1. **State the problem:** Add and subtract the mixed numbers and fractions: $2 \frac{3}{7} + 3 \frac{1}{7} - \frac{4}{7}$. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{3}{7} = \frac{2 \times 7 + 3}{7} = \frac{14 + 3}{7} = \frac{17}{7}$ - $3 \frac{1}{7} = \frac{3 \times 7 + 1}{7} = \frac{21 + 1}{7} = \frac{22}{7}$ 3. **Rewrite the expression with improper fractions:** $$\frac{17}{7} + \frac{22}{7} - \frac{4}{7}$$ 4. **Add and subtract fractions with the same denominator:** $$\frac{17}{7} + \frac{22}{7} - \frac{4}{7} = \frac{17 + 22 - 4}{7} = \frac{35}{7}$$ 5. **Simplify the fraction:** $$\frac{35}{7} = \cancel{\frac{35}{7}} = 5$$ 6. **Final answer:** $5$. The sum of $2 \frac{3}{7} + 3 \frac{1}{7} - \frac{4}{7}$ is $5$.