1
00:00:00,740 --> 00:00:03,400
现在来看看我们是否可以除以更大的数字

2
00:00:03,400 --> 00:00:06,860
只是作为起点，为了除以更大的数字

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

4
00:00:09,920 --> 00:00:14,550
乘法表从一开始，至少到十

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

6
00:00:17,080 --> 00:00:20,055
然后，从1乘以1开始到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
至少当我还在上学时

9
00:00:23,842 --> 00:00:25,340
我们已经学透了12乘以12

10
00:00:25,340 --> 00:00:28,100
但10乘以10可能已经够用了

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

12
00:00:29,770 --> 00:00:32,550
因为要做类似的乘法问题

13
00:00:32,550 --> 00:00:34,150
比如，或者类似的除法问题

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

15
00:00:39,640 --> 00:00:41,118
我可以画25个物体

16
00:00:41,118 --> 00:00:44,558
然后把它们分成五个一组，或者分成五组

17
00:00:44,558 --> 00:00:47,590
然后看看每组有多少个物体

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乘以什么等于25呢，是吗?

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

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

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

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
所以像类似的东西，你会立刻就能说出来

25
00:01:08,849 --> 00:01:11,692
因为你掌握乘法运算表的缘故

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

27
00:01:14,840 --> 00:01:16,243
然后你最好就把5写在那里

28
00:01:16,243 --> 00:01:17,180
不要超过两个，

29
00:01:17,180 --> 00:01:20,040
因为你仍想要注意有标记的地方

30
00:01:20,040 --> 00:01:21,650
你想把5写在某个地方

31
00:01:21,650 --> 00:01:25,480
它每5个一次地算进这个数，或者恰好5次

32
00:01:25,480 --> 00:01:26,190
同样的事情。

33
00:01:26,190 --> 00:01:31,770
如果我说七算进四十九。

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

35
00:01:33,250 --> 00:01:36,772
嗯，你会说，这很像7乘以什么--

36
00:01:36,772 --> 00:01:39,373
你甚至可以，不用问号，把那里留空白

37
00:01:39,388 --> 00:01:43,130
7乘以什么等于49？

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

39
00:01:45,452 --> 00:01:50,090
你知道七乘以七等于四十九。

40
00:01:50,090 --> 00:01:53,145
目前为止我举的例子都是一个数乘以它本身

41
00:01:53,150 --> 00:01:55,030
让我举另一个例子。

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

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

44
00:02:05,102 --> 00:02:09,290
9 乘以什么等于54？

45
00:02:09,290 --> 00:02:10,904
有时，即使你没有记住它

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

47
00:02:14,720 --> 00:02:19,470
9乘以6会比它多9，所以会等于45

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

49
00:02:22,380 --> 00:02:23,590
因此，就如一个起始点，

50
00:02:23,590 --> 00:02:27,253
你需要把你的乘法运算表从1乘以1开始

51
00:02:27,253 --> 00:02:29,250
一直背诵到10乘以10

52
00:02:29,250 --> 00:02:36,689
为了能快点做一些基础且相关的问题

53
00:02:36,700 --> 00:02:38,968
现在，和那些已经解决了的问题一起，我们做一些习题

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

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，这比3乘以10 或者3乘以12还要大

58
00:02:58,440 --> 00:02:58,930
事实上，看

59
00:02:58,930 --> 00:03:00,950
嗯，我做另一题吧

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

61
00:03:04,260 --> 00:03:06,165
并且，如果你知道你关于3的乘法表

62
00:03:06,165 --> 00:03:10,060
你会知道没有哪个数字乘以3准确等于23

63
00:03:10,060 --> 00:03:10,910
我现在就做。

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

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

66
00:03:15,690 --> 00:03:16,870
让我把它们都写出来

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、 对吗？

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

69
00:03:27,700 --> 00:03:29,700
那你该怎么样做这个除法问题呢？

70
00:03:29,700 --> 00:03:34,434
嗯 23内，3的最大倍数是那个？

71
00:03:34,440 --> 00:03:36,640
就是21

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

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

74
00:03:44,150 --> 00:03:48,520
所以你说，3的七倍会在23里

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

76
00:03:50,570 --> 00:03:53,850
因为7乘以3等于21

77
00:03:53,850 --> 00:03:55,750
所以会有剩下来的部分

78
00:03:55,750 --> 00:04:00,170
因为，如果你用23减去21，你会得到余数2

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

80
00:04:08,010 --> 00:04:14,995
余数--可能我会写，行，把单词完整写出来，余数二

81
00:04:15,010 --> 00:04:17,050
因此它不必得出完全没剩余的得数

82
00:04:17,050 --> 00:04:19,790
而且，在将来，我们将学到小数和分数

83
00:04:19,790 --> 00:04:22,747
但是现在，你说，它是完全的7倍

84
00:04:22,747 --> 00:04:24,290
但那只能让我们得到21

85
00:04:24,290 --> 00:04:26,110
还余下2

86
00:04:26,110 --> 00:04:28,507
因此你还可以解决除法问题

87
00:04:28,507 --> 00:04:31,078
尽管不是一个完全的且精确的乘法数字

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

89
00:04:33,310 --> 00:04:37,720
但让我们用一些更大的数字做练习

90
00:04:37,720 --> 00:04:40,520
而且，我想你会在这里看到一种模式。

91
00:04:40,520 --> 00:04:47,058
现在，让我们做4在--

92
00:04:47,058 --> 00:04:51,800
我们将要选一个十分大的数字--344

93
00:04:51,800 --> 00:04:53,694
当你看到它的时候

94
00:04:53,694 --> 00:04:57,850
你可能会说，嘿，老师，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等于48

96
00:04:59,850 --> 00:05:01,340
这是一个大得多的数字

97
00:05:01,340 --> 00:05:02,767
它已经超过

98
00:05:02,767 --> 00:05:05,420
我所知道的4的乘法运算表的范围了

99
00:05:05,420 --> 00:05:08,379
现在我将要告诉你的是 做它的办法

100
00:05:08,379 --> 00:05:10,910
这是需要知道你4的乘法运算表

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

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

103
00:05:16,800 --> 00:05:17,479
你实际上在说，

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

105
00:05:20,430 --> 00:05:22,590
所以这就是 — — 因为这是三百，对吗？

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

107
00:05:24,880 --> 00:05:29,934
但是4在300里面没有100次，或者说--

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

109
00:05:32,810 --> 00:05:34,470
所以你能继续做下去

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

111
00:05:36,260 --> 00:05:41,460
所以现在我们把注意力集中在34上

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

113
00:05:43,900 --> 00:05:46,900
在这里我们可以用我们关于4的乘法表

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

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

116
00:05:56,210 --> 00:05:59,630
所以4选32，9倍多了点，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里面有八次

119
00:06:03,746 --> 00:06:06,089
而且还将会有一点剩余

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

121
00:06:09,032 --> 00:06:10,856
让我们弄清楚剩下来的

122
00:06:10,856 --> 00:06:11,565
其实我们说，

123
00:06:11,565 --> 00:06:14,947
340里面有几十个4？

124
00:06:14,947 --> 00:06:17,807
我们实际上说340里面有80次的4

125
00:06:17,807 --> 00:06:20,020
因为注意我们在十位上写了8

126
00:06:20,020 --> 00:06:22,882
但只是为了我们可以更快地解决这道题

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

128
00:06:24,954 --> 00:06:28,770
但确定你把8写在那里的十位上

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

130
00:06:30,100 --> 00:06:30,970
我们已经知道是什么了

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

132
00:06:34,140 --> 00:06:36,290
然后我们找出其余部分。

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

134
00:06:38,160 --> 00:06:40,400
嗯，4减2等于2

135
00:06:40,400 --> 00:06:42,030
然后这些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，我们是在十位的列上，是吗？

138
00:06:46,120 --> 00:06:48,710
这整个列就在这里，这是十位列

139
00:06:48,710 --> 00:06:55,120
其实我们真正想说的是，340里面有80个4

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

141
00:06:58,350 --> 00:07:00,844
因为我把3写在了百位数列

142
00:07:00,844 --> 00:07:05,701
然后，还有--

143
00:07:05,701 --> 00:07:07,215
让我把这点擦掉

144
00:07:07,215 --> 00:07:08,872
我不想弄一条线在那看起来像--

145
00:07:08,872 --> 00:07:10,510
当我除这一列的时候，看起来像1

146
00:07:10,510 --> 00:07:11,934
但有两个剩下的

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

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

149
00:07:15,740 --> 00:07:16,990
让我把这个4拿下来

150
00:07:16,990 --> 00:07:18,660
因为我不想只是用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拿下来

153
00:07:22,290 --> 00:07:24,440
我换种颜色

154
00:07:24,440 --> 00:07:26,670
然后 — — — 用另一个方式去想它。

155
00:07:26,670 --> 00:07:31,250
我们刚才说344里面有80个4，对吗

156
00:07:31,250 --> 00:07:33,050
我们把8写在十位上

157
00:07:33,050 --> 00:07:35,550
然后 8乘以4等于320

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

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

160
00:07:40,800 --> 00:07:41,631
嗯，我们都知道的

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

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

163
00:07:49,107 --> 00:07:50,685
我们把这写在个位上

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

165
00:07:53,480 --> 00:07:54,560
然后我们减去

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

167
00:07:56,270 --> 00:07:58,490
那是--我们在这里减去，每个都这样

168
00:07:58,490 --> 00:07:59,530
我们得到了0。

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

170
00:08:01,050 --> 00:08:05,850
所以344里面有准确的86个4

171
00:08:05,850 --> 00:08:09,180
如果你把344个物体 分成每组四个

172
00:08:09,180 --> 00:08:10,900
你会得到八十六个组。

173
00:08:10,900 --> 00:08:12,950
或者如果你把它们分成86个组

174
00:08:12,950 --> 00:08:13,880
你会得到每组4个

175
00:08:13,880 --> 00:08:15,640
让我们做更多的几个问题。

176
00:08:15,640 --> 00:08:18,440
我想你已经找到窍门了

177
00:08:18,440 --> 00:08:21,180
让我做七 — — 我会做一个简单的。

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

179
00:08:24,790 --> 00:08:28,387
又一次，好了，这又是超过了7乘以12

180
00:08:28,387 --> 00:08:31,340
等于84，这是你可以从乘法计算表知道的

181
00:08:31,340 --> 00:08:34,650
因此我们用上一题的方法做这条题

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

183
00:08:37,750 --> 00:08:41,220
9里面有1个7

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

185
00:08:44,640 --> 00:08:48,330
然后9减7 得到2

186
00:08:48,330 --> 00:08:51,190
然后你把个位的数拿下来

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

188
00:08:51,770 --> 00:08:53,036
请记住，这看起来像魔术，

189
00:08:53,036 --> 00:08:57,545
但我们是真的说，90里面有10个7

190
00:08:57,545 --> 00:08:59,961
因为我们把1写在十位上

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

192
00:09:02,466 --> 00:09:05,053
对吗？如果你喜欢 你也可以把0写在那里

193
00:09:05,053 --> 00:09:08,380
然后91减70等于21

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

195
00:09:12,640 --> 00:09:15,780
然后你说，21除以7-- 你知道的！

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

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

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

199
00:09:22,710 --> 00:09:24,550
你把它们相互减去

200
00:09:24,550 --> 00:09:26,375
余数为0

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

202
00:09:31,908 --> 00:09:32,530
让我们做另一题。

203
00:09:32,530 --> 00:09:35,863
我不会停下来去解释一下这全部的数位

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，通过这个视频你可以很好地掌握它

206
00:09:41,580 --> 00:09:44,990
所以，让我们来做7--我一直在用7

207
00:09:44,990 --> 00:09:46,510
用一个不同的数字做

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

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

210
00:09:59,440 --> 00:10:00,740
0个

211
00:10:00,740 --> 00:10:01,980
让我继续

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

213
00:10:05,360 --> 00:10:06,820
让我把8写下来

214
00:10:06,820 --> 00:10:09,110
让我在这里画一条线，这样我们就不会感到混乱

215
00:10:09,110 --> 00:10:11,340
让我向下挪一点

216
00:10:11,340 --> 00:10:13,760
我需要在数字上面留点儿空白

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

218
00:10:15,580 --> 00:10:19,590
我们知道 8 乘以7等于56

219
00:10:19,590 --> 00:10:23,330
然后8乘以8等于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
所以不是这个

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

223
00:10:29,876 --> 00:10:31,740
还有些会余下

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

225
00:10:34,600 --> 00:10:35,728
因为我们在做整个60

226
00:10:35,728 --> 00:10:38,799
我们把7写在60的个位上

227
00:10:38,799 --> 00:10:41,062
这是整个数的十位

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

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

230
00:10:47,100 --> 00:10:48,030
就是4

231
00:10:48,030 --> 00:10:48,990
我们可以在脑里把它做出来

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
这是十

234
00:10:51,510 --> 00:10:53,380
这将是五。

235
00:10:53,380 --> 00:10:54,890
十减六等于四。

236
00:10:54,890 --> 00:10:59,930
然后你把这个8拿下来

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

238
00:11:02,750 --> 00:11:06,260
8乘以6等于多少

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里面有6个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
然后你减去

243
00:11:18,180 --> 00:11:19,500
我们也在这里减

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

245
00:11:22,020 --> 00:11:25,260
因此，再一次我们得到余数为零。

246
00:11:25,260 --> 00:11:28,798
所以希望，这能给你一些窍门去解决这些更大的除法问题

247
00:11:28,798 --> 00:11:31,012
而且我们真正需要知道去怎样去做

248
00:11:31,012 --> 00:11:34,242
去解决这些问题的，是我们的乘法运算表

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