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This expression represents a complex fraction, specifically:

\[
\frac{\frac{5}{3}}{\frac{9}{5}}
\]

To simplify it, we proceed by dividing the two fractions. Dividing by a fraction is equivalent to multiplying by its reciprocal. So:

\[
\frac{\frac{5}{3}}{\frac{9}{5}} = \frac{5}{3} \times \frac{5}{9}
\]

Now, multiply the numerators and the denominators:

\[
= \frac{5 \times 5}{3 \times 9} = \frac{25}{27}
\]

Thus, the simplified form of the expression is:

\[
\frac{25}{27}
\]

Would you like more details on any step, or do you have any other questions?

Here are five related questions you might find helpful:
1. How do you simplify a complex fraction in general?
2. What does it mean to take the reciprocal of a fraction?
3. How can you determine if two fractions are equivalent?
4. How can complex fractions appear in real-life applications?
5. What is the difference between multiplying and dividing fractions?

**Tip:** When simplifying complex fractions, always remember that dividing by a fraction is equivalent to multiplying by its reciprocal.

Simplify the complex fraction \( \frac{\frac{5}{3}}{\frac{9}{5}} \).

Learn how to simplify the complex fraction \( \frac{\frac{5}{3}}{\frac{9}{5}} \) by dividing two fractions. This example demonstrates using reciprocals and multiplication of fractions. Suitable for middle school students in Grades 6-8.

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