To solve the expression \( 1 \frac{5}{9} \div \left( -\frac{2}{3} \right) + \left( -2 \frac{3}{5} \right) \), let's break it down step by step.

### Step 1: Convert Mixed Fractions to Improper Fractions
- \( 1 \frac{5}{9} = \frac{14}{9} \)
- \( -2 \frac{3}{5} = -\frac{13}{5} \)

So the expression becomes:
\[
\frac{14}{9} \div \left( -\frac{2}{3} \right) + \left( -\frac{13}{5} \right)
\]

### Step 2: Perform the Division
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{14}{9} \div \left( -\frac{2}{3} \right) = \frac{14}{9} \times \left( -\frac{3}{2} \right)
\]
Multiply the numerators and denominators:
\[
\frac{14 \times (-3)}{9 \times 2} = \frac{-42}{18}
\]
Simplify the fraction:
\[
\frac{-42}{18} = \frac{-7}{3}
\]

### Step 3: Add the Fractions
Now, add \( \frac{-7}{3} \) and \( \frac{-13}{5} \). To add these, find a common denominator, which is 15:
\[
\frac{-7}{3} = \frac{-35}{15}, \quad \frac{-13}{5} = \frac{-39}{15}
\]
Now, add the fractions:
\[
\frac{-35}{15} + \frac{-39}{15} = \frac{-74}{15}
\]

### Final Answer:
The result of the expression is \( \frac{-74}{15} \) or approximately \( -4.93 \).

Would you like more details on any part of this?

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### Related Questions:
1. How do you convert mixed numbers into improper fractions?
2. What are the steps for dividing fractions?
3. How do you simplify fractions after multiplication?
4. How do you find a common denominator when adding fractions?
5. How do you convert improper fractions back to mixed numbers?

**Tip**: When dividing by a fraction, always multiply by its reciprocal to simplify the process!

Learn how to solve the expression 1 5/9 divided by (-2/3) plus (-2 3/5) with this detailed step-by-step solution. This guide covers key concepts such as converting mixed numbers to improper fractions, dividing by fractions, and adding fractions. Ideal for Grades 6-8.

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