Question

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

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

4/13
4 over 13

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

−25/52

Answer 1

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

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

Now, we divide \(-\frac{13}{5}\) by \(\frac{4}{5}\):

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

Multiply the fractions:

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

Now, let's convert \(-\frac{13}{4}\) back to a mixed number:

\(-\frac{13}{4}\) can be expressed as:

\[
-3 \frac{1}{4}
\]

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

\(-3 \frac{1}{4}\)

Thus, the correct answer is:

**−3 1/4**.