What I want to do in this

video is order these fractions from least to greatest. And the easiest way

and the way that I think we can be sure we’ll

get the right answer here is to find a common denominator,

because if we don’t find a common denominator,

these fractions are really hard to compare. 4/9 versus 3/4 versus

4/5, 11/12, 13/15. You can try to estimate

them, but you’ll be able to directly

compare them if they all had the same denominator. So the trick here, or at

least the first trick here, is to try to find that

common denominator. And there’s many ways to do it. You could just pick

one of these numbers and keep taking its multiples

and find that multiple that is divisible by all the rest. Another way to do it is look

at the prime factorization of each of these numbers. And then the least

common multiple of them will have to have at least all

of those prime numbers in it. It has to be composed

of all of these numbers. So let’s do it that second way. And then let’s verify that

it definitely is divisible. So 9 is the same

thing as 3 times 3. So our least common

multiple is going to have at least

one 3 times 3 in it. And then 4 is the same

thing as 2 times 2. So we’re going to also

have to have a 2 times 2 in our prime factorization

of our least common multiple. 5 is a prime number. So we’re going to need

to have a 5 in there. And then 12– I’m going

to do that in yellow. 12 is the same thing

as 2 times 6, which is the same thing as 2 times 3. And so in our least

common multiple, we have to have two 2’s. But we already have two 2’s

right over here from our 4. And we already have

one 3 right over here. Another way to think about it

is something that is divisible by both 9 and 4 is going

to be divisible by 12, because you’re going

to have the two 2’s. And you’re going to have

that one 3 right over there. And then, finally, we need

to be divisible by 15’s prime factors. So let’s look at

15’s prime factors. 15 is the same

thing as 3 times 5. So once again, this number

right over here already has a 3 in it. And it already has a 5 in it. So we’re cool for 15,

for 12, and, obviously, for the rest of them. So this is our least

common multiple. And we can just

take this product. And so this is going to be

equal to 3 times 3 is 9. 9 times 2 is 18. 18 times 2 is 36. 36 times 5, you could do that

in your head if you’re like. But I’ll do it on the

side just in case. 36 times 5, just so

that we don’t mess up. 6 times 5 is 30. 3 times 5 is 15 plus 3 is 180. So our least common

multiple is 180. So we want to rewrite

all of these fractions with 180 in the denominator. So this first fraction,

4/9, is what over 180? To go from 9 to 180, we have to

multiply the denominator by 20. So let me do it this way. So if we do 4/9, to get the

denominator of 9 to be 180, you have to multiply it by 20. And since we don’t

want to change the value of the

fraction, we should also multiply the 4 by 20. So we’re just really

multiplying by 20/20. And so 4/9 is going to be

the same thing as 80/180. Now, let’s do the

same thing for 3/4. Well, what do we have to

multiply the denominator by to get us to 180? So it looks like 45. You could divide 4 into

180 to figure that out. But if you take 4 times

45, 4 times 40 is 160. 4 times 5 is 20. You add them up. You get 180. So if you multiply

the denominator by 45, you also have to multiply

the numerator by 45. 3 times 45 is 120 plus 15. So it’s 135. And the denominator here is 180. Now, let’s do 4/5. To get our

denominator to be 180, what do you have

to multiply 5 by? Let’s see. If you multiply 5 by

30, you’ll get to 150. But then you have another 30. Actually, we know

it right over here. You have to multiply it by 36. Well, then you have to multiply

the numerator by 36 as well. And so our denominator

is going to be 180. Our numerator, 4

times 30 is 120. 4 times 6 is 24. So it’s 144/180. And then we have

only two more to do. So we have our 11/12. So to get the

denominator to be 180, we have to multiply 12

by– so 12 times 10 is 120. Then you have 60 left. So you have to multiply it

by 15, 15 In the denominator, and 15 in the numerator. And so the denominator

gives us 180. And 11 times 15. So 10 times 15 is 150. And then you have one more 15. So it’s going to be 165. And then, finally,

we have 13/15. To get our denominator to be

180, have to multiply it by 12. We already figured out

that 12 times 15 is 180. So you have to

multiply it by 12. That will give us 180

in the denominator. And so you have to also

multiply the numerator by 12, so that we don’t change

the value of the fraction. We know 12 times 12 is 144. You could put one

more 12 in there. You get 156. Did I do that right? 12 plus 144 is going to be 156. So we’ve rewritten

each of these fractions with that new common

denominator of 180. And now, it’s very

easy to compare them. You really just have to

look at the numerators. So the smallest

of the numerators is this 80 right over here. So 4/9 is the smallest. 4/9 is the least

of these numbers. So let me just

write it over here. So this is our ordering. We have 4/9 comes first, which

is the same thing as 80/180. Let me write it

both ways– 80/180. Then the next the

smallest number looks like it’s this

135 right over here. I want to do it in

that same color. The next one is going to

be that 135/180, which is the same thing as 3/4. And then the next one is

going to be– let’s see, we have the 144/180. So this is going to

be the 144/180, which is the same thing as 4/5. And then we have two more. The next is this 156/180. So then we have

our 156/180, which is the same thing as 13/15. And then we have one

left over, the 165/180, which is the same thing– I

want to do that in yellow. We have our 165/180, which

is the same thing as 11/12. And we’re done. We have finished our ordering. So if you’re doing the Khan

Academy module on this, this is what you would input

into that little box there.

Great video! Helps to solve this problem alot faster!

multiply like this: 3x3x2x2x5 = 9x2x10 = 18×10 = 180

thanks for posting this!

Thanks it helps a lot!

Do you have the video on factor tree

yup

THANK YOU Now I won't get in trouble by my math teacher.

i hate this. i had to watch this :0 it sucks oh yea i didnt watch it

Understanding it is so easy

Could you please post a multiple fraction example? One like 3/4 + 5/2 – 9/7 + 3/5 etcétera…

thx now i understand

I can't understand it and it's boring

I can watch it again

is so confusing you better find another way to teach us

You get tutu

"and another way to think about it" please finish the first idea before tangent.

Your videos have helped me so much from homework to studying thank you!

grACIAS

I love it

thank you

Thank you so much :'D

¬_¬ Grrr i,m gonna flip my table over (╯°□°）╯︵ ┻━┻ #TOLDU

:(D

still don't get it but good video

still don't get it but good video

Or just divide the numerator by the denominator on a calculator and see which decimal is closer do 1.

why make it harder?

deep voice

this help me for my math test watching this until2016

Thanks so much I was looking for a website like this then I found it. I was like thus is so awesome. thanks MR.

Thank you so much. It really helped!

when I use the ladder method to find LCM, I get 1800, so I don't think I understand how author gets 180. Can anyone explain?

thanks a lot for helping me in the homework orelse my maths teacher would cancel my lunch break

i done a test and i got 91%

omg i never expected to learn 2 lessons in 1 vid… ordering fractions and finding lcm of alot of numbers 🙂 thank you this helped a lot 😃

this was made only 2 years after i was born woah

This was very helpful I got 100% on my math test thank you khan

I am learning for my class

hi

I love it

Thanks u so much!

12/45 , 56/31, 97/129, 32/ 47, 89/23,

those type of numbers..

how to solve easily. with in a minute..

is there any another process for find out those numbers order easily without using lcm concept??

please reply with me

or link me any another video for it

I did a test and got 100

We already discussed that for the nth time and I always firget about it😂😂 youre a great help

i luv khan academy

their so much better in teaching than my actual teacher

I am watching for my exam quiz

I found an easy way to use with only two fractions: https://youtu.be/N-Y0Kvcnw8g

Let's say I'm studying for my DAT and on the "math" section (quantitative reasoning) I come across a problem of this sort. Compare and order these fractions from smallest to largest or simply state which one is the largest fraction. On a timed exam such as the DAT how can i possibly spend 2+ minutes on a single problem? There's gotta be a quicker way, no?

Was I got a 100% on my test because of this vib thanks a lot

Khan has done it again……..SO very well explained. Thank you!!

or I think you can just divide and rank

ok

and then and then . that is funny

like the vid