50道分数除法及答案，从入门到精通，这些题你会做吗？

，掌握分数除法的计算方法对解决实际问题至关重要，分数除法的核心是将除法转化为乘法，即“除以一个不为零的数，等于乘这个数的倒数”，下面通过50道分数除法题目及详细解析，帮助大家巩固这一知识点。 及答案解析：**

1. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2
2. 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4
3. 7/8 ÷ 1/4 = 7/8 × 4/1 = 28/8 = 7/2
4. 2/5 ÷ 3/10 = 2/5 × 10/3 = 20/15 = 4/3
5. 4/9 ÷ 8/3 = 4/9 × 3/8 = 12/72 = 1/6
6. 5/12 ÷ 10/9 = 5/12 × 9/10 = 45/120 = 3/8
7. 3/7 ÷ 2/7 = 3/7 × 7/2 = 21/14 = 3/2
8. 8/11 ÷ 4/11 = 8/11 × 11/4 = 88/44 = 2
9. 6/13 ÷ 3/13 = 6/13 × 13/3 = 78/39 = 2
10. 9/16 ÷ 3/16 = 9/16 × 16/3 = 144/48 = 3
11. 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2
12. 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3
13. 3/4 ÷ 1/5 = 3/4 × 5/1 = 15/4
14. 4/5 ÷ 1/6 = 4/5 × 6/1 = 24/5
15. 5/6 ÷ 1/7 = 5/6 × 7/1 = 35/6
16. 7/9 ÷ 2/9 = 7/9 × 9/2 = 63/18 = 7/2
17. 8/15 ÷ 4/15 = 8/15 × 15/4 = 120/60 = 2
18. 5/8 ÷ 5/8 = 5/8 × 8/5 = 40/40 = 1
19. 3/10 ÷ 3/10 = 3/10 × 10/3 = 30/30 = 1
20. 7/12 ÷ 7/12 = 7/12 × 12/7 = 84/84 = 1
21. 2/7 ÷ 3/14 = 2/7 × 14/3 = 28/21 = 4/3
22. 4/11 ÷ 2/33 = 4/11 × 33/2 = 132/22 = 6
23. 5/13 ÷ 10/39 = 5/13 × 39/10 = 195/130 = 3/2
24. 9/20 ÷ 3/10 = 9/20 × 10/3 = 90/60 = 3/2
25. 6/25 ÷ 2/5 = 6/25 × 5/2 = 30/50 = 3/5
26. 8/21 ÷ 4/7 = 8/21 × 7/4 = 56/84 = 2/3
27. 10/27 ÷ 5/9 = 10/27 × 9/5 = 90/135 = 2/3
28. 12/35 ÷ 3/7 = 12/35 × 7/3 = 84/105 = 4/5
29. 7/18 ÷ 14/27 = 7/18 × 27/14 = 189/252 = 3/4
30. 5/24 ÷ 15/32 = 5/24 × 32/15 = 160/360 = 4/9
31. 3/16 ÷ 9/20 = 3/16 × 20/9 = 60/144 = 5/12
32. 4/25 ÷ 2/15 = 4/25 × 15/2 = 60/50 = 6/5
33. 5/28 ÷ 10/21 = 5/28 × 21/10 = 105/280 = 3/8
34. 7/30 ÷ 14/45 = 7/30 × 45/14 = 315/420 = 3/4
35. 8/33 ÷ 16/22 = 8/33 × 22/16 = 176/528 = 1/3
36. 9/40 ÷ 3/25 = 9/40 × 25/3 = 225/120 = 15/8
37. 10/49 ÷ 5/14 = 10/49 × 14/5 = 140/245 = 4/7
38. 11/54 ÷ 22/27 = 11/54 × 27/22 = 297/1188 = 1/4
39. 12/65 ÷ 6/13 = 12/65 × 13/6 = 156/390 = 2/5
40. 13/72 ÷ 13/36 = 13/72 × 36/13 = 468/936 = 1/2
41. 1/3 ÷ 2/5 = 1/3 × 5/2 = 5/6
42. 3/5 ÷ 4/7 = 3/5 × 7/4 = 21/20
43. 2/7 ÷ 5/8 = 2/7 × 8/5 = 16/35
44. 4/9 ÷ 7/12 = 4/9 × 12/7 = 48/63 = 16/21
45. 5/11 ÷ 8/15 = 5/11 × 15/8 = 75/88
46. 6/13 ÷ 9/16 = 6/13 × 16/9 = 96/117 = 32/39
47. 7/15 ÷ 10/21 = 7/15 × 21/10 = 147/150 = 49/50
48. 8/17 ÷ 12/25 = 8/17 × 25/12 = 200/204 = 50/51
49. 9/19 ÷ 14/27 = 9/19 × 27/14 = 243/266
50. 10/23 ÷ 15/34 = 10/23 × 34/15 = 340/345 = 68/69

为了更直观地展示部分题目及答案，以下表格列出前10道题的详细计算过程： | 计算过程 | 简化结果 | |------|----------|----------| | 1. 3/4 ÷ 1/2 | 3/4 × 2/1 = 6/4 | 3/2 | | 2. 5/6 ÷ 2/3 | 5/6 × 3/2 = 15/12 | 5/4 | | 3. 7/8 ÷ 1/4 | 7/8 × 4/1 = 28/8 | 7/2 | | 4. 2/5 ÷ 3/10 | 2/5 × 10/3 = 20/15 | 4/3 | | 5. 4/9 ÷ 8/3 | 4/9 × 3/8 = 12/72 | 1/6 | | 6. 5/12 ÷ 10/9 | 5/12 × 9/10 = 45/120 | 3/8 | | 7. 3/7 ÷ 2/7 | 3/7 × 7/2 = 21/14 | 3/2 | | 8. 8/11 ÷ 4/11 | 8/11 × 11/4 = 88/44 | 2 | | 9. 6/13 ÷ 3/13 | 6/13 × 13/3 = 78/39 | 2 | | 10. 9/16 ÷ 3/16 | 9/16 × 16/3 = 144/48 | 3 |

分数除法计算要点总结：

1. 倒数转换：除以一个分数等于乘以这个分数的倒数（分子分母交换位置）。
2. 约分简化：计算前可先约分，或在乘法结果后约分，使计算更简便。
3. 符号处理：若除数为负数，结果符号根据“同号得正，异号得负”确定。
4. 整数处理：整数可看作分母为1的分数（如5=5/1），便于统一计算。

相关问答FAQs：

问题1：分数除法中，为什么可以转化为乘以倒数？
解答：分数除法的转化基于除法的定义和分数的性质，计算3/4 ÷ 1/2，相当于求“3/4”中包含多少个“1/2”，根据分数乘法的意义，3/4 × 2/1 = 6/4 = 3/2，即3/4包含3/2个1/2，从数学推导上看，若a/b ÷ c/d = k，则(a/b) = k × (c/d)，两边同乘d/c得k = (a/b) × (d/c)，因此除法转化为乘法是合理的。

问题2：分数除法结果如何判断是否为最简分数？
解答：分数结果需满足分子分母互质（最大公因数为1），判断方法包括：

• 短除法：用分子分母的公因数连续约分，直至无法再约分（如12/16→3/4）。
• 质因数分解：将分子分母分解质因数，约去相同因数（如18/30=（2×3×3）/（2×3×5）=3/5）。
• 辗转相除法：适用于较大数，如求49/63的最大公因数：63÷49=1余14，49÷14=3余7，14÷7=2余0，故最大公因数为7，49/63=7/9。