1
00:00:01,060 --> 00:00:03,366
欢迎大家

2
00:00:03,366 --> 00:00:05,066
今天我们来讲负数的加减法

3
00:00:05,066 --> 00:00:06,380
让我们开始吧

4
00:00:06,380 --> 00:00:08,510
首先，回顾一下，还记得什么是负数吗？

5
00:00:08,520 --> 00:00:12,080
我们还是来画一条数轴

6
00:00:12,080 --> 00:00:13,295
哎呀，不太直。。。

7
00:00:13,295 --> 00:00:15,190
不过没关系，你们明白就行

8
00:00:15,190 --> 00:00:18,797
好，我们都知道正数是怎么回事儿了

9
00:00:18,797 --> 00:00:24,670
假如这是0

10
00:00:24,670 --> 00:00:25,686
然后是1,2,3,4 等等

11
00:00:25,686 --> 00:00:28,548
那2加2是多少呢，从2开始算

12
00:00:28,548 --> 00:00:30,780
你加上2，也就是往右边走2步

13
00:00:30,780 --> 00:00:31,460
走到了4

14
00:00:31,460 --> 00:00:32,140
这个很自然，很简单

15
00:00:32,150 --> 00:00:33,930
所以说

16
00:00:33,930 --> 00:00:36,130
2加2就等于4

17
00:00:36,140 --> 00:00:38,490
那么，2减去1呢

18
00:00:38,490 --> 00:00:39,840
或者 3减去2呢

19
00:00:39,840 --> 00:00:44,111
我们从3开始，减去2

20
00:00:44,111 --> 00:00:45,658
往左走2步，就到了1

21
00:00:45,658 --> 00:00:51,248
好，我们计算了2加2等于4,3减2等于1

22
00:00:51,248 --> 00:00:52,980
你是不是觉得这太简单了。。。

23
00:00:52,990 --> 00:00:56,990
那，如果1减去3是怎样呢

24
00:00:56,990 --> 00:00:58,150
嗯

25
00:00:58,150 --> 00:01:00,100
其实道理是一样的

26
00:01:00,100 --> 00:01:03,847
我们从1开始，往左走一步

27
00:01:03,847 --> 00:01:06,960
现在我们走到0以下了

28
00:01:06,960 --> 00:01:07,730
这是什么意思呢？

29
00:01:07,730 --> 00:01:08,500
意思就是，我们就开始得到负数了

30
00:01:08,510 --> 00:01:14,930
负1，负2，负3，等等

31
00:01:14,930 --> 00:01:20,909
如果我从1这里开始减去三

32
00:01:20,909 --> 00:01:25,610
向下走三步，停在-2这里

33
00:01:25,620 --> 00:01:30,680
我们就会得到：1-3=-2

34
00:01:30,680 --> 00:01:33,080
其实我们在日常生活中

35
00:01:33,090 --> 00:01:34,729
经常会用到这样的减法

36
00:01:34,729 --> 00:01:37,137
如果我说

37
00:01:37,137 --> 00:01:39,225
今天真冷，气温是1度

38
00:01:39,225 --> 00:01:40,728
而明天还会比今天还要冷3度

39
00:01:40,728 --> 00:01:42,038
你大概已经得到

40
00:01:42,038 --> 00:01:44,502
明天的温度等于-2度了

41
00:01:44,502 --> 00:01:46,925
这个是常识

42
00:01:46,925 --> 00:01:48,040
这就是负数的意义

43
00:01:48,040 --> 00:01:51,132
你还要记住，一个负数的绝对值越大

44
00:01:51,132 --> 00:01:58,090
它的数值就越小

45
00:01:58,090 --> 00:02:01,710
比如-50小于-20

46
00:02:01,710 --> 00:02:04,926
因为在我们的数轴上，-50比-20还要靠左

47
00:02:04,926 --> 00:02:07,160
这些你靠直觉是很容易的出来的

48
00:02:07,170 --> 00:02:08,708
当你一开始接触负数的时候

49
00:02:08,708 --> 00:02:10,185
你可能会觉得，哦50比20大

50
00:02:10,185 --> 00:02:13,860
只不过，你要注意50和20都是负数

51
00:02:13,860 --> 00:02:15,306
让我们来做道题吧

52
00:02:15,306 --> 00:02:19,270
我还是要用上这个数轴

53
00:02:19,280 --> 00:02:22,415
因为它对我能起到很大的帮助

54
00:02:22,415 --> 00:02:26,872
我们来算算5-12

55
00:02:26,872 --> 00:02:29,785
你大概已经

56
00:02:29,785 --> 00:02:34,195
能估算到答案了

57
00:02:34,195 --> 00:02:45,144
但是我还是要画个数轴

58
00:02:45,144 --> 00:02:53,068
从-10开始标上数字

59
00:02:53,068 --> 00:02:58,780
位置有点不够

60
00:02:58,780 --> 00:03:05,155
我应该一开始就把它画出来的。。

61
00:03:05,155 --> 00:03:12,537
就画到5这里

62
00:03:12,537 --> 00:03:14,494
让我把这个箭头重画一遍，留点位置

63
00:03:14,494 --> 00:03:15,548
5-12

64
00:03:15,560 --> 00:03:18,430
让我换个颜色

65
00:03:18,430 --> 00:03:20,945
从5开始，往左数12下

66
00:03:20,945 --> 00:03:22,805
因为我们在减去12

67
00:03:22,805 --> 00:03:33,870
数一下，1,2,3,4,5.....

68
00:03:33,870 --> 00:03:38,262
我们停在了-7

69
00:03:38,262 --> 00:03:39,993
很好玩对吧？

70
00:03:40,000 --> 00:03:42,789
因为12-5等于正7

71
00:03:42,789 --> 00:03:45,580
而5-12等于负7

72
00:03:45,590 --> 00:03:48,900
你想一想

73
00:03:48,900 --> 00:03:52,939
这是为什么？

74
00:03:52,939 --> 00:03:58,918
为什么5和12的差是7？

75
00:03:58,918 --> 00:04:00,038
而在这个情况下

76
00:04:00,038 --> 00:04:01,097
5-12的情况下

77
00:04:01,097 --> 00:04:03,812
我们会得到-7呢？

78
00:04:03,812 --> 00:04:05,162
更奇怪的是5和-7的位置差了这么多？

79
00:04:05,162 --> 00:04:07,496
我刚刚说的似乎让你混乱了。。

80
00:04:07,496 --> 00:04:09,538
不过我们再来试试另一道题吧

81
00:04:09,538 --> 00:04:11,789
从低一点的数字开始

82
00:04:11,789 --> 00:04:18,060
我们刚刚说过，5-12等于-7

83
00:04:18,060 --> 00:04:19,434
让我们再做一道

84
00:04:19,434 --> 00:04:25,843
-3加上5等于几？

85
00:04:25,843 --> 00:04:28,050
我们还是用这个数轴

86
00:04:28,060 --> 00:04:31,490
-3+5

87
00:04:31,490 --> 00:04:33,580
从-3这儿开始

88
00:04:33,580 --> 00:04:38,425
向上数5

89
00:04:38,425 --> 00:04:42,602
得到2

90
00:04:42,602 --> 00:04:44,363
所以我们的答案就是

91
00:04:44,363 --> 00:04:48,790
-3+5=2

92
00:04:48,790 --> 00:04:53,843
又有趣了，5-3也等于2

93
00:04:53,843 --> 00:04:57,007
既然我们看出来5-3和-3+5是一样的

94
00:04:57,007 --> 00:05:00,252
我们就不难发现

95
00:05:00,252 --> 00:05:04,050
这两个式子其实是一个意思

96
00:05:04,050 --> 00:05:07,052
当我们在运算负数的加减法的时候

97
00:05:07,052 --> 00:05:11,640
我们在做的只是很基础的加减法

98
00:05:11,640 --> 00:05:15,456
只不过现在我们的答案

99
00:05:15,456 --> 00:05:18,634
可能会是0以下的数字了

100
00:05:18,634 --> 00:05:19,826
我们再来做一道吧

101
00:05:19,826 --> 00:05:21,587
我问你

102
00:05:21,587 --> 00:05:27,111
2减去-3等于几？

103
00:05:27,111 --> 00:05:30,747
这种情况下，我们中间就有两个减号

104
00:05:30,747 --> 00:05:32,079
你应该这样看待这个问题

105
00:05:32,079 --> 00:05:34,135
中间这两个减号

106
00:05:34,135 --> 00:05:36,140
负负得正，变成了+号

107
00:05:36,140 --> 00:05:40,425
所以我们会得到2+正3

108
00:05:40,425 --> 00:05:43,050
得到5

109
00:05:43,060 --> 00:05:46,305
我们再来做一道题

110
00:05:46,305 --> 00:05:52,866
-7减去-2等于几？

111
00:05:52,866 --> 00:05:58,010
这样，我们把中间的两个减号负负得正

112
00:05:58,020 --> 00:06:00,144
在你的脑海里想象一个数轴

113
00:06:00,144 --> 00:06:03,560
从-7向右挪2步

114
00:06:03,560 --> 00:06:06,224
会得到什么呢？

115
00:06:06,224 --> 00:06:11,392
得到-5

116
00:06:11,392 --> 00:06:13,755
你再想想我们前面的例子

117
00:06:13,755 --> 00:06:16,540
这个也是一样：-7+2等于-5，2-7也等于-5

118
00:06:16,550 --> 00:06:19,351
如果现在的温度是2度

119
00:06:19,351 --> 00:06:22,475
明天比今天冷7度

120
00:06:22,475 --> 00:06:23,230
我们会得到-5度

121
00:06:23,240 --> 00:06:25,253
我们再来做几道，熟能生巧嘛

122
00:06:25,253 --> 00:06:26,847
这些例子是很好的示范方式

123
00:06:26,847 --> 00:06:29,056
大概比我口述还要有用

124
00:06:29,056 --> 00:06:31,104
我们来使劲做题吧~

125
00:06:31,104 --> 00:06:36,473
-7减去3等于几？

126
00:06:36,473 --> 00:06:39,396
我们从-7向左数三位

127
00:06:39,410 --> 00:06:41,386
我们会得到比-7小3的数字

128
00:06:41,386 --> 00:06:45,420
-10，对吧？

129
00:06:45,430 --> 00:06:49,055
你再想想前面的例子，如果是7+3

130
00:06:49,055 --> 00:06:50,762
我们从0上面的7

131
00:06:50,762 --> 00:06:52,504
向右三步

132
00:06:52,504 --> 00:06:54,538
我们会得到正10

133
00:06:54,538 --> 00:06:57,385
所以当你从0下面的7，向左三步

134
00:06:57,385 --> 00:06:58,680
你就会得到-10

135
00:06:58,680 --> 00:06:59,460
再来一道

136
00:06:59,470 --> 00:07:01,048
我知道你理解起来可能会有些困难

137
00:07:01,048 --> 00:07:04,218
不过练习是很好的帮助

138
00:07:04,218 --> 00:07:09,118
我们来算算3减去-5

139
00:07:09,118 --> 00:07:12,360
这两个减号负负得正，变成+号

140
00:07:12,360 --> 00:07:14,570
我们就得到6了

141
00:07:14,570 --> 00:07:17,088
想想前面的例子，3-3等于几？

142
00:07:17,088 --> 00:07:18,687
很简单

143
00:07:18,687 --> 00:07:20,687
0对吧？

144
00:07:20,687 --> 00:07:23,980
那-3减去3呢？

145
00:07:23,990 --> 00:07:26,420
那就是比-3小3的数

146
00:07:26,420 --> 00:07:28,880
就是-6

147
00:07:28,880 --> 00:07:34,030
那-3减去-3呢？

148
00:07:34,040 --> 00:07:35,500
好玩吧

149
00:07:35,500 --> 00:07:40,790
两个减号变成+号，

150
00:07:40,800 --> 00:07:44,028
我们从负3这里开始，向右三步

151
00:07:44,028 --> 00:07:46,060
我们又得到了0

152
00:07:46,060 --> 00:07:48,240
能理解么？

153
00:07:48,250 --> 00:07:49,360
我再来做一遍

154
00:07:49,370 --> 00:07:53,290
-3减去-3

155
00:07:53,290 --> 00:07:56,390
任何数减去它自己都应该等于0

156
00:07:56,390 --> 00:07:57,950
这就是为什么我们得到了0

157
00:07:57,950 --> 00:08:00,868
这同样也是为什么

158
00:08:00,868 --> 00:08:03,183
这两个减号

159
00:08:03,183 --> 00:08:05,498
变成加号了的原因

160
00:08:05,498 --> 00:08:07,429
我们再来做几道题

161
00:08:07,429 --> 00:08:12,140
12减去13

162
00:08:12,140 --> 00:08:13,610
简单吧？

163
00:08:13,620 --> 00:08:17,940
12减去12等于0,12减去13就是-1

164
00:08:17,940 --> 00:08:20,920
因为我们从0又往左走了一步

165
00:08:20,930 --> 00:08:24,670
再来算算8-5

166
00:08:24,670 --> 00:08:27,270
这是个普遍的正数减法，等于3

167
00:08:27,270 --> 00:08:29,640
那么5-8等于几呢？

168
00:08:29,640 --> 00:08:31,988
我们先向左数五步到0

169
00:08:31,988 --> 00:08:35,420
再数3步，得到-3

170
00:08:35,420 --> 00:08:38,500
我在这里再画个数轴

171
00:08:38,500 --> 00:08:43,468
这里是0，这是5

172
00:08:43,468 --> 00:08:47,233
看看，向左数了8步之后

173
00:08:47,233 --> 00:08:48,290
我们就得到3了

174
00:08:48,300 --> 00:08:49,400
你可以用同样的方法计算任何这样的加减法题目

175
00:08:49,400 --> 00:08:51,770
同样也是很好的练习

176
00:08:51,770 --> 00:08:54,113
这一刻应该是个很好的入门了

177
00:08:54,113 --> 00:08:56,220
我建议你多多做练习

178
00:08:56,220 --> 00:08:58,281
因为这些练习

179
00:08:58,281 --> 00:08:58,977
能让你在脑海里产生

180
00:08:58,977 --> 00:08:59,673
很好的镜像印象

181
00:08:59,673 --> 00:09:01,578
比我在黑板上画的任何东西

182
00:09:01,578 --> 00:09:03,990
都要来得有用

183
00:09:03,990 --> 00:09:05,463
所以，你可以试着再做做练习

184
00:09:05,463 --> 00:09:07,494
我去再找一些这样的例子

185
00:09:07,509 --> 00:09:09,140
希望这样你会对负数理解得更多

186
00:09:09,140 --> 00:09:10,533
你也可以参加我们的

187
00:09:10,533 --> 00:09:12,700
负数加减法专题讨论会

188
00:09:12,700 --> 00:09:14,160
我希望你觉得这些东西很有趣

189
00:09:14,160 --> 00:09:15,460
拜拜~