Separating parts referring to the same whole.
4th grade build and decompose fractions plus#
4 plus 3 plus 1 is 8, so you getĨ/8 which is this entire whole.Model and justify decompositions of fractions and explain addition and subtraction of fractions as joining or To get, in terms of eighths, 4/8 plus 3/8 Together, 4/8 plus 3/8 plus 1/8, you are going
Of why that worked, 1/2 is the same thingĪs 4/8- because you see that, we filled in theĤ/8- then you have 3/8, and then you have 1/8. Now, you see, you could makeĪnother whole out of 1/2, plus 3/8, plus 1/8, and And you see that if 1 timesĢ is 2, 4 times 2 is 8. If you took this 1/4Īnd split it into two, so you have two times as And notice, you see that theĢ/8 is the same thing as 1/4. And then let's add anotherĮighths right over here, so 2/8 is going toīe two of these. To be this one right over here, so that's my 1/8. I want to make this one a whole,īecause I want to get to 2, so let me put in a 1/8 there. Now, what's 8/8? Well, 8/8 is a whole, and However I want, but let me just put this as 1, 2, and 3. So what would 3/8 look like? Each of these boxesĪre literally an 1/8 and I could fill it in In four out of the eight sections, which is exactly Sections right over here, 1/2 would be this So how else could we do it? And I'm just going to throwĪ bunch of fractions up there and see what I get. You might notice that Iįilled in two of the eighths, and that's because 1/4Īnd 2/8 is the same thing. So one of those four to beįilled in, just like that. This last hole, is divided into 8 sections. Over here is 2, 2 holes, so let me paint that in. So hopefully that helps give you a visual understanding of what we're doing when we're adding and decomposing these fractions a little bit more.Ībout different ways to represent a mixed number. 4 plus 3 plus 1 is 8, so you get 8/8 which is this entire whole. And if you add all of these together, 4/8 plus 3/8 plus 1/8, you are going to get, in terms of eighths, 4/8 plus 3/8 plus 1/8 is going to be 8/8. And just to make sense of why that worked, 1/2 is the same thing as 4/8- because you see that, we filled in the 4/8- then you have 3/8, and then you have 1/8. Now, you see, you could make another whole out of 1/2, plus 3/8, plus 1/8, and they add up to a whole. You see the 8/8 is the same thing as a whole. And you see that if 1 times 2 is 2, 4 times 2 is 8. If you took this 1/4 and split it into two, so you have two times as many pieces, it becomes 2/8. And notice, you see that the 2/8 is the same thing as 1/4. Well, this is in eighths right over here, so 2/8 is going to be two of these. And then let's add another 2/8, plus another 2/8. So plus 1/8, well, that's going to be this one right over here, so that's my 1/8. I want to make this one a whole, because I want to get to 2, so let me put in a 1/8 there. So I have a whole hole here, so that's 8/8. I still haven't filled this one in yet, but I'll fill in this one right over here. Now, what's 8/8? Well, 8/8 is a whole, and I'll do that over here. So what would 3/8 look like? Each of these boxes are literally an 1/8 and I could fill it in however I want, but let me just put this as 1, 2, and 3. And you see that I just filled in four out of the eight sections, which is exactly half of this first hole. So I'm first going to add 1/2, which is the same thing as 4/8. So how would I represent 1/2 here? Well, if I take one of these holes and I put it into two sections right over here, 1/2 would be this section right over there. So the first thing I'm going to throw out is 1/2. So how else could we do it? And I'm just going to throw a bunch of fractions up there and see what I get. So there I've represented this mixed number, 2 and 1/4.
You might notice that I filled in two of the eighths, and that's because 1/4 and 2/8 is the same thing. So one of those four to be filled in, just like that. So we want one of those four to be filled in- one of those four in orange. So this last piece, this last hole, is divided into 8 sections. And then this right over here is 2, 2 holes, so let me paint that in. So the 2 is this whole region right over here, that's 1. We've cut it up into sections of 8, so it literally is 8/8. You could literally view that if you want. So let's first think about the whole number part, the 2. Actually, let's make it a little bit more interesting. And let's say that our mixed number is 2 and 1/8. Let's now think about different ways to represent a mixed number.
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