Find the quotient and write your answer in mixed number form. Reduce if possible. \[ \left(-2 \frac{2}{3}\right) \div\left(-5 \frac{1}{2}\right) \]

To solve \(\left(-2 \frac{2}{3}\right) \div\left(-5 \frac{1}{2}\right)\), we first convert the mixed numbers to improper fractions. For \(-2 \frac{2}{3}\): \[ -2 \frac{2}{3} = -\left(2 \times 3 + 2\right)/3 = -\frac{8}{3} \] For \(-5 \frac{1}{2}\): \[ -5 \frac{1}{2} = -\left(5 \times 2 + 1\right)/2 = -\frac{11}{2} \] Now we divide the two fractions: \[ -\frac{8}{3} \div -\frac{11}{2} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{8}{3} \times -\frac{2}{11} = \frac{8 \times 2}{3 \times 11} = \frac{16}{33} \] Now, \(\frac{16}{33}\) is already in simplest form because 16 and 33 have no common factors (16 is \(2^4\) and 33 is \(3 \times 11\)). Since \(\frac{16}{33}\) is less than 1, in mixed number form it is: \[ 0 \frac{16}{33} \] Thus, the final answer is: \[ \frac{16}{33} \]