We’re now going to learn how

to go from mixed numbers to improper fractions

and vice versa. So first a little

bit of terminology. What is a mixed number? Well, you’ve probably seen

someone write, let’s say, 2 and 1/2. This is a mixed number. You’re saying why is

it a mixed number? Well, because we’re including a

whole number and a fraction. So that’s why it’s

a mixed number. It’s a whole number

mixed with a fraction. So 2 and 1/2. And I think you have a sense

of what 2 and 1/2 is. It’s some place halfway

between 2 and 3. And what’s an

improper fractional? Well an Improper fraction is a

fraction where the numerator is larger than the denominator. So let’s give an example

of an improper fraction. I’m just going to pick

some random numbers. Let’s say I had 23 over 5. This is an improper fraction. Why? Because 23 is larger than 5. It’s that simple. It turns out that you can

convert an improper fraction into a mixed number or a

mixed number into an improper fraction. So let’s start with the latter. Let’s learn how to do a

mixed number into an improper fraction. So first I’ll just show you

kind of just the basic systematic way of doing it. It’ll always give you the right

answer, and then hopefully I’ll give you a little intuition

for why it works. So if I wanted to convert 2 and

1/2 into an improper fraction or I want to unmix it you could

say, all I do is I take the denominator in the fraction

part, multiply it by the whole number, and add the numerator. So let’s do that. I think if we do enough

examples you’ll get the pattern. So 2 times 2 is 4 plus 1 is 5. So let’s write that. It’s 2 times 2 plus 1,

and that’s going to be the new numerator. And it’s going to be all of

that over the old denominator. So that equals 5/2. So 2 and 1/2 is equal to 5/2. Let’s do another one. Let’s say I had 4 and 2/3. This is equal to — so this

is going to be all over 3. We keep the

denominator the same. And then new numerator is

going to be 3 times 4 plus 2. So it’s going to be 3 times 4,

and then you’re going to add 2. Well that equals 3 times 4 —

order of operations, you always do multiplication first, and

that’s actually the way I taught it how to

convert this anyway. 3 times 4 is 12 plus 2 is 14. So that equals 14 over 3. Let’s do another one. Let’s say I had 6 and 17/18. I gave myself a hard problem. Well, we just keep the

denominator the same. And then new numerator is

going to be 18 times 6 or 6 times 18 plus 17. Well 6 times 18. Let’s see, that’s 60 plus

48 it’s 108, so that equals 108 plus 17. All that over 18. 108 plus 17 is equal

to 125 over 18. So, 6 and 17/18 is

equal to 125 over 18. Let’s do a couple more. And in a couple minutes I’m

going to teach you how to go the other way, how to go from

an improper fraction to a mixed number. And this one I’m going to try

to give you a little bit of intuition for, why what I’m

teaching you actually works. So let’s say 2 and 1/4. If we use the — I guess you’d

call it a system that I just showed you — that equals

4 times 2 plus 1 over 4. Well that equals, 4 times 2

is 8 plus 1 is 9, 9 over 4. I want to give you an intuition

for why this actually works. So 2 and 1/4, let’s actually

draw that, see what it looks like. So let’s put this back into

kind of the pie analogy. So that’s equal to one pie. Two pies. And then let’s say

a 1/4 of a pie. A 1/4 is like this. 2 and 1/4, and ignore

this, this is nothing. It’s not a decimal point —

actually, let me erase it so it doesn’t confuse you even more. So go back to the

pieces of the pie. So there’s 2 and

1/4 pieces of pie. And we want to re-write

this as just how many 1/4s of pie are there total. Well if we take each of these

pieces — I need to change the color — if we take each of

these pieces and we divide it into 1/4s, we can now say how

many total 1/4s of pie do we have? Well we have 1, 2, 3, 4,

5, 6, 7, 8, 9 fourths. Makes sense, right? 2 and 1/4 is the

same thing as 9/4. And this will work

with any fraction. So let’s go the other way. Let’s figure out how to go

from an improper fraction to a mixed number. Let’s say I had 23 over 5. So here we go in the

opposite direction. We actually take the

denominator, we say how many times does it go

into the numerator. And then we figure

out the remainder. So let’s say 5 goes into

23 — well, 5 goes into 23 four times. 4 times 5 is 20. And the remainder is 3. So 23 over 5, we can say

that’s equal to 4 and in the remainder 3 over 5. So it’s 4 and 3/5. Let’s review what we just did. We just took the denominator

and divided it into the numerator. So 5 goes into 23 four times. And what’s left over is 3. So, 5 goes into 23,

4 and 3/5 times. Or another way of saying that

is 23 over 5 is 4 and 3/5. Let’s do another

example like that. Let’s say 17 over 8. What does that equal

as a mixed number? You can actually do this

in your head, but I’ll write it out just so

you don’t get confused. 8 goes into 17 two times. 2 times 8 is 16. 17 minus 16 is 1. Remainder 1. So, 17 over 8 is equal to 2

— that’s this 2 — and 1/8. Because we have

one 8 left over. Let me show you kind of a

visual way of representing this too, so it actually makes sense

how this conversion is working. Let’s say I had 5/2, right? So that literally means I have

5 halves, or if we go back to the pizza or the pie analogy,

let’s draw my five halves of pizza. So let’s say I have one half of

pizza here, and let’s say I have another half

of pizza here. I just flipped it over. So that’s 2. So it’s 1 half, 2 halves. So that’s three halves. And then I have a

fourth half here. These are halves of pizza,

and then I have a fifth half here, right? So that’s 5/2. Well, if we look at this, if we

combine these two halves, this is equal to 1 piece, I have

another piece, and then I have half of a piece, right? So that is equal to 2

and 1/2 pieces of pie. Hopefully that doesn’t

confuse you too much. And if we wanted to do this the

systematic way, we could have said 2 goes into 5 — well, 2

goes into 5 two times, and that 2 is right here. And then 2 times 2 is 4. 5 minus 4 is 1, so the

remainder is 1, and that’s what we use here. And of course, we keep the

denominator the same. So 5/2 equals 2 and 1/2. Hopefully that gives you a

sense of how to go from one mixed number to an improper

fraction, and vice versa, from an improper fraction

to a mixed number. If you’re still confused

let me know and I might make some more modules. Have fun with the exercises.

damnn you're good.. thx alot man

at 8:23 Sal should have said "So that is equal to 2 and 1/2 pies."

Thxs alot this helped me refresh during the summer

Can I tell you something:YOU ARE AWESOME AND KHAN ACADEMY MADE ME GET FULL MARKS IN MY MATHS TEST AND I LEARNED CODING AS WELL! BIG THANKS TO YOU GUYS

:))

I'm 23, and completely forgot all of this. It's kind of exciting to relearn what I may have just glossed over in school as a kid.

i hate math

i love math

They are already preparing me for collage bruh I'm in 6th grade

Don't like this comment, and don't reply I get flooded with notifications

You do math every day when you are at home for example when you order pizza and you ate 2 pieces that's math right there

Why any dislikes to this vedio. Made me very Mad.

i keep fogetting but i need help with 19/5?

oh its make me mad need help how i can't understand

and i'am in a grade 6

SLOW DOWN

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

thanks for the video this helped me

well my live is the john mach

i love ur math vidios!!!!!!!!!!!!!

i love ur math vids!!!!!!!!

my teacher uses you and i use you too

Im in grade 12 and we had a quiz about this. Guess who didnt pass?

i hate math to but this is my summer work

why do u not show your face

Thanks now I know how to do this stuff I am going to 7th grade this is just summer work they gave me

i had to watch this video foreced

Thanks

your too awesome thanks for the help, much kudos

im smart already i got a on my homework

Improper fractions blows my mind 🙁

I am half ASIAN WHY AM NOT SMART

No

Improper proper fractions

I still don't get it

that math make me confused , I'm never seem courses like this , in our country people in middle school practicing equations from level 2 and 3 the high level and aerospace engineering , now i want start college and when i sow that math I'm really confused its crazy

I was forced to watch this 😭😭😭😭😭😭

wow you guys don't know how to put a video of doing whole number subtraction fraction 's I wish you did because I don't know how to do 1 17/12-2/3. http://cdn.kikakeyboard.com/sticker_partnerLoveFace/17.png😕😦😭😔

Sal: "Hope that doesn't confuse you to much." Me: "It does confuse me it confuses me a lot!"

Can you do a video on subtracting mixed numbers from whole numbers

Hello

wow i already know tis stuff mom making meh:]

lol

bruh im in 6th grade they're already teaching us prealgebra

Your like Buddha of math bro

This did not help me with my homework 😡😡

Thx so much

I have a math test tomorrow this helped me prepare

I Describe

I suscribed😃

Omg thank you!! I didn't know to how to do this because I'm to lazy in school and I thought to myself will I even pass 5th grade?? Fractions was so hard but now I under stand how to do this thank you!!

Excellent explanation, Khan Academy always does a great job to refresh or teach math. However, in this particular video was he chewing on food or something? It was driving me nuts half way into the video!

My brain is actually hurting.

I am mom who appreciates you more than words can say. Thank you! Bless you!

lol i was 1 when he uploaded this video

me to

😠😠😠😠😠😠😠

This is really good for my math but I also sorta hate it cause my mother makes me watch it almost everyday. No offense.

Thank you Mr 💗💗

I appreciate you alot and you helped me in my exam.

2:12

This vid helped me a lot and I’m only 8

This really helps

Me too but this really helped

Thank you

You just saved my 6th grade

u suck dude maria pavon

u suck if you hate maths

wow

I’m already past improper fraction and mixed number

hi

Old but helpfull

Thx khan academy I learned so much

hi

this helps with my maths

Math is the best

its good to learn

Math – Mental Abuse To Humans

thank you sir , you helped me a lot.

Khan academy rules

best math video

Thank you so much 🙏 I am here doing homework like some crazy person at this time …btw its 11:02 so yeah I'm last minute 😂💀💀

This helps (no wonder my tablemate is smarter than me he told the class about this channel and now I know why he got 30/37 on a pre-test for fractions)

thank so much

This is soooooooooooooooooooooooooooooooo fun I love doing this stuff It’s the only math I like

This video was created 12 years ago??!!LIKE WHAT????WOW!!!!!

I like so much math

Math is life

This is sooo old lmao like dead serious

For the improper fraction to mixed number what if there is no remainder

You should do a video on how to convert mixed numbers into decimals

Thanks, Mr. Khan. You made it much easier for me.

So, You're Saying That I Was A Pro At This Part In Pre-Algebra Before I Even Start It???

Cool, Because I'm In Fith Grade When I Posted This And At My School, You Learn Pre-Algebra And That Stuff In Sixth Grade All The Way Through To Eighth Grade…

Ok

you have a great way of teaching👌

k

Thank you so much

Thanks that helped me before I used a different strategy but it took so much time this works so much better 👍😀

it was superrrrrrrrrr i love ahan academy very much to study

Well I need to relearn this lol

Thank you you help me

This video is from 12 years ago

I'm watching in 2019 so dont judge me