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.