Which is the largest of the following 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 given fractions is the largest, we can convert each fraction to a decimal and compare their values. Here’s the step-by-step solution:

### Step 1: Convert each fraction to a decimal
1. **Convert \( \frac{2}{3} \)**:
- Divide 2 by 3:
\[ 2 \div 3 = 0.6667 \quad (\text{approximately}) \]

2. **Convert \( \frac{3}{5} \)**:
- Divide 3 by 5:
\[ 3 \div 5 = 0.6 \]

3. **Convert \( \frac{8}{11} \)**:
- Divide 8 by 11:
\[ 8 \div 11 = 0.7273 \quad (\text{approximately}) \]

4. **Convert \( \frac{11}{17} \)**:
- Divide 11 by 17:
\[ 11 \div 17 = 0.6471 \quad (\text{approximately}) \]

### Step 2: Compare the decimal values
- \( \frac{2}{3} \approx 0.6667 \)
- \( \frac{3}{5} = 0.6 \)
- \( \frac{8}{11} \approx 0.7273 \)
- \( \frac{11}{17} \approx 0.6471 \)

### Step 3: Identify the largest value
From the decimal conversions:
- \( 0.6667 \) (for \( \frac{2}{3} \))
- \( 0.6 \) (for \( \frac{3}{5} \))
- \( 0.7273 \) (for \( \frac{8}{11} \))
- \( 0.6471 \) (for \( \frac{11}{17} \))

The largest value is \( 0.7273 \), which corresponds to the fraction \( \frac{8}{11} \).

### Conclusion
Thus, the largest fraction among the given options is:
\[ \frac{8}{11} \]