Dividing fractions and whole number word problems

We are told that Billy has one fourth of a pound of trail mix. He wants to share it equally between himself and his brother. How much trail mix would they each get? So pause this video and try to figure that out.

All right, now let's work through this together. Billy starts with one-fourth of a pound of trail mix. So how could we represent one-fourth? Well, if this is a whole pound, let's just imagine this rectangle is a whole pound. I could divide it into four equal sections. So let's see, this would be roughly two equal sections. And then, if I were to divide each of those into two, now I have four equal sections.

So, Billy is starting with a fourth of a pound. Draw a little bit, try to make it a little bit more equal. Billy is starting with a fourth of a pound, so let's say that is that fourth of a pound that he starts with. He's starting with one fourth of a pound, and he wants to share it equally between himself and his brother.

So he wants to share it equally between two people right over here. What we want to do is essentially say, let's start with our total amount of trail mix, and then we're going to divide it into two equal shares. So when they ask us how much trail mix would they each get, we're really trying to figure out what is this one-fourth divided by two.

So what would that be? Well, what if we were to take all of these four equal sections and divide them into two? I will divide that one into two. I will divide this one into two. I will divide this one into two, and then I would divide this one into two.

Now, what are each of these sections? Well, each of these are now one-eighth. That's a one-eighth right over there. These are the whole divided into eight equal sections. You can see that when you start with that one-fourth and you divide it into two equal sections, so one section and two equal sections right over there, each of those is equal to one-eighth.

So one-fourth divided by two is equal to one-eighth. Let's do another example. We are told Matt is filling containers of rice. Each container holds one-fourth of a kilogram of rice. Then they tell us if Matt has three kilograms of rice, how many containers can he fill?

So like always, pause this video and see if you can figure that out. All right, so let's think about what's going on. We're starting with a total amount—three kilograms of rice—and we're trying to divide it into equal sections. In this case, we're trying to divide it into equal sections of one-fourth of a kilogram.

So we are trying to figure out what three divided by one-fourth is going to be equal to. Now, to imagine that, let's imagine three wholes. This would be three whole kilograms. So that is one whole, this is two holes. I'm trying to make them all the same, but it's hand-drawn, so it's not as exact as I would like. So that's three whole kilograms here, and he wants to divide it into sections of one-fourth.

If you divide it into fourths, how many fourths are you going to have? Well, let's do that. So let's see, if we were to divide it into halves, it would look like this. If you divide these three wholes into halves, but then if you want to divide into fourths, it would look like this.

I'm trying to get it close to equal sections; they should be exactly equal sections. So I am almost there. So there you have it. I've just taken three wholes and I've divided them into fourths.

How many fourths are there? Well, there are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 fourths. So three divided by one-fourth is equal to twelve.

And I encourage you to really think about why this is the case. If you take a whole number like three and you divide it by one-fourth, we're getting a value larger than three, and we're getting a value that is four times three. Think about why that is the case.