1. **State the problem:** Subtract the mixed numbers $28 \frac{2}{4}$ and $5 \frac{2}{3}$ and reduce the result to simplest form. 2. **Convert mixed numbers to improper fractions:** $$28 \frac{2}{4} = 28 + \frac{2}{4} = 28 + \frac{1}{2} = \frac{56}{2} + \frac{1}{2} = \frac{57}{2}$$ $$5 \frac{2}{3} = 5 + \frac{2}{3} = \frac{15}{3} + \frac{2}{3} = \frac{17}{3}$$ 3. **Find a common denominator:** The denominators are 2 and 3. The least common denominator (LCD) is 6. 4. **Convert fractions to have the LCD:** $$\frac{57}{2} = \frac{57 \times 3}{2 \times 3} = \frac{171}{6}$$ $$\frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6}$$ 5. **Subtract the fractions:** $$\frac{171}{6} - \frac{34}{6} = \frac{171 - 34}{6} = \frac{137}{6}$$ 6. **Convert the improper fraction back to a mixed number:** Divide 137 by 6: $$137 \div 6 = 22 \text{ remainder } 5$$ So, $$\frac{137}{6} = 22 \frac{5}{6}$$ 7. **Final answer:** $$28 \frac{2}{4} - 5 \frac{2}{3} = 22 \frac{5}{6}$$