All right, we're going to talk about addition and subtraction of fractions right now. And we've talked about addition. Basically, all we need to know is that for us to add or subtract a fraction, it must have a common denominator. I just like I show you here in these two examples, three sevens plus two sevens. So we have a common denominator or or the denominator on both fractions are seven, and we just add the numerator, three plus two is five. There you go.

All right, if we're going to subtract it, basically again, the same Deal. Okay, common denominator here is seven. All right, we want to subtract three sevens minus two sevens. So all we do is subtract three minus two in the numerator. And our answer is one, seven. That's it.

All right. In the next slide, we're going to see what happens if my denominators are different how I deal with that. So let's go on to the next slide now. All right, so fractions must have the same denominator before they can be added or subtracted. And again, this is called the common denominator. And if you look at this example, here, we right here, we want to add five twelves plus seven 18th.

Well, we just can't do that like we did in the previous slide. Why? Because the the denominators are different. So we got to find the common denominator and One of the ways that we do this and we recommend this way is to find multiples of the denominators. So for instance, we'll take five twelves. First multiples of 12 are 1212 plus 12 is 20.

For 12 plus 12 plus 12 is 3612 plus 12 plus 12 plus 12 is 4812 plus 12 plus 12 plus 12 plus 12 plus 12 is 60, and so forth. All right. So let's let's see what happens when we take multiples of 38. Well, we got 18, then 18 plus 18, is 36. And then 18, again, we add is 5418. Again, is 7218.

Again, is 90. All right, but look at what we got. We got common number that we can use for our denominator as 36. All right, so what did we need? What What did we need to do to get five twelves. To have a denominator of 36, well, we had to multiply 12.

Three times three times 12 is 36, just like we're showing here, so three times 12 is 36. So I multiply the denominator by by three three times again, three times 12 is 36. And what I do when the denominator I have to do the same thing to the numerator, all right, so now I have to multiply the numerator by three, so three times five is 15. I get 36 or 1536. All right, now let's work on seven 18th. Well, we have again, a common multiple of 36.

So how do I get to 36 in the denominator, I multiply that by two. So two times 32 times 18 is 36. What I do in the denominator, I have to do in the numerator. So now I have to multiply the numerator in this case, which is seven. So two times seven is 14. So now I have a common denominator and I can add these fractions.

So now we found our common denominator. And if you can see here, we got 1436 plus 1536. And we just add them up 14, or 15 plus 14 is 29. And we come out with 2936. So what we can say is, when I add 512 plus 718, my answer is 2936. And if we look at that it's in its lowest form.

2936 Is in its slowest form, there is no number that we can divide into both the numerator and the denominator to reduce that. Basically, the only thing that looks like it might would be three. So let's get out calculator. down and do that. So if I take three and divide that into 36 well I get 12. Okay, and let's see what happens when I do 2929 divided by three.

And that's not gonna work. Okay, because that's a decimal fraction. We need a whole number. So we're at our simplest form. That's the answer. 512 plus 718 equals 2936.

Okay, I want to introduce something here called an improper fraction. And when the numerator equals our exceeds the denominator Well, it's improper. Give you an example here five thirds. Well, the numerators five, the denominator is three, five exceeds three, so it's an improper fraction. So what we need to do is to get it into the correct form, we need to convert it into what we call a mixed fraction over here. And basically all we do is in this example, and I'm showing you right here as I divide three into five, all right, and just do the math, as I'm showing here.

So three goes into five one time. three minus five minus three is two, with a remainder of two, I should say. So the answer here is one and two thirds. So five thirds equals one and two thirds. All right, this number here One in two thirds is called a mixed fraction and I've got a mistake in there. That shouldn't be a 397.

I'll correct it when we finished this slide, but that should be a three. Okay, so with that, let's move on to the next slide. Okay, hit hit the pause button for the slide. I just take a couple of minutes and change each improper fraction to a mixed number I, and the answers will be on the next slide. All right, here are the answers. Seven over six is one and a sixth.

14 Thirds equals four and two thirds. six fifths equals one over a fifth. I mean one and one fifth. Nine fourths equals two and one fourth. All right, so I'm getting You have any problems, send me an email, give me a call. Let's go on to the next slide now.

All right, let's do some more problems. I'd like you to do the addition or subtraction of fractions. There's the problems right here. Again, the answers are on the next slide. So hit the pause button, do the problems. And then when you continue, the answers will be available to you.

All right, here are the answers for you. four nights in one plus one nine equals five nights. five nines plus four nines equals one, seven nines plus five nines equals one and one third. All right, that one third is to the simplest form. four nines minus two nights equals two nights. Five Nights minus four Nine c equals one night.

And here we have seven nights minus five nines plus three nights equals five nights. Okay, again, if you need help, need clarification, send me an email. You can see my numbers at the my help numbers at the beginning and the end of the slides. Give me a call. Talk to you soon. This is the last slide in this section.

All right, we're going on to a new section after this. All right, we're going to talk about reciprocals decimal fractions and and other things. So that will be the last one in the in this in this chapter. All right. Talk to you soon.