`2 (3)/(5) + 1 (4)/(5) + 3 (2)/(5`

Options

A. `=7(4)/(7)`
B. `=7(4)/(5)`
C. `=7(3)/(5)`
D. `=5(4)/(5)`

Answer

To solve the problem \(2 \frac{3}{5} + 1 \frac{4}{5} + 3 \frac{2}{5}\), we will follow these steps:

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

- For \(2 \frac{3}{5}\):
\[ 2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \]

- For \(1 \frac{4}{5}\):
\[ 1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5} \]

- For \(3 \frac{2}{5}\):
\[ 3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]

### Step 2: Add the Improper Fractions
Now we add the three improper fractions together:
\[ \frac{13}{5} + \frac{9}{5} + \frac{17}{5} \]

Since all fractions have the same denominator, we can add the numerators directly:
\[ \frac{13 + 9 + 17}{5} \]

### Step 3: Calculate the Sum of the Numerators
Now we calculate the sum of the numerators:
\[ 13 + 9 = 22 \]
\[ 22 + 17 = 39 \]

So, we have:
\[ \frac{39}{5} \]

### Step 4: Convert to Mixed Number (if needed)
To convert \(\frac{39}{5}\) back to a mixed number:
- Divide 39 by 5:
- \(39 \div 5 = 7\) remainder \(4\)

Thus, we can express \(\frac{39}{5}\) as:
\[ 7 \frac{4}{5} \]

### Final Answer
The final answer is:
\[ \frac{39}{5} \text{ or } 7 \frac{4}{5} \]

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