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what I want to explore in this video is the notion of a rate so let's look at some examples of rates that you've probably encountered in your everyday life so if you're driving in your car down the road and you're looking at the speedometer you might see that it says that you are going 35 mph where the mph stands for 35 miles per per hour well what's it saying that's saying well every hour how many miles are you going if you were to stay at that current rate so it's a it could be a measure of speed how much distance are you covering per unit time and most typically when people talk about rates that's what they're talking about they're talking about how much of something that is happening per unit time it doesn't have to be even distance per unit time you might have a you might have your hourly rate for someone who's doing some type of a job they might say that they're making they're making $10 so they're making $10 and actually let me write the dollars out so you'll be the unit's become a little bit more obvious ten dollars dollars per hour dollars per dollars per hour and so once again this is how much money it's not talking about distance anymore how much money is being earned per unit time and so even though rates are often associated with how much something is happening per some unit time and it could be miles per hour a court could be meters per second or in this case it could be your wage it could be dollars per hour rates don't have to be just in those terms in fact you might say alright I have a dessert that I really enjoy but I'm very conscientious about about the number of calories that I consume and you might you might see something like there are 200 calories calories per serving per serving and so this is telling us the number of calories per a certain they'll tell us what a serving is a serving might be a cup or 8 ounces or whatever else and so I could say okay look if I have two servings then I'm going to have 400 calories same way if I work two hours I'm gonna have 20 dollars if I or if I go to ours I'm going to go 70 miles so rates tell it give you a sense it's like how fast is something happening or or how much of one thing is happening for every time something else happens now I can write rate so they look an awful lot like a ratio and these words are actually very related because you see that even how they're written are a tra T their roots are coming from the exact same idea in fact this rate over here 35 miles per hour it could come from hey I just I just went 35 miles in one hour what's the ratio so the ratio of miles to hours and then you could say well if I went 35 well it's the ratio of miles to hours was 35 to 1 or it could have been maybe was 72 2 or something like that but that could have been reduced to 35 to 1 so as a ratio you would typically see it written like this or maybe see it written like see it written like this and sometimes you might even see it written like this 35 miles to 1 hour but now it's starting to resemble more of the special case of a ratio which we call a rate because this is the same thing as 35 instead of writing it out miles per hour you'll often see it written like this miles per miles per hour so these are very very related ideas if you find the ratio between calories and servings well then you're going to be able to write you you are going to be able to express it as a rate and vice versa now why do we care about rates well especially if we're thinking about things like speed without rates it'd be hard to to quantify how fast things are happening otherwise we'd be in the world we're saying hey I'm faster than you or she's faster than me but we wouldn't be able to quantify exactly how fast they are but with rates we can say hey that person ran a hundred meters in 10 seconds they run 10 meters per second we get and we get can quantify exactly how fasting that thing is happening the rate at which is happening here instead of saying hey a cup of that is going to give you it's going to is going to give you more energy or B you know or maybe contribute more to your weight than a cup of that and making these these relative comparisons here you can actually you can actually quantify things and when we study rate we're going to tell you rate a lot in mathematics it's going to be essential in algebra when we look at the rate of change of a line how far it moves in the vertical direction relative to the horizontal direction we're going to call that slope and you can even imagine a slope of a hill is kind of how fast is it climbing for as much as you move forward but we're also going to study rates in detail when we go to calculus in fact the whole basis of differential calculus that you might see later in high school and early college is all about measuring instantaneous rate how fast is something going right now so rates are really really interesting really really important and I would guess that if you just look around your life even over the next few hours you're going to encounter many many many rates