The sum of two rational numbers is `-3`. If one of them is `(-10)/(3)` then the other one is

Options

A. `(-13)/(3)`
B. `(-19)/(3)`
C. `(1)/(3)`
D. `(13)/(3)`

Answer

To find the other rational number when the sum of two rational numbers is -3 and one of them is \(-\frac{10}{3}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The sum of two rational numbers is \(-3\).
- One of the rational numbers is \(-\frac{10}{3}\).
- Let the other rational number be \(x\).

2. **Set Up the Equation:**
- According to the problem, we can write the equation:
\[ x + \left(-\frac{10}{3}\right) = -3 \]
- This simplifies to:
\[ x - \frac{10}{3} = -3 \]

3. **Isolate \(x\):**
- To isolate \(x\), add \(\frac{10}{3}\) to both sides of the equation:
\[ x = -3 + \frac{10}{3} \]

4. **Convert \(-3\) to a Fraction:**
- Convert \(-3\) into a fraction with a denominator of 3:
\[ -3 = -\frac{9}{3} \]
- Now, substitute this back into the equation:
\[ x = -\frac{9}{3} + \frac{10}{3} \]

5. **Combine the Fractions:**
- Since both fractions have the same denominator, we can combine them:
\[ x = \frac{-9 + 10}{3} = \frac{1}{3} \]

6. **Conclusion:**
- Therefore, the other rational number is:
\[ x = \frac{1}{3} \]

### Final Answer:
The other rational number is \(\frac{1}{3}\).