Give the sign of a rational number in which the numerator is negative and the denominator is negative.

Options

A. negative
B. positive
C. can not determine
D. none of the above

Answer

To determine the sign of a rational number where the numerator is negative and the denominator is also negative, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Rational Number**:
Let the rational number be represented as \(\frac{x}{y}\), where \(x\) is the numerator and \(y\) is the denominator.

2. **Assign Signs to the Numerator and Denominator**:
Given that the numerator \(x\) is negative, we can write it as:
\[ x = -a \quad \text{(where \(a\) is a positive number)} \]
Similarly, since the denominator \(y\) is also negative, we can write it as:
\[ y = -b \quad \text{(where \(b\) is a positive number)} \]

3. **Substitute the Values into the Rational Number**:
Now substituting these values into the rational number:
\[ \frac{x}{y} = \frac{-a}{-b} \]

4. **Simplify the Expression**:
When we divide a negative number by another negative number, the negatives cancel out:
\[ \frac{-a}{-b} = \frac{a}{b} \]

5. **Determine the Sign**:
Since both \(a\) and \(b\) are positive, \(\frac{a}{b}\) is also positive. Therefore, the sign of the rational number \(\frac{x}{y}\) is:
\[ \text{Positive} \]

### Final Answer:
The sign of a rational number in which the numerator is negative and the denominator is negative is **Positive**.