What will come in the place of question mark (?) in following questions?
`5(6)/(7) + 8(2)/(14)+9(1)/(7)`= ?

Options

A. `22(3)/(7)`
B. `23(1)/(7)`
C. `24(2)/(7)`
D. `26(1)/(14)`

Answer

To solve the expression \(5\frac{6}{7} + 8\frac{2}{14} + 9\frac{1}{7}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.

1. For \(5\frac{6}{7}\):
\[ 5\frac{6}{7} = \frac{5 \times 7 + 6}{7} = \frac{35 + 6}{7} = \frac{41}{7} \]

2. For \(8\frac{2}{14}\):
\[ 8\frac{2}{14} = \frac{8 \times 14 + 2}{14} = \frac{112 + 2}{14} = \frac{114}{14} \]
We can simplify \(\frac{114}{14}\) by dividing both the numerator and denominator by 2:
\[ \frac{114 \div 2}{14 \div 2} = \frac{57}{7} \]

3. For \(9\frac{1}{7}\):
\[ 9\frac{1}{7} = \frac{9 \times 7 + 1}{7} = \frac{63 + 1}{7} = \frac{64}{7} \]

### Step 2: Add the Improper Fractions
Now we can add the three improper fractions:
\[ \frac{41}{7} + \frac{57}{7} + \frac{64}{7} \]

Since they have the same denominator, we can simply add the numerators:
\[ \frac{41 + 57 + 64}{7} = \frac{162}{7} \]

### Step 3: Convert the Improper Fraction Back to a Mixed Number
To convert \(\frac{162}{7}\) back to a mixed number:
1. Divide 162 by 7:
\[ 162 \div 7 = 23 \quad \text{(whole number)} \]
The remainder is:
\[ 162 - (23 \times 7) = 162 - 161 = 1 \]
Thus, we can express it as:
\[ 23\frac{1}{7} \]

### Final Answer
The answer to the expression \(5\frac{6}{7} + 8\frac{2}{14} + 9\frac{1}{7}\) is:
\[ \boxed{23\frac{1}{7}} \]