Let's analyze and solve the questions from the provided image.

Questions:

1. $\frac{2}{3} \times 6$
2. $4 \div \frac{2}{5}$
3. $3 \frac{1}{4} + 2 \frac{2}{3}$
4. $\sqrt{81}$
5. $3^2 + 4^2$
6. $9 - (4 + 3)$
7. $\sqrt[3]{64}$
8. $1.5 \div 0.5$

Solutions:

1. $\frac{2}{3} \times 6$: $\frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3} = 4$ Answer: 4

2. $4 \div \frac{2}{5}$: $4 \div \frac{2}{5} = 4 \times \frac{5}{2} = \frac{4 \times 5}{2} = \frac{20}{2} = 10$ Answer: 10

3. $3 \frac{1}{4} + 2 \frac{2}{3}$: Convert mixed numbers to improper fractions: $3 \frac{1}{4} = \frac{13}{4}, \quad 2 \frac{2}{3} = \frac{8}{3}$ Find a common denominator (12): $\frac{13}{4} = \frac{39}{12}, \quad \frac{8}{3} = \frac{32}{12}$ Add the fractions: $\frac{39}{12} + \frac{32}{12} = \frac{39 + 32}{12} = \frac{71}{12} \approx 5.92$ Answer: $\frac{71}{12}$ or approximately 5.92

4. $\sqrt{81}$: $\sqrt{81} = 9$ Answer: 9

5. $3^2 + 4^2$: $3^2 + 4^2 = 9 + 16 = 25$ Answer: 25

6. $9 - (4 + 3)$: $9 - (4 + 3) = 9 - 7 = 2$ Answer: 2

7. $\sqrt[3]{64}$: $\sqrt[3]{64} = 4$ Answer: 4

8. $1.5 \div 0.5$: $1.5 \div 0.5 = \frac{1.5}{0.5} = 3$ Answer: 3

Would you like more details on any of these solutions or have any questions?

Here are 8 related questions for further exploration:

1. How do you convert mixed numbers to improper fractions?
2. Can you solve $5 \frac{1}{2} - 2 \frac{3}{4}$?
3. How do you find the cube root of a number?
4. What is the importance of using a common denominator when adding fractions?
5. Can you simplify $\frac{3}{4} \times \frac{8}{5}$?
6. How do you divide fractions by whole numbers?
7. Can you solve $2^3 + 3^3$?
8. What is the process for solving $12 \div 3 \frac{1}{2}$?

Tip: When working with fractions, always simplify your final answer to its lowest terms for clarity and accuracy.