The associative property of addition states that the way in which numbers are grouped when being added does not change their sum.
To understand this better, let’s analyze the examples given:
1. [tex]\((5 + 2) + 3 = 5 + (2 + 3)\)[/tex]
2. [tex]\(3.5 + (1.2 + 9.6) = (3.5 + 1.2) + 9.6\)[/tex]
Here, we can see that in both examples, regardless of how the numbers are grouped, the sum remains the same. The parentheses indicate the grouping of the numbers.
To choose the statement that best describes the associative property of addition, let’s consider each option:
1. [tex]\((a + b) + c = a + b\)[/tex]
This statement is incorrect because the sum on the left-hand side includes [tex]\(c\)[/tex], while the right-hand side omits [tex]\(c\)[/tex].
2. [tex]\(a + (b + c) = (a + b) + c\)[/tex]
This is a valid description of the associative property of addition, showing that the grouping of [tex]\(a, b,\)[/tex] and [tex]\(c\)[/tex] does not matter.
3. [tex]\(a + b + c = c + a + b\)[/tex]
This statement describes the commutative property of addition, which states that the order in which numbers are added does not change the sum.
4. [tex]\(b + c + a = (b + c + a)\)[/tex]
This statement is trivial and true for any grouping due to the associative property, but it doesn't explicitly describe the associative property itself.
Therefore, the statement that best describes the associative property of addition is:
[tex]\[ a + (b + c) = (a + b) + c \][/tex]
The correct choice is the second option.
