Question

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

−234
negative 2 Start Fraction 2 over 25 End Fraction

413
4 over 13

−2552
negative Start Fraction 25 over 52 End Fraction

−314

Answer 1

To find the quotient when dividing \(-2 \frac{3}{5}\) 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 can rewrite the division of fractions:

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

Next, we multiply the fractions:

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

Now, to express \(-\frac{13}{4}\) as a mixed number:

\(-\frac{13}{4} = -3 \frac{1}{4}\)

Comparing our calculated result to the provided choices:

- \(−2 \frac{2}{25}\)
- \(4 \frac{1}{3}\)
- \(−\frac{25}{52}\)
- \(−3 \frac{1}{4}\)

The answer is:

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