Rates with fractions

It's a little daunting because it has fractions, but then when we work through it step-by-step Hopefully, it'll feel a little bit more intuitive so it says Calvin cleans three-fifths of his bathroom with one third of a bottle of cleaning solution at this rate What fraction of the bottle of cleaning Solution will Calvin used to clean his entire bathroom? And like always encourage you to pause the video and try to take a stab at this yourself So as [I] mentioned it's a little bit You know it's a three-fifths of his bathroom with one third of a bottle How do we [think] about this and what my brain does is I'd like to say well How would we like to answer the question what fraction of the bottle of cleaning solution will Calvin used to clean his entire bathroom? So we want to figure out is we want to figure out how many bottles so?? bottles bottles Per let me write it this way So we want to figure out he uses a certain number up with that question mark bottles bottles per Bathroom if we knew this then we have the answer to the question if this would this might be I don't know [two-fifths] Bottles two-fifths of a bottle per bathroom it might be two Bottles per bathroom, but if we know whatever this question mark is then we know the answer How many bottles does he need to take to clean a bathroom or what fraction of a bottle? We don't know, they're hinting that it's a fraction of a bottle but how much of a bottle or how many bottles per bathroom? Or another way to think about this if we want to know if We wanted to express it as a as a rate more mathematically. We could say "question mark bottles bottles per bathroom" and the Reason why this is helpful It makes it clear that look we want to figure out we want to take our Units tell us that we want to divide the number of bottles or the fraction of a bottle it takes To clean the number of bathrooms or certain fraction of the bathrooms. And they tell us over here they tell us that he's able to take one third of a bottle He's able to take one third of a bottle so I could write it here "one third of a bottle to clean to clean three-fifths of a bathroom" three-fifths of a bathroom three-fifths of a bathroom So hopefully it's clear now. Why this was helpful? We say okay, We want to take how many bottles it takes to clean a certain number of bathrooms one third of a bottle take can clean three-fifths of a bathroom and makes it clear that we need to take the one-third and Divide it by three-fifths because then we're going to get bottles per bathroom. We're going to get the rate We're not going to get bathrooms per bottle, we're going to get bottles per bathroom Which is what we care about what fraction of the bottle will It will it take to clean entire bathroom to clean one entire bathroom? So now we just have to take one-third and divide it by three-fifths So this is going to be equal to this is going to be equal to you can write it this way one third divided by three-fifths Divided by three fifths and the units are going to be bottles per bathroom. I'll write it like that Bottles or since if we know that that's going to be a fraction. We could just say bottle per bathroom bottle Bathroom and so this is going to be the same thing as well we're going to have one third divided by three fifths is the same thing as One third times the reciprocal of three fifths, so one-third times five thirds one third times five thirds Bottle per bathroom, so let me write that down bottle per bathroom Bottle per bathroom and what is this going to be? Well, We multiply the numerators 1 times 5 is going to give us 5 and the denominator three times three is ninths There's going to be five ninths of a bottle of a bottle per bathroom Bathroom I wrote these a little bit further apart than I would want to let me write that a little bit closer together five ninths of a bottle per bathroom So just as a reminder of what we did here It could see him a little bit daunting But we said okay look we want how much, what fraction of the bottle to clean his entire bathroom So we care about bottles per bathroom or since we're talking about a fraction I guess we could just say bottle some fraction of a bottle per bathroom so it's bottle divided by Bathrooms that's going to give us the correct rate So it took one third of a bottle to clean Three-fifths of a bathroom so you divide one third by three-fifths You get five ninths of a bottle per bathroom, so this question mark right over here that is five ninths, it takes five ninths of a bottle of cleaning solution to clean his entire bathroom