1
00:00:00,800 --> 00:00:05,320
We have negative 3/4
minus 7/6 minus 3/6.

2
00:00:05,320 --> 00:00:06,790
And there's many
ways to do this.

3
00:00:06,790 --> 00:00:08,520
But it immediately
jumps out at me

4
00:00:08,520 --> 00:00:11,400
that these last two numbers
have a 6 in the denominator.

5
00:00:11,400 --> 00:00:13,270
So I'm going to worry
about these first.

6
00:00:13,270 --> 00:00:17,390
I'm going to view this as
negative 7/6 minus 3/6.

7
00:00:17,390 --> 00:00:21,540
So if we have negative
7/6 minus 3/6,

8
00:00:21,540 --> 00:00:24,930
that's going to be the same
thing as negative 7 minus 3

9
00:00:24,930 --> 00:00:26,620
over 6.

10
00:00:26,620 --> 00:00:28,790
And of course, we
have this negative 3/4

11
00:00:28,790 --> 00:00:30,900
out front that
we're going to add

12
00:00:30,900 --> 00:00:32,110
to whatever we get over here.

13
00:00:32,110 --> 00:00:35,980
So this is these two terms
that I'm adding together.

14
00:00:35,980 --> 00:00:39,770
Negative 7 minus
3 is negative 10.

15
00:00:39,770 --> 00:00:42,610
So it's negative 10 over 6.

16
00:00:42,610 --> 00:00:45,230
And then I'm going to have
to add that to negative 3/4.

17
00:00:52,550 --> 00:00:56,620
And now I have to worry about
finding a common denominator.

18
00:00:56,620 --> 00:01:02,800
Let me write that so
they have a similar size.

19
00:01:02,800 --> 00:01:05,390
So now I have to worry about
finding a common denominator.

20
00:01:05,390 --> 00:01:09,690
What is the smallest number that
is a multiple of both 4 and 6?

21
00:01:09,690 --> 00:01:11,620
Well, it might jump out
at you that it's 12.

22
00:01:11,620 --> 00:01:14,040
You can literally just go
through the multiples of 4.

23
00:01:14,040 --> 00:01:15,890
Or you could look at
the prime factorization

24
00:01:15,890 --> 00:01:16,850
of both of these numbers.

25
00:01:16,850 --> 00:01:18,308
And what's the
smallest number that

26
00:01:18,308 --> 00:01:20,950
has all of the prime
factors of both of these?

27
00:01:20,950 --> 00:01:25,380
So you need two 2s, and
you need a 2 and a 3.

28
00:01:25,380 --> 00:01:29,570
So if you have two 2s and a
3, that's 4 times 3 is 12.

29
00:01:29,570 --> 00:01:34,520
So let's rewrite this
as something over 12

30
00:01:34,520 --> 00:01:37,500
plus something over 12.

31
00:01:40,760 --> 00:01:43,000
Well, to get your
denominator from 4 to 12,

32
00:01:43,000 --> 00:01:44,860
you have to multiply by 3.

33
00:01:44,860 --> 00:01:47,410
So let's multiply our
numerator by 3 as well.

34
00:01:47,410 --> 00:01:50,120
So if we multiply
negative 3 times 3,

35
00:01:50,120 --> 00:01:52,130
you're going to have negative 9.

36
00:01:52,130 --> 00:01:54,260
And to get your
denominator from 6 to 12,

37
00:01:54,260 --> 00:01:56,270
you have to multiply by 2.

38
00:01:56,270 --> 00:01:58,322
So let's multiply our
numerator by 2 as well so

39
00:01:58,322 --> 00:02:00,280
that we don't change the
value of the fraction.

40
00:02:00,280 --> 00:02:02,890
So that's going
to be negative 20.

41
00:02:02,890 --> 00:02:04,490
And now we're ready to add.

42
00:02:04,490 --> 00:02:07,380
Our common denominator is 12.

43
00:02:07,380 --> 00:02:12,690
And so this is going to be
negative 9 plus negative 20,

44
00:02:12,690 --> 00:02:15,531
or we could even write
that as minus 20,

45
00:02:15,531 --> 00:02:18,780
over 12, which is equal to--
and we deserve a drum roll now.

46
00:02:18,780 --> 00:02:23,980
This is negative 29 over 12.

47
00:02:23,980 --> 00:02:26,980
And 29 is a prime
number, so it's not

48
00:02:26,980 --> 00:02:30,090
going to share any common
factors other than 1 with 12.

49
00:02:30,090 --> 00:02:34,794
So we also have this in
the most simplified form.