Whole number divided by a fraction example

Let's see if we can figure out what four divided by two-thirds is. And like always, pause this video and see if you can figure it out on your own.

Well, one way to approach it is to realize that this is the same thing as four times the reciprocal of two-thirds. So, it'd be four times three over two.

And what is this going to be equal to? You could pause the video again if you're so inspired. Well, what you need to realize is this is the same thing: 4 could be written as a fraction as 4 over 1. So, 4 over 1 times 3 halves.

And we've multiplied fractions before. To do that, you just multiply the numerators: 4 times 3 is equal to 12, and you multiply the denominators: 1 times 2 is equal to 2.

12 halves, well, that's the same thing as 6. This is the same thing as 12 divided by 2. But a key question is: why does this make sense?

You know, I said dividing by something is the same thing as multiplying by the reciprocal. And to think about that, let's draw four holes. So, let me draw it in the same red color.

So, let's say that this is one hole right over here. This is two holes, this is three holes, and then this is four holes. So, I have four holes there, and imagine splitting it up into groups that are each two-thirds of a whole.

So actually, let me just divide everything into thirds real fast. I'm going to divide everything into thirds. So, I'm going to make each group a different color.

So, here's one group that is two-thirds. Here is another group that is two-thirds. Here is another group that is—or another section that I could say that represents two-thirds.

Here is another section that represents two-thirds. Here is another section, folks. Let me do that in a different color. Here is another section that can represent two-thirds.

If I take those two blue thirds together, that's two-thirds. And then, last but not least, I have another two-thirds. So, how many sections that are each two-thirds large do I have?

Well, I have one, and then this is two, and then I have three, and then I have four. And then these two combined make my fifth section that is two-thirds large.

And then finally, I have six. So, I have six. I can take four holes and split it into six equal sections that are each two-thirds of a whole.

So, four divided into sections that are two-thirds of a hole, you will get six sections.