Question
What is the quotient when you divide −10/11 by −2/5 ?(1 point) Responses 4/11 Start Fraction 4 over 11 End Fraction 2 3/4 2 Start Fraction 3 over 4 End Fraction −23/11 negative 2 Start Fraction 3 over 11 End Fraction 23/11
Answers
GPT-4o mini
To find the quotient of \(-\frac{10}{11}\) divided by \(-\frac{2}{5}\), we can use the rule that dividing by a fraction is the same as multiplying by its reciprocal.
So we have:
\[
-\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2}
\]
Now, the negatives cancel out:
\[
-\frac{10}{11} \times -\frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22}
\]
Next, we simplify \(\frac{50}{22}\):
Both 50 and 22 can be divided by 2:
\[
\frac{50 \div 2}{22 \div 2} = \frac{25}{11}
\]
Therefore, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
\[
\frac{25}{11}
\]
Thus, the correct response is:
\( \frac{25}{11} \)
(Note: 23/11 or −23/11 were mentioned in the original options, it seems there was a slight confusion. The correct quotient we obtained is \( \frac{25}{11} \) but this was not one of the provided responses.)
So we have:
\[
-\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2}
\]
Now, the negatives cancel out:
\[
-\frac{10}{11} \times -\frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22}
\]
Next, we simplify \(\frac{50}{22}\):
Both 50 and 22 can be divided by 2:
\[
\frac{50 \div 2}{22 \div 2} = \frac{25}{11}
\]
Therefore, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is:
\[
\frac{25}{11}
\]
Thus, the correct response is:
\( \frac{25}{11} \)
(Note: 23/11 or −23/11 were mentioned in the original options, it seems there was a slight confusion. The correct quotient we obtained is \( \frac{25}{11} \) but this was not one of the provided responses.)