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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.

Divide and simplify the expression: 4/5 ÷ (-11/2).

Learn how to divide and simplify the fraction 4/5 ÷ (-11/2) with a detailed step-by-step solution. This problem covers key mathematical concepts such as the division of fractions, the use of reciprocals, and multiplication of fractions. Suitable for students in Grades 6-8.

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