Topic F: Addition and subtraction of fractions by decomposition
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- [Voiceover] Let's give ourselves some practice adding mixed numbers. So let's say I want to add two, let me write it this way. Let's say I want to add two and four sevenths plus three and two sevenths, three and two sevenths. I encourage you to pause this video and try to think about what this is going to be. Well there's a couple of ways that you could tackle it. One way, you could say, well let me just add the nonfraction parts. You could say that two plus three is equal to five, and then you could say that four sevenths plus two sevenths is equal to well four sevenths plus two sevenths is gonna be equal to six sevenths. Hey, wait, wait, wait, how did I, how did I do that? How did I just only add the fraction parts or add the whole parts? Well the way I did that is because two and four sevenths is the same thing as two plus four sevenths. Two and four sevenths, same thing as two plus four sevenths. And then plus three and two sevenths is the same thing as three plus two sevenths, so all I did over here, two and four sevenths plus three and two sevenths, is two plus four sevenths plus three plus two sevenths. And you can swap the order in how this happens. So you could take, you could just switch the order and say this is going to be two plus three, two plus three, plus four sevenths, plus two sevenths. And what we just figured out was that two plus three is equal to five, right over here, and that four sevenths plus two sevenths is equal to six sevenths, just like that. Now let's do a more interesting example. Let's do, let's say that I have three and three fifths, three and three fifths plus five and four fifths. Now what is this going to be equal to? Well if you do the same technique, if you add the three plus the five, you're going to get eight, and then if you add the three fifths plus four fifths, you would get seven fifths. So you get eight and seven fifths. And this wouldn't be wrong. This is eight and seven fifths, if you add these two things together, but it's a little bit strange here because seven fifths is bigger than a whole. So to get a better sense of what number's really being represented here, I want to rewrite this. So eight and seven fifths, this is the same thing as eight plus, and instead of seven fifths, we could say this is the same thing as five fifths, which is a whole, plus two fifths. Now why is that interesting? Because five fifths, notice five fifths plus two fifths, that's seven fifths right over there. Or you can consider five fifths to be one, so this is eight plus one, which is nine, and two fifths, nine and two fifths. So all I did here, I added it the same way that I did the first problem a few seconds ago. But when I realize this fraction part is greater than one, I separated it into one and then a fraction that is less than one, and that whole, I was able to add to the eight to get to nine, and then I would have two fifths left over. Eight and seven fifths, because five fifths is a whole, is the same thing as nine and two fifths. So if I wanted to write this in, I guess, a clearer way, I would say this is nine and two fifths. Three and three fifths plus five and four fifths is nine and two fifths, and once again, we say wait, three plus five is only eight, how did I get a nine? Well that's because three fifths plus four fifths is greater than one.