1. Stating the problem: Simplify the expression $$7 \times \frac{1}{3} + 5 \times \frac{4}{9} - 4 \times \frac{4}{9}$$. 2. Use the distributive property and multiply each integer by the fraction: $$7 \times \frac{1}{3} = \frac{7}{3}$$ $$5 \times \frac{4}{9} = \frac{20}{9}$$ $$4 \times \frac{4}{9} = \frac{16}{9}$$ 3. Substitute back into the expression: $$\frac{7}{3} + \frac{20}{9} - \frac{16}{9}$$ 4. Find a common denominator for the fractions. The denominators are 3 and 9, so the common denominator is 9. 5. Convert $$\frac{7}{3}$$ to ninths: $$\frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9}$$ 6. Now the expression is: $$\frac{21}{9} + \frac{20}{9} - \frac{16}{9}$$ 7. Combine the numerators: $$21 + 20 - 16 = 25$$ 8. So the expression simplifies to: $$\frac{25}{9}$$ 9. This is an improper fraction and can be written as a mixed number: $$\frac{25}{9} = 2 \frac{7}{9}$$ Final answer: $$\frac{25}{9}$$ or $$2 \frac{7}{9}$$.