https://file.aiquickdraw.com/mathbot/file/17267532653755hs1ianc.jpg

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.

Perform the operations and find the value of expressions. Additionally, solve for the unknown number in algebraic equations.

This exercise covers solving arithmetic operations with fractions and decimals, as well as finding unknown numbers in simple algebraic equations. Suitable for students in Grades 6-8.

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