Which is the biggest of the following fractions ?

Options

A. `3/4`
B. `4/5`
C. `5/6`
D. `6/7`

Answer

To determine which of the following fractions is the biggest, we will compare the fractions: \( \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7} \).

### Step 1: Convert each fraction to decimal form
1. **Convert \( \frac{3}{4} \)**:
\[ \frac{3}{4} = 0.75 \]

2. **Convert \( \frac{4}{5} \)**:
\[ \frac{4}{5} = 0.80 \]

3. **Convert \( \frac{5}{6} \)**:
\[ \frac{5}{6} \approx 0.8333 \]

4. **Convert \( \frac{6}{7} \)**:
\[ \frac{6}{7} \approx 0.8571 \]

### Step 2: Compare the decimal values
Now we will list the decimal values we calculated:
- \( \frac{3}{4} = 0.75 \)
- \( \frac{4}{5} = 0.80 \)
- \( \frac{5}{6} \approx 0.8333 \)
- \( \frac{6}{7} \approx 0.8571 \)

### Step 3: Identify the largest decimal value
From the decimal values:
- \( 0.75 \) (from \( \frac{3}{4} \))
- \( 0.80 \) (from \( \frac{4}{5} \))
- \( 0.8333 \) (from \( \frac{5}{6} \))
- \( 0.8571 \) (from \( \frac{6}{7} \))

The largest value is \( 0.8571 \), which corresponds to \( \frac{6}{7} \).

### Conclusion
Thus, the biggest fraction among the given options is:
\[ \frac{6}{7} \]