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The problem asks to divide the fractions: 

\[
\frac{5}{9} \div \frac{2}{3}
\]

To solve a division of fractions, you multiply the first fraction by the reciprocal (or inverse) of the second fraction. The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\).

Thus, the equation becomes:

\[
\frac{5}{9} \times \frac{3}{2}
\]

Now, multiply the numerators and the denominators:

\[
\frac{5 \times 3}{9 \times 2} = \frac{15}{18}
\]

The fraction \(\frac{15}{18}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

\[
\frac{15 \div 3}{18 \div 3} = \frac{5}{6}
\]

So, the answer is:

\[
\frac{5}{6}
\]

Would you like any more details or explanations on this? 

Here are 5 related questions for practice:

1. What is \(\frac{4}{7} \div \frac{5}{3}\)?
2. Simplify \(\frac{8}{12}\) to its lowest terms.
3. Multiply \(\frac{7}{8} \times \frac{3}{4}\).
4. Divide \(\frac{6}{5} \div \frac{2}{7}\).
5. What is the reciprocal of \(\frac{9}{10}\)?

**Tip:** When dividing fractions, remember to always multiply by the reciprocal of the second fraction.

Learn how to divide fractions with a detailed example of dividing 5/9 by 2/3, including steps on multiplying by the reciprocal and simplifying the result to its lowest terms. This guide is suitable for students in Grade 5-6 looking to strengthen their skills in fraction division.

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