Dividing a given quantity into given ratios

[Saumyojit]

Are you digging through months of what I've said to find potential inconsistencies? I feel like I'm being persecuted!

I would never do so .
I respect you a lot.
I actually wanted to understand so I was reading the post no6 trying to understand.
I cannot express my gratitude to you.

Please stop this silly discussion. I don't have the hours you have to spend on looking through these discussions; you are keeping me from things that matter. I am not going to respond to you further.

U can't imagine how much I am getting my confusion clear by asking the questions .
Yes , for you everything that I ask is foolish (it's natural) but for me its legit .
If you don't respond then seriously my maths journey will be over.

Words can have multiple meanings. Suppose that my "mixed" meant actually stirred together, while "mixture" meant "put together in some way", "combination". Your arguing over words is an utter waste of time.

Ok.

if there are 4cups of 1litre milk and 1cup of 1litre water separately(not a mixture) as shown in the diagram , then "cups " refer to quantity and litre refer to units .

I am extremely sorry for this.
I actually wanted to write "container" but wrote quantity .

. If I talk about a cup containing a liter of milk, the cup is clearly the container, not a unit, and therefore not a specific quantity.

Yes this is what I was trying to say .

The unit called "cup" is far less than a liter

Yes one Us customary cup = 236.5 mL

And replace the word "cup" with "litre" when it refers to a unit. Then hopefully you can get back to thinking clearly.

So, 1 cup water to 1cup milk means I can replace the word "cup" with any "unit" of volume right?
It doesn't have to be litre , it can be mL also right.

The word "bottle" in general does not refer to a particular size; it is not a standard unit. In a particular statement, we might use it as a "part" with the implication that we are temporarily considering bottles of the same size, or repeated use of the same bottle,

When you are saying 1 bottle of water to 1 bottle of milk , so reading this I am thinking each bottle has to be same size as bottle represents parts so naturally my doubt arose.
So, here one bottle will mean one part which is equal. But it cannot be treated as a unit.
1bottle of water to 1 bottle of milk
I cannot replace the word bottle with litre right?
But I can replace the word cup as it is defined unit .

"cup" is a defined unit in America. My main point was to distinguish between units proper, and containers, because you have been using "cup" in both ways.

This is one area I am getting confused
"A cup" is a defined unit just like litre, mL...
So , when I am writing it like this
1cup water to 1 cup milk
That means as I saw in wiki page of
"cup as a unit"

a cup generally refers to amount between 200-250 ml so when I see the word cup
I can replace "cup" with any ml value between 200-250 right?

So, 1cup water to 1 cup milk can be 250ml water to 250ml milk (in terms of metric cup)

1 cup water to 1 cup milk
For it to represent 1litre water to 1 litre milk
If I take my cups as "metric cup" then
It has to be 4 cups water to 4 cups milk .
As 250 ml *4 = 1litre

What am I confusing here?

Then how are we replacing the word 1 cup with 1 litre just like that . They are not equivalent right.

So what does "unit" actually mean
I knew that "the metre " is si unit of Length.(1m), 1litre is the Si unit of " capacity"
A unit just provides a description to the magnitude to let the reader know that this magnitude represent what type of quantity or the type of quantity that have been measured.

Is there other meaning of unit other than " talking about 1 of something"

Extremely sorry but please see ??

 

[Dr.Peterson]

Seriously, I don't have time to spend an hour or two a day trying to answer you. I have other things to do. You have to think for yourself, and not be dependent on me or anyone else in particular.

 

[lev888]

I would never do so .
I respect you a lot.
I actually wanted to understand so I was reading the post no6 trying to understand.
I cannot express my gratitude to you.



U can't imagine how much I am getting my confusion clear by asking the questions .
Yes , for you everything that I ask is foolish (it's natural) but for me its legit .
If you don't respond then seriously my maths journey will be over.

Ok.


I am extremely sorry for this.
I actually wanted to write "container" but wrote quantity .

Yes this is what I was trying to say .

Yes one Us customary cup = 236.5 mL



So, 1 cup water to 1cup milk means I can replace the word "cup" with any "unit" of volume right?
It doesn't have to be litre , it can be mL also right.



When you are saying 1 bottle of water to 1 bottle of milk , so reading this I am thinking each bottle has to be same size as bottle represents parts so naturally my doubt arose.
So, here one bottle will mean one part which is equal. But it cannot be treated as a unit.
1bottle of water to 1 bottle of milk
I cannot replace the word bottle with litre right?
But I can replace the word cup as it is defined unit .


This is one area I am getting confused
"A cup" is a defined unit just like litre, mL...
So , when I am writing it like this
1cup water to 1 cup milk
That means as I saw in wiki page of
"cup as a unit"

a cup generally refers to amount between 200-250 ml so when I see the word cup
I can replace "cup" with any ml value between 200-250 right?

So, 1cup water to 1 cup milk can be 250ml water to 250ml milk (in terms of metric cup)

1 cup water to 1 cup milk
For it to represent 1litre water to 1 litre milk
If I take my cups as "metric cup" then
It has to be 4 cups water to 4 cups milk .
As 250 ml *4 = 1litre

What am I confusing here?

Then how are we replacing the word 1 cup with 1 litre just like that . They are not equivalent right.

So what does "unit" actually mean
I knew that "the metre " is si unit of Length.(1m), 1litre is the Si unit of " capacity"
A unit just provides a description to the magnitude to let the reader know that this magnitude represent what type of quantity or the type of quantity that have been measured.

Is there other meaning of unit other than " talking about 1 of something"

Extremely sorry but please see ??

Look up units in the dictionary. They are useful in communicating information about quantities. If we use common units I can say "Use 100 grams of butter for this recipe" and you will understand me - I won't need to come over and explain how much 100 grams of butter is.

 

[Saumyojit]

, 1 cup water to 1cup milk means I can replace the word "cup" with any "unit" of volume right?
It doesn't have to be litre , it can be mL also right.

That means as I saw in wiki page of
"cup as a unit"

a cup generally refers to amount between 200-250 ml so when I see the word cup
I can replace "cup" with any ml value between 200-250 right?

So, 1cup water to 1 cup milk can be 250ml water to 250ml milk (in terms of metric cup)

1 cup water to 1 cup milk
For it to represent 1litre water to 1 litre milk
If I take my cups as "metric cup" then
It has to be 4 cups water to 4 cups milk .
As 250 ml *4 = 1litre

What am I confusing here?

Then how are we replacing the word 1 cup with 1 litre just like that . They are not equivalent right.

If anyone could answer this two parts I will be moving on.
I have tried my best from my side.

 

[Saumyojit]

Look up units in the dictionary. They are useful in communicating information about quantities. If we use common units I can say "Use 100 grams of butter for this recipe" and you will understand me - I won't need to come over and explain how much 100 grams of butter is.

I know what a unit is .
I saw in the dictionary but it didn't answer my doubt in the last post

 

[lev888]

I know what a unit is .
I saw in the dictionary but it didn't answer my doubt in the last post

If you are talking about volume ratios you can use any volume units or containers - doesn't matter what, they cancel, the ratio is a dimensionless quantity. 1 cup of water to 2 cups of milk is 1:2 ratio by volume. 1 litre of water to 2 litres of milk is the same 1:2 ratio by volume.

If you are talking about recipes, then we use amounts with specific units. If you want to prepare exactly the amount the recipe indicates, if the recipe says put in 2 litres of water, then you need to measure exactly 2 litres of water.

 

[Saumyojit]

If you are talking about volume ratios you can use any volume units or containers - doesn't matter what, they cancel, the ratio is a dimensionless quantity. 1 cup of water to 2 cups of milk is 1:2 ratio by volume. 1 litre of water to 2 litres of milk is the same 1:2 ratio by volume.

If you are talking about recipes, then we use amounts with specific units. If you want to prepare exactly the amount the recipe indicates, if the recipe says put in 2 litres of water, then you need to measure exactly 2 litres of water.

Okay so as this is a volume ratio therefore I can replace the word 'cup' with any unit of volume and it doesn't matter whether that 1 cup =1 litre .
1cup of water to 1 cup of milk = 1 ml of water to 1 ml of milk also.
Right?

If I actually wanted to measure 1litre of water for a recipe then using a metric cup suppose I have to use 4 of those to have 1 litre or use the same cup 4 times

 

[lev888]

Okay so as this is a volume ratio therefore I can replace the word 'cup' with any unit of volume and it doesn't matter whether that 1 cup =1 litre .
1cup of water to 1 cup of milk = 1 ml of water to 1 ml of milk also.
Right?

If I actually wanted to measure 1litre of water for a recipe then using a metric cup suppose I have to use 4 of those to have 1 litre or use the same cup 4 times

Yes.

 

[Saumyojit]

Yes.

Talking about 1:1 ratio
So,
1part water to 1 part milk is same as 1cup water to 1 cup milk is the same as 1bottle water to 1 bottle milk is the same as 1litre water to 1 litre milk is the same as 1ml water to 1 ml milk.

Part , units, cups, bottle are the same thing right When I write in the above mentioned form?

When I talk about ratios each part has to be same or each unit has to be same on both the sides.

This has nothing to do with the cup as a unit of volume.
That usage of "cup" as a unit has nothing to do when I say "1cup water to 1 cup milk"
That's comes into play when I measured 250 ml milk suppose, then I would say I measured 1 cup milk ( metric cup) .

If that so then why did drp said

replace the word "cup" with "litre" when it refers to a unit.

In this case of replacement of the word 'cup' with litre ,
The cup refers to a unit means
Unit means part used in the ratio or
1cup = 200-250 ml ( Us standard unit)

Which context is being referred.

The word "bottle" in general does not refer to a particular size

Here Dr p tried to say that "a bottle" in general does not have any standard meaning or size ( can be different) but when I say a "cup" in general
It either means a Us customary cup or a metric cup that are considered as a standard unit.
Right?

But using bottle in ratio format refers to the same size

 

[lev888]

Talking about 1:1 ratio
So,
1part water to 1 part milk is same as 1cup water to 1 cup milk is the same as 1bottle water to 1 bottle milk is the same as 1litre water to 1 litre milk is the same as 1ml water to 1 ml milk.

Part , units, cups, bottle are the same thing right When I write in the above mentioned form?

When I talk about ratios each part has to be same or each unit has to be same on both the sides.

This has nothing to do with the cup as a unit of volume.
That usage of "cup" as a unit has nothing to do when I say "1cup water to 1 cup milk"
That's comes into play when I measured 250 ml milk suppose, then I would say I measured 1 cup milk ( metric cup) .

If that so then why did drp said
In this case of replacement of the word 'cup' with litre ,
The cup refers to a unit means
Unit means part used in the ratio or
1cup = 200-250 ml ( Us standard unit)

Which context is being referred.

Sorry, I don't want to go back and read the whole discussion.
For ratios it doesn't matter what unit/container you use, as long as you can convert both of them into the same unit/container, so that they cancel and the result is dimensionless. E.g. 500g of A to 1kg of B - convert kg to grams and we get 1/2.
When dealing with quantities such is weight and volume you need to use common units, so that there is no misunderstanding. One cup may mean different things in different countries, so it's better to use something more precise.

 

[Saumyojit]

Talking about 1:1 ratio
So,
1part water to 1 part milk is same as 1cup water to 1 cup milk is the same as 1bottle water to 1 bottle milk is the same as 1litre water to 1 litre milk is the same as 1ml water to 1 ml milk.

Part , units, cups, bottle are the same thing right When I write in the above mentioned form?

When I talk about ratios each part has to be same or each unit has to be same on both the sides.

This has nothing to do with the cup as a unit of volume.
That usage of "cup" as a unit has nothing to do when I say "1cup water to 1 cup milk"
That's comes into play when I measured 250 ml milk suppose, then I would say I measured 1 cup milk ( metric cup)

just this part

 

[Saumyojit]

the mixture can still be called 1:4, and still contains 1 cup of water and 4 cups of milk, IF you are using "cup" to refer to the unit

@Dr.Peterson can you just say what did you mean by cup refering to the unit .
Is the word 'unit' means it can be unit of measurement and the "unit" (equal parts) used in the ratio.

1cup of water to 4 cups of milk can be replaced by unit of measurement .

1 litre or ml of water to 4 litre or mL of milk

1cup of water to 4 cups of milk can also be replaced by 'parts'

1 part water to 4 parts cup milk

 

[Saumyojit]

"1 cup water to 4 cups milk" if those are the amounts

why did you say amounts .
Even if they are in a ratio , i could still call them 1 cup water to 4 cups milk

 

[Dr.Peterson]

@Dr.Peterson can you just say what did you mean by cup refering to the unit .
Is the word 'unit' means it can be unit of measurement and the "unit" (equal parts) used in the ratio.

1cup of water to 4 cups of milk can be replaced by unit of measurement .

1 litre or ml of water to 4 litre or mL of milk

1cup of water to 4 cups of milk can also be replaced by 'parts'

1 part water to 4 parts cup milk

I was simply referring to the distinction I made over and over, between the standard U.S. unit of volume equal to half a pint, and any container for drinking from. These are two definitions found in any English dictionary.

 

[lev888]

why did you say amounts .
Even if they are in a ratio , i could still call them 1 cup water to 4 cups milk

Yes, you can.
I should've written "You can say "1 cup water and 4 cups milk" if those are the amounts, regardless of whether the components are mixed."
My point was that to specify amounts you need to include volume info. And that it doesn't matter that components are mixed. Mixing does not change the amount of stuff we added to the mixture.

 

[Saumyojit]

you need to include volume info

here what is the volume info
1 cup water and 4 cups milk
here cup means volume equal to half a pint or can be any value in terms of litre or ml

 

[Saumyojit]

@Dr.Peterson
what is the difference between 1cup water and 2 cups milk
what is the difference between 1cup water to 2 cups milk

In Both the cases, 1cup= 236.5882365ml refers to the Unit

here in the first case , amount is 236.5882365ml water and 236.5882365 * 2 ml milk
here in the second case , amount refers to any multiple of 236.5882365ml water and any multiple of (236.5882365 * 2 ml) milk.

 

[lev888]

@Dr.Peterson
what is the difference between 1cup water and 2 cups milk
what is the difference between 1cup water to 2 cups milk

In Both the cases, 1cup= 236.5882365ml refers to the Unit

here in the first case , amount is 236.5882365ml water and 236.5882365 * 2 ml milk
here in the second case , amount refers to any multiple of 236.5882365ml water and any multiple of (236.5882365 * 2 ml) milk.

Yes, you are correct - the first refers to the amount of the mixture, the second to the ratio of components.
Regarding the amount - I am assuming all involved are on the same page about what exactly 1 cup is as a unit of volume.

 

[Saumyojit]

It isn't the word cup that implies the same size! It's that you are talking about ratios.

@lev888 Doesn't cup inherently mean we are talking about the standard unit size(236.8ml) .
if suppose, the word cup is not used in ratios , 1 cup water and 2 cups milk then also we know we are talking about same size .

 

[lev888]

@lev888 Doesn't cup inherently mean we are talking about the standard unit size(236.8ml) .
if suppose, the word cup is not used in ratios , 1 cup water and 2 cups milk then also we know we are talking about same size .

Take a look:

Guide to Measuring Cups - US vs Metric vs Korean

Measuring cups - US vs Metric vs Korean measurements. How they are all different. Korean cups also have different sizes.

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