To understand the associative property of addition, let's carefully analyze the examples provided in the question.
### First Example
1. Consider the expression [tex]\((5 + 2) + 3\)[/tex].
2. Perform the addition inside the parentheses first: [tex]\(5 + 2 = 7\)[/tex].
3. Then add the remaining number: [tex]\(7 + 3 = 10\)[/tex].
Now consider the expression [tex]\(5 + (2 + 3)\)[/tex]:
1. Perform the addition inside the parentheses first: [tex]\(2 + 3 = 5\)[/tex].
2. Then add the remaining number: [tex]\(5 + 5 = 10\)[/tex].
Both expressions result in [tex]\(10\)[/tex], demonstrating that the order in which the numbers are grouped does not affect the sum.
### Second Example
1. Consider the expression [tex]\(3.5 + (1.2 + 9.6)\)[/tex].
2. Perform the addition inside the parentheses first: [tex]\(1.2 + 9.6 = 10.8\)[/tex].
3. Then add the remaining number: [tex]\(3.5 + 10.8 = 14.3\)[/tex].
Now consider the expression [tex]\((3.5 + 1.2) + 9.6\)[/tex]:
1. Perform the addition inside the parentheses first: [tex]\(3.5 + 1.2 = 4.7\)[/tex].
2. Then add the remaining number: [tex]\(4.7 + 9.6 = 14.3\)[/tex].
Both expressions result in [tex]\(14.3\)[/tex], again showing that the grouping of the numbers does not affect the sum.
### Conclusion
The examples clearly illustrate the associative property of addition, which states that the way in which numbers are grouped when being added does not change their sum. Given the options:
- [tex]\((a + b) + c = a + b\)[/tex]
- [tex]\(a + (b + c) = (a + b) + c\)[/tex]
- [tex]\(a + b + c = c + a + b\)[/tex]
- [tex]\(b + c + a = (b + c) + a\)[/tex]
The statement that best describes the property is:
[tex]\[a + (b + c) = (a + b) + c\][/tex]
This is known as the associative property of addition.
