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

Answer

To find the number that should be added to \(-\frac{3}{5}\) to obtain \(\frac{2}{3}\), we can set up the equation as follows:

1. **Set up the equation**: Let the unknown number be \(x\). According to the problem, we have:
\[ x + \left(-\frac{3}{5}\right) = \frac{2}{3} \]

2. **Rearrange the equation**: To isolate \(x\), we can add \(\frac{3}{5}\) to both sides of the equation:
\[ x = \frac{2}{3} + \frac{3}{5} \]

3. **Find a common denominator**: The denominators are 3 and 5. The least common multiple (LCM) of 3 and 5 is 15. We will convert both fractions to have a denominator of 15:
- For \(\frac{2}{3}\):
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]
- For \(\frac{3}{5}\):
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

4. **Add the fractions**: Now we can add the two fractions:
\[ x = \frac{10}{15} + \frac{9}{15} = \frac{10 + 9}{15} = \frac{19}{15} \]

5. **Conclusion**: The number that should be added to \(-\frac{3}{5}\) to get \(\frac{2}{3}\) is:
\[ x = \frac{19}{15} \]