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### Course: 7th grade foundations (Eureka Math/EngageNY) > Unit 1

Lesson 1: Topic A: Foundations# Intro to ratios

The video explains ratios, which show the relationship between two quantities. Using apples and oranges as an example, it demonstrates how to calculate and reduce ratios (6:9 to 2:3) and how to reverse the ratio (9:6 to 3:2). Created by Sal Khan.

## Want to join the conversation?

- How are ratios used in real world problems?(207 votes)
- Say you have a job as a store employee and your stocking shelves and your boss wants each item to have the same amount as the item next to it. In a quick summary she/he wants you to tell them how much is in each one. You'd count the amount of items in each one and state a ratio.(180 votes)

- What is a ratio?(58 votes)
- Let's say you have to come up with a ratio to show the relationship between red and green mushrooms from this problem:

There are 6 red mushrooms and 3 green mushrooms in a bag.

There are obviously 6 red mushrooms for every 3 green, so you could write a ratio like this:

6:3 or 6/3 or "6 to 3."

You can treat a ratio just like a fraction (which is why you can also write it like one: 6/3), so you can reduce 6/3 to**2/1**.

So in that original bag, there are**2**red mushrooms for every**1**green mushrooms.

Ratios have lots of other uses as well, but I think this will give you a basic idea. Keep watching the videos.(112 votes)

- why do we use ratios if we already have fractions(5 votes)
- People in this world use fractions to show how much of a whole they are talking about. For example, 5/7 would mean 5 out of seven things. Ratios are used to to express how much of 2 or more things are required to make a whole. This can be simplified, for example, instead of saying50:40, I could say 5:4.

You might be saying that you can do the same thing with fractions, which is true. However, in the case of fractions, the numerator is only one number, and it tells only how much of ONE thing is needed out of a whole, and in ratios, it tells you how much of 2 THINGS are required to make a whole.

I hope I answered your question😊(20 votes)

- So, a ratio is the amount of each object in each group?(14 votes)
- Do the ratio numbers have to begin with the number that is explained first? I dont understand, someone please help me out.(34 votes)
- yes for example what is the ratio from pears to apples you are going to do peas first then apples(12 votes)

- how can YOU SIMPLIFY5:11?(19 votes)
- you cant simplify that because it does not have anything in common(14 votes)

- really how are ratios used in real world problems and where at in the world like i don't understand like where(3 votes)
- It's often a statistics sort of thing, but it can be used for any situation that you want to report two values.

Stores= 4 apples to 3 dollars === 4:3

House listings= 4 bed to 1 bath === 4:1

School stats= 50 students to 1 teacher === 50:1

All those show a relation of one thing to another so that people can make decisions.

"75 cents per apple is too expensive! I won't buy it!"

"4 bedrooms and we all need to share a bathroom? Ew, no."

"50 kids per one classroom!? We need more teachers!"(19 votes)

- I think I have a misconcpetion that if ratios are not equivalent then they are not ratios anymore. For example; if 3 pizzas/5 hamburgers is not equal to 6 pizzas/11 hamburgers, then the latter one is not the ratio. But, since we are still comparing numbers in relation to each other, is it true that it is still a ratio and if we have a curve instead of a line, we are still performing ratios?

Since we guage how much y changes in relation to x?(4 votes)- They are still ratios, but they aren't equivalent ratios.

If there are 2 different restaurants, one could have a raito of selling 3 pizzas to 5 hamburgers. The other restaurant could have a different ration of selling 6 pizzas to 11 hamburgers. Its ok in this context for the ratios are different.(12 votes)

- When will we ever need to use ratios for real life conflicts?(4 votes)
- It may seem silly, but ratios can be used for everyday purposes, such as cooking.(9 votes)

- Did you watch the video? Sal gives you the answer to your question at @0:18in the video.(6 votes)

## Video transcript

Voiceover:We've got some apples here and we've got some oranges and what I want to think about
is, what is the ratio, what is the ratio of apples ... Of apples, to oranges? To oranges. To clarify what we're even talking about, a ratio is giving us the relationship between quantities of 2 different things. So there's a couple of ways that we can specify this. We can literally count
the number of apples. 1, 2, 3, 4, 5, 6. So we have 6 apples. And we can say the ratio is going to be 6 to, 6 to ... And then how many oranges do we have? 1, 2, 3, 4, 5, 6, 7, 8, 9. It is 6 to 9. The ratio of apples to oranges is 6 to 9. And you could use a different notation. You could also write it this way. 6 to ... You would still read the
ratio as being 6 to 9. But we don't have to
just satisfy us with this because one way to think about ratios, especially if we're thinking about apples to oranges, is how many apples do we have for a certain number of oranges? When you think about it that way, we can actually reduce these
numbers, as you might have already thought about. Both 6 and 9 are divisible by 3. So just like we can reduce fractions, we can also reduce ratios. So if you divide 6 and 9 both by 3. 6 divided by 3 is 2. 6 divided by 3 is 2. And 9 divided by 3 is 3. So we could also say that the ratio of apples to oranges is 2 to 3. Or if we want to use this notation, 2 to 3. 2 to 3. Now, does that make sense? Well look. We divided each of these groups into 3. So one way to think about it ... If you divide this whole
total into 3 groups. So 1 group, 1 group. 2 groups, 2 groups. And 3 equal groups. We see that in each of those groups, for every 2 apples, for every 2 apples, we have 3 oranges. For 2 apples we have 3 oranges. For 2 apples we have 3 oranges. So, once again, the ratio
of apples to oranges. For every 2 apples we have 3 oranges. But we could think about
things the other way around as well. We could also think about
what is the ratio ... We could also think about
what is the ratio ... Ratio, of oranges to apples? Oranges to apples. And here we would, essentially, switch the numbers. The ratio of oranges to apples. Notice, up here we said apples to oranges which is 6 to 9 or 2
to 3 if we reduce them. And here we're going to say the ratio of oranges to apples, so
we've swapped these 2. So we're going to swap the numbers. Here we have 9 oranges for every 6 apples. So we could say the ratio
is going to be 9 to 6. The ratio is 9 to 6. Or if we want to reduce
it, for every 3 oranges ... So we're going to divide this by 3. So for every 3 oranges we are going to have 2 apples. We are going to have 2 apples. So notice, this is just
exactly what we had up here, but when we had apples to oranges it was 6 to 9. 6 apples for every 9 oranges. And now when it's
oranges to apples, we say it's 9 to 6. 9 oranges for every 6 apples. Or we could say for
every 3 oranges we have exactly 2 apples.