To multiply mixed numbers, we first need to convert them into improper fractions.

1. Convert \(-3 \frac{1}{3}\) to an improper fraction:
   \[
   -3 \frac{1}{3} = \frac{-(3 \times 3 + 1)}{3} = \frac{-10}{3}
   \]

2. Convert \(-2 \frac{7}{10}\) to an improper fraction:
   \[
   -2 \frac{7}{10} = \frac{-(2 \times 10 + 7)}{10} = \frac{-27}{10}
   \]

Now, multiply the two improper fractions:
\[
\frac{-10}{3} \times \frac{-27}{10}
\]

Simplify by canceling the common factor of 10:
\[
\frac{-1}{3} \times \frac{-27}{1} = \frac{27}{3} = 9
\]

Thus, \(-3 \frac{1}{3} \times -2 \frac{7}{10} = 9\).

### Do you want further details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you divide two mixed numbers?
2. Can you explain how to add mixed numbers?
3. What are the steps to subtract mixed numbers?
4. How do you multiply improper fractions?
5. How can mixed numbers be simplified after operations?

**Tip:** When multiplying fractions, always simplify the fractions first to make calculations easier.

Learn how to multiply mixed numbers with the example -3 1/3 x (-2 7/10). This solution demonstrates how to convert mixed numbers into improper fractions and multiply them. Simplifying fractions is also covered. Suitable for students in Grades 6-8.

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