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

Question

Responses

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

−25/52
negative Start Fraction 25 over 52 End Fraction

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

4/13

Answer 1

To find the quotient of \(-2 \frac{3}{5}\) divided by \(\frac{4}{5}\), we can first convert \(-2 \frac{3}{5}\) to an improper fraction.

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

2. Now, divide \(-\frac{13}{5}\) by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4} \]

3. Multiply the fractions: \[ -\frac{13 \cdot 5}{5 \cdot 4} = -\frac{13}{4} \]

Now, we can convert \(-\frac{13}{4}\) into 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 \(\boxed{-3 \frac{1}{4}}\).