If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Ratios and proportions

## Mountain height word problem

Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
Back

## Mountain height word problem

Discussion and questions for this video
in 7:44,i dont understnd the '1/5x have <1/5 yr cellphone.
1 Comment
That's because Sal made an error at 7:40 into the video. Sal says and writes, "One fifth x have less than one fifth year cell phone" when the problem states, "one in five of all students have a cell phone that is one year old or less." To be correct, Sal should have written "1/5 x have < 1 yr cell phone." Hope this helps. Good Luck.
In a nutshell, can some one please explain exactly what a proportion and ratio is? (In the simplest but most knowledgeable way please)
Ratio: The quotient of two quantities that are in the same unit.

Proportion: An equation stating that two ratios are equivalent.

:) (Hope this was Helpful!) (;
1 Comment
What are ratios and what do we use them for?
(This was my question when I was younger, I asked this question because I still haven't seen anyone ask this and I want to share my answer to those who are also curious)
1 Comment
Ratio means (or is defined as) the quotient of two numbers or quantities indicating their relative sizes.

The ratio of a to b is written as a:b or a/b. The first term a is called the antecedent, and the second term b is called the consequent

Ratios are used when there appears a need or utility to compare numbers of quantities with one another

Whenever there's a need to do comparisons numerically, we use ratios and proportions.
For example (I'll give you 3 examples):

a) We compare Frank's age with Bob's age. Frank is 24 years old, while Bob is 12 years old. Therefore we say that the ratio of Frank's age relative to Bob's, is the ratio 2:1 (we read that as : ratio two is to one) OR that proportionately,Frank is twice Bob's age.

b) When we learn in baking that for Aunt Linda's strawberry chiffon cake we would require 4 eggs for every 2 cups of flour, while for Grandma's recipe for butter and walnut cookies we would need 1 egg for every 2 cups of flour, then we could say that (comparing the number of eggs required for the cake in comparison with the number of eggs required to bake the cookies):
the ratio of eggs required for the cake relative to the cookies is 4:1 (four is to one) or that, in order to bake the strawberry chiffon cake properly we need 4 times the number of eggs required to bake the butter and walnut cookies,or 4/1.

c) Comparing the number of years two comets(Comet Klemola and Comet Encke) take orbiting the Sun, if the Comet Klemola orbits the Sun every 11 years while the Comet Encke takes 3 years (not the exact number, you would have to compute the exact period using its precise speed, but for purposes of illustration, let's just say 3 for convenience), then the ratio of the inner cloud orbit (the astronomical term for "orbiting around the Sun") of the Comet Klemola relative to Comet Encke is 11:3 or 11/3.

Ratios are used in obsevation of quantities as well as deriving and formulating quantities. Some of the interesting applications in both Physics and Chemistry are as follows:
1.) Creating new types of alloys, after comparing relative strengths of metals and their other properties
2.) Combining chemicals to form personal care products,after comparing the speed of the effects of various components on the skin (It's not as bad as it sounds...we're talking about adding oatmeal or Vitamin E to soaps and shampoos)
3.) Cooking and baking, after much expereimentation and comparison, to make for instance, a softer, more moist red velvet cake
4.) Probability and statistics (It gets interesting after you've compared your chances for accomplishing many things, given a specific time frame)

etc........
ratio is simialar to fratcions but not completly
Comment
I get it its pretty easy once you get the hang of it but sometimes when you have fractions you have to cross multiply
Comment
how do iu do this
Comment
MOST IMPORTANTLY: Sal wants us to get why cross multiplying works! It's just looking under the hood of the engine. Don't worry cross multiplying is the engine, it will always work! -Cheers!
Comment
You have to divide the number 639 in three parts x, y, z in order that x:z = 5:6 and y:z = 8:9 ? how can i solve this problem?
Comment
It includes a lot of algebra, so it might be a bit complicated.
639= a*b*c (I just switched the letters, it makes it more convenient)
a= (5/6)c
b= (8/9)c
639= (40/54)c^3
862.62=c^3
9.51944..=c
7.93286924..=a
8.4617..=b
x= 7.9328..
y=8.4617..
z=9.5194..
Comment
Please help! I want to prepare for next year in 6th grade. I hear you study this too. Can you help explain it for me?
Comment
The last word problem is frying my brain. If x = total number of students, why would you multiply the total number of students by 1/5, because the 1/5 only applies to those who have phones which is 2/3's of x.

I was thinking how to take 1/5 out of 2/3 and come up with this. If you divide 1/5 by 2/3 (multiply the reciprical) you get 3/10 <- number of students with new phones. Out of 10 students 3 have a new phone. So 7/10th have old phones or 7 out of 10. Is this another way of figuring out this problem? Sorry if this confuses anyone, I am very confused and I need to understand this. Thank you for lessons I need to watch more obviously.
Comment
I think you misunderstood the problem. It says 1/5 out of ALL students, not 1/5 out of students that have a phone.
Comment
The ratio of Science and Arts students in a college is 4:3.If 14 Science students shift to Arts then the ratio becomes 1:1.Find the total strength of Science and Arts students.

How would you solve something like this?
Comment
3/4
3 art students for every 4 sci students
1 Vote
Comment
How does this all work out
Comment
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
1 Vote
Comment
At the very beginning, the first problem, I watched this part about 10 times. I still don't understand what you ares saying. My teacher said to use this website and I love it but some things are still really hard. Especially the proportions. Thank you.
Comment
Can someone please help me to understand what he did at 4:19? I understand that 4800 can be divided by 48 100 times but how is it possible to eliminate these two numbers simply because of this relationship?
Comment
Crossing these numbers out just means that he's doing the division there. Now that he's done, he doesn't need the numbers 48 or 4800, all he needs for the next step is the numerator of that fraction and the result of the other operation (100).
1 Vote
1 Comment
Not really a question but,
Thanks you Sal for being such a lifesaver! Now I understand math!
Comment
Yeah, I just found out today. XD
1 Vote
Comment
Help please!! I don't understand how and why Sal is dividing 44/48 by 4800, when does this rule/option apply and why can that be multiplied by 44. Thank you!!
Comment
What is the difference between ratio and proportion....... It's really getting me confused! Some please help........ Thanks :)
Comment
A ratio is a comparison between two equivalent numbers. A proportion is two ratios that are equal. And yes, they are very similar because they are both comparing numbers.
1 Vote
Comment
why did sal reverse the fraction 13/6 into 6/13 @ at the beginning??
1 Vote
Comment
thnkss
1 Vote
Comment
In problem 2 starting at 6:53 I still a little confused when divideing the different
Thank You
Comment
how do you determine whether a pair of ratios form a proportion?
Comment
So all you need to do is cross multiply and thats how you do ratio?? I really dont get it that much. I will just do prctice on it and see what I can pull together on the video. Jklolfmao19,check me out on Call of Duty Modern Warfare 3 [MW3] for PS3 and Call of Duty Black Ops 2 for Xbox 360...BEACH!!
Comment
I need help...

I don't know whether to simplify the fractions and what should multiply fractions by (x).
example:
((x) x 13/6 = 5/(x) x (x))
Real Problem:
3/9 = y/21
1 Vote
Comment
In this situation, I would simplify the fractions and then cancel them out.

3/9=y/21 can simplify to 1/9=y/7

then you can multiply the demoninators together and get the answer.
Comment
Why do the Xs cancel at 0:48?
1 Vote
Comment
If you multiply by x and divide by x, then you are multiplying by x/x which is 1, so you can just cancel them out.
Comment
At 6:36 Sal says it should be 4 less than 300. shouldn't it be 4 less than 600?
Comment
Yes, he made a mistake in what he said, but what he wrote was still correct.
Comment
There are 1,312 Students in a middle school. On any given day there may be 65 students missing. What is the percentage of students missing on any given day?

Is this the correct way to solve a problem like this?
65/1312 = x/100
1312x = 65(100)
1312x=6500
6500 divided by 1312x
is 4.95%

OR what is the other method of doing this problem? Like solve for x (aka the unknown percentage here)? Besides using proportions how would you go about correctly translating this problem? for example when it say "what is(equals) the percentage of(multply) missing students on any given day? I think it means, 65(P)=1312
or 1312(P)=65
1 Vote
Comment
That is correct. Your answer also makes sense because 10% of 1312 is 131, and 65 is a bit less than half of that.
Comment
7:47, 1/5 year??
1 Vote
Comment
I thought the <1/5 year was a typo...
1 Vote
Comment
how do you know whether to multiply all the numbers together to get the measurement of mt. yukon or not? how do you know thats the way to find out?
1 Vote
Comment
Why 1/5 of a year?
1 Vote
Comment
He made an error. It is <1 year and > 1 year. As a teacher my mouth sometimes works faster than my brain. But his concept is correct.
1 Vote
Comment
how do you answer this? : 7x = 9y
Thanks! :D
1 Vote
Comment
between 1:27 and 2:02, why does 13x=5*6?
1 Vote
Comment
because 13/6 = 5/x and cross multiplication?
1 Vote
Comment
1 Vote
Comment
I don't get the mountain question. If Mont Blanc is 4800 meters high, than what is the size? It says mont elbert was 44/48 the SIZE of Mont Blanc. But what is the size? It doesn't tell me in the problem! |:(
1 Vote
Comment
in a camp 180 students had ration for 20 days. how many students should leave the camp so thatthe same ration may last for 25 days?
1 Vote
Comment
30 students should leave the camp.... :)
1 Vote
Comment
all of the the video the guy goes to fast
Comment
Sylvia,
Use the pause button when you want him to stop so you can think about what he said.
And just click along the time stripe to go back a little if you want him to repeat something.
You have control at Khan Academy.
Comment
what is ratio what is proportion what is the difference
1 Vote
Comment
a ratio is, for example 4:9 but a proportion is 4:9=x:18 usually it is solve for x
1 Vote
Comment
why does it mention mount blane ate 3:32?
1 Vote
Comment
I dont get this at all it is to hard. =(
1 Vote
Comment
What if say the question is x-3/(over)5=7/3
1 Vote
Comment
then d cross multiply and find it out
1 Vote
Comment
So, would the fraction 1/5 equal to the ratio 1:5?
1 Vote
Comment
This discussion area is not meant for answering homework questions.
1 Vote
Comment
At 7:45 and 8:43 I don't understand what he means by 1/5 year. Why isn't it just one year?
1 Vote
Comment
Well, he's just saying that it is 1/5 year, which is 2.4 months. Its just the problem.
1 Vote
Comment
i dont got it at 8:01-10:24
1 Vote
Comment
This is not really a question, more like a shoutouy-
Thanks for helping me pass my math and i might be able to move back up in my math class!!!
Comment
I'm excited for you! That's exactly what's happening to me... sorta. I have a 69% right now and Sal, god of all math, made me understand a WHOLE lot more than my other teacher. Good luck with you :)
Comment
in chemistry class, the girl to boy ratio is 9 to 3

if there are a totalof 60 students, how many girls are there?

from bai3006 the best gamer ever
1 Vote
Comment
at 4:11 working backwards, can u work this out another way besides working backwards?? if so how would we?
1 Vote
Comment
You know, I never really understood it when Sal multiplies a fraction a number, like in the beginning of the video. how did he multiply a fraction by x. I know how to multiply fractions, but I just can't seem to understand that. Help?
1 Vote
Comment
when he multiplies with x, the fraction he multiplied it by becomes opposite like... Example:(x times 3/4 = 4/3)
1 Vote
Comment
if u take 227/12 and 375/3 could make a proportion out of it?????
1 Vote
Comment
It wouldn't be an equal proportion, so nope.
1 Vote
Comment
What is a proportion?
1 Vote
Comment
How do you solve the problem at 2:47. I still don't understand how to solve these kind of problems.
1 Vote
Comment
in 0:06 how did he get the five?
1 Vote
Comment
He used the theory of quadratic's to solve then simplified the remainder of negative number's and got 5. Simple? >.>
1 Vote
Comment
What is the easy way to find out the answer
1 Vote
Comment
i don't get it
1 Vote
Comment
smiles,
Brezy Angel Froehlich (that is all random letters up there)
1 Vote
Comment
A portion is when you give food out depending on who is there by the table. A Pro-portion is a professional version of that, where you give out numbers from one equation to the other equation, making sure to depend on the rules of math, you don't want one of your equation guests getting all 'undefined' on you!
1 Vote
Comment
Isn't Mont Blanc spelled wrong? Isn't it supposed to be Mount Blanc?
1 Vote
Comment
"Mont" is the French word for "mountain". It just happens to look similar to the English word "mount" because French and English both developed much of their vocabulary from Latin. In English the name means "White Mountain", but we just tend to call it "Mont Blanc" regardless.
1 Vote
Comment
this is a great way to learn how to set up porportions
Comment
Yeah its kindof like microsoft paint. if you look close he has like a little kite connected by tiny dots.
1 Vote
Comment
How did he find the answer 6:40?
1 Vote
Comment
why is this so hard
1 Vote
Comment
Man, I Dont Not Understand .
1 Vote
Comment
What Would E And N Stand For ? A Number ?
1 Vote
Comment
there different then other ratios
you need to be advanced for this kind of math
1 Vote
Comment
A family has a total after tax income of $2400/month and a monthly mortgage expense of$800. find the ratio of mortgage expense to after tax income?
1 Vote
1 Comment
1 Vote
Comment
how many killograms equals a gallon? i dont understand how to do this because one is volume and the other is mass
1 Vote
Comment
A gallon of water would have a different mass than a gallon of air or a gallon of mercury. You need to know the density to calculate kilograms per gallon.

But if the problem was "How many kilograms in a gallon of water", you can find a very close estimate.

A cubic centimeter of water has a mass of about 1 gram. A liter of water has a mass of about 1 kilogram. (Density of water varies with temperature, but 1 liter/1kg is a close approximation.)

So if the question was the mass of a gallon of water, you can use the following ratios to find your answer.
1 kg/1 liter
3.78541178 liters/ 1 gallon

I hope that helps
1 Vote
Comment
Hi, at around 9:41, Sal puts the number of students that have a cell phone that is more than 1 year old (the 7/15 x) over the number of people that have cell phones (2/3 x). Can someone give me a bit of intuition about why this makes sense? Thanks in advance.
1 Vote
Comment
6/8,22/28?
using proportional reasoning.
1 Vote
Comment
whats agrivating me is why do you need to multiply anything times x? @00:29 whats the point?
1 Vote
Comment
Bob building a house and garage. the house, garage and driveway and a colour bond fence on three sides, leaving the from of the block unfenced.
have quotes for turf @$7.20 per square metre and colour bond fence @$92 per linear meter. advised to order an extra 5%for both, to allow for joins, short lengths and damaged turf.
find the cost of landscaping the block?
1 Vote
Comment
what does ratio have to do with proportion? Sorry if it seems like a stupid question i just don't know.
1 Vote
Comment
A ratio shows the how the proportion works. A ratio such as 8:3 says that for every 8 of the first item, you will always have 3 of the other. In other words, say were were talking about weight: "These 8 oranges have the same weight as 3 of these big potatoes, so their weights are proportional to each other at a ratio of 8 to 3."
1 Vote
Comment
I don't understand which to multiply by: x or the number below/above x?
1 Vote
Comment
whats the difference of a ratio and a proportion
1 Vote
Comment
w+3/4=5 1/3
solve for w.
1 Vote
Comment
4 5/12 or 53/12
1 Vote
Comment
At 09:09-9:23, did he just just cross multiply?
1 Vote
Comment
Is this more complicated than it looks?
1 Vote
Comment
It's actually less complicated. You just look at the diagonals and multiply them. The products of the diagonals equal each other. Then you just solve!
1 Vote
Comment
Can you simplfiy the proportions before you cross Multiply ?
1 Vote
Comment
Yes, but only if both sides can be simplified.
1 Vote
Comment
HI SAL!! this video helped me understand ratios and propartins
1 Vote
Comment
How do you solve a ratio proportion with slope
1 Vote
Comment
could u specify the question?
1 Vote
Comment
how do u rewrite a quotient as s a ratio using the units in a denominator
1 Vote
Comment
what is the unknown number?
1/3 over 3/8, equals to 2/5 over the unknown number. what is the unknown number? how do i solve this problem/
1 Vote
Comment
(1/3)/(3/8)=(2/5)/(x) // *x, /(1/3), *(3/8)

x=(2/5)*(3/8)/(1/3)
x=3*(2/5)*(3/8)
x=(6/5)*(3/8)
x=(6*3)/(5*8)
x=18/40
x=9/20
1 Vote
Comment
How do I find an actual ratio?
1 Vote
Comment
this takes a lot of time you need to be patient i guess
1 Vote
Comment
Just don't let the equations sit there all lonely. It's hard to go straight up- you'll never convince a 2 on the bottom of 1/2 to climb over that roof. But diagnolly, any number can climb steps, even I can (and I weigh 220 lol). So Bring the lonely numbers from the bottom, to the tops diagnoly across, through the '=' elevator. Just make sure you do it to both numbers, or you end up with a very angry left out number, that will snitch on your teacher to get you marked wrong on the test!
1 Vote
Comment
Hey, I'm having trouble solving 'continued ratios'
For example my problem would look like ;

A : B= 3 : 4 B : C= 3 : 2
What is the continued ratio;
A : B : C ?
1 Vote
Comment
You would find the lowest common multiple between the common variable on one ratio and the common variable on the other.
For this particular example, you would do
A:B x 3 and B:C x 4
or
3 : 4 x 3 and 3:2 x 4

which equals 9 : 12 and 12 : 8, where A is 9, BOTH 12s are B, and C is 8.
From there, because B is common on both ratios, you can form a continued ratio of:
A : B : C = 9 : 12 : 8
1 Vote
Comment
If the total cost of x apples is b cents, what is a general formula for the cost, in cents,
of y apples?
1 Vote
Comment
why did he say the answer for yukon is 4 less than 300 when i was 4 less than 600
1 Vote
Comment
what does x stand for
1 Vote
Comment
x stands for the unknown in your equation. If we have the problem x/4=2/8, we have to solve to find x.
1 Vote
Comment
This video makes no sense to me. I need help ;[
1 Vote
Comment
Just don't let the equations sit there all lonely. It's hard to go straight up- you'll never convince a 2 on the bottom of 1/2 to climb over that roof. But diagnolly, any number can climb steps, even I can (and I weigh 220 lol). So Bring the lonely numbers from the bottom, to the tops diagnoly across, through the '=' elevator. Just make sure you do it to both numbers, or you end up with a very angry left out number, that will snitch on your teacher to get you marked wrong on the test!
1 Vote
Comment
How come at 7:48 its < 1/5 yr cell phone?
1 Vote
Comment
in half an hour the bucket is 1/5 of the way full. What is the rate at which the water is leaking?
1 Vote
Comment
does this pair of ratios form a proportion 3.5/1.2=7/8
1 Vote
Comment
These proportions are very hard
1 Vote
Comment
Why is fractions different from proportions.
1 Vote
Comment
what is 2 plus 2
1 Vote
Comment
what is the numbers for the mathamatical sequence pie
1 Vote
Comment
pi? 3.14159265
1 Vote
Comment
How pressure can be calculated if only height is given ?
Thank you.
1 Vote
Comment
how do i set up this question using ratios? Fanny and Kevin shared a box of markers in the ratio 5:3; fanny gave half of her share to Kevin. Kevin then had 30 more markers than fanny. How many markers did fanny give to Kevin?
1 Vote
Comment
I do not understand where you got your formula: K+(1/2*F) - 1/2*F=30
Now K+(1/2*F) - 1/2*F=K. Please make it simpler.
1 Vote
1 Comment
I need to know how to set up this ratio problem to solve:
The ratio of the number of chickens to the number of ducks on farm was 3:8. There were 40 more ducks than chickens. When half the chickens and some of the ducks were sold, the ratio of the number of chickens to the number of ducks became 3:4. How many ducks were sold?
1 Vote
Comment
First you need to find how many ducks to chickens there were at first using the 3:8 ratio and the 40 more ducks information. Then you have to use the new ratio and solve for change in ducks.
1 Vote
What if X was in the numerator? Can you still multiply to cancel?
1 Vote
Comment
Then you would have to divide.
1 Vote
Comment
the magic that Sal used can also be cross multiplied then it is a basic equation problem.ex.
13/6=5/x 13.x=5.6
1 Vote
Comment
The tallest moutain in Canada is not Mount Yukon, it is Mount Logan.
1 Vote
Comment
Doesn't help the problem.
1 Vote
Comment
i think i may have missed a video......
1 Vote
Comment
why does it become 13/6X? what does it mean? can someone please explain?
1 Vote
Comment
at about 4:21: why is 44/48 multiplied by 4800?
1 Vote
Comment
Ben Nevis is 44/48 size of Mount Blanc. To find out the size of Ben Nevis Sal needed to multiply Mount Blanc by Ben Nevis. In these ratios, Sal needs to find the height of Mount Yukon. In order to do so, he needs to work backwards to get the height of each mountain to answer the following question.

To get the answer for E= 220/67 N Sal needs to get the answer for E=44/48 B and Sal already knows that B= 4800.

E= 44/48 * 4800 (to see work watch the video from 4:03 to 4:36)

Hope that helps!!
1 Vote
Comment
how would you cross multiply
1 Vote
Comment
Just don't let the equations sit there all lonely. It's hard to go straight up- you'll never convince a 2 on the bottom of 1/2 to climb over that roof. But diagnolly, any number can climb steps, even I can (and I weigh 220 lol). So Bring the lonely numbers from the bottom, to the tops diagnoly across, through the '=' elevator. Just make sure you do it to both numbers, or you end up with a very angry left out number, that will snitch on your teacher to get you marked wrong on the test!
1 Vote
Comment
At 4:20, why does Sal divide 4800 by 48? He's supposed to be cross-multiplying, but he divides like this for all three problems and then multiplies what's left over Why?
1 Vote
Comment
maybe because he didn't notice or something like that.
1 Vote
Comment
Sal solution seems complicated. I would have thought if you wanted to figure out what proportion of students of the ones that own cell phones have a cell phone that is older than a year would be 4/5 of 2/3 (1/5 have cell phone less than a year, so that means 4/5 have a cell phone greater than a year) However, this works out to a completely different answer than his. Can someone elaborate?
1 Vote
Comment
If 1/5 have new phones and 4/5 have old phones that means 5/5 students own phones, which is clearly wrong. The initial ratios are given in terms of the total student population (variable x in Sal's explanation). This is why some extra steps had to be taken to convert from total population to just those with phones.
1 Vote
Comment
If 12/8 = x/9 why does it not follow that 3/2 = x/9 in that same equation? Why does simplifying 12/8 as a ratio (and a fraction) not work in that equation?
1 Vote
Comment
Discuss the site

Flag inappropriate posts

Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.

abuse
• disrespectful or offensive
• low quality
• not about the video topic