What well Centre in place of the question mark (?) in the following questions?
`(11)/(13 ) + (6)/(26 ) + (3)/(52 ) =?`

Options

A. `3`
B. `1`
C. `1(7)/(52)`
D. ` 3 (5)/(28)`

Answer

To solve the equation \( \frac{11}{13} + \frac{6}{26} + \frac{3}{52} = ? \), we will follow these steps:

### Step 1: Identify the denominators
The denominators of the fractions are 13, 26, and 52.

### Step 2: Find the Least Common Multiple (LCM)
To add the fractions, we need a common denominator. The LCM of 13, 26, and 52 can be calculated as follows:
- The prime factorization of 13 is \( 13^1 \).
- The prime factorization of 26 is \( 2^1 \times 13^1 \).
- The prime factorization of 52 is \( 2^2 \times 13^1 \).

The LCM is obtained by taking the highest power of each prime:
- For 2, the highest power is \( 2^2 \).
- For 13, the highest power is \( 13^1 \).

Thus, the LCM is \( 2^2 \times 13^1 = 4 \times 13 = 52 \).

### Step 3: Rewrite each fraction with the common denominator
Now we will convert each fraction to have the denominator of 52:
- For \( \frac{11}{13} \):
\[ \frac{11}{13} = \frac{11 \times 4}{13 \times 4} = \frac{44}{52} \]
- For \( \frac{6}{26} \):
\[ \frac{6}{26} = \frac{6 \times 2}{26 \times 2} = \frac{12}{52} \]
- For \( \frac{3}{52} \), it remains \( \frac{3}{52} \).

### Step 4: Add the fractions
Now we can add the fractions:
\[ \frac{44}{52} + \frac{12}{52} + \frac{3}{52} = \frac{44 + 12 + 3}{52} = \frac{59}{52} \]

### Step 5: Convert to a mixed number
To convert \( \frac{59}{52} \) into a mixed number:
- Divide 59 by 52, which gives 1 with a remainder of 7.
- Thus, \( \frac{59}{52} = 1 \frac{7}{52} \).

### Final Answer
The value of the question mark (?) is:
\[ 1 \frac{7}{52} \]

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