https://file.aiquickdraw.com/mathbot/file/1727100515066tgdhb45q.jpg

The problem shown in the image is:

\[
\frac{4}{9} \div \left( \frac{-2}{4} \right)
\]

### Step 1: Division of Fractions
To divide by a fraction, we multiply by its reciprocal. So, the problem becomes:

\[
\frac{4}{9} \times \frac{4}{-2}
\]

### Step 2: Multiply the Fractions
Now, multiply the numerators and the denominators:

\[
\frac{4 \times 4}{9 \times -2} = \frac{16}{-18}
\]

### Step 3: Simplify the Fraction
Both 16 and -18 have a common factor of 2. Simplify:

\[
\frac{16}{-18} = \frac{8}{-9} = -\frac{8}{9}
\]

### Final Answer:
\[
-\frac{8}{9}
\]

This is already in its simplest form as a reduced proper fraction.

Would you like more details or further clarifications? Here are 5 related questions to deepen understanding:

1. How do you multiply and divide negative fractions?
2. What is the general process for simplifying fractions?
3. How do you convert a fraction to a mixed number if applicable?
4. How do reciprocal operations work with division of fractions?
5. Can you show other examples of dividing and multiplying fractions?

**Tip:** Always simplify fractions to their lowest terms to ensure the answer is fully reduced!

Learn how to divide the fractions 4/9 ÷ (-2/4) by multiplying by the reciprocal. Step-by-step solution with simplification, including the handling of negative fractions. Suitable for students in Grades 5-7.

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