1
00:00:00,740 --> 00:00:03,400
現在來看看我們是否可以除以更大的數字

2
00:00:03,400 --> 00:00:06,860
只是作爲起點，爲了除以更大的數字

3
00:00:06,860 --> 00:00:09,920
你至少需要知道乘法運算表

4
00:00:09,920 --> 00:00:14,550
乘法表從一開始，至少到十

5
00:00:14,550 --> 00:00:17,080
一直到10乘以10等於100

6
00:00:17,080 --> 00:00:20,055
然後，從1乘以1開始到2乘以3

7
00:00:20,055 --> 00:00:22,320
一直到10乘以10

8
00:00:22,320 --> 00:00:23,842
至少當我還在上學時

9
00:00:23,842 --> 00:00:25,340
我們已經學透了12乘以12

10
00:00:25,340 --> 00:00:28,100
但10乘以10可能已經夠用了

11
00:00:28,100 --> 00:00:29,770
這是真的只是起點。

12
00:00:29,770 --> 00:00:32,550
因爲要做類似的乘法問題

13
00:00:32,550 --> 00:00:34,150
比如，或者類似的除法問題

14
00:00:34,150 --> 00:00:39,640
假設我用25，我想把它除以5

15
00:00:39,640 --> 00:00:41,118
我可以畫25個物體

16
00:00:41,118 --> 00:00:44,558
然後把它們分成五個一組，或者分成五組

17
00:00:44,558 --> 00:00:47,590
然後看看每組有多少個物體

18
00:00:47,590 --> 00:00:49,562
但最快速的方法是只是思考一下

19
00:00:49,562 --> 00:00:52,930
嗯，5乘以什麽等於25呢，是嗎?

20
00:00:52,930 --> 00:00:58,100
5 × ? = 25

21
00:00:58,100 --> 00:00:59,860
如果你知道乘法運算表，

22
00:00:59,860 --> 00:01:02,070
尤其是5的乘法運算，

23
00:01:02,070 --> 00:01:06,280
你就知道5×5=25

24
00:01:06,280 --> 00:01:08,834
所以像類似的東西，你會立刻就能說出來

25
00:01:08,849 --> 00:01:11,692
因爲你掌握乘法運算表的緣故

26
00:01:11,692 --> 00:01:14,840
5在25裏面出現5次

27
00:01:14,840 --> 00:01:16,243
然後你最好就把5寫在那裏

28
00:01:16,243 --> 00:01:17,180
不要超過兩個，

29
00:01:17,180 --> 00:01:20,040
因爲你仍想要注意有標記的地方

30
00:01:20,040 --> 00:01:21,650
你想把5寫在某個地方

31
00:01:21,650 --> 00:01:25,480
它每5個一次地算進這個數，或者恰好5次

32
00:01:25,480 --> 00:01:26,190
同樣的事情。

33
00:01:26,190 --> 00:01:31,770
如果我說七算進四十九。

34
00:01:31,770 --> 00:01:33,250
有多少次？

35
00:01:33,250 --> 00:01:36,772
嗯，你會說，這很像7乘以什麽--

36
00:01:36,772 --> 00:01:39,373
你甚至可以，不用問號，把那裏留空白

37
00:01:39,388 --> 00:01:43,130
7乘以什麽等於49？

38
00:01:43,130 --> 00:01:45,452
如果你知道乘法運算表，

39
00:01:45,452 --> 00:01:50,090
你知道七乘以七等於四十九。

40
00:01:50,090 --> 00:01:53,145
目前爲止我舉的例子都是一個數乘以它本身

41
00:01:53,150 --> 00:01:55,030
讓我舉另一個例子。

42
00:01:55,030 --> 00:02:01,840
讓我做9在54裏有多少次？

43
00:02:01,840 --> 00:02:05,102
再次，你做它需要知道乘法運算表

44
00:02:05,102 --> 00:02:09,290
9 乘以什麽等於54？

45
00:02:09,290 --> 00:02:10,904
有時，即使你沒有記住它

46
00:02:10,904 --> 00:02:14,720
你可以說 9乘以5等於45

47
00:02:14,720 --> 00:02:19,470
9乘以6會比它多9，所以會等於45

48
00:02:19,470 --> 00:02:22,380
所以9在54裏有6次

49
00:02:22,380 --> 00:02:23,590
因此，就如一個起始點，

50
00:02:23,590 --> 00:02:27,253
你需要把你的乘法運算表從1乘以1開始

51
00:02:27,253 --> 00:02:29,250
一直背誦到10乘以10

52
00:02:29,250 --> 00:02:36,689
爲了能快點做一些基礎且相關的問題

53
00:02:36,700 --> 00:02:38,968
現在，和那些已經解決了的問題一起，我們做一些習題

54
00:02:38,968 --> 00:02:44,015
那可能不完全清晰地在你的乘法運算表裏

55
00:02:44,015 --> 00:02:46,190
例如,我想除以--

56
00:02:46,190 --> 00:02:54,800
我在看用43除以3

57
00:02:54,800 --> 00:02:58,440
再一次，這比3乘以10 或者3乘以12還要大

58
00:02:58,440 --> 00:02:58,930
事實上，看

59
00:02:58,930 --> 00:03:00,950
嗯，我做另一題吧

60
00:03:00,950 --> 00:03:04,260
我做23除以3

61
00:03:04,260 --> 00:03:06,165
並且，如果你知道你關於3的乘法表

62
00:03:06,165 --> 00:03:10,060
你會知道沒有哪個數字乘以3準確等於23

63
00:03:10,060 --> 00:03:10,910
我現在就做。

64
00:03:10,910 --> 00:03:13,280
3乘以1等於3

65
00:03:13,280 --> 00:03:15,690
3乘以2等於6

66
00:03:15,690 --> 00:03:16,870
讓我把它們都寫出來

67
00:03:16,870 --> 00:03:24,690
三三得九、 十二、 十五、 十八、 二十一、 二十四、 對嗎？

68
00:03:24,690 --> 00:03:27,700
3的乘法中沒有23

69
00:03:27,700 --> 00:03:29,700
那你該怎麽樣做這個除法問題呢？

70
00:03:29,700 --> 00:03:34,434
嗯 23內，3的最大倍數是那個？

71
00:03:34,440 --> 00:03:36,640
就是21

72
00:03:36,640 --> 00:03:39,170
3乘以多少等於21

73
00:03:39,170 --> 00:03:44,150
嗯，你知道的，3乘以7等於21

74
00:03:44,150 --> 00:03:48,520
所以你說，3的七倍會在23裏

75
00:03:48,520 --> 00:03:50,570
但它並不是完全得到23

76
00:03:50,570 --> 00:03:53,850
因爲7乘以3等於21

77
00:03:53,850 --> 00:03:55,750
所以會有剩下來的部分

78
00:03:55,750 --> 00:04:00,170
因爲，如果你用23減去21，你會得到余數2

79
00:04:00,170 --> 00:04:08,010
因此你可能寫 23除以3等於7，

80
00:04:08,010 --> 00:04:14,995
余數--可能我會寫，行，把單詞完整寫出來，余數二

81
00:04:15,010 --> 00:04:17,050
因此它不必得出完全沒剩余的得數

82
00:04:17,050 --> 00:04:19,790
而且，在將來，我們將學到小數和分數

83
00:04:19,790 --> 00:04:22,747
但是現在，你說，它是完全的7倍

84
00:04:22,747 --> 00:04:24,290
但那只能讓我們得到21

85
00:04:24,290 --> 00:04:26,110
還余下2

86
00:04:26,110 --> 00:04:28,507
因此你還可以解決除法問題

87
00:04:28,507 --> 00:04:31,078
盡管不是一個完全的且精確的乘法數字

88
00:04:31,078 --> 00:04:33,310
你用更大的數字去除以。

89
00:04:33,310 --> 00:04:37,720
但讓我們用一些更大的數字做練習

90
00:04:37,720 --> 00:04:40,520
而且，我想你會在這裡看到一種模式。

91
00:04:40,520 --> 00:04:47,058
現在，讓我們做4在--

92
00:04:47,058 --> 00:04:51,800
我們將要選一個十分大的數字--344

93
00:04:51,800 --> 00:04:53,694
當你看到它的時候

94
00:04:53,694 --> 00:04:57,850
你可能會說，嘿，老師，我只知道4乘以10 或者4乘以12

95
00:04:57,850 --> 00:04:59,850
4乘以12等於48

96
00:04:59,850 --> 00:05:01,340
這是一個大得多的數字

97
00:05:01,340 --> 00:05:02,767
它已經超過

98
00:05:02,767 --> 00:05:05,420
我所知道的4的乘法運算表的範圍了

99
00:05:05,420 --> 00:05:08,379
現在我將要告訴你的是 做它的辦法

100
00:05:08,379 --> 00:05:10,910
這是需要知道你4的乘法運算表

101
00:05:10,910 --> 00:05:11,889
因此你按所說的做

102
00:05:11,889 --> 00:05:16,800
4在3裏有多少次

103
00:05:16,800 --> 00:05:17,479
你實際上在說，

104
00:05:17,479 --> 00:05:20,430
4在3裏面有多少百次？

105
00:05:20,430 --> 00:05:22,590
所以這就是 — — 因爲這是三百，對嗎？

106
00:05:22,590 --> 00:05:24,880
這是344

107
00:05:24,880 --> 00:05:29,934
但是4在300裏面沒有100次，或者說--

108
00:05:29,949 --> 00:05:32,810
我想最好的思考方法是--4在3裏有0次

109
00:05:32,810 --> 00:05:34,470
所以你能繼續做下去

110
00:05:34,470 --> 00:05:36,260
4在34裏面有多少次

111
00:05:36,260 --> 00:05:41,460
所以現在我們把注意力集中在34上

112
00:05:41,460 --> 00:05:43,900
34裏面有多少個4呢？

113
00:05:43,900 --> 00:05:46,900
在這裡我們可以用我們關於4的乘法表

114
00:05:46,900 --> 00:05:51,950
4--看看，4乘以8等於32

115
00:05:51,950 --> 00:05:56,210
4乘以9等於36

116
00:05:56,210 --> 00:05:59,630
所以4選32，9倍多了點，是不？

117
00:05:59,630 --> 00:06:01,500
36比34大

118
00:06:01,500 --> 00:06:03,746
因此4在34裏面有八次

119
00:06:03,746 --> 00:06:06,089
而且還將會有一點剩余

120
00:06:06,089 --> 00:06:09,032
4在34裏面有8次

121
00:06:09,032 --> 00:06:10,856
讓我們弄清楚剩下來的

122
00:06:10,856 --> 00:06:11,565
其實我們說，

123
00:06:11,565 --> 00:06:14,947
340裏面有幾十個4？

124
00:06:14,947 --> 00:06:17,807
我們實際上說340裏面有80次的4

125
00:06:17,807 --> 00:06:20,020
因爲注意我們在十位上寫了8

126
00:06:20,020 --> 00:06:22,882
但只是爲了我們可以更快地解決這道題

127
00:06:22,882 --> 00:06:24,954
你說34裏面有8次的4

128
00:06:24,954 --> 00:06:28,770
但確定你把8寫在那裏的十位上

129
00:06:28,770 --> 00:06:30,100
8乘以4

130
00:06:30,100 --> 00:06:30,970
我們已經知道是什麽了

131
00:06:30,970 --> 00:06:34,140
8乘以4等於32

132
00:06:34,140 --> 00:06:36,290
然後我們找出其余部分。

133
00:06:36,290 --> 00:06:38,160
34減去32

134
00:06:38,160 --> 00:06:40,400
嗯，4減2等於2

135
00:06:40,400 --> 00:06:42,030
然後這些3都抵消了

136
00:06:42,030 --> 00:06:43,300
所以你只是剩下2

137
00:06:43,300 --> 00:06:46,120
但注意，我們是在十位的列上，是嗎？

138
00:06:46,120 --> 00:06:48,710
這整個列就在這裡，這是十位列

139
00:06:48,710 --> 00:06:55,120
其實我們真正想說的是，340裏面有80個4

140
00:06:55,120 --> 00:06:58,350
80乘以4等於320對嗎？

141
00:06:58,350 --> 00:07:00,844
因爲我把3寫在了百位數列

142
00:07:00,844 --> 00:07:05,701
然後，還有--

143
00:07:05,701 --> 00:07:07,215
讓我把這點擦掉

144
00:07:07,215 --> 00:07:08,872
我不想弄一條線在那看起來像--

145
00:07:08,872 --> 00:07:10,510
當我除這一列的時候，看起來像1

146
00:07:10,510 --> 00:07:11,934
但有兩個剩下的

147
00:07:11,934 --> 00:07:14,270
但我把2寫在十位上

148
00:07:14,270 --> 00:07:15,740
所以事實上 剩余的是20

149
00:07:15,740 --> 00:07:16,990
讓我把這個4拿下來

150
00:07:16,990 --> 00:07:18,660
因爲我不想只是用340去除以

151
00:07:18,660 --> 00:07:20,290
我用344去除以

152
00:07:20,290 --> 00:07:22,290
所以把4拿下來

153
00:07:22,290 --> 00:07:24,440
我換種顏色

154
00:07:24,440 --> 00:07:26,670
然後 — — — 用另一個方式去想它。

155
00:07:26,670 --> 00:07:31,250
我們剛才說344裏面有80個4，對嗎

156
00:07:31,250 --> 00:07:33,050
我們把8寫在十位上

157
00:07:33,050 --> 00:07:35,550
然後 8乘以4等於320

158
00:07:35,550 --> 00:07:38,170
現在其余部分是24

159
00:07:38,170 --> 00:07:40,800
所以 24裏面有多少個4？

160
00:07:40,800 --> 00:07:41,631
嗯，我們都知道的

161
00:07:41,631 --> 00:07:46,158
4乘以6等於24

162
00:07:46,158 --> 00:07:49,107
所以24裏面有6個4

163
00:07:49,107 --> 00:07:50,685
我們把這寫在個位上

164
00:07:50,685 --> 00:07:53,480
6乘以4等於24

165
00:07:53,480 --> 00:07:54,560
然後我們減去

166
00:07:54,560 --> 00:07:56,270
24減24

167
00:07:56,270 --> 00:07:58,490
那是--我們在這裡減去，每個都這樣

168
00:07:58,490 --> 00:07:59,530
我們得到了0。

169
00:07:59,530 --> 00:08:01,050
因此，沒有剩余部分。

170
00:08:01,050 --> 00:08:05,850
所以344裏面有準確的86個4

171
00:08:05,850 --> 00:08:09,180
如果你把344個物體 分成每組四個

172
00:08:09,180 --> 00:08:10,900
你會得到八十六個組。

173
00:08:10,900 --> 00:08:12,950
或者如果你把它們分成86個組

174
00:08:12,950 --> 00:08:13,880
你會得到每組4個

175
00:08:13,880 --> 00:08:15,640
讓我們做更多的幾個問題。

176
00:08:15,640 --> 00:08:18,440
我想你已經找到竅門了

177
00:08:18,440 --> 00:08:21,180
讓我做七 — — 我會做一個簡單的。

178
00:08:21,180 --> 00:08:24,790
91裏面的7

179
00:08:24,790 --> 00:08:28,387
又一次，好了，這又是超過了7乘以12

180
00:08:28,387 --> 00:08:31,340
等於84，這是你可以從乘法計算表知道的

181
00:08:31,340 --> 00:08:34,650
因此我們用上一題的方法做這條題

182
00:08:34,650 --> 00:08:37,750
9裏面有多少個7？

183
00:08:37,750 --> 00:08:41,220
9裏面有1個7

184
00:08:41,220 --> 00:08:44,640
1乘以7等於7

185
00:08:44,640 --> 00:08:48,330
然後9減7 得到2

186
00:08:48,330 --> 00:08:51,190
然後你把個位的數拿下來

187
00:08:51,190 --> 00:08:51,770
21

188
00:08:51,770 --> 00:08:53,036
請記住，這看起來像魔術，

189
00:08:53,036 --> 00:08:57,545
但我們是真的說，90裏面有10個7

190
00:08:57,545 --> 00:08:59,961
因爲我們把1寫在十位上

191
00:08:59,961 --> 00:09:02,466
10乘以7等於70

192
00:09:02,466 --> 00:09:05,053
對嗎？如果你喜歡 你也可以把0寫在那裏

193
00:09:05,053 --> 00:09:08,380
然後91減70等於21

194
00:09:08,380 --> 00:09:12,640
所以91裏面有10個7，余21

195
00:09:12,640 --> 00:09:15,780
然後你說，21除以7-- 你知道的！

196
00:09:15,780 --> 00:09:17,590
7乘以3等於21

197
00:09:17,590 --> 00:09:20,170
所以21裏面有3個7

198
00:09:20,170 --> 00:09:22,710
3乘以7等於21

199
00:09:22,710 --> 00:09:24,550
你把它們相互減去

200
00:09:24,550 --> 00:09:26,375
余數爲0

201
00:09:26,375 --> 00:09:31,908
所以91除以7等於13

202
00:09:31,908 --> 00:09:32,530
讓我們做另一題。

203
00:09:32,530 --> 00:09:35,863
我不會停下來去解釋一下這全部的數位

204
00:09:35,863 --> 00:09:36,800
我想 你知道的

205
00:09:36,800 --> 00:09:41,569
我想，至少，通過這個影片你可以很好地掌握它

206
00:09:41,580 --> 00:09:44,990
所以，讓我們來做7--我一直在用7

207
00:09:44,990 --> 00:09:46,510
用一個不同的數字做

208
00:09:46,510 --> 00:09:56,560
例如，608裏面有多少個8

209
00:09:56,560 --> 00:09:59,440
所以6裏面有多少個8

210
00:09:59,440 --> 00:10:00,740
0個

211
00:10:00,740 --> 00:10:01,980
讓我繼續

212
00:10:01,980 --> 00:10:05,360
60裏面有多少個8

213
00:10:05,360 --> 00:10:06,820
讓我把8寫下來

214
00:10:06,820 --> 00:10:09,110
讓我在這裡畫一條線，這樣我們就不會感到混亂

215
00:10:09,110 --> 00:10:11,340
讓我向下挪一點

216
00:10:11,340 --> 00:10:13,760
我需要在數字上面留點兒空白

217
00:10:13,760 --> 00:10:15,580
所以60裏面有多少個8

218
00:10:15,580 --> 00:10:19,590
我們知道 8 乘以7等於56

219
00:10:19,590 --> 00:10:23,330
然後8乘以8等於64

220
00:10:23,330 --> 00:10:25,640
所以8-- 64是太大了

221
00:10:25,640 --> 00:10:26,770
所以不是這個

222
00:10:26,771 --> 00:10:29,876
所以60裏面的8，有7次

223
00:10:29,876 --> 00:10:31,740
還有些會余下

224
00:10:31,740 --> 00:10:34,600
所以60裏面有7個8

225
00:10:34,600 --> 00:10:35,728
因爲我們在做整個60

226
00:10:35,728 --> 00:10:38,799
我們把7寫在60的個位上

227
00:10:38,799 --> 00:10:41,062
這是整個數的十位

228
00:10:41,062 --> 00:10:44,970
7乘以8，我們知道，是56

229
00:10:44,970 --> 00:10:47,100
60減56

230
00:10:47,100 --> 00:10:48,030
就是4

231
00:10:48,030 --> 00:10:48,990
我們可以在腦裏把它做出來

232
00:10:48,990 --> 00:10:50,270
或者如果我想，我可以借

233
00:10:50,270 --> 00:10:51,510
這是十

234
00:10:51,510 --> 00:10:53,380
這將是五。

235
00:10:53,380 --> 00:10:54,890
十減六等於四。

236
00:10:54,890 --> 00:10:59,930
然後你把這個8拿下來

237
00:10:59,930 --> 00:11:02,738
48裏面有多少個8？

238
00:11:02,750 --> 00:11:06,260
8乘以6等於多少

239
00:11:06,260 --> 00:11:09,210
嗯，八乘以六完全是四十八。

240
00:11:09,210 --> 00:11:13,170
所以8乘以-- 48裏面有6個8

241
00:11:13,170 --> 00:11:17,180
6乘以8是48

242
00:11:17,180 --> 00:11:18,180
然後你減去

243
00:11:18,180 --> 00:11:19,500
我們也在這裡減

244
00:11:19,500 --> 00:11:22,020
48減48=0

245
00:11:22,020 --> 00:11:25,260
因此，再一次我們得到余數爲零。

246
00:11:25,260 --> 00:11:28,798
所以希望，這能給你一些竅門去解決這些更大的除法問題

247
00:11:28,798 --> 00:11:31,012
而且我們真正需要知道去怎樣去做

248
00:11:31,012 --> 00:11:34,242
去解決這些問題的，是我們的乘法運算表

249
00:11:34,242 --> 00:11:38,381
或者多達10乘以10，或者10乘以12