Answer:
Explanation:
If we multiply a positive and a negative fraction, the result is always negative. Therefore, we can form negative quotients by dividing a negative fraction by a positive fraction.
Using the given fractions, the division problems that will have a negative quotient are:
(-1/2) ÷ (4/5)
(-1/2) ÷ (-3/8)
(-3/8) ÷ (4/5)
(-3/8) ÷ (-1/2)
Let's evaluate the first division problem:
(-1/2) ÷ (4/5) = (-1/2) x (5/4) = -5/8
Therefore, one of the division problems has a negative quotient of -5/8.
The number that must be in all of the problems is a negative fraction. This is because we can only obtain a negative quotient by dividing a negative fraction by a positive fraction, and we cannot divide two negative fractions to get a negative quotient.