Example diving a unit fraction by a whole number

So let's see if we can figure out what one-third divided by five is. And I'll give you a hint: try to draw out one-third of a whole and then divide it into five equal sections. Pause this video and try to do that.

All right, now let's try to work through it together. And to help us, as I promised or as I suggested, I guess we said, let's draw a third. So I will represent a whole by that square right over there.

Now let me split it up into three equal sections. So this is all hand drawn with the aid of a computer, so it's not going to be perfect. But let's say that that is three equal sections. It's roughly three equal sections. I didn't do it perfectly, but you hopefully get the idea.

And so one third would be one of those three equal sections. So that's a third right over there that I have just shaded in, and I want to divide it into five. Or I want to divide it by five, I should say. So let's do that.

To divide it by five, I'm going to divide it into five equal sections. If I'm doing, if I'm dividing that one into five equal sections, let me just divide all of the thirds into five equal sections. I'm essentially just going to make five rows here: one, and I'm going to eyeball it, so it's going to be approximate: two, three, and then four and five equal sections.

Notice I now split this whole into one, two, three, four, five rows of equal height. Now, if I go to my original third and divide it by five, I would be left with this right over here. But what fraction is this of the whole?

Well, what I've done now is I've split my whole into 15 equal sections. How do I know that? Well, I could count them: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Or you could just say, look, I had one, two, three thirds, and now each of those have been split into one, two, three, four, five equal sections.

So three times five is 15. So each of these is a fifteenth. And so the one-third divided by five is just one of those fifteenths. So that right over there is one of those fifteenths. So this is going to be equal to one fifteenth, and we are done.