1
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Use < , > , = to compare the two fractions 21/28

2
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and 6/9. So there is a buch of ways to do this.

3
00:00:13,467 --> 00:00:16,200
The easiest way is if they have the same

4
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denominator, we can compare the numerators.

5
00:00:19,267 --> 00:00:22,600
Unfortunately we do not have the same denominators

6
00:00:22,600 --> 00:00:25,667
So we could do is we could find common denominators

7
00:00:25,667 --> 00:00:27,467
for both the fractions and convert both the fractions

8
00:00:27,467 --> 00:00:29,933
to have common denominators and compare the

9
00:00:29,933 --> 00:00:32,867
numerators.Or even more simply we can

10
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simplify them first and then try do it.

11
00:00:35,667 --> 00:00:45,333
So 21/28 , they are both divisibley by 7.

12
00:00:45,333 --> 00:00:48,867
Let us divide the numerator & denominator by 7

13
00:00:48,867 --> 00:00:57,333
21 divide by 7 & 28 divide by 7.

14
00:00:57,333 --> 00:01:00,600
Since we are dividing both by 7, we are not changing

15
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the value of the fraction 21 ÷ 7 = 3

16
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28 ÷ 7 = 4.

17
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So 21/28 = 3/4.

18
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Lets us do the same thing for 6/9

19
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6 & 9 are both divisible by 3

20
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So lets divide both 6 & 9 by 3

21
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6 ÷ 3 = 2

22
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9 ÷ 3 = 3

23
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21/28 = 3/4

24
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6/9 = 2/3

25
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So we really can compare 3/4 & 2/3.

26
00:01:45,667 --> 00:01:52,067
The real benefit of doing this, it is easy to find

27
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common denominators for this than 28 &9

28
00:01:56,667 --> 00:01:59,867
which means we need to multiply larger numbers

29
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here we have smaller numbers.

30
00:02:01,867 --> 00:02:04,667
the common denominator of 3/4 & 2/3 is the LCM

31
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of 4 & 3.

32
00:02:09,733 --> 00:02:13,733
4 & 3 does not share any prime factors with each other

33
00:02:13,733 --> 00:02:17,667
so LCM of 4 & 3 is the product of the 2 numbers

34
00:02:19,667 --> 00:02:22,000
3/4 = /12

35
00:02:22,000 --> 00:02:25,067
2/3 = /12

36
00:02:25,067 --> 00:02:28,933
I got 12 by multiplying 3 & 4 as they have no

37
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common factors. another way to think is

38
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prime factorization of 4 = 2x2

39
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3 is already a prime number, so prime factorization

40
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of 3 is 3.

41
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The number that has all prime factors of 4 & 3 is 2,2 & 3

42
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2x2x3 = 12.This is how we get LCM

43
00:02:53,533 --> 00:03:04,600
to get from 4 to 12 ,you got to multiply 3

44
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We multiply denominator by 3 to get 12

45
00:03:07,733 --> 00:03:14,200
We need to multiply the numerator by 3

46
00:03:14,200 --> 00:03:16,000
3 x 3 = 9

47
00:03:16,000 --> 00:03:18,200
To get from 3 to 12, we multiply denominator by 4

48
00:03:18,200 --> 00:03:21,933
We also have to multiply numerator by 4

49
00:03:21,933 --> 00:03:25,800
4 x 2 = 8

50
00:03:25,800 --> 00:03:34,067
21/28 = 3/4 = 9/12

51
00:03:34,067 --> 00:03:40,867
6/9 = 2/3 = 8/12

52
00:03:40,867 --> 00:03:44,733
Which of these is a greater fraction.

53
00:03:44,733 --> 00:03:48,600
Since we have common denominator, we need to

54
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look at the numerator. We know 9 > 8

55
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So, 21/28 > 6/9

56
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And we are done.

57
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Another way to do is

58
00:04:15,467 --> 00:04:17,533
we need not simply it. just do it for fun.

59
00:04:17,533 --> 00:04:32,200
If we did not simplify it 21/28 & 6/9

60
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LCM of 28 & 9

61
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prime factorization of 28 = 2x2x7

62
00:04:48,933 --> 00:04:51,400
Prime factorization of 9 = 3x3

63
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The LCM of 28 & 9 must contain 2x2x3x3x7

64
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which is esentially 28x9 = 252

65
00:05:06,333 --> 00:05:34,267
The common denominator is going to be 252

66
00:05:34,267 --> 00:05:45,267
To go from 28 to 252 we had to

67
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multiply 28 by 9 ; 28 x 9

68
00:05:48,933 --> 00:05:53,667
So we also have to multiply numerator by 9

69
00:05:53,667 --> 00:06:03,800
21x9 = 189

70
00:06:03,800 --> 00:06:07,533
To go from 9 to 252

71
00:06:07,533 --> 00:06:10,067
we need to multiply by 28.

72
00:06:10,067 --> 00:06:14,667
So we need to multiply numerator by 28

73
00:06:14,667 --> 00:06:23,600
So 6x28 = 168

74
00:06:23,600 --> 00:06:45,333
Now we have a common denominator here

75
00:06:45,333 --> 00:06:48,000
and we can compare the numerator.

76
00:06:48,000 --> 00:06:55,200
189 > 168

77
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So 21/28 > 6/9