomes:

\[
-\frac{18}{7} \times -\frac{5}{6}
\]

Multiplying two negative numbers yields a positive result. Next, multiply the numerators and denominators:

\[
\frac{18 \times 5}{7 \times 6} = \frac{90}{42}
\]

Simplifying \(\frac{90}{42}\) by dividing numerator and denominator by their greatest common divisor (6):

\[
\frac{90 \div 6}{42 \div 6} = \frac{15}{7}
\]

The simplified result is \(\frac{15}{7}\), which corresponds to option **B**.

**Answer: B**
B
gpto1 B B
GPT-4o To solve the problem \(\frac{-\frac{18}{7}}{-\frac{6}{5}}\), we start by dividing two fractions:

\[
\frac{-\frac{18}{7}}{-\frac{6}{5}} = \frac{-\frac{18}{7}}{\frac{-6}{5}}
\]

When dividing by a fraction, we multiply by its reciprocal:

\[
\frac{-\frac{18}{7}}{\frac{-6}{5}} = -\frac{18}{7} \times -\frac{5}{6}
\]

Multiplying the fractions, we get:

\[
-\frac{18}{7} \times -\frac{5}{6} = \frac{18 \times 5}{7 \times 6} = \frac{90}{42}
\]

We can simplify \(\frac{90}{42}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

\[
\frac{90 \div 6}{42 \div 6} = \frac{15}{7}
\]

Thus, the answer is:

\[
\boxed{B}
\]

Answer: B. \(\frac{15}{7}\)
B
llama3.1-70B-Instruct

B
B
llama3.1-405B-Instruct

B. \frac{15}{7}
B
DeepSeek-Coder-V2 B. \frac{15}{7} B
Qwen2-72B-Instruct B. \frac{15}{7} B
baichuan4 B B
doubao B

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, $\frac{-\frac{18}{7}}{-\frac{6}{5}}=-\frac{18}{7}\times(-\frac{5}{6})=\frac{15}{7}$.
B
minimax To solve the given expression, we can multiply the first fraction by the reciprocal of the second fraction:

$$\frac{-\frac{18}{7}}{-\frac{6}{5}} = -\frac{18}{7} \times -\frac{5}{6}$$

Multiplying the numerators and denominators separately, we get:

$$= \frac{18 \times 5}{7 \times 6}$$

$$= \frac{90}{42}$$

Now, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

$$= \frac{90 \div 6}{42 \div 6}$$

$$= \frac{15}{7}$$

So the correct answer is:

B. \frac{15}{7}
B
kimi To solve this problem, we can follow the rules for dividing fractions:

1. Invert the second fraction (the divisor).
2. Multiply the first fraction (the dividend) by the inverted second fraction.

So, we have:

$$\frac{-\frac{18}{7}}{-\frac{6}{5}} = \frac{-\frac{18}{7}}{1} \times \frac{5}{-\frac{6}{1}} = \frac{18}{7} \times \frac{5}{6}$$

Now, multiply the numerators and the denominators:

$$\frac{18 \times 5}{7 \times 6} = \frac{90}{42}$$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

$$\frac{90 \div 6}{42 \div 6} = \frac{15}{7}$$

So the correct answer is B. $\frac{15}{7}$.
B
wenxinyiyan B B
zhipu To solve the expression \(\frac{-\frac{18}{7}}{-\frac{6}{5}}\), we can simplify it step by step.

First, recognize that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:

\[
\frac{-\frac{18}{7}}{-\frac{6}{5}} = -\frac{18}{7} \times -\frac{5}{6}
\]

Next, multiply the numerators and the denominators separately:

\[
-\frac{18}{7} \times -\frac{5}{6} = \frac{(-18) \times (-5)}{7 \times 6}
\]

Since multiplying two negative numbers results in a positive number:

\[
\frac{(-18) \times (-5)}{7 \times 6} = \frac{90}{42}
\]

Now, simplify the fraction \(\frac{90}{42}\) by finding the greatest common divisor (GCD) of 90 and 42. The GCD of 90 and 42 is 6.

Divide both the numerator and the denominator by 6:

\[
\frac{90 \div 6}{42 \div 6} = \frac{15}{7}
\]

So, the simplified result is \(\frac{15}{7}\).

Therefore, the correct answer is:

B. \(\frac{15}{7}\)
B
gpto1 B B
deepseekv3 To solve the expression \(\frac{-\frac{18}{7}}{-\frac{6}{5}}\), follow these steps:

1. **Simplify the negative signs**:
\[
\frac{-\frac{18}{7}}{-\frac{6}{5}} = \frac{\frac{18}{7}}{\frac{6}{5}}
\]

2. **Divide the fractions by multiplying by the reciprocal**:
\[
\frac{\frac{18}{7}}{\frac{6}{5}} = \frac{18}{7} \times \frac{5}{6}
\]

3. **Multiply the numerators and denominators**:
\[
\frac{18 \times 5}{7 \times 6} = \frac{90}{42}
\]

4. **Simplify the fraction by dividing numerator and denominator by 6**:
\[
\frac{90 \div 6}{42 \div 6} = \frac{15}{7}
\]

Thus, the correct answer is:

**B. \(\frac{15}{7}\)**
B