Fraction meaning

Yes. The denominator represents some sort of whole, which must be divided into that many equal parts. In the case of children, we are considering the number of children, and counting one category of them. The numerator is the number of those parts that are chosen.

Fractions can also be defined in a more abstract way, without reference to counting objects. The fraction 2/5 is simply 2 divided by 5: that is, a number that, when multiplied by 5, results in 2 (so that 2/5 of 5 is 2, which is exactly what the girls and boys example means.)
 
You see that 2/5 of the students are boys, right? So 2/5 of 5 is 2. And that is a multiplication: [MATH]\frac{2}{5}\times 5 = 2[/MATH].
 
Dr.Peterson said:
You see that 2/5 of the students are boys, right? So 2/5 of 5 is 2. And that is a multiplication: [MATH]\frac{2}{5}\times 5 = 2[/MATH].
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one thing i need to ask when i am writing 6/2 it could be read as i am dividng 6 apples into groups of 2 each 3 or how many groups of 2 make 6


How will i understand which one is partiton and Quotitive with logic not by rote memorization
 
when i say i am taking 3/4 of pizza that time i am dividing pizza into 4 slices taking 3 ..but if i say there are 3 red pens ..r1 r2 r3 if i take 1/3 of the red pen that means 3 is the total no of red pens (r1 r2 r3) out of those taking 1 whole part suppose r1 or i have divided r1 into 3 equal size parts and taking 1 part which is practically not possible but then again according to the defination of denominator represents the number of equal parts in a whole ...that means here whole represents all the 3 pens right??
 
Saumyojit said:
when i say i am taking 3/4 of pizza that time i am dividing pizza into 4 slices taking 3 ..but if i say there are 3 red pens ..r1 r2 r3 if i take 1/3 of the red pen that means 3 is the total no of red pens (r1 r2 r3) out of those taking 1 whole part suppose r1 or i have divided r1 into 3 equal size parts and taking 1 part which is practically not possible but then again according to the defination of denominator represents the number of equal parts in a whole ...that means here whole represents all the 3 pens right??
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1/3 of three pens is 1 pen.
1/3 of a pen is not quite clear. Let's say you want to measure the length of something and you don't have a ruler. It's perfectly reasonable to say "this length is 1/3 of the length of the red pen".
When you are dividing a pizza everybody knows you are referring to parts of the central 360 degree angle. With a pen, it's not clear which measure we are dividing, so you need to specify - length, weight, etc.
 
Saumyojit said:
one thing i need to ask when i am writing 6/2 it could be read as i am dividing 6 apples into groups of 2 each 3 or how many groups of 2 make 6

How will i understand which one is partiton and Quotitive with logic not by rote memorization
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This is a different question; you are now asking about the meaning of the words "partitive" and "quotative". Frankly, the way you learn the meaning of words is essentially rote memorization, though if you know enough of English and its Latin roots, you can often see why each word means what it does.

In this case, I remember that "quotative" comes from the Latin word for "how many?" (as does "quotient"), and is the thinking we do when we ask "How many parts of this size are there?" So an example would be finding how many sticks of length 4 I can cut from a stick of length 12.

"Partitive" comes from partitioning, as you suggest, and I just remember it is the opposite of "quotative": How long is each stick, if I cut a stick of length 12 into 4 equal pieces? That is, how big is each part?

I had never heard these terms until I first answered a question about it; those how know the terms are generally taking a course in math for teachers (which I subsequently had an opportunity to teach). Here is one such answer I gave:


There are other terms that are more memorable for those who don't know Latin ...
 
Dr.Peterson said:
This is a different question; you are now asking about the meaning of the words "partitive" and "quotative". Frankly, the way you learn the meaning of words is essentially rote memorization, though if you know enough of English and its Latin roots, you can often see why each word means what it does.

In this case, I remember that "quotative" comes from the Latin word for "how many?" (as does "quotient"), and is the thinking we do when we ask "How many parts of this size are there?" So an example would be finding how many sticks of length 4 I can cut from a stick of length 12.

"Partitive" comes from partitioning, as you suggest, and I just remember it is the opposite of "quotative": How long is each stick, if I cut a stick of length 12 into 4 equal pieces? That is, how big is each part?

I had never heard these terms until I first answered a question about it; those how know the terms are generally taking a course in math for teachers (which I subsequently had an opportunity to teach). Here is one such answer I gave:


There are other terms that are more memorable for those who don't know Latin ...
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it is very surprising that u have never heard these terms..
 
I think you misread what I said. I HAVE heard of "quotative" and "partitive" now, obviously; but I HAD not heard them until I was an adult (in my 50's, in fact). They are not commonly used (in America) in teaching children; they are used in talking to teachers about how to teach children. And they are not typically used by mathematicians, but by educators, in my experience.

Are you saying you learned about them in third grade? If so, that is a difference in your curriculum. I suspect most Americans have never heard the terms. (It is possible that the words are now being used in the elementary curriculum, as some educators seem to consider it appropriate to tell children such things; I don't know. But if they are, the parents are probably baffled.)

That doesn't matter. Does what I said help at all?
 
Dr.Peterson said:
I think you misread what I said. I HAVE heard of "quotative" and "partitive" now, obviously; but I HAD not heard them until I was an adult (in my 50's, in fact). They are not commonly used (in America) in teaching children; they are used in talking to teachers about how to teach children. And they are not typically used by mathematicians, but by educators, in my experience.

Are you saying you learned about them in third grade? If so, that is a difference in your curriculum. I suspect most Americans have never heard the terms. (It is possible that the words are now being used in the elementary curriculum, as some educators seem to consider it appropriate to tell children such things; I don't know. But if they are, the parents are probably baffled.)

That doesn't matter. Does what I said help at all?
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i read the explanation in the given link 4 times http://mathforum.org/library/drmath/view/77467.html
I marked fifths to help me scale things.
but why?
 
I had to read the link to realize that "I marked fifths to help me scale things" is a quote from there, not something you are saying you did.

It refers to my picture,

Code: 
So here is a box with length 1, and another with length 1.6 (= 8/5):

             1
   +-------------------+
   |   :   :   :   :   |
   +-------------------+

   +-------------------------------+
   |   :   :   :   :   :   :   :   |
   +-------------------------------+
                  1.6

I marked fifths to help me scale things.

In order to make a box 1.6 units long (that is, 8/5), I had to show how big a fifth is. That is, everything is measured in fifths: 1 is 5/5, 1.6 is 8/5. I could just as well have marked tenths. To show 1.6 on a ruler, it has to be marked in tenths, or at least fifths.
 
Dr.Peterson said:
I had to read the link to realize that "I marked fifths to help me scale things" is a quote from there, not something you are saying you did.

It refers to my picture,

Code: 
So here is a box with length 1, and another with length 1.6 (= 8/5):

             1
   +-------------------+
   |   :   :   :   :   |
   +-------------------+

   +-------------------------------+
   |   :   :   :   :   :   :   :   |
   +-------------------------------+
                  1.6

I marked fifths to help me scale things.

In order to make a box 1.6 units long (that is, 8/5), I had to show how big a fifth is. That is, everything is measured in fifths: 1 is 5/5, 1.6 is 8/5. I could just as well have marked tenths. To show 1.6 on a ruler, it has to be marked in tenths, or at least fifths.
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why everything has to be measured in fifths??
1/1.6 is gives me 5/8 that means out of 8 parts i am considering 5 parts?
 
Take a ruler marked in eighths, and try finding 1.6. Don't you see that it's easier if it's marked in fifths or tenths? And that it is only in the latter case that you can show it exactly? That's all I was saying there. This is not complicated.

But 5/8, of course, can be shown on a ruler marked in eighths, not in fifths.
 
One way to think of 1/1.6 is that we want to divide a single "box" into
1.6 equal "pieces."

Now 1.6 in denominator means i have to divide the one whole box into 8/5 (1.6) equal parts?
then each part will be ...? is my approach correct?
 
Yes, that would be the partitive model, represented by my last pair of pictures in the page you referred to.

Of course, that is only one way to think of it, as you said.
 
One way to think of 1/1.6 is that we want to divide a single "box" into
1.6 equal "pieces" . In this statement size of each equal pieces are given right?

I want to find the size of a "piece" such that 1.6 of them would be 1. here size is not given how many groups will be needed that is given

whats the difference i dont understand
 
Saumyojit said:
One way to think of 1/1.6 is that we want to divide a single "box" into
1.6 equal "pieces" . In this statement size of each equal pieces are given right?
Click to expand...
No, in this partitive model, the 1.6 is the number of pieces. The size is what you want to find.

Saumyojit said:
I want to find the size of a "piece" such that 1.6 of them would be 1. here size is not given how many groups will be needed that is given

whats the difference i dont understand
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In the quotative model, which I gave first, you would be given the size of each piece (1.6 units), and want to know how many you will get. That's the picture in post #31.


Please, when you quote what someone else has said, mark it somehow as a quotation. When you mix my words with yours, I get confused, and waste time figuring out what you are asking.
 
One way to think of 1/1.6 is that we want to divide a single "box" into
1.6 equal "pieces" .
How will i understand this line means 1.6 is the number of pieces not the size of each piece am i not understanding english language??
 
@Dr Peterson
just an analogy

In the quotative model if i take the eg of 12 apples 12/3 that means each group will have 3 ,how many total groups shall be formed

In this box 1/1.6 (denominator greater than numerator ) in quotative model , size of each piece is (1.6 units) but there is only one box with 1.6 length right so why each is being used?

+-------------------------------+
| : : : : : : : |
+-------------------------------+
this is 1.6 box so every block is each piece or the whole is 1.6?
as in apples each groups will have 3 apples per group here in the box case each piece (block right? ) out of those 8 blocks each is 1.6 or each block out of those 8 blocks is 1/5??

i am confused with the term parts,piece,groups..
 
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Saumyojit said:
One way to think of 1/1.6 is that we want to divide a single "box" into 1.6 equal "pieces" .
How will i understand this line means 1.6 is the number of pieces not the size of each piece am i not understanding english language??
Click to expand...

If I say "1.6 pieces", then 1.6 is the number of pieces.

How else would you interpret that?

If I talked about pieces of size 1.6 meters, say, or more generally, "1.6 units", then 1.6 would be the size.

Saumyojit said:
@Dr Peterson
just an analogy

In the quotative model if i take the eg of 12 apples 12/3 that means each group will have 3 ,how many total groups shall be formed

In this box 1/1.6 (denominator greater than numerator ) in quotative model , size of each piece is (1.6 units) but there is only one box with 1.6 length right so why each is being used?

Code: 
[FONT=courier new]+-------------------------------+

   |   :   :   :   :   :   :   :   |

   +-------------------------------+[/FONT]

this is 1.6 box so every block is each piece or the whole is 1.6?
Click to expand...

Possibly you are misreading what I wrote in the article you are asking about because I neglected to say "1.6 units" in describing lengths, calling it "the 1.6 box". That was poor grammar. But I had introduced it by saying, "So here is a box with length 1, and another with length 1.6 (= 8/5)", not "here is a strip of boxes, each 1.6 units long". It is the entire strip (not each little piece of it) that has a length of 1.6 units; I showed it divided into pieces 1/5 unit long, so that 8 of them make a total of 8/5 = 1.6 units.
 
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