Which Of The Following Is An Example Of The Commutative Property?A. \[$(a + B) + C = (b + A) + C\$\]B. \[$(a + B) + C = A + (b + C)\$\]C. \[$a(b + C) = Ab + Ac\$\]

Mar 1, 2025 by ADMIN 164 views

**Understanding the Commutative Property in Mathematics**

The commutative property is a fundamental concept in mathematics that deals with the order of operations. It states that the order of the numbers or variables being added or multiplied does not change the result. In this article, we will explore the commutative property and provide examples to help you understand it better.

What is the Commutative Property?

The commutative property is a property of addition and multiplication that states that the order of the numbers being added or multiplied does not change the result. For example, if we have two numbers, a and b, the commutative property of addition states that a + b = b + a. Similarly, the commutative property of multiplication states that ab = ba.

Examples of the Commutative Property

Let's take a look at some examples of the commutative property:

Addition

Example 1: 2 + 3 = 5
Example 2: 3 + 2 = 5
Example 3: 4 + 1 = 5
Example 4: 1 + 4 = 5

As you can see, the order of the numbers being added does not change the result.

Multiplication

Example 1: 2 × 3 = 6
Example 2: 3 × 2 = 6
Example 3: 4 × 1 = 4
Example 4: 1 × 4 = 4

Again, the order of the numbers being multiplied does not change the result.

Which of the Following is an Example of the Commutative Property?

Now that we have seen some examples of the commutative property, let's take a look at the options provided:

A. ${$ (a + b) + c = (b + a) + c$}$

B. ${$ (a + b) + c = a + (b + c)$}$

C. ${$ a(b + c) = ab + ac$}$

To determine which of the following is an example of the commutative property, we need to analyze each option carefully.

Option A

Option A states that ${$ (a + b) + c = (b + a) + c$}$. This is an example of the commutative property of addition, as the order of the numbers being added does not change the result.

Option B

Option B states that ${$ (a + b) + c = a + (b + c)$}$. This is not an example of the commutative property, as the order of the numbers being added is changed.

Option C

Option C states that ${$ a(b + c) = ab + ac$}$. This is an example of the distributive property, not the commutative property.

Conclusion

In conclusion, the commutative property is a fundamental concept in mathematics that deals with the order of operations. It states that the order of the numbers or variables being added or multiplied does not change the result. We have seen some examples of the commutative property and analyzed the options provided to determine which one is an example of the commutative property.

Key Takeaways

The commutative property is a property of addition and multiplication that states that the order of the numbers being added or multiplied does not change the result.
The commutative property is an important concept in mathematics that helps us understand the order of operations.
We have seen some examples of the commutative property and analyzed the options provided to determine which one is an example of the commutative property.

Final Answer

Based on our analysis, the correct answer is:

A. ${$ (a + b) + c = (b + a) + c$}$

The commutative property is a fundamental concept in mathematics that deals with the order of operations. It states that the order of the numbers or variables being added or multiplied does not change the result. In this article, we will answer some frequently asked questions about the commutative property.

Q: What is the commutative property?

A: The commutative property is a property of addition and multiplication that states that the order of the numbers being added or multiplied does not change the result.

Q: What are the examples of the commutative property?

A: The commutative property can be demonstrated with the following examples:

Addition: a + b = b + a
Multiplication: ab = ba

Q: Is the commutative property true for all numbers?

A: Yes, the commutative property is true for all numbers. It does not matter what numbers you are adding or multiplying, the order of the numbers will not change the result.

Q: Can the commutative property be applied to other mathematical operations?

A: No, the commutative property is only applicable to addition and multiplication. It does not apply to other mathematical operations such as subtraction and division.

Q: What is the difference between the commutative property and the associative property?

A: The commutative property states that the order of the numbers being added or multiplied does not change the result. The associative property states that the order in which we perform addition or multiplication does not change the result.

Q: Can the commutative property be used to simplify mathematical expressions?

A: Yes, the commutative property can be used to simplify mathematical expressions. By rearranging the numbers or variables, we can make the expression easier to work with.

Q: Is the commutative property a fundamental concept in mathematics?

A: Yes, the commutative property is a fundamental concept in mathematics. It is used to understand the order of operations and to simplify mathematical expressions.

Q: Can the commutative property be applied to real-world problems?

A: Yes, the commutative property can be applied to real-world problems. For example, in finance, the commutative property can be used to calculate the total cost of a product by adding the cost of the product and the cost of the shipping.

Q: What are the benefits of understanding the commutative property?

A: Understanding the commutative property has several benefits, including:

Simplifying mathematical expressions: By rearranging the numbers or variables, we can make the expression easier to work with.
Understanding the order of operations: The commutative property helps us understand the order of operations and how to perform mathematical operations correctly.
Solving real-world problems: The commutative property can be applied to real-world problems, making it a valuable tool for problem-solving.

Conclusion

In conclusion, the commutative property is a fundamental concept in mathematics that deals with the order of operations. It states that the order of the numbers or variables being added or multiplied does not change the result. We have answered some frequently asked questions about the commutative property and highlighted its importance in mathematics.

Key Takeaways

The commutative property is a property of addition and multiplication that states that the order of the numbers being added or multiplied does not change the result.
The commutative property is an important concept in mathematics that helps us understand the order of operations.
Understanding the commutative property has several benefits, including simplifying mathematical expressions, understanding the order of operations, and solving real-world problems.

Final Answer

The commutative property is a fundamental concept in mathematics that deals with the order of operations. It states that the order of the numbers or variables being added or multiplied does not change the result. By understanding the commutative property, we can simplify mathematical expressions, understand the order of operations, and solve real-world problems.