To determine which choice shows why the commutative property doesn't work under subtraction, we first need to understand what the commutative property is.
The commutative property states that the order of the numbers does not affect the result of the operation. This property holds true for addition and multiplication. For example:
- Addition: [tex]\(3 + 2 = 2 + 3\)[/tex]
- Multiplication: [tex]\(4 \times 5 = 5 \times 4\)[/tex]
However, subtraction does not follow the commutative property. Let's illustrate this with examples:
For choice A:
- [tex]\(3 + 2 = 5\)[/tex]
- [tex]\(2 + 3 = 5\)[/tex]
Since [tex]\(3 + 2 = 2 + 3\)[/tex], addition is commutative. Thus, choice A is not correct.
For choice B:
- [tex]\(5 - 1 = 4\)[/tex]
- [tex]\(5 - 1 = 4\)[/tex]
Since this is the same operation on both sides, it doesn't demonstrate anything about the commutative property. Thus, choice B is not correct.
For choice C:
- [tex]\(5 + 1 = 6\)[/tex]
- [tex]\(7 - 1= 6\)[/tex]
Both sides are equal, but this statement does not relate to the commutative property at all. Therefore, choice C is not correct.
For choice D:
- [tex]\(5 - 1 = 4\)[/tex]
- [tex]\(1 - 5 = -4\)[/tex]
Since [tex]\(4\)[/tex] is not equal to [tex]\(-4\)[/tex], this demonstrates that changing the order of the numbers in subtraction gives different results, showing that subtraction is not commutative.
Therefore, the correct choice is:
D. [tex]\(5 - 1 \neq 1 - 5\)[/tex]
This choice clearly shows that the commutative property does not hold under subtraction.
