Question

What is the quotient when you divide −10/11 by −2/5 ?(1 point)
Responses

2 3/11
2 Start Fraction 3 over 11 End Fraction

2 3/4
2 Start Fraction 3 over 4 End Fraction

−2 3/11
negative 2 Start Fraction 3 over 11 End Fraction

4/11

Answer 1

To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can multiply \(-\frac{10}{11}\) by the reciprocal of \(-\frac{2}{5}\).

1. Reciprocal of \(-\frac{2}{5}\) is \(-\frac{5}{2}\).
2. Therefore, the calculation becomes:

\[
-\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2}
\]

3. The negatives cancel out:

\[
\frac{10}{11} \times \frac{5}{2}
\]

4. Now perform the multiplication:

\[
\frac{10 \times 5}{11 \times 2} = \frac{50}{22}
\]

5. Simplify \(\frac{50}{22}\):

\[
\frac{50 \div 2}{22 \div 2} = \frac{25}{11}
\]

Now, to express \(\frac{25}{11}\) as a mixed number:

- Divide 25 by 11: \(25 \div 11 = 2\) (quotient) and remainder \(3\).
- Thus, \(\frac{25}{11} = 2 \frac{3}{11}\).

So, the final answer is:

**2 3/11** (which corresponds to "2 Start Fraction 3 over 11 End Fraction").