To add mixed numbers, follow a systematic approach: first, add the whole numbers, then the fractions, and simplify if necessary.

Begin by separating the whole numbers from the fractional components. For instance, when adding $2 \frac{1}{3}$ and $1 \frac{2}{5}$, first calculate the sum of the whole numbers:

Next, focus on adding the fractional parts. To combine $\frac{1}{3}$ and $\frac{2}{5}$, you will need to find a common denominator. The denominators in this case are $3$ and $5$, and the least common multiple (LCM) is $15$. Convert each fraction to this common denominator:

Now you can add the fractions:

Combine the sum of the whole numbers with the sum of the fractions:

This results in the mixed number:

If the fractional part of your result is an improper fraction (where the numerator exceeds the denominator), convert it into a mixed number and add any additional whole number to the existing whole number part. For example, if you had $\frac{17}{15}$, you would convert it to $1 \frac{2}{15}$, adding the $1$ to the whole number part.

Always remember to simplify the fractions when possible. This step-by-step method ensures accurate addition of mixed numbers.