Fill in the blanks.
The product of two rational numbers is always a …………. .

Answer

To solve the question, "The product of two rational numbers is always a ………….", we will follow these steps:

### Step 1: Understand Rational Numbers
Rational numbers are numbers that can be expressed in the form of \( \frac{p}{q} \), where \( p \) and \( q \) are integers, and \( q \neq 0 \).

**Hint:** Remember that rational numbers include integers, fractions, and can be positive or negative.

### Step 2: Define Two Rational Numbers
Let’s consider two rational numbers, say \( a \) and \( b \). We can express them in the form of \( \frac{p}{q} \). For example:
- Let \( a = \frac{m}{n} \) (where \( m \) and \( n \) are integers and \( n \neq 0 \))
- Let \( b = \frac{r}{s} \) (where \( r \) and \( s \) are integers and \( s \neq 0 \))

**Hint:** Choose any two rational numbers to illustrate the concept.

### Step 3: Calculate the Product
Now, we will find the product of these two rational numbers:
\[ a \times b = \frac{m}{n} \times \frac{r}{s} = \frac{m \times r}{n \times s} \]

**Hint:** When multiplying fractions, multiply the numerators together and the denominators together.

### Step 4: Analyze the Result
The result \( \frac{m \times r}{n \times s} \) is still in the form of \( \frac{p}{q} \), where \( p = m \times r \) and \( q = n \times s \). Since both \( p \) and \( q \) are integers and \( q \neq 0 \), the product is also a rational number.

**Hint:** Ensure that the denominator is not zero to confirm it's a rational number.

### Conclusion
Therefore, we can conclude that the product of two rational numbers is always a rational number.

**Final Answer:** The product of two rational numbers is always a **rational number**.