0:00:00.000,0:00:00.800


0:00:00.800,0:00:05.320
We have negative 3/4[br]minus 7/6 minus 3/6.

0:00:05.320,0:00:06.790
And there's many[br]ways to do this.

0:00:06.790,0:00:08.520
But it immediately[br]jumps out at me

0:00:08.520,0:00:11.400
that these last two numbers[br]have a 6 in the denominator.

0:00:11.400,0:00:13.270
So I'm going to worry[br]about these first.

0:00:13.270,0:00:17.390
I'm going to view this as[br]negative 7/6 minus 3/6.

0:00:17.390,0:00:21.540
So if we have negative[br]7/6 minus 3/6,

0:00:21.540,0:00:24.930
that's going to be the same[br]thing as negative 7 minus 3

0:00:24.930,0:00:26.620
over 6.

0:00:26.620,0:00:28.790
And of course, we[br]have this negative 3/4

0:00:28.790,0:00:30.900
out front that[br]we're going to add

0:00:30.900,0:00:32.110
to whatever we get over here.

0:00:32.110,0:00:35.980
So this is these two terms[br]that I'm adding together.

0:00:35.980,0:00:39.770
Negative 7 minus[br]3 is negative 10.

0:00:39.770,0:00:42.610
So it's negative 10 over 6.

0:00:42.610,0:00:45.230
And then I'm going to have[br]to add that to negative 3/4.

0:00:45.230,0:00:52.550


0:00:52.550,0:00:56.620
And now I have to worry about[br]finding a common denominator.

0:00:56.620,0:01:02.800
Let me write that so[br]they have a similar size.

0:01:02.800,0:01:05.390
So now I have to worry about[br]finding a common denominator.

0:01:05.390,0:01:09.690
What is the smallest number that[br]is a multiple of both 4 and 6?

0:01:09.690,0:01:11.620
Well, it might jump out[br]at you that it's 12.

0:01:11.620,0:01:14.040
You can literally just go[br]through the multiples of 4.

0:01:14.040,0:01:15.890
Or you could look at[br]the prime factorization

0:01:15.890,0:01:16.850
of both of these numbers.

0:01:16.850,0:01:18.308
And what's the[br]smallest number that

0:01:18.308,0:01:20.950
has all of the prime[br]factors of both of these?

0:01:20.950,0:01:25.380
So you need two 2s, and[br]you need a 2 and a 3.

0:01:25.380,0:01:29.570
So if you have two 2s and a[br]3, that's 4 times 3 is 12.

0:01:29.570,0:01:34.520
So let's rewrite this[br]as something over 12

0:01:34.520,0:01:37.500
plus something over 12.

0:01:37.500,0:01:40.760


0:01:40.760,0:01:43.000
Well, to get your[br]denominator from 4 to 12,

0:01:43.000,0:01:44.860
you have to multiply by 3.

0:01:44.860,0:01:47.410
So let's multiply our[br]numerator by 3 as well.

0:01:47.410,0:01:50.120
So if we multiply[br]negative 3 times 3,

0:01:50.120,0:01:52.130
you're going to have negative 9.

0:01:52.130,0:01:54.260
And to get your[br]denominator from 6 to 12,

0:01:54.260,0:01:56.270
you have to multiply by 2.

0:01:56.270,0:01:58.322
So let's multiply our[br]numerator by 2 as well so

0:01:58.322,0:02:00.280
that we don't change the[br]value of the fraction.

0:02:00.280,0:02:02.890
So that's going[br]to be negative 20.

0:02:02.890,0:02:04.490
And now we're ready to add.

0:02:04.490,0:02:07.380
Our common denominator is 12.

0:02:07.380,0:02:12.690
And so this is going to be[br]negative 9 plus negative 20,

0:02:12.690,0:02:15.531
or we could even write[br]that as minus 20,

0:02:15.531,0:02:18.780
over 12, which is equal to--[br]and we deserve a drum roll now.

0:02:18.780,0:02:23.980
This is negative 29 over 12.

0:02:23.980,0:02:26.980
And 29 is a prime[br]number, so it's not

0:02:26.980,0:02:30.090
going to share any common[br]factors other than 1 with 12.

0:02:30.090,0:02:34.794
So we also have this in[br]the most simplified form.

0:02:34.794,0:02:35.294