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The problem you're working on asks for the result of:

\[
-1 \frac{2}{5} - 3 \frac{1}{3}
\]

and requires the answer in **mixed number** form. Let's go through the steps to solve it.

### Step 1: Convert mixed numbers to improper fractions.
1. Convert \( -1 \frac{2}{5} \):
   \[
   -1 \frac{2}{5} = -\left(\frac{5 \times 1 + 2}{5}\right) = -\frac{7}{5}
   \]
2. Convert \( 3 \frac{1}{3} \):
   \[
   3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}
   \]

### Step 2: Subtract the improper fractions.
We now have:
\[
-\frac{7}{5} - \frac{10}{3}
\]
To subtract these fractions, we need a common denominator.

- The least common denominator (LCD) of 5 and 3 is 15.
- Rewrite the fractions with a denominator of 15:
  \[
  -\frac{7}{5} = -\frac{21}{15}, \quad \frac{10}{3} = \frac{50}{15}
  \]

Now subtract:
\[
-\frac{21}{15} - \frac{50}{15} = -\frac{71}{15}
\]

### Step 3: Convert the result back to a mixed number.
\[
-\frac{71}{15}
\]
- Divide 71 by 15: \( 71 \div 15 = 4 \) remainder 11.
- So, \( \frac{71}{15} = 4 \frac{11}{15} \), and the negative sign carries over.

Thus, the final answer is:
\[
-4 \frac{11}{15}
\]

### Final Answer:
The solution to \( -1 \frac{2}{5} - 3 \frac{1}{3} \) is:

\[
\boxed{-4 \frac{11}{15}}
\]

Would you like a detailed explanation of any part of the solution? Here are five related questions you might find useful:

1. How do you add or subtract mixed numbers?
2. What is the easiest way to find the least common denominator?
3. Can you explain how to convert improper fractions to mixed numbers?
4. How can I check my subtraction when working with fractions?
5. What are the steps to handle negative mixed numbers?

**Tip:** Always convert mixed numbers to improper fractions before performing operations!

What is -1 2/5 - 3 1/3? Write the answer as a mixed number in simplest form.

Solve the mixed number subtraction problem: -1 2/5 - 3 1/3. Learn to convert mixed numbers to improper fractions, find the least common denominator, and subtract them. Solution provided as a simplified mixed number. Suitable for Grades 6-8.

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