1. **State the problem:** We need to find the difference between the fractions $\frac{7}{11}$ and $\frac{7}{15}$ and express the answer in simplest form. 2. **Formula and rules:** To subtract fractions, we use the formula: $$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$ where $a$, $b$, $c$, and $d$ are integers, and $b$, $d \neq 0$. 3. **Apply the formula:** $$\frac{7}{11} - \frac{7}{15} = \frac{7 \times 15 - 7 \times 11}{11 \times 15} = \frac{105 - 77}{165}$$ 4. **Simplify the numerator:** $$105 - 77 = 28$$ So, $$\frac{28}{165}$$ 5. **Simplify the fraction:** Check if numerator and denominator have common factors. - Factors of 28: 1, 2, 4, 7, 14, 28 - Factors of 165: 1, 3, 5, 11, 15, 33, 55, 165 No common factors other than 1, so the fraction is already in simplest form. **Final answer:** $$\boxed{\frac{28}{165}}$$