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

Question

Responses

−2 3/4
negative 2 Start Fraction 2 over 25 End Fraction

−3 1/4
3 Start Fraction 1 over 4 End Fraction

4 1/3
4 over 13

−25/52

Answer 1

To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we first convert the mixed number \(-2 \frac{3}{5}\) into an improper fraction.

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

2. Now, we have: \[ -\frac{13}{5} \div \frac{4}{5} \]

3. Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{13}{5} \times \frac{5}{4} \]

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

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

So, 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.