In Examples 5 and 6, fill in the blanks to make the statements true.
There are _______ number of rational numbers between two rational numbers.

Answer

To solve the question, we need to determine how many rational numbers can exist between two given rational numbers.

### Step-by-Step Solution:

1. **Understanding Rational Numbers**:
- A rational number is defined as a number that can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \).

2. **Identifying Two Rational Numbers**:
- Let's consider two rational numbers, for example, \( \frac{1}{2} \) and \( \frac{2}{3} \).

3. **Finding Rational Numbers Between Them**:
- To find rational numbers between \( \frac{1}{2} \) and \( \frac{2}{3} \), we can take the average of these two numbers or find other fractions that lie between them.

4. **Inserting Rational Numbers**:
- For any two rational numbers, we can always find another rational number by taking their average:
\[ \text{Average} = \frac{\frac{1}{2} + \frac{2}{3}}{2} = \frac{3 + 4}{12} = \frac{7}{12} \]
- We can also find more rational numbers by considering fractions with larger denominators or by using methods like mediants.

5. **Conclusion**:
- Between any two rational numbers, there are not just a few, but an infinite number of rational numbers that can be found.

### Final Answer:
There are **infinite** number of rational numbers between two rational numbers.

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