The sum of rational numbers is -4. if one of them is `(-11)/(6)`. Find the other .

Answer

To solve the problem step by step, we need to find the other rational number when one of them is given as \(-\frac{11}{6}\) and their sum is \(-4\).

### Step 1: Set up the equation
Let the other rational number be \(x\). According to the problem, the sum of the two rational numbers is:
\[ x + \left(-\frac{11}{6}\right) = -4 \]

### Step 2: Simplify the equation
We can rewrite the equation as:
\[ x - \frac{11}{6} = -4 \]

### Step 3: Isolate \(x\)
To isolate \(x\), we can add \(\frac{11}{6}\) to both sides of the equation:
\[ x = -4 + \frac{11}{6} \]

### Step 4: Convert \(-4\) to a fraction
To add these two numbers, we need to express \(-4\) as a fraction with a denominator of 6. We can do this by multiplying \(-4\) by \(\frac{6}{6}\):
\[ -4 = -\frac{24}{6} \]

### Step 5: Add the fractions
Now we can add the fractions:
\[ x = -\frac{24}{6} + \frac{11}{6} \]
\[ x = \frac{-24 + 11}{6} \]
\[ x = \frac{-13}{6} \]

### Step 6: Conclusion
Thus, the other rational number is:
\[ \boxed{-\frac{13}{6}} \]

---