Multiply Mixed Numbers 172483

1. **Problem:** Calculate the product of mixed numbers. 2. **Formula:** Convert mixed numbers to improper fractions and multiply: $$\text{If } a = m+\frac{n}{d}, b = p+\frac{q}{r}, \text{ then } a \times b = \frac{(md+n)}{d} \times \frac{(pr+q)}{r}$$ 3. **Step-by-step solutions:** **1) $2 \frac{1}{2} \times 2 \frac{2}{3}$** - Convert: $2 \frac{1}{2} = \frac{5}{2}$, $2 \frac{2}{3} = \frac{8}{3}$ - Multiply: $\frac{5}{2} \times \frac{8}{3} = \frac{40}{6}$ - Simplify: $\frac{40}{6} = \frac{\cancel{40}}{\cancel{6}} = \frac{20}{3} = 6 \frac{2}{3}$ **2) $3 \frac{1}{2} \times 4 \frac{1}{4}$** - Convert: $3 \frac{1}{2} = \frac{7}{2}$, $4 \frac{1}{4} = \frac{17}{4}$ - Multiply: $\frac{7}{2} \times \frac{17}{4} = \frac{119}{8}$ - Simplify: $\frac{119}{8} = 14 \frac{7}{8}$ **3) $3 \frac{4}{5} \times 2 \frac{1}{4}$** - Convert: $3 \frac{4}{5} = \frac{19}{5}$, $2 \frac{1}{4} = \frac{9}{4}$ - Multiply: $\frac{19}{5} \times \frac{9}{4} = \frac{171}{20}$ - Simplify: $\frac{171}{20} = 8 \frac{11}{20}$ **4) $4 \frac{1}{10} \times 2 \frac{3}{4}$** - Convert: $4 \frac{1}{10} = \frac{41}{10}$, $2 \frac{3}{4} = \frac{11}{4}$ - Multiply: $\frac{41}{10} \times \frac{11}{4} = \frac{451}{40}$ - Simplify: $\frac{451}{40} = 11 \frac{11}{40}$ **5) $3 \frac{1}{2} \times 2 \frac{1}{2}$** - Convert: $3 \frac{1}{2} = \frac{7}{2}$, $2 \frac{1}{2} = \frac{5}{2}$ - Multiply: $\frac{7}{2} \times \frac{5}{2} = \frac{35}{4}$ - Simplify: $\frac{35}{4} = 8 \frac{3}{4}$ **6) $2 \frac{1}{2} \times 4 \frac{1}{5}$** - Convert: $2 \frac{1}{2} = \frac{5}{2}$, $4 \frac{1}{5} = \frac{21}{5}$ - Multiply: $\frac{5}{2} \times \frac{21}{5} = \frac{105}{10}$ - Simplify: $\frac{105}{10} = \frac{\cancel{105}}{\cancel{10}} = \frac{21}{2} = 10 \frac{1}{2}$ **7) $3 \frac{4}{5} \times 2 \frac{2}{5}$** - Convert: $3 \frac{4}{5} = \frac{19}{5}$, $2 \frac{2}{5} = \frac{12}{5}$ - Multiply: $\frac{19}{5} \times \frac{12}{5} = \frac{228}{25}$ - Simplify: $\frac{228}{25} = 9 \frac{3}{25}$ **8) $4 \frac{4}{5} \times 4 \frac{2}{3}$** - Convert: $4 \frac{4}{5} = \frac{24}{5}$, $4 \frac{2}{3} = \frac{14}{3}$ - Multiply: $\frac{24}{5} \times \frac{14}{3} = \frac{336}{15}$ - Simplify: $\frac{336}{15} = \frac{\cancel{336}}{\cancel{15}} = \frac{112}{5} = 22 \frac{2}{5}$ **9) $4 \frac{4}{5} \times 2 \frac{1}{2}$** - Convert: $4 \frac{4}{5} = \frac{24}{5}$, $2 \frac{1}{2} = \frac{5}{2}$ - Multiply: $\frac{24}{5} \times \frac{5}{2} = \frac{120}{10}$ - Simplify: $\frac{120}{10} = \frac{\cancel{120}}{\cancel{10}} = 12$ **10) $3 \frac{3}{4} \times 4 \frac{5}{8}$** - Convert: $3 \frac{3}{4} = \frac{15}{4}$, $4 \frac{5}{8} = \frac{37}{8}$ - Multiply: $\frac{15}{4} \times \frac{37}{8} = \frac{555}{32}$ - Simplify: $\frac{555}{32} = 17 \frac{11}{32}$ **Final answers:** 1) $6 \frac{2}{3}$ 2) $14 \frac{7}{8}$ 3) $8 \frac{11}{20}$ 4) $11 \frac{11}{40}$ 5) $8 \frac{3}{4}$ 6) $10 \frac{1}{2}$ 7) $9 \frac{3}{25}$ 8) $22 \frac{2}{5}$ 9) $12$ 10) $17 \frac{11}{32}$