1
00:00:00,880 --> 00:00:05,805
现在我想你知道一点什么是乘法

2
00:00:05,805 --> 00:00:09,025
现在我想你知道一点什么是乘法

3
00:00:09,025 --> 00:00:13,315
在这个课程，我会给你很多很多的练习，

4
00:00:13,315 --> 00:00:17,706
也会帮你背熟你的乘法表。

5
00:00:17,706 --> 00:00:20,009
如果你看很多我的课程，你会知道，我不喜欢背熟东西。

6
00:00:20,009 --> 00:00:21,279
如果你看很多我的课程，你会知道，我不喜欢背熟东西。

7
00:00:21,279 --> 00:00:24,540
如果你看很多我的课程，你会知道，我不喜欢背熟东西。

8
00:00:24,550 --> 00:00:26,385
可是背熟乘法表，对你以后的人生会有很大的帮助。

9
00:00:26,385 --> 00:00:31,220
可是背熟乘法表，对你以后的人生会有很大的帮助。

10
00:00:31,220 --> 00:00:33,850
可是背熟乘法表，对你以后的人生会有很大的帮助。

11
00:00:33,850 --> 00:00:36,724
所以我保证，现在开始背乘法表，你将永远不会忘记它。

12
00:00:36,724 --> 00:00:39,547
在你的余生，所有事情都会...

13
00:00:39,547 --> 00:00:41,517
好吧，我不想对你们做出错误的承诺。

14
00:00:41,517 --> 00:00:45,790
但是这比不背熟乘法表要好。

15
00:00:45,790 --> 00:00:47,290
所以，什么是乘法表？

16
00:00:47,290 --> 00:00:49,745
乘法表是关于不同数字

17
00:00:49,745 --> 00:00:50,850
之间相乘的一张表。

18
00:00:50,850 --> 00:00:53,590
让我们现在开始复习.

19
00:00:53,600 --> 00:00:58,900
2乘以1等于多少？

20
00:00:58,900 --> 00:01:02,270
这相当于2加上它自己本身一次。

21
00:01:02,280 --> 00:01:05,010
所以结果等于2

22
00:01:05,010 --> 00:01:07,060
这相当于2加上它自己本身一次。

23
00:01:07,060 --> 00:01:08,059
我不必加任何数

24
00:01:08,059 --> 00:01:09,430
因为只有一个2,。

25
00:01:09,430 --> 00:01:13,460
我也可以把它当做1加自己两次

26
00:01:13,460 --> 00:01:15,390
所以这也相当于1加1。

27
00:01:15,400 --> 00:01:17,580
结果仍然是2.

28
00:01:17,590 --> 00:01:18,210
好了。

29
00:01:18,210 --> 00:01:19,901
所以2乘以1等于2.

30
00:01:19,901 --> 00:01:22,722
如果你看了上一个视频，2乘以0等于多少？

31
00:01:22,722 --> 00:01:23,516
答案是0.

32
00:01:23,516 --> 00:01:26,660
所以你不必记住0的乘法表，

33
00:01:26,670 --> 00:01:30,560
因为任何数乘以0都等于0，或者说0乘以任何数都等于0.

34
00:01:30,560 --> 00:01:31,090
我们来算一下，

35
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2乘以2等于多少？

36
00:01:33,682 --> 00:01:35,988
2乘以2

37
00:01:35,988 --> 00:01:37,254
它等于

38
00:01:37,254 --> 00:01:39,460
我们将要让2加上它自身两次。

39
00:01:39,460 --> 00:01:41,830
即2加2

40
00:01:41,840 --> 00:01:42,770
这只有一种方法，

41
00:01:42,780 --> 00:01:45,480
我可以说，用这个2再加上它自身

42
00:01:45,480 --> 00:01:46,680
但这其实是一回事。

43
00:01:46,680 --> 00:01:47,610
所以，2加2等于多少？

44
00:01:47,620 --> 00:01:49,450
等于4。

45
00:01:49,450 --> 00:01:51,400
2乘以3等于多少？

46
00:01:51,400 --> 00:01:57,900
2乘以3等于2加2加2。

47
00:01:57,900 --> 00:02:03,355
也可以等于3加3。

48
00:02:03,355 --> 00:02:04,905
我们从之前的视频中学到过，

49
00:02:04,920 --> 00:02:07,498
这个题目可以写成这两种形式中的任一种

50
00:02:07,498 --> 00:02:09,380
在任何一种情况下，答案等于多少？

51
00:02:09,397 --> 00:02:10,282
3加3

52
00:02:10,282 --> 00:02:12,028
等于2加2加2

53
00:02:12,028 --> 00:02:14,774
结果等于6

54
00:02:14,774 --> 00:02:15,812
好的。

55
00:02:15,812 --> 00:02:18,138
那么2乘以4等于多少？

56
00:02:18,153 --> 00:02:20,686
2乘以4。

57
00:02:20,686 --> 00:02:26,065
等于2加2加2加2。

58
00:02:26,065 --> 00:02:29,870
请注意，这正相当于2乘以3。

59
00:02:29,870 --> 00:02:32,610
这些相当于2乘以3

60
00:02:32,620 --> 00:02:36,490
但是现在我又加了一个2

61
00:02:36,490 --> 00:02:39,740
所以如果我们不想计算2加2等于4。

62
00:02:39,740 --> 00:02:40,710
4加2等于6.

63
00:02:40,710 --> 00:02:41,802
我们可以说，

64
00:02:41,802 --> 00:02:45,680
瞧，我们已经知道答案了，这些等于6

65
00:02:45,680 --> 00:02:48,300
我们通过上一行算出来的。

66
00:02:48,310 --> 00:02:51,550
我们算出这些等于6，所以我们知道2乘以4

67
00:02:51,560 --> 00:02:55,610
比这些还要多2，所以结果等于8.

68
00:02:55,610 --> 00:02:57,480
这时，我希望你能看出规律。

69
00:02:57,490 --> 00:03:01,907
我们从2乘以1开始，到2乘以2，

70
00:03:01,907 --> 00:03:03,760
到2乘以3，发生什么了？

71
00:03:03,770 --> 00:03:05,500
这些结果是以多少增长的？

72
00:03:05,500 --> 00:03:08,120
从2增长到到4，我们加2。

73
00:03:08,120 --> 00:03:11,300
从4增长到到6，我们加2。

74
00:03:11,310 --> 00:03:13,340
然后，从6增长到8，我们加2.

75
00:03:13,340 --> 00:03:15,685
所以你不用累加，

76
00:03:15,685 --> 00:03:16,950
便可以算出2乘以5等于多少。

77
00:03:16,960 --> 00:03:23,430
2加5等于2加2加2加2加2.

78
00:03:23,430 --> 00:03:26,070
也可以写成5加5.

79
00:03:26,080 --> 00:03:29,110
2乘以4也可以写成4加4.

80
00:03:29,120 --> 00:03:30,490
所以2乘以5等于几？

81
00:03:30,500 --> 00:03:33,090
我们可以把这些都加起来，或者把这两项加起来。

82
00:03:33,090 --> 00:03:36,285
或者我们可以理解为比2乘以4还多2.

83
00:03:36,285 --> 00:03:38,564
所以答案是10.

84
00:03:38,564 --> 00:03:41,780
我将讲解完2的乘法表。

85
00:03:41,780 --> 00:03:45,280
我想你已经看出了其中的规律。

86
00:03:45,280 --> 00:03:47,710
2乘以6，

87
00:03:47,710 --> 00:03:51,580
它等于2加它自身6次。

88
00:03:51,595 --> 00:03:55,369
1次，两次，3次，4次，5次，6次，

89
00:03:55,369 --> 00:03:58,690
它也等于6加自身两次。

90
00:03:58,690 --> 00:04:00,620
这可以被写为任何一种形式。

91
00:04:00,620 --> 00:04:02,980
结果等于12.

92
00:04:02,990 --> 00:04:06,898
再一次，也可看作比2乘以5多2

93
00:04:06,898 --> 00:04:09,710
因为我们多加了一个2

94
00:04:09,710 --> 00:04:12,290
所以结果比10多了2.

95
00:04:12,300 --> 00:04:13,880
我们继续。

96
00:04:13,880 --> 00:04:16,540
2乘以7。

97
00:04:16,550 --> 00:04:20,148
2乘以7等于--

98
00:04:20,163 --> 00:04:24,104
我可以写成2加2加2加2加2--

99
00:04:24,104 --> 00:04:27,230
这写起来很费劲--加2加2

100
00:04:27,240 --> 00:04:27,800
有7个2了吗？

101
00:04:27,810 --> 00:04:31,200
1个，两个，3个，4个，5个，6个，7个。

102
00:04:31,200 --> 00:04:33,849
这和7加7是一回事。

103
00:04:33,849 --> 00:04:37,370
不管你知不知道，答案等于14.

104
00:04:37,370 --> 00:04:39,550
你会发现，这比12多2.

105
00:04:39,560 --> 00:04:43,630
所以12加1加2等于--12加1等于13.

106
00:04:43,630 --> 00:04:45,530
12加2等于14.

107
00:04:45,540 --> 00:04:47,580
好的，我们继续。

108
00:04:47,580 --> 00:04:50,740
2乘以8.

109
00:04:50,750 --> 00:04:53,810
我可以把所有2加起来

110
00:04:53,810 --> 00:04:56,660
或者我可以认为，答案比2乘以7还多2.

111
00:04:56,670 --> 00:04:59,528
所以等于14加2

112
00:04:59,528 --> 00:05:00,470
我在这个数的基础上加2.

113
00:05:00,480 --> 00:05:01,822
所以答案是16.

114
00:05:01,822 --> 00:05:05,610
或者可以看成8加8.

115
00:05:05,620 --> 00:05:06,800
答案仍然是16.

116
00:05:06,810 --> 00:05:08,174
我可以把所有的2写出来，

117
00:05:08,174 --> 00:05:15,040
但是你可以自己做一下，这对你们的学习有好处。

118
00:05:15,040 --> 00:05:17,848
我们快结束了。其实，我们可以一直做下去。

119
00:05:17,848 --> 00:05:19,360
因为不存在所谓的最大的数字。

120
00:05:19,370 --> 00:05:21,510
我可以继续。

121
00:05:21,510 --> 00:05:24,970
2乘以9, 2乘以10,2乘以100,2乘以1000,2乘以1000000.

122
00:05:24,980 --> 00:05:26,642
但是我将乘到12为止

123
00:05:26,642 --> 00:05:28,760
因为这些是人们必须记住的。

124
00:05:28,770 --> 00:05:32,330
但是，如果你想成为一个“数学计算家”

125
00:05:32,330 --> 00:05:34,260
你可以算到20.

126
00:05:34,260 --> 00:05:36,790
我们来计算2乘以9、

127
00:05:36,790 --> 00:05:38,810
它比2乘以8多2.

128
00:05:38,810 --> 00:05:40,990
所以答案是18。

129
00:05:40,990 --> 00:05:42,690
或者可以看成9加9，

130
00:05:42,690 --> 00:05:44,060
仍然等于18.

131
00:05:44,060 --> 00:05:45,930
2乘以10等于多少？

132
00:05:45,940 --> 00:05:47,940
10的乘法表比较有趣。

133
00:05:47,940 --> 00:05:49,550
当我们一会儿完成整个乘法表时，

134
00:05:49,560 --> 00:05:53,040
我们会看到其中的规律。

135
00:05:53,040 --> 00:05:54,640
2乘以10等于多少？

136
00:05:54,640 --> 00:05:56,800
比2乘以9还多2.

137
00:05:56,810 --> 00:05:59,050
答案是20。

138
00:05:59,050 --> 00:06:01,050
或者可看成10加10.

139
00:06:01,060 --> 00:06:03,360
10加上它自身两次。

140
00:06:03,360 --> 00:06:05,060
现在，你发现了其中的奥妙了吗？

141
00:06:05,060 --> 00:06:09,115
它看上去像是2后面加了一个0。

142
00:06:09,115 --> 00:06:10,690
而且，你会发现所有数字乘以10

143
00:06:10,690 --> 00:06:12,295
都等于在这个数字右边加了一个0.

144
00:06:12,295 --> 00:06:14,130
你可以思考一下这是为什么。

145
00:06:14,130 --> 00:06:16,410
你可以把它看作两个10，也就是20.

146
00:06:16,420 --> 00:06:18,000
这正是20的定义。

147
00:06:18,000 --> 00:06:19,540
我们快做完了。

148
00:06:19,550 --> 00:06:21,820
现在计算2乘以11.

149
00:06:21,820 --> 00:06:25,920
2乘以11比这个多2.

150
00:06:25,930 --> 00:06:27,830
答案是22.

151
00:06:27,830 --> 00:06:29,530
这又是一个有趣的规律。

152
00:06:29,540 --> 00:06:32,220
一个数字出现了两遍--一个2，又一个2.

153
00:06:32,220 --> 00:06:33,160
很有趣。

154
00:06:33,170 --> 00:06:35,818
在我们学习其他数字的乘法表时

155
00:06:35,818 --> 00:06:38,690
我们应该注意其中的规律。

156
00:06:38,704 --> 00:06:40,140
最后，

157
00:06:40,140 --> 00:06:42,129
这不是最后，我们可以一直继续，

158
00:06:42,129 --> 00:06:44,682
2乘以……字的颜色太深了。

159
00:06:44,682 --> 00:06:47,059
2乘以12.

160
00:06:47,059 --> 00:06:50,540
2乘以12比2乘以11还多2.

161
00:06:50,550 --> 00:06:51,826
结果是24.

162
00:06:51,826 --> 00:06:54,160
我们也可以写成12加12.

163
00:06:54,170 --> 00:06:56,110
或者也可以写成2加2加2

164
00:06:56,110 --> 00:06:57,840
加2……一共12次。

165
00:06:57,850 --> 00:06:59,660
答案都能算出来24.

166
00:06:59,670 --> 00:07:00,961
这就是2的乘法表

167
00:07:00,961 --> 00:07:01,970
我认为你们应该看出了其中的规律。

168
00:07:01,980 --> 00:07:04,755
每当你用一个更大的数乘以2，

169
00:07:04,755 --> 00:07:06,670
你就在那个数的基础了又加了一个2.

170
00:07:06,680 --> 00:07:08,748
现在，我们找到了其中的规律。

171
00:07:08,748 --> 00:07:11,950
现在我们尝试一下是否可以完成乘法表。

172
00:07:11,950 --> 00:07:16,260
现在我想写下所有的数字。

173
00:07:16,270 --> 00:07:18,485
我们来看一下。

174
00:07:18,485 --> 00:07:19,361
我希望我能写的下。

175
00:07:19,361 --> 00:07:29,430
1,2,3,4,5,6,7,8,9。

176
00:07:29,430 --> 00:07:30,910
实际上，我要从9做起。

177
00:07:30,920 --> 00:07:31,830
我要继续写下去。

178
00:07:31,830 --> 00:07:32,970
9。

179
00:07:32,970 --> 00:07:34,106
但是我写不下了

180
00:07:34,106 --> 00:07:35,680
因为我想让你们看见完整的乘法表。

181
00:07:35,680 --> 00:07:37,045
所以我只能做到9.

182
00:07:37,045 --> 00:07:39,590
但我鼓励你们看完这个视频后自己完成。

183
00:07:39,600 --> 00:07:42,880
如果有时间的话，我也会在这把乘法表完成。

184
00:07:42,880 --> 00:07:45,887
这些是我想乘的第一个数字。

185
00:07:45,887 --> 00:07:52,060
我想用它们乘以1,2,3,4

186
00:07:52,060 --> 00:07:57,650
5,6,7,8和9.

187
00:07:57,650 --> 00:08:00,183
我要开始做了。

188
00:08:00,183 --> 00:08:01,298
首先，

189
00:08:01,298 --> 00:08:03,321
其实我应该把这个1写在下面--

190
00:08:03,321 --> 00:08:04,710
1乘以1等于多少？

191
00:08:04,720 --> 00:08:06,110
这正是我想要呈现的效果。

192
00:08:06,120 --> 00:08:08,730
1乘以1的结果我写在这。

193
00:08:08,730 --> 00:08:09,970
等于1.

194
00:08:09,970 --> 00:08:11,510
1乘以2等于多少？

195
00:08:11,510 --> 00:08:12,400
等于2.

196
00:08:12,410 --> 00:08:13,730
1乘以3呢？

197
00:08:13,740 --> 00:08:14,360
等于3.

198
00:08:14,360 --> 00:08:15,866
1乘以任何数就等于那个数本身。

199
00:08:15,866 --> 00:08:21,360
所以我可以写下4,5,6,7,8,9.

200
00:08:21,370 --> 00:08:23,540
1乘以9等于9.

201
00:08:23,540 --> 00:08:24,540
好了。

202
00:08:24,540 --> 00:08:26,300
现在做2的乘法表。

203
00:08:26,310 --> 00:08:27,570
我用蓝色笔写。

204
00:08:27,570 --> 00:08:30,270
我们用这种颜色做1的乘法表.

205
00:08:30,285 --> 00:08:33,980
用这个深蓝色做2的乘法表。

206
00:08:33,990 --> 00:08:35,250
2乘以1等于多少？

207
00:08:35,250 --> 00:08:36,430
等于2.

208
00:08:36,440 --> 00:08:37,690
它和1乘以2一样。

209
00:08:37,700 --> 00:08:40,000
注意，这两个数字是一样的。

210
00:08:40,000 --> 00:08:41,700
2乘以2等于多少?

211
00:08:41,710 --> 00:08:43,000
等于4

212
00:08:43,000 --> 00:08:44,610
2乘以3等于6.

213
00:08:44,620 --> 00:08:45,840
我们刚才算了这个。

214
00:08:45,840 --> 00:08:49,821
每次增加或乘以一个更大的数，

215
00:08:49,821 --> 00:08:51,190
我们只要加上2即可。

216
00:08:51,190 --> 00:08:52,840
2乘以4等于8.

217
00:08:52,850 --> 00:08:55,110
相当于4乘以2.

218
00:08:55,120 --> 00:08:57,260
2乘以5等于10.

219
00:08:57,260 --> 00:08:59,010
2乘以6等于12.

220
00:08:59,010 --> 00:09:00,660
我每次都加2.

221
00:09:00,670 --> 00:09:03,970
在上面这行，我每步都加上1.在这行，我们每次都加上2.

222
00:09:03,980 --> 00:09:06,830
2乘以7等于14.

223
00:09:06,830 --> 00:09:09,813
2乘以8等于16.

224
00:09:09,813 --> 00:09:12,970
2乘以9等于18.

225
00:09:12,980 --> 00:09:17,789
好了。现在来做3的乘法表。

226
00:09:17,789 --> 00:09:20,508
我用黄色笔写。

227
00:09:20,508 --> 00:09:21,783
我用黄色笔写。

228
00:09:21,783 --> 00:09:23,828
2乘以1等于3.

229
00:09:23,828 --> 00:09:25,350
注意，3乘以1等于3.

230
00:09:25,360 --> 00:09:26,910
1乘以3也等于3.

231
00:09:26,910 --> 00:09:28,740
它们答案是一样的。

232
00:09:28,750 --> 00:09:32,158
3乘以2等于2乘以3.

233
00:09:32,158 --> 00:09:37,640
3乘以2和2乘以3是一回事。

234
00:09:37,640 --> 00:09:39,680
结果是6.

235
00:09:39,690 --> 00:09:40,485
这有点意思。

236
00:09:40,485 --> 00:09:45,690
3加3等于6,2加2加2也等于6.

237
00:09:45,690 --> 00:09:47,780
所以，我们每次都以3增长。

238
00:09:47,780 --> 00:09:48,880
你可以发现其中的规律。

239
00:09:48,880 --> 00:09:51,000
3乘以3等于9。

240
00:09:51,010 --> 00:09:52,852
相当于3加3加3.

241
00:09:52,852 --> 00:09:54,725
我们从3增长到6，6又增长到9.

242
00:09:54,736 --> 00:09:57,001
所以，3乘以4等于12.

243
00:09:57,001 --> 00:09:58,850
我每次都加了3.

244
00:09:58,850 --> 00:10:00,642
12加3等于15.

245
00:10:00,642 --> 00:10:03,404
15加3等于18.

246
00:10:03,404 --> 00:10:05,580
18加3等于21.

247
00:10:05,580 --> 00:10:08,080
21加3等于24.

248
00:10:08,090 --> 00:10:10,500
24加3等于27.

249
00:10:10,500 --> 00:10:13,110
所以3乘以9等于27.

250
00:10:13,120 --> 00:10:14,840
3乘以8等于24.

251
00:10:14,840 --> 00:10:19,094
所以你也可以看成是8加8加8，结果是24.

252
00:10:19,094 --> 00:10:20,180
现在我想

253
00:10:20,180 --> 00:10:21,544
加快一点速度，

254
00:10:21,544 --> 00:10:22,830
因为我们已经找到了规律。

255
00:10:22,840 --> 00:10:24,088
你应该自己完成这些

256
00:10:24,088 --> 00:10:26,970
并且记住我们正在做的这些。

257
00:10:26,980 --> 00:10:30,495
你应该从两个方向都计算到12。

258
00:10:30,495 --> 00:10:31,057
让我们来看看。

259
00:10:31,057 --> 00:10:35,330
4乘以1等于4.

260
00:10:35,330 --> 00:10:37,640
我将以4为增量递增计算。

261
00:10:37,640 --> 00:10:40,080
4加4等于8.

262
00:10:40,090 --> 00:10:41,960
8加4等于12.

263
00:10:41,970 --> 00:10:43,920
12加4等于16.

264
00:10:43,920 --> 00:10:46,450
16加4等于20.

265
00:10:46,460 --> 00:10:48,460
20加4等于24.

266
00:10:48,460 --> 00:10:51,460
4乘以6等于24.

267
00:10:51,470 --> 00:10:52,970
4乘以7等于28.

268
00:10:52,980 --> 00:10:54,250
我每次都加4.

269
00:10:54,250 --> 00:10:58,740
后面两个结果是32和36.

270
00:10:58,750 --> 00:11:01,490
好的，5乘以1.

271
00:11:01,490 --> 00:11:06,670
5乘以1等于5.

272
00:11:06,670 --> 00:11:09,565
其实，我想一直变换颜色，

273
00:11:09,565 --> 00:11:11,400
所以我要像这样一排一排的写。

274
00:11:11,410 --> 00:11:12,570
5乘以1等于5.

275
00:11:12,580 --> 00:11:15,780
5乘以2等于10.

276
00:11:15,780 --> 00:11:17,260
5乘以3等于15.

277
00:11:17,260 --> 00:11:18,430
我将以5为增量递增。

278
00:11:18,440 --> 00:11:20,687
5的乘法表也十分有趣。

279
00:11:20,687 --> 00:11:24,120
因为你加上的每一个数字，如果我们乘5次，

280
00:11:24,120 --> 00:11:25,870
我们以后将会学到偶数和奇数。

281
00:11:25,880 --> 00:11:30,241
但是这个乘法表里的每一些数字都以5结尾，

282
00:11:30,241 --> 00:11:32,240
而另一些数字都以0结尾。

283
00:11:32,250 --> 00:11:34,790
因为，如果你在15的基础上加5，结果是20.

284
00:11:34,790 --> 00:11:41,871
接着是25,30,35,40,45.

285
00:11:41,871 --> 00:11:43,380
好了。

286
00:11:43,380 --> 00:11:47,120
我们用绿色的笔写6的乘法表。

287
00:11:47,120 --> 00:11:48,210
6乘以1等于6.

288
00:11:48,220 --> 00:11:49,080
这很简单。

289
00:11:49,080 --> 00:11:50,800
再加上6，答案是12.

290
00:11:50,800 --> 00:11:52,490
再加上6，答案是18.

291
00:11:52,500 --> 00:11:54,250
再加上6，答案是24.

292
00:11:54,250 --> 00:11:56,220
再加上6，答案是30.

293
00:11:56,220 --> 00:12:01,220
再加上6，得到36,42,48.

294
00:12:01,220 --> 00:12:04,620
48加6等于54.

295
00:12:04,620 --> 00:12:07,620
所以，6乘以9等于54.

296
00:12:07,620 --> 00:12:08,990
我们快完成了。

297
00:12:09,000 --> 00:12:11,610
7乘以1等于7.

298
00:12:11,620 --> 00:12:13,520
7乘以1等于7.

299
00:12:13,520 --> 00:12:15,610
7乘以2等于14.

300
00:12:15,620 --> 00:12:17,740
7乘以3等于21.

301
00:12:17,740 --> 00:12:20,040
7乘以4等于28.

302
00:12:20,040 --> 00:12:23,512
7乘以5,28加7等于多少？

303
00:12:23,512 --> 00:12:25,130
28加2等于30.

304
00:12:25,130 --> 00:12:27,700
然后再加上5，答案是35.

305
00:12:27,710 --> 00:12:29,480
7乘以6等于42.

306
00:12:29,490 --> 00:12:32,640
7乘以7等于49.

307
00:12:32,640 --> 00:12:34,775
7乘以8

308
00:12:34,775 --> 00:12:37,830
等于7加上这个，等于56.

309
00:12:37,830 --> 00:12:41,580
我经常在7乘以8等于56

310
00:12:41,590 --> 00:12:43,610
和6乘以9等于54中间弄混。

311
00:12:43,620 --> 00:12:46,705
所以现在我提醒你们，我经常弄混这两个数，

312
00:12:46,705 --> 00:12:49,389
而你们不应该被这两个数弄混。

313
00:12:49,390 --> 00:12:52,610
你可以认为7乘以8里面有个6，

314
00:12:52,620 --> 00:12:54,850
而6乘以9里面没有6.

315
00:12:54,850 --> 00:12:56,080
这是我记住它们的方法。

316
00:12:56,080 --> 00:12:57,580
7乘以9，

317
00:12:57,580 --> 00:12:59,320
我们再加上一个7，

318
00:12:59,320 --> 00:13:01,152
结果是63.

319
00:13:01,152 --> 00:13:04,830
我用一样的颜色写。

320
00:13:04,840 --> 00:13:08,350
好的。现在是8的乘法表。

321
00:13:08,360 --> 00:13:10,660
8乘以1等于8.

322
00:13:10,660 --> 00:13:12,520
8乘以2等于16.

323
00:13:12,520 --> 00:13:14,090
24.

324
00:13:14,100 --> 00:13:15,690
8乘以3等于24.

325
00:13:15,690 --> 00:13:18,300
如果我们计算3乘以8，结果仍然是24.

326
00:13:18,300 --> 00:13:19,500
对，在那呢。

327
00:13:19,500 --> 00:13:21,110
这两个数相等。

328
00:13:21,120 --> 00:13:22,800
所以我们实际上算了两遍。

329
00:13:22,800 --> 00:13:24,848
在算8乘以3时

330
00:13:24,848 --> 00:13:27,470
和3乘以8时，我们都计算了它。

331
00:13:27,472 --> 00:13:31,210
8乘以4，在前面的数字上再加上8，等于32.

332
00:13:31,220 --> 00:13:32,480
40.

333
00:13:32,490 --> 00:13:34,690
再加8,48.

334
00:13:34,690 --> 00:13:37,270
注意，8乘以6等于48.

335
00:13:37,270 --> 00:13:40,230
6乘以8也等于48.

336
00:13:40,240 --> 00:13:42,450
8乘以7，

337
00:13:42,450 --> 00:13:45,860
我们已经标出了，等于56.

338
00:13:45,870 --> 00:13:48,200
8乘以8等于64.

339
00:13:48,200 --> 00:13:52,010
8乘以9，在这个数上面加8，等于72.

340
00:13:52,010 --> 00:13:54,640
现在来计算9的乘法表。

341
00:13:54,650 --> 00:13:57,260
笔颜色用完了。

342
00:13:57,260 --> 00:13:59,520
我可能会重复用一种或两种颜色。

343
00:13:59,530 --> 00:14:01,100
我再用蓝色。

344
00:14:01,110 --> 00:14:03,280
9乘以1等于9.

345
00:14:03,280 --> 00:14:06,700
9乘以2等于18. 9乘以3--实际上我们已经知道了答案。

346
00:14:06,710 --> 00:14:08,097
我们可以在表中的其他数字找到答案。

347
00:14:08,097 --> 00:14:11,290
因为9乘以3等于3乘以9.

348
00:14:11,290 --> 00:14:13,280
结果是27.

349
00:14:13,280 --> 00:14:14,500
再加上9。

350
00:14:14,500 --> 00:14:18,380
27加9等于36.

351
00:14:18,390 --> 00:14:21,520
36加9等于45.

352
00:14:21,530 --> 00:14:25,331
注意，每次加9，结果将近加了10，

353
00:14:25,331 --> 00:14:26,219
但比10少1.

354
00:14:26,219 --> 00:14:29,970
所以36加10等于46，再减1，结果是45.

355
00:14:29,970 --> 00:14:32,647
注意，这些

356
00:14:32,647 --> 00:14:33,880
我以后会说到。

357
00:14:33,890 --> 00:14:37,510
但是在这一位上，即第二位上

358
00:14:37,520 --> 00:14:38,835
数字从9到8到7到6到5，

359
00:14:38,835 --> 00:14:42,510
并且在这一位上，是1,2,3,4。

360
00:14:42,510 --> 00:14:44,010
这又是个有趣的规律。

361
00:14:44,020 --> 00:14:47,240
另一个有趣的规律是，两个数位上的数字加起来等于9.

362
00:14:47,250 --> 00:14:49,270
3加6等于9,2加7等于9.

363
00:14:49,270 --> 00:14:50,831
我们以后会讨论并且证明这个问题。

364
00:14:50,831 --> 00:14:52,620
我们以后会讨论并且证明这个问题。

365
00:14:52,630 --> 00:14:56,340
9乘以6等于54.

366
00:14:56,350 --> 00:14:58,150
它等于这个数。

367
00:14:58,150 --> 00:15:01,720
9乘以7等于63.

368
00:15:01,730 --> 00:15:03,850
9乘以8等于72.

369
00:15:03,860 --> 00:15:05,910
9乘以9等于81.

370
00:15:05,910 --> 00:15:07,030
不知道你们看不看的到。

371
00:15:07,040 --> 00:15:08,360
等于81。

372
00:15:08,370 --> 00:15:09,480
现在完成了。

373
00:15:09,480 --> 00:15:11,080
现在，我可以继续写下去。

374
00:15:11,080 --> 00:15:13,780
其实，我也应该继续写下去。

375
00:15:13,780 --> 00:15:17,525
但是，我意识到这段视频已经很长了。

376
00:15:17,525 --> 00:15:19,316
我希望你们现在就能记住这些

377
00:15:19,316 --> 00:15:21,200
因为这些在以后的学习中很有用。

378
00:15:21,210 --> 00:15:25,542
我将会在下段视频中完成9以后的乘法表。

379
00:15:25,542 --> 00:15:26,960
下次见！