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 into 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, the expression becomes:

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

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 5, 10, and 3 is

3

0. 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 the expression is:

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

Combine the fractions:

$\frac{12 - 69 - 40}{30} = \frac{12 - (69 + 40)}{30} = \frac{12 - 109}{30} = \frac{-97}{30}$

We can write this improper fraction as a mixed number:

$-\frac{97}{30} = -\frac{3 \times 30 + 7}{30} = -3\frac{7}{30}$

3. Final Answer

$-3\frac{7}{30}$