The product of two rational number is 10. if one of the numbers is -8. find the other .

Answer

To solve the problem step by step, we need to find the other rational number when the product of two rational numbers is given as 10, and one of the numbers is -8.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We know that the product of two rational numbers is 10.
- One of the rational numbers is -8.

2. **Let the Unknown Number be x**:
- We will denote the other rational number as \( x \).

3. **Set Up the Equation**:
- According to the problem, the product of -8 and \( x \) is equal to 10.
- This can be written as:
\[ -8 \times x = 10 \]

4. **Solve for x**:
- To find \( x \), we need to isolate it. We can do this by dividing both sides of the equation by -8:
\[ x = \frac{10}{-8} \]

5. **Simplify the Fraction**:
- Now, simplify \( \frac{10}{-8} \):
\[ x = \frac{10 \div 2}{-8 \div 2} = \frac{5}{-4} = -\frac{5}{4} \]

6. **Conclusion**:
- Therefore, the other rational number is:
\[ x = -\frac{5}{4} \]

### Final Answer:
The other rational number is \( -\frac{5}{4} \).