In each question, what will come in place of question mark?
`12 2/3 – 5 1/3 div 6 2/3 = ?`

Options

A. 8
B. `6 1/3`
C. `5 2/3`
D. None of these

Answer

To solve the equation \( 12 \frac{2}{3} - 5 \frac{1}{3} \div 6 \frac{2}{3} = ? \), we will follow the order of operations (BODMAS/BIDMAS rules).

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

1. \( 12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3} \)
2. \( 5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \)
3. \( 6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \)

Now, the equation looks like this:
\[ \frac{38}{3} - \frac{16}{3} \div \frac{20}{3} \]

### Step 2: Perform Division
Next, we perform the division \( \frac{16}{3} \div \frac{20}{3} \). Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{16}{3} \div \frac{20}{3} = \frac{16}{3} \times \frac{3}{20} = \frac{16 \times 3}{3 \times 20} = \frac{16}{20} = \frac{4}{5} \]

### Step 3: Substitute Back into the Equation
Now, substitute back into the equation:
\[ \frac{38}{3} - \frac{4}{5} \]

### Step 4: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple of 3 and 5 is 15.

Convert both fractions:
1. \( \frac{38}{3} = \frac{38 \times 5}{3 \times 5} = \frac{190}{15} \)
2. \( \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15} \)

### Step 5: Perform the Subtraction
Now we can subtract:
\[ \frac{190}{15} - \frac{12}{15} = \frac{190 - 12}{15} = \frac{178}{15} \]

### Final Answer
Thus, the answer to the equation \( 12 \frac{2}{3} - 5 \frac{1}{3} \div 6 \frac{2}{3} = ? \) is:
\[ \frac{178}{15} \]