`2(1)/(7)-3(1)/(14)+2(2)/(7)=?`

Options

A. `6(5)/(14)`
B. `4(5)/(14)`
C. `2(3)/(14)`
D. None of these

Explanation

To solve the expression \( 2\frac{1}{7} - 3\frac{1}{14} + 2\frac{2}{7} \), we will convert the mixed numbers into improper fractions and then perform the operations step by step.

### Step 1: Convert mixed numbers to improper fractions
1. Convert \( 2\frac{1}{7} \):
\[ 2\frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7} \]

2. Convert \( 3\frac{1}{14} \):
\[ 3\frac{1}{14} = \frac{3 \times 14 + 1}{14} = \frac{42 + 1}{14} = \frac{43}{14} \]

3. Convert \( 2\frac{2}{7} \):
\[ 2\frac{2}{7} = \frac{2 \times 7 + 2}{7} = \frac{14 + 2}{7} = \frac{16}{7} \]

### Step 2: Rewrite the expression
Now, we can rewrite the expression using the improper fractions:
\[ \frac{15}{7} - \frac{43}{14} + \frac{16}{7} \]

### Step 3: Find a common denominator
The least common multiple (LCM) of 7 and 14 is 14. We will convert all fractions to have a denominator of 14:
- For \( \frac{15}{7} \):
\[ \frac{15}{7} = \frac{15 \times 2}{7 \times 2} = \frac{30}{14} \]
- For \( \frac{43}{14} \), it remains the same:
\[ \frac{43}{14} = \frac{43}{14} \]
- For \( \frac{16}{7} \):
\[ \frac{16}{7} = \frac{16 \times 2}{7 \times 2} = \frac{32}{14} \]

### Step 4: Combine the fractions
Now we can combine the fractions:
\[ \frac{30}{14} - \frac{43}{14} + \frac{32}{14} = \frac{30 - 43 + 32}{14} = \frac{19}{14} \]

### Step 5: Final answer
The final answer is:
\[ \frac{19}{14} \]