Find a rationai number bewween \[ \frac{3}{5} \text { and } \frac{2}{3} \]

To find a rational number between \(\frac{3}{5}\) and \(\frac{2}{3}\), we can follow these steps: 1. **Convert the fractions to have a common denominator:** \[ \frac{3}{5} = \frac{9}{15}, \quad \frac{2}{3} = \frac{10}{15} \] 2. **Find a fraction between \(\frac{9}{15}\) and \(\frac{10}{15}\):** Since \(\frac{9}{15}\) and \(\frac{10}{15}\) are consecutive fractions with denominator 15, we need to find a fraction with a larger denominator to create more intermediate fractions. 3. **Choose a larger denominator, such as 30:** \[ \frac{3}{5} = \frac{18}{30}, \quad \frac{2}{3} = \frac{20}{30} \] 4. **Select a fraction between \(\frac{18}{30}\) and \(\frac{20}{30}\):** \[ \frac{19}{30} \] 5. **Verify that \(\frac{19}{30}\) is between \(\frac{3}{5}\) and \(\frac{2}{3}\):** - \(\frac{3}{5} = 0.6\) - \(\frac{19}{30} \approx 0.6333\) - \(\frac{2}{3} \approx 0.6667\) Since \(0.6 < 0.6333 < 0.6667\), \(\frac{19}{30}\) is indeed between \(\frac{3}{5}\) and \(\frac{2}{3}\). **Answer:** One such rational number is \(\boxed{\dfrac{19}{30}}\).