What value will come in place of question mark (?) in the questions given below?
`2 4/12 - 9/7 + 4 1/14 = ?`

Options

A. `5 4/42`
B. `5 4/43`
C. `5 5/42`
D. `4 13/42`

Answer

To solve the equation \(2 \frac{4}{12} - \frac{9}{7} + 4 \frac{1}{14} = ?\), we will follow these steps:

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

1. **Convert \(2 \frac{4}{12}\)**:
\[ 2 \frac{4}{12} = \frac{2 \times 12 + 4}{12} = \frac{24 + 4}{12} = \frac{28}{12} \]
We can simplify \(\frac{28}{12}\) to \(\frac{7}{3}\) (dividing both numerator and denominator by 4).

2. **Convert \(4 \frac{1}{14}\)**:
\[ 4 \frac{1}{14} = \frac{4 \times 14 + 1}{14} = \frac{56 + 1}{14} = \frac{57}{14} \]

Now, we can rewrite the equation as:
\[ \frac{7}{3} - \frac{9}{7} + \frac{57}{14} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators (3, 7, and 14).

- The prime factorization is:
- \(3 = 3^1\)
- \(7 = 7^1\)
- \(14 = 2^1 \times 7^1\)

The LCM is:
\[ LCM = 2^1 \times 3^1 \times 7^1 = 42 \]

### Step 3: Convert Each Fraction to Have the Same Denominator
Now we convert each fraction to have a denominator of 42.

1. **Convert \(\frac{7}{3}\)**:
\[ \frac{7}{3} = \frac{7 \times 14}{3 \times 14} = \frac{98}{42} \]

2. **Convert \(\frac{9}{7}\)**:
\[ \frac{9}{7} = \frac{9 \times 6}{7 \times 6} = \frac{54}{42} \]

3. **Convert \(\frac{57}{14}\)**:
\[ \frac{57}{14} = \frac{57 \times 3}{14 \times 3} = \frac{171}{42} \]

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{98}{42} - \frac{54}{42} + \frac{171}{42} = \frac{98 - 54 + 171}{42} \]

Calculating the numerator:
\[ 98 - 54 = 44 \quad \text{and} \quad 44 + 171 = 215 \]
So, we have:
\[ \frac{215}{42} \]

### Step 5: Convert to Mixed Number
Now we convert \(\frac{215}{42}\) to a mixed number:
\[ 215 \div 42 = 5 \quad \text{(since \(42 \times 5 = 210\))} \]
The remainder is:
\[ 215 - 210 = 5 \]
Thus, we can write:
\[ \frac{215}{42} = 5 \frac{5}{42} \]

### Final Answer
The value that comes in place of the question mark (?) is:
\[ 5 \frac{5}{42} \]