Find the sum
`1(3)/(5) + 2(4)/(5)`

Answer

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

### Step 1: Convert the mixed numbers to improper fractions
A mixed number consists of a whole number and a fraction. To convert a mixed number to an improper fraction, we use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \div \text{Denominator} \]

For \( 1\frac{3}{5} \):
\[ 1\frac{3}{5} = \left(1 \times 5 + 3\right) / 5 = \frac{5 + 3}{5} = \frac{8}{5} \]

For \( 2\frac{4}{5} \):
\[ 2\frac{4}{5} = \left(2 \times 5 + 4\right) / 5 = \frac{10 + 4}{5} = \frac{14}{5} \]

### Step 2: Add the improper fractions
Now we can add the two improper fractions:
\[ \frac{8}{5} + \frac{14}{5} \]
Since the denominators are the same, we can add the numerators directly:
\[ = \frac{8 + 14}{5} = \frac{22}{5} \]

### Step 3: Convert back to a mixed number (if necessary)
To convert \( \frac{22}{5} \) back to a mixed number, we divide the numerator by the denominator:
\[ 22 \div 5 = 4 \quad \text{(whole number)} \]
The remainder is:
\[ 22 - (5 \times 4) = 22 - 20 = 2 \]
Thus, we can write:
\[ \frac{22}{5} = 4\frac{2}{5} \]

### Final Answer
The sum of \( 1\frac{3}{5} + 2\frac{4}{5} \) is \( 4\frac{2}{5} \).

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