Adding and subtracting mixed numbers
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- [Voiceover] Let's get some practice subtracting mixed numbers. So let's say that I had 2 5/8 minus 1 2/8. What is this going to be? I encourage you to pause the video and try to work it out. Well, we can rewrite this, we could write the numbers on top of each other, we could say this is two, in that magenta color, say this is 2 5/8, actually let me write it a little bit further spaced apart, 2 5/8, minus 1 2/8. And then, we can subtract. We could say, okay look, in this column right over here, we are subtracting eighths. We have five eighths, and we're gonna subtract two eighths. If I have five of something and I'm gonna subtract two of them, I'm gonna have three of that something, and in this case we're talking about eighths. So five eighths minus two eighths is going to be three eighths, and then you have two ones minus one one, or two minus one, is going to be one. So this is going to be equal to one and three eighths. Now let's do something more interesting. Let's say that we had 3, I'm just going to make up a number here, 3 2/5 minus 2 3/5, and like always, pause the video and try to work it out. Let's try to work it out this exact same way. So I'm going to rewrite it as 3, let me do that same magenta color, changing colors, we have three and two over five minus two and three over five. Two and three over five. And when you first try to do it, over here you had 5/8 minus 2/8, that was easy to figure out, that's 3/8. But then over here, you have 2/5 minus 3/5. Well, that's hard! 3/5 is larger than 2/5. So what can you do here? Well one option is to regroup. Let's take one, from I guess you could say the ones place, here, so let's take one from this, and then that's going to turn into two. And then one is the same thing as 5/5. So two plus 5/5 is equal to 7/5. So another way of thinking about it, I'll do it over here, we could write, 3 2/5 is the same thing as 2 7/5. 2 7/5. These two things are equivalent. Why? Well I took one away from here to get to two, and then I added that one over here. One is same thing as 5/5. 2/5 plus 5/5 is 7/5. So now if we consider this thing to be 2 7/5, we're ready to subtract. If you say 7/5 minus 3/5, that's going to be 4/5. And then you have two minus two is zero ones, so you're just going to be left with 4/5. So this is just going to be 4/5. Let's do that again. Let's do one where we have to regroup again. And I'll just write it out in a column, up down, to begin with. Let's say that we have 7 1/6, minus 4 5/6. What is this going to be equal to? Well, when we try to subtract 5/6 from 1/6, well that's hard, 5/6 is larger than 1/6. But we can regroup. We could take one from here, so the seven becomes a six. And then we take that one, which is the same thing as 6/6, and add it to 1/6. So 1/6 plus 6/6, is going to be 7/6. Let me be clear what I did. I took one from the seven, and it became six, and one is equal to 6/6, and so I added 6/6 to that 1/6, and I got 7/6. So I took the one from here, and I added it over here, and the whole purpose is, now 7/6 is greater than 5/6. So 7/6 minus 5/6 is, I'll do that orange color, is 2/6, and six minus four is two. So it's gonna be 2 2/6, or, if we wanted to rewrite 2/6, you see they're both divisible by two, this is the same thing as 2 and 1/3 is equivalent to 2/6. So you could also write it like that.