Question

Three of these statements are true.selct them.

A) If a and b are integers and b does not equal zero, then -(a/b) = ( -a ) / b = a / ( -b )
B) The product of any two rational numbers is a rational number.
C) If a and b are integers with opposite signs, and b does not equal zero, then -(a/b) = a/b
D) The quotient of any two nonzero integers is a rational number.

Answer 1

Statements A, B, and D are true. Statement A validates commutativity in division by a negative sign. Statement B asserts the closure property of multiplication for rational numbers, and statement D confirms that any quotient of two nonzero integers is rational.

Step-by-step explanation:

Let's evaluate each statement regarding integers and rational numbers:

1. A) True. The statement -(a/b) = (-a)/b = a/(-b) follows the rules of signs in division, meaning the negative sign can be associated with the numerator or the denominator while maintaining the value of the fraction.
2. B) True. The product of any two rational numbers is indeed a rational number, confirming the closure property of multiplication for rational numbers.
3. C) False. If a and b are integers with opposite signs, then -(a/b) is not equal to a/b; this would negate the fraction completely.
4. D) True. Any quotient of two nonzero integers is a rational number because a rational number is defined as the ratio of two integers, where the denominator is not zero.