1
00:00:00,000 --> 00:00:00,730


2
00:00:00,730 --> 00:00:01,250
Add.

3
00:00:01,250 --> 00:00:03,570
Simplify the answer and write
as a mixed number.

4
00:00:03,570 --> 00:00:06,740
And we have three mixed numbers
here: 3 and 1/2 plus

5
00:00:06,740 --> 00:00:10,130
11 and 2/5 plus 4 and 3/15.

6
00:00:10,130 --> 00:00:13,870
So we've already seen that we
could view this as 3 plus 1/12

7
00:00:13,870 --> 00:00:16,219
plus 11 plus 2/5-- let
me write that down.

8
00:00:16,219 --> 00:00:23,180
This is the same thing as 3
plus 1/12 plus 11 plus 2/5

9
00:00:23,180 --> 00:00:27,330
plus 4 plus 3/15.

10
00:00:27,330 --> 00:00:30,170
The mixed number 3 and 1/12
just literally means 3 and

11
00:00:30,170 --> 00:00:32,840
1/12 or 3 plus 1/12.

12
00:00:32,840 --> 00:00:35,930
And since we're just adding
a bunch of numbers, order

13
00:00:35,930 --> 00:00:37,690
doesn't matter, so we
could add all the

14
00:00:37,690 --> 00:00:39,500
whole numbers at once.

15
00:00:39,500 --> 00:00:46,500
So we have 3 plus 11 plus 4,
and then we can add the

16
00:00:46,500 --> 00:00:57,080
fractions: the 1/12 plus
2/5 plus 3/15.

17
00:00:57,080 --> 00:00:58,650
Now, the blue part's pretty
straightforward.

18
00:00:58,650 --> 00:00:59,540
We're just adding numbers.

19
00:00:59,540 --> 00:01:05,360
3 plus 11 is 14 plus 4 is
18, so that part right

20
00:01:05,360 --> 00:01:06,740
there is just 18.

21
00:01:06,740 --> 00:01:09,080
This will be a little bit
trickier, because we know that

22
00:01:09,080 --> 00:01:12,120
when we add fractions, we have
to have the same denominator.

23
00:01:12,120 --> 00:01:14,590
And now we have to make all
three of these characters have

24
00:01:14,590 --> 00:01:17,030
the same denominator and that
denominator has to be the

25
00:01:17,030 --> 00:01:21,910
least common multiple
of 12 and 5 and 15.

26
00:01:21,910 --> 00:01:24,210
Now, we could just do it kind
of the brute force way.

27
00:01:24,210 --> 00:01:25,530
We could just look
at the multiples.

28
00:01:25,530 --> 00:01:28,310
We could pick one of these guys
and keep taking their

29
00:01:28,310 --> 00:01:31,020
multiples, and then figuring
out whether those multiples

30
00:01:31,020 --> 00:01:34,080
are both divisible
by 5 and 15.

31
00:01:34,080 --> 00:01:36,330
Or the other way we can do
it is take the prime

32
00:01:36,330 --> 00:01:39,590
factorization of each of these
numbers, and just say that the

33
00:01:39,590 --> 00:01:42,670
least common multiple has
to contain the prime

34
00:01:42,670 --> 00:01:45,960
factorization each of these
guys, which means it contains

35
00:01:45,960 --> 00:01:47,200
each of those numbers.

36
00:01:47,200 --> 00:01:48,910
So let me show you what
I'm talking about.

37
00:01:48,910 --> 00:01:54,640
If we take the prime
factorization of 12, 12 is 2

38
00:01:54,640 --> 00:02:03,020
times 6, 6 is 2 times 3, so 12
is equal to 2 times 2 times 3.

39
00:02:03,020 --> 00:02:05,310
That's the prime factorization
of 12.

40
00:02:05,310 --> 00:02:08,940
Now, if we do 5, prime
factorization of 5, well, 5 is

41
00:02:08,940 --> 00:02:12,900
just 1 and 5, so 5 is
a prime number.

42
00:02:12,900 --> 00:02:14,670
It is the prime factorization
of 5.

43
00:02:14,670 --> 00:02:16,210
There's just a 5 there.

44
00:02:16,210 --> 00:02:17,660
This 1 is kind of useless.

45
00:02:17,660 --> 00:02:19,880
So 5 is just 5.

46
00:02:19,880 --> 00:02:23,340
And then 15, let's do 15.

47
00:02:23,340 --> 00:02:25,620
Actually, when I did the prime
factorization of 5, I should

48
00:02:25,620 --> 00:02:27,620
have said, look, 5 is prime.

49
00:02:27,620 --> 00:02:30,880
There's no number larger than
1 that divides into it, so

50
00:02:30,880 --> 00:02:33,070
it's actually silly to even
make a tree there.

51
00:02:33,070 --> 00:02:38,230
And now let's do 15, 15's
prime factorization.

52
00:02:38,230 --> 00:02:43,450
15 is 3 times 5, and now both
of these are prime.

53
00:02:43,450 --> 00:02:48,210
So we need something that has
two 2's and a 3, so let's look

54
00:02:48,210 --> 00:02:49,310
at the 12 right there.

55
00:02:49,310 --> 00:02:55,165
So our denominator has to have
at least two 2's and a 3, so

56
00:02:55,165 --> 00:02:56,080
let's write that down.

57
00:02:56,080 --> 00:02:59,530
So it has to be 2
times 2 times 3.

58
00:02:59,530 --> 00:03:01,390
It has to have at least that.

59
00:03:01,390 --> 00:03:04,120
Now, it also has to have
a 5 there, right?

60
00:03:04,120 --> 00:03:06,380
Because it has to be a
common multiple of 5.

61
00:03:06,380 --> 00:03:09,050
5's another one of those prime
factors, so it's got to have a

62
00:03:09,050 --> 00:03:09,900
5 in there.

63
00:03:09,900 --> 00:03:11,670
It didn't already have a 5.

64
00:03:11,670 --> 00:03:14,390
And then it also has to
have a 3 and a 5.

65
00:03:14,390 --> 00:03:16,550
Well, we already have a 5.

66
00:03:16,550 --> 00:03:20,440
We already have a 3 from the
12, and we already have a 5

67
00:03:20,440 --> 00:03:24,090
from the 5, so this number will
be divisible by all of

68
00:03:24,090 --> 00:03:26,350
them, and you can see that
because you can see it has a

69
00:03:26,350 --> 00:03:30,570
12 in it, it has a 5 in it,
and it has a 15 in it.

70
00:03:30,570 --> 00:03:31,790
So what is this number?

71
00:03:31,790 --> 00:03:33,810
2 times 2 is 4.

72
00:03:33,810 --> 00:03:36,460
4 times 3 is 12.

73
00:03:36,460 --> 00:03:38,640
12 times 5 is 60.

74
00:03:38,640 --> 00:03:43,090
So the least common multiple
of 12, 5 and 15 is 60.

75
00:03:43,090 --> 00:03:45,000
So this is going to be plus.

76
00:03:45,000 --> 00:03:47,490
We're going to be over 60.

77
00:03:47,490 --> 00:03:51,040
So all of these are going
to be over 60.

78
00:03:51,040 --> 00:03:54,160
All of these three fractions
are over 60.

79
00:03:54,160 --> 00:03:56,850
Now, to go from 12 to 60,
we have to multiply the

80
00:03:56,850 --> 00:04:00,110
denominator by 5, so we also
have to multiply the numerator

81
00:04:00,110 --> 00:04:02,930
by 5, so 1 times 5 is 5.

82
00:04:02,930 --> 00:04:05,900
5/60 is the same
thing as 1/12.

83
00:04:05,900 --> 00:04:08,200
To go from 5 to 60 in the
denominator, we have to

84
00:04:08,200 --> 00:04:10,490
multiply by 12, so we
have to do the same

85
00:04:10,490 --> 00:04:11,580
thing for the numerator.

86
00:04:11,580 --> 00:04:15,150
12 times 2 is 24.

87
00:04:15,150 --> 00:04:18,740
The last one, 15 to 60, you have
to multiply by 4, so you

88
00:04:18,740 --> 00:04:20,339
have to do the same thing
in the numerator.

89
00:04:20,339 --> 00:04:27,120
4 times 3 is 12.

90
00:04:27,120 --> 00:04:29,020
And now we have the
same denominator.

91
00:04:29,020 --> 00:04:33,460
We are ready to add.

92
00:04:33,460 --> 00:04:34,380
So let's do that.

93
00:04:34,380 --> 00:04:40,970
So this is going to be 18 plus,
and then over 60, we

94
00:04:40,970 --> 00:04:45,450
have 5 plus 24, which is 29.

95
00:04:45,450 --> 00:04:52,320
29 plus 12, let's see, 29
plus 10 would be 39

96
00:04:52,320 --> 00:04:55,420
plus 2 would be 41.

97
00:04:55,420 --> 00:04:57,940
It would be 41.

98
00:04:57,940 --> 00:05:01,800
And as far as I can tell,
41 and 60 do not

99
00:05:01,800 --> 00:05:04,030
have any common factors.

100
00:05:04,030 --> 00:05:06,230
41 actually looks prime to me.

101
00:05:06,230 --> 00:05:12,220
So the final answer
is 18 and 41/60.

102
00:05:12,220 --> 00:05:15,399