-2 1/4 :(-1 4/11)

To divide the mixed numbers \(-2 \frac{1}{4}\) and \(-1 \frac{4}{11}\), we first need to convert them into improper fractions.

1. Convert \(-2 \frac{1}{4}\): \[ -2 \frac{1}{4} = -\left(2 \times 4 + 1\right) / 4 = -\left(8 + 1\right) / 4 = -\frac{9}{4} \]

2. Convert \(-1 \frac{4}{11}\): \[ -1 \frac{4}{11} = -\left(1 \times 11 + 4\right) / 11 = -\left(11 + 4\right) / 11 = -\frac{15}{11} \]

Now, we need to divide \(-\frac{9}{4}\) by \(-\frac{15}{11}\): \[ -\frac{9}{4} \div -\frac{15}{11} = \frac{9}{4} \times \frac{11}{15} \]

Next, multiply the fractions: \[ \frac{9 \times 11}{4 \times 15} = \frac{99}{60} \]

Now, simplify \(\frac{99}{60}\):

• The greatest common divisor (GCD) of 99 and 60 is 3. \[ \frac{99 \div 3}{60 \div 3} = \frac{33}{20} \]

Since \(\frac{33}{20}\) is an improper fraction, we can convert it back to a mixed number: \[ \frac{33}{20} = 1 \frac{13}{20} \]

Therefore, the final result of \(-2 \frac{1}{4} : (-1 \frac{4}{11})\) is: \[ \frac{33}{20} \text{ or } 1 \frac{13}{20} \]