To multiply the mixed number \( 2 \frac{5}{9} \) by \( \frac{-3}{7} \), follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
\[
2 \frac{5}{9} = \frac{(2 \times 9) + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9}
\]

### Step 2: Multiply the improper fraction by the other fraction.
\[
\frac{23}{9} \times \frac{-3}{7} = \frac{23 \times -3}{9 \times 7} = \frac{-69}{63}
\]

### Step 3: Simplify the fraction.
\[
\frac{-69}{63} = \frac{-23}{21}
\]
Since \( 23 \) and \( 21 \) have no common factors, the fraction is already in its simplest form.

### Final Answer:
\[
\boxed{\frac{-23}{21}}
\]

Would you like further details on this solution?

Here are 5 related questions for more practice:
1. What is \( 3 \frac{2}{5} \times \frac{4}{9} \)?
2. How do you convert a mixed number to an improper fraction?
3. What is the product of \( \frac{-4}{3} \times \frac{5}{8} \)?
4. How do you simplify a fraction like \( \frac{72}{96} \)?
5. Can you explain why multiplying two fractions involves multiplying numerators and denominators?

**Tip:** Always simplify fractions to their lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Discover how to multiply the mixed number (2 5/9) by the fraction (-3/7) with a step-by-step guide. This solution covers converting mixed numbers to improper fractions, multiplying fractions, and simplifying the result. Perfect for Grades 6-8 students looking to practice basic fraction multiplication.

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