(1⋅0.4+2⋅0.5):0.13+[−1+3⋅(−0.1)]:(−0.2)− 
3
  
−0.125
​


Let's solve the expression step by step:

\[
\left( 1 \cdot 0.4 + 2 \cdot 0.5 \right) : 0.13 + \left( -1 + 3 \cdot (-0.1) \right) : (-0.2) - \frac{3}{-0.125}
\]

### Step 1: Simplify inside the parentheses
- \( 1 \cdot 0.4 = 0.4 \)
- \( 2 \cdot 0.5 = 1 \)

So the first part becomes:
\[
0.4 + 1 = 1.4
\]

### Step 2: Simplify the second part inside the parentheses
- \( 3 \cdot (-0.1) = -0.3 \)
- \( -1 + (-0.3) = -1.3 \)

Now the expression becomes:
\[
\frac{1.4}{0.13} + \frac{-1.3}{-0.2} - \frac{3}{-0.125}
\]

### Step 3: Perform the divisions
1. \( \frac{1.4}{0.13} \approx 10.77 \)
2. \( \frac{-1.3}{-0.2} = 6.5 \)
3. \( \frac{3}{-0.125} = -24 \)

### Step 4: Add and subtract the results
\[
10.77 + 6.5 - (-24)
\]
\[
10.77 + 6.5 + 24 = 41.27
\]

Thus, the final result is:
\[
\boxed{41.27}
\]

Do you want more details or have any questions?  
Here are some related questions:
1. How do you handle negative numbers in calculations?
2. What is the difference between multiplication and division of decimals?
3. How do you simplify expressions with multiple operations?
4. What are the rules for order of operations (PEMDAS)?
5. How does dividing by negative numbers affect the result?

**Tip:** Always follow the order of operations (PEMDAS) to simplify complex expressions correctly.

(1⋅0.4+2⋅0.5):0.13+[−1+3⋅(−0.1)]:(−0.2)−3/−0.125

Learn how to solve a complex arithmetic expression involving decimals and negative numbers, step by step. This problem covers key mathematical concepts such as multiplication, division, and handling negative numbers. Ideal for students in Grades 6-8.

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