`1(3)/(5) +5(1)/(3) + 3(2)/(5)` =?

Options

A. `9(2)/(5)`
B. `9(29)/(60)`
C. `10(2)/(5)`
D. `10(1)/(3)`

Answer

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

### Step 1: Convert Mixed Numbers to Improper Fractions
We start by converting each mixed number into an improper fraction.

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

2. **Convert \(5 \frac{1}{3}\)**:
\[ 5 \frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \]

3. **Convert \(3 \frac{2}{5}\)**:
\[ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} \]

### Step 2: Rewrite the Expression
Now, we can rewrite the original expression using these improper fractions:
\[ \frac{8}{5} + \frac{16}{3} + \frac{17}{5} \]

### Step 3: Combine Like Terms
Next, we will combine the fractions with the same denominator:
\[ \frac{8}{5} + \frac{17}{5} = \frac{8 + 17}{5} = \frac{25}{5} = 5 \]

Now, we have:
\[ 5 + \frac{16}{3} \]

### Step 4: Add the Whole Number and the Fraction
To add \(5\) and \(\frac{16}{3}\), we convert \(5\) into a fraction with a denominator of \(3\):
\[ 5 = \frac{5 \times 3}{3} = \frac{15}{3} \]

Now, we can add:
\[ \frac{15}{3} + \frac{16}{3} = \frac{15 + 16}{3} = \frac{31}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{31}{3} \]