Name the property of addition that has been applied.

13)

( 2 + 8) + 1 = ( 8 + 2) + 1

13)

______

A)

Identity

B)

Commutative

C)

Closure

D)

Associative

What is your choice?

Commutative

To determine the property of addition that has been applied in the given equation, let's break down the options:

A) Identity: The identity property of addition states that adding zero to a number does not change its value. However, there is no zero involved in the equation (2 + 8) + 1 = (8 + 2) + 1, so it is not the identity property.

B) Commutative: The commutative property of addition states that the order of the numbers being added does not change the sum. In the given equation, we can see that the numbers 2 and 8 have swapped places in the second set of parentheses: (2 + 8) + 1 = (8 + 2) + 1. This indicates that the commutative property of addition has been applied.

C) Closure: The closure property of addition states that the sum of two real numbers is always a real number. However, the given equation does not provide any information about the nature of the numbers involved, so we cannot determine if the closure property has been applied.

D) Associative: The associative property of addition states that the grouping of numbers being added does not impact the sum. In the given equation, the numbers 2, 8, and 1 are grouped differently in the two sets of parentheses, but the sum remains the same: (2 + 8) + 1 = (8 + 2) + 1. Therefore, the associative property of addition has been applied.

Based on the analysis, the correct answer is D) Associative.