The product of a non-zero rational number and its reciprocal is ________.

Answer

To solve the question "The product of a non-zero rational number and its reciprocal is ________", we can follow these steps:

### Step-by-Step Solution:

1. **Define a Non-Zero Rational Number**:
A rational number can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers, and \( q \neq 0 \). Since we are looking for a non-zero rational number, we can let \( p \) be any integer except zero.

**Hint**: Remember that a rational number is a fraction where both the numerator and denominator are integers, and the denominator cannot be zero.

2. **Identify the Reciprocal**:
The reciprocal of a rational number \( \frac{p}{q} \) is obtained by flipping the fraction, which gives us \( \frac{q}{p} \).

**Hint**: The reciprocal of a fraction is found by swapping its numerator and denominator.

3. **Calculate the Product**:
Now, we need to find the product of the non-zero rational number \( \frac{p}{q} \) and its reciprocal \( \frac{q}{p} \):
\[ \text{Product} = \left(\frac{p}{q}\right) \times \left(\frac{q}{p}\right) \]

4. **Simplify the Product**:
When we multiply these two fractions, we multiply the numerators together and the denominators together:
\[ \text{Product} = \frac{p \times q}{q \times p} = \frac{pq}{pq} \]
Since \( pq \) is not zero (as both \( p \) and \( q \) are non-zero), we can simplify this to:
\[ \text{Product} = 1 \]

5. **Conclusion**:
Therefore, the product of a non-zero rational number and its reciprocal is always equal to 1.

### Final Answer:
The product of a non-zero rational number and its reciprocal is **1**.