What is the quotient when you divide −2 3/5 by 4/5?(1 point)

Question

Responses

4/13

−3 1/4

−25/52

−2 3/4

Answer 1

To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we can follow these steps:

1. Convert the mixed number to an improper fraction: \[ -2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -\frac{13}{5} \]

2. To divide by a fraction, multiply by its reciprocal: \[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4} \]

3. Simplify: \[ -\frac{13 \times 5}{5 \times 4} = -\frac{13}{4} \]

4. Convert \(-\frac{13}{4}\) back to a mixed number: \[ -\frac{13}{4} = -3 \frac{1}{4} \]

Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is \(-3 \frac{1}{4}\).

The correct response is: −3 1/4.