Understanding the Commutative Property Under Subtraction

Oct 13, 2025 by miodeya.com 29 views

Introduction to the Commutative Property

The commutative property is a fundamental concept in mathematics that states that the order of the numbers being added or multiplied does not change the result. In other words, when we add or multiply two numbers, we can swap their positions and the result will remain the same. However, when it comes to subtraction, the commutative property does not hold true. In this article, we will explore the commutative property under subtraction and examine the given options to determine which one is true.

What is the Commutative Property?

The commutative property is a mathematical concept that applies to addition and multiplication, but not to subtraction. When we add or multiply two numbers, we can swap their positions and the result will remain the same. For example:

Addition: 2 + 3 = 3 + 2
Multiplication: 2 × 3 = 3 × 2

However, when it comes to subtraction, the commutative property does not hold true. This means that the order of the numbers being subtracted does change the result.

Understanding the Commutative Property Under Subtraction

When we subtract two numbers, the order of the numbers being subtracted does change the result. For example:

Subtraction: 10 - 9 ≠ 9 - 10

In this case, 10 - 9 = 1, but 9 - 10 = -1. As we can see, the order of the numbers being subtracted changes the result.

Analyzing the Given Options

Now that we have a clear understanding of the commutative property under subtraction, let's analyze the given options:

A) $109 = 10 + 9$

This option is incorrect because the commutative property does not apply to subtraction. The correct calculation would be 10 - 9 = 1, not 109.

B) $10 + 9 = 9 + 10$

This option is correct because the commutative property applies to addition, not subtraction. The correct calculation would be 10 + 9 = 19, which is equal to 9 + 10.

C) $109 = 109$

This option is correct because the commutative property does not apply to subtraction. The correct calculation would be 109 - 109 = 0, which is equal to 109.

D) $109 \neq 910$

This option is incorrect because the commutative property does not apply to subtraction. The correct calculation would be 109 - 109 = 0, not 910.

Conclusion

In conclusion, the commutative property under subtraction does not hold true. The order of the numbers being subtracted does change the result. When analyzing the given options, we can see that option B is the only correct answer because it applies to addition, not subtraction.

Key Takeaways

The commutative property applies to addition and multiplication, but not to subtraction.
The order of the numbers being subtracted does change the result.
The correct calculation for 10 - 9 is 1, not 109.
The correct calculation for 10 + 9 is 19, which is equal to 9 + 10.

Final Thoughts

In conclusion, the commutative property under subtraction is an important concept to understand in mathematics. By analyzing the given options and understanding the commutative property, we can determine which one is true.

Introduction

In our previous article, we explored the commutative property under subtraction and examined the given options to determine which one is true. In this article, we will answer some frequently asked questions about the commutative property under subtraction.

Q: What is the commutative property?

A: The commutative property is a mathematical concept that applies to addition and multiplication, but not to subtraction. When we add or multiply two numbers, we can swap their positions and the result will remain the same.

Q: Why does the commutative property not apply to subtraction?

A: The commutative property does not apply to subtraction because the order of the numbers being subtracted does change the result. For example, 10 - 9 ≠ 9 - 10.

Q: Can you give an example of the commutative property in addition?

A: Yes, here is an example of the commutative property in addition:

Addition: 2 + 3 = 3 + 2

Q: Can you give an example of the commutative property in multiplication?

A: Yes, here is an example of the commutative property in multiplication:

Multiplication: 2 × 3 = 3 × 2

Q: What is the correct calculation for 10 - 9?

A: The correct calculation for 10 - 9 is 1.

Q: What is the correct calculation for 10 + 9?

A: The correct calculation for 10 + 9 is 19.

Q: Why is option A incorrect?

A: Option A is incorrect because the commutative property does not apply to subtraction. The correct calculation would be 10 - 9 = 1, not 109.

Q: Why is option D incorrect?

A: Option D is incorrect because the commutative property does not apply to subtraction. The correct calculation would be 109 - 109 = 0, not 910.

Q: What is the key takeaway from this article?

A: The key takeaway from this article is that the commutative property under subtraction does not hold true. The order of the numbers being subtracted does change the result.

Conclusion

In conclusion, the commutative property under subtraction is an important concept to understand in mathematics. By answering these frequently asked questions, we can gain a better understanding of the commutative property and how it applies to addition, multiplication, and subtraction.

Additional Resources

For more information on the commutative property, visit Math is Fun.
For more information on subtraction, visit Khan Academy.

Final Thoughts

In conclusion, the commutative property under subtraction is a complex concept that requires a deep understanding of mathematics. By answering these frequently asked questions, we can gain a better understanding of the commutative property and how it applies to addition, multiplication, and subtraction.

Key Takeaways

The commutative property applies to addition and multiplication, but not to subtraction.
The order of the numbers being subtracted does change the result.
The correct calculation for 10 - 9 is 1.
The correct calculation for 10 + 9 is 19.

Glossary

Commutative property: A mathematical concept that applies to addition and multiplication, but not to subtraction.
Addition: A mathematical operation that involves combining two or more numbers.
Multiplication: A mathematical operation that involves repeating a number a certain number of times.
Subtraction: A mathematical operation that involves finding the difference between two numbers.