The problem is to evaluate the expression $\frac{2}{5} - 2\frac{3}{10} + 1\frac{1}{3}$.

1. Problem Description

The problem is to evaluate the expression $\frac{2}{5} - 2\frac{3}{10} + 1\frac{1}{3}$.

2. Solution Steps

First, we convert the mixed numbers to improper fractions.

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

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

Now we rewrite the expression:

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

To add or subtract fractions, we need a common denominator. The least common multiple of 5, 10, and 3 is

3

0. We convert each fraction to an equivalent fraction with a denominator of

3

0.

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

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

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

Now we have:

$\frac{12}{30} - \frac{69}{30} + \frac{40}{30} = \frac{12 - 69 + 40}{30} = \frac{-57 + 40}{30} = \frac{-17}{30}$

3. Final Answer

The final answer is $-\frac{17}{30}$.