To find the quotient when dividing \(-\frac{10}{11}\) by \(-\frac{2}{5}\), you can follow these steps:
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Dividing by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the division as: \[ -\frac{10}{11} \div -\frac{2}{5} = -\frac{10}{11} \times -\frac{5}{2} \]
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Now we can multiply the fractions. When multiplying fractions, you multiply the numerators together and the denominators together: \[ -\frac{10}{11} \times -\frac{5}{2} = \frac{10 \times 5}{11 \times 2} \]
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Simplifying this, we have: \[ \frac{50}{22} \]
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Now we can simplify \(\frac{50}{22}\) by finding the greatest common divisor (GCD) of 50 and 22, which is 2: \[ \frac{50 \div 2}{22 \div 2} = \frac{25}{11} \]
Thus, the quotient when \(-\frac{10}{11}\) is divided by \(-\frac{2}{5}\) is \(\frac{25}{11}\).