- Let'ssee if we can figure out what 2/3 divided by five is equal to. Pause this video and seeif you can figure this out. Well, there is a couple ofways that we can approach it. We can first do it in a conceptual way, think about it visually. To do that, let me represent 2/3, so let's say that what I'm drawing right over here is a whole. This is a square, andit represents a whole. Now, I can divide intothree equal sections. I'm gonna try to hand-draw that. So, this is, that looks pretty good, three equal sections here. Each is 1/3, and we have 2/3, so we are really representing all of this stuff right over here. That is two of my thirds. Now, I wanna divide those 2/3 by five. Well, the way I could do this is I could divide it intofive equal sections. But, if I'm doing it, I might as well just divide everything, all the thirds, into five equal sections,so let me do that. So, one, two, three, and thenfour, and five equal sections. So, what is one of thosefive equal sections of my original 2/3? Well, this right over here is one of those five equalsections of my original 2/3. Notice I could draw that, Icould draw another one here, another one here, another onethere, and another one there, and I would have five equalsections that make up those 2/3. But, what does just one of them represent? And if we figure out whatthis represents of the whole, then we know what 2/3 divided by five is. Well, when I took mythirds and I divided them into five equal sections, Iessentially constructed 15ths. How do I know that? Well, I had one, two, three thirds, and then I divided it into one, two, three, four, five sections, so each of these squaresright over here is a 15th. You have three times five, and you could count 'em if you like. And, what we have circled offin red is two of these 15ths. We have 1/15 right over here, and then 2/15 right over there. So, this is going to be equal to 2/15. Now, another way thatyou could think about, and over time this is theway you will approach it, but it's nice to thinkabout it conceptually, when you divide by any number, it's the same thing asmultiplying by the reciprocal. So, five is the same thingas five wholes, or 5/1. And so, 2/3 divided byfive is the same thing as 2/3 times the reciprocal of five, or the reciprocal of 5/1,which is you just swap the numerator and thedenominator, which is 1/5. And so, another way ofthinking about this is this is 1/5 of 2/3, whichit once again will be this section right over here. The way you could compute this, conceptually, you see that this is 2/15, but you could also say well,I could just multiply it. When I multiply fractions I can just multiply the numerators. Two times one is two. We do that same red color. Two times one is two, and then I could multiplythe denominators. Three times five is 15.

And, hopefully, what we just drew out may help make sense ofwhy dividing by something is the same thing asmultiplying by the reciprocal. Then, when you multiply fractions, it's the same thing asmultiplying the numerators to get our new numerator,and then multiplying the denominators to getour new denominator.