# Proportional relationship problems 7th grade

### Ratios and Proportional Relationships | Grade 7 | Common Core Map | Khan Academy

Grade 7: Ratios and Proportional Relationships. questions21 skills . Use proportional relationships to solve multistep ratio and percent problems. Discount . Improve your math knowledge with free questions in "Identify proportional relationships" and thousands of other math skills. Practice setting up and solving proportions to solve word problems. She assumes the relationship between kilometers and fuel is proportional. How many .

Now what would be an example of a non-proportional relationship? We'll stay in this baked goods frame of mind. Let's say you're going to a cake store and you're curious about how much it would cost to buy a cake for different numbers of people. So let's say number of servings, number of servings in one column, and then the cost of the cake. And let me set up two columns right over here.

Pause this video and see if you can figure out whether this is a proportional relationship. If it is, why? If it isn't, why not?

## Rates & proportional relationships

Alright, well let's just think about the ratios again. And here our two variables are the number of servings and the cost of cake. So if we look at the ratio of the servings, servings, to cost, in this first situation it is 10 to 20, and then it is 20 to 30, and then it is 40 to And so to see if these are equivalent ratios, when we go from 10 to 20 on the number of servings, we're multiplying by two. But when we go from 20 to 30 on the cost of the cake, we aren't multiplying by two, we're multiplying by 1.

And similarly, when we go from 20 to 40, we are multiplying by two again, but to go from 30 to 40 we aren't multiplying by two, we're multiplying by one and one third. By one and one third.

### Rates & proportional relationships | 7th grade | Math | Khan Academy

When we multiply our servings by a given amount, we're not multiplying our cost of cake by the same amount. This tells us that this is not proportional. One way to think about proportional relationships, we already said, that the ratio between the variables will be equivalent.

Another way to think about it is one variable will always be some constant times the first variable. So in our first example right over here we said the cups of milk is always two times the number of eggs. We can write that down.

So cups of milk is always going to be equal to two times the number of eggs. And this number right over here, we call that the constant of proportionality.

So let's say we have a and b. And let's say when a is one, b is three. And when a is two, b is six. And when a is 10, b is So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when b is three, a is one.

Or when a is one, b is three.

So three to one. And that's also the case when b is six, a is two.

## Proportional Relationships

Or when a is two, b is six. So it's six to two. So these ratios seem to be the same. But then all of sudden the ratio is different right over here. This is not equal to 35 over So this is not a proportional relationship. In order to be proportional the ratio between the two variables always has to be the same.

So this right over here-- This is not proportional. So the key in identifying a proportional relationship is look at the different values that the variables take on when one variable is one value, and then what is the other variable become?

And then take the ratio between them. Here we took the ratio y to x, and you see y to x, or y divided by x-- the ratio of y to x is always going to be the same here so this is proportional. And you could actually gone the other way.

You could have said, well what's the ratio of x to y?

Well over here it would be one to three, which is the same thing as two to six, which is the same thing as nine to