2. \( \frac{10}{3} \div\left(-\frac{15}{6}\right) \)

To simplify the expression \( \frac{10}{3} \div\left(-\frac{15}{6}\right) \), we can convert the division into multiplication by the reciprocal of the second fraction. This gives us: \[ \frac{10}{3} \times \left(-\frac{6}{15}\right) \] Next, we can simplify both fractions. The \(6\) in the numerator of the second fraction and the \(15\) in the denominator can be reduced: \(-\frac{6}{15} = -\frac{2}{5}\) (by dividing both the numerator and denominator by 3). Now, we multiply: \[ \frac{10}{3} \times -\frac{2}{5} = -\frac{20}{15} \] Finally, simplify \(-\frac{20}{15}\) to get: \(-\frac{4}{3}\) So, the final answer is: \[ -\frac{4}{3} \]