Applying the Commutative Property to Multiplication

Oct 13, 2025 by magicalceylontours.com 102 views

The commutative property in mathematics is a fundamental concept that states that the order of the numbers being added or multiplied does not change the result. In this article, we will explore the commutative property across multiplication and determine which of the given options demonstrates this property for the expression $$2 \times 10 \times 7$$.

What is the Commutative Property?

The commutative property is a mathematical concept that applies to both addition and multiplication. In the case of multiplication, the commutative property states that the order of the numbers being multiplied does not change the result. This means that if we have two numbers, a and b, then the product of a and b is the same as the product of b and a.

Mathematically, this can be represented as:

a × b = b × a

Applying the Commutative Property to Multiplication

Now that we have a basic understanding of the commutative property, let's apply it to the given expression $$2 \times 10 \times 7$$. To demonstrate the commutative property, we need to show that the order of the numbers being multiplied does not change the result.

Option A: $$2 \times (10 \times 7)$$

Let's start by evaluating option A: $$2 \times (10 \times 7)$$. To do this, we need to follow the order of operations (PEMDAS):

Multiply 10 and 7: 10 × 7 = 70
Multiply 2 and 70: 2 × 70 = 140

So, option A evaluates to 140.

Option B: $$(2 \times 10) \times 7$$

Next, let's evaluate option B: $$(2 \times 10) \times 7$$. Again, we need to follow the order of operations (PEMDAS):

Multiply 2 and 10: 2 × 10 = 20
Multiply 20 and 7: 20 × 7 = 140

So, option B also evaluates to 140.

Option C: $$(2 \times 7) \times 10$$

Finally, let's evaluate option C: $$(2 \times 7) \times 10$$. Once again, we need to follow the order of operations (PEMDAS):

Multiply 2 and 7: 2 × 7 = 14
Multiply 14 and 10: 14 × 10 = 140

So, option C also evaluates to 140.

Conclusion

Based on our evaluations, we can see that all three options A, B, and C demonstrate the commutative property across multiplication for the expression $$2 \times 10 \times 7$$. Each option evaluates to the same result, 140, regardless of the order in which the numbers are multiplied.

Why is the Commutative Property Important?

The commutative property is an important concept in mathematics because it helps us to simplify complex expressions and make calculations easier. By understanding the commutative property, we can rearrange the order of numbers being added or multiplied without changing the result.

Real-World Applications of the Commutative Property

The commutative property has many real-world applications in fields such as engineering, physics, and computer science. For example, in engineering, the commutative property is used to simplify complex calculations involving multiple variables. In physics, the commutative property is used to describe the behavior of particles at the atomic and subatomic level.

Conclusion

In conclusion, 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. By understanding the commutative property, we can simplify complex expressions and make calculations easier. In this article, we demonstrated the commutative property across multiplication for the expression $$2 \times 10 \times 7$$ and showed that all three options A, B, and C evaluate to the same result, 140.

Final Thoughts

The commutative property is an important concept in mathematics that has many real-world applications. By understanding the commutative property, we can simplify complex calculations and make our work easier. Whether you are a student, a teacher, or a professional, the commutative property is an essential concept to understand and apply in your work.

References

[1] Khan Academy. (n.d.). Commutative Property. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4
Frequently Asked Questions (FAQs) about 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 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 mathematical concept that states that the order of the numbers being added or multiplied does not change the result. In other words, if we have two numbers, a and b, then the sum of a and b is the same as the sum of b and a.

Q: What are the different types of commutative properties?

A: There are two types of commutative properties: addition and multiplication. The commutative property of addition states that the order of the numbers being added does not change the result, while the commutative property of multiplication states that the order of the numbers being multiplied does not change the result.

Q: How do I apply the commutative property in real-life situations?

A: The commutative property is used in many real-life situations, such as in engineering, physics, and computer science. For example, in engineering, the commutative property is used to simplify complex calculations involving multiple variables. In physics, the commutative property is used to describe the behavior of particles at the atomic and subatomic level.

Q: Can I use the commutative property with fractions and decimals?

A: Yes, you can use the commutative property with fractions and decimals. For example, if we have the expression 1/2 + 1/4, we can use the commutative property to rewrite it as 1/4 + 1/2.

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

A: Yes, you can use the commutative property with negative numbers. For example, if we have the expression -2 + 3, we can use the commutative property to rewrite it as 3 + (-2).

Q: Can I use the commutative property with exponents?

A: Yes, you can use the commutative property with exponents. For example, if we have the expression 2^3 + 2^2, we can use the commutative property to rewrite it as 2^2 + 2^3.

Q: Can I use the commutative property with variables?

A: Yes, you can use the commutative property with variables. For example, if we have the expression x + y, we can use the commutative property to rewrite it as y + x.

Q: What are some common mistakes to avoid when using the commutative property?

A: Some common mistakes to avoid when using the commutative property include:

Not following the order of operations (PEMDAS)
Not using the correct notation (e.g. using + instead of ×)
Not considering the properties of the numbers being added or multiplied (e.g. negative numbers, fractions, decimals)

Q: How can I practice using the commutative property?

A: You can practice using the commutative property by working on math problems that involve addition and multiplication. You can also try using the commutative property with different types of numbers, such as fractions, decimals, and negative numbers.

Conclusion

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. By understanding the commutative property, you can simplify complex calculations and make your work easier. In this article, we have answered some frequently asked questions about the commutative property and provided some tips for practicing using it.

References

[1] Khan Academy. (n.d.). Commutative Property. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4c4