# Mixed numbers and improper fractions | Fractions | Pre-Algebra | Khan Academy

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
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.

## 100 thoughts on “Mixed numbers and improper fractions | Fractions | Pre-Algebra | Khan Academy”

1. Aqua Nightingale says:

damnn you're good.. thx alot man

2. Ellen Metzger says:

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

3. Bryn Hanson says:

Thxs alot this helped me refresh during the summer

4. TheLegendPlz says:

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
:))

5. John Wilson says:

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.

6. maria pavon says:

i hate math

7. Sabidofamily Forever says:

i love math

8. Jake Parker says:

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

9. cometfused says:

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

10. Ryan Shiwmangal says:

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

11. Varinder Singh says:

12. LilyLimee says:

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

13. thats good for children like me Lainez says:

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

14. thats good for children like me Lainez says:

and i'am in a grade 6

SLOW DOWN

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

16. Gamer Hotline says:

thanks for the video this helped me

17. Snowball says:

well my live is the john mach

18. destructive alien says:

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

19. destructive alien says:

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

20. Neinty Nein says:

my teacher uses you and i use you too

21. Ed sup says:

22. Born2shine Vlogs says:

i hate math to but this is my summer work

23. Tim Payne says:

why do u not show your face

24. Kingmarc_. says:

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

25. Messi is boss 2 says:

i had to watch this video foreced

26. DOJJA MON says:

Thanks

27. Art Universe says:

your too awesome thanks for the help, much kudos

28. Cam2 Myanmar says:

im smart already i got a on my homework

29. JM Veda says:

Improper fractions blows my mind 🙁

30. Toxic Rick says:

I am half ASIAN WHY AM NOT SMART

31. Anujwa Kumaar says:

No

32. Anujwa Kumaar says:

Improper proper fractions

33. GMKP says:

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

35. An Epic Gamer says:

I was forced to watch this 😭😭😭😭😭😭

36. kpop_lover 123388 says:

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😕😦😭😔

37. Jim and Maria Hart says:

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

38. Alan Sasson says:

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

39. NoahDaGamer says:

Hello

40. Malkyung Hwang says:

wow i already know tis stuff mom making meh:]

41. Malkyung Hwang says:

lol

42. ETHAN HOANG says:

43. Javier Hernandez says:

Your like Buddha of math bro

44. Rickeyea Singleton says:

This did not help me with my homework 😡😡

45. Bijeta Kalakheti says:

Thx so much

46. Bijeta Kalakheti says:

I have a math test tomorrow this helped me prepare

47. Bryn Ramich says:

I Describe

48. Bryn Ramich says:

I suscribed😃

49. Gigi Romero says:

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!!

50. Eduardo Gallardo says:

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!

51. Anony Mous says:

My brain is actually hurting.

52. GesuVeritas says:

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

53. Aisha Duverger says:

lol i was 1 when he uploaded this video

54. Johnson Kolleh says:

me to

55. Johnson Kolleh says:

😠😠😠😠😠😠😠

56. Daredeath 900 says:

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

57. Mohannad Mohammed Salah el din Salah Eldin says:

Thank you Mr 💗💗

58. Mohannad Mohammed Salah el din Salah Eldin says:

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

59. HERO KIDS TV says:

2:12

60. HERO KIDS TV says:

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

61. Ginger Lewis says:

This really helps

62. B0ssQu33n101 Roblox says:

Me too but this really helped

63. A Line says:

Thank you

64. Martin Gonzalez says:

You just saved my 6th grade

65. Samurai says:

u suck dude maria pavon

66. Samurai says:

u suck if you hate maths

67. Herman Boston says:

wow

68. Daniel Zheng says:

I’m already past improper fraction and mixed number

69. Hayden Waters says:

hi

70. Christian Bainat says:

71. lohit Vlogz says:

Thx khan academy I learned so much

72. Jack STENNETT says:

hi

73. Jack STENNETT says:

this helps with my maths

74. Aznumi25 says:

Math is the best

75. Anisha Ggirl says:

its good to learn

76. Gacha Animator says:

Math – Mental Abuse To Humans

77. sunil john says:

thank you sir , you helped me a lot.

78. Beverly ann polito says:

best math video

80. Michele Nieto says:

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 😂💀💀

81. XxHollyARTxX says:

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)

82. sama habib says:

thank so much

83. nilam bhatt says:

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

84. delisa shrestha says:

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

85. Yani yani says:

I like so much math
Math is life

86. c00l_k!d says:

This is sooo old lmao like dead serious

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

88. Olivia Nestor says:

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

89. BOSCO CHUNG says:

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

90. Akuji K. says:

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…

91. HERO KIDS TV says:

Ok

92. Tuba Rehan says:

you have a great way of teaching👌

93. Tuba Rehan says:

k

94. Aniiya C says:

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

97. Aleksandra Makari says:

Well I need to relearn this lol

98. Marki Daniel says:

Thank you you help me

99. oofingnoob9 yt says:

This video is from 12 years ago

100. oofingnoob9 yt says:

I'm watching in 2019 so dont judge me