which statement is correct
responses
Division is communicative but not associative
Division is communicative but not associative
Division is both communicative and associative
Division is both communicative and associative
Division is associative but not communicative
Division is associative but not communicative
Division is neither communicative nor associative
The correct statement is: Division is associative but not communicative.
The correct statement is "Division is neither communicative nor associative."
To determine which statement is correct regarding division, we need to understand the meanings of "communicative" and "associative" in mathematics.
In mathematics, an operation is said to be communicative if changing the order of the operands does not change the result. For example, in the case of addition, if you add 2 and 3, the result is the same as when you add 3 and 2. So, addition is communicative.
On the other hand, an operation is said to be associative if the grouping of the operands does not change the result. For example, in the case of addition, if you add (2 + 3) + 4, the result is the same as when you add 2 + (3 + 4). So, addition is associative.
Now, let's evaluate the given statements one by one.
Statement 1: "Division is communicative but not associative."
To check if this statement is correct, we need to test the communicative property. For example, if we divide 10 by 5, the result is 2. If we reverse the order and divide 5 by 10, the result is 0.5. Since the results are different, division is not communicative. Therefore, statement 1 is incorrect.
Statement 2: "Division is both communicative and associative."
To check if this statement is correct, we need to test both properties. As we have already determined that division is not communicative, this statement is incorrect.
Statement 3: "Division is associative but not communicative."
To check if this statement is correct, we need to test the associativity property. For example, if we divide (10 ÷ 5) ÷ 2, the result is 1. If we associate the operands as 10 ÷ (5 ÷ 2), the result is 4. Therefore, division is not associative. So, statement 3 is incorrect.
Statement 4: "Division is neither communicative nor associative."
Given the results of the previous evaluations, this statement is correct. Division is neither communicative nor associative.
Therefore, the correct statement is: "Division is neither communicative nor associative."