To determine which expression illustrates the associative property of addition, let's carefully analyze each given expression and evaluate its validity based on the associative property.
### Associative Property of Addition
The associative property of addition states that the way numbers are grouped in an addition expression does not affect their sum. Specifically, for any three numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], the property is given by:
[tex]\[ (a + b) + c = a + (b + c) \][/tex]
### Evaluating Each Expression
Let's evaluate the given expressions one by one:
1. [tex]\((3 + 19) - 12 = (3 + 12) - 19\)[/tex]
- Left-hand side: [tex]\( (3 + 19) - 12 = 22 - 12 = 10 \)[/tex]
- Right-hand side: [tex]\( (3 + 12) - 19 = 15 - 19 = -4 \)[/tex]
- Since [tex]\( 10 \neq -4 \)[/tex], this expression does not hold true.
2. [tex]\( 3 + (19 - 12) = 3 + (19 + 12) \)[/tex]
- Left-hand side: [tex]\( 3 + (19 - 12) = 3 + 7 = 10 \)[/tex]
- Right-hand side: [tex]\( 3 + (19 + 12) = 3 + 31 = 34 \)[/tex]
- Since [tex]\( 10 \neq 34 \)[/tex], this expression does not hold true.
3. [tex]\( (3 + 19) - 12 = 3 + (19 - 12) \)[/tex]
- Left-hand side: [tex]\( (3 + 19) - 12 = 22 - 12 = 10 \)[/tex]
- Right-hand side: [tex]\( 3 + (19 - 12) = 3 + 7 = 10 \)[/tex]
- Since [tex]\( 10 = 10 \)[/tex], this expression holds true and demonstrates the associative property.
4. [tex]\( 3 + (19 - 12) = 3 - (19 + 12) \)[/tex]
- Left-hand side: [tex]\( 3 + (19 - 12) = 3 + 7 = 10 \)[/tex]
- Right-hand side: [tex]\( 3 - (19 + 12) = 3 - 31 = -28 \)[/tex]
- Since [tex]\( 10 \neq -28 \)[/tex], this expression does not hold true.
### Conclusion
The expression that illustrates the associative property of addition is:
[tex]\[ (3 + 19) - 12 = 3 + (19 - 12) \][/tex]
This expression holds true and demonstrates that changing the grouping of the numbers in addition does not change the sum.
