Worksheet for students to practice identifying properties of real numbers, including commutative, associative, and distributive properties.

Let's solve this "Properties of Real Numbers Worksheet" step by step, explaining each answer clearly.

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Part A: Fill in the blanks with the correct Property of Real Numbers

We are given a word bank:

- Commutative Property of Addition
- Associative Property of Addition
- Distributive Property
- Commutative Property of Multiplication
- Associative Property of Multiplication

Each property must be used once.

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#### 1. ________ changes the order in which you add an expression.

> This refers to changing the order of numbers when adding.
> Example: $ 3 + 5 = 5 + 3 $

✔ Answer: Commutative Property of Addition

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#### 2. ________ shares multiplication across addition.

> This means multiplying a number by a sum is the same as multiplying it by each addend and then adding.
> Example: $ a(b + c) = ab + ac $

✔ Answer: Distributive Property

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#### 3. ________ changes the grouping in which you add an expression.

> This refers to changing the grouping (parentheses) when adding.
> Example: $ (2 + 3) + 4 = 2 + (3 + 4) $

✔ Answer: Associative Property of Addition

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#### 4. ________ changes the grouping in which you multiply an expression.

> This refers to changing the grouping when multiplying.
> Example: $ (2 \times 3) \times 4 = 2 \times (3 \times 4) $

✔ Answer: Associative Property of Multiplication

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#### 5. ________ changes the order in which you multiply an expression.

> This refers to changing the order of numbers when multiplying.
> Example: $ 6 \times 5 = 5 \times 6 $

✔ Answer: Commutative Property of Multiplication

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✔ So, Part A answers:
1. Commutative Property of Addition
2. Distributive Property
3. Associative Property of Addition
4. Associative Property of Multiplication
5. Commutative Property of Multiplication

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Part B: Identify the property represented by each expression

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#### 6. $ 6 \times 5 = 5 \times 6 $

> The order of multiplication is changed.

✔ Answer: Commutative Property of Multiplication

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#### 7. $ 79 + 81 = 81 + 79 $

> The order of addition is changed.

✔ Answer: Commutative Property of Addition

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#### 8.
$$
\begin{align*}
14 \times (a + b) &= 14 \times a + 14 \times b
\end{align*}
$$

> Multiplication is distributed over addition.

✔ Answer: Distributive Property

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#### 9. $ 67 + (18 + 1) = (67 + 18) + 1 $

> The grouping of addition is changed.

✔ Answer: Associative Property of Addition

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#### 10. $ 90 \times (78 \times 444) = (90 \times 78) \times 444 $

> The grouping of multiplication is changed.

✔ Answer: Associative Property of Multiplication

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✔ Final Answers:

#### Part A:
1. Commutative Property of Addition
2. Distributive Property
3. Associative Property of Addition
4. Associative Property of Multiplication
5. Commutative Property of Multiplication

#### Part B:
6. Commutative Property of Multiplication
7. Commutative Property of Addition
8. Distributive Property
9. Associative Property of Addition
10. Associative Property of Multiplication

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