Explanation:

To determine the largest fraction among $5/8, 2/3, 7/9, 3/5$, we can convert them to decimal form for easy comparison. 1. **Convert $5/8$ to decimal:** $5 \div 8 = 0.625$ 2. **Convert $2/3$ to decimal:** $2 \div 3 = 0.6666...$ (a repeating decimal) 3. **Convert $7/9$ to decimal:** $7 \div 9 = 0.7777...$ (a repeating decimal) 4. **Convert $3/5$ to decimal:** $3 \div 5 = 0.6$ \nNow, let's compare these decimal values: $0.625$ $0.666...$ $0.777...$ $0.600$ \nArranging them in ascending order: $0.6 < 0.625 < 0.666... < 0.777...$\nThe largest decimal value is $0.777...$, which corresponds to the fraction $\frac{7}{9}$. \nAlternatively, we could find a common denominator for all fractions. The denominators are $8, 3, 9, 5$. The Least Common Multiple (LCM) of these numbers is $360$. $\frac{5}{8} = \frac{5 \times 45}{8 \times 45} = \frac{225}{360}$ $\frac{2}{3} = \frac{2 \times 120}{3 \times 120} = \frac{240}{360}$ $\frac{7}{9} = \frac{7 \times 40}{9 \times 40} = \frac{280}{360}$ $\frac{3}{5} = \frac{3 \times 72}{5 \times 72} = \frac{216}{360}$\nComparing the numerators ($225, 240, 280, 216$), $280$ is the largest, so $\frac{280}{360}$ or $\frac{7}{9}$ is the largest fraction. \nLet's evaluate the options:\nOption (1) $5/8$: This is $0.625$, which is not the largest.\nOption (2) $2/3$: This is $0.666...$, which is not the largest.\nOption (3) $3/5$: This is $0.6$, which is the smallest.\nOption (4) $7/9$: This is $0.777...$, which is the largest. \nTherefore, the largest fraction is $\frac{7}{9}$. The correct option is (4) $7/9$.