Final answer:
An equivalent expression with the same quotient as -3/8 and -8/-3 is 8/3 and 3/-8, because dividing by a number is the same as multiplying by its reciprocal.
Step-by-step explanation:
The student is asking for an expression that would have the same quotient as the division of two fractions: -3/8 and -8/-3. To maintain the same quotient, we can take the reciprocal of the two numbers, since dividing by a number is the same as multiplying by its reciprocal. Therefore, one such expression with the same quotient would be 8/3 and 3/-8. This utilizes the rule that when two negative numbers are multiplied or divided, the result is positive, just like when two positive numbers multiply.
To maintain the same quotient, we choose the reciprocal pairs: 8/3 and 3/-8. Importantly, the negative signs of the original fractions result in a positive quotient, adhering to the rule that the product or division of two negatives yields a positive outcome. Therefore, the expression 8/3 divided by -3/8 is equivalent to the original division of -3/8 divided by -8/-3, preserving the same quotient.