Visually dividing whole numbers by unit fractions

• [Narrator] If five is divided into pieces that are each one half of a whole, how many pieces are there? And this would be the equivalent of saying, "What is five divided by 1/2?" And they help us out with this visual. So pause this video and see if you can figure out what that is. How many pieces would you get if you divide five into pieces that are each one half of a whole?

All right, now let's work through this together. So here on this number line we go from zero to five, and then notice they've divided into pieces that are each a half of a whole. This is one piece right over here. So how many of those halves, so this right over here is one half, how many of those halves does it take to make five? Well, two halves make a whole, and we have five wholes. So it's going to be five times two, or 10. And we see that right over here. One half, two, three, four, five, six, seven, eight, nine, 10 halves make five wholes. So this is going to be equal to 10.

So five divided into pieces of one half, or five wholes divided into pieces of one half would be equal to 10 pieces. Let's do another example. So we have a similar question here. Here we're asked, "If three wholes are divided into pieces that are each 1/6 of a whole, how many pieces are there?" Once again, pause this video and think about it.

Well, they really help us out with this visual because we have three wholes. This is one whole, two whole, and then three wholes, and then we have divided them into pieces that are each 1/6 of a whole. This is a sixth right over here, this is a sixth right over here, so each of these are sixths. And so, if we look at this, we have six sixths in a whole, and so in three wholes we're gonna have six, 12, 18 pieces. And you could literally just count these up. But it makes sense. If you take three wholes and you divide it into sixths, so this is a sixth right over here, each of these wholes are going to be six sixths, so three wholes are going to be three times six sixths, or 18 sixths. There you go.