﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.43,0:00:02.67,Default,,0000,0000,0000,,我們做一些有理數相加的問題 Dialogue: 0,0:00:02.78,0:00:05.49,Default,,0000,0000,0000,,我說有理數這個詞是因爲 Dialogue: 0,0:00:05.49,0:00:08.20,Default,,0000,0000,0000,,這本書上是這樣講的 但是更常用的術語是 Dialogue: 0,0:00:08.20,0:00:10.39,Default,,0000,0000,0000,,分數相加 Dialogue: 0,0:00:10.44,0:00:13.42,Default,,0000,0000,0000,,我們浏覽一下這些題 Dialogue: 0,0:00:13.42,0:00:15.02,Default,,0000,0000,0000,,看看這些例子 Dialogue: 0,0:00:15.02,0:00:19.48,Default,,0000,0000,0000,,我們先算一下3/7+2/7 Dialogue: 0,0:00:19.86,0:00:23.75,Default,,0000,0000,0000,,分母相同 所以只需要把分子相加 Dialogue: 0,0:00:24.10,0:00:28.43,Default,,0000,0000,0000,,分母是7 3+2=5 Dialogue: 0,0:00:28.64,0:00:29.78,Default,,0000,0000,0000,,這就是a的解題過程 Dialogue: 0,0:00:30.70,0:00:33.35,Default,,0000,0000,0000,,我每隔一題做一次 如果全部都做得話需要好長時間 Dialogue: 0,0:00:33.35,0:00:36.58,Default,,0000,0000,0000,,沒有永遠那麽長 但比我想用的時間要長 Dialogue: 0,0:00:36.58,0:00:42.94,Default,,0000,0000,0000,,所以直接做c 5/16+5/12 Dialogue: 0,0:00:42.94,0:00:44.96,Default,,0000,0000,0000,,分母不同 Dialogue: 0,0:00:44.96,0:00:47.84,Default,,0000,0000,0000,,必須找出公分母 最小公分母 Dialogue: 0,0:00:47.84,0:00:50.89,Default,,0000,0000,0000,,其實可以是這兩個數的任意公倍數 Dialogue: 0,0:00:50.89,0:00:53.19,Default,,0000,0000,0000,,但是爲了簡便 我們求最小公倍數 Dialogue: 0,0:00:53.87,0:00:58.39,Default,,0000,0000,0000,,那麽16和12的最小公倍數是什麽？ Dialogue: 0,0:00:58.52,0:01:01.80,Default,,0000,0000,0000,,我們來看一下 16乘以2是32 還沒完 Dialogue: 0,0:01:01.80,0:01:03.43,Default,,0000,0000,0000,,乘以3是48 Dialogue: 0,0:01:03.56,0:01:04.73,Default,,0000,0000,0000,,48看起來可以 Dialogue: 0,0:01:04.75,0:01:06.85,Default,,0000,0000,0000,,12除48等於4 Dialogue: 0,0:01:06.99,0:01:10.41,Default,,0000,0000,0000,,所以用48做公分母 Dialogue: 0,0:01:13.89,0:01:19.15,Default,,0000,0000,0000,,16要乘以3才能得到48 Dialogue: 0,0:01:19.15,0:01:22.47,Default,,0000,0000,0000,,所以這裡的5也要乘以3 Dialogue: 0,0:01:23.82,0:01:25.76,Default,,0000,0000,0000,,我們只是把分子分母同時 Dialogue: 0,0:01:25.76,0:01:27.86,Default,,0000,0000,0000,,乘以某數 所以實際上它沒有變 Dialogue: 0,0:01:28.20,0:01:30.43,Default,,0000,0000,0000,,那麽5乘以3等於15 Dialogue: 0,0:01:31.03,0:01:36.42,Default,,0000,0000,0000,,從這裡的12到48 Dialogue: 0,0:01:36.71,0:01:38.50,Default,,0000,0000,0000,,需要乘以4 Dialogue: 0,0:01:38.88,0:01:42.01,Default,,0000,0000,0000,,我們若要把5經變換變成這裡的分子 Dialogue: 0,0:01:42.01,0:01:43.85,Default,,0000,0000,0000,,需要乘以4 Dialogue: 0,0:01:44.01,0:01:46.29,Default,,0000,0000,0000,,5乘以4等於20 Dialogue: 0,0:01:46.86,0:01:49.50,Default,,0000,0000,0000,,現在分母相同了 Dialogue: 0,0:01:49.99,0:01:54.02,Default,,0000,0000,0000,,將等於 分母是48 Dialogue: 0,0:01:54.21,0:02:01.12,Default,,0000,0000,0000,,15加20 是35 Dialogue: 0,0:02:01.31,0:02:02.75,Default,,0000,0000,0000,,可以約分嗎？ Dialogue: 0,0:02:02.75,0:02:05.05,Default,,0000,0000,0000,,我們來看一下 5不能整除48 Dialogue: 0,0:02:05.05,0:02:06.77,Default,,0000,0000,0000,,7不能整除48 Dialogue: 0,0:02:06.86,0:02:08.02,Default,,0000,0000,0000,,這道題這樣就做完了 Dialogue: 0,0:02:08.33,0:02:13.68,Default,,0000,0000,0000,,我們來做一下e Dialogue: 0,0:02:13.99,0:02:19.89,Default,,0000,0000,0000,,8/25+7/10 Dialogue: 0,0:02:19.89,0:02:22.91,Default,,0000,0000,0000,,又一次 分母不相同 Dialogue: 0,0:02:23.05,0:02:24.96,Default,,0000,0000,0000,,但是我們可以解決 Dialogue: 0,0:02:25.58,0:02:27.07,Default,,0000,0000,0000,,我們來看一下 Dialogue: 0,0:02:27.07,0:02:29.75,Default,,0000,0000,0000,,50是能被這兩個數整除的最小的數 Dialogue: 0,0:02:29.98,0:02:31.73,Default,,0000,0000,0000,,25乘以2是50 Dialogue: 0,0:02:32.03,0:02:36.73,Default,,0000,0000,0000,,8/25 爲了得到公分母50 同時乘以2 Dialogue: 0,0:02:37.00,0:02:40.03,Default,,0000,0000,0000,,所以8必須乘以2 Dialogue: 0,0:02:40.03,0:02:41.92,Default,,0000,0000,0000,,將是16/50 Dialogue: 0,0:02:42.76,0:02:47.59,Default,,0000,0000,0000,,然後是7/10 我們讓分母變成50 Dialogue: 0,0:02:47.89,0:02:54.80,Default,,0000,0000,0000,,10乘以5等於50 所以7也要乘以5 Dialogue: 0,0:02:54.86,0:02:57.48,Default,,0000,0000,0000,,變成35/50 Dialogue: 0,0:02:57.67,0:03:01.36,Default,,0000,0000,0000,,現在分母相等 是50 Dialogue: 0,0:03:01.65,0:03:04.14,Default,,0000,0000,0000,,16加35 等於多少？ Dialogue: 0,0:03:05.05,0:03:09.76,Default,,0000,0000,0000,,10加35等於45 再加6等於51 Dialogue: 0,0:03:10.36,0:03:13.83,Default,,0000,0000,0000,,所以是51/50 Dialogue: 0,0:03:14.57,0:03:16.80,Default,,0000,0000,0000,,做一下g Dialogue: 0,0:03:16.99,0:03:18.44,Default,,0000,0000,0000,,換一種顏色做 Dialogue: 0,0:03:19.56,0:03:21.57,Default,,0000,0000,0000,,第g題 Dialogue: 0,0:03:22.04,0:03:27.47,Default,,0000,0000,0000,,題目中給出7/15 Dialogue: 0,0:03:27.47,0:03:33.16,Default,,0000,0000,0000,,我用別的顏色寫第二項 加上2/9 Dialogue: 0,0:03:33.45,0:03:35.49,Default,,0000,0000,0000,,又一次 分母不同 Dialogue: 0,0:03:35.56,0:03:36.95,Default,,0000,0000,0000,,需要找出公分母 Dialogue: 0,0:03:37.54,0:03:41.70,Default,,0000,0000,0000,,能被15和9整除的最小的數是多少？ Dialogue: 0,0:03:41.70,0:03:44.68,Default,,0000,0000,0000,,我們來看一下 15乘以2等於30 不對 不能被9整除 Dialogue: 0,0:03:44.89,0:03:47.82,Default,,0000,0000,0000,,15乘以3等於45 這樣可以 Dialogue: 0,0:03:47.82,0:03:49.37,Default,,0000,0000,0000,,45可以被9整除 Dialogue: 0,0:03:50.32,0:03:51.98,Default,,0000,0000,0000,,所以我們用45做公分母 Dialogue: 0,0:03:52.35,0:03:59.72,Default,,0000,0000,0000,,15乘以3等於45 7乘以3等於21 Dialogue: 0,0:03:59.88,0:04:01.81,Default,,0000,0000,0000,,這兩個分數是相等的 Dialogue: 0,0:04:02.48,0:04:05.95,Default,,0000,0000,0000,,加上 分母是45 Dialogue: 0,0:04:06.06,0:04:10.82,Default,,0000,0000,0000,,從9到45 需要乘以5 Dialogue: 0,0:04:11.05,0:04:15.97,Default,,0000,0000,0000,,爲了得到那裏的分子 分子也要乘以5 Dialogue: 0,0:04:15.97,0:04:17.75,Default,,0000,0000,0000,,那麽2乘以5等於10 Dialogue: 0,0:04:18.04,0:04:21.81,Default,,0000,0000,0000,,2/9和10/45相等 Dialogue: 0,0:04:22.34,0:04:23.92,Default,,0000,0000,0000,,現在把它們相加 Dialogue: 0,0:04:24.57,0:04:27.35,Default,,0000,0000,0000,,把分母爲45的兩個分數相加 Dialogue: 0,0:04:27.35,0:04:32.12,Default,,0000,0000,0000,,21加10等於31 這樣就做完了 Dialogue: 0,0:04:33.01,0:04:36.05,Default,,0000,0000,0000,,我們再做下面這道題 一道應用題 Dialogue: 0,0:04:36.68,0:04:40.16,Default,,0000,0000,0000,,Nadia Peter和Ian湊錢買 Dialogue: 0,0:04:40.16,0:04:41.15,Default,,0000,0000,0000,,一加侖的冰淇淋 Dialogue: 0,0:04:41.66,0:04:44.47,Default,,0000,0000,0000,,Nadia年齡最大 得到的零花錢最多 Dialogue: 0,0:04:44.66,0:04:50.54,Default,,0000,0000,0000,,她出1/2的錢 那麽Nadia出了一半的錢 Dialogue: 0,0:04:50.54,0:04:53.47,Default,,0000,0000,0000,,這表示Nadia出的錢 Dialogue: 0,0:04:53.87,0:04:58.87,Default,,0000,0000,0000,,Ian年齡居中 出1/3的錢 Dialogue: 0,0:04:58.98,0:05:01.54,Default,,0000,0000,0000,,那麽Ian出1/3的錢 Dialogue: 0,0:05:02.02,0:05:03.31,Default,,0000,0000,0000,,這代表Ian Dialogue: 0,0:05:03.78,0:05:06.60,Default,,0000,0000,0000,,Peter的年齡最小 得到的零花錢也最少 Dialogue: 0,0:05:06.60,0:05:08.23,Default,,0000,0000,0000,,出1/4的錢 Dialogue: 0,0:05:09.25,0:05:17.19,Default,,0000,0000,0000,,那麽Peter出1/4的錢 Dialogue: 0,0:05:17.19,0:05:19.49,Default,,0000,0000,0000,,他們認爲這些錢足夠了 Dialogue: 0,0:05:19.69,0:05:21.21,Default,,0000,0000,0000,,當他們去結賬時 Dialogue: 0,0:05:21.21,0:05:23.56,Default,,0000,0000,0000,,發現他們忘了算入消費稅 Dialogue: 0,0:05:23.56,0:05:24.94,Default,,0000,0000,0000,,擔心錢不夠 Dialogue: 0,0:05:25.23,0:05:28.08,Default,,0000,0000,0000,,令人驚訝的是 他們的錢正好夠了 Dialogue: 0,0:05:28.53,0:05:32.09,Default,,0000,0000,0000,,求消費稅是冰淇淋價格的幾分之幾？ Dialogue: 0,0:05:32.54,0:05:36.04,Default,,0000,0000,0000,,我們來看一下 如果我們把價格的1/2 1/3 1/4加起來 Dialogue: 0,0:05:36.04,0:05:36.87,Default,,0000,0000,0000,,看看得到了什麽 Dialogue: 0,0:05:37.56,0:05:39.39,Default,,0000,0000,0000,,我們必須先找到公分母 Dialogue: 0,0:05:39.79,0:05:43.77,Default,,0000,0000,0000,,2 3 4的最小公倍數 Dialogue: 0,0:05:44.22,0:05:47.13,Default,,0000,0000,0000,,我們來看一下 是12 對不對？ Dialogue: 0,0:05:47.13,0:05:50.01,Default,,0000,0000,0000,,12可以被2整除 也可以被3和4整除 Dialogue: 0,0:05:50.33,0:05:56.16,Default,,0000,0000,0000,,1/2等於6/12 Dialogue: 0,0:05:56.64,0:05:58.89,Default,,0000,0000,0000,,2乘以6等於12 Dialogue: 0,0:05:58.97,0:06:00.48,Default,,0000,0000,0000,,1乘以6等於6 Dialogue: 0,0:06:00.54,0:06:01.27,Default,,0000,0000,0000,,它們是相等的 Dialogue: 0,0:06:01.27,0:06:02.50,Default,,0000,0000,0000,,6是12的1/2 Dialogue: 0,0:06:03.77,0:06:08.54,Default,,0000,0000,0000,,1/3 如果把12當成公分母 Dialogue: 0,0:06:08.54,0:06:11.37,Default,,0000,0000,0000,,3變成12要乘以4 Dialogue: 0,0:06:11.55,0:06:13.67,Default,,0000,0000,0000,,那麽用1乘以4 Dialogue: 0,0:06:14.51,0:06:16.66,Default,,0000,0000,0000,,4/12等於1/3 Dialogue: 0,0:06:17.46,0:06:22.81,Default,,0000,0000,0000,,然後是1/4 如果12是公分母 Dialogue: 0,0:06:23.01,0:06:26.04,Default,,0000,0000,0000,,4變成12要乘以3 Dialogue: 0,0:06:26.04,0:06:29.42,Default,,0000,0000,0000,,所以分子也乘以3 等於3 Dialogue: 0,0:06:30.00,0:06:31.18,Default,,0000,0000,0000,,我們把這幾項加起來 Dialogue: 0,0:06:31.33,0:06:36.64,Default,,0000,0000,0000,,那麽6/12加3/12加4/12等於 Dialogue: 0,0:06:36.64,0:06:40.46,Default,,0000,0000,0000,,分母是12 分子是6加4 Dialogue: 0,0:06:40.46,0:06:47.53,Default,,0000,0000,0000,,加3 等於6加4等於10 再加3等於13 Dialogue: 0,0:06:47.53,0:06:50.80,Default,,0000,0000,0000,,等於13/12 Dialogue: 0,0:06:50.99,0:06:52.91,Default,,0000,0000,0000,,這是一個假分數 Dialogue: 0,0:06:53.00,0:06:56.35,Default,,0000,0000,0000,,或者我們可以說它和 Dialogue: 0,0:06:56.35,0:07:02.68,Default,,0000,0000,0000,,12/12+1/12是相等的 或者說 Dialogue: 0,0:07:02.88,0:07:04.40,Default,,0000,0000,0000,,12/12等於1 Dialogue: 0,0:07:04.54,0:07:05.83,Default,,0000,0000,0000,,12除以12等於1 Dialogue: 0,0:07:05.83,0:07:09.70,Default,,0000,0000,0000,,這就是1又1/12 Dialogue: 0,0:07:10.20,0:07:11.33,Default,,0000,0000,0000,,所以他們把錢湊起來後 Dialogue: 0,0:07:11.33,0:07:18.20,Default,,0000,0000,0000,,得到的總數是他們要買的冰淇淋價格的 Dialogue: 0,0:07:18.20,0:07:18.81,Default,,0000,0000,0000,,1又1/12倍 Dialogue: 0,0:07:19.21,0:07:22.41,Default,,0000,0000,0000,,這道題問冰淇淋價格的幾分之幾是消費稅？ Dialogue: 0,0:07:22.41,0:07:24.29,Default,,0000,0000,0000,,這是他們要付的錢 Dialogue: 0,0:07:24.76,0:07:29.42,Default,,0000,0000,0000,,所以很明顯 1表示不含稅的冰淇淋的價格 Dialogue: 0,0:07:29.62,0:07:32.31,Default,,0000,0000,0000,,所以1/12表示附加的消費稅 Dialogue: 0,0:07:32.57,0:07:38.72,Default,,0000,0000,0000,,所以這道題的答案是：價格的1/12爲附加的消費稅