Which of the following fractions is greater than than `3/4` and lesser than `3/2` ?

Options

A. `6/11`
B. `6/5`
C. `1/4`
D. `3/7`

Answer

To determine which of the given fractions is greater than \( \frac{3}{4} \) and less than \( \frac{3}{2} \), we can follow these steps:

### Step 1: Convert the fractions to decimal form
First, we convert \( \frac{3}{4} \) and \( \frac{3}{2} \) into decimal form for easier comparison.

\[ \frac{3}{4} = 0.75 \]
\[ \frac{3}{2} = 1.5 \]

### Step 2: List the options
The options given are:
1. \( \frac{6}{11} \)
2. \( \frac{6}{5} \)
3. \( \frac{1}{4} \)
4. \( \frac{3}{7} \)

### Step 3: Convert each fraction to decimal form
Now, we will convert each of the options to decimal form.

- For \( \frac{6}{11} \):
\[ 6 \div 11 \approx 0.545 \quad (\text{less than } 0.75) \]

- For \( \frac{6}{5} \):
\[ 6 \div 5 = 1.2 \quad (\text{greater than } 0.75 \text{ and less than } 1.5) \]

- For \( \frac{1}{4} \):
\[ 1 \div 4 = 0.25 \quad (\text{less than } 0.75) \]

- For \( \frac{3}{7} \):
\[ 3 \div 7 \approx 0.428 \quad (\text{less than } 0.75) \]

### Step 4: Compare the results
Now we compare the decimal values with the range \( (0.75, 1.5) \):

- \( \frac{6}{11} \approx 0.545 \) (not in range)
- \( \frac{6}{5} = 1.2 \) (in range)
- \( \frac{1}{4} = 0.25 \) (not in range)
- \( \frac{3}{7} \approx 0.428 \) (not in range)

### Conclusion
The only fraction that is greater than \( \frac{3}{4} \) and less than \( \frac{3}{2} \) is \( \frac{6}{5} \).

### Final Answer
The correct option is \( \frac{6}{5} \).

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