1. **State the problem:** We want to subtract $2 \frac{1}{2}$ from $5 \frac{4}{9}$, and first convert both to improper fractions. 2. **Convert $5 \frac{4}{9}$ to an improper fraction:** Multiply the whole number 5 by the denominator 9 and add the numerator 4: $$5 \times 9 + 4 = 45 + 4 = 49$$ So, $$5 \frac{4}{9} = \frac{49}{9}$$ 3. **Convert $2 \frac{1}{2}$ to an improper fraction:** Multiply the whole number 2 by the denominator 2 and add the numerator 1: $$2 \times 2 + 1 = 4 + 1 = 5$$ So, $$2 \frac{1}{2} = \frac{5}{2}$$ 4. **Find a common denominator:** Denominators are 9 and 2, their least common denominator is 18. 5. **Convert both fractions to have denominator 18:** $$\frac{49}{9} = \frac{49 \times 2}{9 \times 2} = \frac{98}{18}, \quad \frac{5}{2} = \frac{5 \times 9}{2 \times 9} = \frac{45}{18}$$ 6. **Subtract the fractions:** $$\frac{98}{18} - \frac{45}{18} = \frac{98 - 45}{18} = \frac{53}{18}$$ 7. **Simplify or convert to mixed number:** $$\frac{53}{18} = 2 \frac{17}{18}$$ because $18 \times 2 = 36$ and $53 - 36 = 17$. **Final answer:** $$2 \frac{17}{18}$$