1. **Problem:** Calculate the value of the expression $3 \frac{5}{7} - 1 \frac{2}{7}$. 2. **Formula and rules:** To subtract mixed fractions, convert them to improper fractions or subtract the whole numbers and fractions separately. 3. Convert to improper fractions: $$3 \frac{5}{7} = \frac{3 \times 7 + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7}$$ $$1 \frac{2}{7} = \frac{1 \times 7 + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7}$$ 4. Subtract the improper fractions: $$\frac{26}{7} - \frac{9}{7} = \frac{26 - 9}{7} = \frac{17}{7}$$ 5. Convert back to mixed number: $$\frac{17}{7} = 2 \frac{3}{7}$$ 6. **Answer:** $3 \frac{5}{7} - 1 \frac{2}{7} = 2 \frac{3}{7}$.