【分数加减结合律简便计算50道】在数学运算中，合理运用运算定律可以大大提升计算效率和准确性。其中，分数的加减法结合律是简化计算的重要方法之一。通过合理地调整运算顺序，可以将相同的分母合并、或先进行部分运算，从而减少计算步骤，提高准确率。
本文整理了50道分数加减结合律简便计算题，帮助学生掌握这一技巧，并通过表格形式展示每道题的详细解答过程与答案。
一、分数加减结合律简介
分数的加减法结合律指的是：
a + b + c = (a + b) + c = a + (b + c)
对于减法，也可以适当使用结合律（注意符号变化）。
在实际计算中，我们可以根据题目中的分母是否相同，选择合适的组合方式，使计算更加简便。
二、50道分数加减结合律简便计算题及答案
| 序号 | 题目 | 解答过程 | 答案 |
| 1 | 1/2 + 1/3 + 1/6 | 1/2 + 1/6 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 2 | 3/4 + 1/8 + 1/8 | 1/8 + 1/8 = 1/4; 3/4 + 1/4 = 1 | 1 |
| 3 | 2/5 + 3/10 + 1/10 | 3/10 + 1/10 = 4/10 = 2/5; 2/5 + 2/5 = 4/5 | 4/5 |
| 4 | 5/6 - 1/3 - 1/6 | 5/6 - 1/6 = 4/6 = 2/3; 2/3 - 1/3 = 1/3 | 1/3 |
| 5 | 7/8 + 1/8 - 3/4 | 7/8 + 1/8 = 1; 1 - 3/4 = 1/4 | 1/4 |
| 6 | 1/2 + 2/3 + 1/6 | 1/2 + 1/6 = 2/3; 2/3 + 2/3 = 4/3 | 4/3 |
| 7 | 3/5 + 2/10 + 1/5 | 2/10 = 1/5; 3/5 + 1/5 = 4/5; 4/5 + 1/5 = 1 | 1 |
| 8 | 4/7 + 3/7 - 2/7 | 4/7 + 3/7 = 7/7 = 1; 1 - 2/7 = 5/7 | 5/7 |
| 9 | 5/9 + 1/3 + 1/9 | 5/9 + 1/9 = 6/9 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 10 | 1/4 + 3/8 + 1/8 | 3/8 + 1/8 = 4/8 = 1/2; 1/4 + 1/2 = 3/4 | 3/4 |
| 11 | 2/3 + 1/6 + 1/6 | 1/6 + 1/6 = 2/6 = 1/3; 2/3 + 1/3 = 1 | 1 |
| 12 | 7/10 - 2/5 - 1/10 | 2/5 = 4/10; 7/10 - 4/10 = 3/10; 3/10 - 1/10 = 2/10 = 1/5 | 1/5 |
| 13 | 3/4 + 1/2 - 1/4 | 3/4 - 1/4 = 2/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
| 14 | 5/6 + 1/6 - 1/3 | 5/6 + 1/6 = 6/6 = 1; 1 - 1/3 = 2/3 | 2/3 |
| 15 | 2/5 + 1/10 + 3/10 | 1/10 + 3/10 = 4/10 = 2/5; 2/5 + 2/5 = 4/5 | 4/5 |
| 16 | 3/8 + 5/8 - 1/4 | 3/8 + 5/8 = 8/8 = 1; 1 - 1/4 = 3/4 | 3/4 |
| 17 | 1/3 + 2/6 + 1/3 | 2/6 = 1/3; 1/3 + 1/3 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 18 | 4/9 + 2/9 + 1/9 | 4/9 + 2/9 = 6/9 = 2/3; 2/3 + 1/9 = 7/9 | 7/9 |
| 19 | 5/7 + 1/7 - 2/7 | 5/7 + 1/7 = 6/7; 6/7 - 2/7 = 4/7 | 4/7 |
| 20 | 1/2 + 1/4 + 1/4 | 1/4 + 1/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
| 21 | 3/5 + 1/5 + 1/5 | 3/5 + 1/5 = 4/5; 4/5 + 1/5 = 1 | 1 |
| 22 | 7/12 + 1/12 + 2/12 | 7/12 + 1/12 = 8/12 = 2/3; 2/3 + 2/12 = 2/3 + 1/6 = 5/6 | 5/6 |
| 23 | 2/3 + 1/6 + 1/6 | 1/6 + 1/6 = 2/6 = 1/3; 2/3 + 1/3 = 1 | 1 |
| 24 | 5/8 + 1/8 + 1/4 | 5/8 + 1/8 = 6/8 = 3/4; 3/4 + 1/4 = 1 | 1 |
| 25 | 3/7 + 2/7 + 1/7 | 3/7 + 2/7 = 5/7; 5/7 + 1/7 = 6/7 | 6/7 |
| 26 | 4/5 + 1/10 + 1/10 | 1/10 + 1/10 = 2/10 = 1/5; 4/5 + 1/5 = 1 | 1 |
| 27 | 1/2 + 3/4 - 1/4 | 3/4 - 1/4 = 2/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
| 28 | 5/6 + 1/3 - 1/6 | 5/6 - 1/6 = 4/6 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 29 | 2/5 + 1/5 + 2/5 | 2/5 + 1/5 = 3/5; 3/5 + 2/5 = 1 | 1 |
| 30 | 7/10 + 1/10 + 1/5 | 7/10 + 1/10 = 8/10 = 4/5; 4/5 + 1/5 = 1 | 1 |
| 31 | 3/4 + 1/8 + 1/8 | 1/8 + 1/8 = 2/8 = 1/4; 3/4 + 1/4 = 1 | 1 |
| 32 | 5/9 + 2/9 + 1/9 | 5/9 + 2/9 = 7/9; 7/9 + 1/9 = 8/9 | 8/9 |
| 33 | 2/3 + 1/6 + 1/6 | 1/6 + 1/6 = 2/6 = 1/3; 2/3 + 1/3 = 1 | 1 |
| 34 | 4/7 + 2/7 - 1/7 | 4/7 + 2/7 = 6/7; 6/7 - 1/7 = 5/7 | 5/7 |
| 35 | 1/2 + 1/3 + 1/6 | 1/2 + 1/6 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 36 | 5/8 + 1/8 + 1/4 | 5/8 + 1/8 = 6/8 = 3/4; 3/4 + 1/4 = 1 | 1 |
| 37 | 3/5 + 1/10 + 1/10 | 1/10 + 1/10 = 2/10 = 1/5; 3/5 + 1/5 = 4/5 | 4/5 |
| 38 | 7/12 + 1/12 + 2/12 | 7/12 + 1/12 = 8/12 = 2/3; 2/3 + 2/12 = 2/3 + 1/6 = 5/6 | 5/6 |
| 39 | 1/3 + 2/6 + 1/3 | 2/6 = 1/3; 1/3 + 1/3 = 2/3; 2/3 + 1/3 = 1 | 1 |
| 40 | 4/5 + 1/5 - 1/10 | 4/5 + 1/5 = 1; 1 - 1/10 = 9/10 | 9/10 |
| 41 | 2/7 + 3/7 + 1/7 | 2/7 + 3/7 = 5/7; 5/7 + 1/7 = 6/7 | 6/7 |
| 42 | 3/4 + 1/2 - 1/4 | 3/4 - 1/4 = 2/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
| 43 | 5/6 + 1/6 - 1/3 | 5/6 + 1/6 = 6/6 = 1; 1 - 1/3 = 2/3 | 2/3 |
| 44 | 1/2 + 1/4 + 1/4 | 1/4 + 1/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
| 45 | 2/3 + 1/6 + 1/6 | 1/6 + 1/6 = 2/6 = 1/3; 2/3 + 1/3 = 1 | 1 |
| 46 | 7/8 + 1/8 - 3/4 | 7/8 + 1/8 = 1; 1 - 3/4 = 1/4 | 1/4 |
| 47 | 5/9 + 1/9 + 2/9 | 5/9 + 1/9 = 6/9 = 2/3; 2/3 + 2/9 = 8/9 | 8/9 |
| 48 | 3/5 + 2/5 + 1/5 | 3/5 + 2/5 = 5/5 = 1; 1 + 1/5 = 6/5 | 6/5 |
| 49 | 4/7 + 2/7 + 1/7 | 4/7 + 2/7 = 6/7; 6/7 + 1/7 = 7/7 = 1 | 1 |
| 50 | 1/2 + 3/4 - 1/4 | 3/4 - 1/4 = 2/4 = 1/2; 1/2 + 1/2 = 1 | 1 |
三、总结
通过以上50道题目的练习，可以看出合理运用分数加减结合律可以显著提高计算效率，尤其是在处理多个分数相加减时，灵活调整运算顺序能有效避免复杂的通分操作，从而节省时间并减少出错概率。
建议学生在日常练习中多尝试使用结合律，逐步培养良好的运算习惯和思维能力。
