1. **State the problem:** We need to perform the subtraction $ \frac{1}{7} - \frac{1}{11} $ and simplify the answer. 2. **Formula and rules:** To subtract fractions, we find a common denominator, subtract the numerators, and simplify if possible. 3. **Find the common denominator:** The denominators are 7 and 11. The least common denominator (LCD) is $7 \times 11 = 77$. 4. **Rewrite each fraction with the LCD:** $$\frac{1}{7} = \frac{1 \times 11}{7 \times 11} = \frac{11}{77}$$ $$\frac{1}{11} = \frac{1 \times 7}{11 \times 7} = \frac{7}{77}$$ 5. **Subtract the fractions:** $$\frac{11}{77} - \frac{7}{77} = \frac{11 - 7}{77} = \frac{4}{77}$$ 6. **Simplify the fraction:** $\frac{4}{77}$ cannot be simplified further because 4 and 77 have no common factors other than 1. **Final answer:** $\frac{4}{77}$