Algebra worksheet focusing on identifying properties of real numbers with 13 numbered problems.

It looks like you've uploaded a worksheet titled "Properties of Real Numbers Worksheet", which asks students to identify the property being used in each given equation. However, I can't view images directly, so I can’t see the actual content of the image.

But since you've provided the text of the worksheet in your message, I’ll go ahead and solve it based on that. Here’s the worksheet as you wrote it:

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Algebra
Name: _________________________
Properties of Real Numbers Worksheet

Write the property being used in the corresponding blank.

1. $ (5 + 2) + (–4) = 5 + (2 + –4) $
2. $ 9p + 0 = 9p $
3. $ 8 \cdot 1 = 8 $
4. $ 5 \cdot 3 = 3 \cdot 5 $
5. $ 4 \cdot 2 = 8 $
6. $ 12 \cdot 4 = 4 \cdot 12 $
7. $ 189 + 29 = 29 + 189 $
8. $ 4(1 + 11) = 4 \cdot 1 + 4 \cdot 11 $
9. $ (2 \cdot 4)(3 + 2) = (2 \cdot 4)(3 + 2) $
10. $ 3 + 9 = 9 + 3 $
11. $ 4 \cdot (3 + 8) = 4 \cdot 3 + 4 \cdot 8 $
12. $ \sqrt{25} = 5 $
13. $ 17 \cdot 0 = 0 $

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Now, let's analyze each one and identify the correct property of real numbers.

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1. $ (5 + 2) + (–4) = 5 + (2 + –4) $

- This shows that grouping doesn't change the sum.
- Property: Associative Property of Addition

✔ Answer: Associative Property of Addition

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2. $ 9p + 0 = 9p $

- Adding zero doesn’t change the value.
- Property: Additive Identity Property

✔ Answer: Additive Identity Property

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3. $ 8 \cdot 1 = 8 $

- Multiplying by 1 doesn’t change the value.
- Property: Multiplicative Identity Property

✔ Answer: Multiplicative Identity Property

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4. $ 5 \cdot 3 = 3 \cdot 5 $

- Order of multiplication doesn’t matter.
- Property: Commutative Property of Multiplication

✔ Answer: Commutative Property of Multiplication

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5. $ 4 \cdot 2 = 8 $

- This is just a multiplication fact; no property is being demonstrated here.
- But if we're forced to name a property, this is not showing any specific property—it's just computation.
- However, since it's listed, perhaps it's meant to be Closure Property (the product of two real numbers is a real number), but that's not typically tested this way.
- Alternatively, maybe it's a typo or placeholder.
- But looking at context, probably no property is intended here, or it might be Closure under multiplication.

Wait — actually, this is just a true statement, not an identity or transformation. It may be intended to be skipped, but likely it's meant to show Closure Property.

But most worksheets don't list closure unless specified.

Let’s assume it’s a mistake or not a property question. But since it’s listed, and all others are properties, maybe it's meant to be Closure Property of Multiplication.

✔ Answer: Closure Property of Multiplication (if required)

Alternatively: No property (but unlikely). Let's keep it as Closure Property.

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6. $ 12 \cdot 4 = 4 \cdot 12 $

- Again, order of multiplication doesn’t matter.
- Property: Commutative Property of Multiplication

✔ Answer: Commutative Property of Multiplication

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7. $ 189 + 29 = 29 + 189 $

- Order of addition doesn’t matter.
- Property: Commutative Property of Addition

✔ Answer: Commutative Property of Addition

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8. $ 4(1 + 11) = 4 \cdot 1 + 4 \cdot 11 $

- Distributing multiplication over addition.
- Property: Distributive Property

✔ Answer: Distributive Property

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9. $ (2 \cdot 4)(3 + 2) = (2 \cdot 4)(3 + 2) $

- This is an identity: both sides are the same.
- It's reflexive — something equals itself.
- Property: Reflexive Property of Equality

✔ Answer: Reflexive Property of Equality

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10. $ 3 + 9 = 9 + 3 $

- Order of addition doesn’t matter.
- Property: Commutative Property of Addition

✔ Answer: Commutative Property of Addition

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11. $ 4 \cdot (3 + 8) = 4 \cdot 3 + 4 \cdot 8 $

- Multiplication distributed over addition.
- Property: Distributive Property

✔ Answer: Distributive Property

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12. $ \sqrt{25} = 5 $

- This is a simplification of a square root.
- Not a property of real numbers in terms of operations.
- But note: $ \sqrt{25} = 5 $ because $ 5^2 = 25 $, so it's about square roots.
- No standard algebraic property applies here.
- Possibly Definition of Square Root or Principal Square Root, but not a "property" like commutative or distributive.

So this one might be not a property or undefined in the context.

Alternatively, some might say Identity of Square Roots, but that’s not standard.

Likely, this is a mistake or not a property.

But if we must assign, maybe Definition of Square Root.

✔ Answer: Definition of Square Root (or not applicable)

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13. $ 17 \cdot 0 = 0 $

- Any number times zero is zero.
- Property: Multiplicative Property of Zero (or Zero Product Property, but more precisely Multiplication by Zero)

Actually, the correct term is:
> Multiplicative Property of Zero: For any real number $ a $, $ a \cdot 0 = 0 $

✔ Answer: Multiplicative Property of Zero

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Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | Associative Property of Addition |
| 2 | Additive Identity Property |
| 3 | Multiplicative Identity Property |
| 4 | Commutative Property of Multiplication |
| 5 | Closure Property of Multiplication *(or possibly not applicable)* |
| 6 | Commutative Property of Multiplication |
| 7 | Commutative Property of Addition |
| 8 | Distributive Property |
| 9 | Reflexive Property of Equality |
| 10 | Commutative Property of Addition |
| 11 | Distributive Property |
| 12 | Definition of Square Root *(not a standard property)* |
| 13 | Multiplicative Property of Zero |

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Notes:

- Problems 5 and 12 are questionable because they aren’t demonstrating a standard property like commutative, associative, etc.
- #5: Just a multiplication fact → possibly Closure Property
- #12: A definition, not a property → best labeled as Definition of Square Root or Not a property
- If this is for a classroom, teachers often accept Closure Property for #5 and Definition of Square Root for #12.

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Let me know if you want these answers filled into the blank lines format!