`16-2-:7+6xx2=?`

Options

A. `16`
B. `14`
C. `27(5)/(7)`
D. none of these

Answer

To solve the expression \( 16 - 2 \div 7 + 6 \times 2 \), we will follow the BODMAS/BIDMAS rule, which stands for Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

### Step-by-Step Solution:

1. **Identify the operations**: The expression contains subtraction, division, addition, and multiplication.
\[ 16 - 2 \div 7 + 6 \times 2 \]

2. **Perform division and multiplication first**:
- Calculate \( 2 \div 7 \):
\[ 2 \div 7 = \frac{2}{7} \]
- Calculate \( 6 \times 2 \):
\[ 6 \times 2 = 12 \]

Now the expression looks like this:
\[ 16 - \frac{2}{7} + 12 \]

3. **Convert whole numbers to fractions**: To perform addition and subtraction, we can convert the whole numbers into fractions with a common denominator. The common denominator for \( 16 \) and \( 12 \) with \( \frac{2}{7} \) is \( 7 \).
- Convert \( 16 \) to a fraction:
\[ 16 = \frac{16 \times 7}{7} = \frac{112}{7} \]
- Convert \( 12 \) to a fraction:
\[ 12 = \frac{12 \times 7}{7} = \frac{84}{7} \]

Now the expression is:
\[ \frac{112}{7} - \frac{2}{7} + \frac{84}{7} \]

4. **Combine the fractions**: Since all fractions have the same denominator, we can combine them:
\[ \frac{112 - 2 + 84}{7} = \frac{194}{7} \]

5. **Convert the improper fraction to a mixed number**: To convert \( \frac{194}{7} \) into a mixed number:
- Divide \( 194 \) by \( 7 \):
\[ 194 \div 7 = 27 \quad \text{(whole number)} \]
- Calculate the remainder:
\[ 194 - (27 \times 7) = 194 - 189 = 5 \]
- Thus, we can express it as:
\[ 27 \frac{5}{7} \]

### Final Answer:
\[ 16 - 2 \div 7 + 6 \times 2 = 27 \frac{5}{7} \]