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## 7th grade

### Course: 7th grade > Unit 4

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?

- 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?(8 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. :)(12 votes)

- 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...(11 votes)
- 9 years and nobody responded(6 votes)

- I should probably pay attention instead of scrolling comments lol(7 votes)
- same here, procrastinator club i guess(3 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! :)(6 votes) - Could i get some help with proportion problems?(4 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.(5 votes)

- anyone else just scrolling the comments cause your teacher blocks everything else?(5 votes)
- Yes, same. This fr.(2 votes)

- So really in0:34he just listed out what was in the problem straight forward. Right?(4 votes)
- I get it now.. I just divide or multiply.(1 vote)
- zoechaplain is not human.. their species just simply divides and multiplies amongst the human race.. they are among us(4 votes)

- what does the word Ratio mean?(4 votes)
- A ratio, written as two numbers with a colon (:) between them, is just a way of saying "For every (number) of these, there's (this amount) of those." It's a way to compare the quantities (the amounts) of two things.

For example, if you have 2 apples and 3 oranges, the ratio of apples to oranges is 2:3 which is read "2 to 3" ; Or for every 2 apples, there are 3 oranges. And what makes ratios useful is that it's a way of showing that however one number increases, the other increases the same way. This example shows a ratio in its simplest form.

To go more in-depth, ratios also follow the rules of fractions (and can be expressed as them.) For example, we know that One-half, two-fourths, and three-sixths are all equal. We can reduce them all to one-half. Ratios follow the same rules. If you have 3 apples, and 6 oranges the ratio is 3:6 (three to six) which is equal to 1:2 (one to two). For every 1 apple, there's 2 oranges. If you already know fractions, ratios are very simple to understand.(1 vote)

## 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.