The problem in the image involves dividing fractions:

$\frac{\frac{9}{2}}{\frac{2}{3}}$

Solution:

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

$\frac{\frac{9}{2}}{\frac{2}{3}} = \frac{9}{2} \times \frac{3}{2}$

Step 1: Multiply the numerators

$9 \times 3 = 27$

Step 2: Multiply the denominators

$2 \times 2 = 4$

Step 3: Simplify the result

$\frac{27}{4}$

This is an improper fraction. Converting it to a mixed number:

$\frac{27}{4} = 6 \, \frac{3}{4}$

Final Answer:

$\boxed{\frac{27}{4} \text{ or } 6 \, \frac{3}{4}}$

Would you like a more detailed breakdown or clarification on any step?

Here are 5 related questions to deepen understanding:

1. How do you multiply two fractions?
2. How do you convert an improper fraction into a mixed number?
3. What is the reciprocal of a fraction, and how is it used in division?
4. How can the result be checked for accuracy?
5. Can the fraction $\frac{27}{4}$ be simplified further?

Tip: Always simplify your fractions after performing operations to get the cleanest form of your answer.