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Problem Analysis

Here's a summary of the relevant problems visible on the page:

Task 12:

• Calculate only one of the two given expressions. Justify your choice.
  • a) $315 - 113 - 285 + 5 - 0.7$
  • b) $18 - 2 + 5 - 8 - 4 + 0.5$
  • c) $-1 + 8 - 3 + 2.5$

Task 13:

• Find the error. Describe what was done incorrectly, then calculate the correct solution.

Task 14:

• "Emmi claims that the signs can be switched in subtraction if one also switches the numbers." Verify Emmi's statement.

Specific Task (Boxes A, B, and C)

• Evaluate different expressions involving sums and differences.

Let me go through some of these questions.

Solutions and Explanations

Task 12

Let’s solve the given problems:

1. a) $315 - 113 - 285 + 5 - 0.7$

   • Calculate in steps:
     • $315 - 113 = 202$
     • $202 - 285 = -83$
     • $-83 + 5 = -78$
     • $-78 - 0.7 = -78.7$

   Thus, the result is $-78.7$.

2. b) $18 - 2 + 5 - 8 - 4 + 0.5$

   • Calculate in steps:
     • $18 - 2 = 16$
     • $16 + 5 = 21$
     • $21 - 8 = 13$
     • $13 - 4 = 9$
     • $9 + 0.5 = 9.5$

   Thus, the result is $9.5$.

3. c) $-1 + 8 - 3 + 2.5$

   • Calculate in steps:
     • $-1 + 8 = 7$
     • $7 - 3 = 4$
     • $4 + 2.5 = 6.5$

   Thus, the result is $6.5$.

Task 13

• This task asks you to identify an error in some given calculations. Without the specific examples, I’ll provide a general approach:
  • Common Mistake Types:
    • Incorrect order of operations.
    • Forgetting to properly apply negative signs.
    • Misplacing decimal points.

Task 14

• Emmi's Claim About Switching Subtraction Signs:
  • In general, subtraction is not commutative. For subtraction $a - b$, switching $a$ and $b$ gives $b - a$, which results in a different value unless $a = b$.

Boxed Tasks (A, B, and C)

Let me solve those too:

• A: $12 + 0.95 - 1.55 - 0.55$

  • Step-by-step:
    • $12 + 0.95 = 12.95$
    • $12.95 - 1.55 = 11.4$
    • $11.4 - 0.55 = 10.85$
  • Result: $10.85$

• B: $12 + 0.95 - 1.55 - 5.5$

  • Step-by-step:
    • $12 + 0.95 = 12.95$
    • $12.95 - 1.55 = 11.4$
    • $11.4 - 5.5 = 5.9$
  • Result: $5.9$

• C: $0.95 - 0.55 + 12 - 1.55$

  • Step-by-step:
    • $0.95 - 0.55 = 0.4$
    • $0.4 + 12 = 12.4$
    • $12.4 - 1.55 = 10.85$
  • Result: $10.85$

Summary

• For Task 12, I solved the calculations for parts (a), (b), and (c).
• For Task 13, I provided insights on typical error-checking strategies.
• For Boxed Tasks A, B, and C, we found the results $10.85$, $5.9$, and $10.85$, respectively.

Would you like to explore any of these solutions in more detail, or do you have further questions?

Follow-Up Questions

1. What are some common mistakes people make when calculating multiple subtractions?
2. Why does the order of operations matter when solving expressions?
3. How can negative numbers impact the result of arithmetic operations?
4. What strategies can you use to avoid errors in complex calculations?
5. How do you interpret the signs when performing addition and subtraction of negative numbers?

Tip

When working with multiple operations involving addition and subtraction, always solve step-by-step and double-check each step to minimize errors.