The sum of two rational numbers is `-4.` If one of them is `(-11)/(5)`, find the other.

Options

A. `(-3)/(5) `
B. `(-4)/(5) `
C. `(-9)/(5) `
D. `(-2)/(5) `

Answer

To find the other rational number when the sum of two rational numbers is -4 and one of them is \(-\frac{11}{5}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given information**:
- The sum of two rational numbers is \(-4\).
- One of the rational numbers is \(-\frac{11}{5}\).
- Let the other rational number be \(x\).

2. **Set up the equation**:
- According to the problem, we can write the equation:
\[ -\frac{11}{5} + x = -4 \]

3. **Isolate \(x\)**:
- To find \(x\), we need to isolate it on one side of the equation. We can do this by adding \(\frac{11}{5}\) to both sides:
\[ x = -4 + \frac{11}{5} \]

4. **Convert \(-4\) to a fraction with a common denominator**:
- The number \(-4\) can be expressed as a fraction with a denominator of 5:
\[ -4 = -\frac{20}{5} \]
- Now, we can rewrite the equation:
\[ x = -\frac{20}{5} + \frac{11}{5} \]

5. **Combine the fractions**:
- Since both fractions have the same denominator, we can combine them:
\[ x = \frac{-20 + 11}{5} = \frac{-9}{5} \]

6. **Final answer**:
- Therefore, the other rational number is:
\[ x = -\frac{9}{5} \]

### Summary:
The other rational number is \(-\frac{9}{5}\).