Multiplying fractions is a fundamental concept in mathematics, particularly in Key Stage 3. It involves taking two fractions and finding their product, which can often be used in various real-world contexts. In this topic, students will learn how to multiply fractions and simplify the results.

Understanding Multiplying Fractions

When multiplying fractions, the process is straightforward:

  1. Multiply the Numerators: The numerator is the top number of the fraction. When multiplying fractions, you multiply the numerators together.
  2. Multiply the Denominators: The denominator is the bottom number of the fraction. Similarly, multiply the denominators together.
  3. Simplify the Result: If possible, reduce the resulting fraction to its simplest form.

Example

For example, to multiply the fractions \frac{2}{3}

and \frac{4}{5}
, you would:

  1. Multiply the numerators: 2 \times 4 = 8
    .
  2. Multiply the denominators: 3 \times 5 = 15
    .
  3. The result is \frac{8}{15}
    , which is already in its simplest form.

Questions

Easy Level Questions

  1. Multiply \frac{1}{2} \times \frac{1}{4}
    .
  2. Multiply \frac{3}{5} \times \frac{2}{3}
    .
  3. Multiply \frac{1}{3} \times \frac{1}{6}
    .
  4. Multiply \frac{2}{7} \times \frac{3}{5}
    .
  5. Multiply \frac{4}{9} \times \frac{1}{3}
    .
  6. Multiply \frac{5}{6} \times \frac{2}{5}
    .
  7. Multiply \frac{1}{2} \times \frac{3}{4}
    .
  8. Multiply \frac{2}{5} \times \frac{1}{2}
    .
  9. Multiply \frac{1}{4} \times \frac{3}{2}
    .
  10. Multiply \frac{3}{10} \times \frac{2}{5}
    .
  11. Multiply \frac{2}{3} \times \frac{1}{5}
    .
  12. Multiply \frac{1}{2} \times \frac{2}{6}
    .
  13. Multiply \frac{4}{8} \times \frac{3}{4}
    .
  14. Multiply \frac{5}{9} \times \frac{1}{3}
    .
  15. Multiply \frac{1}{5} \times \frac{2}{8}
    .
  16. Multiply \frac{3}{4} \times \frac{1}{2}
    .
  17. Multiply \frac{6}{10} \times \frac{1}{5}
    .
  18. Multiply \frac{1}{3} \times \frac{2}{4}
    .
  19. Multiply \frac{5}{7} \times \frac{3}{2}
    .
  20. Multiply \frac{1}{6} \times \frac{3}{3}
    .

Medium Level Questions

  1. Multiply \frac{3}{4} \times \frac{2}{5}
    .
  2. Multiply \frac{7}{10} \times \frac{3}{8}
    .
  3. Multiply \frac{2}{3} \times \frac{5}{6}
    .
  4. Multiply \frac{4}{5} \times \frac{2}{9}
    .
  5. Multiply \frac{3}{8} \times \frac{4}{5}
    .
  6. Multiply \frac{5}{12} \times \frac{3}{7}
    .
  7. Multiply \frac{1}{2} \times \frac{3}{8}
    .
  8. Multiply \frac{3}{5} \times \frac{7}{12}
    .
  9. Multiply \frac{2}{7} \times \frac{5}{4}
    .
  10. Multiply \frac{4}{9} \times \frac{6}{11}
    .
  11. Multiply \frac{5}{8} \times \frac{3}{4}
    .
  12. Multiply \frac{7}{12} \times \frac{2}{3}
    .
  13. Multiply \frac{3}{10} \times \frac{8}{15}
    .
  14. Multiply \frac{5}{6} \times \frac{4}{5}
    .
  15. Multiply \frac{1}{3} \times \frac{7}{9}
    .
  16. Multiply \frac{2}{5} \times \frac{5}{8}
    .
  17. Multiply \frac{6}{11} \times \frac{3}{7}
    .
  18. Multiply \frac{2}{3} \times \frac{3}{10}
    .
  19. Multiply \frac{4}{5} \times \frac{7}{9}
    .
  20. Multiply \frac{8}{15} \times \frac{1}{2}
    .

Hard Level Questions

  1. Multiply \frac{7}{8} \times \frac{5}{6}
    .
  2. Multiply \frac{3}{4} \times \frac{2}{7}
    .
  3. Multiply \frac{9}{10} \times \frac{3}{5}
    .
  4. Multiply \frac{11}{12} \times \frac{5}{8}
    .
  5. Multiply \frac{13}{15} \times \frac{2}{3}
    .
  6. Multiply \frac{7}{9} \times \frac{4}{11}
    .
  7. Multiply \frac{5}{12} \times \frac{9}{14}
    .
  8. Multiply \frac{8}{15} \times \frac{7}{10}
    .
  9. Multiply \frac{14}{25} \times \frac{3}{7}
    .
  10. Multiply \frac{5}{18} \times \frac{12}{13}
    .
  11. Multiply \frac{3}{14} \times \frac{16}{21}
    .
  12. Multiply \frac{11}{16} \times \frac{5}{12}
    .
  13. Multiply \frac{2}{9} \times \frac{6}{7}
    .
  14. Multiply \frac{7}{10} \times \frac{1}{4}
    .
  15. Multiply \frac{9}{16} \times \frac{5}{8}
    .
  16. Multiply \frac{1}{2} \times \frac{17}{30}
    .
  17. Multiply \frac{2}{11} \times \frac{9}{16}
    .
  18. Multiply \frac{3}{5} \times \frac{14}{18}
    .
  19. Multiply \frac{4}{7} \times \frac{6}{10}
    .
  20. Multiply \frac{15}{16} \times \frac{2}{5}
    .

Answers and Explanations

Easy Level Answers

  1. \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8}
  2. \frac{3}{5} \times \frac{2}{3} = \frac{3 \times 2}{5 \times 3} = \frac{6}{15} = \frac{2}{5}
    (simplified)
  3. \frac{1}{3} \times \frac{1}{6} = \frac{1 \times 1}{3 \times 6} = \frac{1}{18}
  4. \frac{2}{7} \times \frac{3}{5} = \frac{2 \times 3}{7 \times 5} = \frac{6}{35}
  5. \frac{4}{9} \times \frac{1}{3} = \frac{4 \times 1}{9 \times 3} = \frac{4}{27}
  6. \frac{5}{6} \times \frac{2}{5} = \frac{5 \times 2}{6 \times 5} = \frac{10}{30} = \frac{1}{3}
    (simplified)
  7. \frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
  8. \frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}
    (simplified)
  9. \frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}
  1. \frac{3}{10} \times \frac{2}{5} = \frac{3 \times 2}{10 \times 5} = \frac{6}{50} = \frac{3}{25}
    (simplified)
  2. \frac{2}{3} \times \frac{1}{5} = \frac{2 \times 1}{3 \times 5} = \frac{2}{15}
  3. \frac{1}{2} \times \frac{2}{6} = \frac{1 \times 2}{2 \times 6} = \frac{2}{12} = \frac{1}{6}
    (simplified)
  4. \frac{4}{8} \times \frac{3}{4} = \frac{4 \times 3}{8 \times 4} = \frac{12}{32} = \frac{3}{8}
    (simplified)
  5. \frac{5}{9} \times \frac{1}{3} = \frac{5 \times 1}{9 \times 3} = \frac{5}{27}
  6. \frac{1}{5} \times \frac{2}{8} = \frac{1 \times 2}{5 \times 8} = \frac{2}{40} = \frac{1}{20}
    (simplified)
  7. \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}
  8. \frac{6}{10} \times \frac{1}{5} = \frac{6 \times 1}{10 \times 5} = \frac{6}{50} = \frac{3}{25}
    (simplified)
  9. \frac{1}{3} \times \frac{2}{4} = \frac{1 \times 2}{3 \times 4} = \frac{2}{12} = \frac{1}{6}
    (simplified)
  10. \frac{5}{7} \times \frac{3}{2} = \frac{5 \times 3}{7 \times 2} = \frac{15}{14} = 1 \frac{1}{14}
    (mixed number)
  11. \frac{1}{6} \times \frac{3}{3} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18} = \frac{1}{6}
    (simplified)

Medium Level Answers

  1. \frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20} = \frac{3}{10}
    (simplified)
  2. \frac{7}{10} \times \frac{3}{8} = \frac{7 \times 3}{10 \times 8} = \frac{21}{80}
  3. \frac{2}{3} \times \frac{5}{6} = \frac{2 \times 5}{3 \times 6} = \frac{10}{18} = \frac{5}{9}
    (simplified)
  4. \frac{4}{5} \times \frac{2}{9} = \frac{4 \times 2}{5 \times 9} = \frac{8}{45}
  5. \frac{3}{8} \times \frac{4}{5} = \frac{3 \times 4}{8 \times 5} = \frac{12}{40} = \frac{3}{10}
    (simplified)
  6. \frac{5}{12} \times \frac{3}{7} = \frac{5 \times 3}{12 \times 7} = \frac{15}{84} = \frac{5}{28}
    (simplified)
  7. \frac{1}{2} \times \frac{3}{8} = \frac{1 \times 3}{2 \times 8} = \frac{3}{16}
  8. \frac{3}{5} \times \frac{7}{12} = \frac{3 \times 7}{5 \times 12} = \frac{21}{60} = \frac{7}{20}
    (simplified)
  9. \frac{2}{7} \times \frac{5}{4} = \frac{2 \times 5}{7 \times 4} = \frac{10}{28} = \frac{5}{14}
    (simplified)
  10. \frac{4}{9} \times \frac{6}{11} = \frac{4 \times 6}{9 \times 11} = \frac{24}{99} = \frac{8}{33}
    (simplified)
  11. \frac{5}{8} \times \frac{3}{4} = \frac{5 \times 3}{8 \times 4} = \frac{15}{32}
  12. \frac{7}{12} \times \frac{2}{3} = \frac{7 \times 2}{12 \times 3} = \frac{14}{36} = \frac{7}{18}
    (simplified)
  13. \frac{3}{10} \times \frac{8}{15} = \frac{3 \times 8}{10 \times 15} = \frac{24}{150} = \frac{4}{25}
    (simplified)
  14. \frac{5}{6} \times \frac{4}{5} = \frac{5 \times 4}{6 \times 5} = \frac{20}{30} = \frac{2}{3}
    (simplified)
  15. \frac{1}{3} \times \frac{7}{9} = \frac{1 \times 7}{3 \times 9} = \frac{7}{27}
  16. \frac{2}{5} \times \frac{5}{8} = \frac{2 \times 5}{5 \times 8} = \frac{10}{40} = \frac{1}{4}
    (simplified)
  17. \frac{6}{11} \times \frac{3}{7} = \frac{6 \times 3}{11 \times 7} = \frac{18}{77}
  18. \frac{2}{3} \times \frac{3}{10} = \frac{2 \times 3}{3 \times 10} = \frac{6}{30} = \frac{1}{5}
    (simplified)
  19. \frac{4}{5} \times \frac{7}{9} = \frac{4 \times 7}{5 \times 9} = \frac{28}{45}
  20. \frac{8}{15} \times \frac{1}{2} = \frac{8 \times 1}{15 \times 2} = \frac{8}{30} = \frac{4}{15}
    (simplified)

Hard Level Answers

  1. \frac{7}{8} \times \frac{5}{6} = \frac{7 \times 5}{8 \times 6} = \frac{35}{48}
  2. \frac{3}{4} \times \frac{2}{7} = \frac{3 \times 2}{4 \times 7} = \frac{6}{28} = \frac{3}{14}
    (simplified)
  3. \frac{9}{10} \times \frac{3}{5} = \frac{9 \times 3}{10 \times 5} = \frac{27}{50}
  4. \frac{11}{12} \times \frac{5}{8} = \frac{11 \times 5}{12 \times 8} = \frac{55}{96}
  5. \frac{13}{15} \times \frac{2}{3} = \frac{13 \times 2}{15 \times 3} = \frac{26}{45}
  6. \frac{7}{9} \times \frac{4}{11} = \frac{7 \times 4}{9 \times 11} = \frac{28}{99}
  7. \frac{5}{12} \times \frac{9}{14} = \frac{5 \times 9}{12 \times 14} = \frac{45}{168} = \frac{15}{56}
    (simplified)
  8. \frac{8}{15} \times \frac{7}{10} = \frac{8 \times 7}{15 \times 10} = \frac{56}{150} = \frac{28}{75}
    (simplified)
  9. \frac{14}{25} \times \frac{3}{7} = \frac{14 \times 3}{25 \times 7} = \frac{42}{175} = \frac{6}{25}
    (simplified)
  10. \frac{5}{18} \times \frac{12}{13} = \frac{5 \times 12}{18 \times 13} = \frac{60}{234} = \frac{10}{39}
    (simplified)
  11. \frac{3}{14} \times \frac{16}{21} = \frac{3 \times 16}{14 \times 21} = \frac{48}{294} = \frac{8}{49}
    (simplified)
  12. \frac{11}{16} \times \frac{5}{12} = \frac{11 \times 5}{16 \times 12} = \frac{55}{192}
  13. \frac{2}{9} \times \frac{6}{7} = \frac{2 \times 6}{9 \times 7} = \frac{12}{63} = \frac{4}{21}
    (simplified)
  14. \frac{7}{10} \times \frac{1}{4} = \frac{7 \times 1}{10 \times 4} = \frac{7}{40}
  15. \frac{9}{16} \times \frac{5}{8} = \frac{9 \times 5}{16 \times 8} = \frac{45}{128}
  16. \frac{1}{2} \times \frac{17}{30} = \frac{1 \times 17}{2 \times 30} = \frac{17}{60}
  17. \frac{2}{11} \times \frac{9}{16} = \frac{2 \times 9}{11 \times 16} = \frac{18}{176} = \frac{9}{88}
    (simplified)
  18. \frac{3}{5} \times \frac{14}{18} = \frac{3 \times 14}{5 \times 18} = \frac{42}{90} = \frac{7}{15}
    (simplified)
  19. \frac{4}{7} \times \frac{6}{10} = \frac{4 \times 6}{7 \times 10} = \frac{24}{70} = \frac{12}{35}
    (simplified)
  20. \frac{15}{16} \times \frac{2}{5} = \frac{15 \times 2}{16 \times 5} = \frac{30}{80} = \frac{3}{8}
    (simplified)