What should come in place of the question mark (?) in the following questions ?
1 4/7 + 1 3/5 + 1 1/3 = ?

Options

A. (547)/(105)
B. (458)/(105)
C. (453)/(105)
D. (543)/(105)

Answer

To solve the problem \( 1 \frac{4}{7} + 1 \frac{3}{5} + 1 \frac{1}{3} = ? \), we will follow these steps:

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

1. For \( 1 \frac{4}{7} \):
\[ 1 \frac{4}{7} = \frac{7 \times 1 + 4}{7} = \frac{11}{7} \]

2. For \( 1 \frac{3}{5} \):
\[ 1 \frac{3}{5} = \frac{5 \times 1 + 3}{5} = \frac{8}{5} \]

3. For \( 1 \frac{1}{3} \):
\[ 1 \frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3} \]

### Step 2: Add the Improper Fractions
Now we need to add the fractions \( \frac{11}{7} + \frac{8}{5} + \frac{4}{3} \). To do this, we first find the least common multiple (LCM) of the denominators \( 7, 5, \) and \( 3 \).

### Step 3: Find the LCM of the Denominators
The LCM of \( 7, 5, \) and \( 3 \) is \( 105 \).

### Step 4: Convert Each Fraction to Have the Common Denominator
Now we convert each fraction to have a denominator of \( 105 \):

1. For \( \frac{11}{7} \):
\[ \frac{11}{7} = \frac{11 \times 15}{7 \times 15} = \frac{165}{105} \]

2. For \( \frac{8}{5} \):
\[ \frac{8}{5} = \frac{8 \times 21}{5 \times 21} = \frac{168}{105} \]

3. For \( \frac{4}{3} \):
\[ \frac{4}{3} = \frac{4 \times 35}{3 \times 35} = \frac{140}{105} \]

### Step 5: Add the Converted Fractions
Now we can add the fractions:
\[ \frac{165}{105} + \frac{168}{105} + \frac{140}{105} = \frac{165 + 168 + 140}{105} = \frac{473}{105} \]

### Step 6: Simplify the Result
The fraction \( \frac{473}{105} \) is already in its simplest form.

### Final Answer
Thus, the answer to the question is:
\[ \frac{473}{105} \]