30道分数简便运算（30道分数简便运算及答案）

## 分数简便运算30题详解

简介:

分数简便运算是在保证计算结果不变的前提下，运用运算定律和性质，使计算过程简化，从而提高计算效率的方法。 熟练掌握分数简便运算，对于提高数学运算能力至关重要。本篇文章提供30道分数简便运算题，并详细讲解其解题思路，帮助读者更好地理解和掌握分数简便运算技巧。### 一、 加减法简便运算

1. 利用加法结合律和交换律:

1. (1/2 + 1/3) + 2/3 = 1/2 + (1/3 + 2/3) = 1/2 + 1 = 3/2 2. 1/4 + 3/5 + 3/4 + 2/5 = (1/4 + 3/4) + (3/5 + 2/5) = 1 + 1 = 2 3. 2/7 + 5/9 + 5/7 + 4/9 = (2/7 + 5/7) + (5/9 + 4/9) = 1 + 1 = 2

2. 利用减法性质:

4. 5/6 - 1/3 - 1/6 = (5/6 - 1/6) - 1/3 = 2/3 - 1/3 = 1/3 5. 7/8 - 1/4 - 3/8 = (7/8 - 3/8) - 1/4 = 1/2 - 1/4 = 1/4### 二、 乘除法简便运算

1. 利用乘法结合律和交换律:

6. 2/3 × 3/4 × 4/5 = (2/3 × 3/4) × 4/5 = 1/2 × 4/5 = 2/5 7. 5/6 × 1/2 × 12/5 = (5/6 × 12/5) × 1/2 = 2 × 1/2 = 1 8. 3/7 × 14/9 × 3/2 = (3/7 × 14/7) × 3/2 = 2 × 3/2 = 3

2. 利用除法性质和乘法倒数:

9. 2/5 ÷ 3/4 × 3/2 = 2/5 × 4/3 × 3/2 = 8/10 = 4/5 10. 3/8 ÷ 1/4 ÷ 3/2 = 3/8 × 4/1 × 2/3 = 24/24 = 1### 三、 混合运算简便运算11. 1/2 + 1/3 × 2/5 = 1/2 + 2/15 = 11/30 12. 2/3 × (1/4 + 1/2) = 2/3 × 3/4 = 1/2 13. (5/6 - 1/3) ÷ 1/2 = (5/6 - 2/6) × 2 = 1/2 × 2 = 1 14. 1/2 + 1/4 - 1/8 × 2 = 1/2 + 1/4 - 1/4 = 1/2 15. 3/4 × (1/2 + 1/3) - 1/6 = 3/4 × 5/6 - 1/6 = 5/8 - 1/6 = 11/24### 四、 包含带分数的简便运算16. 1又1/2 + 2又1/3 = 3 + 1/2 + 1/3 = 3 + 5/6 = 23/6 17. 3又1/4 - 1又1/2 = 2 - 1/4 = 7/4 18. 2又1/2 × 1又1/3 = 5/2 × 4/3 = 10/3 19. 4又1/2 ÷ 2又1/4 = 9/2 ÷ 9/4 = 9/2 × 4/9 = 2 20. 1又1/2 + 2又1/3 - 1又1/6 = 3 + 1/2 + 1/3 - 1 -1/6 = 2 + (3/6 + 2/6 - 1/6) = 2 + 2/3 = 8/3### 五、 稍复杂的简便运算21. (1/2 + 1/3) × (2/3 - 1/6) = 5/6 × 1/2 = 5/12 22. 1/2 ÷ (1/3 + 1/4) = 1/2 ÷ 7/12 = 1/2 × 12/7 = 6/7 23. (2/3 + 1/4) ÷ (1/2 -1/6) = 11/12 ÷ 1/3 = 11/12 × 3 = 11/4 24. (1/2 × 2/3) + (1/3 × 3/4) = 1/3 + 1/4 = 7/12 25. (1 - 1/3) ÷ (1/2 + 1/6) = 2/3 ÷ 2/3 = 1### 六、 包含小数的分数简便运算26. 1/2 + 0.25 = 1/2 + 1/4 = 3/4 27. 3/4 - 0.5 = 3/4 - 1/2 = 1/4 28. 0.75 × 2/3 = 3/4 × 2/3 = 1/2 29. 2/5 ÷ 0.4 = 2/5 ÷ 2/5 = 1 30. 0.25 + 1/4 × 2 = 1/4 + 1/2 = 3/4

注意:

以上只是一些例题，实际运算中需要根据具体题目灵活运用各种简便运算方法。 熟能生巧，多练习才能更好地掌握分数简便运算技巧。

分数简便运算30题详解**简介:**分数简便运算是在保证计算结果不变的前提下，运用运算定律和性质，使计算过程简化，从而提高计算效率的方法。 熟练掌握分数简便运算，对于提高数学运算能力至关重要。本篇文章提供30道分数简便运算题，并详细讲解其解题思路，帮助读者更好地理解和掌握分数简便运算技巧。

一、 加减法简便运算**1. 利用加法结合律和交换律:**1. (1/2 + 1/3) + 2/3 = 1/2 + (1/3 + 2/3) = 1/2 + 1 = 3/2 2. 1/4 + 3/5 + 3/4 + 2/5 = (1/4 + 3/4) + (3/5 + 2/5) = 1 + 1 = 2 3. 2/7 + 5/9 + 5/7 + 4/9 = (2/7 + 5/7) + (5/9 + 4/9) = 1 + 1 = 2**2. 利用减法性质:**4. 5/6 - 1/3 - 1/6 = (5/6 - 1/6) - 1/3 = 2/3 - 1/3 = 1/3 5. 7/8 - 1/4 - 3/8 = (7/8 - 3/8) - 1/4 = 1/2 - 1/4 = 1/4

二、 乘除法简便运算**1. 利用乘法结合律和交换律:**6. 2/3 × 3/4 × 4/5 = (2/3 × 3/4) × 4/5 = 1/2 × 4/5 = 2/5 7. 5/6 × 1/2 × 12/5 = (5/6 × 12/5) × 1/2 = 2 × 1/2 = 1 8. 3/7 × 14/9 × 3/2 = (3/7 × 14/7) × 3/2 = 2 × 3/2 = 3**2. 利用除法性质和乘法倒数:**9. 2/5 ÷ 3/4 × 3/2 = 2/5 × 4/3 × 3/2 = 8/10 = 4/5 10. 3/8 ÷ 1/4 ÷ 3/2 = 3/8 × 4/1 × 2/3 = 24/24 = 1

三、 混合运算简便运算11. 1/2 + 1/3 × 2/5 = 1/2 + 2/15 = 11/30 12. 2/3 × (1/4 + 1/2) = 2/3 × 3/4 = 1/2 13. (5/6 - 1/3) ÷ 1/2 = (5/6 - 2/6) × 2 = 1/2 × 2 = 1 14. 1/2 + 1/4 - 1/8 × 2 = 1/2 + 1/4 - 1/4 = 1/2 15. 3/4 × (1/2 + 1/3) - 1/6 = 3/4 × 5/6 - 1/6 = 5/8 - 1/6 = 11/24

四、 包含带分数的简便运算16. 1又1/2 + 2又1/3 = 3 + 1/2 + 1/3 = 3 + 5/6 = 23/6 17. 3又1/4 - 1又1/2 = 2 - 1/4 = 7/4 18. 2又1/2 × 1又1/3 = 5/2 × 4/3 = 10/3 19. 4又1/2 ÷ 2又1/4 = 9/2 ÷ 9/4 = 9/2 × 4/9 = 2 20. 1又1/2 + 2又1/3 - 1又1/6 = 3 + 1/2 + 1/3 - 1 -1/6 = 2 + (3/6 + 2/6 - 1/6) = 2 + 2/3 = 8/3

五、 稍复杂的简便运算21. (1/2 + 1/3) × (2/3 - 1/6) = 5/6 × 1/2 = 5/12 22. 1/2 ÷ (1/3 + 1/4) = 1/2 ÷ 7/12 = 1/2 × 12/7 = 6/7 23. (2/3 + 1/4) ÷ (1/2 -1/6) = 11/12 ÷ 1/3 = 11/12 × 3 = 11/4 24. (1/2 × 2/3) + (1/3 × 3/4) = 1/3 + 1/4 = 7/12 25. (1 - 1/3) ÷ (1/2 + 1/6) = 2/3 ÷ 2/3 = 1

六、 包含小数的分数简便运算26. 1/2 + 0.25 = 1/2 + 1/4 = 3/4 27. 3/4 - 0.5 = 3/4 - 1/2 = 1/4 28. 0.75 × 2/3 = 3/4 × 2/3 = 1/2 29. 2/5 ÷ 0.4 = 2/5 ÷ 2/5 = 1 30. 0.25 + 1/4 × 2 = 1/4 + 1/2 = 3/4**注意:** 以上只是一些例题，实际运算中需要根据具体题目灵活运用各种简便运算方法。 熟能生巧，多练习才能更好地掌握分数简便运算技巧。