What are rational numbers? Give Examples of five positive and five negative rational numbers. Is there any rational number which is neither positive nor negative? Name it.

Answer

### Step-by-Step Solution:

1. **Definition of Rational Numbers**:
- Rational numbers are defined as numbers that can be expressed in the form of \( \frac{p}{q} \) where:
- \( p \) and \( q \) are integers.
- \( q \) is not equal to 0.
- \( p \) and \( q \) can be co-prime (they have no common factors other than 1).

2. **Examples of Positive Rational Numbers**:
- Positive rational numbers are those that are greater than zero. Here are five examples:
1. \( \frac{2}{5} \)
2. \( \frac{3}{5} \)
3. \( \frac{6}{5} \)
4. \( \frac{1}{2} \)
5. \( \frac{5}{2} \)

3. **Examples of Negative Rational Numbers**:
- Negative rational numbers are those that are less than zero. Here are five examples:
1. \( -\frac{2}{5} \)
2. \( -\frac{3}{5} \)
3. \( -\frac{8}{7} \)
4. \( -\frac{4}{5} \)
5. \( -\frac{1}{3} \)

4. **Rational Number that is Neither Positive nor Negative**:
- The rational number that is neither positive nor negative is **0**. It is considered a neutral number.