The associative property of addition states that the way in which numbers are grouped in an addition operation does not affect their sum. It is usually expressed as [tex]\((a + b) + c = a + (b + c)\)[/tex].
Let's analyze each expression to determine which one illustrates the associative property of addition:
1. Expression: [tex]\((3 + 19) - 12 = (3 + 12) - 19\)[/tex]
- Left side: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- Right side: [tex]\((3 + 12) - 19 = 15 - 19 = -4\)[/tex]
- Since [tex]\(10 \neq -4\)[/tex], this expression does not illustrate the associative property.
2. Expression: [tex]\(3 + (19 - 12) = 3 + (19 + 12)\)[/tex]
- Left side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Right side: [tex]\(3 + (19 + 12) = 3 + 31 = 34\)[/tex]
- Since [tex]\(10 \neq 34\)[/tex], this expression does not illustrate the associative property.
3. Expression: [tex]\((3 + 19) - 12 = 3 + (19 - 12)\)[/tex]
- Left side: [tex]\((3 + 19) - 12 = 22 - 12 = 10\)[/tex]
- Right side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Since [tex]\(10 = 10\)[/tex], this expression illustrates the associative property of addition because both sides are equal.
4. Expression: [tex]\(3 + (19 - 12) = 3 - (19 + 12)\)[/tex]
- Left side: [tex]\(3 + (19 - 12) = 3 + 7 = 10\)[/tex]
- Right side: [tex]\(3 - (19 + 12) = 3 - 31 = -28\)[/tex]
- Since [tex]\(10 \neq -28\)[/tex], this expression does not illustrate the associative property.
Therefore, the expression that illustrates the associative property of addition is:
[tex]\[
(3 + 19) - 12 = 3 + (19 - 12)
\][/tex]
This corresponds to the third option.
