分数乘分数计算题60道，怎么算又快又准？

，掌握其计算方法对后续学习分数除法、百分数等知识具有奠基作用，分数乘分数的计算法则为“分子相乘的积作分子，分母相乘的积作分母”，计算时需注意能约分的要先约分，使结果化为最简分数，以下通过60道不同难度的分数乘分数计算题，帮助同学们巩固这一知识点，题目从基础巩固到综合提升逐步展开，并附有详细解析和表格归纳,最后以FAQs形式解答常见疑问。

基础巩固题（20道）

1. (\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3} = \frac{1}{6})
2. (\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2})（约分）
3. (\frac{3}{5} \times \frac{2}{7} = \frac{3 \times 2}{5 \times 7} = \frac{6}{35})
4. (\frac{4}{9} \times \frac{1}{2} = \frac{4 \times 1}{9 \times 2} = \frac{4}{18} = \frac{2}{9})
5. (\frac{5}{6} \times \frac{3}{10} = \frac{5 \times 3}{6 \times 10} = \frac{15}{60} = \frac{1}{4})
6. (\frac{1}{4} \times \frac{2}{5} = \frac{1 \times 2}{4 \times 5} = \frac{2}{20} = \frac{1}{10})
7. (\frac{2}{7} \times \frac{3}{8} = \frac{2 \times 3}{7 \times 8} = \frac{6}{56} = \frac{3}{28})
8. (\frac{3}{10} \times \frac{5}{9} = \frac{3 \times 5}{10 \times 9} = \frac{15}{90} = \frac{1}{6})
9. (\frac{4}{15} \times \frac{3}{4} = \frac{4 \times 3}{15 \times 4} = \frac{12}{60} = \frac{1}{5})
10. (\frac{5}{12} \times \frac{2}{5} = \frac{5 \times 2}{12 \times 5} = \frac{10}{60} = \frac{1}{6})
11. (\frac{1}{3} \times \frac{1}{5} = \frac{1 \times 1}{3 \times 5} = \frac{1}{15})
12. (\frac{2}{5} \times \frac{4}{7} = \frac{2 \times 4}{5 \times 7} = \frac{8}{35})
13. (\frac{3}{8} \times \frac{2}{3} = \frac{3 \times 2}{8 \times 3} = \frac{6}{24} = \frac{1}{4})
14. (\frac{5}{9} \times \frac{1}{3} = \frac{5 \times 1}{9 \times 3} = \frac{5}{27})
15. (\frac{7}{10} \times \frac{2}{7} = \frac{7 \times 2}{10 \times 7} = \frac{14}{70} = \frac{1}{5})
16. (\frac{1}{6} \times \frac{3}{4} = \frac{1 \times 3}{6 \times 4} = \frac{3}{24} = \frac{1}{8})
17. (\frac{4}{7} \times \frac{5}{8} = \frac{4 \times 5}{7 \times 8} = \frac{20}{56} = \frac{5}{14})
18. (\frac{2}{9} \times \frac{3}{5} = \frac{2 \times 3}{9 \times 5} = \frac{6}{45} = \frac{2}{15})
19. (\frac{3}{11} \times \frac{2}{3} = \frac{3 \times 2}{11 \times 3} = \frac{6}{33} = \frac{2}{11})
20. (\frac{5}{13} \times \frac{1}{5} = \frac{5 \times 1}{13 \times 5} = \frac{5}{65} = \frac{1}{13})

进阶提升题（20道）

21. (\frac{2}{3} \times \frac{4}{5} \times \frac{3}{8} = \frac{2 \times 4 \times 3}{3 \times 5 \times 8} = \frac{24}{120} = \frac{1}{5})（连续乘法，先约分）
22. (\frac{3}{4} \times \frac{2}{7} \times \frac{5}{6} = \frac{3 \times 2 \times 5}{4 \times 7 \times 6} = \frac{30}{168} = \frac{5}{28})
23. (\frac{5}{6} \times \frac{7}{10} \times \frac{3}{14} = \frac{5 \times 7 \times 3}{6 \times 10 \times 14} = \frac{105}{840} = \frac{1}{8})
24. (\frac{2}{9} \times \frac{3}{4} \times \frac{1}{3} = \frac{2 \times 3 \times 1}{9 \times 4 \times 3} = \frac{6}{108} = \frac{1}{18})
25. (\frac{4}{5} \times \frac{1}{2} \times \frac{10}{3} = \frac{4 \times 1 \times 10}{5 \times 2 \times 3} = \frac{40}{30} = \frac{4}{3})
26. (\frac{3}{7} \times \frac{14}{15} \times \frac{5}{6} = \frac{3 \times 14 \times 5}{7 \times 15 \times 6} = \frac{210}{630} = \frac{1}{3})
27. (\frac{5}{8} \times \frac{4}{9} \times \frac{3}{10} = \frac{5 \times 4 \times 3}{8 \times 9 \times 10} = \frac{60}{720} = \frac{1}{12})
28. (\frac{2}{11} \times \frac{3}{8} \times \frac{4}{9} = \frac{2 \times 3 \times 4}{11 \times 8 \times 9} = \frac{24}{792} = \frac{1}{33})
29. (\frac{7}{12} \times \frac{3}{14} \times \frac{2}{5} = \frac{7 \times 3 \times 2}{12 \times 14 \times 5} = \frac{42}{840} = \frac{1}{20})
30. (\frac{1}{3} \times \frac{6}{7} \times \frac{2}{5} = \frac{1 \times 6 \times 2}{3 \times 7 \times 5} = \frac{12}{105} = \frac{4}{35})
31. (\frac{3}{5} \times \frac{10}{21} \times \frac{7}{9} = \frac{3 \times 10 \times 7}{5 \times 21 \times 9} = \frac{210}{945} = \frac{2}{9})
32. (\frac{4}{9} \times \frac{3}{16} \times \frac{8}{15} = \frac{4 \times 3 \times 8}{9 \times 16 \times 15} = \frac{96}{2160} = \frac{2}{45})
33. (\frac{5}{12} \times \frac{9}{20} \times \frac{4}{27} = \frac{5 \times 9 \times 4}{12 \times 20 \times 27} = \frac{180}{6480} = \frac{1}{36})
34. (\frac{2}{7} \times \frac{14}{25} \times \frac{5}{8} = \frac{2 \times 14 \times 5}{7 \times 25 \times 8} = \frac{140}{1400} = \frac{1}{10})
35. (\frac{3}{10} \times \frac{5}{18} \times \frac{9}{20} = \frac{3 \times 5 \times 9}{10 \times 18 \times 20} = \frac{135}{3600} = \frac{3}{80})
36. (\frac{7}{15} \times \frac{3}{14} \times \frac{10}{21} = \frac{7 \times 3 \times 10}{15 \times 14 \times 21} = \frac{210}{4410} = \frac{1}{21})
37. (\frac{4}{11} \times \frac{22}{35} \times \frac{5}{12} = \frac{4 \times 22 \times 5}{11 \times 35 \times 12} = \frac{440}{4620} = \frac{2}{21})
38. (\frac{5}{13} \times \frac{26}{45} \times \frac{9}{20} = \frac{5 \times 26 \times 9}{13 \times 45 \times 20} = \frac{1170}{11700} = \frac{1}{10})
39. (\frac{2}{17} \times \frac{34}{51} \times \frac{3}{4} = \frac{2 \times 34 \times 3}{17 \times 51 \times 4} = \frac{204}{3468} = \frac{1}{17})
40. (\frac{3}{19} \times \frac{38}{57} \times \frac{3}{8} = \frac{3 \times 38 \times 3}{19 \times 57 \times 8} = \frac{342}{8664} = \frac{1}{24})

综合拓展题（20道）

41. (\frac{1}{2} \times \frac{2}{3} + \frac{3}{4} \times \frac{4}{5})（混合运算，先乘加）
    (= \frac{1}{3} + \frac{3}{5} = \frac{5}{15} + \frac{9}{15} = \frac{14}{15})
42. (\frac{2}{5} \times \frac{3}{7} - \frac{1}{5} \times \frac{3}{7})（乘法分配律）
    (= \left(\frac{2}{5} - \frac{1}{5}\right) \times \frac{3}{7} = \frac{1}{5} \times \frac{3}{7} = \frac{3}{35})
43. (\left(\frac{1}{3} + \frac{2}{5}\right) \times \frac{15}{16})（分配律）
    (= \frac{1}{3} \times \frac{15}{16} + \frac{2}{5} \times \frac{15}{16} = \frac{5}{16} + \frac{3}{8} = \frac{5}{16} + \frac{6}{16} = \frac{11}{16})
44. (\frac{4}{9} \times \left(\frac{3}{8} + \frac{5}{12}\right))
    (= \frac{4}{9} \times \frac{9}{24} + \frac{4}{9} \times \frac{5}{12} = \frac{1}{6} + \frac{5}{27} = \frac{9}{54} + \frac{10}{54} = \frac{19}{54})
45. (\frac{5}{6} \times \frac{7}{10} \times \frac{12}{35} \times \frac{5}{8})（连续乘法，交叉约分）
    (= \frac{5 \times 7 \times 12 \times 5}{6 \times 10 \times 35 \times 8} = \frac{2100}{1680} = \frac{5}{4})
46. (\left(\frac{2}{3} \times \frac{3}{4}\right) \times \left(\frac{4}{5} \times \frac{5}{6}\right))（结合律）
    (= \frac{1}{2} \times \frac{2}{3} = \frac{1}{3})
47. (\frac{3}{4} \times \frac{5}{6} \times \frac{7}{8} \times \frac{8}{7} \times \frac{6}{5})（逆用乘法，约分后为1）
    (= \frac{3}{4} \times \left(\frac{5}{6} \times \frac{6}{5}\right) \times \left(\frac{7}{8} \times \frac{8}{7}\right) = \frac{3}{4} \times 1 \times 1 = \frac{3}{4})
48. (\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{5}{6})（连续约分）
    (= \frac{1}{6})
49. (\frac{7}{12} \times \frac{5}{14} + \frac{3}{8} \times \frac{4}{9})
    (= \frac{5}{24} + \frac{1}{6} = \frac{5}{24} + \frac{4}{24} = \frac{9}{24} = \frac{3}{8})
50. (\left(\frac{1}{4} - \frac{1}{6}\right) \times \frac{12}{5})
    (= \frac{1}{12} \times \frac{12}{5} = \frac{1}{5})
51. (\frac{2}{5} \times \frac{3}{4} \times \frac{5}{6} \times \frac{4}{3})（交叉约分后为1）
    (= 1)
52. (\frac{9}{10} \times \left(\frac{2}{3} - \frac{1}{5}\right) \times \frac{5}{6})
    (= \frac{9}{10} \times \frac{7}{15} \times \frac{5}{6} = \frac{9 \times 7 \times 5}{10 \times 15 \times 6} = \frac{315}{900} = \frac{7}{20})
53. (\frac{3}{7} \times \frac{14}{15} \times \frac{5}{6} \times \frac{9}{10})
    (= \frac{3 \times 14 \times 5 \times 9}{7 \times 15 \times 6 \times 10} = \frac{1890}{6300} = \frac{3}{10})
54. (\left(\frac{1}{2} + \frac{1}{3} + \frac{1}{4}\right) \times \frac{12}{13})
    (= \frac{1}{2} \times \frac{12}{13} + \frac{1}{3} \times \frac{12}{13} + \frac{1}{4} \times \frac{12}{13} = \frac{6}{13} + \frac{4}{13} + \frac{3}{13} = \frac{13}{13} = 1)
55. (\frac{5}{8} \times \frac{4}{9} \times \frac{3}{10} \times \frac{2}{7})
    (= \frac{5 \times 4 \times 3 \times 2}{8 \times 9 \times 10 \times 7} = \frac{120}{5040} = \frac{1}{42})
56. (\frac{7}{16} \times \frac{8}{21} \times \frac{3}{14} \times \frac{4}{9})
    (= \frac{7 \times 8 \times 3 \times 4}{16 \times 21 \times 14 \times 9} = \frac{672}{42336} = \frac{1}{63})
57. (\frac{2}{15} \times \frac{3}{8} \times \frac{4}{9} \times \frac{5}{12})
    (= \frac{2 \times 3 \times 4 \times 5}{15 \times 8 \times 9 \times 12} = \frac{120}{12960} = \frac{1}{108})
58. (\frac{3}{20} \times \frac{5}{18} \times \frac{9}{25} \times \frac{10}{27})
    (= \frac{3 \times 5 \times 9 \times 10}{20 \times 18 \times 25 \times 27} = \frac{1350}{243000} = \frac{1}{180})
59. (\frac{11}{24} \times \frac{6}{33} \times \frac{4}{15} \times \frac{25}{16})
    (= \frac{11 \times 6 \times 4 \times 25}{24 \times 33 \times 15 \times 16} = \frac{6600}{190080} = \frac{11}{316} = \frac{1}{28.727…})（注：实际计算中应避免复杂分数，此处为示例，建议先约分：(\frac{11}{24} \times \frac{6}{33} = \frac{1}{12})，(\frac{4}{15} \times \frac{25}{16} = \frac{5}{12})，再相乘得(\frac{5}{144})）
60. (\left(\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}\right) \div \left(\frac{5}{6} \times \frac{6}{7} \times \frac{7}{8}\right))（结合分数除法）
    (= \frac{2}{5} \div \frac{5}{8} = \frac{2}{5} \times \frac{8}{5} = \frac{16}{25})

分数乘分数计算技巧总结表

相关问答FAQs

问：分数乘分数计算时，一定要先约分吗？能不能先算出积再约分？
答：两种方法都可以，但先约分能简化计算，减少大数运算的难度，例如计算(\frac{2}{3} \times \frac{3}{4})，若先约分，(\frac{2}{3})的3和(\frac{3}{4})的3约去，得(\frac{2}{4} = \frac{1}{2})；若先算积，(\frac{2 \times 3}{3 \times 4} = \frac{6}{12})，再约分得(\frac{1}{2})，结果相同，但先约分更高效，尤其对于分子分母较大的分数。

问：分数乘法的混合运算中，什么时候用乘法分配律更简便？
答：当算式中有相同因数时，用乘法分配律可简化计算，\frac{2}{5} \times \frac{3}{7} - \frac{1}{5} \times \frac{3}{7})，观察到两个乘法算式都有因数(\frac{3}{7})，可提取公因数：(\left(\frac{2}{5} - \frac{1}{5}\right) \times \frac{3}{7} = \frac{1}{5} \times \frac{3}{7} = \frac{3}{35})，避免分别计算再相减,减少步骤和出错概率。