1. **State the problem:** Multiply mixed numbers and fractions, and find the missing numerator in the fractions represented by squares. 2. **Recall the formula:** To multiply mixed numbers and fractions, first convert mixed numbers to improper fractions, then multiply numerators and denominators. 3. **Problem (1):** $2\frac{1}{3} \times \frac{1}{4} = \frac{\square}{3} \times \frac{1}{4}$ Convert $2\frac{1}{3}$ to improper fraction: $$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ So the missing numerator $\square = 7$. 4. **Problem (2):** $1\frac{2}{5} \times \frac{1}{4}$ Convert $1\frac{2}{5}$ to improper fraction: $$1\frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{7}{5}$$ Multiply: $$\frac{7}{5} \times \frac{1}{4} = \frac{7 \times 1}{5 \times 4} = \frac{7}{20}$$ 5. **Problem (3):** $3\frac{1}{3} \times \frac{2}{7}$ Convert $3\frac{1}{3}$ to improper fraction: $$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$ Multiply: $$\frac{10}{3} \times \frac{2}{7} = \frac{10 \times 2}{3 \times 7} = \frac{20}{21}$$ 6. **Problem (4):** $\frac{1}{7} \times 5\frac{1}{2} = \frac{1}{7} \times \frac{\square}{2}$ Convert $5\frac{1}{2}$ to improper fraction: $$5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2}$$ So the missing numerator $\square = 11$. 7. **Problem (5):** $\frac{1}{6} \times 4\frac{1}{3}$ Convert $4\frac{1}{3}$ to improper fraction: $$4\frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3}$$ Multiply: $$\frac{1}{6} \times \frac{13}{3} = \frac{1 \times 13}{6 \times 3} = \frac{13}{18}$$ 8. **Problem (6):** $\frac{2}{7} \times 2\frac{1}{5}$ Convert $2\frac{1}{5}$ to improper fraction: $$2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$$ Multiply: $$\frac{2}{7} \times \frac{11}{5} = \frac{2 \times 11}{7 \times 5} = \frac{22}{35}$$ **Final answers:** (1) $\frac{7}{3} \times \frac{1}{4}$ (2) $\frac{7}{20}$ (3) $\frac{20}{21}$ (4) $\frac{1}{7} \times \frac{11}{2}$ (5) $\frac{13}{18}$ (6) $\frac{22}{35}$