Examples of the Commutative Property

Oct 13, 2025 by leolavanderia.com.br 85 views

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, it is a property that allows us to rearrange the numbers in an expression without affecting the final answer. In this article, we will explore the commutative property and identify which expression shows this property.

What is the Commutative Property?

The commutative property is a mathematical concept that applies to both addition and multiplication. It states that the order of the numbers being added or multiplied does not change the result. For example, in addition, the commutative property states that:

a + b = b + a

Similarly, in multiplication, the commutative property states that:

a × b = b × a

Examples of the Commutative Property

Let's consider some examples to illustrate the commutative property:

2 + 3 = 5 (in this case, we can rearrange the numbers to get 3 + 2 = 5)
4 × 2 = 8 (in this case, we can rearrange the numbers to get 2 × 4 = 8)
5 + 0 = 5 (in this case, we can rearrange the numbers to get 0 + 5 = 5)

Which Expression Shows the Commutative Property?

Now that we have a good understanding of the commutative property, let's examine the given expressions to determine which one shows this property.

A. $ (2+3)+4=2+(3+4) $

This expression shows the associative property, not the commutative property. The associative property states that the order in which we add or multiply numbers does not change the result. In this case, we can rearrange the numbers to get (2 + 3) + 4 = 2 + (3 + 4), but this is an example of the associative property, not the commutative property.

B. $ 4 \times 2=2 \times 4 $

This expression shows the commutative property. The commutative property states that the order of the numbers being multiplied does not change the result. In this case, we can rearrange the numbers to get 4 × 2 = 2 × 4, which is an example of the commutative property.

C. $ 3+0=3 $

This expression shows the identity property of addition, not the commutative property. The identity property of addition states that when we add 0 to a number, the result is the same number. In this case, we can rearrange the numbers to get 0 + 3 = 3, but this is an example of the identity property of addition, not the commutative property.

D. $ 5-5=0 $

This expression shows the inverse property of addition, not the commutative property. The inverse property of addition states that when we add a number to its opposite, the result is 0. In this case, we can rearrange the numbers to get 5 - 5 = 0, but this is an example of the inverse property of addition, not the commutative property.

Conclusion

In conclusion, the expression that shows the commutative property is:

$ 4 \times 2=2 \times 4 $

This expression illustrates the commutative property, which states that the order of the numbers being multiplied does not change the result. We can rearrange the numbers to get 4 × 2 = 2 × 4, which is an example of the commutative property.

Frequently Asked Questions

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.

Q: Which expression shows the commutative property?

A: The expression $ 4 \times 2=2 \times 4 $ shows the commutative property.

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, while the associative property states that the order in which we add or multiply numbers does not change the result.

Q: What is the identity property of addition?

A: The identity property of addition states that when we add 0 to a number, the result is the same number.

Q: What is the inverse property of addition?

A: The inverse property of addition states that when we add a number to its opposite, the result is 0.