Ratios and proportions

# Advanced ratios, proportions, and rates

## Mountain height word problem

Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
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## 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)
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
I get it its pretty easy once you get the hang of it but sometimes when you have fractions you have to cross multiply
how do iu do this
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!
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?
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..
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?
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.
I think you misunderstood the problem. It says 1/5 out of ALL students, not 1/5 out of students that have a phone.
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?
3/4
3 art students for every 4 sci students
How does this all work out
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
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.
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?
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).
Not really a question but,
Thanks you Sal for being such a lifesaver! Now I understand math!
Yeah, I just found out today. XD
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!!
What is the difference between ratio and proportion....... It's really getting me confused! Some please help........ Thanks :)
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.
why did sal reverse the fraction 13/6 into 6/13 @ at the beginning??
thnkss
In problem 2 starting at 6:53 I still a little confused when divideing the different
Thank You
how do you determine whether a pair of ratios form a proportion?
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!!
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
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.
Why do the Xs cancel at 0:48?
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.
At 6:36 Sal says it should be 4 less than 300. shouldn't it be 4 less than 600?
Yes, he made a mistake in what he said, but what he wrote was still correct.
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
That is correct. Your answer also makes sense because 10% of 1312 is 131, and 65 is a bit less than half of that.
7:47, 1/5 year??
I thought the <1/5 year was a typo...
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?
Why 1/5 of a year?
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.
how do you answer this? : 7x = 9y
Thanks! :D
between 1:27 and 2:02, why does 13x=5*6?
because 13/6 = 5/x and cross multiplication?
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! |:(
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?
30 students should leave the camp.... :)
all of the the video the guy goes to fast
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.
what is ratio what is proportion what is the difference
a ratio is, for example 4:9 but a proportion is 4:9=x:18 usually it is solve for x
why does it mention mount blane ate 3:32?
I dont get this at all it is to hard. =(
What if say the question is x-3/(over)5=7/3
then d cross multiply and find it out
So, would the fraction 1/5 equal to the ratio 1:5?
This discussion area is not meant for answering homework questions.
At 7:45 and 8:43 I don't understand what he means by 1/5 year. Why isn't it just one year?
Well, he's just saying that it is 1/5 year, which is 2.4 months. Its just the problem.
i dont got it at 8:01-10:24
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!!!
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 :)
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
at 4:11 working backwards, can u work this out another way besides working backwards?? if so how would we?
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?
when he multiplies with x, the fraction he multiplied it by becomes opposite like... Example:(x times 3/4 = 4/3)
if u take 227/12 and 375/3 could make a proportion out of it?????
It wouldn't be an equal proportion, so nope.
What is a proportion?
How do you solve the problem at 2:47. I still don't understand how to solve these kind of problems.
in 0:06 how did he get the five?
He used the theory of quadratic's to solve then simplified the remainder of negative number's and got 5. Simple? >.>
What is the easy way to find out the answer
i don't get it
smiles,
Brezy Angel Froehlich (that is all random letters up there)
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!
Isn't Mont Blanc spelled wrong? Isn't it supposed to be Mount Blanc?
"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.
this is a great way to learn how to set up porportions
Yeah its kindof like microsoft paint. if you look close he has like a little kite connected by tiny dots.
How did he find the answer 6:40?
why is this so hard
Man, I Dont Not Understand .
What Would E And N Stand For ? A Number ?
there different then other ratios
you need to be advanced for this kind of math
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?
how many killograms equals a gallon? i dont understand how to do this because one is volume and the other is mass
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
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.
6/8,22/28?
using proportional reasoning.
whats agrivating me is why do you need to multiply anything times x? @00:29 whats the point?
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?
what does ratio have to do with proportion? Sorry if it seems like a stupid question i just don't know.
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."
I don't understand which to multiply by: x or the number below/above x?
whats the difference of a ratio and a proportion
w+3/4=5 1/3
solve for w.
4 5/12 or 53/12
At 09:09-9:23, did he just just cross multiply?
Is this more complicated than it looks?
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!
Can you simplfiy the proportions before you cross Multiply ?
Yes, but only if both sides can be simplified.
HI SAL!! this video helped me understand ratios and propartins
How do you solve a ratio proportion with slope
could u specify the question?
how do u rewrite a quotient as s a ratio using the units in a denominator
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/
(1/3)/(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
How do I find an actual ratio?
this takes a lot of time you need to be patient i guess
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!
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 ?
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
If the total cost of x apples is b cents, what is a general formula for the cost, in cents,
of y apples?
why did he say the answer for yukon is 4 less than 300 when i was 4 less than 600
what does x stand for
x stands for the unknown in your equation. If we have the problem x/4=2/8, we have to solve to find x.
This video makes no sense to me. I need help ;[
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!
How come at 7:48 its < 1/5 yr cell phone?
in half an hour the bucket is 1/5 of the way full. What is the rate at which the water is leaking?
does this pair of ratios form a proportion 3.5/1.2=7/8
These proportions are very hard
Why is fractions different from proportions.
what is 2 plus 2
what is the numbers for the mathamatical sequence pie