Let's break down the problems from the image you provided.

Task 1: Simplification

You are asked to simplify or evaluate the following expressions:

1. a)
   $-3 \frac{5}{9} \cdot \left( 1 \frac{1}{8} - \frac{7}{20} \right)$ We'll convert the mixed numbers to improper fractions first, then perform the arithmetic.

2. b)
   $-7.25 \cdot 7.35 - 7.25 \cdot 2.65$ This is a straightforward calculation involving decimals.

3. c)
   $\left( -2 \frac{1}{3} + 4 \frac{1}{5} \right) \div \frac{7}{15}$ First, convert the mixed numbers to improper fractions, then simplify.

Task 2: Evaluating the Expression

You are asked to find the value of the following expressions:

1. a)
   $-4.5 + 4.5 + 0.4$ This is a simple sum of decimals.

2. b)
   $12.4 \cdot 0.3 + 2.9 \cdot 0.3$ This involves multiplication and addition of decimals.

3. c)
   $\frac{25}{36} \div \left( \frac{5}{9} - \frac{5}{12} \right)$ Here, subtract fractions first, then divide.

Task 3: Finding the Unknown Value

You are asked to solve for the unknown variable $x$:

1. a)
   $3.1 \cdot x = -12.09$ Solve for $x$.

2. b)
   $-47 = \frac{10.34}{x}$ Solve for $x$.

3. c)
   $x \cdot 5.2 = -105$ Solve for $x$.

I'll start by solving the first expression in Task 1.

Task 1: Expression 1a

First, we convert the mixed numbers to improper fractions:

• $3 \frac{5}{9} = \frac{32}{9}$
• $1 \frac{1}{8} = \frac{9}{8}$
• $\frac{7}{20}$ remains the same.

Thus, the expression becomes: $-\frac{32}{9} \cdot \left( \frac{9}{8} - \frac{7}{20} \right)$

Let me calculate this.The simplified result for the first expression:

$-3 \frac{5}{9} \cdot \left( 1 \frac{1}{8} - \frac{7}{20} \right) = -\frac{124}{45} \approx -2.755$

Would you like to proceed with more calculations or need further details? Here are 5 relative questions to consider:

1. How do you simplify expressions involving mixed numbers and improper fractions?
2. What is the difference between mixed numbers and improper fractions?
3. Can you express $-\frac{124}{45}$ as a decimal, and when might it be useful?
4. What are the steps for handling nested fractions in arithmetic expressions?
5. How do you convert a mixed number into an improper fraction?

Tip: Always simplify fractions before performing multiplications and divisions to make calculations easier.