Answer :
To identify the property used in the equation
[tex]\[ (-2) + 6 + 1 = 1 + 6 + (-2) \][/tex]
we need to examine the structure of the equation and the elements involved.
### Step-by-Step Analysis:
1. Starting with the Left Side:
[tex]\[ (-2) + 6 + 1 \][/tex]
2. Looking at the Right Side:
[tex]\[ 1 + 6 + (-2) \][/tex]
You can see that the elements on both sides of the equation are the same: -2, 6, and 1. However, the order in which these elements are added together is different.
### Recognizing the Property:
When we observe that changing the order of the numbers being added does not affect the sum, we recognize a specific property of addition.
3. Identify the Property:
This characteristic is known as the Commutative Property of Addition. The Commutative Property of Addition states that the order of the addends does not change the sum. Mathematically, it can be expressed as:
[tex]\[ a + b + c = c + b + a \][/tex]
Here, replacing [tex]\( a = -2 \)[/tex], [tex]\( b = 6 \)[/tex], and [tex]\( c = 1 \)[/tex] into the structure of the commutative property confirms that:
[tex]\[ (-2) + 6 + 1 = 1 + 6 + (-2) \][/tex]
Thus, the property exhibited in this equation is correctly identified as the Commutative Property of Addition.
[tex]\[ (-2) + 6 + 1 = 1 + 6 + (-2) \][/tex]
we need to examine the structure of the equation and the elements involved.
### Step-by-Step Analysis:
1. Starting with the Left Side:
[tex]\[ (-2) + 6 + 1 \][/tex]
2. Looking at the Right Side:
[tex]\[ 1 + 6 + (-2) \][/tex]
You can see that the elements on both sides of the equation are the same: -2, 6, and 1. However, the order in which these elements are added together is different.
### Recognizing the Property:
When we observe that changing the order of the numbers being added does not affect the sum, we recognize a specific property of addition.
3. Identify the Property:
This characteristic is known as the Commutative Property of Addition. The Commutative Property of Addition states that the order of the addends does not change the sum. Mathematically, it can be expressed as:
[tex]\[ a + b + c = c + b + a \][/tex]
Here, replacing [tex]\( a = -2 \)[/tex], [tex]\( b = 6 \)[/tex], and [tex]\( c = 1 \)[/tex] into the structure of the commutative property confirms that:
[tex]\[ (-2) + 6 + 1 = 1 + 6 + (-2) \][/tex]
Thus, the property exhibited in this equation is correctly identified as the Commutative Property of Addition.
