Learniling Multiplying mixed numbers Grade 5 Fractions Worksheet Show all work! Find the product. 1. \( 1 \frac{2}{4} \times 3 \frac{5}{6}=\frac{6}{4} \times \frac{23}{6}=\frac{133}{24}=5 \frac{152}{24} 1 \frac{1}{6} \times 2 \frac{6}{12}= \) \( \qquad \) simplify \( 5 \frac{18}{24}=5 \frac{3}{4} \) 3. \( 2 \frac{1}{2} \times 3 \frac{4}{5}= \) \( \qquad \) 4. \( 3 \frac{1}{3} \times 1 \frac{4}{10}= \) \( \qquad \) 5. \( 3 \frac{3}{4} \times 3 \frac{2}{9}= \) \( \qquad \) 6. \( 3 \frac{5}{6} \times 2 \frac{1}{2}= \) \( \qquad \) 7. \( 1 \frac{1}{2} \times 3 \frac{1}{2}= \) \( \qquad \) 8. \( 1 \frac{8}{12} \times 3 \frac{2}{10}= \) \( \qquad \) 9. \( 3 \frac{2}{6} \times 3 \frac{2}{3}= \) \( \qquad \) 10. \( 3 \frac{4}{5} \times 2 \frac{3}{4}= \) \( \qquad \) 11. \( 1 \frac{3}{4} \times 1 \frac{2}{4}= \) \( \qquad \) 12. \( 2 \frac{4}{5} \times 1 \frac{1}{12}= \) \( \qquad \) 13. \( 1 \frac{5}{8} \times 2 \frac{6}{8}= \) \( \qquad \) 14. \( 3 \frac{2}{3} \times 1 \frac{1}{2}= \) \( \qquad \)

To multiply mixed numbers, we first convert them into improper fractions, then multiply the fractions, and finally convert the result back into a mixed number if necessary. Let's solve each problem step by step. ### 1. \( 1 \frac{2}{4} \times 3 \frac{5}{6} \) 1. Convert to improper fractions: - \( 1 \frac{2}{4} = \frac{4 \cdot 1 + 2}{4} = \frac{6}{4} \) - \( 3 \frac{5}{6} = \frac{6 \cdot 3 + 5}{6} = \frac{23}{6} \) 2. Multiply the fractions: \[ \frac{6}{4} \times \frac{23}{6} = \frac{6 \cdot 23}{4 \cdot 6} = \frac{138}{24} \] 3. Simplify: \[ \frac{138}{24} = \frac{69}{12} = 5 \frac{9}{12} = 5 \frac{3}{4} \] ### 2. \( 1 \frac{1}{6} \times 2 \frac{6}{12} \) 1. Convert to improper fractions: - \( 1 \frac{1}{6} = \frac{6 \cdot 1 + 1}{6} = \frac{7}{6} \) - \( 2 \frac{6}{12} = \frac{12 \cdot 2 + 6}{12} = \frac{30}{12} = \frac{5}{2} \) 2. Multiply the fractions: \[ \frac{7}{6} \times \frac{5}{2} = \frac{7 \cdot 5}{6 \cdot 2} = \frac{35}{12} \] 3. Convert back to mixed number: \[ \frac{35}{12} = 2 \frac{11}{12} \] ### 3. \( 2 \frac{1}{2} \times 3 \frac{4}{5} \) 1. Convert to improper fractions: - \( 2 \frac{1}{2} = \frac{5}{2} \) - \( 3 \frac{4}{5} = \frac{19}{5} \) 2. Multiply the fractions: \[ \frac{5}{2} \times \frac{19}{5} = \frac{5 \cdot 19}{2 \cdot 5} = \frac{19}{2} \] 3. Convert back to mixed number: \[ \frac{19}{2} = 9 \frac{1}{2} \] ### 4. \( 3 \frac{1}{3} \times 1 \frac{4}{10} \) 1. Convert to improper fractions: - \( 3 \frac{1}{3} = \frac{10}{3} \) - \( 1 \frac{4}{10} = \frac{14}{10} = \frac{7}{5} \) 2. Multiply the fractions: \[ \frac{10}{3} \times \frac{7}{5} = \frac{10 \cdot 7}{3 \cdot 5} = \frac{70}{15} = \frac{14}{3} \] 3. Convert back to mixed number: \[ \frac{14}{3} = 4 \frac{2}{3} \] ### 5. \( 3 \frac{3}{4} \times 3 \frac{2}{9} \) 1. Convert to improper fractions: - \( 3 \frac{3}{4} = \frac{15}{4} \) - \( 3 \frac{2}{9} = \frac{29}{9} \) 2. Multiply the fractions: \[ \frac{15}{4} \times \frac{29}{9} = \frac{15 \cdot 29}{4 \cdot 9} = \frac{435}{36} \] 3. Convert back to mixed number: \[ \frac{435}{36} = 12 \frac{3}{36} = 12 \frac{1}{12} \] ### 6. \( 3 \frac{5}{6} \times 2 \frac{1}{2} \) 1. Convert to improper fractions: - \( 3 \frac{5}{6} = \frac{23}{6} \) - \( 2 \frac{1}{2} = \frac{5}{2} \) 2. Multiply the fractions: \[ \frac{23}{6} \times \frac{5}{2} = \frac{115}{12} \] 3. Convert back to mixed number: \[ \frac{115}{12} = 9 \frac{7}{12} \] ### 7. \( 1 \frac{1}{2} \times 3 \frac{1}{2} \) 1. Convert to improper fractions: - \( 1 \frac{1}{2} = \frac{3}{2} \) - \( 3 \frac{1}{2} = \frac{7}{2} \) 2. Multiply the fractions: \[ \frac{3}{2} \times \frac{7}{2} = \frac{21}{4} \] 3. Convert back to mixed number: \[ \frac{21}{4} = 5 \frac{1}{4} \] ### 8. \( 1 \frac{8}{12} \times 3 \frac{2}{10} \) 1. Convert to improper fractions: - \( 1 \frac{8}{12} = \frac{20}{12} = \frac{5}{3} \) - \( 3 \frac{2}{10} = \frac{32}{10} = \frac{16}{5} \) 2. Multiply the fractions: \[ \frac{5}{3} \times \frac{16}{5} = \frac{16}{3} \] 3. Convert back to mixed number: \[ \frac{16}{3} = 5 \frac{1}{3} \] ### 9. \( 3 \frac{2}{6} \times 3 \frac{2}{3} \) 1. Convert to improper fractions: - \( 3 \frac{2}{6} = \frac{20}{6} = \frac{10}{3} \)