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Let's go through each question and solve them step by step.

### Problem 6:
\[
\frac{2}{5} \div \frac{2}{3}
\]
This becomes:
\[
\frac{2}{5} \times \frac{3}{2} = \frac{6}{10} = \frac{3}{5}
\]

### Problem 7:
\[
\frac{1}{5} \div 4 \frac{2}{3}
\]
Convert \( 4 \frac{2}{3} \) to an improper fraction:
\[
4 \frac{2}{3} = \frac{14}{3}
\]
Now, perform the division:
\[
\frac{1}{5} \div \frac{14}{3} = \frac{1}{5} \times \frac{3}{14} = \frac{3}{70}
\]

### Problem 8:
\[
2 \div \frac{5}{4}
\]
This is equivalent to:
\[
2 \times \frac{4}{5} = \frac{8}{5}
\]

### Problem 9:
\[
\frac{5}{9} \div 2 \frac{2}{3}
\]
Convert \( 2 \frac{2}{3} \) to an improper fraction:
\[
2 \frac{2}{3} = \frac{8}{3}
\]
Now, perform the division:
\[
\frac{5}{9} \div \frac{8}{3} = \frac{5}{9} \times \frac{3}{8} = \frac{15}{72} = \frac{5}{24}
\]

### Problem 10:
\[
\frac{2}{7} \div 4 \frac{2}{3}
\]
Convert \( 4 \frac{2}{3} \) to an improper fraction:
\[
4 \frac{2}{3} = \frac{14}{3}
\]
Now, perform the division:
\[
\frac{2}{7} \div \frac{14}{3} = \frac{2}{7} \times \frac{3}{14} = \frac{6}{98} = \frac{3}{49}
\]

Would you like any further details or clarifications on these solutions?

### Related Questions:
1. What is the process for dividing fractions?
2. How can mixed numbers be converted into improper fractions?
3. What are the steps for simplifying a complex fraction?
4. Can multiplication help simplify division problems involving fractions?
5. How can you cross-multiply to simplify division of two fractions?

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

Solve the following fraction problems: 6. (2/5) ÷ (2/3), 7. (1/5) ÷ 4(2/3), 8. 2 ÷ (5/4), 9. (5/9) ÷ 2(2/3), 10. (2/7) ÷ 4(2/3).

Practice dividing fractions and mixed numbers with step-by-step solutions. Problems include dividing fractions like (2/5) ÷ (2/3) and (5/9) ÷ 2(2/3). Learn how to convert mixed numbers into improper fractions and simplify your answers. Suitable for students in Grades 6-8.

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