What will come in the place of (?) mark in following question.
`8 (1)/(2) - 4 (5)/(6) = ? - 3 (7)/(12)`

Options

A. `3 (1)/(4)`
B. `3 (5)/(12)`
C. `2 (7)/(12)`
D. `7 (1)/(4)`

Answer

To solve the equation \( 8 \frac{1}{2} - 4 \frac{5}{6} = ? - 3 \frac{7}{12} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For \( 8 \frac{1}{2} \):
\[ 8 \frac{1}{2} = 8 \times 2 + 1 = 16 + 1 = 17 \Rightarrow \frac{17}{2} \]

- For \( 4 \frac{5}{6} \):
\[ 4 \frac{5}{6} = 4 \times 6 + 5 = 24 + 5 = 29 \Rightarrow \frac{29}{6} \]

- For \( 3 \frac{7}{12} \):
\[ 3 \frac{7}{12} = 3 \times 12 + 7 = 36 + 7 = 43 \Rightarrow \frac{43}{12} \]

### Step 2: Rewrite the Equation
Now, we can rewrite the equation using the improper fractions:
\[ \frac{17}{2} - \frac{29}{6} = ? - \frac{43}{12} \]

### Step 3: Find a Common Denominator
To subtract the fractions on the left side, we need a common denominator. The least common multiple of 2 and 6 is 6.

- Convert \( \frac{17}{2} \) to have a denominator of 6:
\[ \frac{17}{2} = \frac{17 \times 3}{2 \times 3} = \frac{51}{6} \]

Now, we can rewrite the equation:
\[ \frac{51}{6} - \frac{29}{6} = ? - \frac{43}{12} \]

### Step 4: Perform the Subtraction
Now, we can subtract the fractions on the left side:
\[ \frac{51}{6} - \frac{29}{6} = \frac{51 - 29}{6} = \frac{22}{6} = \frac{11}{3} \]

### Step 5: Rewrite the Equation Again
Now, we have:
\[ \frac{11}{3} = ? - \frac{43}{12} \]

### Step 6: Isolate the Question Mark
To isolate the question mark, we can add \( \frac{43}{12} \) to both sides:
\[ ? = \frac{11}{3} + \frac{43}{12} \]

### Step 7: Find a Common Denominator Again
The least common multiple of 3 and 12 is 12. Convert \( \frac{11}{3} \) to have a denominator of 12:
\[ \frac{11}{3} = \frac{11 \times 4}{3 \times 4} = \frac{44}{12} \]

### Step 8: Perform the Addition
Now we can add the fractions:
\[ ? = \frac{44}{12} + \frac{43}{12} = \frac{44 + 43}{12} = \frac{87}{12} \]

### Step 9: Convert Back to Mixed Number
Now, convert \( \frac{87}{12} \) back to a mixed number:
\[ 87 \div 12 = 7 \quad \text{(with a remainder of 3)} \]
So, \( \frac{87}{12} = 7 \frac{3}{12} = 7 \frac{1}{4} \).

### Final Answer
Therefore, the value that comes in place of the question mark is:
\[ \boxed{7 \frac{1}{4}} \]