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

Saumyojit said:
@Jomo @Dr.Peterson My intution suggests that if i am eating 3 slices out of 11 of 1st pizza and 2 slices out of 11 of 2nd pizza; then eating 5 slices out of 22 . But in mathemtical notation we write 5/11. why so.. i know the lcm logic
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In this example every pizza in the shop is divided into 11 slices, not 22 slices. Therefore you are buying 5/11 of a single, whole, pizza. It doesn't matter that the pizza restaurant had, say, 10 whole pizzas in stock before your arrival (a total of 110 slices). All that matters is that you have purchased 5 slices. The remaining 105 slices left in the shop after your visit are still the property of the restaurant. Do you really think that you purchased 5/110 (less than 5%) of a whole pizza?
 
Cubist said:
In this example every pizza in the shop is divided into 11 slices, not 22 slices. Therefore you are buying 5/11 of a single, whole, pizza.
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I know i buy 3 out of 11 of 1st pizza and 2 out of 11 slices of 2nd pizza. Therefore I am buying 5/11 from 2 whole pizzas not single!
 
Saumyojit said:
I know i buy 3 out of 11 of 1st pizza and 2 out of 11 slices of 2nd pizza. Therefore I am buying 5/11 from 2 whole pizzas not single!
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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.
 
Dr.Peterson said:
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.
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5/11 of a pizza how .. those 5 slices belong to 2 diff pizzas so 5/11 of two pizzas ? i am hearing the first time the usage of absolute & relative quantity in fractions. Relative to what 2 pizzas or whole ..did not get the meaning sir.
U said "5/22 is a relative quantity, a ratio of part to whole" 5/11 is also a part to whole ratio
@Dr.Peterson
 
Saumyojit said:
@Jomo @Dr.Peterson My intution suggests that if i am eating 3 slices out of 11 of 1st pizza and 2 slices out of 11 of 2nd pizza; then eating 5 slices out of 22 . But in mathemtical notation we write 5/11. why so.. i know the lcm logic
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5/(22/2) for 1 pie. Yes, you ate 5/22 of 2 pies which equals 5/11 of one pie. So you are right! But you need to say that you ate 5/11 of a pie or 5/22 of two pies. The choice is up to you!
 
Jomo said:
5/(22/2) for 1 pie. Yes, you ate 5/22 of 2 pies which equals 5/11 of one pie. So you are right! But you need to say that you ate 5/11 of a pie or 5/22 of two pies. The choice is up to you!
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@Jomo @Dr.Peterson 5/11 of one pie means the considered slices belong to only one kind of pie from which i ate ; where in the question 5 slices that i ate comes from both of 2 pies. Not fitting in my mind..

Doc said "Your fraction 5/22 is a relative quantity, a ratio of part to whole" relative to what? 2 pizzas or 22 slices total?
If it was 5/11 then its a absolute quantity nothing relative as said in post23 as there is one unit. "My intution suggest that in 5/11 ; 5 slices i consider relative to 11 slices . 5/11 is also a relative quantity acc to my unsure intution.

Why sir said part to whole ? 5/11 or 5/22 are both part to whole ratio. Did he mean something else significant by part to whole?
 
Do you know what a unit is? It is something like a meter or a kilogram or a pound or a day, used for describing a quantity (in an absolute sense, relative to a fixed standard, not a specific situation).

Here we are thinking of ONE PIE as the unit of measure for a quantity of pizza. That is a natural unit.

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 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.
 
Dr.Peterson said:
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 I would explicitly call it "1/16 of the bag" or "1/16 of the flour I started with".
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suppose 4 cups of each 20 gm;total 80gm of flour.Each box is worth 1/4th of 20gm=5gms.Each box can hold 5gms of flour.
Now if i take 1gm of flour from first cup,2gm frm second cup ,1gm each from last two cups . Then i use 5gms from all the 4 cups of flour and conclude that i used 1/4 of a cup of flour. I dont know am i right or not?
1/4 of a cup of flour ; numerator means 5 gms of flour(1 part) i am using from a cup of 20 gms (4 parts)of flour.
 
Saumyojit said:
@Jomo @Dr.Peterson 5/11 of one pie means the considered slices belong to only one kind of pie from which i ate ; where in the question 5 slices that i ate comes from both of 2 pies.
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where in the question 5 slices that i ate comes from both of 2 pies. It doesn't matter! Do you really think that if you ate all 5 slices from pie A or all 5 slices from pie B or some from each totaling 5 slices that you ate different amounts? Do you really think that your stomach will know the difference? It must if you are eating different amounts of pizza.
 
Jomo said:
Do you really think that your stomach will know the difference?
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I was purely talking from a mathemtical point of view. It seemed very untuitive to me. But as doc told there is a rule in fractions "only the former (using a consistent unit) is addition of fractions " so i need to accept it and move on.

See my post no28
 
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5 slices i consider relative to 11 slices of one pie.

To say you ate 5/11 has no meaning at all! You ate 5/11 of something and you must state that something. I ate 5/11 of one pie or I ate 5/22 of two pies. Note that i ate 5/22 of two pies is the same as eating 5/11 of 1 pie.
 
@Jomo I ate 5/22 of 2 pizzas of each size 1/11 . Which one is the quantity and amount? 1/11 that is the size can i say it is the qunatity , 5 is the amount ? and the whole 2 pizzas are ...what? amt or qunatity? Or it does not matter too much in math the english terms.
@JeffM see my post 28
 
This is making me laugh.

Amount, quantity, it doesn't really matter what you call it. Those are English terms for a mathematical idea. Just stay consistent with one of them to avoid as much confusion as possible.
 
Saumyojit said:
suppose 4 cups of each 20 gm;total 80gm of flour.Each box is worth 1/4th of 20gm=5gms.Each box can hold 5gms of flour.
Now if i take 1gm of flour from first cup,2gm frm second cup ,1gm each from last two cups . Then i use 5gms from all the 4 cups of flour and conclude that i used 1/4 of a cup of flour. I dont know am i right or not?
1/4 of a cup of flour ; numerator means 5 gms of flour(1 part) i am using from a cup of 20 gms (4 parts)of flour.
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Of course you're right. Why do you doubt it? You've added 1/20 + 2/20 + 1/20 + 1/20 = 1/4 cup

I probably shouldn't have used "cup", as you are unaware that this is a standard unit of volume (equal to about 250 ml).
 
Dr.Peterson said:
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"
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but in ur eg u said i would not call it "1/16" that means the original fractions were 1/4+1/4+1/4+1/4 thats the only way i would have mistakenly got 16 in the denom; if the fractions were those then acc to my 20gms eg i have taken 5gms from each 4cups so i conclude that i have used 1 full of a cup of fluor not 1/4 of a cup of flour.
The eg that u have given in post 27 how can i depict in fractions before addition. 1/20 +1/20+1/20+1/20 ;yes it is giving me 1/4 of a cup but it is not mistakenly given me 1/16 if i add denom then it is 1/80...
 
It's time for some music in this thread:- youtube link ( you might need to skip, or watch, an advert before the song plays)

This video animates the division of pizzas into an equal number of slices before adding/ subtracting slices. Initially it clearly shows that each slice has very different area, so it doesn't make sense to add/ subtract these slices. So each pizza is then divided into the LCM number of slices and you can see that the shaded areas can remain EXACTLY the same - but now both pizzas are carved into slices of equal area. This means that adding/ subtracting the equal sized slices makes sense!

And even better, I swear that one of the girls singing is Beyoncé. I guess it makes sense that she'd be great at math, so that she can keep track of her record sales ;)

Watch out for the damning pizza assessment lyric, "It smelled so good we had to give it a sniff" ?
 
Saumyojit said:
but in ur eg u said i would not call it "1/16" that means the original fractions were 1/4+1/4+1/4+1/4 thats the only way i would have mistakenly got 16 in the denom; if the fractions were those then acc to my 20gms eg i have taken 5gms from each 4cups so i conclude that i have used 1 full of a cup of fluor not 1/4 of a cup of flour.
The eg that u have given in post 27 how can i depict in fractions before addition. 1/20 +1/20+1/20+1/20 ;yes it is giving me 1/4 of a cup but it is not mistakenly given me 1/16 if i add denom then it is 1/80...
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I was saying that 1/4 of a cup is 1/16 of the 4-cup bag. And this has nothing to do with your 20-gram cups. I said it in post #27, before your #28.
 
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