1. **State the problem:** We need to convert the fractions $\frac{3}{4}$, $\frac{9}{22}$, $\frac{7}{8}$, and $-\frac{5}{11}$ to equivalent fractions with a common denominator called the Least Common Denominator (LCD). 2. **Find the LCD:** The denominators are 4, 22, 8, and 11. - Prime factors: 4 = $2^2$, 22 = $2 \times 11$, 8 = $2^3$, 11 = $11$ - The LCD must include the highest powers of all prime factors: $2^3$ (from 8) and $11$ (from 11 or 22). - So, LCD = $2^3 \times 11 = 8 \times 11 = 88$. 3. **Convert each fraction to have denominator 88:** - $\frac{3}{4} = \frac{3 \times 22}{4 \times 22} = \frac{66}{88}$ - $\frac{9}{22} = \frac{9 \times 4}{22 \times 4} = \frac{36}{88}$ - $\frac{7}{8} = \frac{7 \times 11}{8 \times 11} = \frac{77}{88}$ - $-\frac{5}{11} = -\frac{5 \times 8}{11 \times 8} = -\frac{40}{88}$ 4. **Final answer:** The equivalent fractions with the common denominator 88 are: $$\frac{66}{88}, \frac{36}{88}, \frac{77}{88}, -\frac{40}{88}$$ This process allows us to compare or add/subtract fractions easily because they share the same denominator.