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# Intro to rates

Rates are essential in understanding everyday situations, such as speed, wages, and food consumption. They help us measure and compare quantities, like miles per hour or calories per serving. Rates are closely related to ratios and play a significant role in math subjects like algebra and calculus, making them crucial for problem-solving and analysis.

## Want to join the conversation?

- What is the easiest method for solving rates(81 votes)
- You divide the numerator by the denominator. (The numerator is usually the variable y, while the denominator is usually the variable x.)(10 votes)

- What is the difference between a rate and a unit rate mathematically?(29 votes)
- 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 us1:20. He earns $20 per hour. So, in this problem the unit rate was1:20. Hope this helped!
*(sorry about the*1:20, it isn’t meant to be a benchmark)(31 votes)

- what is the difference between rates and unit rates?(14 votes)
- A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. ... When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.

sorry that is so long to read and you will probably think that is boring! ;)(52 votes)

- HI! I'm confused. I don't understand what the difference is between *ratio and rates.* Aren't they
*basically*the same thing?(19 votes)- They are similar, but ratios are just numbers, rates are numbers with some sort of units with them (miles per hour, tablespoons per teaspoon, etc.).(27 votes)

- Because the rate in which you are doing something changes, do you take the average?(21 votes)
- In the real world a rate (such as speed) is constantly changing.

So yes, you will have to average the speeds to find the average rate over a certain amount of time.(9 votes)

- What is the easiest way to do this (and a 5th grader can understand it)🤔??(10 votes)
- 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.(21 votes)

- 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:(10 votes)- To answer you question, just divide

Murray: 58/2 = 29 problems per minute.

See if you can find the rest and select the appropriate answer.(13 votes)

- How would I solve this?: A bus leaves Oak City at9:10AM 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)10:40AM

B)10:50AM

C)11:00AM

D)11:10AM

E)11:20AM(5 votes)- 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 time9:10am:

==> Answer is B,10:50am(14 votes)

- 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)
- 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.(7 votes)

- What is the most common or useful method(8 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.