Final answer:
The quotients equivalent to -5/8 are options A (-5/8) and C (5/-8), as they maintain the negative sign of the original fraction. The positive and double negative options are not equivalent because they result in a positive quotient.
Step-by-step explanation:
To find the quotients equivalent to -5/8, we need to understand how division works with negative numbers. The rule is that a negative number divided by a positive number, or a positive number divided by a negative number, will result in a negative quotient. On the other hand, a negative number divided by a negative number will result in a positive quotient. Therefore, let's evaluate the options given.
A. -5/8 is the same as the original fraction, so it is equivalent.
B. 5/8 is not equivalent because it is positive.
C. 5/-8 is equivalent because it represents a positive number divided by a negative number, yielding a negative quotient, which matches the signs of the original fraction.
D. -(5/-8) is equivalent. When simplifying this expression, the negatives cancel out, resulting in a positive, which is not equivalent to the original fraction.
E. -5/-8 is not equivalent because, like option D, the negatives cancel each other out, making it a positive quotient.
The equivalent quotients to -5/8 are options A, which is the original fraction, and C, which is a positive number divided by a negative number, resulting in the same negative quotient as the original.