1
00:00:00,540 --> 00:00:04,565
在上次的视频中，我们学习了从1至9的乘法口诀表

2
00:00:04,565 --> 00:00:06,960
可是上次我演示的时间不够了，不过，其实这是个好事情

3
00:00:06,960 --> 00:00:11,266
因为从1到9是乘法口诀表的核心基础

4
00:00:11,266 --> 00:00:14,702
不难看出，如果你掌握了从1到9的乘法口诀表

5
00:00:14,702 --> 00:00:16,720
那么用1和9之间的任何数字

6
00:00:16,720 --> 00:00:18,816
乘以1和9之间的任何数字

7
00:00:18,816 --> 00:00:21,670
你就能轻易的用乘法算出结果

8
00:00:21,670 --> 00:00:22,642
可是我现在想演示的是

9
00:00:22,642 --> 00:00:29,810
来做完10，11和12的乘法口诀表

10
00:00:29,820 --> 00:00:33,680
那么，什么是10乘以--让我们从数字0开始

11
00:00:33,680 --> 00:00:35,980
10乘以0

12
00:00:35,990 --> 00:00:39,030
任何数字乘以0都等于0

13
00:00:39,030 --> 00:00:40,375
10次0相加还是等于0

14
00:00:40,375 --> 00:00:43,933
0+0+0。。加10次还是等于10

15
00:00:43,933 --> 00:00:46,107
10乘1等于多少呢？

16
00:00:46,122 --> 00:00:48,034
10乘以1

17
00:00:48,034 --> 00:00:49,982
好，这个就是1次数字10

18
00:00:49,990 --> 00:00:52,740
或者是10次数字1相加

19
00:00:52,750 --> 00:00:53,890
等于10

20
00:00:53,890 --> 00:00:56,490
我觉得在这点上不需要我多说你就能算出来

21
00:00:56,500 --> 00:00:58,447
10乘2得多少呢？

22
00:00:58,447 --> 00:00:59,961
10乘以2

23
00:00:59,961 --> 00:01:02,660
我该换一个颜色写这个，但是我忘啦

24
00:01:02,670 --> 00:01:04,060
10乘以2

25
00:01:04,060 --> 00:01:08,950
等于10加10，也就是20

26
00:01:08,950 --> 00:01:09,550
很好

27
00:01:09,560 --> 00:01:12,650
注意，从上面开始，我们第一次结果得到一个10

28
00:01:12,650 --> 00:01:15,210
我们从这再一次得到一个20

29
00:01:15,210 --> 00:01:17,690
那么10乘3得多少呢？

30
00:01:17,700 --> 00:01:20,546
嗯，这个就是10加10再加10

31
00:01:20,546 --> 00:01:24,539
或者我们可以把这个看成是10乘2再加上一个10

32
00:01:24,539 --> 00:01:26,485
结果等于30

33
00:01:26,485 --> 00:01:27,385
10乘4呢？

34
00:01:27,385 --> 00:01:28,670
我希望你注意到了这个规律

35
00:01:28,680 --> 00:01:32,450
10乘4等于40

36
00:01:32,450 --> 00:01:37,400
看到这了吧，10乘以4就等于“4-0”

37
00:01:37,400 --> 00:01:42,030
如果我问来你，10乘以---

38
00:01:42,040 --> 00:01:44,860
让我来还一个颜色--5？

39
00:01:44,870 --> 00:01:50,260
好吧，结果是50

40
00:01:50,260 --> 00:01:56,410
10乘以任何数字，得到的结果就是任何数字后面加一个0

41
00:01:56,410 --> 00:01:57,702
那么10的乘法口诀表

42
00:01:57,702 --> 00:01:59,315
你几乎就不用怎么死记硬背

43
00:01:59,315 --> 00:02:01,378
好，咱们接着往下继续

44
00:02:01,378 --> 00:02:04,109
10乘6得多少呢？

45
00:02:04,109 --> 00:02:06,840
结果就是--6-0！

46
00:02:06,840 --> 00:02:08,340
6-0

47
00:02:08,340 --> 00:02:11,090
10乘7呢？

48
00:02:11,090 --> 00:02:12,315
70

49
00:02:12,315 --> 00:02:13,340
10乘8？

50
00:02:13,340 --> 00:02:14,920
这个太好笑了

51
00:02:14,930 --> 00:02:16,810
10乘以8等于80

52
00:02:16,810 --> 00:02:19,020
10乘9呢？

53
00:02:19,030 --> 00:02:20,315
90

54
00:02:20,315 --> 00:02:21,590
10乘10呢？

55
00:02:21,590 --> 00:02:23,708
哦现在这个才有意思

56
00:02:23,708 --> 00:02:26,882
10乘10，也就是这个10--

57
00:02:26,882 --> 00:02:29,523
让我来写清楚一下

58
00:02:29,523 --> 00:02:32,180
我来换一种橘色来写

59
00:02:32,180 --> 00:02:33,302
10乘10

60
00:02:33,302 --> 00:02:38,571
也就是10-0，或者说10后面加一个0

61
00:02:38,571 --> 00:02:41,702
就是这样的。看到了吧，无论什么数字乘以10，就在数字后面加一个0

62
00:02:41,702 --> 00:02:42,725
就得到了这个乘法结果

63
00:02:42,725 --> 00:02:43,950
所以这是100

64
00:02:43,960 --> 00:02:45,520
同时我希望你明白了为什么这个结果等于这个数

65
00:02:45,530 --> 00:02:47,900
我就是把10这个数字加了10遍

66
00:02:47,900 --> 00:02:51,700
那么每一个10，你从10，20，30依次算得的

67
00:02:51,710 --> 00:02:54,240
30也就相当于3个10相加或者10个3相加

68
00:02:54,250 --> 00:02:58,250
90也是10个9相加，或者9个10相加

69
00:02:58,250 --> 00:03:00,450
让我们继续

70
00:03:00,460 --> 00:03:05,120
然后10乘11就等于11后面加一个0

71
00:03:05,120 --> 00:03:06,960
也就说11-0

72
00:03:06,960 --> 00:03:13,070
最后，10乘12等于，120

73
00:03:13,080 --> 00:03:17,370
接下来，就是为了好玩，以上这些可以作为你的10的乘法口诀表

74
00:03:17,370 --> 00:03:20,460
但是现在你明白了其中的规律，你可以随意算这些乘法

75
00:03:20,470 --> 00:03:28,266
如果然我来问你，5732乘以10等于多少？

76
00:03:28,266 --> 00:03:29,691
结果会是多少呢？

77
00:03:29,691 --> 00:03:32,547
它就等于这个数字后面加一个0

78
00:03:32,547 --> 00:03:34,650
所以结果就是----我先不说出来

79
00:03:34,650 --> 00:03:39,080
5732后面加一个0

80
00:03:39,090 --> 00:03:40,122
还有就是让你知道一下

81
00:03:40,122 --> 00:03:42,445
我在这个数字后面写的这个小逗号

82
00:03:42,445 --> 00:03:45,882
这个就是为了能够读数字的时候更容易一点

83
00:03:45,882 --> 00:03:47,942
那么，你加一个逗号，你从个位数这边开始

84
00:03:47,942 --> 00:03:49,740
每三个数字你放一个逗号

85
00:03:49,750 --> 00:03:53,080
所以这个地方，我在这放一个逗号

86
00:03:53,080 --> 00:03:54,960
我就把这个逗号加在这个地方

87
00:03:54,960 --> 00:03:56,640
现在我很容易就能读出这个数

88
00:03:56,650 --> 00:03:59,690
这个逗号在这并没有加上或者取消任何数字

89
00:03:59,690 --> 00:04:01,190
它的作用就是帮我把这个数字变得更容易读

90
00:04:01,190 --> 00:04:07,890
现在这个5732乘以10就等于57，320

91
00:04:07,900 --> 00:04:09,195
我只需要在这加一个0

92
00:04:09,195 --> 00:04:12,708
但是那个是个很容易理解的乘法运算

93
00:04:12,708 --> 00:04:15,239
而且你注意到了吧，我们用5000乘以10

94
00:04:15,239 --> 00:04:19,070
所以当我们计算乘法时，我们得到了50000多的一个数字

95
00:04:19,070 --> 00:04:21,940
这个其实和5乘以10 等于50差不多的意思

96
00:04:21,950 --> 00:04:24,848
但是用的不是5，而是一个5000

97
00:04:24,848 --> 00:04:28,050
所以我得到了50，000什么什么和其他后面这些数字

98
00:04:28,060 --> 00:04:30,940
我们在以后的视频中会更多的学习如何计算这类问题

99
00:04:30,940 --> 00:04:32,512
但是，我觉得我得借此向你们介绍这个规律

100
00:04:32,512 --> 00:04:34,922
也就是这个在后面加一个0的小技巧

101
00:04:34,922 --> 00:04:37,690
你可以完全掌握这个10的乘法口诀表

102
00:04:37,690 --> 00:04:40,132
下面让我们来看11的乘法口诀表

103
00:04:40,132 --> 00:04:42,137
这些11的口诀表，开始的时候

104
00:04:42,152 --> 00:04:43,224
嗯，开始会比较容易

105
00:04:43,224 --> 00:04:47,140
但是随着数字越变越大，计算会越来越有点难

106
00:04:47,140 --> 00:04:49,000
好，11乘以0

107
00:04:49,000 --> 00:04:51,500
这个太容易，就等于0！

108
00:04:51,510 --> 00:04:52,820
11乘以1

109
00:04:52,830 --> 00:04:54,000
也很容易

110
00:04:54,000 --> 00:04:56,000
就等于11

111
00:04:56,010 --> 00:04:57,350
11乘以2？

112
00:04:57,360 --> 00:04:59,270
下面我们来看这个计算规律

113
00:04:59,270 --> 00:05:03,420
可以写成11+11，或者我们也可以算11次数字2的相加

114
00:05:03,430 --> 00:05:06,450
结果是22

115
00:05:06,450 --> 00:05:11,510
如果我们用11乘3，结果就等于33

116
00:05:11,510 --> 00:05:15,550
11乘4，等于4-4

117
00:05:15,560 --> 00:05:16,970
我觉得你开始认为这个很容易理解了吧

118
00:05:16,970 --> 00:05:18,980
11乘5等于多少呢？

119
00:05:18,990 --> 00:05:20,930
11x5等于55

120
00:05:20,930 --> 00:05:23,000
注意，我就把5写两遍

121
00:05:23,000 --> 00:05:24,930
那么11乘以6呢？

122
00:05:24,930 --> 00:05:27,320
等于66

123
00:05:27,330 --> 00:05:30,820
11乘以7呢？ 等于84？哦，不对

124
00:05:30,830 --> 00:05:32,260
我在逗你呢

125
00:05:32,260 --> 00:05:33,710
我客不想把你搞糊涂

126
00:05:33,720 --> 00:05:34,255
但是，答案不是这个。不对

127
00:05:34,255 --> 00:05:36,910
没错，答案应该是77！

128
00:05:36,910 --> 00:05:37,902
7-7

129
00:05:37,902 --> 00:05:39,418
你就把这个数字写两遍

130
00:05:39,418 --> 00:05:41,086
7-7！

131
00:05:41,086 --> 00:05:42,630
让我换一个颜色来写

132
00:05:42,630 --> 00:05:46,250
11乘以8等于88

133
00:05:46,260 --> 00:05:50,420
11乘以9等于99

134
00:05:50,420 --> 00:05:52,405
行，那11乘12等于多少呢？

135
00:05:52,405 --> 00:05:54,495
11乘以12

136
00:05:54,495 --> 00:05:56,728
哦，不好意思，我错过了10。

137
00:05:56,750 --> 00:05:58,140
11乘以10

138
00:05:58,140 --> 00:06:00,150
你大概想说，应该是10再写一遍10

139
00:06:00,160 --> 00:06:00,720
错啦！

140
00:06:00,730 --> 00:06:01,410
那个完全错啦

141
00:06:01,410 --> 00:06:05,090
根本不是10-10

142
00:06:05,100 --> 00:06:06,844
那么，那个刚才我们用的小技巧

143
00:06:06,844 --> 00:06:08,433
就是两个数字重复写一遍的那个

144
00:06:08,433 --> 00:06:10,056
仅仅适用于一位数的数字

145
00:06:10,056 --> 00:06:11,602
也就是说，那个仅仅适用于从1到9的数字相乘

146
00:06:11,602 --> 00:06:12,825
11乘以10

147
00:06:12,825 --> 00:06:14,570
嗯，其实我们可以用几种方法来想这个问题

148
00:06:14,570 --> 00:06:16,740
我们可以在99后面加上11

149
00:06:16,750 --> 00:06:20,873
那么这变成了，99加11

150
00:06:20,888 --> 00:06:21,995
是什么呢？

151
00:06:21,995 --> 00:06:23,390
正好等于110

152
00:06:23,390 --> 00:06:24,809
我马上来给你展示一下怎么做这个

153
00:06:24,809 --> 00:06:28,879
哦，我希望你已经看过了怎么做两位数的加法的视频演示

154
00:06:28,879 --> 00:06:30,210
那这个结果就等于110

155
00:06:30,220 --> 00:06:34,153
或者你也可以从我们刚才学的的那个10的乘法口诀表的方法里方法

156
00:06:34,157 --> 00:06:36,652
在刚才，我们讲过11乘以10就等于11后面加一个0

157
00:06:36,652 --> 00:06:37,844
那么你得到了110

158
00:06:37,859 --> 00:06:39,590
那个位置是一个11

159
00:06:39,590 --> 00:06:42,541
最后，让我们来看11乘12

160
00:06:42,541 --> 00:06:44,694
11乘以12？

161
00:06:44,694 --> 00:06:46,007
实在是不容易记住这个口诀

162
00:06:46,007 --> 00:06:47,080
你只能想办法背一下这个规律

163
00:06:47,080 --> 00:06:48,180
或者你可以说，看吧

164
00:06:48,180 --> 00:06:51,310
这个就是11乘11再加11

165
00:06:51,310 --> 00:06:53,130
对不起，我老是跳过一些数

166
00:06:53,140 --> 00:06:55,410
让我们先来做11乘11

167
00:06:55,420 --> 00:06:56,700
咱们来确保这个地方能看清楚

168
00:06:56,700 --> 00:07:00,590
我们在做11乘12之前先来做11乘11

169
00:07:00,600 --> 00:07:05,480
那么11乘11就是11乘10再加11

170
00:07:05,490 --> 00:07:07,270
所以我们在这加上11

171
00:07:07,270 --> 00:07:13,120
11加上110等于121

172
00:07:13,120 --> 00:07:13,755
事实上，你看到了吧

173
00:07:13,755 --> 00:07:17,831
实际上这有一个11以上的数的乘法计算规则

174
00:07:17,846 --> 00:07:20,240
但是那个我还是放到以后的视频里面详细介绍

175
00:07:20,250 --> 00:07:23,715
好，最后，我们来看11乘12

176
00:07:23,715 --> 00:07:26,157
11乘以12

177
00:07:26,157 --> 00:07:28,552
我们可以用11相加12次

178
00:07:28,552 --> 00:07:30,760
也可以用12相加11次

179
00:07:30,760 --> 00:07:31,260
或者我们可以说

180
00:07:31,260 --> 00:07:37,910
嘿，这个就是11乘11再加11

181
00:07:37,910 --> 00:07:38,840
那么得多少呢？

182
00:07:38,850 --> 00:07:40,800
你可以把这个再加上11

183
00:07:40,810 --> 00:07:41,350
得到什么？

184
00:07:41,350 --> 00:07:45,975
你的结果是132

185
00:07:45,975 --> 00:07:49,551
我就说吧这个121再加上11

186
00:07:49,551 --> 00:07:50,998
就得到了132

187
00:07:50,998 --> 00:07:52,154
现在，另外还有一种方法就是，嗯

188
00:07:52,154 --> 00:07:54,028
10乘以12等于多少？

189
00:07:54,028 --> 00:07:54,987
10乘以12

190
00:07:54,987 --> 00:07:56,160
我们之前算过的

191
00:07:56,170 --> 00:07:58,570
那个结果是120

192
00:07:58,570 --> 00:08:00,888
那好，11乘以12

193
00:08:00,888 --> 00:08:03,038
因为我们是把12相加10次后再多加一次

194
00:08:03,038 --> 00:08:04,933
就是比那个再多12

195
00:08:04,933 --> 00:08:06,690
所以结果还是等于132

196
00:08:06,700 --> 00:08:10,090
那么有两种方法，都能得到同样的结果

197
00:08:10,100 --> 00:08:14,118
很好！现在我们来做12的乘法口诀表

198
00:08:14,118 --> 00:08:15,173
12的乘法口诀表

199
00:08:15,173 --> 00:08:16,378
你刚才已经知道了这些

200
00:08:16,378 --> 00:08:19,709
你已经准备好了来解决任何乘法运算的问题

201
00:08:19,709 --> 00:08:22,390
那个我们还是放到以后的视频再详细说

202
00:08:22,390 --> 00:08:23,983
还是，12乘0

203
00:08:23,983 --> 00:08:25,575
太容易啦，答案是0

204
00:08:25,575 --> 00:08:26,420
12乘1

205
00:08:26,430 --> 00:08:27,330
还是非常容易

206
00:08:27,330 --> 00:08:28,480
答案是12

207
00:08:28,490 --> 00:08:29,920
现在开始是有趣的部分了

208
00:08:29,930 --> 00:08:33,490
现在开始我们每次运算都增加12

209
00:08:33,505 --> 00:08:37,160
12乘2等于24

210
00:08:37,160 --> 00:08:40,041
12加12等于24，是吧？

211
00:08:40,041 --> 00:08:43,230
12 乘以--哦，这不是22

212
00:08:43,240 --> 00:08:44,160
我来重新写

213
00:08:44,160 --> 00:08:50,250
12乘3，那么就是12+12+12

214
00:08:50,250 --> 00:08:53,980
或者我们也可以把这儿写成12乘2

215
00:08:53,990 --> 00:08:56,070
我看我的脑子今天有点走神

216
00:08:56,070 --> 00:09:00,670
我们也可以把这个改写成12乘2再加12

217
00:09:00,670 --> 00:09:03,770
或者我们还可以写成24加12

218
00:09:03,770 --> 00:09:07,020
哪种都行，所有这些的结果都是等于36

219
00:09:07,030 --> 00:09:10,400
同时注意了，其实就是那里再加上12

220
00:09:10,400 --> 00:09:12,240
12乘4

221
00:09:12,250 --> 00:09:17,190
12乘4等于48

222
00:09:17,190 --> 00:09:18,270
有好多种方法你可以算出这个结果来

223
00:09:18,270 --> 00:09:21,155
你可以用11乘4得到44

224
00:09:21,155 --> 00:09:24,697
是不是？11乘4等于44

225
00:09:24,697 --> 00:09:30,029
然后你再加上一个4，就是你加了12次4

226
00:09:30,029 --> 00:09:32,851
或者你可以用12乘3等于36

227
00:09:32,851 --> 00:09:36,940
然后你再加一个12上去，就得到了48

228
00:09:36,950 --> 00:09:38,261
那种方法都可以

229
00:09:38,261 --> 00:09:40,300
这个是因为你可以用从任何一个方向进行相乘

230
00:09:40,300 --> 00:09:42,300
咱们继续说

231
00:09:42,300 --> 00:09:47,840
12乘5等于60

232
00:09:47,850 --> 00:09:51,694
10次5相加等于50，11次5相加就是55

233
00:09:51,694 --> 00:09:55,538
所以12次5相加就是60

234
00:09:55,538 --> 00:09:59,014
12乘6，等于多少啊？

235
00:09:59,014 --> 00:10:00,570
就是在这个基础上再加上12

236
00:10:00,580 --> 00:10:02,630
结果就等于72

237
00:10:02,630 --> 00:10:04,515
12乘以7？

238
00:10:04,515 --> 00:10:06,710
再来一个12

239
00:10:06,720 --> 00:10:09,747
72再加一个12，等于84

240
00:10:09,747 --> 00:10:13,157
知道嘛，我是认真的。事实上我比你们都大好多岁

241
00:10:13,157 --> 00:10:17,262
可是在我头脑里，我还是老得确认

242
00:10:17,262 --> 00:10:20,700
我得在12的乘法口诀表里面找到那些我背的分毫不差的部分，

243
00:10:20,700 --> 00:10:23,018
就好比，嗯，12乘5，然后有时候在我的脑袋里我想

244
00:10:23,018 --> 00:10:24,090
好吧，让我再来加上一个12

245
00:10:24,100 --> 00:10:26,290
对的，我记的完全正确

246
00:10:26,290 --> 00:10:28,480
12乘6等于72

247
00:10:28,490 --> 00:10:29,020
好的

248
00:10:29,020 --> 00:10:31,320
然后是12乘8

249
00:10:31,330 --> 00:10:33,685
在12乘7的结果上再加一个12

250
00:10:33,685 --> 00:10:35,400
等于96

251
00:10:35,400 --> 00:10:39,370
12乘9

252
00:10:39,370 --> 00:10:42,504
好，你在这个上面再加12。结果应该是108

253
00:10:42,504 --> 00:10:44,510
1-0-8

254
00:10:44,510 --> 00:10:46,700
然后是12乘10

255
00:10:46,700 --> 00:10:48,332
这个非常简单

256
00:10:48,332 --> 00:10:51,380
是吧？我们就在这个12后面加一个0。得到了120

257
00:10:51,380 --> 00:10:54,200
或者我们也可以在这个108上面加12

258
00:10:54,210 --> 00:10:55,570
那个方法都行

259
00:10:55,570 --> 00:10:58,290
12乘11

260
00:10:58,290 --> 00:10:59,406
这个我们做过了

261
00:10:59,406 --> 00:11:01,948
你在这个基础上再加12，得到了132

262
00:11:01,948 --> 00:11:05,077
最后来看12乘12

263
00:11:05,077 --> 00:11:08,931
这个等于144

264
00:11:08,931 --> 00:11:10,246
这个恰好向我们证明了

265
00:11:10,246 --> 00:11:13,777
如果我有一打的一打鸡蛋（一打是12个）

266
00:11:13,777 --> 00:11:17,010
或者比如说，我认为合计其实就是12个一打相加

267
00:11:17,010 --> 00:11:18,400
结果就是144个鸡蛋

268
00:11:18,410 --> 00:11:20,700
所以，其实在生活中，你将有很多机会见到这个数字

269
00:11:20,710 --> 00:11:22,550
比你想象的多很多次

270
00:11:22,550 --> 00:11:27,402
但是不管怎样，我们现在把所有的乘法口诀表都讲完了

271
00:11:27,410 --> 00:11:30,918
我真的特别希望你能够花些时间来把他们都背下来

272
00:11:30,920 --> 00:11:32,538
自己做点小提卡

273
00:11:32,538 --> 00:11:37,100
或者用我的网站上面的那个小软件工具

274
00:11:37,100 --> 00:11:38,850
你可以自己试试

275
00:11:38,860 --> 00:11:41,730
截止到2009年9月，他们都还正常的运行着

276
00:11:41,730 --> 00:11:45,044
我有很久一段时间没去碰它了，不过我正打算最近把他们再重新弄一下

277
00:11:45,044 --> 00:11:48,117
如果你在2009年正在看这个视频

278
00:11:48,117 --> 00:11:50,410
嗯，我可能不太会让它消失

279
00:11:50,420 --> 00:11:53,358
但是希望你们很快能用上一个更新更好版本的软件应用

280
00:11:53,360 --> 00:11:55,020
但是你必须得练习

281
00:11:55,020 --> 00:11:56,610
你应该让你的家长来考考你

282
00:11:56,620 --> 00:11:58,090
你应该自己弄点带备注的卡片

283
00:11:58,090 --> 00:12:00,853
你在上学的路上自己练习算算这些数--

284
00:12:00,853 --> 00:12:02,180
12乘9等于多少？

285
00:12:02,190 --> 00:12:03,740
11乘11等于几？

286
00:12:03,750 --> 00:12:05,305
你得把每个题目自己做一遍

287
00:12:05,305 --> 00:12:08,690
因为在你未来的人生中你将会因此而受益匪浅

288
00:12:08,690 --> 00:12:10,630
下次视频见！