To calculate the sum $-4 \frac{4}{9} + 2 \frac{5}{9}$, follow these steps:

Step 1: Convert mixed numbers to improper fractions

$-4 \frac{4}{9} = -\left(4 \times 9 + 4\right)/9 = -40/9$ $2 \frac{5}{9} = \left(2 \times 9 + 5\right)/9 = 23/9$

Step 2: Perform the addition

Add the fractions: $-40/9 + 23/9 = \frac{-40 + 23}{9} = \frac{-17}{9}$

Step 3: Convert the result back to a mixed number

$-17/9 = -1 \frac{8}{9}$

Final Answer:

$-4 \frac{4}{9} + 2 \frac{5}{9} = -1 \frac{8}{9}$

Would you like a detailed explanation or clarification on any step?

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Here are 5 related questions to practice:

1. What is $3 \frac{2}{7} - 5 \frac{3}{7}$?
2. Add $1 \frac{4}{5}$ and $-3 \frac{2}{5}$.
3. Simplify: $-6 \frac{5}{8} + 4 \frac{3}{8}$.
4. Subtract $2 \frac{1}{4}$ from $-1 \frac{3}{4}$.
5. Find the sum of $-7 \frac{2}{3}$ and $5 \frac{5}{6}$.

Tip: Always simplify mixed numbers to improper fractions for easier addition or subtraction!