Solve: 4/11 + 2/7 + 3/5

Options

A. 37/35
B. 481/385
C. 13/35
D. 37/385

Answer

To solve the expression \( \frac{4}{11} + \frac{2}{7} + \frac{3}{5} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
We need to find the LCM of the denominators 11, 7, and 5.

- The prime factors of 11 are \( 11^1 \).
- The prime factors of 7 are \( 7^1 \).
- The prime factors of 5 are \( 5^1 \).

Since all these numbers are prime, the LCM is simply the product of these numbers:
\[ \text{LCM} = 11 \times 7 \times 5 = 385 \]

### Step 2: Convert Each Fraction to Have the Common Denominator
Now we will convert each fraction to have the denominator of 385.

1. For \( \frac{4}{11} \):
\[ \frac{4}{11} = \frac{4 \times 35}{11 \times 35} = \frac{140}{385} \]
(since \( 385 \div 11 = 35 \))

2. For \( \frac{2}{7} \):
\[ \frac{2}{7} = \frac{2 \times 55}{7 \times 55} = \frac{110}{385} \]
(since \( 385 \div 7 = 55 \))

3. For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 77}{5 \times 77} = \frac{231}{385} \]
(since \( 385 \div 5 = 77 \))

### Step 3: Add the Converted Fractions
Now we can add the fractions:
\[ \frac{140}{385} + \frac{110}{385} + \frac{231}{385} = \frac{140 + 110 + 231}{385} \]

Calculating the numerator:
\[ 140 + 110 + 231 = 481 \]

So, we have:
\[ \frac{481}{385} \]

### Final Answer
Thus, the solution to \( \frac{4}{11} + \frac{2}{7} + \frac{3}{5} \) is:
\[ \frac{481}{385} \]