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Mischa dives from a platform 5 meters above the water, and her dive takes her 2.1 meters below the surface. The total distance she dives is the sum of the 5 meters above the water and the 2.1 meters below the water.

### Total Distance Calculation:
The total distance is:
\[
5 + 2.1 = 7.1 \, \text{meters}
\]
This distance is the total length from the platform to the deepest point she reaches.

Let's analyze each option:

1. **\(|5 - (-2.1)|\)**:  
   This simplifies to \(|5 + 2.1|\), which equals \( |7.1| \). This is correct because it calculates the total distance as the sum of 5 meters above water and 2.1 meters below.

2. **\(|-(2.1) - (-5)|\)**:  
   This simplifies to \(|-2.1 + 5|\), which equals \(|2.9|\). This is incorrect because it doesn't give the total distance Mischa dives.

3. **\(|2.1 - 5|\)**:  
   This simplifies to \(|-2.9|\), which equals \(2.9\). This is incorrect because it doesn't give the total distance.

4. **\(|-(2.1) - 5|\)**:  
   This simplifies to \(|-2.1 - 5|\), which equals \(|-7.1|\), or just \(7.1\). This is correct because it accurately represents the total distance she dives.

5. **\(|5 + (-2.1)|\)**:  
   This simplifies to \(|5 - 2.1|\), which equals \(|2.9|\). This is incorrect because it doesn't give the total distance.

### Correct Answers:
- **\(|5 - (-2.1)|\)** (first option)
- **\(|-(2.1) - 5|\)** (fourth option)

Would you like more details or have any questions? Here are 5 relative questions to expand the information:

1. How do absolute values help in determining distances in mathematical problems?
2. Can you explain why \( |5 - (-2.1)| \) and \( |-(2.1) - 5| \) give the same distance?
3. What role does the order of operations play in simplifying these expressions?
4. Why is the absolute value used in distance calculations like this one?
5. How would the expression change if Mischa only dived 2 meters instead of 2.1 meters?

**Tip**: Absolute values are often used when working with distances because distance is always non-negative, no matter the direction of movement (upward or downward).

Mischa dives from a platform that is 5 meters above water. Her dive takes her 2.1 meters below the surface of the water. Which expression could represent the distance, in meters, that Mischa dives? Select all that apply.

Explore how to calculate the total distance of Mischa's dive using absolute values and addition of rational numbers. Mischa dives from 5 meters above water to 2.1 meters below the surface, leading to multiple correct expressions for the total distance. Perfect for Grades 6-8 students.

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