The value of `(5-2div4xx[5-(3-4)]+5xx4div2" of "4)/(4+4div8" of "2xx(8-5)xx2div3-8div2" of "8)` is

Options

A. `{:(9)/(8):}`
B. `{:(9)/(4):}`
C. `{:(15)/(32):}`
D. `{:(89)/(4):}`

Answer

To solve the expression \( \frac{5 - 2 \div 4 \text{ of } [5 - (3 - 4)] + 5 \times 4 \div 2 \text{ of } 4}{4 + 4 \div 8 \text{ of } 2 \times (8 - 5) \times 2 \div 3 - 8 \div 2 \text{ of } 8} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Solve the innermost brackets
First, we simplify the expression inside the brackets:
- For the numerator:
- \( 3 - 4 = -1 \)
- So, \( 5 - (-1) = 5 + 1 = 6 \)

- For the denominator:
- \( 8 - 5 = 3 \)

Now, we can rewrite the expression as:
\[ \frac{5 - 2 \div 4 \text{ of } 6 + 5 \times 4 \div 2 \text{ of } 4}{4 + 4 \div 8 \text{ of } 2 \times 3 \times 2 \div 3 - 8 \div 2 \text{ of } 8} \]

### Step 2: Solve the 'of' operations
Next, we handle the 'of' operations (which means multiplication):
- In the numerator:
- \( 2 \text{ of } 4 = 2 \times 4 = 8 \)
- \( 5 \text{ of } 4 = 5 \times 4 = 20 \)

So, the numerator becomes:
\[ 5 - 2 \div 8 + 20 \div 2 \]

- In the denominator:
- \( 4 \text{ of } 8 = 4 \times 8 = 32 \)
- \( 4 \text{ of } 2 = 4 \times 2 = 8 \)

Now, the denominator becomes:
\[ 4 + 4 \div 32 \times 3 \times 2 \div 3 - 8 \div 16 \]

### Step 3: Solve the divisions
Now we perform the divisions:
- In the numerator:
- \( 2 \div 8 = \frac{1}{4} \)
- \( 20 \div 2 = 10 \)

So, the numerator is:
\[ 5 - \frac{1}{4} + 10 = 15 - \frac{1}{4} = \frac{60 - 1}{4} = \frac{59}{4} \]

- In the denominator:
- \( 4 \div 32 = \frac{1}{8} \)
- \( 8 \div 16 = \frac{1}{2} \)

So, the denominator becomes:
\[ 4 + \frac{1}{8} \times 3 \times 2 \div 3 - \frac{1}{2} \]
Since \( \frac{1}{8} \times 3 \times 2 \div 3 = \frac{1}{8} \times 2 = \frac{1}{4} \), the denominator is:
\[ 4 + \frac{1}{4} - \frac{1}{2} = 4 + \frac{1}{4} - \frac{2}{4} = 4 - \frac{1}{4} = \frac{16 - 1}{4} = \frac{15}{4} \]

### Step 4: Final division
Now we have:
\[ \frac{\frac{59}{4}}{\frac{15}{4}} = \frac{59}{15} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{59}{15} \]