Dividing a whole number by a fraction

- Let's see if we can figure out what 4 divided by 2/3 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 4 times the reciprocal of 2/3. So it'd be 4 times 3 over 2, 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 3/2, 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. 12/2, 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 wholes. So let me draw it in the same red color. So let's say that this is one whole right over here. This is two wholes. This is three wholes. And then this is four wholes. So I have four wholes there. And imagine splitting it up into groups that are each 2/3 of a whole. So actually, let me just divide everything into 1/3s real fast. So I'm gonna divide everything into 1/3s, into 1/3s. So I'm gonna make each group a different color. So here's one group that is 2/3. Here's another group that is 2/3. Here is another group that is, or another section, that I could say, that represents 2/3. Here is another section that represents 2/3. Here is another section. Folks, let me do that in a different color. Here is, here is another section that can represent 2/3 if I take those two blue 1/3s together. That's 2/3, and then last but not least, I have another 2/3. So how many sections that are each 2/3 large do I have? Well, I have one, and then these is two, and then I have three, and then I have four, and then these two combined make a, make my fifth section that is 2/3 large, and then finally, I have six. So I have six. I can take four wholes and split it into six equal sections that are each 2/3 of a whole. So 4 divided into sections that are 2/3 of a whole, you will get 6 sections.