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### Course: Pre-algebra > Unit 3

Lesson 1: Intro to ratios# Part:whole ratios

In this video, we explore ratios using apples and oranges. We find the simplified ratio of apples to total fruit (2:5) and learn to represent ratios as fractions (2/5). The fraction indicates that 2/5 of the fruit are apples. Key definitions include ratio, simplified ratio, and fraction notation. Created by Sal Khan.

## Want to join the conversation?

- In a problem before, we had 32 1/2 times 2. Supposedly, the answer was 65, I'm a little bit confuse why that is the answer, shouldnt we convert the mixed # into a improper fraction and then multiply by 2?

HELP(40 votes)- As you said, you can turn 32 1/2 to fraction first then multiply it by 2. It'll look like this: 65/2 * 2 = 65. You can also do it like this: 32 1/2 is the same as 32.5 so multiply it by 2 and you get 65.(43 votes)

- At2:12, are ratios the exact same as fractions? And what is the point of having two different ways of expressing the same thing?(1 vote)
- You could consider fractions to be a specific kind of ratio in the same way that a square is a specific kind of rectangle. The point of having two ways of expressing them is that they deal with information slightly differently:

A fraction describes a single quantity based on its relationship to another quantity. In this example, the quantity of apples related to the quantity of total fruit. "2/5 of them are apples". This is clear and specific, and you can use it in equations.

Ratios are more flexible. They can be more complicated than fractions and contain more information, but that also makes them harder to use. In the video's example, the ratio of apples to oranges could be expressed as 2:3. You could also add a third number for total fruit; Apples to oranges to total fruit are 2:3:5. Now you can tell just by looking at the numbers that all of the fruit are either apples or oranges, that the fraction that are apples is 2/5 and that the fraction that are oranges is 3/5. However, you couldn't use 2:3:5 in an equation the same way you can with a fraction because it doesn't identify what quantity you are measuring.

Tl;dr: Ratios can give you more information about a complicated data set. Fractions can be used in equations but can't contain as much information. Simple ratios with only two terms can be written as fractions and are equivalent to them.(18 votes)

- At a soccer tournament 12 teams are wearing red shirts, 6 teams are wearing blue shirts, 4 teams are wearing orange shirts, and 2 teams are wearing white shirts.

For every 2 teams at the tournament, there is 1 team wearing*_______*shirts.

Choose 1 answer:

(Choice A)

Red

(Choice B)

Blue

(Choice C)

Orange

(Choice D)

White(23 votes)- You're looking for the shirt color that appears once every two teams, so it would have half of the teams that the total does. Since the total is 12 teams, our color should have half of those, which is 6 teams. 6 teams are wearing blue shirts.(18 votes)

- Can 400 percent be a ratio?(4 votes)
- Yes, it can when we convert 400% to a fraction. 400% can also be written as 400/100, and therefore the ratio will become
. (400:100*This is not supposed to be a video benchmark*)(4 votes)

- What is the difference of a
**ratio and a fraction**?(3 votes)- A ratio is a fraction that looks different:
`5/6 = 5:6`

If you mean a subtraction problem, you can't subtract them.

Hope this helps!(2 votes)

- I need help with this a lot i can't do this can someone help me?(2 votes)
- There are several ways to compare things, so we could have about 3 dogs for every 2 cats in America. You can have a ratio of dogs to cats (3:2), cats to dogs (2:3) or you could have dogs to total where total requires you to add all the parts so dogs to total (3:5) or cats to total (2:5). We could not use the word pets because this is broader than just cats and dogs. With dogs to total, we could have equivalent ratios for smaller subsections such as 3:5,6:10,9:15,12:20, etc. all of which could reduce down to 3:5, but one might be ratio of dogs to total in a house, one might be on a farm, in a block, or in a neighborhood. What parts are confusing you?(4 votes)

- are the ratio of apples 🍎 to oranges 🍊 a ratio? because I wouldn’t be able to say it the other way around Right?(3 votes)
- You can say it in
ways. For example, you had**both****5 blue**marbles,**8 red**marbles, and**2 clear**marbles. In this the ratio of blue to red marbles is 5:8. Meaning there are 5 blue ones for every 8 red ones. But, you could do it the opposite way too. The ratio of red to blue marbles would be 8:5, meaning there are 8 red ones for every 5 blue ones. Same goes for the clear marbles. Hope this helped!(2 votes)

- i am stuck on ratio can you help?(0 votes)
- Hey, you can see Part to Whole ratios as fractions. Lets say, the ratio of blue sofas to total amount of sofas is3:11. You can also see it has 3/11. It doesn't work with part to part ratios though, so pay close attention before answering!(6 votes)

- I did not know you could write ratio's as a fraction,You learn something new every day!!(2 votes)
- If the staff to inmate ratio is 1:5,8 and you have 2585 inmates how many staff members will be employed?(2 votes)
- IDK, but i know that that many criminals is dangerous!(1 vote)

## Video transcript

Voiceover:Let's think
about another scenario involving ratios. In this case, let's think about the ratio of the number of apples. Number of apples to ... Instead of taking the ratio of the number of apples to the number of oranges, let's take the number of apples to the number of fruit. The number of fruit
that we have over here. And I encourage you to pause the video and think about that on your own. Well, how many total apples do we have? We have 2, 4, 6, 8 apples. So we're going to have 8 apples. And then how much total fruit do we have? Well we have 8 apples and we have 3, 6, 9, 12 oranges. So our total fruit is 8 plus 12. We have 20 pieces of fruit. So this ratio is going to be 8 to ... 8 to 20. Or, if we want to write
this in a more reduced form, we can divide both of these by 4. 4 is their greatest common divisor. And so this is the same thing as a ratio. 8 divided by 4 is 2 and
20 divided by 4 is 5. So 2 to 5. Now, does this make sense? Well, if we divide ... If we divide everything into groups of 4. So ... Or if we divide into 4
groups, I should say. So 1 group, 2 groups,
3 groups, and 4 groups. That's the largest number of groups that we can divide these into so that we don't have to cut up the apples or the oranges. We see that in each
group, for every 2 apples we have 1, 2, 3, 4, 5 pieces of fruit. For every 2 apples we
have 5 pieces of fruit. This is actually a good opportunity for us to introduce another
way of representing ... Another way of representing
ratios, and that's using fraction notation. So we could also represent this ratio as 2 over 5. As the fraction 2 over 5. Whenever we put it in
the fraction it's very important to recognize
what this represents. This is telling us the fraction of fruit that are apples. So we could say 2/5 of the fruit ... Of the fruit ... Of the number of fruit,
I guess I could say. Of number of fruit ... Of fruit is equal to the number of apples. Right, I'm just going to say 2/5 of fruit if we're just speaking
in more typical terms. 2/5 of fruit are apples. Are, are apples. So, once again, this is introducing another way of representing ratios. We could say that the
ratio of apples to fruit, once again, it could be 2 to 5 like that. It could be 2, instead of putting this little colon there we could literally write out the word to. 2 to 5. Or we could say it's
2/5, the fraction 2/5, which would sometimes be read as 2 to 5. This is also, when it's written this way, you could also read that as a ratio, depending on the context. In a sentence like this
I would read this as 2/5 of the fruit are apples.