Example dividing a whole by a unit fraction

Let's think about what 3 divided by 1/4 is equal to. Pause this video and see if you can figure it out on your own. And I'll give you a hint: take three holes and divide it into pieces, or sections, that are each one-fourth of a hole. Then think about how many sections you have.

All right, now let's work through this together. Now let me draw three holes. And so let's say, this is — I'm going to hand draw it, so it's not going to be perfect — but let's say that is one hole right over there. This is two holes right over there, and then I have my third hole just like that.

Now I'm going to divide it into pieces that are, or sections that are, each one-fourth of a hole. So this first hole is four pieces that are each one-fourth each, or four-fourths. And then I have another four-fourths right over here. And then I have another four-fourths right over here.

Another way to think about it is I took the three holes and I divided it into fourths. So if you divide it into fourths, how many pieces am I going to have? Well, this is pretty straightforward. You have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 pieces. And I didn't even have to count that; each hole is going to be four fourths. So three holes is going to be three times four fourths, or 12 pieces, or 12 sections.

So that is going to be equal to 12. Another way to think about it is if you take three and you divide it into equal sections that are each a fourth, you're going to have 12 equal sections.