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let's think a little bit about what it means to multiply fractions say I want to multiply 1/2 times 1/4 well one way to think about this is we could view this as 1/2 of 1/4 and what do I mean there well let me take a whole let me take a whole here and let me divide it into fourths so let me divide it into fourths so I'll divide it into four equal sections and so 1/4 would be one of these four equal sections but we want to take 1/2 of that so how do we take half of that well we could divide this into two equal sections and then just take one of them so divide it into two equal sections and then take one of them so we're taking this pink area is 1/2 and we're going to take or say this pink area this whole pink area is 1/4 and now we're going to take half of it we're now going to take half of it so that's this yellow square right over here but what fraction of the whole does this yellow represent well it's now represents one out of one two three four five six seven eight equal sections so this right over here represents this represents one-eighth of the whole and so we see conceptually that 1/2 times 1/4 it completely makes sense that 1/2 of 1/4 should be 1/8 and it hopefully makes sense that you get this eight by multiplying the 2 times the four you started with four equal sections but then you divided each of those four equal sections into two equal sections so then you have eight total equal sections that you split your hole into let's do another example but now let's multiply two fractions that don't have ones in the numerator so let's multiply let's multiply 2/3 2/3 times times 4/5 and I encourage you now to pause the video and do something very similar to what I did just did try to represent 4/5 of a whole and then try to represent 2/3 of that 4/5 and see what fraction of the whole you actually have pause now so let's think about this let's represent 4/5 so if I have a hole like this let me try to divide it into five equal sections five equal sections so let's say that is one equal section that is two equal sections that is three four and five I can do a better job in distance is always the hard part drawing my best to make them look at least like equal sections two three four and five I think you get the point here I'm trying to make them equal sections and we want 4/5 so we want four of these five equal sections so this would be one of the five equal sections two of them three of them and then four of them so that right over there is 4/5 now we can view this as 2/3 of the 4/5 so how can we think about that well we could take this section and divide it into thirds so let's do that divide it into thirds so we're going to write it into three equal sections so that's one third and then two thirds so we took each of the five equal sections and we divided them into three equal sections now what's going to be 2/3 of the 4/5 well that's going to be that's going to be this part right over here so let me make this clear this this is one-third of the 4/5 and then if we could this would be 2/3 of the 4/5 so this right over here would be 2/3 of the 4/5 or 2/3 times 4/5 but what fraction of the whole does that represent well how many total how many total equal sections do we now have well we have one two three four five six seven eight nine ten 11 12 13 14 15 so we have 15 equal sections which is in the new color we have 15 equal sections and that makes sense we started with five equal sections but then we divided each of those into three equal sections so now we have five times three total equal sections and then how many of those are now colored in well we see it's two times four one two three four five six seven eight or how many how many of them are in the 2/3 of the 4/5 I should say and there's 8 of them 8 of the 15 equal sections and so there you have it it should hopefully now make visual sense or it makes conceptual sense that 2/3 times 4/5 you can obviously compute it by just multiplying the numerators 2 times 4 is 8 and then multiplying the denominators 3 times 5 is 15 but hopefully this down makes conceptual sense as 2/3 of 4/5