Arrange `(4)/(5), (7)/(8), (6)/(7), (5)/(6)` in the ascending order :

Options

A. `(4)/(5),(7)/(8),(6)/(7),(5)/(6)`
B. `(5)/(6),(6)/(7),(7)/(8),(4)/(5)`
C. `(4)/(5),(5)/(6),(6)/(7),(7)/(8)`
D. `(7)/(8),(6)/(7),(5)/(6),(4)/(5)`

Answer

To arrange the fractions \( \frac{4}{5}, \frac{7}{8}, \frac{6}{7}, \frac{5}{6} \) in ascending order, we will first convert each fraction to a decimal form for easier comparison.

### Step 1: Convert each fraction to decimal

1. **Convert \( \frac{4}{5} \)**:
\[ \frac{4}{5} = 0.8 \]

2. **Convert \( \frac{7}{8} \)**:
\[ \frac{7}{8} = 0.875 \]

3. **Convert \( \frac{6}{7} \)**:
\[ \frac{6}{7} \approx 0.8571 \quad (\text{approximately}) \]

4. **Convert \( \frac{5}{6} \)**:
\[ \frac{5}{6} \approx 0.8333 \quad (\text{approximately}) \]

### Step 2: List the decimal values

Now we have the following decimal values:
- \( \frac{4}{5} = 0.8 \)
- \( \frac{7}{8} = 0.875 \)
- \( \frac{6}{7} \approx 0.8571 \)
- \( \frac{5}{6} \approx 0.8333 \)

### Step 3: Compare the decimal values

Now we can compare the decimal values:
- \( 0.8 \) (from \( \frac{4}{5} \))
- \( 0.8333 \) (from \( \frac{5}{6} \))
- \( 0.8571 \) (from \( \frac{6}{7} \))
- \( 0.875 \) (from \( \frac{7}{8} \))

### Step 4: Arrange in ascending order

From the comparisons, we can see that:
1. \( 0.8 \) (which is \( \frac{4}{5} \))
2. \( 0.8333 \) (which is \( \frac{5}{6} \))
3. \( 0.8571 \) (which is \( \frac{6}{7} \))
4. \( 0.875 \) (which is \( \frac{7}{8} \))

Thus, the fractions in ascending order are:
\[ \frac{4}{5}, \frac{5}{6}, \frac{6}{7}, \frac{7}{8} \]

### Final Answer:
The fractions arranged in ascending order are:
\[ \frac{4}{5} < \frac{5}{6} < \frac{6}{7} < \frac{7}{8} \]