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### Course: 7th grade > Unit 1

Lesson 1: Constant of proportionality- Rates & proportional relationships FAQ
- Introduction to proportional relationships
- Identifying constant of proportionality graphically
- Constant of proportionality from graph
- Constant of proportionality from graphs
- Identifying the constant of proportionality from equation
- Constant of proportionality from equation
- Constant of proportionality from equations
- Constant of proportionality from tables
- Constant of proportionality from tables
- Constant of proportionality from table (with equations)
- Constant of proportionality from tables (with equations)

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# Rates & proportional relationships FAQ

Frequently asked questions about rates and proportional relationships

## Why do we need to learn about rates and proportions?

Rates and proportions are important concepts in math that can help us understand relationships between different quantities. They come up frequently in everyday life - for example, when we're comparing prices, figuring out how much of an ingredient to use in a recipe, or determining how fast we need to travel to reach a destination on time.

## What is a constant of proportionality?

A constant of proportionality is a number that relates two quantities in a proportional relationship. For example, if we say that $y$ is proportional to $x$ , we might write the equation $y=kx$ , where $k$ is the constant of proportionality.

The constant of proportionality is another name for the unit rate. Suppose Zion skips rope at a constant rate, and they skip over a jump rope $135$ times in $3$ minutes. There are two unit rates:

, which simplifies to$\frac{135}{3}$ , skips per minute$45$ , which simplifies to$\frac{3}{135}$ , minutes per skip$\frac{1}{45}$

To tell which unit rate to use, we need to know the meaning of $x$ in the equation. Suppose $x$ represents the number of minutes and $y$ represents the number of skips. Then the constant of proportionality would be $45$ , the unit rate that had the number of minutes in the denominator.

Try it yourself with our Compare constants of proportionality exercise.

## How do we identify proportional relationships?

There are a few ways we can tell if two quantities are proportional to each other. We might see that the ratio between the two quantities is always the same, or we might see that a graph of the two quantities forms a straight line through the origin (the point where both $x$ and $y$ are equal to $0$ ).

Try it yourself with our Identify proportional relationships exercise.

## How do we write and solve proportions?

To write a proportion, we set two rates equal to each other. For example, we might say $\frac{2}{4}}={\displaystyle \frac{6}{12}$ .

Solving a proportion just means finding the missing value in the proportion. For example, if we know that $8$ out of $12$ oranges are ripe, and we want to figure out how many out of $24$ oranges would be ripe at the same rate, we can set up a proportion like this: $\frac{8}{12}}={\displaystyle \frac{x}{24}$ . Notice that we use the same rate $\frac{\text{ripe oranges}}{\text{total oranges}}$ on both sides of the equation.

From there, we can use one of the methods for solving equations.

Solving the equation can take an extra step if the unknown is in the denominator of the equation. Suppose we had set up the equation using the rate $\frac{\text{total oranges}}{\text{ripe oranges}}$ instead.

Try it yourself with our Solving proportions exercise.

## Want to join the conversation?

- It is pretty confusing.(38 votes)
- im so confused this makes no sense(13 votes)

- this is confuzleing(22 votes)
- this is confuzleing，but i'll keep going(22 votes)
- this is soo confusing and im still in 6th grade I'm soo disappointed in my self(11 votes)
- Try this:

1. listen again and again, and try to understand what they are saying. chances are, you get a better understanding after rereading

2. listen to the videos! they help!

3. do the questions, and if u can't do it try to look at the answer method to understand how to get the answer

4. try reviewing your foundations and basics,try to understand fractions, multiplication and division and how they work with each other

also, since you are in 6th grade, it's perfectly understandable that you can't understand this! in my school, i prob learnt this in grade 8 so keep trying!(12 votes)

- bro why is this getting over my brain?(15 votes)
- math hard that's a fact(3 votes)

- Will this help me in my daily life?(11 votes)
- I think so
**Sarcastically**(2 votes)

- I'm so confused @_@(16 votes)
- Not confusing lolll.(0 votes)

- I feel like this is more steps, correct me if im wrong but if 8 over 12 is comparing to x over 24, 12 and 24 is the denominator what gets 12 over to 24? 12 times 2 would give you 24, do the same thing to the numerator; 8 times 2, you'd end up with 16 ripe over 24 total, this could be vice versa if the if the unknown value is the denominator.(7 votes)
- finally someone gets me. You are correct andrewa297 but when I found that out my teachers told me that isn't the correct process. I didn't listen. But later I went on to do larger numbers and then I realized that having a process is better. the way they explain it is quite lengthy and confusing, so I think you should try cross multiplication. search it up:)(9 votes)

- Is it just variables? like x and y, it just represents a number right?(7 votes)