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It looks like you're working on multiplying mixed numbers. Let's go through the problems one by one.

### Problem 6:
\[
2 \frac{1}{3} \times 3 \frac{1}{2}
\]

First, convert the mixed numbers to improper fractions:
- \( 2 \frac{1}{3} = \frac{7}{3} \)
- \( 3 \frac{1}{2} = \frac{7}{2} \)

Now multiply the fractions:
\[
\frac{7}{3} \times \frac{7}{2} = \frac{49}{6}
\]

So, the result is:
\[
\frac{49}{6}
\]
Or as a mixed number:
\[
8 \frac{1}{6}
\]

### Problem 7:
\[
\frac{2}{4} \times 4 \frac{6}{9}
\]

First, convert \( 4 \frac{6}{9} \) to an improper fraction:
- Simplify \( \frac{6}{9} \) to \( \frac{2}{3} \).
- \( 4 \frac{2}{3} = \frac{14}{3} \)

Now multiply the fractions:
\[
\frac{2}{4} \times \frac{14}{3} = \frac{1}{2} \times \frac{14}{3} = \frac{14}{6}
\]

Simplify:
\[
\frac{14}{6} = \frac{7}{3} = 2 \frac{1}{3}
\]

### Problem 8:
\[
3 \frac{2}{3} \times \frac{4}{5}
\]

Convert \( 3 \frac{2}{3} \) to an improper fraction:
- \( 3 \frac{2}{3} = \frac{11}{3} \)

Now multiply:
\[
\frac{11}{3} \times \frac{4}{5} = \frac{44}{15}
\]

This is the final answer:
\[
2 \frac{14}{15}
\]

### Problem 9:
\[
6 \frac{2}{3} \times \frac{2}{6}
\]

Convert \( 6 \frac{2}{3} \) to an improper fraction:
- \( 6 \frac{2}{3} = \frac{20}{3} \)

Now multiply:
\[
\frac{20}{3} \times \frac{2}{6} = \frac{40}{18}
\]

Simplify:
\[
\frac{40}{18} = \frac{20}{9} = 2 \frac{2}{9}
\]

### Problem 10:
\[
6 \frac{3}{8} \times 7 \frac{3}{4}
\]

Convert the mixed numbers:
- \( 6 \frac{3}{8} = \frac{51}{8} \)
- \( 7 \frac{3}{4} = \frac{31}{4} \)

Now multiply:
\[
\frac{51}{8} \times \frac{31}{4} = \frac{1581}{32}
\]

This can be simplified, but it is already an improper fraction.

---

Do you need any more details or clarifications?

Here are 5 related questions to consider:
1. How do you convert a mixed number into an improper fraction?
2. What is the general rule for multiplying fractions?
3. How can you simplify fractions after multiplication?
4. How do you convert an improper fraction back to a mixed number?
5. What happens if one of the fractions is negative?

**Tip:** Always simplify fractions before multiplying to make calculations easier!

Multiplying mixed numbers: 2 1/3 * 3 1/2, 2/4 * 4 6/9, 3 2/3 * 4/5, 6 2/3 * 2/6, 6 3/8 * 7 3/4

Learn how to multiply mixed numbers like 2 1/3 and 3 1/2 by converting them to improper fractions and simplifying the result. Detailed step-by-step solutions for fractions and mixed numbers. Suitable for Grades 5-7.

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