What will come in place of question mark(?) in the following questions?
`7(11)/(12)xx6(7)/(19)div7(1)/3xx8/(11)=?`

Options

A. 9
B. 11
C. 2
D. 5

Answer

To solve the equation \( 7\frac{11}{12} \times 6\frac{7}{19} \div 7\frac{1}{3} \times \frac{8}{11} = ? \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert each mixed number into an improper fraction.

1. \( 7\frac{11}{12} = \frac{7 \times 12 + 11}{12} = \frac{84 + 11}{12} = \frac{95}{12} \)
2. \( 6\frac{7}{19} = \frac{6 \times 19 + 7}{19} = \frac{114 + 7}{19} = \frac{121}{19} \)
3. \( 7\frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3} \)

Now we can rewrite the equation as:
\[ \frac{95}{12} \times \frac{121}{19} \div \frac{22}{3} \times \frac{8}{11} \]

### Step 2: Change Division to Multiplication
To change the division into multiplication, we multiply by the reciprocal of the fraction:
\[ \frac{95}{12} \times \frac{121}{19} \times \frac{3}{22} \times \frac{8}{11} \]

### Step 3: Simplify the Expression
Now we can simplify the expression step by step.

1. Combine the fractions:
\[ \frac{95 \times 121 \times 3 \times 8}{12 \times 19 \times 22 \times 11} \]

2. Factor and cancel common terms:
- \( 95 = 5 \times 19 \)
- \( 121 = 11 \times 11 \)
- \( 12 = 4 \times 3 \)
- \( 22 = 2 \times 11 \)

Now substituting these back into the equation:
\[ \frac{(5 \times 19) \times (11 \times 11) \times 3 \times 8}{(4 \times 3) \times 19 \times (2 \times 11) \times 11} \]

3. Cancel out common factors:
- \( 19 \) cancels with \( 19 \)
- \( 11 \) cancels with one \( 11 \)
- \( 3 \) cancels with \( 3 \)

This simplifies to:
\[ \frac{5 \times 11 \times 8}{4 \times 2 \times 11} \]

4. Further simplify:
- \( 11 \) cancels with \( 11 \)
- \( 8 \div 4 = 2 \)
- \( 2 \div 2 = 1 \)

Now we are left with:
\[ 5 \times 1 = 5 \]

### Final Answer
Thus, the value at the question mark is:
\[ ? = 5 \]