7/11:(8/11+4/33)

To solve the expression \( \frac{7}{11} : \left( \frac{8}{11} + \frac{4}{33} \right) \), we first need to simplify the expression inside the parentheses.

1. Find a common denominator for the fractions inside the parentheses. The denominators are 11 and 33. The least common multiple of 11 and 33 is 33.

   • Convert \( \frac{8}{11} \) to have a denominator of 33: \[ \frac{8}{11} = \frac{8 \times 3}{11 \times 3} = \frac{24}{33} \]

2. Now add \( \frac{24}{33} \) and \( \frac{4}{33} \): \[ \frac{24}{33} + \frac{4}{33} = \frac{24 + 4}{33} = \frac{28}{33} \]

3. Now substitute this back into the original expression: \[ \frac{7}{11} : \frac{28}{33} \]

   This is equivalent to multiplying by the reciprocal: \[ \frac{7}{11} \times \frac{33}{28} \]

4. Multiply the fractions: \[ = \frac{7 \times 33}{11 \times 28} \] Simplifying each part:

   • \( 11 \) goes into \( 33 \) three times: \[ = \frac{7 \times 3}{28} = \frac{21}{28} \]

5. Finally, simplify \( \frac{21}{28} \): \[ = \frac{21 \div 7}{28 \div 7} = \frac{3}{4} \]

Thus, the final answer is: \[ \frac{3}{4} \]