Let's first understand the associative property of addition through a detailed step-by-step solution using the provided numerical result that relates to the expression involving the associative property of addition.
1. Step 1: Understand the associative property of addition.
- The associative property of addition states that for any three numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], the way in which the numbers are grouped in an addition operation does not change the result.
- Symbolically, this means: [tex]\( (a + b) + c = a + (b + c) \)[/tex].
2. Step 2: Apply the associative property to the given example:
- Let's consider the first example: [tex]\((5 + 2) + 3 = 5 + (2 + 3)\)[/tex].
3. Step 3: Compute both sides of the equation:
- Compute the left side: [tex]\((5 + 2) + 3\)[/tex].
- First, add [tex]\(5\)[/tex] and [tex]\(2\)[/tex]: [tex]\( 5 + 2 = 7 \)[/tex].
- Then, add [tex]\(7\)[/tex] and [tex]\(3\)[/tex]: [tex]\( 7 + 3 = 10 \)[/tex].
- Compute the right side: [tex]\(5 + (2 + 3)\)[/tex].
- First, add [tex]\(2\)[/tex] and [tex]\(3\)[/tex]: [tex]\( 2 + 3 = 5 \)[/tex].
- Then, add [tex]\(5\)[/tex] and [tex]\(5\)[/tex]: [tex]\( 5 + 5 = 10 \)[/tex].
4. Step 4: Compare both sides of the equation:
- The left side [tex]\((5 + 2) + 3\)[/tex] yields [tex]\( 10 \)[/tex].
- The right side [tex]\(5 + (2 + 3)\)[/tex] also yields [tex]\( 10 \)[/tex].
- Hence, both sides are equal: [tex]\(10 = 10\)[/tex].
5. Step 5: Confirm that the associative property holds:
- Since both sides of the equation yield the same result, the associative property of addition holds true for [tex]\(5\)[/tex], [tex]\(2\)[/tex], and [tex]\(3\)[/tex].
- Therefore, [tex]\((5 + 2) + 3 = 5 + (2 + 3)\)[/tex] illustrates the associative property.
6. Step 6: Choose the correct statement:
- We are asked to select the statement that best describes the associative property of addition from the given 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 correct statement is:
- [tex]\(a + (b + c) = (a + b) + c\)[/tex].
To summarize, based on the associative property of addition and the example provided:
The best statement that describes the associative property is:
[tex]\[ a + (b + c) = (a + b) + c \][/tex]
