1
00:00:00,530 --> 00:00:01,674
如果之前的練習你都做了

2
00:00:01,674 --> 00:00:04,729
並且已經記住了乘法表

3
00:00:04,729 --> 00:00:08,785
那麽你應該有這種感覺

4
00:00:08,785 --> 00:00:11,058
可能自己已經可以解決任何乘法問題了！

5
00:00:11,058 --> 00:00:12,699
你只需要記住--

6
00:00:12,699 --> 00:00:14,340
怎麽說呢--

7
00:00:14,350 --> 00:00:15,836
記住運算的一般步驟就可以了

8
00:00:15,836 --> 00:00:17,760
但是我不是要教大家做題步驟

9
00:00:17,760 --> 00:00:20,280
而是這種運算的本質和原理

10
00:00:20,280 --> 00:00:23,420
先來做一些

11
00:00:23,420 --> 00:00:30,119
你可能覺得自己不會的題目吧

12
00:00:30,119 --> 00:00:31,865
16×9

13
00:00:31,865 --> 00:00:32,858
16乘以9

14
00:00:32,858 --> 00:00:36,004
你可以會說

15
00:00:36,004 --> 00:00:38,790
老師 我沒有記住16的乘法表

16
00:00:38,790 --> 00:00:41,214
不可能會做這個題

17
00:00:41,214 --> 00:00:43,294
但是我要告訴你的是

18
00:00:43,294 --> 00:00:45,262
你一定會做！

19
00:00:45,262 --> 00:00:46,532
因爲我們可以把這個問題分解成

20
00:00:46,532 --> 00:00:49,710
你會做的題目

21
00:00:49,710 --> 00:00:52,240
到底怎麽做呢？

22
00:00:52,250 --> 00:00:54,820
首先是9乘以這個數的個位

23
00:00:54,820 --> 00:00:56,760
9×6

24
00:00:56,770 --> 00:01:01,090
這個大家肯定都會的

25
00:01:01,100 --> 00:01:03,380
我寫在這邊

26
00:01:03,380 --> 00:01:05,861
9×6=54

27
00:01:05,861 --> 00:01:08,975
知道乘法表就可以得出來

28
00:01:08,975 --> 00:01:11,935
那麽要寫下54來

29
00:01:11,935 --> 00:01:13,710
但是只能把4寫在個位這裡

30
00:01:13,710 --> 00:01:17,004
5是進位

31
00:01:17,004 --> 00:01:19,755
這就是運算的步驟

32
00:01:19,755 --> 00:01:21,113
在做加法時

33
00:01:21,128 --> 00:01:24,113
如果産生了大於9的數

34
00:01:24,113 --> 00:01:28,429
就要進位

35
00:01:28,429 --> 00:01:29,329
這種運算就是進位 沒什麽別的描述方法了

36
00:01:29,329 --> 00:01:31,158
然後9×1

37
00:01:31,158 --> 00:01:33,490
9乘以1

38
00:01:33,500 --> 00:01:35,650
這個很簡單

39
00:01:35,650 --> 00:01:38,670
9×1=9

40
00:01:38,680 --> 00:01:40,740
任何數乘以1都等於本身

41
00:01:40,750 --> 00:01:45,144
但是上邊還有個進位5

42
00:01:45,144 --> 00:01:47,102
9×1=9

43
00:01:47,102 --> 00:01:50,160
還要再加上5

44
00:01:50,160 --> 00:01:55,638
所以再加5

45
00:01:55,638 --> 00:01:57,702
得到什麽呢？

46
00:01:57,702 --> 00:01:59,689
9×1+5

47
00:01:59,689 --> 00:02:00,590
得14

48
00:02:00,590 --> 00:02:04,180
我寫在這裡

49
00:02:04,180 --> 00:02:06,534
14

50
00:02:06,534 --> 00:02:08,440
這樣就得出結果了

51
00:02:08,440 --> 00:02:12,260
16×9=144

52
00:02:12,260 --> 00:02:14,655
如果你一直記到12的乘法表的話

53
00:02:14,655 --> 00:02:17,499
應該要注意到144=12×12

54
00:02:17,499 --> 00:02:19,220
不過只知道9×6和9×1

55
00:02:19,220 --> 00:02:20,540
也可以解出這個難題

56
00:02:20,550 --> 00:02:22,160
現在你可能說 老師

57
00:02:22,160 --> 00:02:25,150
這不過是你耍的一個小把戲

58
00:02:25,150 --> 00:02:27,920
這怎麽可能呢？是爲什麽？

59
00:02:27,930 --> 00:02:32,870
大家應該經常這麽問

60
00:02:32,870 --> 00:02:34,980
不要只是被動的接受我說的話

61
00:02:34,990 --> 00:02:36,930
不要死記公式方法

62
00:02:36,930 --> 00:02:37,865
生搬硬套

63
00:02:37,865 --> 00:02:40,760
那麽 我換個寫法給大家解釋一下

64
00:02:40,770 --> 00:02:44,190
可以把16改成10--

65
00:02:44,190 --> 00:02:46,960
在這裡寫吧

66
00:02:46,960 --> 00:02:50,830
16=10+6

67
00:02:50,840 --> 00:02:52,810
把16拆開了

68
00:02:52,810 --> 00:02:56,490
當然9也可以拆

69
00:02:56,500 --> 00:02:59,580
不過只是一位數 可以留著

70
00:02:59,590 --> 00:03:00,990
就像這樣

71
00:03:00,990 --> 00:03:02,880
下面來看看這個問題究竟怎麽回事

72
00:03:02,880 --> 00:03:04,390
在這寫一個乘法號

73
00:03:04,400 --> 00:03:06,050
首先要用9乘以6

74
00:03:06,060 --> 00:03:08,310
你可能要問

75
00:03:08,310 --> 00:03:10,707
老師你爲什麽要這麽分16呢？

76
00:03:10,707 --> 00:03:11,838
其實我是把16的個位和

77
00:03:11,838 --> 00:03:15,400
十位拆開

78
00:03:15,400 --> 00:03:16,528
這個從右數的第二列

79
00:03:16,528 --> 00:03:21,740
這可不是個1 而是10

80
00:03:21,750 --> 00:03:25,060
16左邊的1是10 所以拆成10+6

81
00:03:25,060 --> 00:03:27,270
這就是這麽拆的原因

82
00:03:27,280 --> 00:03:29,340
好 現在來運算

83
00:03:29,340 --> 00:03:30,580
跟剛剛的方法一樣

84
00:03:30,590 --> 00:03:32,847
9×6--

85
00:03:32,847 --> 00:03:35,410
寫下來

86
00:03:35,410 --> 00:03:36,773
9×6=54

87
00:03:36,773 --> 00:03:39,537
但是這裡不寫54

88
00:03:39,537 --> 00:03:40,685
而是拆成50+4

89
00:03:40,685 --> 00:03:42,166
9×6=50+4

90
00:03:42,166 --> 00:03:46,730
好了 這一列代表個位

91
00:03:46,740 --> 00:03:48,330
畫一條虛線來分開

92
00:03:48,340 --> 00:03:50,470
這邊是個位

93
00:03:50,470 --> 00:03:52,370
只能寫一個4

94
00:03:52,380 --> 00:03:55,854
但還要寫50

95
00:03:55,854 --> 00:03:57,830
要找個地方寫50

96
00:03:57,840 --> 00:03:59,827
慣例是--

97
00:03:59,827 --> 00:04:01,710
至少我學的是這樣--

98
00:04:01,710 --> 00:04:03,479
把50寫在這上邊

99
00:04:03,479 --> 00:04:06,620
當然也可以寫在下面

100
00:04:06,620 --> 00:04:09,952
只要記得

101
00:04:09,952 --> 00:04:14,853
運算時得到十位有個50就行

102
00:04:14,853 --> 00:04:16,278
可以把50寫在這

103
00:04:16,278 --> 00:04:18,860
跟第一個題做的一樣

104
00:04:18,870 --> 00:04:20,430
只寫一個5

105
00:04:20,430 --> 00:04:22,831
剛剛就是只寫了一個5

106
00:04:22,831 --> 00:04:25,043
因爲這個5是在十位的

107
00:04:25,043 --> 00:04:26,860
實際上代表的是50

108
00:04:26,870 --> 00:04:28,709
十位的1就是10

109
00:04:28,709 --> 00:04:33,850
不過現在我要寫50

110
00:04:33,850 --> 00:04:35,850
這樣大家看的比較清楚 就代表50 或者10

111
00:04:35,850 --> 00:04:39,010
然後 9×10=？

112
00:04:39,010 --> 00:04:40,543
9×10

113
00:04:40,543 --> 00:04:45,620
這個我們也記過的

114
00:04:45,620 --> 00:04:50,553
任何數乘以10就是這個數後邊添個0

115
00:04:50,553 --> 00:04:51,872
得90

116
00:04:51,872 --> 00:04:53,406
9×10=90

117
00:04:53,406 --> 00:04:54,925
再加50

118
00:04:54,925 --> 00:04:57,342
90+50

119
00:04:57,342 --> 00:04:58,882
等於多少呢？

120
00:04:58,882 --> 00:05:00,250
是140

121
00:05:00,250 --> 00:05:02,180
9×10=90

122
00:05:02,190 --> 00:05:06,125
90+50=140

123
00:05:06,125 --> 00:05:07,230
爲了跟之前寫的保持一致

124
00:05:07,240 --> 00:05:09,020
可以把140寫成100+40

125
00:05:09,020 --> 00:05:13,207
所以我們要把40放在這裡

126
00:05:13,207 --> 00:05:16,154
百位進1

127
00:05:16,154 --> 00:05:19,440
但是100不知道放在哪

128
00:05:19,450 --> 00:05:22,001
可以寫在這

129
00:05:22,001 --> 00:05:24,860
可以--

130
00:05:24,870 --> 00:05:35,155
也可以寫在這

131
00:05:35,155 --> 00:05:37,774
寫在這裡

132
00:05:37,774 --> 00:05:39,255
很多地方可以寫

133
00:05:39,255 --> 00:05:40,510
這個100

134
00:05:40,510 --> 00:05:41,800
但是最重要的一點不要忘記

135
00:05:41,800 --> 00:05:42,820
這個一百是在百位上

136
00:05:42,820 --> 00:05:47,130
分開線我剛沒畫

137
00:05:47,140 --> 00:05:49,950
這樣再寫一個100

138
00:05:49,950 --> 00:05:52,840
得到是100+40+4

139
00:05:52,850 --> 00:05:54,820
即144

140
00:05:54,820 --> 00:05:56,000
希望大家能聽懂

141
00:05:56,010 --> 00:05:59,560
再來多做幾個題

142
00:05:59,560 --> 00:06:02,100
多看例題是很重要的

143
00:06:02,110 --> 00:06:04,184
計算55×8

144
00:06:04,184 --> 00:06:07,170
55×8

145
00:06:07,180 --> 00:06:08,183
差不多的例題

146
00:06:08,183 --> 00:06:11,910
要用8開始乘

147
00:06:11,920 --> 00:06:14,714
8×5

148
00:06:14,714 --> 00:06:18,830
我先寫下來

149
00:06:18,830 --> 00:06:27,260
8×5=40

150
00:06:27,270 --> 00:06:28,950
把0寫在這

151
00:06:28,950 --> 00:06:31,240
進位4

152
00:06:31,250 --> 00:06:33,050
然後又是8×5

153
00:06:33,050 --> 00:06:36,550
還是40

154
00:06:36,550 --> 00:06:40,470
不過再加上進位4 是44

155
00:06:40,470 --> 00:06:43,590
代表的是440

156
00:06:43,600 --> 00:06:46,540
你可以像我上個題一樣

157
00:06:46,550 --> 00:06:49,750
把55拆成50+5再分別乘以8

158
00:06:49,750 --> 00:06:52,045
不過做的題多了

159
00:06:52,045 --> 00:06:53,480
應該大家會習慣這麽運算的

160
00:06:53,490 --> 00:06:55,580
再做一個--

161
00:06:55,580 --> 00:06:57,960
換個顏色

162
00:06:57,970 --> 00:07:01,790
淺紅色

163
00:07:01,800 --> 00:07:02,562
用78乘以--

164
00:07:02,562 --> 00:07:06,175
乘以7

165
00:07:06,175 --> 00:07:08,190
8×7

166
00:07:08,190 --> 00:07:09,680
8×7=56

167
00:07:09,680 --> 00:07:13,810
寫下來--這又是一個新題

168
00:07:13,820 --> 00:07:16,804
8×7=56

169
00:07:16,804 --> 00:07:25,865
把6寫在下邊 進位5寫在上邊

170
00:07:25,865 --> 00:07:27,600
7×7=49

171
00:07:27,600 --> 00:07:31,390
7乘以7得49

172
00:07:31,390 --> 00:07:33,070
還要加上邊的5

173
00:07:33,080 --> 00:07:35,287
再加上5

174
00:07:35,287 --> 00:07:36,847
49+5=？

175
00:07:36,847 --> 00:07:38,360
是54

176
00:07:38,370 --> 00:07:40,330
7×7=49

177
00:07:40,330 --> 00:07:42,950
49+5=54

178
00:07:42,950 --> 00:07:46,240
得546

179
00:07:46,250 --> 00:07:47,535
不久前你可能還覺得

180
00:07:47,535 --> 00:07:49,120
光用1-12的乘法表

181
00:07:49,120 --> 00:07:50,150
肯定求不出78的乘法表

182
00:07:50,160 --> 00:07:51,940
但大家可以看到過程其實非常簡單

183
00:07:51,940 --> 00:07:54,510
再多做幾個

184
00:07:54,520 --> 00:07:57,760
一直算到不能再算爲止

185
00:07:57,760 --> 00:07:59,135
算到精疲力竭爲止

186
00:07:59,135 --> 00:08:04,147
89×3

187
00:08:04,147 --> 00:08:06,689
89×3=？

188
00:08:06,689 --> 00:08:09,177
3×9=27

189
00:08:09,177 --> 00:08:20,374
7寫在個位

190
00:08:20,374 --> 00:08:23,178
向十位進位2

191
00:08:23,178 --> 00:08:24,712
因爲27=20+7

192
00:08:24,712 --> 00:08:27,992
兩個10就是20

193
00:08:27,992 --> 00:08:29,562
加7是27

194
00:08:29,562 --> 00:08:32,480
然後3×8=24

195
00:08:32,480 --> 00:08:34,446
3×8=24

196
00:08:34,446 --> 00:08:35,870
上邊還有一個2的進位

197
00:08:35,870 --> 00:08:37,870
還要再加2

198
00:08:37,880 --> 00:08:39,430
得26

199
00:08:39,440 --> 00:08:41,670
3×8=24

200
00:08:41,670 --> 00:08:45,080
24+2=26

201
00:08:45,090 --> 00:08:48,640
結果是267

202
00:08:48,640 --> 00:08:49,820
再做一個

203
00:08:49,830 --> 00:08:52,184
不過我要加難度了

204
00:08:52,184 --> 00:08:54,397
在你覺得

205
00:08:54,397 --> 00:08:56,742
這些都會做的時候

206
00:08:56,742 --> 00:08:58,530
我再出一個能難到你的！

207
00:08:58,530 --> 00:09:02,178
239×6

208
00:09:02,178 --> 00:09:03,682
本來是要做

209
00:09:03,682 --> 00:09:10,160
兩位數乘一位數的影片的

210
00:09:10,160 --> 00:09:10,902
不過這題也是告訴大家

211
00:09:10,902 --> 00:09:13,788
不管是幾位數去乘一個一位數

212
00:09:13,788 --> 00:09:14,645
你都是可以做的

213
00:09:14,645 --> 00:09:18,360
步驟大同小異

214
00:09:18,360 --> 00:09:19,973
大家可以猜一猜這個要怎麽做

215
00:09:19,973 --> 00:09:21,400
6×9=？

216
00:09:21,400 --> 00:09:24,490
在這裡寫

217
00:09:24,500 --> 00:09:27,830
6×9

218
00:09:27,830 --> 00:09:32,200
這個之前算過了

219
00:09:32,200 --> 00:09:34,140
54

220
00:09:34,140 --> 00:09:36,390
把4寫在這

221
00:09:36,400 --> 00:09:38,790
5放在十位

222
00:09:38,800 --> 00:09:41,490
因爲這個54中的5就是5個10

223
00:09:41,490 --> 00:09:43,800
好

224
00:09:43,800 --> 00:09:46,380
然後是6×3

225
00:09:46,380 --> 00:09:49,228
6×3

226
00:09:49,228 --> 00:09:52,610
得18

227
00:09:52,610 --> 00:09:57,350
上邊還有一個5

228
00:09:57,350 --> 00:10:01,140
還要加5

229
00:10:01,140 --> 00:10:02,290
18+5=？

230
00:10:02,300 --> 00:10:03,490
6×3=18 18+5=23

231
00:10:03,500 --> 00:10:06,710
澄清一點

232
00:10:06,710 --> 00:10:08,320
並不是用6×3+5

233
00:10:08,320 --> 00:10:09,770
你看

234
00:10:09,770 --> 00:10:12,251
在這個問題裏

235
00:10:12,251 --> 00:10:15,025
3其實是30

236
00:10:15,025 --> 00:10:17,365
只不過寫的是3

237
00:10:17,370 --> 00:10:18,620
但這其實是6×30+50

238
00:10:18,620 --> 00:10:20,120
因爲39的3是3個10 或者是30

239
00:10:20,130 --> 00:10:21,830
那麽

240
00:10:21,840 --> 00:10:23,500
雖然這裡說6×3=18

241
00:10:23,500 --> 00:10:25,497
18+5=23

242
00:10:25,497 --> 00:10:26,740
實際得到的其實是230

243
00:10:26,740 --> 00:10:29,090
把3放在十位

244
00:10:29,090 --> 00:10:35,210
我換個顏色來寫

245
00:10:35,210 --> 00:10:38,197
用個跟上邊不一樣的

246
00:10:38,197 --> 00:10:40,980
結果是23

247
00:10:40,980 --> 00:10:42,869
把3放在十位

248
00:10:42,869 --> 00:10:46,615
向百位進2 寫上邊

249
00:10:46,615 --> 00:10:53,058
差不多就做完了 再乘最後一次

250
00:10:53,058 --> 00:10:53,814
6×2

251
00:10:53,814 --> 00:10:56,210
這個很簡單

252
00:10:56,220 --> 00:10:58,320
得12

253
00:10:58,320 --> 00:10:59,900
但是上邊還有進位2

254
00:10:59,900 --> 00:11:01,260
所以還要再加2

255
00:11:01,260 --> 00:11:03,380
+2

256
00:11:03,390 --> 00:11:06,202
等於什麽呢？

257
00:11:06,202 --> 00:11:08,130
12+2=14

258
00:11:08,145 --> 00:11:10,125
寫4

259
00:11:10,130 --> 00:11:13,960
6×2=12

260
00:11:13,970 --> 00:11:18,675
12+2=14

261
00:11:18,675 --> 00:11:20,841
把4寫在下邊

262
00:11:20,841 --> 00:11:23,254
如果這裡還有更高位的話就寫在上邊

263
00:11:23,270 --> 00:11:27,140
但是沒有了

264
00:11:27,140 --> 00:11:34,370
所以直接寫在這就可以了

265
00:11:34,370 --> 00:11:36,348
239×6

266
00:11:36,348 --> 00:11:38,961
=1434

267
00:11:38,961 --> 00:11:40,707
再做一個

268
00:11:40,710 --> 00:11:44,158
需要清一些空間出來

269
00:11:44,158 --> 00:11:47,350
既然已經增加難度了

270
00:11:47,360 --> 00:11:50,460
下面來做一個四位數的吧

271
00:11:50,460 --> 00:11:52,032
7362×--

272
00:11:52,032 --> 00:11:54,552
難點的--9

273
00:11:54,552 --> 00:11:56,872
9×2=？

274
00:11:56,872 --> 00:12:00,494
我就不再寫在旁邊了

275
00:12:00,494 --> 00:12:05,024
大家應該已經明白這個套路了

276
00:12:05,024 --> 00:12:07,200
9×2=？