Advanced ratios and proportions
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Mountain height word problem
Using some basic algebra to solve what looks like a hairy word problem that involves proportions.
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 Let's start with a warm up ratio problem.
 Then we can tackle some harder word problems. So I have the
 ratio 13/6 is equal to 5/x.
 I don't like having this x in the denominator, so let's
 multiply both sides of this equation by x.
 So if I multiply both sides by x, what's going to happen?
 On the right hand side, this x cancels out with that x.
 And then the left hand side going to become 13 over 6x is
 equal to you're just going to have a 5 there.
 And then to solve for x, you just multiply both sides by
 the inverse of 13/6.
 6/13.
 These, obviously, cancel out.
 That's why I multiplied it by the inverse.
 And you get x is equal to 5 times 6, which is 30/13.
 Now one way that you might see this done it's kind of
 skipping a step is called cross multiplying.
 You look at a ratio like this, and you immediately say the
 numerator on this side times the denominator on that side
 is equal to the numerator on this side times the
 denominator on that side.
 Let me write that out.
 So you might sometimes see people immediately go to let
 me just rewrite the problem actually So that original
 problem was 13/6 is equal to 5/x.
 You might sometimes immediately see someone go to
 13 times x is equal to 5 times 6.
 And it might look like magic.
 How does that work out?
 Why does that make sense?
 And really, all they're doing to get to this point is they
 are simultaneously multiplying both sides of the equation by
 both denominators.
 Let me show you what I mean.
 If I multiply both sides of this equation by 6 and an x,
 what's going to happen?
 If I multiply it by 6x times both sides of this equation
 And where did I get the 6?
 From here.
 Where did I get the x?
 From there.
 Both denominators.
 What's going to happen?
 On this side of the equation, the 6 is going to cancel out
 with this denominator.
 And on the right hand side of the equation, the x is going
 to cancel with this denominator.
 So you're going to be left with 13 times x is
 equal to 5 times 6.
 So nothing fancy there.
 You're just multiplying by the denominators of both sides of
 the equation.
 And it looks like you're cross multiplying.
 13x is equal to 5 times 6.
 And then from here, of course, you divide both sides by 13.
 You get x is equal to 30/13.
 Now that we're all warmed up, let's tackle some actual word
 problems.
 So we have the highest mountain in
 Canada is Mount Yukon.
 It is 298/67 the size of then Ben Nevis.
 Let's Y for Yukon is equal to 298/67 the size of let's say
 N for Nevis.
 That's what this in green tells us.
 The highest peak in Scotland.
 Mount Elbert in Colorado is the highest peak
 in the Rocky Mountains.
 Mount Elbert so we have this other information here Mount
 Elbert is 220/67 the height of Ben Nevis.
 So let's say, E for Elbert.
 E is equal to 22/67 times Nevis.
 Times the same Ben Nevis, right there.
 And they're telling us more.
 And, it is 44/48 the size of Mont Blanc.
 So Elbert is equal to 44/48 the size of Mont Blanc.
 Let's write B for Mount Blanc.
 They also tell us Mont Blanc is 4,800 meters high.
 Mont Blanc is 4,800.
 meters high.
 So B is equal to 4,800.
 And they ask us, how high is Mount Yukon?
 So we have to figure out Y.
 So let's see if we can work backwards, and figure out all
 the variables in between.
 So let's start with this information here.
 B is equal to 4,800.
 E is equal to 44/48 times B.
 So E so Elbert is equal to 44/48 times Mont Blanc, which
 is 4,800 meters.
 Now if you divide that by 48 4,800 divided by 48 is 100.
 So Elbert is 44 times 100 meters high.
 So it's equal to 4,400 meters.
 Fair enough.
 Now we can use this information and
 substitute it over here.
 We get Elbert, which is 4,400 meters high, is equal to
 220/67 times Ben Nevis.
 N for Nevis.
 To solve for Nevis, we multiply both sides by the
 inverse of this coefficient right here.
 So we multiply both sides by 67/220.
 So times 67/220.
 The 67 cancels with that 67.
 That 220 cancels with that 220.
 And then you get let's see, if I take 4,400 divided by
 220 440 divided by 220 is 2.
 So this is going to be 20.
 So 4,400 divided by 220 is just 20.
 So you get Nevis is equal to I'll swap sides.
 So Ben Nevis is equal to 67 times 20 meters.
 And now that's what?
 1,340 meters.
 Is that is right?
 Well, lets just leave it like that, because we could
 actually it looks like that's 67 I'm going to leave Nevis
 as 67 times 20 meters.
 And substitute it right there.
 So Yukon I'll just go down here, because I have more real
 estate there Yukon is equal to 298 over 67 times the
 height of Nevis.
 Nevis is 67 times 20.
 So times 67 times 20.
 Well I can divide 67 by 67, and I get Yukon is
 298 times 20 meters.
 So Yukon is equal to 298 times 20.
 And what is that equal to?
 That is equal to Let's see that's 2 times 298
 is going to be 396.
 Oh sorry, it's going to be 596.
 This is almost 300, so it should be close to 600.
 This is 2 less than 300, so this should
 be 4 less than 300.
 And then, I have a 0 here.
 So it's going to be 5,960 meters.
 And we are done.
 Let's do one more of these word problems. All right.
 At a large high school, it is estimated that 2 out of every
 3 students have a cell phone.
 And 1 in 5 of all students have a cellphone that is one
 year old or less.
 All right.
 So let's think about it.
 Let's say that x is equal to the total number of students.
 This first line, 2 out of 3 students have a cell phone, so
 we could say that 2/3 x have cell phone.
 That's what that green statement tells us.
 And then that purple statement 1 in 5 of all
 students have a cellphone that is one year old or less.
 So 1/5 x have less than 1/5 year cell phone.
 So they want to know, out of the students who own a cell
 phone so it's out of this that's our denominator.
 So let me write that down.
 That is our denominator.
 So out of the students who have a cellphone that's
 right there they want to know what proportion owns a
 phone that is more than one year old.
 So how many students have a cell phone that is more than
 one year old?
 Well, we could take the total number that have a cellphone,
 which is 2/3 x.
 2/3 of all the students have a cell phone.
 We can subtract out all of the students that have a new
 cellphone a cell phone that is less than one year.
 Remember they're saying more than one year here.
 So we want to subtract out all the students with the new
 cellphone, minus 1/5x, and you will then have the proportion
 of students who have this right here.
 This is right here.
 This is, have greater than 1/5 year cell phone.
 They have a phone, but it's more than 1/5 years old.
 This is all of them that have a cellphone.
 We subtract out the new ones.
 So this is, essentially, all of the people who have an
 older than oneyear old cell phone.
 So to solve this, we just subtract the fractions.
 So this is just going to be, let's see, 2/3 is the same
 thing as 10/15.
 That's 2/3 minus 1/5.
 The same thing as 3/15 x.
 Which is equal to 10 minus 3 is 7/15 x.
 Is the total proportion of students that's this
 orange what proportion owns a phone that is more
 than one year old?
 It's 7/15 x.
 That's an actual number.
 So if you want to know, out of the students who own a cell
 phone so out of the students who own a cell phone, right
 there 2/3x, what proportion owns a phone that it is more
 than one year old?
 This is the number that own a cellphone that is more than
 one year old.
 And this whole value is the proportion out of the students
 who have a cell phone.
 Lucky for us, the x's cancel out.
 And we are left with this is equal to 7/15 times the
 inverse of the denominator.
 You divide by 2/3.
 That's the same thing as multiplying by 3/2.
 And what does this equal to?
 Divide by 3.
 We are left with 7/10.
 So of the students who own a cell phone, 7 out of 10 of the
 students who own a cell phone, own a cell phone that is more
 than one year old.
 And we are done.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
in 7:44,i dont understnd the '1/5x have <1/5 yr cellphone.
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.
no your not idiot just ask for help dont let yourself down you just need a little help with math
cuz he messed up. its 1 year
listen. Watch the video until you understand. That is what I do. It helps a lot.
Sal messed up, which is probably why. He messed up when writing his answer thing
he was trying to write an arrow the the > is an arrow (i could be wrong tho so just double check)
Ok thanks! I'm an idiot but whatever!
Guys! Whether Sal messed up or not he still tries his hardest and takes out a lot of time to make these videos. Appreciate them! Plus, he doesn't mess up a lot.
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!) (;
Proportion: An equation stating that two ratios are equivalent.
:) (Hope this was Helpful!) (;
ratio and proportions are in a nutshell  if you get 1 almond in a bag for every 2 walnuts in the same bag it means you have 2 walnuts and 1 almond well if you get 2 almonds then by that standard you should have 4 walnuts. it can be written as 1 almond : 2 walnuts or 1 almond / 2 walnuts the ratio will always be in equal proportions so if you increase the top to a 2 almonds / x walnuts you have to increase the bottom by the same amount so 2 almonds / 4 walnuts.
the way to test if the problem is = or in proportion is to cross multiply so 1/2 = 2/4 you multiply the numerator on the one side by the denominator on the other so 1 x 4 = 4 and 2 x 2 = 4 so since both numbers come to 4 they are in proportion. hope this helps.
the way to test if the problem is = or in proportion is to cross multiply so 1/2 = 2/4 you multiply the numerator on the one side by the denominator on the other so 1 x 4 = 4 and 2 x 2 = 4 so since both numbers come to 4 they are in proportion. hope this helps.
A ratio and proportion is nothing more than _a part of a whole divided by a whole_. To get into a little better explination, think of a sport's season. Even if you don't like sports, if you are needing to know how many games a team won that year compared to how many they lost, a ratio of _how many games won_ divided by _how many game total_, should be able to tell you whether or not you should be betting your money on that team.
A proportion is saying that two _ratios_ are the same. For example, 1/2 = 2/4 is a true proportion because if you multiply *both* the numorator and the denominator of 1/2 by 2, you get 2/4, which, when reduced, is 1/2. Hope this helps(:
A proportion is saying that two _ratios_ are the same. For example, 1/2 = 2/4 is a true proportion because if you multiply *both* the numorator and the denominator of 1/2 by 2, you get 2/4, which, when reduced, is 1/2. Hope this helps(:
A ratio is L compared to M.
A Proportion is saying the ratio between L and M is the same as the ratio between C and W
Example
3:9....................................................states that 3 and 9 have a relationship
9 : 27 ...................................................Same thing, 9 and 27 have a relationship
1:3::3:9::9::27..................................Says 1 and 3 have the same relationship as 3 and 9, also as 9 and 27. (A colon between them means you are stating them as a ratio. Two colon mean that you are setting them, (or that they are) related to each other in the same way.
Example of an Algebraic proportional problem
3:5::X:Y Set a new proportion where Y is 4.5 times what it is now.
Answer 3 :22.5::X:Y
Hope I didn't confuse you and helped.
A Proportion is saying the ratio between L and M is the same as the ratio between C and W
Example
3:9....................................................states that 3 and 9 have a relationship
9 : 27 ...................................................Same thing, 9 and 27 have a relationship
1:3::3:9::9::27..................................Says 1 and 3 have the same relationship as 3 and 9, also as 9 and 27. (A colon between them means you are stating them as a ratio. Two colon mean that you are setting them, (or that they are) related to each other in the same way.
Example of an Algebraic proportional problem
3:5::X:Y Set a new proportion where Y is 4.5 times what it is now.
Answer 3 :22.5::X:Y
Hope I didn't confuse you and helped.
```
*Ratio* : _The quotient of two quantities that are in the same unit_.
*Proportion* : _An equation stating that two ratios are equivalent_.
``` hope this helps
*Ratio* : _The quotient of two quantities that are in the same unit_.
*Proportion* : _An equation stating that two ratios are equivalent_.
``` hope this helps
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)
(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........
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
Meh I think it is easy
Yes, a ratio is similar to fractions I think you can even write a ratio as a fraction!
For example: 3:5
3/5 (3 over 5)
For example: 3:5
3/5 (3 over 5)
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 Khan do it.
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!
Just pay attention to the video. Over time, you will most definetly understand.
A portion is when you give food out depending on who is there by the table. A Proportion 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!
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
To answer your original question
x= 7.9328..
y=8.4617..
z=9.5194..
x*y*z equals your number (639).
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
To answer your original question
x= 7.9328..
y=8.4617..
z=9.5194..
x*y*z equals your number (639).
Thanks a lot =)
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?
Sal, please help with this question:
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?
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?
There are 112 sci students and 84 art students.
Hope that helped! plz vote up!
Hope that helped! plz vote up!
3/4
3 art students for every 4 sci students
3 art students for every 4 sci students
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 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.
Not really a question but,
Thanks you Sal for being such a lifesaver! Now I understand math!
Thanks you Sal for being such a lifesaver! Now I understand math!
LOL you know there is a comment section at the top below the video right? XD
Yeah, I just found out today. XD
How does this all work out
Proportions are direct comparisons between two numbers.
They are only expressed using fractions.
They are only expressed using fractions.
I don't really know, I just started at Khan Academy. Hope it helps!
This is a 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!!
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).
at 5:31 the sun was awesome
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
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.
In problem 2 starting at 6:53 I still a little confused when divideing the different
varibles can someone please explain?
Thank You
varibles can someone please explain?
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!!
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.
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
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.
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.
why did sal reverse the fraction 13/6 into 6/13 @ at the beginning??
When you multiply a fraction by itself, you have to multiply the original by the inverse, which is just the fraction flip upside down.
Make sense?
Make sense?
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.
They are very similar ideas. Both are comparisons of numbers.
examples: The ratio of students to teachers is 18 to 1.
The proportion of boys in the class is 6 out of 10.
I suppose more often proportion is used to compare something to the total, but mathematically they are the same.
examples: The ratio of students to teachers is 18 to 1.
The proportion of boys in the class is 6 out of 10.
I suppose more often proportion is used to compare something to the total, but mathematically they are the same.
Man, I Dont Not Understand .
Why can't I use cross simplification on ratio equations? If 12/8 = x/9 why does it not follow that 1/2 = x/3?
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.
w+3/4=5 1/3
solve for w.
solve for w.
What does proportion mean again :D
it is all so confusing! Please Please explain it again.:D
smiles,
Brezy Angel Froehlich (that is all random letters up there)
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 Proportion 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!
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!
why are we multiplying by nevis i understand nevis is same size but why multiply 2:55
plz answer
plz answer
I dont get this at all it is to hard. =(
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?
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.
HI SAL!! this video helped me understand ratios and propartins
I have a 4"x 6" photo, I would like to increase the size to 30" x ?" to maintain proper proportions. Thank you.
.8 or just 8?
the unknown side would be .8
In 5:32, why is the height of Ben Nevis left as 67 times 20?
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.
It's spelled correctly.
http://en.wikipedia.org/wiki/Mont_Blanc
http://en.wikipedia.org/wiki/Mont_Blanc
How do I find 2/5 pound of mixed nuts for 2.50
a man brought a house for Rs.5 lacs and rents it.He puts 12.5% of each month's rent aside for repairs, pays Rs.1660 as annnual taxes and 10% on his investment there after..The monthly rent of the house=??
What if say the question is x3/(over)5=7/3
then d cross multiply and find it out
Do you have worksheets which would help me with ratio and proportion
If you don't understand ratio and proportion, you should try the practice problems.
If you are having trouble with any subject, the practice problems are a great solution.
How do I find an actual ratio?
What is the technical definition of a proportion? #confused
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?
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?
How would you solve the equation: 4:n:5=5:8:m? How would I find the value of the two variables?
You'd need to do it one piece at a time. Start with 4/n = 5/8, then do 4/5=5/m.
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
there different then other ratios
you need to be advanced for this kind of math
you need to be advanced for this kind of math
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.
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.
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.
how would you cross multiply
a/b = c/d > a*d = b*c
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!
At 09:099:23, did he just just cross multiply?
i think i may have missed a video......
In the second problem, the one of the cell phones, you subtract the quantity of students who have a new cell phone out of the students who have a cell phone.
Why do you do another step, if that was what the problem wanted to know?
Why do you do another step, if that was what the problem wanted to know?
at 4:11 working backwards, can u work this out another way besides working backwards?? if so how would we?
I need help solving this problem. Michael walked 6 miles in 40 minutes. How long did it take him to walk the first 2 miles?
well all you have to do is divisde. if he walked 6 miles in 40 minuets, then he must of walked 3 miles in 20. then l 1/2 miles in 10. then 1 in about 7.5. so it is 15 minuets
Wait, you two have different answers. Who is correct?
Well, 2 miles is a third of the total of 6 miles Michael walked, so it took him one third of the 40 minutes.
How much is a third of 40 minutes? You divide 40/3 and you get 13 and 1/3, so the answer is 13 and 1/3 minutes, and if you want to really make your teacher happy you can tell him that one third of a minute is 20 seconds, so the final answer would be: 13 minutes and 20 seconds.
Cheers,
How much is a third of 40 minutes? You divide 40/3 and you get 13 and 1/3, so the answer is 13 and 1/3 minutes, and if you want to really make your teacher happy you can tell him that one third of a minute is 20 seconds, so the final answer would be: 13 minutes and 20 seconds.
Cheers,
why did he say the answer for yukon is 4 less than 300 when i was 4 less than 600
why does it become 13/6X? what does it mean? can someone please explain?
The height of a building is 3 3/8 in. on a scale drawing. Find the actual height of the building if the scale used is 1 in. : 4 ft.
3 3/8 = 27/8, 4 ft = 48 in.
27/8 : x = 1 : 48
x = 162 in. = 13.5 ft.
The building is 13 and a half feet tall.
27/8 : x = 1 : 48
x = 162 in. = 13.5 ft.
The building is 13 and a half feet tall.
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.
he does not use a mouse
Help me Sal, I really need alot of help on my preparation for CCAT testing.
A hare and a jackal are running a race.Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare,the jackal takes 5 leaps.Find the ratio of their speeds.
A. 64:25
B.8:5
C.5:8
D.25:64
I don't understand how the choices even relate to the question. Please help
A hare and a jackal are running a race.Three leaps of the hare are equal to four leaps of the jackal. For every six leaps of the hare,the jackal takes 5 leaps.Find the ratio of their speeds.
A. 64:25
B.8:5
C.5:8
D.25:64
I don't understand how the choices even relate to the question. Please help
I don't understand which to multiply by: x or the number below/above x?
These proportions are very hard
how do you answer this? : 7x = 9y
Thanks! :D
Thanks! :D
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!!!
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 :)
Thats so true!! I am in love and I have driven myself crazy with the joy of it! Spread the word so more kids can learn!!!
what is wrong the fact that they are looking towards mr. khan to get help?! they are getting better and i praise them for that!
Be kind to other students. You can vote ten times each hour you are working on the site. Remember to vote for good questions and answers both. Badges are awarded at 10, 25, and 50 up votes.
hey can i go to bed???:/
please im tired:/
tahts wrong why because you did not do it right ok
in 0:06 how did he get the five?
That is just part of the problem. He didnt solve anything anything to get it.
He used the theory of quadratic's to solve then simplified the remainder of negative number's and got 5. Simple? >.>
if u take 227/12 and 375/3 could make a proportion out of it?????
It wouldn't be an equal proportion, so nope.
how do u rewrite a quotient as s a ratio using the units in a denominator
The tallest moutain in Canada is not Mount Yukon, it is Mount Logan.
how do you crossmultiply?
To cross multiply you simplify the vertical fraction ex: 6/8=3/4 and the say the problem is 3/4=x/2 you do 3*2=4x and then 6=4x and then divide both sides by four, (to cancel the four on the right) and you get 1.5
It takes Joaquin 1/5 hour to hike 1/4 mile. What is Joaquin's unit rate, in miles per hour?
My parents bought a house in Austin for 2 million dollars. The total, which was 3 million and 32 dollars, was some(x) amount of money with 5% tax. How much is the 'some amount of money'?And they bought a riverboat for 1/341 of the some amount of money. How much is the riverboat?
AR 735 why dud he put y in fir 1/6
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
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
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?
I think that this question can only be solved using algebra.
Let's make F as the number of markers Fanny has, and K as the number of markers Kevin has.
F/K= 5/3
Now, it changes.
K+(1/2*F)1/2*F=30
Now, K+(1/2*F)1/2*F is just K.
K=30
It means, that the original number of markers Kevin has is 30. Let's test this out
If Kevin had 30 markers, then Fanny had 50, and she gave him 25.
5025=25, 30+25=55.
Kevin now has 30 more markers.
To answer your question Fanny gave Kevin 25 markers.
Hope I helped you!
Let's make F as the number of markers Fanny has, and K as the number of markers Kevin has.
F/K= 5/3
Now, it changes.
K+(1/2*F)1/2*F=30
Now, K+(1/2*F)1/2*F is just K.
K=30
It means, that the original number of markers Kevin has is 30. Let's test this out
If Kevin had 30 markers, then Fanny had 50, and she gave him 25.
5025=25, 30+25=55.
Kevin now has 30 more markers.
To answer your question Fanny gave Kevin 25 markers.
Hope I helped you!
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.
Now K+(1/2*F)  1/2*F=K. Please make it simpler.
How do you solve the problem at 2:47. I still don't understand how to solve these kind of problems.
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
13/6=5/x 13.x=5.6
i get it now..
can someone put a question for me to solve in the comments?
Please help, I am in desperate need!
can someone put a question for me to solve in the comments?
Please help, I am in desperate need!
Wait... why do you 7/15(x) / 2/3(x) or 7/15(3/2) = 7/10 at the end? Question: Out of the students who own a cell phone, which is 2/3(x), what proportion owns a phone that is more than one year old/not 1/5(x)? so.. 2/3(x)  1/5(x) = 7/15(x) <Isn't that just the answer???? why are we doing the other stuff at the end of the vid?
Because the question is "what proportion owns a cell phone that is more than one year old out of the students *who own a cell phone*". It's not asking "out of *all* the students", which is what 7/15(x) is.
What is the answer to this question,
A Honda is 22/93 the weight of a Toyota, and the Toyata weighs twentytons.
How many ounces does the Honda weigh?
A Honda is 22/93 the weight of a Toyota, and the Toyata weighs twentytons.
How many ounces does the Honda weigh?
T = weight of Toyota
H = weight of Honda
T = 20 tons
H = 22/93 * T > H = 440/93 tons
440/93 tons * 32000 ounces/ton = 151,397.849 ounces
H = weight of Honda
T = 20 tons
H = 22/93 * T > H = 440/93 tons
440/93 tons * 32000 ounces/ton = 151,397.849 ounces
I get it but I don't. For example if I have 6/x=9/5 if I cross multiply I get it right every time but the problem is I can't cross multiply when I have x+3/1=11/5. So my problem starts at the very beginning because on the first set if I don't multiply and instead I chose to solve for X first I don't get the right answer like this: 6/x . x= 9/5 . x ok so that cancels out the x and leaves me with 6=9/5 . x, then I multiply both sides of the equation by 9/5 to get rid of this part and I end up with 6=54/5 which is not the same from the cross multiplication which is 30/9. Why do I sometimes get this problem and some times I don't when I do the exact same steps every time? Now I did noticed that Sal sometimes flips the fraction, but How do I know when to do that, how do I know which term I should cancel out first in order to get the correct answer every time?
I believe you are solving for x incorrectly
6/x = 9/5. Multiply both sides by x
(6/x)*x = (9/5)*x
6 = 9x/5 Multiply both sides by 5
6*5 = (9x/5)*5
30 = 9x and divide by 9 to isolate x.
30/9 = 9/x
10/3 = x
When you have 9x/5 (or as you wrote it, 9/5 . x) you can't cancel it out by multiplying by 9/5. You have to multiply by the reciprocal/inverse, 5/9, which is what happened in the solution above (except in more steps). Just to show you
6 * (5/9) = (9/5 . x) * (5/9)
30/9 = x
10/3 = x
6/x = 9/5. Multiply both sides by x
(6/x)*x = (9/5)*x
6 = 9x/5 Multiply both sides by 5
6*5 = (9x/5)*5
30 = 9x and divide by 9 to isolate x.
30/9 = 9/x
10/3 = x
When you have 9x/5 (or as you wrote it, 9/5 . x) you can't cancel it out by multiplying by 9/5. You have to multiply by the reciprocal/inverse, 5/9, which is what happened in the solution above (except in more steps). Just to show you
6 * (5/9) = (9/5 . x) * (5/9)
30/9 = x
10/3 = x
This one is really hard, especially with all the "big" fractions like 228/448, etc. Is there an easy way to tackle these problems? I am only starting to understand this! Aren't proportions just comparing numbers and/or fractions to each other?
yes, you can simplify these fractions. So 228/448 is equal to 57/112.
i like this questen 2:42
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! :(
4,*,9,131/2 are in proportion then * is
What is 2.8 hours to 3 days? I changed days to hours and changed 2.8 to 2.48 hours then "x" by 100 to get a whole number but still don't understand.
Well, 3 days is 72 hours, right? So you have the ratio 2.8 : 72. One mistake you have is changing 2.8 to 2.48; you are correct in thinking that 0.8 hours is the same as 48 minutes, but it's completely unnecessary to change 2.8 hrs to 2 hrs 48 mins because that gives you two different units (hours and minutes) when, in order to solve the problem, you must have just one unit (hours), which is the reason you changed days to hours in the first place.
So, back to the problem, you have 2.8 : 72. You can multiply by ten to get 28 : 720. The greatest common factor of 28 and 720 is 4; dividing both numbers by 4, you get 7 hrs : 180 hrs.
So, back to the problem, you have 2.8 : 72. You can multiply by ten to get 28 : 720. The greatest common factor of 28 and 720 is 4; dividing both numbers by 4, you get 7 hrs : 180 hrs.
How come at 7:48 its < 1/5 yr cell phone?
How do I find the length of similar figure
I keep getting a different answer for the first problem and I'm not sure why.
E = 4800(44/48) = 4400
4400 = (220/67)N = (4400)(67) = 220N = 1340N
Y = 1340(289/67) = 1340(4.31343287) = 5780
Or worked out another way (1340/1)(289/67) = 387,260/67 = 5780.
Kahn's answer is 5960. What am I doing wrong.?
E = 4800(44/48) = 4400
4400 = (220/67)N = (4400)(67) = 220N = 1340N
Y = 1340(289/67) = 1340(4.31343287) = 5780
Or worked out another way (1340/1)(289/67) = 387,260/67 = 5780.
Kahn's answer is 5960. What am I doing wrong.?
You flipped two digits around accidentally. The equation for Y is 298/67, but you wrote 289/67. : )
How pressure can be calculated if only height is given ?
Please help.
Thank you.
Please help.
Thank you.
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!
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!
A portion is when you give food out depending on who is there by the table. A Proportion 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!
Hi
trying to solve the problems in "proportion 1" I found myself stucked. I make an example
if I have 6/5 = x/7 I solve by doing (6/5 * 7/x) = (x/7 * 7/x)
Now let's have a look at this one
6/5 = 7/x. Assuming that the previous method is universal I should proceed in this way
(6/5 * x/7) = (7/x * x/7). The problem is that the system tells me "no man, this is wrong. You have to do (6/5 * x/1) = (7/x * x/1)".
It's fine for me. But I have this simple question: why? I really cannot understand it (I know I'm probably quite dumb).
trying to solve the problems in "proportion 1" I found myself stucked. I make an example
if I have 6/5 = x/7 I solve by doing (6/5 * 7/x) = (x/7 * 7/x)
Now let's have a look at this one
6/5 = 7/x. Assuming that the previous method is universal I should proceed in this way
(6/5 * x/7) = (7/x * x/7). The problem is that the system tells me "no man, this is wrong. You have to do (6/5 * x/1) = (7/x * x/1)".
It's fine for me. But I have this simple question: why? I really cannot understand it (I know I'm probably quite dumb).
does this pair of ratios form a proportion 3.5/1.2=7/8
I am having a hard time understanding this, especially since Sal made a mistake at 7:36. Maybe I need to figure it out on my own?!
cant i just use cross products to solve these problems. i mean thats what i am doing and it works.
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.
why do you have to put an x
You mean at the beginning? He is setting a problem, which he then works out. x stands for "some number".
The problem is, 13/6 = 5/"some number". What is the number?
The problem is, 13/6 = 5/"some number". What is the number?
thank you Barry Desborough
I need some help solving this please?: 8/(x+3)=1/x +1
I still dont understand the mountain problem! Could someone help me?
I don't get the mountain question. How'd he get Ben Nevis's size?
a bag contains 20 kg of rice and another bag contains 60 kg of wheat, find the ratio of the amount of rice to that of wheat.what is the ratio of rice to the total weight ?
Report a mistake in the video
Example:
At 2:33, Sal said "single bonds" but meant "covalent bonds."
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