Which of the following fractions lie between `(1)/(5)` and `(1)/(4)`
`A 7/33, B 4/11 , C 13/57 , D 7/17`

Options

A. A and B
B. A and C
C. B,C and D
D. A,B and D

Explanation

To determine which of the given fractions lies between \( \frac{1}{5} \) and \( \frac{1}{4} \), we can follow these steps:

### Step 1: Convert \( \frac{1}{5} \) and \( \frac{1}{4} \) to decimal form.
- \( \frac{1}{5} = 0.2 \)
- \( \frac{1}{4} = 0.25 \)

### Step 2: List the given fractions.
- A: \( \frac{7}{33} \)
- B: \( \frac{4}{11} \)
- C: \( \frac{13}{57} \)
- D: \( \frac{7}{17} \)

### Step 3: Convert each fraction to decimal form.
1. **For A: \( \frac{7}{33} \)**
\[ \frac{7}{33} \approx 0.2121 \quad (\text{approximately}) \]

2. **For B: \( \frac{4}{11} \)**
\[ \frac{4}{11} \approx 0.3636 \quad (\text{approximately}) \]

3. **For C: \( \frac{13}{57} \)**
\[ \frac{13}{57} \approx 0.2281 \quad (\text{approximately}) \]

4. **For D: \( \frac{7}{17} \)**
\[ \frac{7}{17} \approx 0.4118 \quad (\text{approximately}) \]

### Step 4: Compare the decimal values with \( 0.2 \) and \( 0.25 \).
- \( 0.2 < 0.2121 < 0.25 \) (A is between)
- \( 0.2 < 0.3636 \) (B is not between)
- \( 0.2 < 0.2281 < 0.25 \) (C is between)
- \( 0.4118 > 0.25 \) (D is not between)

### Conclusion:
The fractions that lie between \( \frac{1}{5} \) and \( \frac{1}{4} \) are:
- A: \( \frac{7}{33} \)
- C: \( \frac{13}{57} \)

### Final Answer:
The correct options are A and C.

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