Rewrite the Given Expression Using the Commutative Property of Multiplication

Oct 13, 2025 by pynkocean.com 47 views

Rewrite the Given Expression Using the Commutative Property of Multiplication

Understanding the Commutative Property of Multiplication

The commutative property of multiplication is a fundamental concept in mathematics that states that the order of the factors in a multiplication problem does not change the result. In other words, when we multiply two numbers together, we can change the order of the numbers and still get the same result. This property is denoted by the equation: a × b = b × a.

Applying the Commutative Property to the Given Expression

The given expression is: (5 × 2n) + 9. To rewrite this expression using the commutative property of multiplication, we need to change the order of the factors in the multiplication problem. Specifically, we need to move the 2n to the left of the 5.

Using the commutative property, we can rewrite the expression as:

(2n × 5) + 9

Why the Commutative Property is Important

The commutative property of multiplication is an important concept in mathematics because it allows us to simplify complex multiplication problems. By changing the order of the factors, we can make the problem easier to solve and understand. Additionally, the commutative property is a fundamental concept in algebra and is used extensively in solving equations and inequalities.

Real-World Applications of the Commutative Property

The commutative property of multiplication has many real-world applications. For example, in business, the commutative property is used to calculate the cost of goods sold. By changing the order of the factors, we can simplify the calculation and get the correct answer. In science, the commutative property is used to calculate the area of a rectangle. By changing the order of the factors, we can simplify the calculation and get the correct answer.

Examples of Using the Commutative Property

Here are a few examples of using the commutative property of multiplication:

3 × 4 = 4 × 3 (the order of the factors does not change the result)
2 × 5 = 5 × 2 (the order of the factors does not change the result)
4 × 3 × 2 = 2 × 3 × 4 (the order of the factors does not change the result)

Conclusion

In conclusion, the commutative property of multiplication is an important concept in mathematics that allows us to simplify complex multiplication problems. By changing the order of the factors, we can make the problem easier to solve and understand. The commutative property has many real-world applications and is used extensively in solving equations and inequalities.

Rewriting the Given Expression Using the Commutative Property

To rewrite the given expression using the commutative property of multiplication, we need to change the order of the factors in the multiplication problem. Specifically, we need to move the 2n to the left of the 5.

Using the commutative property, we can rewrite the expression as:

(2n × 5) + 9

Final Answer

The final answer is: (2n × 5) + 9
Q&A: Commutative Property of Multiplication

Frequently Asked Questions

The commutative property of multiplication is a fundamental concept in mathematics that can be confusing for some students. In this article, we will answer some frequently asked questions about the commutative property of multiplication.

Q: What is the commutative property of multiplication?

A: The commutative property of multiplication is a mathematical concept that states that the order of the factors in a multiplication problem does not change the result. In other words, when we multiply two numbers together, we can change the order of the numbers and still get the same result.

Q: How do I apply the commutative property of multiplication?

A: To apply the commutative property of multiplication, you need to change the order of the factors in the multiplication problem. Specifically, you need to move one of the factors to the left or right of the other factor.

Q: What are some examples of using the commutative property of multiplication?

A: Here are a few examples of using the commutative property of multiplication:

3 × 4 = 4 × 3 (the order of the factors does not change the result)
2 × 5 = 5 × 2 (the order of the factors does not change the result)
4 × 3 × 2 = 2 × 3 × 4 (the order of the factors does not change the result)

Q: Why is the commutative property of multiplication important?

A: The commutative property of multiplication is an important concept in mathematics because it allows us to simplify complex multiplication problems. By changing the order of the factors, we can make the problem easier to solve and understand.

Q: Can I use the commutative property of multiplication with fractions?

A: Yes, you can use the commutative property of multiplication with fractions. For example:

1/2 × 3/4 = 3/4 × 1/2 (the order of the factors does not change the result)

Q: Can I use the commutative property of multiplication with decimals?

A: Yes, you can use the commutative property of multiplication with decimals. For example:

2.5 × 3.8 = 3.8 × 2.5 (the order of the factors does not change the result)

Q: Can I use the commutative property of multiplication with negative numbers?

A: Yes, you can use the commutative property of multiplication with negative numbers. For example:

-2 × 3 = 3 × -2 (the order of the factors does not change the result)

Q: Can I use the commutative property of multiplication with variables?

A: Yes, you can use the commutative property of multiplication with variables. For example:

2x × 3 = 3 × 2x (the order of the factors does not change the result)

Conclusion

In conclusion, the commutative property of multiplication is an important concept in mathematics that allows us to simplify complex multiplication problems. By changing the order of the factors, we can make the problem easier to solve and understand. We hope that this article has helped to answer some of the frequently asked questions about the commutative property of multiplication.

Additional Resources

If you are looking for additional resources to help you understand the commutative property of multiplication, here are a few suggestions:

Khan Academy: Commutative Property of Multiplication
Mathway: Commutative Property of Multiplication
IXL: Commutative Property of Multiplication

Final Answer

The final answer is: The commutative property of multiplication is a fundamental concept in mathematics that states that the order of the factors in a multiplication problem does not change the result.