The value of `5-: [ 5+8-{4+(4 "of" 2-: 4) -(2-: 4) - (2 -: 4 "of" 2 )}]` is

Options

A. `5//8`
B. `20//31`
C. `20//29`
D. `20//33`

Answer

To solve the expression \( 5 -: [ 5 + 8 - \{ 4 + (4 \text{ of } 2 -: 4) - (2 -: 4) - (2 -: 4 \text{ of } 2) \}] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the Expression**:
\[ 5 -: [ 5 + 8 - \{ 4 + (4 \text{ of } 2 -: 4) - (2 -: 4) - (2 -: 4 \text{ of } 2) \}] \]

2. **Calculate "of"**:
The term "of" in this context means multiplication. Therefore, we first calculate \( 4 \text{ of } 2 \) and \( 2 \text{ of } 2 \):
\[ 4 \text{ of } 2 = 4 \times 2 = 8 \]

3. **Rewrite the Expression**:
Substitute the calculated values back into the expression:
\[ 5 -: [ 5 + 8 - \{ 4 + (8 -: 4) - (2 -: 4) - (2 -: 8) \}] \]

4. **Calculate the Divisions**:
Now, calculate the divisions:
- \( 8 -: 4 = 2 \)
- \( 2 -: 4 = 0.5 \)
- \( 2 -: 8 = 0.25 \)

5. **Rewrite the Expression Again**:
Substitute these values back:
\[ 5 -: [ 5 + 8 - \{ 4 + 2 - 0.5 - 0.25 \}] \]

6. **Calculate Inside the Curly Brackets**:
Now simplify inside the curly brackets:
\[ 4 + 2 - 0.5 - 0.25 = 4 + 2 - 0.75 = 5.25 \]

7. **Rewrite the Expression**:
Substitute this value back:
\[ 5 -: [ 5 + 8 - 5.25 ] \]

8. **Calculate the Square Bracket**:
Now simplify inside the square brackets:
\[ 5 + 8 - 5.25 = 13 - 5.25 = 7.75 \]

9. **Final Calculation**:
Now we perform the division:
\[ 5 -: 7.75 = \frac{5}{7.75} = \frac{5 \times 100}{775} = \frac{500}{775} = \frac{20}{31} \]

10. **Final Answer**:
The final value of the expression is:
\[ \frac{20}{31} \]