WEBVTT
1
00:00:00.000 --> 00:00:07.000
Alright, what I'd like to do is show you how to solve an equation with fractional coefficients.
2
00:00:07.000 --> 00:00:16.000
First one on the problem, on a two-step problem, what I've taught you before is to always do your inverse operations.
3
00:00:16.000 --> 00:00:21.000
So you're going to subtract or add first and then we do our multiplication multiplied by.
4
00:00:21.000 --> 00:00:25.000
So what you could do is go ahead and subtract two-thirds on both sides.
5
00:00:25.000 --> 00:00:30.000
And that would go ahead and once you can get you can subtract your two-thirds on both sides.
6
00:00:30.000 --> 00:00:34.000
And then you go ahead and you know multiply to get your answer.
7
00:00:34.000 --> 00:00:36.000
So actually you know let me just go ahead and do this on the other side.
8
00:00:36.000 --> 00:00:43.000
And I'm going to actually show you an easier method without fractions for those of you that are definitely scared of them.
9
00:00:43.000 --> 00:00:48.000
Our old method applies. Since we're adding our two-thirds to the k, you subtract two-thirds.
10
00:00:48.000 --> 00:00:56.000
Okay, so I get 5, 6, k equals two-thirds.
11
00:00:56.000 --> 00:01:03.000
Then I'm now multiplying a 5, 6 times k. So I'm going to divide by a fraction.
12
00:01:03.000 --> 00:01:14.000
But we like to say, we like to use instead divided by a fraction. We just multiply by the reciprocal.
13
00:01:14.000 --> 00:01:25.000
Therefore, this can't allow k now equals 12 over 15, which can reproduce down to 4th.
14
00:01:25.000 --> 00:01:30.000
Okay, so let's go and double check to see if our answer is going to make sense over here.
15
00:01:30.000 --> 00:01:34.000
Rather than using these fractions, I don't like dealing with fractions. This is perfectly correct.
16
00:01:34.000 --> 00:01:38.000
However, if I'm going to solve this problem, I want to get rid of the fractions.
17
00:01:38.000 --> 00:01:47.000
So if I notice that this problem is divided by 6, I want to make sure what I'm going to do is I'm going to multiply everything by our common denominator.
18
00:01:47.000 --> 00:01:51.000
And what that's doing is that's kind of undoing the division that's happening in each 20 fractions.
19
00:01:51.000 --> 00:01:55.000
So if I look at the common denominator between all three of these fractions is 6.
20
00:01:55.000 --> 00:02:04.000
So if I multiply every fraction by 6, what I've just done is now eliminated,
21
00:02:04.000 --> 00:02:09.000
eliminating our fractions. 6 divided by 3 is 2. That's what I post that up there.
22
00:02:09.000 --> 00:02:21.000
So now I have 5k is equal to, I'm sorry, 5k plus 4 is equal to 8.
23
00:02:21.000 --> 00:02:34.000
All right, so now I subtract the 4 on both sides. 5k equals 4 divided by 5.
24
00:02:34.000 --> 00:02:37.000
Okay, equals 4th. So you guys have two different methods to solve for this.
25
00:02:37.000 --> 00:02:42.000
You can solve your traditional way with fractions. You all know how to solve for fractions by now.
26
00:02:42.000 --> 00:02:50.000
So this method does work. Another way to get rid of the fractions is multiply by your common denominator to every term.
27
00:02:50.000 --> 00:02:52.000
And then go ahead and solve this as well.
28
00:02:52.000 --> 00:03:21.000
All right, so that's how you solve an equation with fractional coefficients.