## Denominator vs numerator - getting confused on which is which

Yttrium2 - 2-10-2019 at 09:25

Okay so I know the numerator goes on top of the denominator, but when doing word problems involving division, I get uncertain which numbers to divide by.

I've seen explanations of division, and have been using the Khan academy, but I've yet to see information pertaining to this.

Can someone explain the general sense of what goes where, when and why?

Such as price per quantity gives us a price per item

What else?

I can typically work myself through division problems, but at times I do get the two mixed up, and will have to flip my problem around

The best I understand is that the top number gets broken into groups pertaining to the numerical value of the denominator.

Praxichys - 2-10-2019 at 10:00

Unit analysis is your friend. I would suggest watching some videos on that. Have you reached algebra yet? It will determine how I need to approach the explanation.
Ubya - 2-10-2019 at 11:54

4/5
4 divided by 5
4:5
You have for things and you have to divide them in 5
I have 10 candies to share with my 3 friends, each friend gets 10/3 candies (3.3333)

You need elementary school

Yttrium2 - 2-10-2019 at 13:23

I've been redoing the khanacademy, I was at 40% completion of the world of math and now I'm at about 35%-- or so...

I do not need elementary school! I'm in the 6th grade!

Perhaps I did skip over the explanations to the division problems I wasn't having difficulty with, perhaps my answer lie in there.

The way you said "You have for things and you have to divide them in 5"

Seems like it may help me.

I'll bring up the specific instances of when I get them crossed.

I do know how to divide / do some dimensional analysis, I just get things crossed on occasion.

SWIM - 2-10-2019 at 21:05

 Quote: Originally posted by Yttrium2 I've been redoing the khanacademy, I was at 40% completion of the world of math and now I'm at about 35%-- or so... I do not need elementary school! I'm in the 6th grade! Perhaps I did skip over the explanations to the division problems I wasn't having difficulty with, perhaps my answer lie in there. The way you said "You have for things and you have to divide them in 5" Seems like it may help me. I'll bring up the specific instances of when I get them crossed. I do know how to divide / do some dimensional analysis, I just get things crossed on occasion.

Congratulations!

After over 4 years asking questions on this board you've finally climber to the apex of your intellectual achievement by getting into the 6th grade!

You were apparently either a 1st grader when you started posting here, or have been making scant progress over the last 4 years.

I think you better try to get a bit more serious about your education or you may find yourself facing The Wrath of Kahn Academy.

They'll send a very buff Ricardo Montalban in an uncombed grey wig to straighten you out and believe me you don't want that.

MrHomeScientist - 3-10-2019 at 10:22

And according to his first post here they've got 1st graders learning about enthalpy and "monoatomic gas phase atoms" now - impressive!
Yttrium2 - 3-10-2019 at 12:39

I've been redoing stuff, I did seem to have a lot of gaps in my math understanding. Although, I do realize you can spend forever polishing the basics, doing review or affirming what you've already learned in different questions... I may be conflating things here, but there seems to come a time when making forward progress is necessary to get to the finish line. I honestly maybe only needed to review algebra/algebra2 to be ready for the precalc that I wasn't ready for. However, I decided to work my ways from the ground up, making sure I iron out all the problems in elementary understanding. I recommend it if you are serious about chemistry.

I've gone from kindergarten to 6th grade in a little over a month,

Watch yourselves, I'm quickly improving on math, and I'm going through everything with a fine tooth comb! I am likely able to do some problems that would stump a few of you.

It's supposed to bring back problems that one has already mastered to keep things fresh, which I like. I do believe that if you're not using something you've practiced that after a while it becomes forgotten. So one is basically learning one new thing, and forgotting something.

It seems like I've forgotten a lot about English, I've fulfilled the requirement, but I don't think I remember much.

Now the only things I'm really having difficulty with is the world of math, everything from the basics up till linear equations and differential algebra. It really is a large investment of time and soul. I should be more serious about not smoking if I'm placing so much vested interest into myself/am working so hard on building myself up.

And to take risks just seems dumb when one has worked so hard to build themselves up, to risk it and throw away ones potential and abilities would be one of the if not the worst mistakes.

Any comments? I'm sure someone is going to say if your having so much difficulty with math you should rethink chemistry-- the thing is is that it's not necessarily easy, or hard, but it takes time. Months to years to polish and perfect everything.

I've also, eventually, have to grasp a foreign language. I'm living really close to Mexico, perhaps Spanish is what I should learn, though I initially tried Mandarin and still think it's probably the more useful, interesting of the languages.

I know I don't have time for everything, I really do need to make more than scant progress and this is what I've been trying to do.

One thing that troubles me is that eventually I need a break from math to decompress. Sometimes I'll over do it and get burnt out for a day or two, additionally, I'm only at my sharpest for a Max of around 30 minutes, then I'll need a break. After a day of group meetings I seem to want to lay down a lot but this may be making the problem worse.

Id like to find the best decompression activities so I can study for longer/find ways that ill be able to survive a 2.5 hour math lectiure, once more. I am getting older, but wiser.

### word problems

sodium_stearate - 3-10-2019 at 17:02

"per" means divide.

"of" means multiply.

A fraction is a division problem that someone was
too lazy to complete.

[Edited on 4-10-2019 by sodium_stearate]

### Math

Yttrium2 - 3-10-2019 at 17:20

[Edited on 10/4/2019 by Yttrium2]

Geocachmaster - 3-10-2019 at 17:42

You want the price for one cookie, so the answer that you want is in dollars per cookie. That means dollars divided by cookies, so nine dollars divided by 15 cookies equals 9/15 or \$0.60 per cookie.
Yttrium2 - 3-10-2019 at 17:44

How would this be setup as a proportion so that units cancel?

9/15 = x/1 this would give 9=15x

ok, I think I got it now.

My question was how do we know what to divide by, Geocachmaster answered the question.

I appreciate every bodies time

[Edited on 10/4/2019 by Yttrium2]

RedDwarf - 3-10-2019 at 17:48

 Quote: Originally posted by Yttrium2 additionally, I'm only at my sharpest for a Max of around 30 minutes, then I'll need a break

Please let us know when/if this 30 minutes occurs so that we know which posts to try and answer

Yttrium2 - 3-10-2019 at 17:59

edited

[Edited on 10/4/2019 by Yttrium2]

Ubya - 3-10-2019 at 22:39

 Quote: One thing that troubles me is that eventually I need a break from math to decompress. Sometimes I'll over do it and get burnt out for a day or two, additionally, I'm only at my sharpest for a Max of around 30 minutes, then I'll need a break.

if you get this for sixth grade math i seriously worry for you, when you'll get to trigonometry, derivatives, integrals and differentials you are going to have a breakdown after 5 minutes

 Quote: Watch yourselves, I'm quickly improving on math, and I'm going through everything with a fine tooth comb! I am likely able to do some problems that would stump a few of you.

mhh that's funny

### just suck it up!

sodium_stearate - 4-10-2019 at 08:41

Sounds like you need to stop whining and knuckle down
and learn to concentrate for extended periods of time.

Nobody ever said this is easy, or fun.

It is work. It always takes serious work to make meaningful
accomplishments in life.

The ability to concentrate one's mind on one thing for
the required amount of time it takes to accomplish any task
is part of a thing called "self control".

Self control is also the mechanism that keeps most of us
obeying society's rules, staying out of trouble, using
proper judgment, etc.

Self control also plays a large part in mental and physical
stamina, which is the ability to hang in there and get things
done which require extended physical and mental endurance.

Again, it's not always fun nor even enjoyable.
If it was always fun and enjoyable, they would not
bother calling it work. Instead they'd call it
"Happy Fun Time".

But it's not that. It's mostly work, and it tends to separate
out the men from the boys.

Yttrium2 - 4-10-2019 at 15:44

heh, thanks for the pep talk

but I ain't whining, I enjoy math and chemistry. It is happy fun time!

p.s. -- I like your quote^

[Edited on 10/5/2019 by Yttrium2]

### Edison

sodium_stearate - 5-10-2019 at 09:43

Thanks. The reference to Edison is because he was a
very down to earth practical kind of a guy. He was a very
decent chemist, but not much of a mathematician.

One other quote of his goes something like this:
"I do not need to be a great mathematician, I can hire
one if I need one. They could not ever hire me however."

The key thing that helped make him a success was his
ability to concentrate indefinitely on solving a problem.
Edison was motivated.

It all boils down to motivation.

CharlieA - 5-10-2019 at 14:56

@sodium stearate: right on!!!
Yttrium2 - 9-10-2019 at 11:42

So there is 128fl oz per gallon. I have a 32 oz water bottle and I want to know how many bottles there are per gallon,

What would the English expression be, such as the previous example it was price per cookie?

It's kind of confusion because it's 128/32 and that means how many times does 32 go into 128.

What's the verbal saying for this division problem so it gets set up correctly.

I may be conflating things.

Bottles per 128oz's?

Eeek

*Bottles per gallon would be 32/128*

[Edited on 10/9/2019 by Yttrium2]

Praxichys - 9-10-2019 at 12:01

 Quote: Bottles per gallon would be 32/128

No. I think your disconnect is a misunderstanding of the units. Try this:

Edit: Fixed image for clarity. Also the plurals in this example are a mess but I think it makes the point anyhow.

[Edited on 9-10-2019 by Praxichys]

mayko - 9-10-2019 at 17:28

maybe this will clear things up....

### 2 containers

sodium_stearate - 10-10-2019 at 07:16

You can think of it as 2 containers.

One container holds a gallon, or 128 fl oz.
The other container holds a quart, or 32 fl oz.

Container #1 has 128 fl oz per container.
Container #2 has 32 fl oz per container.

The problem deals with establishing the ratio of
the two containers.

Get the ratio first, then worry about how you'd like
to interpret that ratio after you get it.

It's either 1 to 4, or 4 to 1, depending upon how
you look at it.

It always helps to first get all the numbers down to
the least common denominator so that you can clearly
see the ratio. For this one, you can do it in your head
easily, just start dividing both numbers by two
until you cannot do it any more.

128/32=64/16=32/8=16/4=8/2=4/1

Standing inside the quart container looking over
at the gallon one, you'd say, "It would take 4 of these to fill
that"

Standing inside the gallon container and looking over at the
much smaller quart container, you'd say, "That small
container over there could only hold one quarter of what's
in here".

You have to dissect this stuff up, down, sideways, inside out,
backward, forward, all for a month of Sundays in order to
be able to fully grasp all of what it really means.

MrHomeScientist - 10-10-2019 at 09:44

What Praxichys is doing is called dimensional analysis. This was supremely helpful for me in physics classes (which is where I learned it). Just look at the units that the answer is in, and rearrange the given values so you end up with the right units. In physics, this usually gets you the right answer (except if you forget a constant - damn you 2π!).