Which of the following is equal to the opposite of −45?

−|−45|
−|45|
−(−45)
−45

Let's break down each of the given options and compare them with the opposite of \( -45 \).

### The opposite of \( -45 \):
The opposite of \( -45 \) is simply \( 45 \). This is because the opposite of a negative number is the corresponding positive number.

Now let's evaluate each option:

1. **\( -| -45 | \)**:
   - The absolute value of \( -45 \) is \( 45 \).
   - So, \( -| -45 | = -45 \), which is not the opposite of \( -45 \).

2. **\( -| 45 | \)**:
   - The absolute value of \( 45 \) is \( 45 \).
   - So, \( -| 45 | = -45 \), which is not the opposite of \( -45 \).

3. **\( -(-45) \)**:
   - The negative of \( -45 \) is \( 45 \).
   - So, \( -(-45) = 45 \), which is indeed the opposite of \( -45 \).

4. **\( -45 \)**:
   - This is already \( -45 \), which is not the opposite of \( -45 \).

### Conclusion:
The correct answer is **\( -(-45) \)**.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. What is the absolute value of a negative number?
2. How does the opposite of a number relate to its sign?
3. Can the opposite of a positive number be negative?
4. What happens when you negate an already negative number?
5. What is the difference between absolute value and negation?

**Tip**: The opposite of any number is simply the number with the opposite sign. If the number is negative, the opposite is positive, and vice versa.

Explore how to find the opposite of -45 with a detailed breakdown of absolute values, negation, and opposites. This problem demonstrates key arithmetic concepts, including the rules for finding opposites and handling absolute values. Ideal for students in Grades 6-8.

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