Properties of Multiplication (zero, identity, commutative) | Live ... - Free Printable

Problem Analysis:

The task involves identifying and applying three fundamental properties of multiplication:
1. Zero Property of Multiplication: Any number multiplied by zero equals zero.
2. Identity Property of Multiplication: Any number multiplied by 1 equals the number itself.
3. Commutative Property of Multiplication: The order of factors does not change the product (i.e., \( a \times b = b \times a \)).

We will solve each part step by step.

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Part 1: Identify the Properties

#### 1. \( 7 \times 9 = 9 \times 7 \)
- This equation shows that the order of multiplication does not affect the result.
- Property: Commutative property of multiplication.

#### 2. \( 4 \times 0 = 0 \)
- Any number multiplied by zero equals zero.
- Property: Zero property of multiplication.

#### 3. \( 0 \times 9 = 0 \)
- Any number multiplied by zero equals zero.
- Property: Zero property of multiplication.

#### 4. \( 8 \times 1 = \)
- Any number multiplied by 1 equals the number itself.
- Property: Identity property of multiplication.
- Result: \( 8 \times 1 = 8 \).

#### 5. \( 3 \times 6 = 6 \times 3 \)
- This equation shows that the order of multiplication does not affect the result.
- Property: Commutative property of multiplication.

#### 6. \( 1 \times 25 = 25 \times 1 \)
- This equation shows that the order of multiplication does not affect the result.
- Property: Commutative property of multiplication.

#### 7. \( 327 \times 0 = 0 \)
- Any number multiplied by zero equals zero.
- Property: Zero property of multiplication.

#### 8. \( 1 \times 489 = 489 \times 1 \)
- This equation shows that the order of multiplication does not affect the result.
- Property: Commutative property of multiplication.

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Part 2: Complete the Equations for Zero Property

#### 9. \( 7 \times \_ = 0 \)
- For the product to be zero, one of the factors must be zero.
- Answer: \( 7 \times 0 = 0 \).

#### 10. \( 16 \times 0 = \_ \)
- Any number multiplied by zero equals zero.
- Answer: \( 16 \times 0 = 0 \).

#### 11. \( \_ \times 24 = 0 \)
- For the product to be zero, one of the factors must be zero.
- Answer: \( 0 \times 24 = 0 \).

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Part 3: Complete the Equations for Identity Property

#### 12. \( 5 \times 1 = \_ \)
- Any number multiplied by 1 equals the number itself.
- Answer: \( 5 \times 1 = 5 \).

#### 13. \( \_ \times 27 = 27 \)
- Any number multiplied by 1 equals the number itself.
- Answer: \( 1 \times 27 = 27 \).

#### 14. \( 8 \times \_ = 8 \)
- Any number multiplied by 1 equals the number itself.
- Answer: \( 8 \times 1 = 8 \).

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Part 4: Complete the Equations for Commutative Property

#### 15. \( 6 \times 4 = \_ \times 6 \)
- The commutative property states that \( a \times b = b \times a \).
- Answer: \( 6 \times 4 = 4 \times 6 \).

#### 16. \( 4 \times 8 = \_ \times \_ \)
- The commutative property states that \( a \times b = b \times a \).
- Answer: \( 4 \times 8 = 8 \times 4 \).

#### 17. \( 53 \times 3 = 3 \times \_ \)
- The commutative property states that \( a \times b = b \times a \).
- Answer: \( 53 \times 3 = 3 \times 53 \).

#### 18. \( \_ \times 3 = \_ \times 16 \)
- The commutative property states that \( a \times b = b \times a \).
- Answer: \( 16 \times 3 = 3 \times 16 \).

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Final Answers:

1. Commutative property
2. Zero property
3. Zero property
4. Identity property; \( 8 \)
5. Commutative property
6. Commutative property
7. Zero property
8. Commutative property

9. \( 0 \)
10. \( 0 \)
11. \( 0 \)

12. \( 5 \)
13. \( 1 \)
14. \( 1 \)

15. \( 4 \)
16. \( 8, 4 \)
17. \( 53 \)
18. \( 16, 3 \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{1. Commutative property} \\
\text{2. Zero property} \\
\text{3. Zero property} \\
\text{4. Identity property; } 8 \\
\text{5. Commutative property} \\
\text{6. Commutative property} \\
\text{7. Zero property} \\
\text{8. Commutative property} \\
\text{9. } 0 \\
\text{10. } 0 \\
\text{11. } 0 \\
\text{12. } 5 \\
\text{13. } 1 \\
\text{14. } 1 \\
\text{15. } 4 \\
\text{16. } 8, 4 \\
\text{17. } 53 \\
\text{18. } 16, 3 \\
\end{array}
}
\]