We are asked to evaluate the expression $\frac{2}{5} + 2\frac{3}{10} - 1\frac{1}{3}$.

1. Problem Description

We are asked to evaluate the expression $\frac{2}{5} + 2\frac{3}{10} - 1\frac{1}{3}$.

2. Solution Steps

First, convert the mixed numbers to improper fractions:

$2\frac{3}{10} = \frac{2 \times 10 + 3}{10} = \frac{20 + 3}{10} = \frac{23}{10}$

$1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$

So, the expression becomes:

$\frac{2}{5} + \frac{23}{10} - \frac{4}{3}$

Find a common denominator. The least common multiple of 5, 10, and 3 is

3

0. Convert each fraction to have a denominator of 30:

$\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}$

$\frac{23}{10} = \frac{23 \times 3}{10 \times 3} = \frac{69}{30}$

$\frac{4}{3} = \frac{4 \times 10}{3 \times 10} = \frac{40}{30}$

Now, we can rewrite the expression as:

$\frac{12}{30} + \frac{69}{30} - \frac{40}{30}$

Combine the fractions:

$\frac{12 + 69 - 40}{30} = \frac{81 - 40}{30} = \frac{41}{30}$

Now, we can express the result as a mixed number:

$\frac{41}{30} = 1\frac{11}{30}$

3. Final Answer

$1\frac{11}{30}$