1
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2
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They want us to subtract these two numbers and simplify the

3
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answer and write as a mixed number.

4
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We're going to do it two ways.

5
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The first way, we're going to turn both of these into

6
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improper fractions and see what we get.

7
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And then the other way, we're going to subtract the whole

8
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number parts and then subtract the fraction parts and see

9
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what we get.

10
00:00:17,690 --> 00:00:20,420
So if we turn them both into improper fractions, let's

11
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first turn 8 and 2/3 into an improper fraction.

12
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So it has 3 in the denominator, and

13
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3 times 8 is 24.

14
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24 plus 2 is 26.

15
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So 8 and 2/3 is the same thing as 26/3.

16
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And 5 and 5/6, so we're going to subtract.

17
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We're going to have 6 in the denominator.

18
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6 times 5 is 30.

19
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30 plus 5 is 35.

20
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So this simplifies as an improper fraction to 35/6.

21
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Now to subtract, we have to have a common denominator.

22
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3 and 6 are not the same denominator, but they are both

23
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divisible into 6.

24
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6 is the least common multiple of 3 and 6.

25
00:00:59,280 --> 00:01:02,590
So let's turn them both into something over 6.

26
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So the 26/3, if we put it over 6, to go from 3 to 6 in the

27
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denominator, we have to multiply by 2, so we have to

28
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do the same thing in the numerator.

29
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We have to multiply 2 times 26, which is 52.

30
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So it's going to be 52/6 minus-- we don't have to

31
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change this one here in orange.

32
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It's already over 6-- minus 36/6, which is going to be

33
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equal to-- what's 52 minus 35?

34
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Let's see, if you add 5 to 35, you get to 40.

35
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15 will get you to 50, and so we want 2 more, so

36
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it's going to be 17.

37
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So it's 17/6.

38
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This is as an improper fraction.

39
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Now, if we want to write it as a mixed number, we say how

40
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many times does 6 go into 17?

41
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Well, 6 times 2 is 12, so that works.

42
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6 times 3 is too big.

43
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It's 18, so it goes in two times.

44
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Now, if you take it into it two times, you get 12, and

45
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then you have 5 left over, right?

46
00:02:01,890 --> 00:02:05,609
To go from 12 to 17, you need 5 so you have 5 left over.

47
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You could say 6 goes into 17 two times, remainder 5, so 17

48
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over 6 is 2 and 5/6.

49
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And we're done!

50
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Now this is kind of the improper fraction route, which

51
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it'll always work.

52
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It'll always work.

53
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Sometimes it's easier or harder, but

54
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it will always work.

55
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Actually, either route will always work, but I tend to do

56
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it this way.

57
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Let's do it separating out the whole number and the

58
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fractional parts.

59
00:02:31,259 --> 00:02:33,885
So first we could view this as 8 minus 5.

60
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So let's do this.

61
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8 minus 5-- that's subtracting the whole number parts-- plus

62
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2/3 minus 5/6.

63
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Now, 8 minus 5, that's easy.

64
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That's 3.

65
00:02:49,699 --> 00:02:52,209
And then over here, though, we have an interesting-- well,

66
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let's try to work it out.

67
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Let me do this in a different color.

68
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We want a common denominator here, and we already saw that

69
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6 is the least common multiple of 3 and 5, so we could write

70
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them both with 6 as the denominator.

71
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5/6 already has 6 as the denominator.

72
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We don't have to do anything there.

73
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To go from 3 to 6 in the denominator here, we have to

74
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multiply by 2, so let's do the same thing with this 2.

75
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2 times 2 is 4.

76
00:03:18,669 --> 00:03:24,269
So this results in 4/6 minus 5/6, which will give us-- and

77
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we haven't covered it yet-- a negative number.

78
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If you take 5 from 4, you're going to go below 0.

79
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Now, if we don't want to deal with that negative number,

80
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what we could do, and this is essentially the same idea as

81
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regrouping or borrowing, although they shouldn't call

82
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it borrowing, they should call it taking, is we can

83
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rewrite this 3.

84
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That's why this can get a little bit tricky sometimes.

85
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Let me do it over here.

86
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Let me draw a line here so we don't get the two ways of

87
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doing the problem confused.

88
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We can rewrite the 3 as 2 plus 1, but instead of writing it

89
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as 1, we could write it as 6/6, right?

90
00:04:00,120 --> 00:04:02,830
6 over 6 is 1 plus 2 is 3.

91
00:04:02,830 --> 00:04:05,500
And then, if we add it to these guys, so

92
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plus 4/6 minus 5/6.

93
00:04:10,250 --> 00:04:12,129
Now, what happened by doing that?

94
00:04:12,129 --> 00:04:15,530
Well, if we throw this 6/6 into the mix and then we had

95
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the 4/6 and then we subtract the 5 from it, then we're

96
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going to have a positive number, so let's to do it.

97
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So we get this 2 right here.

98
00:04:24,110 --> 00:04:30,550
So it's 2 plus, and then over 6, we have 6 plus 4--

99
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let me write it.

100
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6 plus 4 minus 5.

101
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Now, what's this going to equal?

102
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This is going to be this 2 and what over 6?

103
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104
00:04:43,220 --> 00:04:48,070
6 plus 4 is 10 minus 5 is 5.

105
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So you have 2 and 5/6, which is exactly what we

106
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got the other way.

107
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