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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.

Multiply the following mixed numbers and fractions: 38. 2 1/2 * 4/5, 39. 3/5 * 1/3, 42. 3/4 * 1 1/3, 43. 3/4 * 2/5, 46. 1 3/10 * 18, 47. 15 * 2 4/9, 50. 5/7 * 3 1/8, 51. 2 4/5 * 4 1/16.

Solve multiplication problems involving mixed numbers and fractions. Learn how to convert mixed numbers to improper fractions and simplify the result. Suitable for Grades 6-8 students.

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