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The problem you're working on asks for the product of:

\[
-2 \frac{4}{5} \times \left(-3 \frac{1}{2}\right)
\]

Let's go through the solution step by step.

### Step 1: Convert the mixed numbers to improper fractions.
1. Convert \( -2 \frac{4}{5} \):
   \[
   -2 \frac{4}{5} = -\left(\frac{5 \times 2 + 4}{5}\right) = -\frac{14}{5}
   \]
2. Convert \( -3 \frac{1}{2} \):
   \[
   -3 \frac{1}{2} = -\left(\frac{2 \times 3 + 1}{2}\right) = -\frac{7}{2}
   \]

### Step 2: Multiply the improper fractions.
Now multiply:
\[
-\frac{14}{5} \times -\frac{7}{2}
\]
When multiplying fractions, multiply the numerators and the denominators:
\[
\frac{14 \times 7}{5 \times 2} = \frac{98}{10}
\]

### Step 3: Simplify the result.
Now simplify \( \frac{98}{10} \):
\[
\frac{98}{10} = 9 \frac{8}{10}
\]
Reduce the fraction \( \frac{8}{10} \) to \( \frac{4}{5} \), so the final result is:
\[
9 \frac{4}{5}
\]

### Final Answer:
The product of \( -2 \frac{4}{5} \times -3 \frac{1}{2} \) is:

\[
\boxed{9 \frac{4}{5}}
\]

Would you like a detailed explanation of any part of the solution? Here are five related questions you might find helpful:

1. How do you multiply two mixed numbers?
2. Why do you need to convert mixed numbers to improper fractions before multiplying?
3. How do you simplify a fraction after multiplying?
4. Can you explain how to multiply fractions with negative signs?
5. How do you convert improper fractions back to mixed numbers?

**Tip:** When multiplying two negative numbers, the result will always be positive!

What is the product of -2 4/5 × (-3 1/2)?

Learn how to multiply the mixed numbers -2 4/5 and -3 1/2. This detailed solution walks you through converting mixed numbers to improper fractions, multiplying them, and simplifying the result. Perfect for students in Grades 6-8.

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