Which of the following fractions is greatest `(7)/(12), (11)/(16), (12)/(17), (13)/(18), (31)/(36)` ?

Options

A. `(13)/(18)`
B. `(12)/(17)`
C. `(31)/(36)`
D. `(7)/(12)`

Answer

To determine which of the given fractions is the greatest, we will convert each fraction to its decimal form. This will allow us to easily compare their values.

### Step 1: Convert each fraction to decimal form.

1. **Convert \( \frac{7}{12} \)**:
\[ \frac{7}{12} = 7 \div 12 \approx 0.5833 \]

2. **Convert \( \frac{11}{16} \)**:
\[ \frac{11}{16} = 11 \div 16 \approx 0.6875 \]

3. **Convert \( \frac{12}{17} \)**:
\[ \frac{12}{17} = 12 \div 17 \approx 0.7059 \]

4. **Convert \( \frac{13}{18} \)**:
\[ \frac{13}{18} = 13 \div 18 \approx 0.7222 \]

5. **Convert \( \frac{31}{36} \)**:
\[ \frac{31}{36} = 31 \div 36 \approx 0.8611 \]

### Step 2: Compare the decimal values.

Now we will list the decimal values we calculated:
- \( \frac{7}{12} \approx 0.5833 \)
- \( \frac{11}{16} \approx 0.6875 \)
- \( \frac{12}{17} \approx 0.7059 \)
- \( \frac{13}{18} \approx 0.7222 \)
- \( \frac{31}{36} \approx 0.8611 \)

### Step 3: Identify the greatest fraction.

From the decimal values, we can see that:
- \( 0.8611 \) (from \( \frac{31}{36} \)) is the largest value.

### Conclusion:

Thus, the greatest fraction among the given options is:
\[ \frac{31}{36} \]