小学奥数《简便计算》.doc

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简便计算
一、加减法巧算之凑整与组合思想

1、198919881987198619851984198319821981198019791978…987654321

练习1、199198197196195194…54321

2、加法金字塔，计算下面数的和：

&nbsp; &nbsp; &nbsp;

练习2、

&nbsp;

3、计算：191991999…

练习3、计算：999999…

二、乘除法巧算之提取公因数与组合思想

1、200019991999199819981997199719961996199519951994

2、200820072006200620072008

练习2、200820072006200620072008

3、333332332333332333333332

练习3、19911992199219921992199119911991

三、四则混合巧算之综合技巧[来源:学,科,网Z
1、235711131719÷38÷51÷65÷77

练习1、(11109…321)÷(22242527)

2、

练习2、333333333333999999777777

3、

练习3、14285714285714285763

四、小数计算与换元思想、循环小数互化与错位相减技巧

1、1.13.35.57.79.911.1113.1315.1517.1719.19

2、0.00.10.20.30.70.8

练习2、0.0.1250.0.1（结果保留三位小数）

3、

4、

练习4、

5、(＋)() ()()

练习5、

五、估算、放缩综合技巧

1、求数a…的整数部分。

练习1、 A8.88.988.9988.99988.99998，A的整数部分是 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;。

2、求下式中S的整数部分：S

练习2、求数的整数部分是几？

3、2.454.052.464.042.474.032.484.022.494.01

练习3、8.011.248.021.238.031.22的整数部分是多少？

4、

练习4、

5、与50的大小

六、分数计算之拆分、裂项与通项归纳

1、

练习1、

2、

练习2、

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
8个90
30、＋＋＋…＋
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 9个19

练习30、2004×20032002－2002×20032004

七、计算综合之复杂分数裂项与整数裂项强化篇
1、
1×2×4＋2×4×8＋3×6×12＋…＋100×200×400
&nbsp; &nbsp;1×3×9＋2×6×18＋3×9×27＋…＋100×300×900

练习1、
&nbsp; &nbsp; &nbsp; 1×2×4×6＋2×4×8×12＋3×6×12×18＋…＋100×200×400×600
&nbsp; &nbsp; &nbsp; 1×3×6×9＋2×6×12×18＋3×9×18×27＋…＋100×300×600×900

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1
2、 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; + &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; 1×2×3 &nbsp; &nbsp; &nbsp;2×3×4 &nbsp; &nbsp; &nbsp;3×4×5 &nbsp; &nbsp; &nbsp; 9×10×11

练习2、 &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 1
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; —————＋—————＋—————＋…＋——————
&nbsp; &nbsp; &nbsp; &nbsp; 1×2×3×4 &nbsp;2×3×4×5 &nbsp;3×4×5×6 &nbsp; &nbsp; &nbsp;9×10×11×12
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;

3、 ＋＋＋＋＋＋

练习3、＋＋＋＋＋＋＋＋＝__________。

&nbsp; &nbsp; &nbsp; &nbsp; 32＋1 &nbsp; &nbsp; 52＋1 &nbsp; &nbsp; &nbsp;72＋1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 19932＋1 &nbsp; &nbsp;19952＋1
&nbsp;4、 &nbsp;——— ＋ ——— ＋ &nbsp; &nbsp; &nbsp; &nbsp;＋ … ＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;＋ &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; 32－1 &nbsp; &nbsp; 52－1 &nbsp; &nbsp; &nbsp;72－1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 19932－1 &nbsp; &nbsp;19952－1

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;22＋1 &nbsp; &nbsp; 32＋1 &nbsp; &nbsp; &nbsp;42＋1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;20052＋1 &nbsp;
&nbsp; &nbsp;练习4、 &nbsp; ——— ＋ ——— ＋ ——— ＋ … ＋ ————
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;22－1 &nbsp; 32－1 &nbsp; &nbsp; &nbsp;42－1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;20052－1

5、1×2＋2×3＋3×4＋…＋99×100

练习5、4×5＋5×6＋6×7＋…＋19×20

6、[(－＋－＋－)－1]÷＝_________。

八、计算综合之复杂公式

&nbsp; &nbsp; &nbsp; 12＋22＋32＋…＋20062
1、 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; 1＋2＋3＋…＋2006

练习1、 ()2 &nbsp; +()2＋…＋()2

2、()3 &nbsp;+()3＋…＋()3

3、 1×2×3＋2×3×4＋3×4×5＋…＋8×9×10

练习3、1×2＋2×3＋3×4＋4×5＋5×6＋6×7＋7×8＋8×9＋9×10

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;3 &nbsp; &nbsp; &nbsp; &nbsp; 5 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;21
&nbsp; 4、 &nbsp; &nbsp; &nbsp; ＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;＋…＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;12 &nbsp; &nbsp; &nbsp;12＋22 &nbsp; &nbsp; 12＋22＋32 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 12＋22＋…＋102

练习4、 &nbsp; 2 &nbsp; &nbsp; &nbsp; &nbsp; 6 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;12 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;110
&nbsp; &nbsp; &nbsp; &nbsp; —— ＋ ———— ＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ＋…＋ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;13 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;13＋23 &nbsp; &nbsp; &nbsp; &nbsp; 13＋23＋33 &nbsp; &nbsp; &nbsp; &nbsp; 13＋23＋…＋103

九、综合计算
1、++++ + &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;

练习1、（1）+++…..+ &nbsp; &nbsp; （2）+++ +

2、1－+－+－
&nbsp; &nbsp;

练习2、1－+－+

3、+++++ &nbsp; &nbsp; &nbsp; &nbsp;

练习3、（1）+++………+ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; （2） ++++

4、（1）1234+2341+3412+4123 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; （2）23456+34562+45623+56234+62345

练习4、（1）45678+56784+67845+78456+84567 &nbsp;

5、1+++·····+

练习5、

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