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The given expression is:

\[
\frac{-\frac{5}{9}}{\frac{7}{4}}
\]

This is a complex fraction, and we simplify it by dividing the numerator by the denominator.

### Steps to simplify:

1. Rewrite the division as multiplication by the reciprocal of the denominator:

\[
-\frac{5}{9} \div \frac{7}{4} = -\frac{5}{9} \times \frac{4}{7}
\]

2. Multiply the fractions:

\[
-\frac{5 \times 4}{9 \times 7} = -\frac{20}{63}
\]

So, the simplified answer is:

\[
-\frac{20}{63}
\]

Let me know if you'd like more details or have any questions.

### Related Questions:
1. How do you divide fractions step-by-step?
2. What are the common mistakes when simplifying complex fractions?
3. How would this process change if the fraction were positive?
4. What is the reciprocal of a fraction, and why is it used in division?
5. How can you simplify fractions like \(-\frac{20}{63}\) further?

### Tip:
When dividing fractions, always remember to multiply by the reciprocal of the divisor.

Perform the operation and simplify: (-5/9) ÷ (7/4)

Learn how to simplify complex fractions such as (-5/9) ÷ (7/4). This guide explains the step-by-step process of dividing fractions using the reciprocal and how to multiply fractions for a simplified answer. Suitable for Grades 6-8 students.

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