Find: `1(2)/(5)+2(1)/(3)`

Answer

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

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

For \(1 \frac{2}{5}\):
- Multiply the whole number (1) by the denominator (5): \(1 \times 5 = 5\)
- Add the numerator (2): \(5 + 2 = 7\)
- So, \(1 \frac{2}{5} = \frac{7}{5}\)

For \(2 \frac{1}{3}\):
- Multiply the whole number (2) by the denominator (3): \(2 \times 3 = 6\)
- Add the numerator (1): \(6 + 1 = 7\)
- So, \(2 \frac{1}{3} = \frac{7}{3}\)

### Step 2: Add the Improper Fractions
Now we need to add \(\frac{7}{5}\) and \(\frac{7}{3}\). To do this, we need a common denominator.

The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.

### Step 3: Convert Fractions to Have a Common Denominator
Now we convert both fractions to have the common denominator of 15.

For \(\frac{7}{5}\):
- Multiply the numerator and denominator by 3:
\[ \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \]

For \(\frac{7}{3}\):
- Multiply the numerator and denominator by 5:
\[ \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \]

### Step 4: Add the Converted Fractions
Now we can add the two fractions:
\[ \frac{21}{15} + \frac{35}{15} = \frac{21 + 35}{15} = \frac{56}{15} \]

### Step 5: Convert Back to Mixed Number (if required)
The fraction \(\frac{56}{15}\) can be converted back to a mixed number:
- Divide 56 by 15, which gives us 3 with a remainder of 11.
- So, \(\frac{56}{15} = 3 \frac{11}{15}\).

### Final Answer
Thus, \(1 \frac{2}{5} + 2 \frac{1}{3} = \frac{56}{15}\) or \(3 \frac{11}{15}\).

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