Main content

### Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 1: Rate problems with fractions# Rates with fractions

Sal solves an example problem with rates with fractions.

## Want to join the conversation?

- What happens if there is a fraction that's like 4 3/4??(30 votes)
- you change the mixed number to a improper fraction 4 3/4=19/4(77 votes)

- who created math and why? what did we do to deserve this?(34 votes)
- to answer your question, who made math? = (The Sumerians were the first civilization to create a counting system. Many scientists concur that addition, subtraction, multiplication, and division are among the oldest and most fundamental mathematical operations, having been used for more than 4,000 years.)

why does math exist? = (It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math.)

what did we do to deserve it? = (My fellow friend, we did absolutely nothing to deserve it!)

hopes this helps!(49 votes)

- What is a reciprocal?

Is it just the reverse of something?(14 votes)- The reciprocal of a fraction is it flipped. For example, the reciprocal of 1/5 is 5/1 (which is 5.)

The reciprocal of an integer, is 1 divided by the integer. For example, the reciprocal of 5 is 1/5 and the reciprocal of 98 is 1/98(36 votes)

- Im still super confused💀(19 votes)
- me too bro these videos dont help(21 votes)

- I'm so confused...why am I dividing(16 votes)
- Since the question is asking "how many bottles will it take to clean the bathroom (or how many fractions of a bottle) " you need to divide the number of bottles per bathroom.

"per" just means divide.

Its like saying "I have 10 pickles and 2 jars. how many pickles will it take to fill each jar?"

simple, divide the number of pickles by the number of jars.

Except in the video, there are no pickles, and no jars. Instead, there are bottles of soap and bathrooms.

Hope this answer was helpful!(10 votes)

- math makes me want to cry(22 votes)
- fr bro whats the point in math(0 votes)

- Lets say hypothetically i have a missle on its way to europe and the mass is 1/4 of the weight how big of an impact will it have?(15 votes)
- How much charge did you give the missle? Not that it would help. I still couldn’t do it.(3 votes)

- math-

its hard

stressful

i cried in one of my classes

but think money

dividing or splitting money to your homies(10 votes) - why is math like this.(7 votes)
- this totlally makes sense. (dying on the inside as they fail for the 658th time at the exercise)(9 votes)
- yeah that is so true(1 vote)

## Video transcript

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