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### Course: Operations and Algebraic Thinking 222-226 > Unit 1

Lesson 6: Writing & solving proportions# Proportion word problem: cookies

A recipe for oatmeal cookies calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is needed for a big batch of cookies that uses 9 cups of oatmeal? Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- This just confused me, and I tried to do the problems for the Proportions 1 thing, Im confused now, because these are to difficult to me... help please...(39 votes)
- 9 years and nobody responded(38 votes)

- I should probably pay attention instead of scrolling comments lol(38 votes)
- wow that's relatable(5 votes)

- About proportions...some definitions say "one variable related to another variable by a constant ratio". But the proportionality test

says x/(f(x))=k, where k is constant. So any equation of a line would work, as long as the line intersects (0,0)? In physics,

we are taught that current, voltage, and resistance are proportional to each other in a simple circuit - current is zero when voltage is zero. But what about Farenheit to Celcius conversion? Isn't C proportional to F? Mathematically speaking,

I would say no, but logically I would say yes...apparently proportionality gets used (wrongly) interchangeably with linearity.? In the C F problem, what is the proper term for the C F relationship?(12 votes)- I don't know much about physics, but I can teach you what proportions are in math. So you mentioned x/(f(x))=k? Close. It's y/x=k. y can also be f(x) though. A proportion is basically a relationship between two numbers that is always constant. If you were to graph a proportion, it would be a straight line that passes through the origin (0,0). In the F and C question you had, the relationship would be F=1.8C+32, or f(C)=1.8C+32. It is not proportional because it doesn't pass through the origin. It instead has a y-intercept of (0,32). An equation can be a linear equation, but it may not always be proportional.

Hope this helps. :)(21 votes)

- anyone else just scrolling the comments cause your teacher blocks everything else?(19 votes)
- Could i get some help with proportion problems?(5 votes)
- You could do cross-multiplication to solve proportions, but remember that the unknown value is always the denominator in the answer. It works because you want to isolate the variable, so you could multiply the side with the variable by the denominator and then do that with the other side. Then simplify the fraction.(7 votes)

- I knew the answer before the first 30 secs of the vid(8 votes)
- How about if you have a problem like this?

Jim uses 3 cups of peaches to yield 4 jars of peach jam. He also makes strawberry-peach jam. He uses equal amounts of strawberries and peaches. How many cups of strawberries does Jim need to yield 10 jars of strawberry-peach jam? If someone could walk me through how to do the problem and why that would be greatly appreciated! Thanks in advance! :)(5 votes) - thanks sal but what if i do it this way 2/3.9/1 and then simplify it and still get 6 is it correct(4 votes)
*Hey Bryan A. I feel bad for you. You have waited 11 years and your question still hasn't been answered*(5 votes)

- I still want my mcdonalds cookies😭(6 votes)
- Let me just share here how important Math is even when you are hating it cos a lot of things don't come naturally and perfectly alright to feel that way. 99% struggle with Math initially- Very few are born geniuses to whom Math comes naturally. It is really important to spend more time, rewatch these amazing tutorials to get a complete grasp. Remember, everything is interrelated in Math so it is crucial you get all the basics right or else you will always feel lost. I'm 30 years old and I'm back here to refresh my memory on math so I can tutor my kids better. Math is everywhere- Computers, Business, etc. So just keep at it. Don't give up and the efforts you put here will reap tremendous benefits in the future. Also, feel free to explore more youtubers on Youtube as sometimes things clicks better when we try different ways.

Nonetheless, the best way is to simply play around with the problem.

For eg- the concept of an equation is a marvellous thing.

We can start with 1=1 and to keep it that way we need to do on the right what we do to the left and vice versa because 1=1 by definiton means they are equal.

so if I do 1*5 = 1, the equation becomes invalid cos the lest is 5 and the right is still 1- so we do 1*5 = 1*5. We basically keep doing the same thing even when thigns get more abstract. So just playing with the basic equation and trying to manipulate it in as many ways as possible builds a good intuition to solving these problems which are super important in day to day life.(5 votes)

## Video transcript

A recipe for oatmeal cookies
calls for 2 cups of flour for every 3 cups of oatmeal. How much flour is
needed for a big batch of cookies that uses
9 cups of oatmeal? So let's think about
what they're saying. They're saying 2 cups of flour. So 2 cups of flour for
every 3 cups of oatmeal. And so they're
saying, how much flour is needed for a big
batch of cookies that uses 9 cups of oatmeal? Now we're going to
go to a situation where we are using
9 cups of oatmeal. Let me write it this
way-- 9 cups of oatmeal. And I'll show you a
couple of different ways to think about it. And whatever works
for you, that works. So one way to think about
it, so we're wondering. We're going to
say, look, we know if we have 3 cups of oatmeal,
we should use 2 cups of flour. But what we don't know is if
we have 9 cups of oatmeal, how many cups of
flour do we use? That's what they're asking us. But if we're going
from 3 cups of oatmeal to 9 cups of oatmeal, how much
more oatmeal are we using? Well, we're using three
times more oatmeal, Right? We're multiplying by 3. 3 cups of oatmeal and
9 cups of oatmeal, we're using 3 times the oatmeal. Well, if we want to use
flour in the same proportion, we have to use 3
times the flour. So then we're also going to
multiply the flour times 3. We're going to multiply
the flour times 3, so we're going to have
to use 6 cups of flour. Ignore that question mark. And that answers the question. That's how much flour we need
for a big batch of cookies that uses 9 cups of oatmeal. The other thing is you
could set up a proportion. You could say 2 cups of
flour over 3 cups of oatmeal is equal to question mark. And instead of
writing question mark, I'll put a variable in there. Actually, let me put
a question mark there just so you really
understand it is equal to a question
mark in a box number cups of flour over
9 cups of oatmeal. And so I like this
first way we did it because it's really
just common sense. If we're tripling the
oatmeal, then we're going to have to
triple the flour to make the recipe in
the same proportion. Another way, once you set
up an equation like this, is actually to do a
little bit of algebra. Some people might call
it cross-multiplying, but that
cross-multiplying is still using a little bit of algebra. And I'll show you why they're
really the same thing. In cross-multiplication,
whenever you have a proportion
set up like this, people will multiply
the diagonals. So when you use
cross-multiplication, you'll say that 2 times 9
must be equal to question mark times 3, must be equal to
whatever is in this question mark, the number of
cups of flour times 3. Or we get 18 is
equal to whatever our question mark was times 3. So the number of cups of
flour we need to use times 3 needs to be equal to 18. What times 3 is equal 18? You might be able to
do that in your head. That is 6. Or you could divide both sides
by 3, and you will get 6. So we get question
mark in a box needs to be equal to 6 cups of flour. Same answer we got through
kind of common sense. Now, you might be
wondering, hey, this cross-multiplying doesn't
make any intuitive sense. Why does that work? If I have something set up
like this proportion set up, why does it work that if I
take the denominator here and multiply it by the
numerator there that that needs to be equal
to the numerator here times the
denominator there? And that comes from
straight up algebra. And to do that, I'm just going
to rewrite this part as x just to simplify the
writing a little bit. So we have 2/3 is equal to--
instead of that question mark, I'll write x over 9. And in algebra,
all you're saying is that this
quantity over here is equal to this
quantity over here. So if you do anything
to what's on the left, if you want it to
still be equal, if the thing on the right
still needs to be equal, you have to do the
same thing to it. Now, what we want to do is we
want to simplify this so all we have on the
right-hand side is an x. So what can we
multiply this by so that we're just left with an x? So that we've solved for x? Well, if we multiply
this times 9, the 9's are going to cancel out. So let's multiply
the right by 9. But of course, if we
multiply the right by 9, we have to still
multiply the left by 9. Otherwise they still
wouldn't be equal. If they were equal before
being multiplied by 9, for them to still be equal, you have to
multiply 9 times both sides. On the right-hand side,
the 9's cancel out, so you're just left with an x. On the left-hand side, you have
9 times 2/3, or 9/1 times 2/3. Or this is equal to 18/3. And we know that 18/3
is the same thing as 6. So these are all
legitimate ways to do it. I wanted you to understand
that what I'm doing right here is algebra. That's actually the reasoning
why cross-multiplication works. But for a really simple
problem like this, you could really just
use common sense. If you're increasing the cups
of oatmeal by a factor of 3, then increase the cups of
flour by a factor of 3.