Let's go over the multiplication of mixed numbers and fractions step by step. I'll solve the first few problems in detail.

38. $2 \frac{1}{2} \times \frac{4}{5}$

1. Convert the mixed number $2 \frac{1}{2}$ to an improper fraction: $2 \frac{1}{2} = \frac{5}{2}$
2. Now multiply: $\frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10} = 2$ So, the answer is 2.

39. $\frac{3}{5} \times \frac{1}{3}$

Multiply the two fractions: $\frac{3}{5} \times \frac{1}{3} = \frac{3 \times 1}{5 \times 3} = \frac{3}{15} = \frac{1}{5}$ So, the answer is $\frac{1}{5}$.

42. $\frac{3}{4} \times 1 \frac{1}{3}$

1. Convert the mixed number $1 \frac{1}{3}$ to an improper fraction: $1 \frac{1}{3} = \frac{4}{3}$
2. Now multiply: $\frac{3}{4} \times \frac{4}{3} = \frac{3 \times 4}{4 \times 3} = \frac{12}{12} = 1$ So, the answer is 1.

43. $\frac{3}{4} \times \frac{2}{5}$

Multiply the two fractions: $\frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20} = \frac{3}{10}$ So, the answer is $\frac{3}{10}$.

Would you like me to continue solving the remaining problems or provide additional details on any specific ones?

Here are 5 follow-up questions you can explore:

1. How do you convert a mixed number to an improper fraction?
2. What happens when you multiply two improper fractions?
3. How can you simplify a product of fractions?
4. What is the relationship between multiplying fractions and whole numbers?
5. How do you convert an improper fraction back to a mixed number?

Tip: Always simplify your fractions at the end of a multiplication process to get the most reduced form.