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我們做一些有理數相加的問題

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我說有理數這個詞是因爲

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這本書上是這樣講的 但是更常用的術語是

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分數相加

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我們浏覽一下這些題

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看看這些例子

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我們先算一下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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這就是a的解題過程

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我每隔一題做一次 如果全部都做得話需要好長時間

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沒有永遠那麽長 但比我想用的時間要長

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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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必須找出公分母 最小公分母

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其實可以是這兩個數的任意公倍數

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但是爲了簡便 我們求最小公倍數

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那麽16和12的最小公倍數是什麽？

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我們來看一下 16乘以2是32 還沒完

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乘以3是48

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48看起來可以

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12除48等於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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所以這裡的5也要乘以3

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我們只是把分子分母同時

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乘以某數 所以實際上它沒有變

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那麽5乘以3等於15

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從這裡的12到48

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需要乘以4

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我們若要把5經變換變成這裡的分子

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需要乘以4

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5乘以4等於20

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現在分母相同了

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將等於 分母是48

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15加20 是35

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可以約分嗎？

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我們來看一下 5不能整除48

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7不能整除48

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這道題這樣就做完了

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我們來做一下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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但是我們可以解決

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我們來看一下

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50是能被這兩個數整除的最小的數

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25乘以2是50

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8/25 爲了得到公分母50 同時乘以2

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所以8必須乘以2

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將是16/50

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然後是7/10 我們讓分母變成50

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10乘以5等於50 所以7也要乘以5

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變成35/50

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現在分母相等 是50

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16加35 等於多少？

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10加35等於45 再加6等於51

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所以是51/50

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做一下g

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換一種顏色做

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第g題

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題目中給出7/15

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我用別的顏色寫第二項 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整除的最小的數是多少？

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我們來看一下 15乘以2等於30 不對 不能被9整除

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15乘以3等於45 這樣可以

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45可以被9整除

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所以我們用45做公分母

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15乘以3等於45 7乘以3等於21

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這兩個分數是相等的

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加上 分母是45

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從9到45 需要乘以5

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爲了得到那裏的分子 分子也要乘以5

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那麽2乘以5等於10

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2/9和10/45相等

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現在把它們相加

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把分母爲45的兩個分數相加

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21加10等於31 這樣就做完了

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我們再做下面這道題 一道應用題

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Nadia Peter和Ian湊錢買

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一加侖的冰淇淋

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Nadia年齡最大 得到的零花錢最多

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她出1/2的錢 那麽Nadia出了一半的錢

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這表示Nadia出的錢

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Ian年齡居中 出1/3的錢

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那麽Ian出1/3的錢

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這代表Ian

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Peter的年齡最小 得到的零花錢也最少

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出1/4的錢

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那麽Peter出1/4的錢

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他們認爲這些錢足夠了

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當他們去結賬時

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發現他們忘了算入消費稅

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擔心錢不夠

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令人驚訝的是 他們的錢正好夠了

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求消費稅是冰淇淋價格的幾分之幾？

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我們來看一下 如果我們把價格的1/2 1/3 1/4加起來

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看看得到了什麽

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我們必須先找到公分母

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2 3 4的最小公倍數

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我們來看一下 是12 對不對？

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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等於6/12

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2乘以6等於12

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1乘以6等於6

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它們是相等的

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6是12的1/2

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1/3 如果把12當成公分母

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3變成12要乘以4

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那麽用1乘以4

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4/12等於1/3

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然後是1/4 如果12是公分母

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4變成12要乘以3

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所以分子也乘以3 等於3

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我們把這幾項加起來

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那麽6/12加3/12加4/12等於

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分母是12 分子是6加4

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加3 等於6加4等於10 再加3等於13

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等於13/12

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這是一個假分數

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或者我們可以說它和

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12/12+1/12是相等的 或者說

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12/12等於1

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12除以12等於1

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這就是1又1/12

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所以他們把錢湊起來後

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得到的總數是他們要買的冰淇淋價格的

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1又1/12倍

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這道題問冰淇淋價格的幾分之幾是消費稅？

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這是他們要付的錢

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所以很明顯 1表示不含稅的冰淇淋的價格

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所以1/12表示附加的消費稅

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所以這道題的答案是：價格的1/12爲附加的消費稅