Which is the largest of the fol lowing fractions ?
`(2)/(3),(3)/(5),(8)/(11),(11)/(17)`

Options

A. `(8)/(11)`
B. `(3)/(5)`
C. `(11)/(17)`
D. `(2)/(3)`

Answer

To determine which of the fractions \(\frac{2}{3}, \frac{3}{5}, \frac{8}{11}, \frac{11}{17}\) is the largest, we can compare them using cross multiplication. Here’s a step-by-step solution:

### Step 1: Compare \(\frac{2}{3}\) and \(\frac{3}{5}\)

To compare \(\frac{2}{3}\) and \(\frac{3}{5}\), we can cross-multiply:

\[ 2 \times 5 = 10 \]
\[ 3 \times 3 = 9 \]

Since \(10 > 9\), we conclude that:

\[ \frac{2}{3} > \frac{3}{5} \]

### Step 2: Compare \(\frac{2}{3}\) and \(\frac{8}{11}\)

Next, we compare \(\frac{2}{3}\) and \(\frac{8}{11}\):

\[ 2 \times 11 = 22 \]
\[ 3 \times 8 = 24 \]

Since \(22 < 24\), we conclude that:

\[ \frac{8}{11} > \frac{2}{3} \]

### Step 3: Compare \(\frac{8}{11}\) and \(\frac{11}{17}\)

Now, we compare \(\frac{8}{11}\) and \(\frac{11}{17}\):

\[ 8 \times 17 = 136 \]
\[ 11 \times 11 = 121 \]

Since \(136 > 121\), we conclude that:

\[ \frac{8}{11} > \frac{11}{17} \]

### Conclusion

After comparing all fractions, we find that:

\[ \frac{8}{11} > \frac{2}{3}, \quad \frac{8}{11} > \frac{3}{5}, \quad \frac{8}{11} > \frac{11}{17} \]

Thus, the largest fraction among the given options is:

\[ \boxed{\frac{8}{11}} \]