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Showing Revision 10 created 04/23/2012 by girl990.

1. Welcome to the presentation

2. on adding and subtracting negative numbers.
3. So let's get started.
4. So what is a negative number, first of all?
5. Well, let me draw a number line.
6. Well it's not much of a line,
7. but I think you'll get the picture.
8. So we're used to the positive numbers, so if that's 0
9. you have one, you have 2, you have 3, you have 4
10. and you keep going.
11. And if I were to say what's 2+2
12. you'd start at 2, and then you'd add 2
13. you'd get to 4.
14. I mean most of us it's second nature.
15. But if you actually drew it on a number line,
16. you'd say 2+2=4
17. And if I asked you what's 2-1
18. or let's say what's 3-2
19. If you start at 3 and you subtracted 2
20. you would end up at 1
21. That's 2+2=4, and 3-2=1
22. And this is a joke for you.
23. Now what if I were to say what is 1-3?
24. Huh.
25. Well, it's the same thing.
26. You start at 1 and we're going to go 1--
27. well, now we're going to go below 0
28. what happens below 0?
29. Well then you start going to the negative numbers.
30. -1, -2, -3, and so on.
31. So if I start at 1 right here, so 1-3
32. so I go 1,2,3, I end up at -2
33. So 1-3=-2
34. This is something that you're probably already doing
36. If I were to tell you that
37. boy, it's very cold today, it's one degree,
38. but tomorrow it's going to be three degrees colder,
39. you might already know intuitively,
40. well then we're going to be
41. at a temperature of negative two degrees.
42. So that's all a negative number means.
43. And just remember when a negative number is big,
44. so like -50, that's actually colder than -20, right?
45. So a -50 is actually even a smaller number than -20
46. because it's even further to the left of -20
47. That's just something you'll get an intuitive feel for.
48. Sometimes when you start you feel like
49. oh, 50 is a bigger number than 20
50. but it's a -50 as opposed to a 50
51. So let's do some problems,
52. and I'm going to keep using the number line
53. because I think it's useful
54. So let's do the problem 5-12
55. I think you already might have an intuition
56. of what this equals.
57. But let me draw a line, 5-12
59. I think I'm going to run out of space-- -7, -6, -5
60. I should have this pre-drawn -- -4, -3, -2, -1
61. 0,1,2,3,4, and I'll put 5 right here.
62. I'm gonna push this arrow out a little bit. Okay.
63. 5-12
64. So if we start at 5-- let me use a different color--
65. we start at 5 right here and we're going to go to the left 12
66. because we're subtracting 12
67. So then we go 1,2,3...
68. Negative 7
69. That's pretty interesting.
70. Because it also happens to be
71. that 12 - 5 = +7
72. So, I want you to think a little bit about why that is.
73. Why the difference between 12 and 5 is 7,
74. and the difference between
75. -- well, I guess it's either way.
76. In this situation we're also saying
77. that the difference between 5 and 12 is -7,
78. but the numbers are that far apart,
79. but now we're starting with the lower number.
80. I think that last sentence just completely confused you,
81. but we'll keep moving forward.
82. We just said 5-12=-7
83. Let's do another one.
84. What's -3+5?
85. Well, let's use the same number line.
86. Let's go to -3 plus 5
87. So we're going to go to the right 5
88. One, two, three, four, five.
89. It's a two.
90. It equals two.
91. So -3 + 5 = 2
92. That's interesting because 5 - 3 is also equal to 2
93. Well, it turns out that 5 - 3 is the same thing,
94. it's just another way of writing 5 plus -3
95. or -3 plus 5
96. A general, easy way to always do negative numbers
97. is it's just like regular addition and subtraction,
98. but now when we subtract
99. we can go to the left below zero
100. Let's do another one.
101. So what happens when you get
102. let's say, 2 minus -3?
103. Well, if you think about how it should work out,
104. I think this will make sense.
105. But it turns out that the negative number,
106. the negative signs actually cancel out.
107. So this is the same thing as 2 plus +3
108. and that just equals 5
109. Another way you could say is-- let's do another one--
110. what is -7 minus -2?
111. Well that's the same thing as -7 + 2
112. And remember, so we're doing to start at -7
113. and we're going to move 2 to the right.
114. So if we move 1 to the right we go to -6
115. and then we move 2 to the right we get -5
116. That makes sense because -7 + 2
117. that's the same thing as 2 - 7
118. If it's two degrees and
119. it gets seven degrees colder, it's -5
120. Let's do a bunch of these.
121. I think the more you do, the more practice you have,
122. and the modules explain it pretty well.
123. Probably better than I do.
124. So let's just do a ton of problems.
125. So if I said -7 - 3
126. Well, now we're going to go 3 to the left of -7
127. We're going to get 3 less than -7
128. so that's -10, right?
129. That makes sense, because if we had 7 + 3
130. we're at 7 to the right of 0
131. and we're going to go 3 more to the right of 0
132. and we get positive 10
133. So for 7 to the left of 0 and go 3 more to the left,
134. we're going to get -10
135. Let's do a bunch more.
136. I know I'm probably confusing you,
137. but practice is what's going to really help us.
138. So let's say 3 minus -3
139. well, these negatives cancel out,
140. so that just equals 6
141. What's 3-3?
142. Well, 3-3, that's easy.
143. That's just 0
144. What's -3 nimus 3?
145. Well now we're going to get 3 less than -3
146. well that's -6
147. What's -3 minus -3
148. Interesting.
149. Well, the minuses cancel out, so you get -3 plus 3
150. Well, if we start 3 to the left of 0 and we move 3 to the right,
151. we end up at 0 again.
152. So that makes sense, right?
153. Let me do that again.
154. -3 minus -3
155. Anything minus itself should equal 0, right?
156. That's why that equals 0
157. And that's why it makes sense that
158. those two negatives cancel out
159. and that's the same thing as this.
160. Let's do a bunch more.
161. Let's do 12 - 13
162. That's pretty easy.
163. Well, 12 - 12 = 0, so12 - 13 = -1
164. because we're going to go 1 the left of 0
165. Let's do 8 - 5
166. Well, this one is just a normal problem, that's 3
167. What's 5 - 8?
168. Well, we're going to go all the way to 0
169. and then 3 more to the left of 0, so it's -3
170. I could draw a number line here.
171. If this is 0, this is 5
172. and now we're going to go to left 8,
173. then we end up at -3
174. You could do that for all of these.
175. That actually might be a good exercise.
176. I think this will give you good introduction
177. and I recommend that you just do the modules,
178. because the modules actually
179. especially if you do the hints
180. it has a pretty nice graphic
181. that's a lot nicer than
182. anything I could draw on this chalkboard.
183. So, try that out
184. and I'm going to try to record some more modules
185. that hopefully won't confuse you as badly.
186. You could also attend the seminar
187. on adding and subtracting negative numbers.
188. I hope you have fun!
189. Bye.