Which Expression Is An Example Of The Associative Property Of Multiplication?A. $7(8+9)=119$ B. $7 \times 8 \times 9=8 \times 9 \times 7$ C. $7+9+8=9+7+8$ D. $(7 \times 8) \times 9=7 \times(8 \times 9$\]

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The Associative Property of Multiplication is a fundamental concept in mathematics that helps us simplify complex multiplication problems. It states that when we multiply three or more numbers together, the order in which we multiply them does not change the result. In this article, we will explore the Associative Property of Multiplication and identify which of the given expressions is an example of this property.

What is the Associative Property of Multiplication?

The Associative Property of Multiplication is a mathematical property that allows us to regroup or rearrange the numbers in a multiplication problem without changing the result. This property is denoted by the following equation:

(a × b) × c = a × (b × c)

This means that when we multiply three numbers together, we can group them in any order and still get the same result.

Examples of the Associative Property of Multiplication

Let's consider a few examples to illustrate the Associative Property of Multiplication:

  • 2 × (3 × 4) = (2 × 3) × 4
  • 5 × (6 × 7) = (5 × 6) × 7
  • 8 × (9 × 10) = (8 × 9) × 10

As you can see, the order in which we multiply the numbers does not change the result.

Which Expression is an Example of the Associative Property of Multiplication?

Now, let's examine the given expressions and determine which one is an example of the Associative Property of Multiplication:

A. 7(8+9)=1197(8+9)=119

This expression is not an example of the Associative Property of Multiplication. The expression involves the distributive property, which states that a single operation can be distributed over multiple terms.

B. 7×8×9=8×9×77 \times 8 \times 9=8 \times 9 \times 7

This expression is an example of the Associative Property of Multiplication. The order in which we multiply the numbers does not change the result.

C. 7+9+8=9+7+87+9+8=9+7+8

This expression is not an example of the Associative Property of Multiplication. The expression involves the commutative property of addition, which states that the order of the numbers does not change the result.

D. (7×8)×9=7×(8×9)(7 \times 8) \times 9=7 \times(8 \times 9)

This expression is an example of the Associative Property of Multiplication. The order in which we multiply the numbers does not change the result.

Conclusion

In conclusion, the Associative Property of Multiplication is a fundamental concept in mathematics that helps us simplify complex multiplication problems. The property states that when we multiply three or more numbers together, the order in which we multiply them does not change the result. The correct answer to the question is:

  • B. 7×8×9=8×9×77 \times 8 \times 9=8 \times 9 \times 7
  • D. (7×8)×9=7×(8×9)(7 \times 8) \times 9=7 \times(8 \times 9)

Both expressions are examples of the Associative Property of Multiplication.

Additional Examples and Exercises

Here are some additional examples and exercises to help you practice the Associative Property of Multiplication:

  • 3 × (4 × 5) = (3 × 4) × 5
  • 6 × (7 × 8) = (6 × 7) × 8
  • 9 × (10 × 11) = (9 × 10) × 11

Try to solve these exercises and see if you can identify the Associative Property of Multiplication in each expression.

Real-World Applications of the Associative Property of Multiplication

The Associative Property of Multiplication has many real-world applications in fields such as engineering, physics, and computer science. For example:

  • In engineering, the Associative Property of Multiplication is used to calculate the stress and strain on materials.
  • In physics, the Associative Property of Multiplication is used to calculate the momentum and energy of objects.
  • In computer science, the Associative Property of Multiplication is used to optimize algorithms and data structures.

The Associative Property of Multiplication is a fundamental concept in mathematics that helps us simplify complex multiplication problems. However, many students and professionals may have questions about this property. In this article, we will answer some of the most frequently asked questions about the Associative Property of Multiplication.

Q: What is the Associative Property of Multiplication?

A: The Associative Property of Multiplication is a mathematical property that allows us to regroup or rearrange the numbers in a multiplication problem without changing the result. This property is denoted by the following equation:

(a × b) × c = a × (b × c)

Q: What are some examples of the Associative Property of Multiplication?

A: Here are some examples of the Associative Property of Multiplication:

  • 2 × (3 × 4) = (2 × 3) × 4
  • 5 × (6 × 7) = (5 × 6) × 7
  • 8 × (9 × 10) = (8 × 9) × 10

Q: How does the Associative Property of Multiplication differ from the Commutative Property of Multiplication?

A: The Associative Property of Multiplication and the Commutative Property of Multiplication are two separate properties. The Commutative Property of Multiplication states that the order of the numbers in a multiplication problem does not change the result. For example:

  • 2 × 3 = 3 × 2
  • 4 × 5 = 5 × 4

The Associative Property of Multiplication, on the other hand, states that the order in which we multiply three or more numbers together does not change the result.

Q: Can the Associative Property of Multiplication be applied to addition and subtraction?

A: No, the Associative Property of Multiplication cannot be applied to addition and subtraction. The Associative Property of Addition and the Associative Property of Subtraction are separate properties that apply to those operations.

Q: How is the Associative Property of Multiplication used in real-world applications?

A: The Associative Property of Multiplication has many real-world applications in fields such as engineering, physics, and computer science. For example:

  • In engineering, the Associative Property of Multiplication is used to calculate the stress and strain on materials.
  • In physics, the Associative Property of Multiplication is used to calculate the momentum and energy of objects.
  • In computer science, the Associative Property of Multiplication is used to optimize algorithms and data structures.

Q: Can the Associative Property of Multiplication be applied to fractions and decimals?

A: Yes, the Associative Property of Multiplication can be applied to fractions and decimals. For example:

  • (1/2) × (3/4) = (1/2) × (3/4)
  • (2/3) × (4/5) = (2/3) × (4/5)

Q: How can I practice the Associative Property of Multiplication?

A: There are many ways to practice the Associative Property of Multiplication. Here are a few suggestions:

  • Use online resources such as Khan Academy or Mathway to practice multiplication problems.
  • Use a calculator to check your answers and see if you can identify the Associative Property of Multiplication in each problem.
  • Try to solve multiplication problems in your head or on paper without using a calculator.

Conclusion

In conclusion, the Associative Property of Multiplication is a fundamental concept in mathematics that helps us simplify complex multiplication problems. By understanding this property, we can make calculations more efficient and solve problems more easily. We hope that this article has helped to answer some of the most frequently asked questions about the Associative Property of Multiplication.