WEBVTT

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接下来利用分配律来解题

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分配律的意思

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就是说

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假设有a(b+c)

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需要用a乘以这个括号里的内容

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那么a要同时与b和c相乘

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所以也就等于ab+ac

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而不是ab+c

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按照分配律这么做是完全正确的

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我来举个例子

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假设5（3+7）

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如果是按照四则运算顺序来做

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大家会看到这就是5・10

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5・10得50

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这是正确答案

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现在用分配律来解

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原式等于5・3+5・7

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也就是15+35

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还是50

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要是5只乘3 那么得到15

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再加7是22 答案就不对了

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所以5乘的是整个括号

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括号里的数字都要乘5

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5乘的是括号内数的和

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好

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道理明白了 现在来应用 做一些习题

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看（a）

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1/2(x-y)-4

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1/2乘的是整个括号

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所以原式等于1/2x-1/2y-4

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这就做完了

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再看（c）

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6+（x-5）+7

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其实

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这个题并不牵扯分配律的内容

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直接把括号去掉就可以

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6加上后边的

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也就是6+x-5+7

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或者可以这么看 6+--

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后边是2

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-5+7=2 2+6=8

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所以结果是8+x

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这个也做完了

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还不错

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刚做的是（c）

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下面做（e）

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4(m+7)-6(4-m)

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用分配律来看

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4・m是4m 4・7=28

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然后后边的计算有两种方法

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先来看第一种

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可以是保留括号 减6・4=24

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6・-m=-6m

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注意 可以直接用-6乘

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那么-6m就是正的了 但是我是分两步来做的

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先乘6 再乘-1

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原式等于4m+28--

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把负号分配进括号

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或者看成是-1乘以括号

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-1・24是-24

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-1・-6m是6m

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下面来把m的项加起来 4m+6m得10m

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然后是常数项

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28-24得4

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看下边的题目

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运用分配律

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化简下列分式

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那么我还是隔一个做一个吧

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第一道题 （8x+12）/4

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之所以说是分配律

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可以看成是整个分子除以4

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既然整个要除以4

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那么每一项都要除以4

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可以看成是

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1/4(8x+12)

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这两个式子是等价的

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每个数都除以4

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也就是每个数都乘以1/4

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要是这么做的话

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式子等于8x/4+12/4

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反而有点像分式的加法

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8/4=2

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这就是2x+3

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这是一种方法

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或者还可以这么做

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1/4・8x=2x 1/4・12=3 结果是2x+3

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不管怎样 结果是一样的

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来看（c）

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（11x+12）/2

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仿照前一个题

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这个可以等于

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11/2 x

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或者11x/2

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加12/2=6

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再来做一道

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（e）

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这个比较不一样

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分式前边有个负号

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然后是（6z-2）/3

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那么首先可以看成

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是-1/3（6z-2）

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这两个式子是等价的

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大家看

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这是-1/3

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可以把括号前边加个1

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这样就是-1/3（6z-2）

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然后就可以用分配律了

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-1/3・6z就是-2z

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-1/3・-2

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负号抵消 得2/3

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就做完了