# Solving percent problems | Decimals | Pre-Algebra | Khan Academy

percent, amount, and base in this problem. And they ask us, 150 is
25% of what number? They don’t ask us to solve it,
but it’s too tempting. So what I want to do is first
us to solve. But first, I want to answer
this question. And then we can think about what
the percent, the amount, and the base is, because
those are just words. Those are just definitions. The important thing is
to be able to solve a problem like this. So they’re saying 150 is
25% of what number? Or another way to view this,
150 is 25% of some number. So let’s let x, x is equal
to the number that 150 is 25% of, right? That’s what we need
to figure out. 150 is 25% of what number? That number right here
we’re seeing is x. So that tells us that if we
start with x, and if we were to take 25% of x, you could
imagine, that’s the same thing as multiplying it by 25%, which
is the same thing as multiplying it, if you
view it as a decimal, times 0.25 times x. These two statements
number, you take 25% of it, or you multiply it by 0.25, that
is going to be equal to 150. 150 is 25% of this number. And then you can solve for x. So let’s just start with
this one over here. Let me just write it separately,
so you understand what I’m doing. 0.25 times some number
is equal to 150. Now there’s two ways
we can do this. We can divide both sides of this
equation by 0.25, or if you recognize that four quarters
make a dollar, you could say, let’s multiply both
sides of this equation by 4. You could do either one. I’ll do the first, because
that’s how we normally do algebra problems like this. So let’s just multiply
both by 0.25. That will just be an x. And then the right-hand side
will be 150 divided by 0.25. And the reason why I wanted to
is really it’s just good practice dividing
by a decimal. So let’s do that. So we want to figure out what
150 divided by 0.25 is. And we’ve done this before. When you divide by a decimal,
what you can do is you can make the number that you’re
dividing into the other number, you can turn this into
a whole number by essentially shifting the decimal
two to the right. But if you do that for the
number in the denominator, you also have to do that
to the numerator. So right now you can view
this as 150.00. If you multiply 0.25 times
100, you’re shifting the decimal two to the right. Then you’d also have to do
that with 150, so then it becomes 15,000. Shift it two to the right. So our decimal place
becomes like this. So 150 divided by 0.25
is the same thing as 15,000 divided by 25. And let’s just work it
out really fast. So 25 doesn’t go into 1, doesn’t
go into 15, it goes into 150, what is that? Six times, right? If it goes into 100 four
times, then it goes into 150 six times. 6 times 0.25 is– or actually,
this is now a 25. We’ve shifted the decimal. This decimal is sitting
right over there. So 6 times 25 is 150. You subtract. You get no remainder. Bring down this 0 right here. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. Bring down this last 0. 25 goes into 0 zero times. 0 times 25 is 0. Subtract. No remainder. So 150 divided by 0.25
is equal to 600. And you might have been able
to do that in your head, because when we were at this
point in our equation, 0.25x is equal to 150, you could
have just multiplied both sides of this equation
times 4. 4 times 0.25 is the same
thing as 4 times 1/4, which is a whole. And 4 times 150 is 600. So you would have gotten
it either way. And this makes total sense. If 150 is 25% of some number,
that means 150 should be 1/4 of that number. It should be a lot smaller than
that number, and it is. 150 is 1/4 of 600. Now let’s answer their
actual question. Identify the percent. Well, that looks like 25%,
that’s the percent. The amount and the base
in this problem. And based on how they’re wording
it, I assume amount means when you take the 25% of
the base, so they’re saying that the amount– as my best
sense of it– is that the amount is equal to the percent
times the base. Let me do the base in green. So the base is the number you’re
taking the percent of. The amount is the quantity
that that percentage represents. So here we already saw
the percent is 25%. That’s the percent. The number that we’re taking
25% of, or the base, is x. The value of it is 600. We figured it out. And the amount is 150. This right here is the amount. The amount is 150. 150 is 25% of the
base, of 600. The important thing is how
you solve this problem. The words themselves, you know,
those are all really just definitions.

### 93 Replies to “Solving percent problems | Decimals | Pre-Algebra | Khan Academy”

1. norwayte says:

Good one – doing it in slow motion and color coded.

2. jsr9422 says:

thanks a lot 🙂

3. nando5561 says:

good video

4. Junerey Piojo says:

Is/Of = %/100

5. Saif AlZubaidi says:

cool, what program r u usin?

6. Vianney Rodriguez says:

People are always asking me where i go to school. I tell em khanacademy

7. Glory7studios says:

just do this
150 * 100/25

۞

8. Dimensions100 says:

My dad's whole family is full of teachers….after I learn from this, I'm gonna pass this gift called KhanAcademy on to them.

9. SaKomunikasyong Glooball says:

dota players are so lucky, these percent problems are a bit easy for them

10. Mathew Lin says:

Anyone notice at 3:12 he draws a cat face

11. Matt Mazur says:

Anyone know what software/inputs he is using to create this video?

12. danielwild794 says:

just multiply the % by the number

what program is that ?? 🙂

14. minhaj khan says:

what confused……………….
8(

15. Yousra Isaac says:

In Khan we trust!!!!! <3

16. Megan Elizabeth says:

This is still very hard .

17. tyler burg says:

Nadia took two practice exams to prepare for her college entrance exam. On the first practice exam, she scored one thousand one hundred. After studying, her score increased by thirty percent. What was her score on the second practice exam?

one thousand one hundred thirty

one thousand four hundred

one thousand four hundred thirty

one thousand five hundred seventy-one

This was on my flvs class 😀 awesome

18. Ama O says:

u r a life saver!!

19. Trekole says:

I am going to use your work to study for the GRE, but I don't know which book you're using? Please let me know, thanks!

20. Aimee Rudd says:

Dude! You so rock! Thanks for your help!

21. Maximilian Cole says:

it all makes sense now

22. Its. Ric0 says:

THAnks man you helped i wondering if i should subscribe

23. Dominick Hall says:

hi

24. Destroyer_Of_All says:

subscribe to Destroyer_Of_All

25. BabelaSweet says:

hi i hope u can help me. I am looking for a formula to fin the following:
I need to know 3 things. subtotal, 7% of subtotal, total (sum of subtotal and 7%)
I have the total which is 4100 and i know the percent used to calculate that is 7%…how can I find out which the SUBTOTAL number should be?

26. Chili Pepper Gaming says:

THANK YOU

27. Solid Director says:

Daurde Sandstorm

28. Quincy Smith says:

At 3:03 when he was writing 150 as 150.00 and then he was carrying the decimal, the two zeroes at the end of it wight he carried decimal line under it made it look like a :3 face. lol

29. jovan singh says:

khan acedemy

30. Christina Gabriel says:

I have been watching your videos for YEARS and I cannot thank you enough for all the help you've given me!!!!!!!

31. Everett Brown says:

these vidieos are geting me through school. i went in to school unconfodent but now iam cofodent and ready for a test

32. Ameil Tirant says:

33. MrCowman says:

You go way to fast in all of your videos, still love you though.

34. Kasie Hernandez says:

thank you sooo much helps me alot

35. Kitzya says:

I just did 150×4 and I got 600 ._.

36. Tiernan McDougall says:

u know war u r awesome

37. Tiernan McDougall says:

THX THX THX

38. Sanay .S. says:

You could have just done 4*150

39. Michaela says:

So what Is 150 25% of? Oh lemme see. Since 4 quarters make a dollar. (25×4=100) so that means 150×4=600 since 150 is only a quarter of the number. Yall make it overly complicated for no reason.

40. Lucas Langer says:

thx very helpful u r awsome
😉

41. Mijaz Mljaz says:

It is easy

42. Raj Thomas says:

Can u do a video with percents with proportion

43. miami boy187 says:

iiiy papi

44. david bean says:

Thanks for doing the process instead of using a calculator

45. Seattle206723 says:

In the First 1:53 minutes I was saying the mans a Genius.

46. maxwolf 22 says:

it doent understand wath a shit
=(((((

47. Videogamer 2014 says:

You do all of you act like jerks who try teach you important academic skills needed in your life. Micheala im talking to you

48. Junie Joseph says:

cool

49. Evelyn Reyes says:

Thx really helpful. But still not sure

50. maxwolf 22 says:

you now well fock you

51. Grace Higley says:

there is no sound

52. Wellem Evangelista says:

To solve percentage I think it's much easier to use what we call " Regra de três" ( rule of tree, literally). In this problem it was obvious that we could multiply for 4, but in other cases this way is better. (IN MY OPINION).

150= 25 | 25x = 150.100
X = 100| X = 15000/25=600

If 150 is 25% of X, so X is 100%.

150 times 100 is equal 15000;
25 times X is equal 25X ;

— you can take out the last two zeros if you want to make it easier, and at the end you add them back.—

So 150 by 25 is 6 (plus those two zeros you took off before) it is 600.

I hope you got it, I'm not a native English speaker, I'm just trying to help.

53. hiten chaudhary says:

you could also do 150+150+150+150 =600

54. Lj Wilkerson says:

Or you can just do 150×4

55. Lj Wilkerson says:

So this is the slower way

56. lala#77 rules says:

150 is 25% of 600

57. Christian Anthony Maninang says:

I really don't understand to solve by using the formula triangle can you make a video about the formula triangle

58. KKGGT says:

look at the bottom right corner of 3:26 you see my face

59. jeanab100 says:

you help me

60. jeanab100 says:

i still do not understand

61. Yalda Noori says:

This is confusing.

62. slope. says:

thanks

63. Jasmin Panumpang says:

Green screen?

64. andrejustin bayarong says:

tnx you help me

@1:32 — what is the "it" ??

66. IQIS_ MYGIRL says:

Thank u

67. Nicholas Dillon says:

I have to watch this for test corrections

68. comedy and documentary says:

You cn alw

69. comedy and documentary says:

You can always just do 150×25-.

70. Tsering Dorjee says:

WOW this really helped out with my test

71. Ivan Leung says:

this is useful

72. lavinth says:

By the 1st minute I was able to understand very clearly. Thank you.

73. AnthoCal12 says:

THANK YOU

74. zeezo bluoshi says:

We can solve it much easier by multiplying 150 by 25 then divide it by 100 that will answer 600

75. The Llama says:

76. YNS KNAVE says:

I do not get it

77. Tomislav Pavlovic says:

78. Rania Rezwana says:

Admit it. You're here because you have a test😅

79. Eva Li says:

Who else is watching this for a last-minute test?

80. Tim Yin says:

wrong video 4 me
lol i found de wrong video

81. The Khans says:

wow, this guy is a GENIOUS… MY MIND IS BLOWN

82. santi Bergonzi says:

60-0 equals 60 not 0

83. William Clark says:

84. Silver Unknown says:

:[] ……………………………

85. Tahjai Patrick says:

this is a grate video

86. Josie Berast says:

Still makes no sense

You could have timed it by 4

88. Llawliet Otero says:

is not 37.5?

89. zoe mr. clean says:

This video is for nine years of people cramming for a test.

90. Czar Tuzon says:

you could have saved time by just multiplying 150 into 4

91. bu says:

SAVED ME FROM THIS HOMEWORK 🤢💘

92. Mr Jaws says:

Ohhhhhhhhhhh after I watched I finally understand clearly.

93. Maria Sajini Durairaj says:

We could have done this method
25
_ × 100
150