Let's analyze the equation step by step:
[tex]\[
3 + [7 + (-4)] = (3 + 7) + (-4)
\][/tex]
The property used in this equation is the Associative Property of Addition. The Associative Property states that the way in which numbers are grouped when being added does not affect the sum. In other words, changing the grouping of numbers in an addition problem does not change the result.
Let's break down the equation:
1. Original Equation:
[tex]\[
3 + [7 + (-4)]
\][/tex]
On the left side of the equation, you have [tex]\(3\)[/tex] added to the sum of [tex]\(7\)[/tex] and [tex]\(-4\)[/tex].
2. Grouping Change:
[tex]\[
(3 + 7) + (-4)
\][/tex]
On the right side of the equation, the grouping of the numbers has been changed. Now, [tex]\(3\)[/tex] and [tex]\(7\)[/tex] are grouped together first, and their sum is then added to [tex]\(-4\)[/tex].
The Associative Property of Addition allows us to change the grouping without changing the sum.
To verify, let's compute the sums step by step:
1. Left Side Calculation:
[tex]\[
7 + (-4) = 3
\][/tex]
[tex]\[
3 + 3 = 6
\][/tex]
2. Right Side Calculation:
[tex]\[
3 + 7 = 10
\][/tex]
[tex]\[
10 + (-4) = 6
\][/tex]
Both the left side and the right side of the equation yield the same result:
[tex]\[
3 + [7 + (-4)] = 6
\][/tex]
[tex]\[
(3 + 7) + (-4) = 6
\][/tex]
Thus, we have:
[tex]\[
3 + [7 + (-4)] = (3 + 7) + (-4)
\][/tex]
This confirms that the equation is true under the Associative Property of Addition. Therefore, the property used in the equation:
[tex]\[
3 + [7 + (-4)] = (3 + 7) + (-4)
\][/tex]
is the Associative Property of Addition.
