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

Question

Responses

−234
negative 2 Start Fraction 2 over 25 End Fraction

−314
3 Start Fraction 1 over 4 End Fraction

−

Answer 1

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

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

2. Now, we divide by \(\frac{4}{5}\): \[ -\frac{13}{5} \div \frac{4}{5} \]

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

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

Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is: \[ -\frac{13}{4} \]

In mixed number form, this is: \[ -3 \frac{1}{4} \]

Therefore, the correct response is: −3 Start Fraction 1 over 4 End Fraction