1
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We have to rewrite the following fractions

2
00:00:05,067 --> 00:00:09,733
with fraction with least common denominator

3
00:00:09,733 --> 00:00:16,200
So LCD of the 2 fractions is going to be the LCM

4
00:00:16,200 --> 00:00:21,133
of both of these denominators over here.

5
00:00:21,133 --> 00:00:25,467
and if we can make this as common denominators

6
00:00:25,467 --> 00:00:29,133
we can add the two fractions

7
00:00:29,133 --> 00:00:31,800
First let us find the LCM,

8
00:00:31,800 --> 00:00:49,200
let me write it out LCD of 8 & 6

9
00:00:49,200 --> 00:00:58,133
is going to be the LCM of 8 & 6

10
00:00:58,133 --> 00:01:00,800
and a couple of ways to think about the LCM

11
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you could really take the multiples of 8 & 6

12
00:01:03,267 --> 00:01:08,600
and see what their smallest common multiple is.

13
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Multiples of 6 - 6,12,18,24,30... i can keep going

14
00:01:20,867 --> 00:01:27,267
and the multiples of 8 are 8,16,24,. looks like

15
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we are done. I have found a common multiple

16
00:01:32,733 --> 00:01:35,467
it is the smallest multiple they have other

17
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common multiples like 48,72 and we can go on

18
00:01:39,867 --> 00:01:43,400
but this is their smallest common multiple

19
00:01:43,400 --> 00:01:50,933
So it is 24. Another way to find the LCM is

20
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take the prime factorization of 6 - 2x3

21
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and the LCM of 6 must have one 2 & one 3

22
00:02:02,600 --> 00:02:13,667
what is the prime factorization of 8 is 2x2x2.

23
00:02:13,667 --> 00:02:16,467
Inorder to be divisible by 8 we need to have three 2's

24
00:02:16,467 --> 00:02:19,133
in the prime factorization. To be divisible by 6

25
00:02:19,133 --> 00:02:23,800
we need to have 2,3 and to be divisible by 8 we need

26
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three 2's, we have only one 2 so we add a couple more

27
00:02:28,867 --> 00:02:42,133
so thsi is now divisible by 6 & 8

28
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So 2x2x2x3 = 24. So LCM of 8 & 6

29
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which is the LCD also is 24

30
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So we want to write each of this fractions as

31
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24 as their denominator.

32
00:03:01,600 --> 00:03:09,733
So lets start with 2/8, i want to write that as / 24

33
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so get the denominator as 24,

34
00:03:13,400 --> 00:03:17,533
we need to multiply the denominator by 3

35
00:03:17,533 --> 00:03:19,400
inorder not to change the fraction, we need to

36
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multiply the numerator also by the same number

37
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so we will multiply numerator by 3 ; 2x3=6

38
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so 2/8 = 6/24

39
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2/8 x 3/3 = 6/24

40
00:03:46,867 --> 00:03:59,800
and lets do the same things with 5/6

41
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5/6 = / 24, i will do it in a different colour, blue

42
00:04:09,533 --> 00:04:13,067
to get the denominator from 6 to 24, we need

43
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to multiply by 4, so we need to multiply

44
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numerator also by 4 so 5x4 = 20

45
00:04:24,800 --> 00:04:28,133
5/6 = 20/24

46
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so we have written both the fractions with common denominator

47
00:04:33,400 --> 99:59:59,999
So we are done