1
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Find the sum 15 plus
negative 46 plus 29.

2
00:00:05,310 --> 00:00:07,630
Let's just think about
this first part over here

3
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where we have 15
plus negative 46.

4
00:00:13,060 --> 00:00:16,420
And we'll worry about
the plus 29 later on.

5
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So let's just do
15-- let me do that

6
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in a different color--
plus negative 46.

7
00:00:26,677 --> 00:00:27,760
I'll do it in that orange.

8
00:00:30,959 --> 00:00:33,250
Let me draw a number line
here, just so we can properly

9
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visualize what is going on.

10
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That's my number line.

11
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And we're starting at 15.

12
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So let's draw a 0 over here.

13
00:00:44,790 --> 00:00:47,270
And so we're starting at 15.

14
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15 could be right over here.

15
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So this is 15.

16
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Let me draw a big fat arrow
to signify this is 15.

17
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15 has an absolute value of
15, so the length of this arrow

18
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would be 15.

19
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Now we're adding
negative 46 to that 15.

20
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This is equivalent
to 15 minus 46,

21
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which means we are going to
move 46 spots to the left of 15.

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A negative sign or
a minus means we're

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moving to the left
on the number line.

24
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So we're going to
move 46 to the left.

25
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We're starting at 15, and we are
going to move 46 to the left.

26
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So the length of this arrow
right here is going to be 46,

27
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and we're moving to the left.

28
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This is the negative 46
that we're adding to the 15.

29
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We're going to end up
at some point over here.

30
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That point is clearly 0.

31
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Because we were 15 to the right.

32
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Now we're going to
move 46 to the left.

33
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So we're definitely going
to be to the left of 0.

34
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It's definitely going
to be a negative number.

35
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And we can even think
about the absolute value

36
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of that negative number.

37
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We can just visualize it.

38
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This yellow arrow
has a length of 15.

39
00:02:05,790 --> 00:02:09,000
This orange arrow
has a length of 46.

40
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The blue arrow that
I'm about to draw,

41
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which is the sum
of these two, is

42
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going to have this
length right over here.

43
00:02:18,310 --> 00:02:21,340
And just visually,
how can we figure out

44
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the length of this
blue part if we

45
00:02:23,410 --> 00:02:25,020
know the length of
this orange part

46
00:02:25,020 --> 00:02:27,320
and we know the length
of this yellow part?

47
00:02:27,320 --> 00:02:28,600
Well, it's just going
to be the difference.

48
00:02:28,600 --> 00:02:30,683
It's just going to be the
difference of these two.

49
00:02:30,683 --> 00:02:32,980
So the absolute
value of the sum is

50
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going to be the difference
between this length, 46,

51
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and 15.

52
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Let me just figure
that out, 46 minus 15.

53
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6 minus 5 is 1.

54
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4 minus 1 is 3.

55
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So the length of this
is going to be 31,

56
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and it's going to be
31 to the left of 0.

57
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So this is going to be
negative 31 right over here.

58
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We know that this first part
over here is negative 31,

59
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and then to that we
are going to add 29.

60
00:03:05,080 --> 00:03:06,657
So we're going to add 29.

61
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Let me do that in another color.

62
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What does that mean?

63
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That means that we're going
to start at negative 31,

64
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and we're going to
move 29 to the right.

65
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We're adding 29, so we're
going to move 29 to the right.

66
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So maybe that gets
us right about there.

67
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I'm trying to draw an
arrow of length 29.

68
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I can draw a cleaner
looking arrow than that.

69
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I'll do it right
over here, actually.

70
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So then we're going to
move 29 over to the right.

71
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That's the 29 part.

72
00:03:38,350 --> 00:03:41,600
Now this is a positive
29, and so how

73
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do we figure out what this is?

74
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This is 29 right here
that we're adding.

75
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This is going to land us right
over here on the number line.

76
00:03:51,990 --> 00:03:54,160
So how do we figure out
what number that is?

77
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Well, once again, we
can just visualize it.

78
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And eventually you won't have
to draw number lines and stuff,

79
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but I think it'll
be useful here.

80
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We're starting at negative 31.

81
00:04:02,540 --> 00:04:05,720
We're adding 29 to it, so it's
going to make it less negative.

82
00:04:05,720 --> 00:04:08,690
But we're still
adding less than 31,

83
00:04:08,690 --> 00:04:10,750
so we're not going to get
all the way back to 0.

84
00:04:10,750 --> 00:04:12,583
We're still going to
have a negative number.

85
00:04:15,950 --> 00:04:18,000
But how could we figure
out the absolute value

86
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of that negative
number, its distance?

87
00:04:19,870 --> 00:04:22,410
Well, once again, that little
white part right there,

88
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that white part plus
this 29, is going

89
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to equal 31, if you just
think of absolute value,

90
00:04:28,334 --> 00:04:29,750
if we don't think
about the signs,

91
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if we just think
about the length.

92
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Or another way to think
about it, 31 minus 29

93
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will give us the length
of that white part.

94
00:04:36,640 --> 00:04:38,600
And of course, it's
going to be negative,

95
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because the negative
number here is

96
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larger than the positive number.

97
00:04:41,740 --> 00:04:43,480
And we're adding the 2.

98
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If we do 31 minus 29, you
could borrow and all of that,

99
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but that's clearly just
going to be equal to 2.

100
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You could say that's 11.

101
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This is a 2.

102
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You subtract, this
is equal to 2.

103
00:04:56,600 --> 00:05:00,010
But since it's
negative 31 plus 29,

104
00:05:00,010 --> 00:05:01,350
it's going to be a negative 2.

105
00:05:01,350 --> 00:05:02,808
We're still going
to stay negative.

106
00:05:02,808 --> 00:05:05,630
We haven't moved far to
the right enough to pass 0.

107
00:05:05,630 --> 00:05:08,265
So this right here is
going to be negative 2.

108
00:05:08,265 --> 00:05:09,640
Or another way to
think about it,

109
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the length of this white
bar, the absolute value,

110
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is going to be 2.

111
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2 plus 29 is 31.

112
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But we're operating to the
left of 0, so it's negative 31.

113
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This is negative 2.

114
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Anyway, hopefully you
found that useful.

115
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And let me make it clear.

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Our final answer is negative 2.