Find the quotient and write your answer in mixed number form. Reduce if possible. \[ \left(7 \frac{2}{3}\right) \div\left(-1 \frac{3}{5}\right) \]

To find the quotient of \( 7 \frac{2}{3} \) divided by \( -1 \frac{3}{5} \), we first convert the mixed numbers to improper fractions. For \( 7 \frac{2}{3} \): \[ 7 \frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{21 + 2}{3} = \frac{23}{3} \] For \( -1 \frac{3}{5} \): \[ -1 \frac{3}{5} = \frac{-1 \times 5 - 3}{5} = \frac{-5 - 3}{5} = \frac{-8}{5} \] Now we will divide \( \frac{23}{3} \) by \( \frac{-8}{5} \). Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{23}{3} \div \frac{-8}{5} = \frac{23}{3} \times \frac{-5}{8} = \frac{23 \times -5}{3 \times 8} = \frac{-115}{24} \] Now we convert \( \frac{-115}{24} \) into a mixed number. We divide \( 115 \) by \( 24 \): \[ 115 \div 24 = 4 \quad \text{(remainder } 19\text{)} \] So, \[ \frac{-115}{24} = -4 \frac{19}{24} \] Thus, the final answer in mixed number form is: \[ \boxed{-4 \frac{19}{24}} \]