1
00:00:00,090 --> 00:00:03,330
既然我们稍微了解了

2
00:00:03,330 --> 00:00:04,290
正数和负数乘法的计算

3
00:00:04,290 --> 00:00:06,280
思考一下怎么求解正数或负数的除法

4
00:00:06,280 --> 00:00:07,750
大家将发现

5
00:00:07,750 --> 00:00:10,050
这是个非常相似的方法

6
00:00:10,050 --> 00:00:11,880
如果它们都是正数

7
00:00:11,880 --> 00:00:15,280
得到正的答案 如果其中一个是负数

8
00:00:15,280 --> 00:00:18,220
或另一个 不全是负数 将得到负的答案

9
00:00:18,220 --> 00:00:19,640
如果它们都是负数

10
00:00:19,640 --> 00:00:22,100
负号抵消了 得到正的答案

11
00:00:22,100 --> 00:00:24,710
大家实践一下 我建议大家暂停视频

12
00:00:24,710 --> 00:00:26,160
计算这些式子

13
00:00:26,160 --> 00:00:28,050
看看能不能求得

14
00:00:28,050 --> 00:00:29,030
跟我一样的答案

15
00:00:29,030 --> 00:00:32,480
8÷(-2)

16
00:00:32,480 --> 00:00:35,140
如果是8÷2

17
00:00:35,140 --> 00:00:37,690
答案是4

18
00:00:37,690 --> 00:00:41,320
既然两个数中有一个是负数

19
00:00:41,320 --> 00:00:42,700
就是这个

20
00:00:42,700 --> 00:00:45,580
答案将是负数

21
00:00:45,580 --> 00:00:47,350
所以8÷(-2)

22
00:00:47,350 --> 00:00:49,190
等于-4

23
00:00:49,190 --> 00:00:53,060
-16÷4

24
00:00:53,060 --> 00:00:54,120
大家要非常小心

25
00:00:54,120 --> 00:00:56,090
如果是

26
00:00:56,090 --> 00:00:57,650
16除以4

27
00:00:57,650 --> 00:00:59,190
答案是4

28
00:00:59,190 --> 00:01:02,200
因为有一个数是负数

29
00:01:02,200 --> 00:01:04,720
两个数中有一个是负数

30
00:01:04,720 --> 00:01:07,560
我将得到负的答案

31
00:01:07,560 --> 00:01:09,760
现在有

32
00:01:09,760 --> 00:01:11,540
(-30)÷(-5)

33
00:01:11,540 --> 00:01:14,660
如果是30÷5

34
00:01:14,660 --> 00:01:16,740
会得到6

35
00:01:16,740 --> 00:01:20,280
因为是负数除以负数

36
00:01:20,280 --> 00:01:22,150
负号抵消了

37
00:01:22,150 --> 00:01:25,070
答案仍是6

38
00:01:25,070 --> 00:01:26,550
也可以在这里写正号

39
00:01:26,550 --> 00:01:27,350
但没有必要

40
00:01:27,350 --> 00:01:29,800
这等于6

41
00:01:29,800 --> 00:01:31,780
负数除以负数

42
00:01:31,780 --> 00:01:33,530
就像是负数乘以负数

43
00:01:33,530 --> 00:01:35,960
将得到正的答案

44
00:01:35,960 --> 00:01:38,680
18除以2

45
00:01:38,680 --> 00:01:39,980
这是个有点陷阱的问题

46
00:01:39,980 --> 00:01:41,900
在谈论负数之前

47
00:01:41,900 --> 00:01:43,660
大家就知道怎么做了

48
00:01:43,660 --> 00:01:46,600
这里是正数除以正数

49
00:01:46,600 --> 00:01:48,340
将得到正数

50
00:01:48,340 --> 00:01:52,260
将得到+9

51
00:01:52,260 --> 00:01:55,300
现在我们做些有趣的问题

52
00:01:55,300 --> 00:01:57,620
这是某种复合问题

53
00:01:57,620 --> 00:02:01,100
题中有乘法也有除法

54
00:02:01,100 --> 00:02:03,270
首先在这儿 根据题目写法

55
00:02:03,270 --> 00:02:05,220
我们把分子乘出来

56
00:02:05,220 --> 00:02:07,410
大家不熟悉点号的话

57
00:02:07,410 --> 00:02:09,560
这是乘法的另一种写法

58
00:02:09,560 --> 00:02:11,640
我可以将x写在这儿

59
00:02:11,640 --> 00:02:13,100
大家将在代数学中看到

60
00:02:13,100 --> 00:02:15,100
点乘是非常常见的

61
00:02:15,100 --> 00:02:17,100
因为X会有其它用处

62
00:02:17,100 --> 00:02:23,070
大家不想将它与字母X混淆

63
00:02:23,070 --> 00:02:25,000
X在代数学中很常见

64
00:02:25,000 --> 00:02:27,140
这就是为什么这里使用了点

65
00:02:27,140 --> 00:02:29,390
这里说

66
00:02:29,390 --> 00:02:31,400
分子是(-7)乘以3

67
00:02:31,400 --> 00:02:32,950
取这个数

68
00:02:32,950 --> 00:02:34,560
把它除以-1

69
00:02:34,560 --> 00:02:37,570
这个分子 -7・3

70
00:02:37,570 --> 00:02:40,810
+7乘以3等于21

71
00:02:40,810 --> 00:02:43,520
既然其中有一个是负数

72
00:02:43,520 --> 00:02:45,580
答案将是-21

73
00:02:45,580 --> 00:02:47,340
这将等于-21

74
00:02:47,340 --> 00:02:48,650
除以-1

75
00:02:48,650 --> 00:02:50,610
所以是

76
00:02:50,610 --> 00:02:51,640
(-21)÷(-1)

77
00:02:51,640 --> 00:02:54,610
负数除以负数得到正数

78
00:02:54,610 --> 00:02:57,310
这等于+21

79
00:02:57,310 --> 00:02:58,980
把计算法则都写下来

80
00:02:58,980 --> 00:03:04,280
如果用正数除以负数

81
00:03:04,280 --> 00:03:06,730
将得到负数

82
00:03:06,730 --> 00:03:10,980
如果用负数除以正数

83
00:03:10,980 --> 00:03:13,350
将得到负数

84
00:03:13,350 --> 00:03:17,260
如果用负数除以负数

85
00:03:17,260 --> 00:03:19,650
将得到正数

86
00:03:19,650 --> 00:03:24,610
如果用正数除以正数

87
00:03:24,610 --> 00:03:26,970
将得到正数

88
00:03:26,970 --> 00:03:28,980
我们再做最后一题

89
00:03:28,980 --> 00:03:30,280
这里全是乘法

90
00:03:30,280 --> 00:03:30,950
不过这很有趣

91
00:03:30,950 --> 00:03:32,540
因为有三个数相乘

92
00:03:32,540 --> 00:03:33,550
我们还没有做完

93
00:03:33,550 --> 00:03:36,390
可以按照从左边往右边的顺序乘

94
00:03:36,390 --> 00:03:38,680
先思考一下

95
00:03:38,680 --> 00:03:40,280
(-2)×(-7)

96
00:03:40,280 --> 00:03:42,260
(-2)×(-7)

97
00:03:42,260 --> 00:03:43,300
它们都是负数

98
00:03:43,300 --> 00:03:45,300
负号抵消了 从这里得到

99
00:03:45,300 --> 00:03:46,410
这个结果

100
00:03:46,410 --> 00:03:49,080
将得到+14

101
00:03:49,080 --> 00:03:51,050
要用+14做乘法

102
00:03:51,050 --> 00:03:54,730
乘以这个-1 乘以-1

103
00:03:54,730 --> 00:03:57,590
用正数乘以负数

104
00:03:57,590 --> 00:03:59,170
有一个是负数

105
00:03:59,170 --> 00:04:01,040
将得到负数答案

106
00:04:01,040 --> 00:04:04,170
我们将得到-14

107
00:04:04,170 --> 00:04:06,160
我再给大家一些题目

108
00:04:06,160 --> 00:04:08,130
一些有陷阱的题目

109
00:04:08,130 --> 00:04:10,160
如果有

110
00:04:10,160 --> 00:04:13,190
0÷(-5)呢

111
00:04:13,190 --> 00:04:15,900
这是0/(-5)

112
00:04:15,900 --> 00:04:18,960
0除以任何一个非零数

113
00:04:18,960 --> 00:04:21,440
将等于0

114
00:04:21,440 --> 00:04:23,440
如果倒过来呢？

115
00:04:23,440 --> 00:04:26,530
如果有-5÷0会怎样呢？

116
00:04:26,530 --> 00:04:28,380
我们不知道

117
00:04:28,380 --> 00:04:29,480
除以0得到什么

118
00:04:29,480 --> 00:04:30,740
我们还没有定义

119
00:04:30,740 --> 00:04:35,070
有多种方法来概念化理解这个

120
00:04:35,070 --> 00:04:37,840
传统上来说这是未定义的

121
00:04:37,840 --> 00:04:39,520
我们没有定义

122
00:04:39,520 --> 00:04:42,520
某个量除以0时的结果

123
00:04:42,520 --> 00:04:45,900
同样的 当0除以0时

124
00:04:45,900 --> 00:04:50,720
结果也是没有定义的