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Intro to rates

Sal introduces rates using examples like 35 miles per hour and 10 dollars per hour.

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  • blobby green style avatar for user Isabella Betteh
    What is the easiest method for solving rates
    (38 votes)
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  • piceratops tree style avatar for user Jo21Mixels
    What is the difference between a rate and a unit rate mathematically?
    (23 votes)
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    • duskpin ultimate style avatar for user Ruchita Patel
      Just like a unit fraction when the numerator is 1, representing 1 piece of the whole, a unit rate is when the rate is representing 1 quantity of the rate. Take this problem as an example: Jake worked at a bakery. He earns $80 every 4 hours. How much does he earn every hour? The ratio of hours to money is 4:80, so to get the unit rate we have to divide by four which gives us . He earns $20 per hour. So, in this problem the unit rate was . Hope this helped!
      (sorry about the , it isn’t meant to be a benchmark)
      (13 votes)
  • duskpin ultimate style avatar for user Saima
    what is the difference between rates and unit rates?
    (8 votes)
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  • starky tree style avatar for user EpicPhantom
    Because the rate in which you are doing something changes, do you take the average?
    (17 votes)
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  • female robot ada style avatar for user anish
    HI! I'm confused. I don't understand what the difference is between *ratio and rates.* Aren't they basically the same thing?
    (10 votes)
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  • duskpin seedling style avatar for user alec reed
    The following table shows how many multiplication problems 4 students were able to solve in different amounts of time. For example, Murray solved 58 problems in 2 minutes.
    Student Problems Minutes
    Murray 58 2
    Kris 78 3
    Logan 84 3
    Taylor 92 4 Which student solved problems at a rate of 28 per minute?
    Choose 1 answer:
    (8 votes)
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  • duskpin ultimate style avatar for user Ƹ̵̡Ӝ̵̨̄Ʒ꧁𝕃𝕚𝕝𝕪 ℍ꧂ ฅ^•ﻌ•^ฅ
    What is the easiest way to do this (and a 5th grader can understand it)🤔??
    (6 votes)
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    • leafers sapling style avatar for user Addie
      This is the way I learned it, and I hope this helps. Say you are going on a vacation. You know that it takes two hours to go 50 miles, and that you will be traveling 120 miles. You need to figure out how long it will take you to go 120 miles. It takes 2 hours for 50 miles, so you would write it as a fraction. 2/50. You don't know the amount of time it will take you to go 120 miles, so the time is your variable, x. x/120.
      Next, you would set it up in an equation.
      2/50 = x/120
      Now you need to pair the 2 with the 50 and the 120 with the x. In every equation like this, you will always pair the first number with the variable and the second number with the third number. Now the equation looks like this:
      50x = 2 x 120. All you have to do now is multiply the right side and divide it by the coefficient (the number next to the variable)
      2 x 120 = 240
      240 divided by 50 = 4.8
      This gets rid of the 50, leaving you with x = 4.8.
      It takes 4.8 hours to go 120 miles.
      (9 votes)
  • female robot grace style avatar for user inquisitivechild
    How would I solve this?: A bus leaves Oak City at AM traveling at a speed of 45 mph. 25 minutes later, a car leaves Oak City in the same direction as the bus at 60 mph. At what time would the car catch up with the bus?

    Answer choices:
    A) AM
    B) AM
    C) AM
    D) AM
    E) AM
    (4 votes)
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    • cacteye green style avatar for user Nights Dawn
      This is the way I would do it:

      Let's say "t" is the number of minutes the bus drove until the car caught up.

      Distance bus drove: 45 mph * t
      Distance car drove: 60 mph * (t - 25 mins)

      The distance the bus drove at time "t" is the same as the distance the car drove, because they start at the same location.
      ==> 45 * t = 60 * (t - 25)
      <==> 45t = 60t - 1500
      <==> 1500 = 60t - 45t = 15t
      <==> 100 = t

      The car caught up after 100 minutes. Apply that to the starting time am:
      ==> Answer is B, am
      (10 votes)
  • blobby green style avatar for user chloe
    What is the most common or useful method
    (7 votes)
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  • duskpin seedling style avatar for user aminmehwish
    Is it possible to simplify rates? Because I found you can simplify ratios. So, since the ideas are so similar you should probably be able to do some of the same stuff with them, right?
    (6 votes)
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    • stelly blue style avatar for user Kim Seidel
      Yes, you can simplify rates just like you do ratios.

      However, if you are working with unit rates, the process is a little different. With unit rates, we force the denominator to = 1. For example, if you drive 250 miles in 5 hours and you need the unit rate of miles per hour, you divide 250/50 = 50 miles per hr.

      Hope this helps.
      (2 votes)

Video transcript

- [Voiceover] 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 M-P-H, where the M-P-H stands for 35 miles per, per hour. Well, what's that saying? That's saying, well, every hour, how many miles are you going if you were to stay at that current rate. So, 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. And, it doesn't have to be even distance per unit time, you might have a, you might have your hourly rate for someone who is 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 the units become a little bit more obvious, 10 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, or it could be meters per second, or, in this case, it could be a wage, it could be dollars per hour. Rates don't have to be just in those terms. In fact, you might say, "All right, "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 serving. And they'll tell us what a serving is. A serving might be a cup or eight ounces or whatever else. And, so, I could say, "Okay, look, if I have two servings, "then I'm gonna have 400 calories. "Same way, if I work two hours, I'm gonna have 20 dollars. "If I, or if I go two hours, "I'm gonna go 70 miles." So, rates give you a sense. It's like, how fast is something happening? Or how much of one thing is happening for every time something else happens? Now, I can write rates so they look an awful lot like a ratio. And, these words are, actually, very related, 'cause you see that even how they're written. R-A-T, R-A-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, I went 35, "the ratio miles to hours "was 35 to one." Or it could have been, maybe it was 70 to two or something like that. But, that could have been reduced to 35 to one. 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 one 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're 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 would be hard to quantify how fast things are happening. Otherwise, we'd be in a world where 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 can quantify exactly how fast that thing is happening, the rate at which it is happening. Here, instead of saying, "Hey, a cup of that "is gonna give you, is gonna give you more energy, or, maybe, contribute more to your weight than a cup of that, and making these relative comparisons, here, you can actually, you can actually quantify things. And when we study rate, we're gonna study rate a lot in mathematics. It's gonna 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 gonna call that "slope". And you can even imagine the slope of a hill as how fast is it climbing for as much as you move forward. But we're also gonna 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.