Work out the following :
`2""4/5+3""3/5`

Answer

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

### Step 1: Convert 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:
\[ \text{Improper Fraction} = ( \text{Whole Number} \times \text{Denominator} ) + \text{Numerator} \div \text{Denominator} \]

For \(2 \frac{4}{5}\):
- Whole Number = 2
- Numerator = 4
- Denominator = 5

Calculating:
\[ 2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]

For \(3 \frac{3}{5}\):
- Whole Number = 3
- Numerator = 3
- Denominator = 5

Calculating:
\[ 3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \]

### Step 2: Add the Improper Fractions
Now we can add the two improper fractions:
\[ \frac{14}{5} + \frac{18}{5} \]
Since the denominators are the same, we can add the numerators directly:
\[ = \frac{14 + 18}{5} = \frac{32}{5} \]

### Step 3: Convert the Improper Fraction Back to a Mixed Number
To convert \(\frac{32}{5}\) back to a mixed number, we divide the numerator by the denominator:
- \(32 \div 5 = 6\) (whole number part)
- Remainder: \(32 - (5 \times 6) = 32 - 30 = 2\)

So, we can express \(\frac{32}{5}\) as:
\[ 6 \frac{2}{5} \]

### Final Answer
Thus, the final answer is:
\[ 2 \frac{4}{5} + 3 \frac{3}{5} = 6 \frac{2}{5} \]

---