To identify the property used in the equation:
[tex]\[
(-2) + 6 + 1 = 1 + 6 + (-2)
\][/tex]
we need to observe the equation and understand how the numbers are rearranged. Let's break it down step-by-step:
1. Original Equation: We start with the given equation:
[tex]\[
(-2) + 6 + 1 = 1 + 6 + (-2)
\][/tex]
2. Left Side of the Equation: On the left side of the equation, we have:
[tex]\[
(-2) + 6 + 1
\][/tex]
3. Right Side of the Equation: On the right side of the equation, we have:
[tex]\[
1 + 6 + (-2)
\][/tex]
4. Comparison of Both Sides: Looking closely at both sides:
- Left side: [tex]\((-2) + 6 + 1\)[/tex]
- Right side: [tex]\(1 + 6 + (-2)\)[/tex]
5. Rearrangement of Terms: Notice that the terms on both sides are the same: [tex]\(-2\)[/tex], [tex]\(6\)[/tex], and [tex]\(1\)[/tex]. They have simply been rearranged.
6. Property Identified: The principle that allows us to rearrange the numbers in an addition equation without changing the sum is known as the Commutative Property of Addition. This property states that the order in which numbers are added doesn't affect the final sum.
Therefore, the property used in the equation:
[tex]\[
(-2) + 6 + 1 = 1 + 6 + (-2)
\][/tex]
is the Commutative Property of Addition.
