To determine which expression illustrates the associative property of addition, let's analyze the options provided one by one.
1. Option 1: [tex]\((3 + 19) - 12 = (3 + 12) - 19\)[/tex]
- Evaluate the left side: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- Evaluate the right side: [tex]\((3 + 12) - 19 = 15 - 19 = -4\)[/tex]
- Since [tex]\(10 \neq -4\)[/tex], this is not an example showing the associative property of addition.
2. Option 2: [tex]\(3 + (19 - 12) = 3 + (19 + 12)\)[/tex]
- Evaluate the left side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Evaluate the right side: [tex]\(3 + (19 + 12) = 3 + 31 = 34\)[/tex]
- Since [tex]\(10 \neq 34\)[/tex], this is not an example showing the associative property of addition.
3. Option 3: [tex]\((3 + 19) - 12 = 3 + (19 - 12)\)[/tex]
- Evaluate the left side: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- Evaluate the right side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Since [tex]\(10 = 10\)[/tex], this equality is true and demonstrates the associative property of addition.
4. Option 4: [tex]\(3 + (19 - 12) = 3 - (19 + 12)\)[/tex]
- Evaluate the left side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Evaluate the right side: [tex]\(3 - (19 + 12) = 3 - 31 = -28\)[/tex]
- Since [tex]\(10 \neq -28\)[/tex], this is not an example showing the associative property of addition.
Thus, the expression that illustrates the associative property of addition is [tex]\((3 + 19) - 12 = 3 + (19 - 12)\)[/tex].
