1. **State the problem:** Convert the fractions $\frac{2}{5}$, $\frac{7}{12}$, $\frac{3}{4}$, and $\frac{-5}{6}$ to equivalent fractions with a common denominator. 2. **Find the Least Common Denominator (LCD):** The denominators are 5, 12, 4, and 6. - Prime factors: - 5 = 5 - 12 = 2^2 \times 3 - 4 = 2^2 - 6 = 2 \times 3 - The LCD is the product of the highest powers of all prime factors: $$\text{LCD} = 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60$$ 3. **Convert each fraction to have denominator 60:** - For $\frac{2}{5}$: $$\frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60}$$ - For $\frac{7}{12}$: $$\frac{7}{12} = \frac{7 \times 5}{12 \times 5} = \frac{35}{60}$$ - For $\frac{3}{4}$: $$\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}$$ - For $\frac{-5}{6}$: $$\frac{-5}{6} = \frac{-5 \times 10}{6 \times 10} = \frac{-50}{60}$$ 4. **Final answer:** The equivalent fractions with the common denominator 60 are: $$\frac{24}{60}, \frac{35}{60}, \frac{45}{60}, \frac{-50}{60}$$