What should be added to `(-5)/(7)` to get `(-2)/(3)`?

Answer

To solve the question "What should be added to \(-\frac{5}{7}\) to get \(-\frac{2}{3}\)?", we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Equation**:
Let \( x \) be the number that needs to be added to \(-\frac{5}{7}\). According to the problem, we can write the equation:
\[ -\frac{5}{7} + x = -\frac{2}{3} \]

2. **Isolate \( x \)**:
To find \( x \), we need to isolate it on one side of the equation. We can do this by adding \(\frac{5}{7}\) to both sides:
\[ x = -\frac{2}{3} + \frac{5}{7} \]

3. **Find a Common Denominator**:
The denominators are 3 and 7. The least common multiple (LCM) of 3 and 7 is 21. We will convert both fractions to have a denominator of 21:
- For \(-\frac{2}{3}\):
\[ -\frac{2}{3} = -\frac{2 \times 7}{3 \times 7} = -\frac{14}{21} \]
- For \(\frac{5}{7}\):
\[ \frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21} \]

4. **Combine the Fractions**:
Now we can add the two fractions:
\[ x = -\frac{14}{21} + \frac{15}{21} = \frac{1}{21} \]

5. **Final Answer**:
Therefore, the number that should be added to \(-\frac{5}{7}\) to get \(-\frac{2}{3}\) is:
\[ x = \frac{1}{21} \]