Which one of the following is the greatest ?

Options

A. `(9)/(7)`
B. `(4)/(3)`
C. `(3)/(2)`
D. `(5)/(6)`

Answer

To determine which of the given fractions is the greatest, we will convert each fraction to its decimal form and then compare the decimal values.

### Step-by-Step Solution:

1. **Convert each fraction to decimal:**
- For the first fraction \( \frac{9}{7} \):
\[ \frac{9}{7} = 1.2857 \quad (\text{approximately } 1.29) \]
- For the second fraction \( \frac{4}{3} \):
\[ \frac{4}{3} = 1.3333 \quad (\text{approximately } 1.33) \]
- For the third fraction \( \frac{3}{2} \):
\[ \frac{3}{2} = 1.5 \]
- For the fourth fraction \( \frac{5}{6} \):
\[ \frac{5}{6} = 0.8333 \quad (\text{approximately } 0.84) \]

2. **List the decimal values:**
- \( \frac{9}{7} \approx 1.29 \)
- \( \frac{4}{3} \approx 1.33 \)
- \( \frac{3}{2} = 1.5 \)
- \( \frac{5}{6} \approx 0.84 \)

3. **Compare the decimal values:**
- Now we compare the decimal values:
- \( 1.29 \) (from \( \frac{9}{7} \))
- \( 1.33 \) (from \( \frac{4}{3} \))
- \( 1.5 \) (from \( \frac{3}{2} \))
- \( 0.84 \) (from \( \frac{5}{6} \))

4. **Identify the greatest value:**
- Among \( 1.29, 1.33, 1.5, \) and \( 0.84 \), the greatest value is \( 1.5 \).

5. **Conclusion:**
- Therefore, the greatest fraction among the given options is \( \frac{3}{2} \).

### Final Answer:
The greatest fraction is \( \frac{3}{2} \) (Option C).