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## 7th grade (Eureka Math/EngageNY)

### Unit 1: Lesson 2

Topic B: Unit rate and constant of proportionality- Intro to rates
- Unit rates
- Solving unit rate problem
- Solving unit price problem
- Constant of proportionality from equation
- Constant of proportionality from equations
- Identifying constant of proportionality graphically
- Constant of proportionality from graphs
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)
- Comparing proportionality constants
- Compare constants of proportionality
- Interpret proportionality constants
- Interpret constants of proportionality
- Worked example: Solving proportions
- Solving proportions
- Writing proportions example
- Writing proportions
- Proportion word problem: cookies
- Proportion word problem: hot dogs
- Proportion word problems
- Equations for proportional relationships
- Writing proportional equations from tables
- Writing proportional equations
- Interpreting graphs of proportional relationships
- Identify proportional relationships from graphs
- Interpreting graphs of proportional relationships
- Interpret constant of proportionality in graphs

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# Interpret proportionality constants

Sal interpret what the constant of proportionality means in a context.

## Want to join the conversation?

- at3:10i don't understand why the answer isn't answer B. Can anyone help?(22 votes)
- It's SImple!
`d = 2c`

where`d`

stands for`dollar`

and`c`

stands for`cupcake`

.

Let's say we were given the value where`c = 1`

and we had to find`d`

, this means that we have to find the price of one cupcake. So let's substitute the value in the formula.`d = 2(1) = 2`

or it can also be written as`d = 2 * 1 = 2`

This also means that for each cupcake we are charged 2 dollars!**Remember**`2c`

in the formula doesn't mean**2 cupcakes**. It's that the**cupcakes are just being multiplied by 2***Hope you got it! Feel free to ask if you have any doubts!*(41 votes)

- I'm still really confused :/(12 votes)
- What do you need help with? (sry for the extremely late response)(3 votes)

- This whole concept confuses me. If d=2c, and if d is dollars, and c is cupcakes, the equation directly reads dollar equals two cupcake, which means that one dollar equals two cupcakes, so I should get two cupcakes for one dollar. Even if I divide d by two, I get d/2=c, and if I divide a dollar by two, I get 50 cents equals one cupcake. I just don't understand how Sal got the answer that it is two dollars per cupcake. I saw his formula but the formula doesn't make sense. Can someone please help?(9 votes)
- Necroposting, but maybe my comment will be helpful to others who go through this lesson at a later date. Let
**d**be*the amount of dollars to pay*and**c***the number of cupcakes*. Then**d=2c**can be interpreted as*the amount of dollars to pay is 2 times the number of cupcakes*. Hope this helps.(8 votes)

- bruh this is mad confusing.(12 votes)
- What specifically do you need help with?(0 votes)

- how would h equal 1/5(3 votes)
- It took me a while to understand this, too. I was reading the equation as a very direct statement instead of solving for d, which is probably what you are doing, too. Here's a breakdown:

d=5h

This seems like 1 of d (1 cm) is equal to 5 of h (5 hours), right? But that's not solving for d - that's assigning a value of 1 to d and then interpreting it as a statement rather than an equation.

d=5h

d (whatever this number is) is the equivalent of 5 of h. So, if h has a value of 1 (one hour), then to get the value of d, we have to multiply the value of h by 5. We are not saying literally 5 hours - we are saying the value of the depth in cm is the equivalent of 5 times the value of h.

So let's give h a value of 1, because each of h is a single hour. That means the equation reads like this: d = 5 x 1. This means the ratio of d to h is 5:1, or that the value of h is 1/5 that of d.

I hope this helps!(6 votes)

- All of this makes sense to me, but has anyone encountered the euro/dollar question in practice? I can't figure out how to solve it.

For those who haven't seen it, e (euro) = 17/20 d (dollar)

They then ask how many euros we need for one dollar, and vice versa.

I don't even know where to start... someone explain?(2 votes)- Take your equation and solve for "d". You would divide both sides by 17/20 or multiply both sides by 20/17. YOu end up with:

20/17 e (euro) = d (dollar)

This tells you 1 dollar = 20/17 euros or 1 3/17 euros.(4 votes)

- How does this work with fractions?(3 votes)
- but b kinda makes sense because you can sell cupcakes for a dollar which makes it more difficult and confusing to just pick A for some of ya saying "oh A dosn't makes sense" i know i said it to not putting any words into any bodys mouth just saying not confusing you just saying what comes to mind(3 votes)
- I've been having the hardest time with these. A ratio of 6 books to 21 dollars is a b:d ratio of6:21. But, the algebraic equivalent is not 6b=21d, but the opposite, 21b=6d. It seems counter-intuitive. I think the reason I've been confused is because I got used to doing something like 6/21 x b/d in dimensional analysis. But that's an expression rather than an equation. If I think of it as the equation 6/21 = b/d, then I can divide both sides by one of the units and get the rate/constant=. So, the heart of my confusion seems to be this question: why do I represent this idea of books to dollars as an inverted equation in linear algebra, but multiply quantities directly by their units as an expression in dimensional analysis? I think if I understood why these are opposite, I would stop making this silly mistake.(3 votes)
- 0:50this is confusing because d is already 1d so 1cm therefore it should take 5 hours. 1d=5h.(3 votes)
- We are trying to solve for h. I believe that you have a typo. The correct equation is actually 1 = 5h, in which h=1/5.(0 votes)

## Video transcript

- [Instructor] We can
calculate the depth d of snow, in centimeters, that
accumulates in Harper's yard during the first h hours of a snowstorm using the equation d is
equal to five times h. So d is the depth of snow in centimeters, h is time that elapses in hours. How many hours does it take
for one centimeter of snow to accumulate in Harper's yard? Pause this video and see
if you can figure that out. All right so we wanna figure out what h gives us a d of one centimeter. Remember d is measured in centimeters. So we really just need
to solve the equation one centimeter, when d is equal to one, what is h going to be? And to solve for h we just need to divide both sides by five. So you divide both sides by five, the coefficient on the h, and you are left with h is equal to 1/5. And the unit for h is hours, 1/5 of an hour. So 1/5 of an hour. If they had minutes there, then you would say well 1/5 of an hour, there's 60 minutes,
well this is 12 minutes. But they just want it
as a number of hours, so 1/5 of an hour. How many centimeters of snow accumulates in per hour? Or this is a little bit of a typo. How many centimeters of snow accumulate in we could say one hour, in one hour, or they could have said how many centimeters of
snow accumulate per hour. That's another way of thinking about it. So we could get rid of per hour. So pause the video and see
if you can figure that out. Well there's a couple of
ways to think about it. Perhaps the easiest one is to say, well what is d when h is equal to one? And so we could just say d when h is equal to one, when only one hour has elapsed, well it's going to be five times one which is equal to five, and our units for d are in centimeters. So five centimeters. Let's do another example. Betty's Bakery calculates
the total price d in dollars for c cupcakes using the equation d is equal to two c. What does two mean in this situation? So pause this video and see if
you can answer this question. So remember d is in
dollars for c cupcakes. Now one way to think about it is, what happens if we take d
is equal to two times c, what happens if we divide both sides by c? You have d over c is equal to two. And so what would be the
units right over here? Well we have dollars, d dollars, over c cupcakes. So this would be $2, because that's the units
for d, per cupcake, dollars per cupcake. This is the unit rate per cupcake. How much do you have to pay per cupcake? So which of these
choices match up to that? The bakery charges $2 for each cupcake, yeah $2 per cupcake, that looks right. The bakery sells two
cupcakes for a dollar. No that would be two cupcakes per dollar, not $2 per cupcake. The bakery sells two types of cupcakes. No no we're definitely not
talking about two types of cupcakes, they're just
talking about cupcakes generally, or I guess one type of
cupcake, we don't know, but just cupcakes generally
is $2 per cupcake.