Final answer:
Division expressions with negative quotients can be created using the fractions -(1)/(2), (4)/(5), and -3, and by flipping the fraction during division to multiply by its reciprocal, resulting in negative quotients such as -15/4, -4/15, and -5/8.
Step-by-step explanation:
To write three different division expressions that each have a negative quotient using at least two of the fractions -(1)/(2), (4)/(5), and -3 in each expression, we can create the following examples:
-3 ÷ (4)/(5) = -3 × (5)/(4) = -15/4 or -3.75, which is a negative quotient.
(4)/(5) ÷
-3 =
(4)/(5) ×
-(1)/(3) =
-4/15, another negative quotient.
-(1)/(2) ÷
(4)/(5) = -(1)/(2) ×
(5)/(4) =
-5/8, which is also a negative quotient.
Keep in mind that when dividing by a fraction, it is equivalent to multiplying by its reciprocal. This means we flip the numerator and denominator of the fraction we are dividing by.