Let’s try to learn a thing

or two about ratios. So ratios are just expressions

that compare quantities. So that might just be a fancy

way– let me just –of saying something that you may

or may not understand. So let me give you

actual examples. If I have 10 horses

and I have 5 dogs. And someone were to come to

me and say Sal, what is the ratio is of horses to dogs? So I want to know how many

horses do I have for some number of dogs. So I could say I have 10

horses for every 5 dogs. So I could say the ratio of

horses to dogs is 10:5. Or I could also write

that as a fraction. I could say the ratio of

horses to dogs is 10/5. Or I could just write it out. I could say it is 10 to 5. These all are saying

the same thing. And the thing I write first,

or the thing that I write on top, is the number of horses. So this is the number

of horses right there. That’s the number of horses. And that’s all the

number of horses. If I wanted to talk about the

number of dogs, this is the number of dogs, that’s the

number of dogs, or that’s the number of dogs. I’m just– These are all

just expressions that are comparing two quantities. Now, I just said I have 10

horses for every 5 dogs. But what does that mean? That means I have 5

horses for every 1 dog. Sorry. Not 5 horses for every 1 dog. It means I have 2 horses

for every 1 dog, right? If for 5 dogs I have 10, that

means that for every 1 of these dogs, there are 2 horses. For every one of– every 2 of

these horses, there’s 1 dog. I just kind of reasoned

through that. So this is– I have 2

horses for every 1 dog. But how do you get there? How do you get

from 10:5 to 2:1? Well you can think of what’s

the biggest number that divides into both of these numbers? What’s their greatest

common divisor? I have a whole video on that. The biggest number that divides

into both of these guys is 5. So you divide both of them by 5

and you can kind of get this ratio into a reduced form. And if I write it here, it

would be the same thing as 2/1 or 2 to 1. And so what’s interesting about

ratios, it isn’t literally, or doesn’t always have to be

literally, the number of horses and the numbers of

dogs you have. What a ratio tells you

is how many horses do I have for every dog. Or how many dogs do I

have for every horse. Now, just to make things clear,

what if someone asked me what is the ratio of dogs to horses? So what’s the difference

in these two statements? Here I said horses to dogs. Here I’m saying dogs to horses. So, since I’ve switched the

ratio– What I’m looking for– I’m looking for the ratio

of dogs to horses, I switch the numbers. So dogs– For every 5

dogs, I have 10 horses. Or if I divide both of

these by 5, for every 1 dog, I have 5 horses. So the ratio of dogs to

horses is 5:10 or 1:5. Or you could write it this way. 1 to– I can write it– Let

me write it down here. 1/5. Or I could write 1 to 5. And the general convention–

This wouldn’t be necessarily incorrect. That’s not wrong. But the general convention is

to get your ratio or your fraction, if you want to call

it that, into the simplest form or into this reduced

form right there. Let’s just do a couple

of other examples. Let’s say I have 20 apples. Let’s say I have 40 oranges. And let’s say that I

have 60 strawberries. Now what is the ratio of apples

to oranges to strawberries? I could write it like this. I could write what is the ratio

of– I’ll write it like this –apples:oranges:strawberries? Well I can start off by

literally saying, well for 60 strawberries– for every 60

strawberries, I have 40 oranges and I have 20 apples. And this would be legitimate. You could say the ratio

of apples to oranges to strawberries are 20:40– Sorry. 20:40:60. And that wouldn’t be wrong. But we saw before, we could

put into reduced form. So we think of what’s the

largest number that divides into all three of these? We can’t just do it into two of

these now because now my ratio has three actual quantities. Well the largest number

that divides into all of these guys is 20. If we divide all of them by 20,

we can then say for every 1 apple, I now have– you divide

this guy by 20 –I have 2 oranges, and I have

3 strawberries. So the ratio of

apples to oranges to strawberries is 1:2:3. And I got that, in every

case, by just dividing these guys all by 20. I divided by 20. I think you get

the general idea. If someone were to ask you

what’s the ratio of– Let me just write it down because it

never hurts to have a little bit more clarification. If someone wanted to know

the ratio of strawberries to oranges– Let me get

into my orange color. Strawberries to

oranges to apples. I thought I was going

to do that in yellow. To apples. What is this ratio going to be? Well for every 3 strawberries,

I have 2 oranges and I have 1 apple. So then it would be 3:2:1. The general idea is whatever

order someone asks you for the different items, you put– the

ratio is going to be in that same exact order. Now, in all of the examples so

far I gave you the number of quantity– the quantity of

things we had and I– we figured out the ratio. What if it went the other way? What if I told you a ratio? What if I said the ratio of

boys to girls in a classroom is– Let’s say the ratio

of boys to girls is 2/3. Which I could’ve also written

as 2:3 just like that. So for every 2 boys, I have

3 girls or for every 3 girls, I have 2 boys. And let’s say that there are

40 students in the classroom. And then someone were to ask

you how many girls are there? How many girls are

in the classroom? So this seems a little

bit more convoluted than what we did before. We know the total number of

students and we know the ratio. But how many girls

are in the room? So let’s think

about it this way. The fact that the ratio

of boys to girls– I’ll write it like this. Boys– Maybe I’ll be

stereotypical with the colors. The ratio of boys to

girls is equal to 2:3. Hate to be so stereotypical,

but it doesn’t hurt. 2:3. The ratio of boys

to girls is 2:3. So this stands for every

3 girls, there’s 2 boys. For every 2 boys,

there’s 3 girls. But what does it also say? It also says for every 5

students, there are what? There are 2 boys and 3 girls. Now why is this

statement helpful? Well how many groups of

5 students do I have? I have 40 students in my

class right there, right? I have 40 students in my class. And for every 5 students,

there are 2 boys and 3 girls. So how many groups of

5 students do I have? So I have a total

of 40 students. Let me do it in

this purple color. I have 40 students and then

there are 5 students per group. And I figured out that group

just by looking at the ratio. For every 5 students, I

have 2 boys and 3 girls. How many groups of 5

students do I have? So that means that I have 8

groups– 40 divided by 5 –I have 8 groups of 5 students. Now we’re wondering how

many girls there are. So each group is going

to have 3 girls. So how many girls do I have? I have 8 groups, each

of them have 3 girls. So I have 8 groups times 3

girls per group is equal to 24 girls in the classroom. And you could do the same

exercise with boys. How many boys are there? There’s a couple of

ways you could do it. You could say for every

group, there are 2 boys. There’s 8 groups. There’s 16 boys. Or you could say

there’s 40 students. 24 of them are girls. 40 minus 24 is 16. So either way you

get to 16 boys. And if you want to pick

up a fast way to do it. It would be identical. You’d say look, 2 plus 3 is 5. For every 5 students,

2 boys, 3 girls. How many groups are there? You say 40 divided by 5

is equal to 8 groups. Every group has 3 girls. So you do 8 times 3 is

equal to 24 girls. Let’s do one that’s a little

bit harder than that. Let’s do one where I say that

the ratio of let’s say– Well let’s go back

to the farm example. The ratio of sheep–

I’ll do sheep in white. The ratio of sheep to–

I don’t know –chickens to– I don’t know. What’s another farm animal? –to pigs. The ratio of sheep to chicken

to pigs– Maybe I should just say chicken right there. The ratio of sheep to chicken

to pigs– Or chickens. I should say chickens. Is– Let’s say the

ratio is 2:5:10. And notice, I can’t

reduce this anymore. There’s no number that

divides into all of these. So this is the ratio if

sheep to chickens to pigs. And let’s say that I have

a total of 51 animals. And I want to know how

many chickens do I have. Well we do the same idea. For every 2 sheep, I have 5

chickens and I have 10 pigs. That tells me for every 17

animals– So every group of 17 animals, what do I have? And where did I get 17 from? I just added 2 plus 5 plus 10. For every 17 animals,

I’m going to have– Let me pick a new color. I’m going to have 2 sheep,

5 chickens, and 10 pigs. Now, how many groups of

17 animals do I have? I have a total of 51 animals. So if there’s 17 animals per

group, 51 animals divided by 17 animals per group. I have 3 groups of 17 animals. Now I want to know

how many chickens. Every group has 5 chickens. We already know that. And I have 3 groups. So I have 3 groups. Every group has 5 chickens. So I’m going to have 3

times 5 chickens, which is equal to 15 chickens. Not too bad. All I did is add these up and

say for every 17 animals, I’ve got 5 chickens. I’ve got 3 groups of 17. So for each of those

groups, I have 5 chickens. 3 times 5 is 15 chicken. You could use the same process

to figure out the number sheep or pigs you might have.

I kinda get it

Learned this in 5th grade gifted

"Let's use the stereotypical colors for boys and girls."

this is a vey usefull vidio my dad makes me revid this and see it all over again it is every good and i hope that other poeple learn for, this too

Thank you, this video has helped me

Bro you would be the best teacher ever

Even Gr.6 Darn hard.

So i have a question

If 700coins are shared among A,B and C. It is known that the ratio of A to B is 6:7, and the ratio of A to C is 2:5. Find the number of coins in C's share.

So my problem is, I know

A:B =6:7 , A:C= 2:5

But to find C's share out of 700, I need to find A:B:C, how do I calculate that?

Hello people stressing because you didn’t listen in class!hehe

its 1 to 2 not i too 5

Really "Ratio of dogs lo horses"

I came hare after while trying to make bread. Original recepy calls for 425ml of water for every 500g of flour. I wanted to put 700g flour and I was baffled how much water I should put…

THANK YOU SO MUCH FOR EXPLAINING I LOVE YOUR WEBSITE

THIS IS LIT IM TOTALLY GONNA PASS MY TEST

I hope I’ll pass my test tomorrow

this helped me with homework

I haven't done ratios in 20 years. I was trying to help my daughter and the way her lesson explains ratios is impossible for me to understand and it wasn't jogging my memory. Your explanation was so, so easy to understand and helped us greatly. Thank you!

thanks god i got a full mark on my ratio and rates exam thanks god your here bro your so helpful

Now i know how to do i was stuck when is the mid test Thanks

me no under stand

In general, the practice of writing a ratio in fraction notation needs to stop, both for clarity and to stop confusing new students.

My Brain is dead

5:10 isnt equal to 1:5***

YAY THANKS I PASSED MY TEST

Please make khan academy available for Windows 7

Please😥😦🙏🙏

Its an error showing ratio as 1:5 . Its actually 1:2.

Lol is this guy a 1984 person,or a video just playing the anne Frank meme.but ijust make it

am i the only one who likes his handwriting

#3:42 you made a mistake because if you divided 1 by 5 10 should be divided by 5 to which would give you 2 not 1

proportion?????

Thx, you helped me alot

You got the second part wrong sir

studying for ISEE! so stressful, good luck on any test you have!

very help thank

mere

1:2 not 1:5

11:25 – should have made the sheep black!

So it would be 2?

Thank you

What?

¿What software are you using to explain this? Thank you in forward!

I don't get it

Help needed is it 1:5 or 1:2 in 3:20

5:10 is 1:2 hahaha typo

Who is watching this video while having test for tomorrow

Why is 1:5🤔🤔🤔

This helped my daughter in year 6😊

Not 10/5 it is 5/10=1/2

Is it necessary that you should divide with the smallest number first?

I really enjoyed the best video i had ever seen

This was so helpful, thank you! I wish my siblings and I had been taught this way in elementary school, and I wish this method of teaching was the standard/expectation for all math teachers! I did notice the error with the dogs to horses ratio, but despite that, this video was GREAT!

Hi

I’m confused and have one more time to take this CNA math exam

the 383 dislikes are English majors = )

I GOT HORSES IT THE BACK!!

I am pretty sure 5:10 is 1:2

2019 anyone?

#QuickMath

7th grader here doing this weird online school thing and thought i did know how to do ratios and proportions but nah nvm i do💀

Ratio of me learning anything at school 0 : 0

5:44 So basically, if you have a two-digit number that is even and the second digit is zero, you take the number of which it is doubled from?

So let's say 80. I technically have to use 4, correct?

Thanks…this helped me alot…God bless you

you divided wrong in 3:55 5 divided by 5 is 1 but 10 divided 5 is 2

Thank you! this helped a lot!

Loved the way you explained this. Thank you!

i guess he just mistakenly wrote the ratio 10:5 is 1:5 ,I am sure that that is supposed to be 1:2

I am 100% sure he mistakenly wrote that,the formula he told a moment ago contradicts this one

Am I the only smart kid in the comments doing extra work in 6th grade

Thx this help me with my homework and class

Thanks for the lesson. I'd like to ask a question. When you say. "For every 5 dogs, I have 10 horses." Does this remain constant over time? For example. If 5 dogs were born. Would you also have another 10 horses giving birth?

Sorry if this is confusing.

I have a test tomorrow.. Wish me luck!

1 to 2, not 1 to 5 (the video has a mistake)

thank you soòòòoooooooooooooooooooooooo much it really helped

8:55

Thanks it will help in my exam

3:25 fail: V 1 like is a correct explain for Khan academy

how did it become 1:5??? I'm confused right now…

Thank u so much for this it’s so so explicit

Ratio of boys to girls is. 1:1.5 why complicate it more than that

woah. I'm in 9th grade now and tryna learn this, when I realize this video was uploaded in 2009. I was 4 o.O

this is stupid

you did it wrong on the first one it IS 1:2

You literally just saved my life

This is great helped me with my homeowork

What is the ratio of green to blue

this was helpful thx

10 divided by five is two not 5

Who here is from Manvel,TX

You are wayyy better than my math Professor. He never gives examples or info.

hope i past my test

This has helped me a lot!!! Thank you Khan academy!😀

This helped a lot thanks

honestly not gonna lie, my teacher would give me questions like this on a peace of paper when i was in the 3rd grade, which i loved to do considering it got easier and easier the more i did them but ever since than i have never really payed much attention to much and now regret that i do.

Test is on Friday lol

10:40

I don't get it

Isn't it 60 bc the ratio is 2:3 and there are 40 boys in the classroom so for girls it should be greater than 40

so 2/40 = 3/x cross multiply

2x = 120 divide each side by 2

x = 60

The ratio 5:10 reduced is 1:2

man i take algebra 1 while im in grade 8 causeim to smart regular students take it in grade 9

Hi, all teachers in Khan youtube, thank you so much always.

THANK YOU! You just save me for my math test

who else felt stupid and looked in the comments to see if it was actually 1:2 instead of 1:5