Which Choice Shows The Associative Property Of Addition?A. $6 + (9 + 14) = 6 + (14 + 9$\]B. $6 + (9 + 14) = (6 + 9) + 14$C. $6 + (9 + 14) = (9 + 14) + 6$D. $6 + (9 + 14) = (6 + 14) + 9$

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The associative property of addition is a fundamental concept in mathematics that helps us simplify complex arithmetic expressions. It states that when we add three or more numbers, the way we group the numbers does not change the result. In this article, we will explore the associative property of addition and identify the correct choice that demonstrates this property.

What is the Associative Property of Addition?

The associative property of addition is a mathematical property that allows us to regroup the numbers in an addition problem without changing the result. It states that for any three numbers a, b, and c, the following equation holds:

a + (b + c) = (a + b) + c

This property is called associative because it allows us to associate or group the numbers in different ways without affecting the result.

Example of the Associative Property of Addition

Let's consider an example to illustrate the associative property of addition. Suppose we want to add 6, 9, and 14. We can group the numbers in different ways, but the result will be the same.

6 + (9 + 14) = ?

Using the associative property of addition, we can regroup the numbers as follows:

6 + (9 + 14) = (6 + 9) + 14

Now, let's calculate the result:

(6 + 9) = 15 15 + 14 = 29

So, 6 + (9 + 14) = 29.

Which Choice Shows the Associative Property of Addition?

Now that we have understood the associative property of addition, let's examine the given choices to identify the correct one.

A. 6+(9+14)=6+(14+9)6 + (9 + 14) = 6 + (14 + 9)

This choice does not demonstrate the associative property of addition. The numbers are not grouped in a way that allows us to regroup them without changing the result.

B. 6+(9+14)=(6+9)+146 + (9 + 14) = (6 + 9) + 14

This choice demonstrates the associative property of addition. We can regroup the numbers as (6 + 9) + 14, which is equivalent to 6 + (9 + 14).

C. 6+(9+14)=(9+14)+66 + (9 + 14) = (9 + 14) + 6

This choice does not demonstrate the associative property of addition. The numbers are not grouped in a way that allows us to regroup them without changing the result.

D. 6+(9+14)=(6+14)+96 + (9 + 14) = (6 + 14) + 9

This choice does not demonstrate the associative property of addition. The numbers are not grouped in a way that allows us to regroup them without changing the result.

Conclusion

In conclusion, the correct choice that demonstrates the associative property of addition is:

B. 6+(9+14)=(6+9)+146 + (9 + 14) = (6 + 9) + 14

This choice shows that we can regroup the numbers without changing the result, which is the fundamental concept of the associative property of addition.

Understanding the Importance of the Associative Property of Addition

The associative property of addition is an essential concept in mathematics that helps us simplify complex arithmetic expressions. It allows us to regroup the numbers in different ways without affecting the result. This property is used extensively in various mathematical operations, including addition, subtraction, multiplication, and division.

Real-World Applications of the Associative Property of Addition

The associative property of addition has numerous real-world applications. For example, in finance, it is used to calculate the total cost of a purchase. Suppose we want to buy a product that costs $6, and we have a discount of $9 and a tax of $14. We can use the associative property of addition to calculate the total cost as follows:

6 + (9 + 14) = (6 + 9) + 14

Using the associative property of addition, we can regroup the numbers as (6 + 9) + 14, which is equivalent to 6 + (9 + 14).

Tips for Remembering the Associative Property of Addition

To remember the associative property of addition, you can use the following tips:

  • Use the word "associate": When you see the word "associate" in a mathematical problem, think of the associative property of addition.
  • Regroup the numbers: When you see a complex arithmetic expression, try to regroup the numbers in different ways to see if the result changes.
  • Use the commutative property: The commutative property of addition states that the order of the numbers does not change the result. You can use this property to simplify complex arithmetic expressions.

Conclusion

The associative property of addition is a fundamental concept in mathematics that helps us simplify complex arithmetic expressions. However, many students and professionals may have questions about this property. In this article, we will answer some frequently asked questions about the associative property of addition.

Q: What is the associative property of addition?

A: The associative property of addition is a mathematical property that allows us to regroup the numbers in an addition problem without changing the result. It states that for any three numbers a, b, and c, the following equation holds:

a + (b + c) = (a + b) + c

Q: Why is the associative property of addition important?

A: The associative property of addition is important because it helps us simplify complex arithmetic expressions. By regrouping the numbers in different ways, we can make calculations easier and more efficient.

Q: How do I apply the associative property of addition in real-life situations?

A: The associative property of addition has numerous real-world applications. For example, in finance, it is used to calculate the total cost of a purchase. Suppose we want to buy a product that costs $6, and we have a discount of $9 and a tax of $14. We can use the associative property of addition to calculate the total cost as follows:

6 + (9 + 14) = (6 + 9) + 14

Using the associative property of addition, we can regroup the numbers as (6 + 9) + 14, which is equivalent to 6 + (9 + 14).

Q: Can I use the associative property of addition with subtraction?

A: Yes, you can use the associative property of addition with subtraction. However, you need to be careful when subtracting numbers. The associative property of addition states that a + (b + c) = (a + b) + c. When subtracting numbers, you need to use the opposite operation, which is addition.

Q: Can I use the associative property of addition with multiplication and division?

A: Yes, you can use the associative property of addition with multiplication and division. However, you need to be careful when multiplying and dividing numbers. The associative property of addition states that a + (b + c) = (a + b) + c. When multiplying and dividing numbers, you need to use the opposite operation, which is subtraction.

Q: How do I remember the associative property of addition?

A: To remember the associative property of addition, you can use the following tips:

  • Use the word "associate": When you see the word "associate" in a mathematical problem, think of the associative property of addition.
  • Regroup the numbers: When you see a complex arithmetic expression, try to regroup the numbers in different ways to see if the result changes.
  • Use the commutative property: The commutative property of addition states that the order of the numbers does not change the result. You can use this property to simplify complex arithmetic expressions.

Q: What are some common mistakes to avoid when using the associative property of addition?

A: Some common mistakes to avoid when using the associative property of addition include:

  • Not regrouping the numbers correctly: Make sure to regroup the numbers in different ways to see if the result changes.
  • Not using the commutative property: The commutative property of addition states that the order of the numbers does not change the result. Make sure to use this property to simplify complex arithmetic expressions.
  • Not checking the result: Make sure to check the result of the calculation to ensure that it is correct.

Conclusion

In conclusion, the associative property of addition is a fundamental concept in mathematics that helps us simplify complex arithmetic expressions. By understanding the associative property of addition, we can solve mathematical problems more efficiently and effectively. We hope that this article has answered some of your frequently asked questions about the associative property of addition.