The reciprocal of a negative rational number

Options

A. `" is a positive rational number "`
B. `" is a negative rational number "`
C. `" can be either a positive or a negative rational number "`
D. `" does not exist "`

Answer

To find the reciprocal of a negative rational number, we can follow these steps:

### Step-by-Step Solution:

1. **Identify a Negative Rational Number**:
Let's take a negative rational number. For example, we can choose \(-\frac{2}{3}\).

2. **Understand the Concept of Reciprocal**:
The reciprocal of a number \(x\) is defined as \(\frac{1}{x}\). For a rational number \(\frac{a}{b}\), the reciprocal is \(\frac{b}{a}\).

3. **Calculate the Reciprocal of the Negative Rational Number**:
For our chosen negative rational number \(-\frac{2}{3}\), the reciprocal would be:
\[ \text{Reciprocal} = \frac{1}{-\frac{2}{3}} = -\frac{3}{2} \]

4. **Conclusion**:
The reciprocal of the negative rational number \(-\frac{2}{3}\) is \(-\frac{3}{2}\). Thus, we can conclude that the reciprocal of a negative rational number is also a negative rational number.

### Final Answer:
The reciprocal of a negative rational number is also a negative rational number.

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