Concept:To compare fractions and find the largest one, we can convert them to equivalent fractions with a common denominator.Explanation:We are given the fractions $\frac{5}{7}$, $\frac{3}{5}$, $\frac{9}{14}$, and $\frac{8}{15}$.To compare them, we find the Least Common Multiple (LCM) of the denominators 7, 5, 14, and 15.The LCM of 7, 5, 14, and 15 is 210.Now, we convert each fraction to an equivalent fraction with a denominator of 210:For $\frac{5}{7}$: Multiply numerator and denominator by $\frac{210}{7} = 30$. So, $\frac{5}{7} = \frac{5 \times 30}{7 \times 30} = \frac{300}{210}$.For $\frac{3}{5}$: Multiply numerator and denominator by $\frac{210}{5} = 42$. So, $\frac{3}{5} = \frac{3 \times 42}{5 \times 42} = \frac{126}{210}$.For $\frac{9}{14}$: Multiply numerator and denominator by $\frac{210}{14} = 15$. So, $\frac{9}{14} = \frac{9 \times 15}{14 \times 15} = \frac{135}{210}$.For $\frac{8}{15}$: Multiply numerator and denominator by $\frac{210}{15} = 14$. So, $\frac{8}{15} = \frac{8 \times 14}{15 \times 14} = \frac{112}{210}$.Now we compare the numerators: 300, 126, 135, and 112.The largest numerator is 300, which corresponds to the fraction $\frac{5}{7}$.Answer:The largest fraction is $\frac{5}{7}$.The correct option is A.