I will solve the math problems displayed on the board step-by-step. Let's go through each question carefully.

1) $\frac{1}{2} \times 0.3 \div \frac{3}{4}$

1. First, calculate $\frac{1}{2} \times 0.3$: $\frac{1}{2} \times 0.3 = \frac{0.3}{2} = 0.15$

2. Next, divide by $\frac{3}{4}$: $0.15 \div \frac{3}{4} = 0.15 \times \frac{4}{3} = \frac{0.6}{3} = 0.2$

   So, the answer to the first question is 0.2.

2) $\frac{2}{5} \div \frac{1}{2} \times 0.8$

1. First, calculate $\frac{2}{5} \div \frac{1}{2}$: $\frac{2}{5} \div \frac{1}{2} = \frac{2}{5} \times 2 = \frac{4}{5}$

2. Then, multiply by 0.8: $\frac{4}{5} \times 0.8 = \frac{4 \times 0.8}{5} = \frac{3.2}{5} = 0.64$

   The answer to the second question is 0.64.

3) $0.2 \div \frac{3}{4} \times \frac{2}{7}$

1. First, calculate $0.2 \div \frac{3}{4}$: $0.2 \div \frac{3}{4} = 0.2 \times \frac{4}{3} = \frac{0.8}{3} = 0.2667$

2. Then, multiply by $\frac{2}{7}$: $0.2667 \times \frac{2}{7} = \frac{0.5334}{7} \approx 0.0762$

   The answer to the third question is approximately 0.0762.

4) $0.4 \times 1\frac{2}{3} \div 0.15$

1. Convert $1\frac{2}{3}$ to an improper fraction: $1\frac{2}{3} = \frac{5}{3}$

2. Now calculate $0.4 \times \frac{5}{3}$: $0.4 \times \frac{5}{3} = \frac{2}{5} \times \frac{5}{3} = \frac{2}{3} = 0.6667$

3. Next, divide by 0.15: $0.6667 \div 0.15 = \frac{0.6667}{0.15} \approx 4.4447$

   The answer to the fourth question is approximately 4.4447.

5) $\frac{5}{6} \times 0.025 \times \frac{3}{4}$

1. First, calculate $\frac{5}{6} \times 0.025$: $\frac{5}{6} \times 0.025 = \frac{5 \times 0.025}{6} = \frac{0.125}{6} \approx 0.02083$

2. Now, multiply by $\frac{3}{4}$: $0.02083 \times \frac{3}{4} = \frac{0.06249}{4} \approx 0.0156$

   The answer to the fifth question is approximately 0.0156.

Do you have any questions, or would you like more details on any step?

Here are 5 related questions for further practice:

1. What is the result of $\frac{3}{5} \times 0.7 \div \frac{2}{3}$?
2. Solve $\frac{4}{7} \div 0.5 \times \frac{1}{3}$.
3. Calculate $0.25 \times \frac{2}{3} \div 0.2$.
4. What is $\frac{7}{8} \times 0.4 \div \frac{5}{6}$?
5. Find the value of $0.3 \div \frac{4}{5} \times \frac{1}{2}$.

Tip: Always simplify fractions or convert them to decimals before performing operations for easier calculations.