1. **State the problem:** Multiply each pair of mixed numbers, cancel common factors before multiplying, and write the answer as a mixed number in simplest form. 2. **Formula and rules:** - Convert mixed numbers to improper fractions: $a\frac{b}{c} = \frac{ac+b}{c}$. - Multiply fractions: $\frac{m}{n} \times \frac{p}{q} = \frac{mp}{nq}$. - Cancel common factors before multiplying to simplify. - Convert the result back to a mixed number. 3. **Work through each part:** a) $2\frac{1}{4} \times 1\frac{2}{5}$ - Convert: $2\frac{1}{4} = \frac{9}{4}$, $1\frac{2}{5} = \frac{7}{5}$ - Multiply: $\frac{9}{4} \times \frac{7}{5} = \frac{63}{20}$ - Convert to mixed number: $\frac{63}{20} = 3\frac{3}{20}$ b) $1\frac{1}{4} \times 4\frac{1}{5}$ - Convert: $1\frac{1}{4} = \frac{5}{4}$, $4\frac{1}{5} = \frac{21}{5}$ - Cancel common factors: $\frac{\cancel{5}}{4} \times \frac{21}{\cancel{5}} = \frac{1}{4} \times 21 = \frac{21}{4}$ - Convert: $\frac{21}{4} = 5\frac{1}{4}$ c) $2\frac{1}{7} \times 2\frac{1}{6}$ - Convert: $2\frac{1}{7} = \frac{15}{7}$, $2\frac{1}{6} = \frac{13}{6}$ - Multiply: $\frac{15}{7} \times \frac{13}{6} = \frac{195}{42}$ - Simplify fraction: $\frac{195}{42} = \frac{65}{14}$ (dividing numerator and denominator by 3) - Convert: $\frac{65}{14} = 4\frac{9}{14}$ 4. Cancel common factors before multiplying: - $\frac{15}{7} \times \frac{13}{6}$ - Factors: 15 = 3 \times 5, 6 = 2 \times 3 - Cancel 3: $\frac{\cancel{3} \times 5}{7} \times \frac{13}{2 \times \cancel{3}} = \frac{5}{7} \times \frac{13}{2} = \frac{65}{14}$ 5. Continue with remaining parts: d) $5\frac{1}{2} \times 2\frac{4}{33}$ - Convert: $5\frac{1}{2} = \frac{11}{2}$, $2\frac{4}{33} = \frac{70}{33}$ - Cancel common factors: - $\frac{11}{2} \times \frac{70}{33}$ - 11 and 33 share factor 11: $\frac{\cancel{11}}{2} \times \frac{70}{3 \times \cancel{11}} = \frac{1}{2} \times \frac{70}{3} = \frac{70}{6}$ - Simplify $\frac{70}{6} = \frac{35}{3}$ - Convert: $\frac{35}{3} = 11\frac{2}{3}$ e) $2\frac{1}{5} \times 1\frac{1}{5}$ - Convert: $2\frac{1}{5} = \frac{11}{5}$, $1\frac{1}{5} = \frac{6}{5}$ - Multiply: $\frac{11}{5} \times \frac{6}{5} = \frac{66}{25}$ - Convert: $\frac{66}{25} = 2\frac{16}{25}$ f) $8\frac{1}{3} \times 2\frac{7}{10}$ - Convert: $8\frac{1}{3} = \frac{25}{3}$, $2\frac{7}{10} = \frac{27}{10}$ - Cancel common factors: - $\frac{25}{3} \times \frac{27}{10}$ - 25 and 10 share factor 5: $\frac{5 \times 5}{3} \times \frac{27}{2 \times 5} = \frac{5}{3} \times \frac{27}{2} = \frac{135}{6}$ - Simplify $\frac{135}{6} = \frac{45}{2}$ - Convert: $\frac{45}{2} = 22\frac{1}{2}$ **Final answers:** a) $3\frac{3}{20}$ b) $5\frac{1}{4}$ c) $4\frac{9}{14}$ d) $11\frac{2}{3}$ e) $2\frac{16}{25}$ f) $22\frac{1}{2}$