题目内容
计算下面各题，写出主要过程．
[2
+（5.4-2
）×1
]÷6
1
+2
+3
+4
+5
+6
（
+
+
+
）×（
+
+
+
）-（
+
+
+
+
）×（
+
+
）
[2
| 1 |
| 3 |
| 2 |
| 3 |
| 2 |
| 3 |
| 8 |
| 9 |
1
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
（
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
考点：分数的巧算,整数、分数、小数、百分数四则混合运算
专题：计算问题（巧算速算）
分析：（1）首先将每个分数都化成假分数，然后反复使用乘法分配律简算即可．
（2）将
分成
-
，
分成
-
…然后简算即可．
（3）首先根据乘法分配律将原式转化成（
+
+
+
）×（
+
+
）+（
+
+
+
）×
-（
+
+
+
）×（
+
+
）-
×（
+
+
），然后再根据乘法分配律简算即可．
（2）将
| 1 |
| 6 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 12 |
| 1 |
| 3 |
| 1 |
| 4 |
（3）首先根据乘法分配律将原式转化成（
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
解答：
解：（1）[2
+（5.4-2
）×1
]÷6
=[
+（
-
）×
]×
=[
+
×
-
×
]×
=[
+9-
]×
=
×
+9×
-
×
=
+
-
=1
（2）1
+2
+3
+4
+5
+6
=（1+2+3+4+5+6）+
+
+
+
+
+
=21+
-
+
-
+
-
+
-
+
-
+
-
=21+
-
=21
（3）（
+
+
+
）×（
+
+
+
）-（
+
+
+
+
）×（
+
+
）
=（
+
+
+
）×（
+
+
）+（
+
+
+
）×
-（
+
+
+
）×（
+
+
）-
×（
+
+
）
=（
+
+
+
）×
-
×（
+
+
）
=
×
+（
+
+
）×
-
×（
+
+
）
=
| 1 |
| 3 |
| 2 |
| 3 |
| 2 |
| 3 |
| 8 |
| 9 |
=[
| 7 |
| 3 |
| 27 |
| 5 |
| 8 |
| 3 |
| 5 |
| 3 |
| 9 |
| 62 |
=[
| 7 |
| 3 |
| 27 |
| 5 |
| 5 |
| 3 |
| 8 |
| 3 |
| 5 |
| 3 |
| 9 |
| 62 |
=[
| 7 |
| 3 |
| 40 |
| 9 |
| 9 |
| 62 |
=
| 7 |
| 3 |
| 9 |
| 62 |
| 9 |
| 62 |
| 40 |
| 9 |
| 9 |
| 62 |
=
| 21 |
| 62 |
| 81 |
| 62 |
| 40 |
| 62 |
=1
（2）1
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
=（1+2+3+4+5+6）+
| 1 |
| 6 |
| 1 |
| 12 |
| 1 |
| 20 |
| 1 |
| 30 |
| 1 |
| 42 |
| 1 |
| 56 |
=21+
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 5 |
| 1 |
| 5 |
| 1 |
| 6 |
| 1 |
| 6 |
| 1 |
| 7 |
| 1 |
| 7 |
| 1 |
| 8 |
=21+
| 1 |
| 2 |
| 1 |
| 8 |
=21
| 3 |
| 8 |
（3）（
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
=（
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
=（
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
=
| 1 |
| 5 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
| 1 |
| 13 |
| 1 |
| 13 |
| 1 |
| 7 |
| 1 |
| 9 |
| 1 |
| 11 |
=
| 1 |
| 65 |
点评：此题主要考查了根据算式中各个数的特点适当变形，以及运用乘法分配律简算的能力．
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