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我们做一些有理数相加的问题

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我说有理数这个词是因为

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这本书上是这样讲的 但是更常用的术语是

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分数相加

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我们浏览一下这些题

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看看这些例子

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我们先算一下3/7+2/7

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分母相同 所以只需要把分子相加

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分母是7 3+2=5

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这就是a的解题过程

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我每隔一题做一次 如果全部都做得话需要好长时间

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没有永远那么长 但比我想用的时间要长

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所以直接做c 5/16+5/12

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分母不同

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必须找出公分母 最小公分母

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其实可以是这两个数的任意公倍数

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但是为了简便 我们求最小公倍数

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那么16和12的最小公倍数是什么？

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我们来看一下 16乘以2是32 还没完

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乘以3是48

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48看起来可以

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12除48等于4

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所以用48做公分母

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16要乘以3才能得到48

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所以这里的5也要乘以3

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我们只是把分子分母同时

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乘以某数 所以实际上它没有变

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那么5乘以3等于15

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从这里的12到48

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需要乘以4

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我们若要把5经变换变成这里的分子

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需要乘以4

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5乘以4等于20

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现在分母相同了

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将等于 分母是48

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15加20 是35

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可以约分吗？

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我们来看一下 5不能整除48

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7不能整除48

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这道题这样就做完了

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我们来做一下e

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8/25+7/10

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又一次 分母不相同

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但是我们可以解决

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我们来看一下

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50是能被这两个数整除的最小的数

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25乘以2是50

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8/25 为了得到公分母50 同时乘以2

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所以8必须乘以2

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将是16/50

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然后是7/10 我们让分母变成50

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10乘以5等于50 所以7也要乘以5

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变成35/50

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现在分母相等 是50

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16加35 等于多少？

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10加35等于45 再加6等于51

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所以是51/50

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做一下g

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换一种颜色做

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第g题

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题目中给出7/15

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我用别的颜色写第二项 加上2/9

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又一次 分母不同

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需要找出公分母

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能被15和9整除的最小的数是多少？

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我们来看一下 15乘以2等于30 不对 不能被9整除

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15乘以3等于45 这样可以

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45可以被9整除

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所以我们用45做公分母

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15乘以3等于45 7乘以3等于21

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这两个分数是相等的

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加上 分母是45

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从9到45 需要乘以5

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为了得到那里的分子 分子也要乘以5

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那么2乘以5等于10

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2/9和10/45相等

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现在把它们相加

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把分母为45的两个分数相加

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21加10等于31 这样就做完了

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我们再做下面这道题 一道应用题

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Nadia Peter和Ian凑钱买

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一加仑的冰淇淋

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Nadia年龄最大 得到的零花钱最多

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她出1/2的钱 那么Nadia出了一半的钱

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这表示Nadia出的钱

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Ian年龄居中 出1/3的钱

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那么Ian出1/3的钱

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这代表Ian

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Peter的年龄最小 得到的零花钱也最少

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出1/4的钱

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那么Peter出1/4的钱

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他们认为这些钱足够了

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当他们去结账时

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发现他们忘了算入消费税

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担心钱不够

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令人惊讶的是 他们的钱正好够了

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求消费税是冰淇淋价格的几分之几？

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我们来看一下 如果我们把价格的1/2 1/3 1/4加起来

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看看得到了什么

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我们必须先找到公分母

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2 3 4的最小公倍数

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我们来看一下 是12 对不对？

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12可以被2整除 也可以被3和4整除

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1/2等于6/12

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2乘以6等于12

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1乘以6等于6

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它们是相等的

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6是12的1/2

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1/3 如果把12当成公分母

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3变成12要乘以4

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那么用1乘以4

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4/12等于1/3

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然后是1/4 如果12是公分母

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4变成12要乘以3

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所以分子也乘以3 等于3

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我们把这几项加起来

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那么6/12加3/12加4/12等于

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分母是12 分子是6加4

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加3 等于6加4等于10 再加3等于13

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等于13/12

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这是一个假分数

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或者我们可以说它和

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12/12+1/12是相等的 或者说

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12/12等于1

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12除以12等于1

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这就是1又1/12

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所以他们把钱凑起来后

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得到的总数是他们要买的冰淇淋价格的

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1又1/12倍

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这道题问冰淇淋价格的几分之几是消费税？

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这是他们要付的钱

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所以很明显 1表示不含税的冰淇淋的价格

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所以1/12表示附加的消费税

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所以这道题的答案是：价格的1/12为附加的消费税