Which one of the following statements is not true for integers?

2019

Which one of the following statements is not true for integers?

Answer: B. Division is commutative.To determine which statement is not true for integers, we evaluate each property. Multiplication of integers is associative, meaning (a × b) × c = a × (b ×…

  1. A.

    Multiplication is associative.

  2. B.

    Division is commutative.

  3. C.

    1 is the multiplicative identity.

  4. D.

    Subtraction is not commutative.

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Correct answer: B

To determine which statement is not true for integers, we evaluate each property. Multiplication of integers is associative, meaning (a × b) × c = a × (b × c), so Option A is true. The number 1 acts as the multiplicative identity because multiplying any integer by 1 leaves it unchanged, making Option C true. Subtraction is not commutative since changing the order changes the result (e.g., 5 - 3 ≠ 3 - 5), confirming Option D is true. However, division is not commutative for integers; swapping the dividend and divisor changes the quotient (e.g., 6 ÷ 2 = 3, but 2 ÷ 6 is not an integer). Therefore, the statement that division is commutative is false. Option B is the correct answer.

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