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, convert the mixed numbers to improper fractions.

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

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

The expression becomes:

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

Find a common denominator for 5, 10, and

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

3

0.

Convert each fraction to an equivalent fraction with a denominator of

3

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

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

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

The expression is now:

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

Combine the fractions:

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

The answer is $-\frac{41}{30}$.

We can express this as a mixed number:

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

3. Final Answer

$-\frac{41}{30}$ or $-1\frac{11}{30}$