Question

For any two nonzero integers, does the product and quotient have the same sign or not, and why?

A. The product and quotient always have the same sign.
B. The product and quotient never have the same sign.
C. The product and quotient may have the same sign or not, depending on the integers.
D. The sign of the product and quotient is random and unpredictable.

Answer 1

The product and quotient of any two nonzero integers A. always have the same sign.

Step-by-step explanation:

For any two nonzero integers, the product and quotient do indeed have the same sign. This is because the rules for multiplication and division regarding signs are the same:

• When two positive numbers are multiplied or divided, the answer has a positive sign (e.g., 2 x 3 = 6 or 6 / 3 = 2).
• When two negative numbers are multiplied or divided, the answer also has a positive sign (e.g., (-4) x (-3) = 12 or (-4) / (-2) = 2).
• When the two numbers multiplied or divided have opposite signs, the answer has a negative sign (e.g., (-3) x 2 = -6 or (-6) / 2 = -3).

Therefore, the correct answer to whether the product and quotient of two nonzero integers have the same sign is: A. The product and quotient always have the same sign.