https://file.aiquickdraw.com/mathbot/file/174051670551058mh5h5b.jpg

Let's break down the math problems from the image:

### Problem 19:
\[
-2\frac{2}{5} \times \frac{17}{8}
\]

We need to multiply a mixed number and a fraction. First, convert the mixed number into an improper fraction:
\[
2\frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{12}{5}
\]

Now the problem becomes:
\[
-\frac{12}{5} \times \frac{17}{8}
\]

Multiply the numerators and the denominators:
\[
\frac{-12 \times 17}{5 \times 8} = \frac{-204}{40}
\]

Simplify the fraction:
\[
\frac{-204}{40} = \frac{-51}{10}
\]

So, the answer is:
\[
-5\frac{1}{10}
\]

### Problem 20:
\[
\left( -3\frac{3}{20} \right) \times \left( -1\frac{1}{9} \right)
\]

Again, we will convert the mixed numbers to improper fractions. 

For \( -3\frac{3}{20} \):
\[
3\frac{3}{20} = \frac{(3 \times 20) + 3}{20} = \frac{63}{20}
\]
This is negative, so the fraction is:
\[
-\frac{63}{20}
\]

For \( -1\frac{1}{9} \):
\[
1\frac{1}{9} = \frac{(1 \times 9) + 1}{9} = \frac{10}{9}
\]
This is also negative, so the fraction is:
\[
-\frac{10}{9}
\]

Now multiply the two fractions:
\[
-\frac{63}{20} \times -\frac{10}{9} = \frac{63 \times 10}{20 \times 9} = \frac{630}{180}
\]

Simplify the fraction:
\[
\frac{630}{180} = \frac{7}{2}
\]

So, the answer is:
\[
3\frac{1}{2}
\]

---

Would you like further clarification or additional steps for these problems? Feel free to ask!

Here are 5 related questions to deepen your understanding:
1. How do you simplify improper fractions?
2. What is the method for multiplying mixed numbers?
3. How do you simplify a fraction after multiplication?
4. Can you give examples of adding or subtracting mixed numbers?
5. What are the differences between multiplying and dividing fractions?

**Tip:** Always convert mixed numbers into improper fractions before performing any operations.

Learn how to multiply mixed numbers and simplify fractions with detailed step-by-step solutions. These problems involve converting mixed numbers to improper fractions, multiplying fractions, and simplifying the results. Suitable for students in Grades 6-8.

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