小李同学在学习完有理数的运算后,对运算产生了浓厚的兴趣,他借助有理数的运算,定义一种新运算“
”,运算规定:对于任意有理数
,都有
,如
.
(1)计算
的值.
(2)计算
的值.
(3)当
在数轴上的位置如图所示时,化简
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70d930718f7db55a6d63c27d9eb4fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203a8617cd3b5d8d94d1d5b28ea35f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9345bfde45ee8c18a85b268a7778835a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaabe06369bbdd4341f507934bb8872d.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c19f133b5d67aaf16bded813050c8.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b72017ada431d780a27944f5503b98.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fcc6bf525f2f64c7f231090e9bfdae3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/98b30a8e-906c-4df9-93c5-10b2edc4bcb9.png?resizew=191)
更新时间:2022-11-21 07:14:45
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【推荐2】有理数a,b,c在数轴上的位置如图所示,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/23853361-da7a-483c-a44a-64e100c841cd.png?resizew=276)
(1)用“>”“<”或“=”填空:
b______0,
______0,
______0,
______0;
(2)化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421a473589d5abdd504fdb110828611a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/23853361-da7a-483c-a44a-64e100c841cd.png?resizew=276)
(1)用“>”“<”或“=”填空:
b______0,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea712984ea5017140e20bee226fd5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9db8d3facff8f90f28a936fc5b3ab878.png)
(2)化简:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9e1322cf41b689ddc21f075bb76e0c.png)
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【推荐1】有理数a、b、在数轴上的位置如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/90706625-e8b6-44b8-bc6b-96dce6d0bb33.png?resizew=379)
(1)用“>”或“<”填空:a+b 0,c﹣b 0;
(2)化简:|a+b|+|c|﹣|c﹣b|.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/16/90706625-e8b6-44b8-bc6b-96dce6d0bb33.png?resizew=379)
(1)用“>”或“<”填空:a+b 0,c﹣b 0;
(2)化简:|a+b|+|c|﹣|c﹣b|.
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【推荐2】(1)数 a , b , c 在数轴上的位置如图 1 所示且| a || c |:
![](https://img.xkw.com/dksih/QBM/2020/3/19/2422737029627904/2423081633185792/STEM/45d80329b04d4e21a1f995a732c79a43.png?resizew=393)
①填空:| a | , | b a | ,| 2b | .
②化简:| c b | | b a | | a b | .
( 2) a , b , c 大小关系如图 2, 下列各式① b a (c) 0 ; ② (a) b c 0 ;③
④ bc a 0 ;⑤| a b | | c b | | a c | 2b ,其中正确的有 .
![](https://img.xkw.com/dksih/QBM/2020/3/19/2422737029627904/2423081633185792/STEM/45d80329b04d4e21a1f995a732c79a43.png?resizew=393)
①填空:| a | , | b a | ,| 2b | .
②化简:| c b | | b a | | a b | .
( 2) a , b , c 大小关系如图 2, 下列各式① b a (c) 0 ; ② (a) b c 0 ;③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38aa5e6dcc15e19a36c57bffa4b3f55c.png)
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【推荐1】【阅读材料】问题:如何计算
呢?小红带领的数学兴趣小组通过探索完成了这道题的计算.
他们的解法如下:
解:原式=
.
根据材料,请你完成下列计算:
(1)计算:
;
(2)直接写出结果:
=___________;
(3)计算:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacc0efaf0162f834529cc18f8b317f4.png)
他们的解法如下:
解:原式=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d6d0c6c38605c94096a1de207c4a67.png)
根据材料,请你完成下列计算:
(1)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fef1d72bd5a951c383b08aadc42c0b.png)
(2)直接写出结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df9889963ded9c5ffa951856d8dfbf72.png)
(3)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381210e63fc86183da80508b3c2025a1.png)
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【推荐1】阅读材料:“整体思想”是数学解题中的一种重要的思想方法,它在多项式的化简与求值中应用极为广泛.我们知道,
.类似的我们可以把
看成一个整体,则
.请尝试解决:
(1)把
看成一个整体,合并
______;
(2)已知
,求
的值;
(3)已知
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8b9951cf116639b864c9269f6de918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8280bdbac2fa4e050c6ac329f30446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef4105b95c9656c61954014d6ba72d4.png)
(1)把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897aeafa8da0737baa70f64fdf55c269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26cebbb097b55c947a080a600b11f40.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef01e74ca41689fc7449c496c786f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe78079a5fa5c769d73abadc156bfba5.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd503ba2da57af31b83b7f7c956d0452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1684f37e3661b8701f3d1726c24d536d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627236d8c85f1f4829efce0152db670c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89594dcc4e665904d98ee33fd7df3714.png)
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