﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:01.06,0:00:03.37,Default,,0000,0000,0000,,歡迎大家 Dialogue: 0,0:00:03.37,0:00:05.07,Default,,0000,0000,0000,,今天我們來講負數的加減法 Dialogue: 0,0:00:05.07,0:00:06.38,Default,,0000,0000,0000,,讓我們開始吧 Dialogue: 0,0:00:06.38,0:00:08.51,Default,,0000,0000,0000,,首先，回顧一下，還記得什麽是負數嗎？ Dialogue: 0,0:00:08.52,0:00:12.08,Default,,0000,0000,0000,,我們還是來畫一條數軸 Dialogue: 0,0:00:12.08,0:00:13.30,Default,,0000,0000,0000,,哎呀，不太直。。。 Dialogue: 0,0:00:13.30,0:00:15.19,Default,,0000,0000,0000,,不過沒關係，你們明白就行 Dialogue: 0,0:00:15.19,0:00:18.80,Default,,0000,0000,0000,,好，我們都知道正數是怎麽回事兒了 Dialogue: 0,0:00:18.80,0:00:24.67,Default,,0000,0000,0000,,假如這是0 Dialogue: 0,0:00:24.67,0:00:25.69,Default,,0000,0000,0000,,然後是1,2,3,4 等等 Dialogue: 0,0:00:25.69,0:00:28.55,Default,,0000,0000,0000,,那2加2是多少呢，從2開始算 Dialogue: 0,0:00:28.55,0:00:30.78,Default,,0000,0000,0000,,你加上2，也就是往右邊走2步 Dialogue: 0,0:00:30.78,0:00:31.46,Default,,0000,0000,0000,,走到了4 Dialogue: 0,0:00:31.46,0:00:32.14,Default,,0000,0000,0000,,這個很自然，很簡單 Dialogue: 0,0:00:32.15,0:00:33.93,Default,,0000,0000,0000,,所以說 Dialogue: 0,0:00:33.93,0:00:36.13,Default,,0000,0000,0000,,2加2就等於4 Dialogue: 0,0:00:36.14,0:00:38.49,Default,,0000,0000,0000,,那麽，2減去1呢 Dialogue: 0,0:00:38.49,0:00:39.84,Default,,0000,0000,0000,,或者 3減去2呢 Dialogue: 0,0:00:39.84,0:00:44.11,Default,,0000,0000,0000,,我們從3開始，減去2 Dialogue: 0,0:00:44.11,0:00:45.66,Default,,0000,0000,0000,,往左走2步，就到了1 Dialogue: 0,0:00:45.66,0:00:51.25,Default,,0000,0000,0000,,好，我們計算了2加2等於4,3減2等於1 Dialogue: 0,0:00:51.25,0:00:52.98,Default,,0000,0000,0000,,你是不是覺得這太簡單了。。。 Dialogue: 0,0:00:52.99,0:00:56.99,Default,,0000,0000,0000,,那，如果1減去3是怎樣呢 Dialogue: 0,0:00:56.99,0:00:58.15,Default,,0000,0000,0000,,嗯 Dialogue: 0,0:00:58.15,0:01:00.10,Default,,0000,0000,0000,,其實道理是一樣的 Dialogue: 0,0:01:00.10,0:01:03.85,Default,,0000,0000,0000,,我們從1開始，往左走一步 Dialogue: 0,0:01:03.85,0:01:06.96,Default,,0000,0000,0000,,現在我們走到0以下了 Dialogue: 0,0:01:06.96,0:01:07.73,Default,,0000,0000,0000,,這是什麽意思呢？ Dialogue: 0,0:01:07.73,0:01:08.50,Default,,0000,0000,0000,,意思就是，我們就開始得到負數了 Dialogue: 0,0:01:08.51,0:01:14.93,Default,,0000,0000,0000,,負1，負2，負3，等等 Dialogue: 0,0:01:14.93,0:01:20.91,Default,,0000,0000,0000,,如果我從1這裡開始減去三 Dialogue: 0,0:01:20.91,0:01:25.61,Default,,0000,0000,0000,,向下走三步，停在-2這裡 Dialogue: 0,0:01:25.62,0:01:30.68,Default,,0000,0000,0000,,我們就會得到：1-3=-2 Dialogue: 0,0:01:30.68,0:01:33.08,Default,,0000,0000,0000,,其實我們在日常生活中 Dialogue: 0,0:01:33.09,0:01:34.73,Default,,0000,0000,0000,,經常會用到這樣的減法 Dialogue: 0,0:01:34.73,0:01:37.14,Default,,0000,0000,0000,,如果我說 Dialogue: 0,0:01:37.14,0:01:39.23,Default,,0000,0000,0000,,今天真冷，氣溫是1度 Dialogue: 0,0:01:39.23,0:01:40.73,Default,,0000,0000,0000,,而明天還會比今天還要冷3度 Dialogue: 0,0:01:40.73,0:01:42.04,Default,,0000,0000,0000,,你大概已經得到 Dialogue: 0,0:01:42.04,0:01:44.50,Default,,0000,0000,0000,,明天的溫度等於-2度了 Dialogue: 0,0:01:44.50,0:01:46.93,Default,,0000,0000,0000,,這個是常識 Dialogue: 0,0:01:46.93,0:01:48.04,Default,,0000,0000,0000,,這就是負數的意義 Dialogue: 0,0:01:48.04,0:01:51.13,Default,,0000,0000,0000,,你還要記住，一個負數的絕對值越大 Dialogue: 0,0:01:51.13,0:01:58.09,Default,,0000,0000,0000,,它的數值就越小 Dialogue: 0,0:01:58.09,0:02:01.71,Default,,0000,0000,0000,,比如-50少於-20 Dialogue: 0,0:02:01.71,0:02:04.93,Default,,0000,0000,0000,,因爲在我們的數軸上，-50比-20還要靠左 Dialogue: 0,0:02:04.93,0:02:07.16,Default,,0000,0000,0000,,這些你靠直覺是很容易的出來的 Dialogue: 0,0:02:07.17,0:02:08.71,Default,,0000,0000,0000,,當你一開始接觸負數的時候 Dialogue: 0,0:02:08.71,0:02:10.19,Default,,0000,0000,0000,,你可能會覺得，哦50比20大 Dialogue: 0,0:02:10.19,0:02:13.86,Default,,0000,0000,0000,,只不過，你要注意50和20都是負數 Dialogue: 0,0:02:13.86,0:02:15.31,Default,,0000,0000,0000,,讓我們來做道題吧 Dialogue: 0,0:02:15.31,0:02:19.27,Default,,0000,0000,0000,,我還是要用上這個數軸 Dialogue: 0,0:02:19.28,0:02:22.42,Default,,0000,0000,0000,,因爲它對我能起到很大的幫助 Dialogue: 0,0:02:22.42,0:02:26.87,Default,,0000,0000,0000,,我們來算算5-12 Dialogue: 0,0:02:26.87,0:02:29.79,Default,,0000,0000,0000,,你大概已經 Dialogue: 0,0:02:29.79,0:02:34.20,Default,,0000,0000,0000,,能估算到答案了 Dialogue: 0,0:02:34.20,0:02:45.14,Default,,0000,0000,0000,,但是我還是要畫個數軸 Dialogue: 0,0:02:45.14,0:02:53.07,Default,,0000,0000,0000,,從-10開始標上數字 Dialogue: 0,0:02:53.07,0:02:58.78,Default,,0000,0000,0000,,位置有點不夠 Dialogue: 0,0:02:58.78,0:03:05.16,Default,,0000,0000,0000,,我應該一開始就把它畫出來的。。 Dialogue: 0,0:03:05.16,0:03:12.54,Default,,0000,0000,0000,,就畫到5這裡 Dialogue: 0,0:03:12.54,0:03:14.49,Default,,0000,0000,0000,,讓我把這個箭頭重畫一遍，留點位置 Dialogue: 0,0:03:14.49,0:03:15.55,Default,,0000,0000,0000,,5-12 Dialogue: 0,0:03:15.56,0:03:18.43,Default,,0000,0000,0000,,讓我換個顏色 Dialogue: 0,0:03:18.43,0:03:20.95,Default,,0000,0000,0000,,從5開始，往左數12下 Dialogue: 0,0:03:20.95,0:03:22.81,Default,,0000,0000,0000,,因爲我們在減去12 Dialogue: 0,0:03:22.81,0:03:33.87,Default,,0000,0000,0000,,數一下，1,2,3,4,5..... Dialogue: 0,0:03:33.87,0:03:38.26,Default,,0000,0000,0000,,我們停在了-7 Dialogue: 0,0:03:38.26,0:03:39.99,Default,,0000,0000,0000,,很好玩對吧？ Dialogue: 0,0:03:40.00,0:03:42.79,Default,,0000,0000,0000,,因爲12-5等於正7 Dialogue: 0,0:03:42.79,0:03:45.58,Default,,0000,0000,0000,,而5-12等於負7 Dialogue: 0,0:03:45.59,0:03:48.90,Default,,0000,0000,0000,,你想一想 Dialogue: 0,0:03:48.90,0:03:52.94,Default,,0000,0000,0000,,這是爲什麽？ Dialogue: 0,0:03:52.94,0:03:58.92,Default,,0000,0000,0000,,爲什麽5和12的差是7？ Dialogue: 0,0:03:58.92,0:04:00.04,Default,,0000,0000,0000,,而在這個情況下 Dialogue: 0,0:04:00.04,0:04:01.10,Default,,0000,0000,0000,,5-12的情況下 Dialogue: 0,0:04:01.10,0:04:03.81,Default,,0000,0000,0000,,我們會得到-7呢？ Dialogue: 0,0:04:03.81,0:04:05.16,Default,,0000,0000,0000,,更奇怪的是5和-7的位置差了這麽多？ Dialogue: 0,0:04:05.16,0:04:07.50,Default,,0000,0000,0000,,我剛剛說的似乎讓你混亂了。。 Dialogue: 0,0:04:07.50,0:04:09.54,Default,,0000,0000,0000,,不過我們再來試試另一道題吧 Dialogue: 0,0:04:09.54,0:04:11.79,Default,,0000,0000,0000,,從低一點的數字開始 Dialogue: 0,0:04:11.79,0:04:18.06,Default,,0000,0000,0000,,我們剛剛說過，5-12等於-7 Dialogue: 0,0:04:18.06,0:04:19.43,Default,,0000,0000,0000,,讓我們再做一道 Dialogue: 0,0:04:19.43,0:04:25.84,Default,,0000,0000,0000,,-3加上5等於幾？ Dialogue: 0,0:04:25.84,0:04:28.05,Default,,0000,0000,0000,,我們還是用這個數軸 Dialogue: 0,0:04:28.06,0:04:31.49,Default,,0000,0000,0000,,-3+5 Dialogue: 0,0:04:31.49,0:04:33.58,Default,,0000,0000,0000,,從-3這兒開始 Dialogue: 0,0:04:33.58,0:04:38.43,Default,,0000,0000,0000,,向上數5 Dialogue: 0,0:04:38.43,0:04:42.60,Default,,0000,0000,0000,,得到2 Dialogue: 0,0:04:42.60,0:04:44.36,Default,,0000,0000,0000,,所以我們的答案就是 Dialogue: 0,0:04:44.36,0:04:48.79,Default,,0000,0000,0000,,-3+5=2 Dialogue: 0,0:04:48.79,0:04:53.84,Default,,0000,0000,0000,,又有趣了，5-3也等於2 Dialogue: 0,0:04:53.84,0:04:57.01,Default,,0000,0000,0000,,既然我們看出來5-3和-3+5是一樣的 Dialogue: 0,0:04:57.01,0:05:00.25,Default,,0000,0000,0000,,我們就不難發現 Dialogue: 0,0:05:00.25,0:05:04.05,Default,,0000,0000,0000,,這兩個式子其實是一個意思 Dialogue: 0,0:05:04.05,0:05:07.05,Default,,0000,0000,0000,,當我們在運算負數的加減法的時候 Dialogue: 0,0:05:07.05,0:05:11.64,Default,,0000,0000,0000,,我們在做的只是很基礎的加減法 Dialogue: 0,0:05:11.64,0:05:15.46,Default,,0000,0000,0000,,只不過現在我們的答案 Dialogue: 0,0:05:15.46,0:05:18.63,Default,,0000,0000,0000,,可能會是0以下的數字了 Dialogue: 0,0:05:18.63,0:05:19.83,Default,,0000,0000,0000,,我們再來做一道吧 Dialogue: 0,0:05:19.83,0:05:21.59,Default,,0000,0000,0000,,我問你 Dialogue: 0,0:05:21.59,0:05:27.11,Default,,0000,0000,0000,,2減去-3等於幾？ Dialogue: 0,0:05:27.11,0:05:30.75,Default,,0000,0000,0000,,這種情況下，我們中間就有兩個減號 Dialogue: 0,0:05:30.75,0:05:32.08,Default,,0000,0000,0000,,你應該這樣看待這個問題 Dialogue: 0,0:05:32.08,0:05:34.14,Default,,0000,0000,0000,,中間這兩個減號 Dialogue: 0,0:05:34.14,0:05:36.14,Default,,0000,0000,0000,,負負得正，變成了+號 Dialogue: 0,0:05:36.14,0:05:40.43,Default,,0000,0000,0000,,所以我們會得到2+正3 Dialogue: 0,0:05:40.43,0:05:43.05,Default,,0000,0000,0000,,得到5 Dialogue: 0,0:05:43.06,0:05:46.31,Default,,0000,0000,0000,,我們再來做一道題 Dialogue: 0,0:05:46.31,0:05:52.87,Default,,0000,0000,0000,,-7減去-2等於幾？ Dialogue: 0,0:05:52.87,0:05:58.01,Default,,0000,0000,0000,,這樣，我們把中間的兩個減號負負得正 Dialogue: 0,0:05:58.02,0:06:00.14,Default,,0000,0000,0000,,在你的腦海浬想象一個數軸 Dialogue: 0,0:06:00.14,0:06:03.56,Default,,0000,0000,0000,,從-7向右挪2步 Dialogue: 0,0:06:03.56,0:06:06.22,Default,,0000,0000,0000,,會得到什麽呢？ Dialogue: 0,0:06:06.22,0:06:11.39,Default,,0000,0000,0000,,得到-5 Dialogue: 0,0:06:11.39,0:06:13.76,Default,,0000,0000,0000,,你再想想我們前面的例子 Dialogue: 0,0:06:13.76,0:06:16.54,Default,,0000,0000,0000,,這個也是一樣：-7+2等於-5，2-7也等於-5 Dialogue: 0,0:06:16.55,0:06:19.35,Default,,0000,0000,0000,,如果現在的溫度是2度 Dialogue: 0,0:06:19.35,0:06:22.48,Default,,0000,0000,0000,,明天比今天冷7度 Dialogue: 0,0:06:22.48,0:06:23.23,Default,,0000,0000,0000,,我們會得到-5度 Dialogue: 0,0:06:23.24,0:06:25.25,Default,,0000,0000,0000,,我們再來做幾道，熟能生巧嘛 Dialogue: 0,0:06:25.25,0:06:26.85,Default,,0000,0000,0000,,這些例子是很好的示範方式 Dialogue: 0,0:06:26.85,0:06:29.06,Default,,0000,0000,0000,,大概比我口述還要有用 Dialogue: 0,0:06:29.06,0:06:31.10,Default,,0000,0000,0000,,我們來使勁做題吧~ Dialogue: 0,0:06:31.10,0:06:36.47,Default,,0000,0000,0000,,-7減去3等於幾？ Dialogue: 0,0:06:36.47,0:06:39.40,Default,,0000,0000,0000,,我們從-7向左數三位 Dialogue: 0,0:06:39.41,0:06:41.39,Default,,0000,0000,0000,,我們會得到比-7小3的數字 Dialogue: 0,0:06:41.39,0:06:45.42,Default,,0000,0000,0000,,-10，對吧？ Dialogue: 0,0:06:45.43,0:06:49.06,Default,,0000,0000,0000,,你再想想前面的例子，如果是7+3 Dialogue: 0,0:06:49.06,0:06:50.76,Default,,0000,0000,0000,,我們從0上面的7 Dialogue: 0,0:06:50.76,0:06:52.50,Default,,0000,0000,0000,,向右三步 Dialogue: 0,0:06:52.50,0:06:54.54,Default,,0000,0000,0000,,我們會得到正10 Dialogue: 0,0:06:54.54,0:06:57.39,Default,,0000,0000,0000,,所以當你從0下面的7，向左三步 Dialogue: 0,0:06:57.39,0:06:58.68,Default,,0000,0000,0000,,你就會得到-10 Dialogue: 0,0:06:58.68,0:06:59.46,Default,,0000,0000,0000,,再來一道 Dialogue: 0,0:06:59.47,0:07:01.05,Default,,0000,0000,0000,,我知道你理解起來可能會有些困難 Dialogue: 0,0:07:01.05,0:07:04.22,Default,,0000,0000,0000,,不過練習是很好的幫助 Dialogue: 0,0:07:04.22,0:07:09.12,Default,,0000,0000,0000,,我們來算算3減去-5 Dialogue: 0,0:07:09.12,0:07:12.36,Default,,0000,0000,0000,,這兩個減號負負得正，變成+號 Dialogue: 0,0:07:12.36,0:07:14.57,Default,,0000,0000,0000,,我們就得到6了 Dialogue: 0,0:07:14.57,0:07:17.09,Default,,0000,0000,0000,,想想前面的例子，3-3等於幾？ Dialogue: 0,0:07:17.09,0:07:18.69,Default,,0000,0000,0000,,很簡單 Dialogue: 0,0:07:18.69,0:07:20.69,Default,,0000,0000,0000,,0對吧？ Dialogue: 0,0:07:20.69,0:07:23.98,Default,,0000,0000,0000,,那-3減去3呢？ Dialogue: 0,0:07:23.99,0:07:26.42,Default,,0000,0000,0000,,那就是比-3小3的數 Dialogue: 0,0:07:26.42,0:07:28.88,Default,,0000,0000,0000,,就是-6 Dialogue: 0,0:07:28.88,0:07:34.03,Default,,0000,0000,0000,,那-3減去-3呢？ Dialogue: 0,0:07:34.04,0:07:35.50,Default,,0000,0000,0000,,好玩吧 Dialogue: 0,0:07:35.50,0:07:40.79,Default,,0000,0000,0000,,兩個減號變成+號， Dialogue: 0,0:07:40.80,0:07:44.03,Default,,0000,0000,0000,,我們從負3這裡開始，向右三步 Dialogue: 0,0:07:44.03,0:07:46.06,Default,,0000,0000,0000,,我們又得到了0 Dialogue: 0,0:07:46.06,0:07:48.24,Default,,0000,0000,0000,,能理解麽？ Dialogue: 0,0:07:48.25,0:07:49.36,Default,,0000,0000,0000,,我再來做一遍 Dialogue: 0,0:07:49.37,0:07:53.29,Default,,0000,0000,0000,,-3減去-3 Dialogue: 0,0:07:53.29,0:07:56.39,Default,,0000,0000,0000,,任何數減去它自己都應該等於0 Dialogue: 0,0:07:56.39,0:07:57.95,Default,,0000,0000,0000,,這就是爲什麽我們得到了0 Dialogue: 0,0:07:57.95,0:08:00.87,Default,,0000,0000,0000,,這同樣也是爲什麽 Dialogue: 0,0:08:00.87,0:08:03.18,Default,,0000,0000,0000,,這兩個減號 Dialogue: 0,0:08:03.18,0:08:05.50,Default,,0000,0000,0000,,變成加號了的原因 Dialogue: 0,0:08:05.50,0:08:07.43,Default,,0000,0000,0000,,我們再來做幾道題 Dialogue: 0,0:08:07.43,0:08:12.14,Default,,0000,0000,0000,,12減去13 Dialogue: 0,0:08:12.14,0:08:13.61,Default,,0000,0000,0000,,簡單吧？ Dialogue: 0,0:08:13.62,0:08:17.94,Default,,0000,0000,0000,,12減去12等於0,12減去13就是-1 Dialogue: 0,0:08:17.94,0:08:20.92,Default,,0000,0000,0000,,因爲我們從0又往左走了一步 Dialogue: 0,0:08:20.93,0:08:24.67,Default,,0000,0000,0000,,再來算算8-5 Dialogue: 0,0:08:24.67,0:08:27.27,Default,,0000,0000,0000,,這是個普遍的正數減法，等於3 Dialogue: 0,0:08:27.27,0:08:29.64,Default,,0000,0000,0000,,那麽5-8等於幾呢？ Dialogue: 0,0:08:29.64,0:08:31.99,Default,,0000,0000,0000,,我們先向左數五步到0 Dialogue: 0,0:08:31.99,0:08:35.42,Default,,0000,0000,0000,,再數3步，得到-3 Dialogue: 0,0:08:35.42,0:08:38.50,Default,,0000,0000,0000,,我在這裡再畫個數軸 Dialogue: 0,0:08:38.50,0:08:43.47,Default,,0000,0000,0000,,這裡是0，這是5 Dialogue: 0,0:08:43.47,0:08:47.23,Default,,0000,0000,0000,,看看，向左數了8步之後 Dialogue: 0,0:08:47.23,0:08:48.29,Default,,0000,0000,0000,,我們就得到3了 Dialogue: 0,0:08:48.30,0:08:49.40,Default,,0000,0000,0000,,你可以用同樣的方法計算任何這樣的加減法題目 Dialogue: 0,0:08:49.40,0:08:51.77,Default,,0000,0000,0000,,同樣也是很好的練習 Dialogue: 0,0:08:51.77,0:08:54.11,Default,,0000,0000,0000,,這一刻應該是個很好的入門了 Dialogue: 0,0:08:54.11,0:08:56.22,Default,,0000,0000,0000,,我建議你多多做練習 Dialogue: 0,0:08:56.22,0:08:58.28,Default,,0000,0000,0000,,因爲這些練習 Dialogue: 0,0:08:58.28,0:08:58.98,Default,,0000,0000,0000,,能讓你在腦海浬産生 Dialogue: 0,0:08:58.98,0:08:59.67,Default,,0000,0000,0000,,很好的鏡像印象 Dialogue: 0,0:08:59.67,0:09:01.58,Default,,0000,0000,0000,,比我在黑板上畫的任何東西 Dialogue: 0,0:09:01.58,0:09:03.99,Default,,0000,0000,0000,,都要來得有用 Dialogue: 0,0:09:03.99,0:09:05.46,Default,,0000,0000,0000,,所以，你可以試著再做做練習 Dialogue: 0,0:09:05.46,0:09:07.49,Default,,0000,0000,0000,,我去再找一些這樣的例子 Dialogue: 0,0:09:07.51,0:09:09.14,Default,,0000,0000,0000,,希望這樣你會對負數理解得更多 Dialogue: 0,0:09:09.14,0:09:10.53,Default,,0000,0000,0000,,你也可以參加我們的 Dialogue: 0,0:09:10.53,0:09:12.70,Default,,0000,0000,0000,,負數加減法專題討論會 Dialogue: 0,0:09:12.70,0:09:14.16,Default,,0000,0000,0000,,我希望你覺得這些東西很有趣 Dialogue: 0,0:09:14.16,0:09:15.46,Default,,0000,0000,0000,,拜拜~