问题


There is a single choice question about high school mathematics. Answer the question by replying A, B, C or D.
Question: Find $-\dfrac{1}{-3}\cdot\cfrac{1}{~\frac{1}{-3}~}.$
A. 1
B. -1
C. 0
D. 2
Answer:

答案

模型 模型答案 正确答案
金声玉亮2.0

A.
Final Answer: The final answer is A. I hope it is correct.
B
deepseekr1

The problem involves simplifying the expression \(-\dfrac{1}{-3} \cdot \cfrac{1}{\frac{1}{-3}}\). Breaking it down:

1. **First term**: \(-\dfrac{1}{-3}\). Dividing two negatives gives a positive: \(\dfrac{1}{3}\).
2. **Second term**: \(\cfrac{1}{\frac{1}{-3}}\). Dividing by a fraction is equivalent to multiplying by its reciprocal: \(1 \times (-3) = -3\).
3. **Multiply the results**: \(\dfrac{1}{3} \times (-3) = -1\).

The final result is \(-1\), corresponding to **option B**.

**Answer:** B
B
gpto1 B B
GPT-4o To solve the expression \(-\dfrac{1}{-3}\cdot\cfrac{1}{~\frac{1}{-3}~}\), let's break it down step by step.

First, simplify \(-\dfrac{1}{-3}\):
\[
-\dfrac{1}{-3} = \dfrac{1}{3}
\]

Next, simplify \(\cfrac{1}{~\frac{1}{-3}~}\):
\[
\frac{1}{\frac{1}{-3}} = -3
\]

Now, multiply the results of these two simplifications:
\[
\dfrac{1}{3} \cdot (-3) = -1
\]

Therefore, the answer is:
\[
\boxed{-1}
\]

So, the correct choice is:
B. -1
B
llama3.1-70B-Instruct

A
The given expression is equivalent to $-\dfrac{1}{-3}\cdot\left(-3\right)$, which is equivalent to $\dfrac{1}{3}\cdot\left(-3\right)$, or $-1$. Note that 1/3 and –3 are examples of reciprocals.
B
llama3.1-405B-Instruct

A
The best answer is A.
B
DeepSeek-Coder-V2 A. 1 B
Qwen2-72B-Instruct A. 1 B
baichuan4 A B
doubao First, $-\frac{1}{-3}=\frac{1}{3}$. And $\frac{1}{\frac{1}{-3}}=1\div\frac{1}{-3}=1\times(-3)=-3$. Then $\frac{1}{3}\times(-3)=-1$. So the answer is B. B
minimax Let's solve the expression step by step:

$-\dfrac{1}{-3}\cdot\cfrac{1}{~\frac{1}{-3}~}$

First, we simplify the fractions:

$-\dfrac{1}{-3}$ simplifies to $1$ because the negatives cancel each other out.

Next, we look at the second fraction. The expression $\frac{1}{-3}$ is in the denominator of the fraction, so we flip it to get $-3$ in the numerator:

$\cfrac{1}{~\frac{1}{-3}~}$ simplifies to $-3$.

Now we multiply the two simplified expressions:

$1 \cdot (-3) = -3$

However, this result is not among the options provided. It seems there might be a mistake in the options or in the interpretation of the question. If we follow the original expression strictly, the answer would be $-3$, which is not listed in the options A, B, C, or D. Please double-check the question and options. If there is a typo or mistake, please correct it and I can re-evaluate the expression.
B
kimi To solve the expression \(-\dfrac{1}{-3}\cdot\cfrac{1}{~\frac{1}{-3}~}\), we can follow these steps:

1. Simplify the first fraction: \(-\dfrac{1}{-3} = \dfrac{1}{3}\) because the negatives cancel each other out.
2. Simplify the second fraction: \(\cfrac{1}{~\frac{1}{-3}~} = -3\) because flipping the fraction \(\dfrac{1}{-3}\) gives us \(-3\).
3. Now multiply the simplified fractions: \(\dfrac{1}{3} \cdot (-3) = -1\).

So the correct answer is \(\boxed{B. -1}\).
B
wenxinyiyan B B
zhipu To solve the expression \( -\dfrac{1}{-3} \cdot \cfrac{1}{~\frac{1}{-3}~} \), let's break it down step by step.

First, simplify \( -\dfrac{1}{-3} \):
\[ -\dfrac{1}{-3} = \dfrac{1}{3} \]

Next, simplify \( \cfrac{1}{~\frac{1}{-3}~} \):
\[ \cfrac{1}{~\frac{1}{-3}~} = -3 \]

Now, multiply the two simplified expressions:
\[ \dfrac{1}{3} \cdot (-3) = -1 \]

So, the answer is:
\[ B. -1 \]

Therefore, the correct answer is B.
B
gpto1 B B
deepseekv3 Let's solve the expression step by step:

The expression is:
\[
-\dfrac{1}{-3} \cdot \cfrac{1}{\dfrac{1}{-3}}
\]

1. **Simplify \(-\dfrac{1}{-3}\):**
\[
-\dfrac{1}{-3} = \dfrac{1}{3}
\]

2. **Simplify \(\cfrac{1}{\dfrac{1}{-3}}\):**
\[
\cfrac{1}{\dfrac{1}{-3}} = -3
\]

3. **Multiply the two results:**
\[
\dfrac{1}{3} \cdot (-3) = -1
\]

Thus, the final answer is \(-1\).

**Answer:** B
B