The sum of two rational numbers is -5. If one of them is `(-13)/(6)`, find the other.

Options

A. `(-15)/(6) `
B. `(-11)/(6) `
C. `(-13)/(6) `
D. `(-17)/(6) `

Answer

To solve the problem step by step, we need to find the other rational number when the sum of two rational numbers is -5, and one of them is \(-\frac{13}{6}\).

### Step 1: Set up the equation
Let the other rational number be \(x\). According to the problem, we have:
\[ -\frac{13}{6} + x = -5 \]

### Step 2: Isolate \(x\)
To find \(x\), we need to isolate it on one side of the equation. We can do this by adding \(\frac{13}{6}\) to both sides of the equation:
\[ x = -5 + \frac{13}{6} \]

### Step 3: Convert -5 to a fraction
To add \(-5\) and \(\frac{13}{6}\), we need to express \(-5\) as a fraction with a denominator of 6. We can do this by writing:
\[ -5 = -\frac{30}{6} \]
Now, we can rewrite the equation:
\[ x = -\frac{30}{6} + \frac{13}{6} \]

### Step 4: Combine the fractions
Since both fractions have the same denominator, we can combine them:
\[ x = \frac{-30 + 13}{6} \]
\[ x = \frac{-17}{6} \]

### Step 5: Final answer
Thus, the other rational number is:
\[ x = -\frac{17}{6} \]

### Summary
The other rational number that, when added to \(-\frac{13}{6}\), gives a sum of \(-5\) is \(-\frac{17}{6}\).