1. **State the problem:** Subtract the mixed numbers $17 \frac{4}{9}$ and $12 \frac{2}{3}$. 2. **Convert mixed numbers to improper fractions:** $17 \frac{4}{9} = \frac{17 \times 9 + 4}{9} = \frac{153 + 4}{9} = \frac{157}{9}$ $12 \frac{2}{3} = \frac{12 \times 3 + 2}{3} = \frac{36 + 2}{3} = \frac{38}{3}$ 3. **Find a common denominator:** The denominators are 9 and 3. The least common denominator (LCD) is 9. 4. **Convert fractions to have the same denominator:** $\frac{157}{9}$ stays the same. $\frac{38}{3} = \frac{38 \times 3}{3 \times 3} = \frac{114}{9}$ 5. **Subtract the fractions:** $$\frac{157}{9} - \frac{114}{9} = \frac{157 - 114}{9} = \frac{43}{9}$$ 6. **Convert the improper fraction back to a mixed number:** Divide 43 by 9: 43 ÷ 9 = 4 remainder 7. So, $\frac{43}{9} = 4 \frac{7}{9}$. 7. **Final answer:** $$17 \frac{4}{9} - 12 \frac{2}{3} = 4 \frac{7}{9}$$