The problem shown in the image asks to divide and simplify the following expression:

$\frac{4}{5} \div \left( \frac{-11}{2} \right)$

Step-by-Step Solution:

1. Division of Fractions Rule: Dividing by a fraction is the same as multiplying by its reciprocal. So the expression becomes: $\frac{4}{5} \times \left( \frac{-2}{11} \right)$ This is because the reciprocal of $\frac{-11}{2}$ is $\frac{-2}{11}$.

2. Multiplying Fractions: Now, multiply the numerators and denominators: $\frac{4 \times -2}{5 \times 11} = \frac{-8}{55}$

Thus, the simplified result of the division is: $\frac{-8}{55}$

Would you like more details or have any questions on this process? Here are some related questions you could explore:

1. What is the reciprocal of a negative fraction?
2. How do you multiply two fractions?
3. Why does division by a fraction involve multiplying by its reciprocal?
4. How do you simplify a fraction after multiplication?
5. Can this fraction be further simplified?

Tip: Always remember that when dividing by a fraction, you can multiply by its reciprocal to simplify the operation.