https://file.aiquickdraw.com/mathbot/file/1726016463759vu2a4zk2.jpg

Let's analyze the pairs of expressions to determine which ones are equivalent.

### Option A:
- **Expression 1:** \( 65 - 15 \)
- **Expression 2:** \( 65 + (-15) \)

Simplifying both:
- \( 65 - 15 = 50 \)
- \( 65 + (-15) = 65 - 15 = 50 \)

These two expressions are equivalent.

### Option B:
- **Expression 1:** \( 18 - 4 \)
- **Expression 2:** \( 18 + (-4) \)

Simplifying both:
- \( 18 - 4 = 14 \)
- \( 18 + (-4) = 18 - 4 = 14 \)

These two expressions are equivalent.

### Option C:
- **Expression 1:** \( 37 - (-45) \)
- **Expression 2:** \( 45 + (-37) \)

Simplifying both:
- \( 37 - (-45) = 37 + 45 = 82 \)
- \( 45 + (-37) = 45 - 37 = 8 \)

These two expressions are **not** equivalent.

### Option D:
- **Expression 1:** \( -24 - (-11) \)
- **Expression 2:** \( 11 + (-24) \)

Simplifying both:
- \( -24 - (-11) = -24 + 11 = -13 \)
- \( 11 + (-24) = 11 - 24 = -13 \)

These two expressions are equivalent.

### Conclusion:
The two pairs of equivalent expressions are **A** and **D**.

Would you like any further explanation or have any questions?

Here are some related questions to consider:

1. What is the difference between subtracting a number and adding its negative?
2. How can you identify equivalent expressions without simplifying them fully?
3. What happens when you subtract a negative number?
4. How can this concept be applied to solving algebraic equations?
5. What is the general rule for adding and subtracting positive and negative numbers?

**Tip:** When dealing with expressions involving subtraction of negatives, remember that subtracting a negative is equivalent to adding the positive.

Which expressions are equivalent? Select the two that apply.

Explore how to identify equivalent expressions by simplifying integer operations in addition and subtraction. This guide provides a clear explanation on handling negative numbers, suitable for middle school students.

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