(完整word版)比和比例知识点梳理.pdf

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1、知识点一:比和比例的联系与区别比比例意义表示两数相除表示两个比相等的式子各部分名称9：6=1.5 前项比号后项比值9：6=3：2基本性质比的前项和后项同时乘或除以相同的数（0 除外），比值不变。在比例里，两个外项的积等于两个内项的积。化简比的依据。解比例的依据。知识点二：比和分数、除法的联系名称联系比前项：（比号）后项比值分数分子（分数线）分母分数值除法被除数（除号）除数商知识点三：求比值和化简比意义方法结果求比值前项除以后项所得的商用前项除以后项一个数（是整数、分数或小数）化简比把两个数的比化简成最简单的整数比前项和后项同时乘或除以相同的数（0 除外），也可以用求比 值 的 方法，用前项除以

2、后项，得出一个分数值。一个比知识点四：正比例和反比例的意义和判断方法1、正比例的意义：两种相关联的量，一种量变化另一种量也随着变化，如果这两种量中相对应的两个数的比值（商）一定，这两种量就叫做成正比例的量，它们的关系叫做正比例关系。正比例的关系式：kxy（一定）文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文

3、档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK

4、8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10

5、Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6

6、HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z

7、8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6

8、ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B

9、5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P52、反比例的意义：两种相关联的量，一种量变化另一种量也随着变化，如果这两种量中相对应的两个数的积一定，这两种量就叫做成反比例的量，它们的关系叫做正比例关系。反比例的关系式：kxy（一定）3、判断正、反比例的方法：一找二看三判断（1）找变量：分析数量关系，确定哪两种量是相关联的量。（2）看定量，分析这两种相关联的量，它们之间的关系是商一定还是积一定。（3）判断：如果商一定，就成正比例；如果积一定就成反比例；如果商和积都不是定量，就不成比例4、正比例、反比例的区别与联系名称不同点相同点意义不相同变化方向不

10、相同关系式不同正比例两种量中相对应的两个数的比值，也就是商一一种量扩大（或缩小），另一种量也随之 扩 大kxy（一定）两种相关联的量，一种量变化另一种量也随着文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R

11、10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X

12、6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P

13、2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I

14、6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F

15、9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P

16、5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5定（或 缩

17、小）。变化反比例两种量中相对应的两个数的积一定一种量扩大（或缩小），另一种量也随之 缩 小（或 扩大）。kxy（一定）知识点五：用比例知识解决问题1、按比例分配问题（1）按比例分配应用题：把一个量按照一定的比分配成几部分，求每个部分数量各是多少的应用题叫做按比例分配应用题。（2）解题方法一般方法：把比转化成为分数，用分数方法解答，即先求出总分数，然后求出各部分量占总量的几分之几，最后按照求一个数的几分之几多少的解题方法，分别求出各部分的量是多少归一法：把比看做分得的分数，先求出各部分的总分数，然后再用“总量总份数=平均每份的量（归文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 Z

18、N2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5

19、C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档

20、编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8

21、Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y

22、10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 H

23、M1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8

24、P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5一）”，再用“一份的量各部分量所对应的份数”，求出各部分的量。用比例知识解答：首先设未知量为。再根据题中“已知比等于相对应的量的比”作为等量关系式列出含有 x 的比例式，再解比例求出x。2、用正、反比例知识解答应用题的步骤（1）分析

25、数量关系。判断成什么比例。（）找等量关系。如果成正比例，则按等比找等量关系式；如果成反比例，则按等积找等量关系式。（）解比例式。设未知数为x，并代入等量关系式，得正比例式或反比例式。（）解比例。（）检验并写出答语。文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z

26、8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6

27、ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B

28、5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文

29、档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK

30、8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10

31、Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5文档编码:CK8Z7R10Y10X6 HM1P2Z8P1I6 ZN2F9B5C5P5