1. **State the problem:** Calculate $2 \frac{3}{7} - 1 \frac{2}{3}$. 2. **Convert mixed numbers to improper fractions:** $$2 \frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}$$ $$1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$$ 3. **Find common denominator:** The denominators are 7 and 3. The least common denominator (LCD) is 21. 4. **Convert fractions to have the LCD:** $$\frac{17}{7} = \frac{17 \times 3}{7 \times 3} = \frac{51}{21}$$ $$\frac{5}{3} = \frac{5 \times 7}{3 \times 7} = \frac{35}{21}$$ 5. **Subtract the fractions:** $$\frac{51}{21} - \frac{35}{21} = \frac{51 - 35}{21} = \frac{16}{21}$$ 6. **Simplify if possible:** 16 and 21 have no common factors other than 1, so the fraction is already in simplest form. 7. **Final answer:** $$2 \frac{3}{7} - 1 \frac{2}{3} = \frac{16}{21}$$