To solve the expression:

\[
-4 \frac{3}{10} + -5 \frac{1}{10}
\]

### Step-by-Step Breakdown:

1. Convert the mixed numbers to improper fractions:

\[
-4 \frac{3}{10} = -\left(4 + \frac{3}{10}\right) = -\left(\frac{40}{10} + \frac{3}{10}\right) = -\frac{43}{10}
\]
\[
-5 \frac{1}{10} = -\left(5 + \frac{1}{10}\right) = -\left(\frac{50}{10} + \frac{1}{10}\right) = -\frac{51}{10}
\]

2. Add the two improper fractions:

\[
-\frac{43}{10} + -\frac{51}{10} = -\frac{43 + 51}{10} = -\frac{94}{10}
\]

3. Simplify the fraction if possible:

\[
-\frac{94}{10} = -\frac{47}{5}
\]

4. Convert back to a mixed number:

\[
-\frac{47}{5} = -9 \frac{2}{5}
\]

### Final Answer:
\[
-9 \frac{2}{5}
\]

Would you like more details or explanations?

Here are 5 related questions to practice:
1. What is \( 3 \frac{1}{2} + 5 \frac{3}{4} \)?
2. How do you subtract mixed numbers like \( 7 \frac{2}{3} - 4 \frac{5}{6} \)?
3. How do you simplify \( -\frac{60}{15} \)?
4. Can you multiply \( 2 \frac{3}{4} \times 1 \frac{1}{2} \)?
5. What is \( 4 \frac{1}{5} + 3 \frac{4}{5} \)?

**Tip**: When adding or subtracting mixed numbers, always convert them to improper fractions first!

Learn how to add mixed numbers like –4 3/10 and –5 1/10 with a step-by-step breakdown. This problem covers converting mixed numbers to improper fractions, adding improper fractions, and simplifying the result. Suitable for students in Grades 6-8.

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