What should come in place of the question mark (?) in the following questions:
`4 (1)/(3) + 3 (1)/(4) - 1 (1)/(12) = ?`

Options

A. `6 1/2`
B. `6 5/12`
C. `4 1/2`
D. `1 1/12`

Answer

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

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

- For \( 4 \frac{1}{3} \):
\[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \]

- For \( 3 \frac{1}{4} \):
\[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]

- For \( 1 \frac{1}{12} \):
\[ 1 \frac{1}{12} = \frac{1 \times 12 + 1}{12} = \frac{12 + 1}{12} = \frac{13}{12} \]

### Step 2: Rewrite the Equation
Now we can rewrite the equation using the improper fractions:
\[ \frac{13}{3} + \frac{13}{4} - \frac{13}{12} = ? \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators (3, 4, and 12). The LCM is 12.

### Step 4: Convert Each Fraction to Have a Common Denominator
Now we convert each fraction to have a denominator of 12:

- For \( \frac{13}{3} \):
\[ \frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12} \]

- For \( \frac{13}{4} \):
\[ \frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \]

- For \( \frac{13}{12} \):
\[ \frac{13}{12} = \frac{13}{12} \quad (\text{remains the same}) \]

### Step 5: Substitute Back into the Equation
Now we can substitute these back into the equation:
\[ \frac{52}{12} + \frac{39}{12} - \frac{13}{12} \]

### Step 6: Combine the Fractions
Combine the fractions:
\[ \frac{52 + 39 - 13}{12} = \frac{78}{12} \]

### Step 7: Simplify the Result
Now simplify \( \frac{78}{12} \):
\[ \frac{78 \div 6}{12 \div 6} = \frac{13}{2} \]

### Step 8: Convert Back to Mixed Number
Convert \( \frac{13}{2} \) back to a mixed number:
\[ \frac{13}{2} = 6 \frac{1}{2} \]

Thus, the final answer is:
\[ ? = 6 \frac{1}{2} \]