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)