Which statement is correct?(1 point)
Responses
Division is commutative but not associative.
Division is commutative but not associative.
Division is neither commutative nor associative.
Division is neither commutative nor associative.
Division is both commutative and associative.
Division is both commutative and associative.
Division is associative but not commutative.
Division is associative but not commutative.
WRONG
The correct statement is: "Division is associative but not commutative."
The correct statement is:
Division is neither commutative nor associative.
To understand why division is neither commutative nor associative, let's first define what these terms mean in mathematics:
1. Commutative: A binary operation (such as addition or multiplication) is commutative if changing the order of the operands does not change the result. For example, 2 + 3 = 3 + 2 is true for addition, making it a commutative operation.
2. Associative: A binary operation is associative if the grouping of the operands does not change the result. In other words, it doesn't matter how you group the terms, the final outcome remains the same. For example, (2 + 3) + 4 = 2 + (3 + 4) is true for addition, making it an associative operation.
Now, let's consider division:
1. Division is not commutative because changing the order of the operands does change the result. For example, 4 ÷ 2 = 2, but 2 ÷ 4 = 0.5. So, the result of the division operation depends on the order in which the numbers are written.
2. Division is not associative either because changing the grouping of the terms also changes the result. For example, (4 ÷ 2) ÷ 2 = 1 ÷ 2 = 0.5, but 4 ÷ (2 ÷ 2) = 4 ÷ 1 = 4. Again, the result depends on how the terms are grouped.
Therefore, the correct statement is that division is neither commutative nor associative.