Which statement is correct?(1 point)
Responses
Division is both commutative and associative.
Division is both commutative and associative.
Division is associative but not commutative.
Division is associative but not commutative.
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 neither commutative nor associative.
The correct statement is: Division is neither commutative nor associative.
The correct statement is: Division is neither commutative nor associative.
To understand this, let's first explain what commutative and associative properties mean in mathematics.
1. Commutative property: It refers to the order of operations. If a mathematical operation is commutative, it means that changing the order of the operands (numbers being operated upon) does not affect the result. For example, in addition, switching the order of numbers does not change the sum: 3 + 2 = 2 + 3.
2. Associative property: It refers to the grouping of operands. If a mathematical operation is associative, it means that grouping the operations in different ways does not affect the result. For example, in addition, the grouping of numbers can be changed without changing the sum: (2 + 3) + 4 = 2 + (3 + 4).
Now, let's apply these properties to division:
1. Division is not commutative: The order of division does affect the result. For example, 4 divided by 2 is equal to 2 (4 ÷ 2 = 2), but if you reverse the order, 2 divided by 4 is 0.5 (2 ÷ 4 = 0.5). Therefore, the commutative property does not hold for division.
2. Division is not associative: The grouping of divisions does affect the result. For example, (8 divided by 4) divided by 2 is equal to 1 (8 ÷ 4 ÷ 2 = 1), but if you change the grouping to 8 divided by (4 divided by 2), the result is 4 (8 ÷ (4 ÷ 2) = 4). Therefore, the associative property does not hold for division.
Based on these explanations, we conclude that division is neither commutative nor associative.