To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can use the property that dividing by a fraction is equivalent to multiplying by its reciprocal.
-
First, find the reciprocal of \(-\frac{2}{5}\): \[ \text{Reciprocal of } -\frac{2}{5} = -\frac{5}{2} \]
-
Now, multiply \(-\frac{10}{11}\) by \(-\frac{5}{2}\): \[ -\frac{10}{11} \times -\frac{5}{2} = \frac{10 \times 5}{11 \times 2} = \frac{50}{22} \]
-
Now, simplify \(\frac{50}{22}\): \[ \frac{50}{22} = \frac{25}{11} \quad (\text{dividing both the numerator and the denominator by 2}) \]
-
Now, convert \(\frac{25}{11}\) to a mixed number: \[ 25 \div 11 = 2 \quad \text{and the remainder is } 3. \] So, \(\frac{25}{11} = 2 \frac{3}{11}\).
Thus, the quotient when you divide \(-\frac{10}{11}\) by \(-\frac{2}{5}\) is: \[ \boxed{2 \frac{3}{11}} \]
1 answer