Multiplication Properties worksheet - Free Printable

Problem Analysis:

The worksheet focuses on identifying and applying multiplication properties. Let's solve each part step by step.

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#### Part 1: Identify the Multiplication Property Used in Each Equation

1. Equation: \( 2365 \times 1 = 2365 \)
- Property: This demonstrates the Identity Property of Multiplication.
- Explanation: Any number multiplied by 1 remains unchanged.
- Answer: Identity Property

2. Equation: \( 8 \times 100 = 100 \times 8 \)
- Property: This demonstrates the Commutative Property of Multiplication.
- Explanation: The order of factors does not affect the product.
- Answer: Commutative Property

3. Equation: \( (11 \times 2) \times 8 = 11 \times (2 \times 8) \)
- Property: This demonstrates the Associative Property of Multiplication.
- Explanation: The grouping of factors does not affect the product.
- Answer: Associative Property

4. Equation: \( 1200 \times 0 = 1200 \)
- Property: This equation is incorrect as written. The correct result should be \( 1200 \times 0 = 0 \).
- Corrected Equation: \( 1200 \times 0 = 0 \)
- Property: This demonstrates the Zero Property of Multiplication.
- Explanation: Any number multiplied by 0 equals 0.
- Answer: Zero Property

5. Equation: \( 9 \times 3 = 3 \times 9 \)
- Property: This demonstrates the Commutative Property of Multiplication.
- Explanation: The order of factors does not affect the product.
- Answer: Commutative Property

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#### Part 2: Compute the Following Multiplication Equations Mentally Using the Multiplication Properties Learned

6. Equation: \( 23214 \times 1 \)
- Property Used: Identity Property of Multiplication
- Explanation: Any number multiplied by 1 remains unchanged.
- Solution: \( 23214 \times 1 = 23214 \)

7. Equation: \( 16 \times (2 \times 1) \)
- Property Used: Associative Property of Multiplication
- Explanation: Grouping does not matter. First, compute \( 2 \times 1 = 2 \), then multiply by 16.
- Solution: \( 16 \times (2 \times 1) = 16 \times 2 = 32 \)

8. Equation: \( 1231 \times 0 \)
- Property Used: Zero Property of Multiplication
- Explanation: Any number multiplied by 0 equals 0.
- Solution: \( 1231 \times 0 = 0 \)

9. Equation: \( (20 \times 1) \times 5 \)
- Property Used: Associative Property of Multiplication
- Explanation: Grouping does not matter. First, compute \( 20 \times 1 = 20 \), then multiply by 5.
- Solution: \( (20 \times 1) \times 5 = 20 \times 5 = 100 \)

10. Equation: \( 200 \times 10 \)
- Property Used: Basic Multiplication
- Explanation: Multiply the numbers directly.
- Solution: \( 200 \times 10 = 2000 \)

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Final Answers:

1. Identity Property
2. Commutative Property
3. Associative Property
4. Zero Property
5. Commutative Property

6. \( 23214 \)
7. \( 32 \)
8. \( 0 \)
9. \( 100 \)
10. \( 2000 \)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{Identity Property} \\
2. & \text{Commutative Property} \\
3. & \text{Associative Property} \\
4. & \text{Zero Property} \\
5. & \text{Commutative Property} \\
6. & 23214 \\
7. & 32 \\
8. & 0 \\
9. & 100 \\
10. & 2000 \\
\end{array}
}
\]