`1/3+[4 3/4-(3 1/6-2 1/3)]`
The value of `(1/5" of "5div 1/5)div(1/5 div 1/5 xx 1/5)` lies between :

Options

A. `10.2` and `10.8`
B. `4.2` and `4.4`
C. `8.2` and `8.8`
D. `0.4` and `0.9`

Answer

To solve the expression \( \frac{1}{3} + \left[ 4 \frac{3}{4} - \left( 3 \frac{1}{6} - 2 \frac{1}{3} \right) \right] \), we will follow the order of operations (BODMAS/BIDMAS) which stands for Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction.

### Step-by-Step Solution:

1. **Convert Mixed Numbers to Improper Fractions:**
- \( 4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \)
- \( 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \)
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \)

2. **Substitute the Improper Fractions into the Expression:**
\[ \frac{1}{3} + \left[ \frac{19}{4} - \left( \frac{19}{6} - \frac{7}{3} \right) \right] \]

3. **Solve the Inner Bracket:**
- To subtract \( \frac{19}{6} - \frac{7}{3} \), we need a common denominator. The LCM of 6 and 3 is 6.
- Convert \( \frac{7}{3} \) to sixths: \( \frac{7}{3} = \frac{14}{6} \)
- Now, perform the subtraction:
\[ \frac{19}{6} - \frac{14}{6} = \frac{5}{6} \]

4. **Substitute Back into the Expression:**
\[ \frac{1}{3} + \left[ \frac{19}{4} - \frac{5}{6} \right] \]

5. **Solve the Larger Bracket:**
- To subtract \( \frac{19}{4} - \frac{5}{6} \), we need a common denominator. The LCM of 4 and 6 is 12.
- Convert both fractions:
- \( \frac{19}{4} = \frac{57}{12} \) (since \( 19 \times 3 = 57 \))
- \( \frac{5}{6} = \frac{10}{12} \) (since \( 5 \times 2 = 10 \))
- Now, perform the subtraction:
\[ \frac{57}{12} - \frac{10}{12} = \frac{47}{12} \]

6. **Final Addition:**
- Now we add \( \frac{1}{3} + \frac{47}{12} \).
- Convert \( \frac{1}{3} \) to twelfths: \( \frac{1}{3} = \frac{4}{12} \)
- Now add:
\[ \frac{4}{12} + \frac{47}{12} = \frac{51}{12} \]

7. **Convert to Mixed Number:**
- \( \frac{51}{12} = 4 \frac{3}{12} = 4 \frac{1}{4} \)

8. **Decimal Conversion:**
- The decimal value of \( 4 \frac{1}{4} = 4.25 \).

### Conclusion:
The final value of the expression is \( 4.25 \).