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.