1. **State the problem:** We need to compare the fractions $\frac{6}{8}$, $\frac{6}{9}$, and $\frac{6}{10}$ by finding a common denominator (LCD) to easily compare their sizes. 2. **Find the Least Common Denominator (LCD):** The denominators are 8, 9, and 10. - Prime factors: - 8 = $2^3$ - 9 = $3^2$ - 10 = $2 \times 5$ - LCD is the product of the highest powers of all primes: $$\text{LCD} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360$$ 3. **Convert each fraction to have denominator 360:** - $\frac{6}{8} = \frac{6 \times 45}{8 \times 45} = \frac{270}{360}$ - $\frac{6}{9} = \frac{6 \times 40}{9 \times 40} = \frac{240}{360}$ - $\frac{6}{10} = \frac{6 \times 36}{10 \times 36} = \frac{216}{360}$ 4. **Compare the numerators:** - $270 > 240 > 216$ 5. **Conclusion:** Since the denominators are the same, the fraction with the largest numerator is the largest. Therefore, the order is: $$\frac{6}{10} < \frac{6}{9} < \frac{6}{8}$$ This means $\frac{6}{8}$ is the largest and $\frac{6}{10}$ is the smallest among the three fractions. 6. **Explanation:** Finding the LCD allows us to compare fractions by converting them to equivalent fractions with the same denominator. This makes it easy to see which fraction is larger or smaller by simply comparing numerators.