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Rate problems

In this math lesson, we learn to find unit rates and use them to solve problems. We first calculate the rate for one unit, like cars washed per day or cost per battery. Then, we multiply the unit rate by the desired quantity to find the answer. This method simplifies complex problems and helps us understand real-world situations.

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Video transcript

- [Instructor] So we're told that Lynnette can wash 95 cars in five days. How many cars can Lynnette wash in 11 days? So like always, pause this video and see if you can figure this out. So the way that I would like to tackle it is given the information they gave us, 95 cars in five days, can we figure out how many cars she can wash per day? How many cars in one day? And then we could just multiply that by 11 to figure out how many she could wash in 11 days. So there's 95 cars in five days and so instead of five, if we were to say one day, one day, well, to go from five days to one day, we divide by five. So the number of cars she can do in one day, that would be that divided by five. In either case, we would divide by five and what's 95 divided by five? You might recognize that well, look, five times 20 is equal to 100. So five times 19 is 95. So you might recognize that's 19 cars in one day or if that math I just did seems a little bit too fast, you could just take five into 95. Five goes into nine one time, one times five is five, subtract, nine minus five is four, bring down that five, five goes into 45 nine times, nine times five is 45 and it goes in perfectly. There's no remainder. So all I did is I divided both of these numbers by five to figure out how many she can wash per day. So she can wash 19 cars in one day, 19 cars per day and so if I wanna figure out how many she can wash in 11 days, so in 11 days, well, now, I am just multiplying by 11. So if I multiply 19 times 11, what am I going to get? Well, if you're good at the mental mathematics, you might recognize 19 times 10 would be 190 and then you would have one more 19 so that would be 209 cars or you could just multiply 19 times 11. One times 19 is 19 and then one times 19 is 19. Add 'em together, you get 209. So she can wash 209 cars in 11 days. Let's do another example. Here, we are told at the market, eight batteries cost $10. How much do six batteries cost? Once again, pause this video and try to figure it out. Well, I'm gonna do the same technique. If eight batteries cost $10, let's figure out how much one battery costs. So one battery costs what? Figure that out. Well, it's going to be 1/8th. To go from eight to one, I divide by eight. So what happens when I divide 10 by eight? That's gonna be my per battery cost. So 10 divided by eight is the same thing as 5/4 which is the same thing as one and 1/4 which is the same thing if we're talking in terms of money, it might be more useful to write it like one and 25 hundredths or one battery costs $1.25. And so when they're saying six batteries, how much do six batteries cost, well, if we're going to six batteries cost, we're multiplying the number of batteries times six now. So what's $1.25 times six? So it's gonna be $6 plus another $1.50 'cause six times 25 is 150. So it's gonna be $7.50 and just to make sure the math I just did was right, let's multiply $1.25 times six. Six times five is 30. Six times two is 12 plus three is 15. Six times one is six plus one is seven and we have a total of two digits behind the decimal so there you have it, you have $7.50. Now, there's other ways that you could tackle this. You could say that hey, this is, six batteries is gonna cost 6/8ths as much as eight batteries but that's a little bit confusing, at least for my brain. I like to go just down to the unit cost you could say, the cost per battery and then multiply it by six. It gives me more comfort in understanding what I'm doing.