The sum of two rational numbers is `-2`. If one of the numbers is `(-14)/(5)`, find the other.

Options

A. `(7)/(5) `
B. `(9)/(5) `
C. `(4)/(5) `
D. `(8)/(5) `

Answer

To solve the problem step by step, we need to find the other rational number when the sum of two rational numbers is given as \(-2\) and one of the numbers is \(-\frac{14}{5}\).

### 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:
\[ -\frac{14}{5} + x = -2 \]

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = -2 + \frac{14}{5} \]

### Step 3: Convert \(-2\) to a Fraction
To perform the addition, we need to express \(-2\) as a fraction with a denominator of \(5\):
\[ -2 = -\frac{10}{5} \]

### Step 4: Substitute and Add the Fractions
Now, substitute \(-\frac{10}{5}\) into the equation:
\[ x = -\frac{10}{5} + \frac{14}{5} \]
Now, since both fractions have the same denominator, we can add them directly:
\[ x = \frac{-10 + 14}{5} = \frac{4}{5} \]

### Step 5: Conclusion
Thus, the other rational number is:
\[ x = \frac{4}{5} \]

### Summary of Steps:
1. Set up the equation based on the sum of the two rational numbers.
2. Isolate the variable \(x\).
3. Convert the integer \(-2\) into a fraction.
4. Substitute and perform the addition of fractions.
5. Conclude with the value of \(x\).