Why-do-the-denominators-need-to-be-the-same-when-adding-the-fractions

I was saying that 1/4 of a cup is 1/16 of the 4-cup bag.
Yes they are equivalent ratios.

I might use 1/4 of a cup of flour as a measurement
We use kg or pound as a unit to measure weight .
We use weighing scale as a measurement device .(in case of measuring weight)

In case of pizza( 1/3 of a pizza + 2/3 of a pizza ) I know the unit is "of a pizza" but is 1/3 of a pizza is being used as a measurement ??

Here you say "I might use 1/4 of a cup of flour as a measurement"
"of a cup " is the unit that I got it
But what is your implication by using
"1/4 of a cup "

If you are saying in this sense
There are 4 cups (each cup divided into 4 parts)of flour .
I took like this
1/4 of a cup + 2/4 of a cup + 1/4 of a cup+ 1/4 of a cup = 5/4 of a cup
I will not say 5/16 of a cup .
That will be wrong.
Is this are you referring or something else??
 
Last edited:
I know the unit is "of a pizza"
"of a cup " is the unit that I got it
Well, not quite. The units are "pizzas" and "cups", not prepositional phrases.

We use kg or pound as a unit to measure weight .
We use weighing scale as a measurement device .(in case of measuring weight)
Are you aware that a cup is a unit of volume used in America? We buy devices marked in units of cups to measure with.

In case of pizza( 1/3 of a pizza + 2/3 of a pizza ) I know the unit is "of a pizza" but is 1/3 of a pizza is being used as a measurement ??

Here you say "I might use 1/4 of a cup of flour as a measurement"
"of a cup " is the unit that I got it
But what is your implication by using
"1/4 of a cup "
How is it not clear that 1/3 of a pizza is a certain (measured) quantity of pizza, and 1/4 of a cup is a certain (measured) amount of flour? Why would they not be measurements?

If you are saying in this sense
There are 4 cups (each cup divided into 4 parts)of flour .
I took like this
1/4 of a cup + 2/4 of a cup + 1/4 of a cup+ 1/4 of a cup = 5/4 of a cup
I will not say 5/16 of a cup .
That will be wrong.
Is this are you referring or something else??
You didn't quote the whole thing you're apparently referring to, so I have to:
Similarly, I might use 1/4 of a cup of flour as a measurement. If there were 4 cups of flour in the bag I took it from, that wouldn't affect the quantity I measured out. I would not call it "1/16" -- unless I wanted to know how much of the bag I used, in which [case] I would explicitly call it "1/16 of the bag" or "1/16 of the flour I started with". That is what I referred to as a relative amount -- relative to a certain total amount.
Where do you get 5/4 of a cup from that??

If there are 4 cups of flour in a bag, that would mean I could fill 4 measuring cups with flour; each cup consists of 4 quarter-cups. So there are a total of 16 quarter-cups; and each quarter-cup is 1/16 of the whole bagful.

But if you are ignoring the 4 cups that you mentioned, and just supposing, separately that you have four quantities, 1/4, 2/4, 1/4, and 1/4 cup respectively, then, yes, the total is 5/4 of a cup. Of course that's not 5/4 of a cup. But is it 5/16 of the bagful I started with in the example, because each cup is 1/4 of the bag.

My point there was that you have to state what the fraction is based on -- 1/4 cup in the example is the same as 1/16 of a bagful, and just saying 1/16 doesn't communicate the quantity adequately.
 
Are you aware that a cup is a unit of volume used in America?
Yes I saw in the link .
1 standard Us cup =238.8888 ml
Also the measuring cup picture which is nicely marked in terms of mL (250) and fraction of a cup.
The units are "pizzas" and "cups
Yes
How is it not clear that 1/3 of a pizza is a certain (measured) quantity of pizza, and 1/4 of a cup is a certain (measured) amount of flour? Why would they not be measurements
Yes they are measured quantities .



each cup consists of 4 quarter-cups. So there are a total of 16 quarter-cups; and each quarter-cup is 1/16 of the whole bagful.
Yes I understood this paragraph.
Quarter cups means each '1/4 th part' right.
So 4 cups means 16 of those.
Got it.

Iif that would mean I could fill 4 measuring cups with flour
Okay you are saying There are 4 measuring cups in the bag right?
|_|_|_|_| 4 measuring cup.(each block represent it)
These four measuring cups are already filled with fluor from the beginning right?
I am just following what you said above.
Each measuring cup holds as I saw from wiki 250 ml that means every cup is holding 250 ml(I don't know the conversion btwn ml to grams) of fluor . Total is 250* 4

Then why did you said "I could fill 4 measuring cups" when we started with the proposition " if there are 4 cups of flour in a bag". Already the cups are filled right?


But if you are ignoring the 4 cups that you mentioned,
I don't know how am I ignoring 4 cups .
See I thought in this way,
1: I have one extra measuring cup A which is labeled as (Just like the picture of measuring cup in Wiki) 1/4 ,2/4 , 3/4 and 1 cup and this is not in the bag . This I will use to take out amt of flour I Will need from the 4 cups in the bag


Beside that, I have four separate cups in a Bag ,each cup Divided into 4 parts and each cup is filled fully with fluor .
Now I took 1/4 th cup of fluor from the first cup with the help of A
Then I took 2/4 th cup of flour from the second cup with the help of A....so on
I got this fraction : 1/4 of a cup + 2/4 of a cup + 1/4 of a cup + 1/4 of a cup
Now the total amount that I got is by adding each fraction = 5/4 of a cup of flour



1/4, 2/4, 1/4, and 1/4 cup respectively, then, yes, the total is 5/4 of a cup.
Yes you said it.
But why did you said
Of course that's not 5/4 of a cup.
?

it 5/16 of the bagful I started with in the example
5/4 of a cup = 5/16 of 4 cups (4 cup = bagful)
Right?
because each cup is 1/4 of the bag.
Yes this I understood .
1 cup = 1/4 * 4 cups
1/4 cup in the example is the same as 1/16 of a bagful, and just saying 1/16 doesn't communicate the quantity adequately.
Yes I understood
 
Last edited:
Okay you are saying There are 4 measuring cups in the bag right?
|_|_|_|_| 4 measuring cup.(each block represent it)
These four measuring cups are already filled with flour from the beginning right?
I am just following what you said above.
Each measuring cup holds as I saw from wiki 250 ml that means every cup is holding 250 ml(I don't know the conversion btwn ml to grams) of fluor . Total is 250* 4

Then why did you said "I could fill 4 measuring cups" when we started with the proposition " if there are 4 cups of flour in a bag". Already the cups are filled right?
No. A cup is a unit of volume. What is in the bag is just flour, not cups! But there is as much flour as it takes to fill four cups; you could put the flour in cups if you wanted to.

In the same way, a 4 meter rope is not 4 meter stick; it is as long as 4 sticks.

See I thought in this way,
1: I have one extra measuring cup A which is labeled as (Just like the picture of measuring cup in Wiki) 1/4 ,2/4 , 3/4 and 1 cup and this is not in the bag . This I will use to take out amt of flour I Will need from the 4 cups in the bag
Yes, that is how it works. Except it appears you don't really understand:

Beside that, I have four separate cups in a Bag ,each cup Divided into 4 parts and each cup is filled fully with fluor .
Now I took 1/4 th cup of fluor from the first cup with the help of A
Then I took 2/4 th cup of flour from the second cup with the help of A....so on
I got this fraction : 1/4 of a cup + 2/4 of a cup + 1/4 of a cup + 1/4 of a cup
Now the total amount that I got is by adding each fraction = 5/4 of a cup of flour
No, there are no cups in the bag!!!

Try rethinking it all knowing that there is only flour in the bag, as much as it takes to fill four standard cups.

But I have to ask: Do you not have any sort of measuring cups in your country? How do you measure liters? How can you not understand this?

Obviously I never should have mentioned cups in the first place
 
Try rethinking it all knowing that there is only flour in the bag, as much as it takes to fill four standard cups

okay there is total (250*4 ml) fluor in the bag

The amount is equivalent to 4 standard cups . And yes a cup is a unit of volume.
Okay you told to rethink so I thought about this para
I might use 1/4 of a cup of flour as a measurement. If there were 4 cups of flour in the bag I took it from, that wouldn't affect the quantity I measured out. I would not call it "1/16" -- unless I wanted to know how much of the bag I used, in which I would explicitly call it "1/16 of the bag" or "1/16 of the flour I started with". That is what I referred to as a relative amount -- relative to a certain total amount.
Okay I am taking out 1/4 of a cup of flour from the whole amount or from the bag.
1/4 * 250ml = 62.5ml
So I took out 1/4 of a cup (62.5ml of fluor)

And if I wanted to know how much of the bag I used then I will tell I took 1/16 of the bag or 1/16 of the 4 cup bag or 1/16 of the fluor I started with . These 3 are all relative amounts as they're being considered wrt to total weight or volume (1000ml) of the bag .
So total or whole refers to bagful.

Although, As they are all equivalent the amount of fluor I am measuring or taking out in the end is the same 62.5 ml.

So, what was the main point you are trying to convey when you actually said 3 months ago . You are trying to make me explain the difference between absolute Vs relative quantity right and with the former only I can add two fractions consistently.
Right??

Another thing you said
a ratio of part to whole: 5/22 of thetwopizzas
1/16 of 4 cups is a part to whole ratio .
[Part is 1 and whole is 16 parts or 4 cups]
So , can I say in 1/4 of a cup this is also a part to whole ratio .
[Part is 1 and whole is 4 parts or one cup]
If not, why?

Now coming back to post 42 I see
But if you are ignoring the 4 cups that you mentioned, and just supposing, separately that you have four quantities, 1/4, 2/4, 1/4, and 1/4 cup respectively, then, yes, the total is 5/4 of a cup. Of course that's not 5/4 of a cup. But is it 5/16 of the bagful I started with in the example, because each cup is 1/4 of the bag.
See now I know that there was only fluor in the bag which amounts to 4 cups .
This is another situation we are talking about :
I took out fluor from the bag with the help of measuring cup 4 times
These are the 4 quantities I took out suppose : 1/4, 2/4, 1/4, and 1/4 cup respectively, then, yes, the total fluor I took out is 5/4 of a cup .(5/4 * 250 ml= 312.5 ml of flour). I can also say in terms of how much of the bag I used : 5/16 of 4 cups or 5/16 of the whole bag ..
Okay no worries.

But you kind of confused me with this line
" Of course that's not 5/4 of a cup."
What are you saying here.
Really I spent some 4 hours in this part trying to interpret.
 
okay there is total (250*4 ml) fluor in the bag
You don't need to express it in metric; the mere fact that a unit is consistent is enough to treat it as a unit on its own. All that matters is that it is a volume. I could measure a volume in handfuls, as long as I always use the same hand(s); or a distance in paces, as long as I step the same distance in every pace, without having to even think about how many milliliters or meters each is. In fact, that's the purpose of the word "parts" in talking about ratios.

Also, you should be aware, in case you ever do any baking in America, that our cup is not equal to 250 mL. The latter is sometimes called a metric cup, and the same measuring cup often shows both units. (The lines for 1 cup and 250 mL don't line up.) See here: http://www.ibiblio.org/units/dictC.html

cup (c) [1] a traditional unit of volume used in recipes in the United States. One cup equals 1/2 (liquid) pint, or 8 fluid ounces. Technically, one cup equals exactly 14.4375 cubic inches or approximately 236.6 milliliters, not that anyone measures quite so precisely in the kitchen. American cooks use the same size cup for measuring both liquid and dry substances. In Canada, a cup is equal to 8 Imperial fluid ounces (13.8710 cubic inches or 227.3 milliliters). In Britain, cooks sometimes used a similar but larger unit called the breakfast cup, equal to 10 Imperial fluid ounces. The British cup equals 1/2 Imperial pint, but the Canadian cup is only 0.4 Imperial pint.​
cup (c) [2] an informal metric unit of volume equal to 250 milliliters, commonly used in recipes in Australia.​
cup (c) [3] an informal unit of volume for coffee. The size of a cup of coffee varies according to local custom, but a typical size is about 5 fluid ounces or 150 milliliters.​

By the way, the word in English is "flour", not "fluor". Fluor, according to my dictionary, is a mineral also called fluorite, which I would not use for baking unless I wanted to make glass.

Clearly I should have used something other than cups of flour in my example, to save both of us hours of wasted time.

So, what was the main point you are trying to convey when you actually said 3 months ago . You are trying to make me explain the difference between absolute Vs relative quantity right and with the former only I can add two fractions consistently.
Right??
Yes, that's what I said I was saying ... or more specifically, that 1/16 is meaningless without knowing what it is 1/16 OF. And I want you to understand it, more than to explain it.

1/16 of 4 cups is a part to whole ratio .
[Part is 1 and whole is 16 parts or 4 cups]
So , can I say in 1/4 of a cup this is also a part to whole ratio .
[Part is 1 and whole is 4 parts or one cup]
If not, why?
Yes, you can say that. In the latter case, the whole is one cup, and that corresponds to 4 parts in this ratio.

I took out fluor from the bag with the help of measuring cup 4 times
These are the 4 quantities I took out suppose : 1/4, 2/4, 1/4, and 1/4 cup respectively, then, yes, the total fluor I took out is 5/4 of a cup .(5/4 * 250 ml= 312.5 ml of flour). I can also say in terms of how much of the bag I used : 5/16 of 4 cups or 5/16 of the whole bag ..
Okay no worries.
What confuses me here is, what made you decide to take out four amounts that are not the same? Why did you introduce that idea?

But given that you arbitrarily decided to do that, your conclusions are correct. And please don't bother to answer my question; I am not curious enough to waste still more time on nothing.

But you kind of confused me with this line
" Of course that's not 5/4 of a cup."
What are you saying here.
Really I spent some 4 hours in this part trying to interpret.
I probably meant to say 5/16! I think you really need to learn not to obsess over details. Haven't we told you before, sometimes what you read is just a mistake, and you need to skip over it?
 
I probably meant to say 5/16!
If you have once checked after writing , then you could correct that part.
I tend to believe everything you write bcoz i am amateur in maths and you are my prof.

What confuses me here is, what made you decide to take out four amounts that are not the same? Why did you introduce that idea?But given that you arbitrarily decided to do that, your conclusions are correct.
I thought there were four cups initially (wrong thinking) and coz we were talking about adding fraction before you gave that fluor post , so I thought this relative and absolute quantity confusion will only arise in terms of adding fraction.


Yes, you can say that. In the latter case, the whole is one cup, and that corresponds to 4 parts in this ratio.
So any fraction I write is a relative quantity then . Any whole if we write like 1 pizza , 1 cup is a absolute quantity.
Now coming back to ,
1/3 of a pizza + 1/3 of a pizza = 2/3 of a pizza . ("A Pizza is the unit" and it has to be kept consistent ) Although the total (2/3 of a pizza)that I am getting is a relative quantity right? . So 2/3 of a pizza is not a absolute quantity then.

1/3 of a pizza + 1/3 of a pizza = 2/6 of a pizza ( here the total is wrong as I have taken 6 parts but I forgot to mention that I am considering 6 parts out of both the two pizzas) So 2/6 of two pizzas.

The fractions 3/11 and 2/11 refer to 3/11 of a pizza, and 2/11 of a pizza. The unit here is one pizza. Each fraction represents an absolute quantity, and when we add them, we have 5/11 of a pizza -- that is, 5 slices, each of which is 1/11 of a pizza.
I understood everything.
A pizza is the unit and it's a rule that I have to keep the units same.

Both 3/11 of a pizza, and 2/11 of a pizza
also in some sense are two relative quantities as I told you in the above post.
But when I will add them then each fraction will be a absolute quantity right?

What is the context then (can you provide some eg) ; when should I consider a fraction as a relative or a absolute quantity
 
Last edited:
If you have once checked after writing , then you could correct that part.
I tend to believe everything you write bcoz i am amateur in maths and you are my prof.
You need to learn not to believe everything you read. (And I don't have the power to go back and correct what I wrote in the past here.) But in any case, I proofread what I write far more than most people here seem to.

And no, I am not your prof.

I thought there were four cups initially (wrong thinking) and coz we were talking about adding fraction before you gave that fluor post , so I thought this relative and absolute quantity confusion will only arise in terms of adding fraction.
Without going back to check, I believe we were talking not about adding fractions, but about models of adding fractions, and you were misusing them. The topic under discussion does not arise in adding fractions (which are abstract), but only in talking about models of them, which you are doing excessively.

1/3 of a pizza + 1/3 of a pizza = 2/3 of a pizza . ("A Pizza is the unit" and it has to be kept consistent ) Although the total (2/3 of a pizza)that I am getting is a relative quantity right? . So 2/3 of a pizza is not a absolute quantity then.

1/3 of a pizza + 1/3 of a pizza = 2/6 of a pizza ( here the total is wrong as I have taken 6 parts but I forgot to mention that I am considering 6 parts out of both the two pizzas) So 2/6 of two pizzas.
I'm not sure that "relative vs absolute quantity" is really the right distinction to be making. But why would you think 2/3 of a pizza is not an absolute quantity?

Since the second paragraph is knowingly wrong, why bother saying it? That just isn't the right way to express what you are doing, so don't.

What is the context then (can you provide some eg) ; when should I consider a fraction as a relative or a absolute quantity
I suspect you are taking whatever I originally said about that out of context. If you want to go back and find it, maybe you can show me what I said and I can explain. As I said, I don't think this is a useful distinction to be making, and this whole discussion is pointless.
 
why would you think 2/3 of a pizza is not an absolute quantity?
The fractions 3/11 and 2/11 refer to 3/11 of a pizza, and 2/11 of a pizza. The unit here is one pizza. Each fraction represents an absolute quantity, and when we add them, we have 5/11 of a pizza -- that is, 5 slices, each of which is 1/11 of a pizza.

Your fraction 5/22 is a relative quantity, a ratio of part to whole: 5/22 of the two pizzas
u said it here "relative quantity" means a ratio of part to whole .
3/11 of a pizza and 2/11 of a pizza both are part to whole ratio right?
3 and 2 are parts and 11parts or whole 1 pizza is the whole in the part to whole .

3/11 of a pizza and 2/11 of a pizza---- they are relative quantities aren't they ?
You said each represents a absolute quantity which I agree but each fraction is representing a part to whole also, so it is relative ?
 
As I've said, I don't think absolute vs. relative is really the appropriate distinction.

u said it here "relative quantity" means a ratio of part to whole.
No, that wasn't a definition! In that sense, everything is relative (to something).

In your quote you omitted part of the context, which I had to look for in order to see what my point was (bold is what you omitted):
We have several times mentioned the importance of a unit in discussing fractions.

The fractions 3/11 and 2/11 refer to 3/11 of a pizza, and 2/11 of a pizza. The unit here is one pizza. Each fraction represents an absolute quantity, and when we add them, we have 5/11 of a pizza -- that is, 5 slices, each of which is 1/11 of a pizza.

Your fraction 5/22 is a relative quantity, a ratio of part to whole: 5/22 of the two pizzas from which you took them. Each has a meaning; but only the former (using a consistent unit) is addition of fractions.
The context was that you were using fractions without indicating a consistent unit (not, there, in the sense of a standard unit, but of what value is "1" in relation to the fraction). You had said, "Therefore I am buying 5/11 from 2 whole pizzas not single!" The fraction 5/11 is not a fraction of the two pizzas, but of one pizza; and that's what I meant by "absolute" in that particular context. When you add fractions, they must all be relative to the same unit, and that is what I meant by "absolute"! What I meant by "relative" was that the amount taken was 5/22 of something other than the unit being used for the two fractions being added. I don't think that was quite the right word to use. So don't waste time trying to analyze the word; instead, try to understand the overall concepts.

One of the reasons I am avoiding you is that you keep taking things out of context (and making the context so voluminous that I can't keep track of it). As you are obsessive in your questions, I am obsessive about feeling I have to answer thoroughly and correctly, and I just can't afford to do that. This is just one more example. It took far too long to dig into this to figure out what I meant about something that really doesn't matter.
 
Top