If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains ***.kastatic.org** and ***.kasandbox.org** are unblocked.

Main content

Current time:0:00Total duration:5:07

CCSS.Math:

I have an interesting rate problem here and at first 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 use 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 3/5 of his bathroom with one third of a bottle how do we think about this and what my brain does is I like to say well how would we like to answer the question what fraction of the bottle of cleaning solution will Calvin use to clean his entire bathroom so we want to figure out is we want to figure out how many bottles so question mark question mark bottles bottles / let me write it this way so we want to figure out he uses a certain number up with that question mark bottles bottles / 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 / bathroom it might be two bottles per bathroom but if we know whatever this question mark is and we know the answer how many bottles doesn't need to take to clean a bathroom or what fraction of a bottle we don't know that they're 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 bathroom and the reason why this is helpful it makes it clear that look we want to figure out we want to take our unit to 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 a certain fraction of the bathrooms and they tell us over here they tell us that it 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 it makes it clear that we need to take the 1/3 and divide it by 3/5 because then we're going to get bottles per bathroom we're gonna get the rate we're not going to get bathrooms per bottle we're gonna 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 1/3 and divided it by 3/5 so this is going to be equal to this is going to be equal to I can write it this way 1/3 divided by 3/5 divided by 3/5 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 can just say bottle per bathroom bottle for bathroom and so this is going to be the same thing as well we're gonna have 1/3 divided by 3/5 is the same thing as 1/3 times the reciprocal of 3/5 so 1/3 times 5/3 one-third times 5/3 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 3 times 3 is Knights 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 five ninths of a bottle / bathroom so just as a reminder of what we did here it could see him a little bit daunting but we said okay look he we want how much I'm 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 bottled / bathrooms that's gonna give us the correct rate so 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