The sum of two rational numbers is `(-2)/(3)`. If one of them is `(-8)/(15)`, find the other.

Answer

To find the other rational number when the sum of two rational numbers is given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the sum of two rational numbers is \(-\frac{2}{3}\) and one of the numbers is \(-\frac{8}{15}\). We need to find the other number.

2. **Set Up the Equation**: Let the other rational number be \(x\). According to the problem, we can write the equation:
\[ -\frac{8}{15} + x = -\frac{2}{3} \]

3. **Isolate \(x\)**: To find \(x\), we rearrange the equation:
\[ x = -\frac{2}{3} - \left(-\frac{8}{15}\right) \]
This simplifies to:
\[ x = -\frac{2}{3} + \frac{8}{15} \]

4. **Find a Common Denominator**: The denominators are 3 and 15. The least common multiple (LCM) of 3 and 15 is 15. We need to express \(-\frac{2}{3}\) with a denominator of 15:
\[ -\frac{2}{3} = -\frac{2 \times 5}{3 \times 5} = -\frac{10}{15} \]

5. **Combine the Fractions**: Now we can substitute back into the equation:
\[ x = -\frac{10}{15} + \frac{8}{15} \]

6. **Perform the Addition**: Since the denominators are the same, we can combine the numerators:
\[ x = \frac{-10 + 8}{15} = \frac{-2}{15} \]

7. **Final Answer**: Therefore, the other rational number is:
\[ x = -\frac{2}{15} \]

### Summary:
The other rational number is \(-\frac{2}{15}\).