What is the value of :
`(12 " "of" "6 div 9 + 12 xx 4 -(2xx 4 - 5))/(12 div 3 xx 4 (2 xx 4 - 5)) ?`

Options

A. `(27)/(22)`
B. `(53)/(48)`
C. `(27)/(19)`
D. `(21)/(9)`

Answer

To solve the expression \((12 \text{ of } 6 \div 9 + 12 \times 4 - (2 \times 4 - 5)) / (12 \div 3 \times 4 (2 \times 4 - 5))\), we will break it down step by step.

### Step 1: Simplify the expression inside the parentheses
First, we need to simplify the expression \(2 \times 4 - 5\):
\[ 2 \times 4 = 8 \]
\[ 8 - 5 = 3 \]
So, \(2 \times 4 - 5 = 3\).

### Step 2: Substitute back into the main expression
Now we can substitute this value back into the main expression:
\[ (12 \text{ of } 6 \div 9 + 12 \times 4 - 3) / (12 \div 3 \times 4 \times 3) \]

### Step 3: Calculate \(12 \text{ of } 6\)
The term \(12 \text{ of } 6\) can be interpreted as \(12 \times 6\):
\[ 12 \times 6 = 72 \]

### Step 4: Continue simplifying the numerator
Now we can rewrite the numerator:
\[ (72 \div 9 + 12 \times 4 - 3) \]
Calculate \(72 \div 9\):
\[ 72 \div 9 = 8 \]
Calculate \(12 \times 4\):
\[ 12 \times 4 = 48 \]
Now substitute these values back:
\[ (8 + 48 - 3) \]
Calculate \(8 + 48 - 3\):
\[ 8 + 48 = 56 \]
\[ 56 - 3 = 53 \]
So, the numerator simplifies to \(53\).

### Step 5: Simplify the denominator
Now we simplify the denominator:
\[ (12 \div 3 \times 4 \times 3) \]
Calculate \(12 \div 3\):
\[ 12 \div 3 = 4 \]
Now substitute this back:
\[ 4 \times 4 \times 3 \]
Calculate \(4 \times 4\):
\[ 4 \times 4 = 16 \]
Now calculate \(16 \times 3\):
\[ 16 \times 3 = 48 \]
So, the denominator simplifies to \(48\).

### Step 6: Combine the results
Now we can combine the results from the numerator and denominator:
\[ \frac{53}{48} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{53}{48} \]