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

Responses

−2552
negative Start Fraction 25 over 52 End Fraction

413
4 over 13

−314
3 Start Fraction 1 over 4 End Fraction

−234

1 answer

To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), you first need to convert the mixed number 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 divide \(-\frac{13}{5}\) by \(\frac{4}{5}\):

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

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

  3. Therefore, the final result is \(-\frac{13}{4}\), which can also be expressed as \(-3 \frac{1}{4}\) as a mixed number.

Looking at the provided options, the correct response is:

−314 (which represents \(-3 \frac{1}{4}\)).