题目内容
（2012?湖北）计算：(
+
+
+
)-(
+
+
+
)+(
+
+
+
)-(
+
+
+
)=
．
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 6 |
| 1 |
| 8 |
| 1 |
| 3 |
| 1 |
| 6 |
| 1 |
| 9 |
| 1 |
| 12 |
| 1 |
| 4 |
| 1 |
| 8 |
| 1 |
| 12 |
| 1 |
| 16 |
| 1 |
| 5 |
| 1 |
| 10 |
| 1 |
| 15 |
| 1 |
| 20 |
| 65 |
| 144 |
| 65 |
| 144 |
分析：通过分析可知，本式中的各个括号中分数的分母分别和1、2、3、4存在倍数关系，所以原式=
×(1+
+
+
)-
×(1+
+
+
)+
×(1+
+
+
)-
×(1+
+
+
)，然后据分配律进行巧算即可．
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
解答：解：（
+
+
+
）-（
+
+
+
）+（
+
+
+
）+（
+
+
+
）
=
×(1+
+
+
)-
×(1+
+
+
)+
×(1+
+
+
)-
×(1+
+
+
)，
=(1+
+
+
)×(
-
+
-
)，
=
×
，
=
．
| 1 |
| 2 |
| 2 |
| 4 |
| 1 |
| 8 |
| 1 |
| 16 |
| 1 |
| 3 |
| 1 |
| 6 |
| 1 |
| 9 |
| 1 |
| 12 |
| 1 |
| 4 |
| 1 |
| 8 |
| 1 |
| 12 |
| 1 |
| 16 |
| 1 |
| 5 |
| 1 |
| 10 |
| 1 |
| 15 |
| 1 |
| 20 |
=
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
=(1+
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 5 |
=
| 25 |
| 12 |
| 13 |
| 60 |
=
| 65 |
| 144 |
点评：完成本题要认真分析每括号中的每组数据，找出它们之间的共同点，然后再进行巧算．
练习册系列答案
相关题目
