Fraction meaning

[Dr.Peterson]

As i was following ur post ur equation stands like this "1/5 *x=1/8th" i see that 1/5 of my quantity is 1/8th . I dont get it where is the "5 times of 1/5 "

OKAY What i observed just now 1/5 *x =1/8th --> then u multiplyed both sides by 5 i get

EQUATION: 5 *1/8=5 *1/5*x --> which means one of my quantity (5*1/8 lhs part ) is 5 times 1/5 of my quantity(x)

This is what u are trying to mean

I never said "5 times of 1/5", which is poor grammar. Please at least quote correctly!

But also, please understand that in my explanation that you are trying to understand, I was giving in to a request for a visual explanation of a division that most teachers would not even try to explain with a picture, so it is a stretch! And in my explanation I was therefore avoiding equations and using words. As I said in a part you haven't quoted, "I agree with Dr. Jerry, that ultimately you need to think of division at a higher level than pictures of boxes." Since you are using equations here, you literally do not need to understand my attempt to use words. I am serious about this. You are beyond that.

Also, you have been admonished a couple times not to use text abbreviations like "u", which are very distracting in a mathematical context! You apparently have not bothered to look at the guidelines that were referred to, which say, "Try to use halfway-decent English. No, this isn't Englishhelp.com, but you'll get more help if you spell correctly. Actually, I don't care if you spell a few words wrong, but the IM speak will probably cause some people to skip over "ur" question. If we can't understand it, we can't help." I don't make an issue of such things, but I have made it clear that I am annoyed having to read your long, confusing posts, and the least you could do would be to show this much respect for those you are asking for help.

End of diatribe.

It appears that you do understand that "5 times 1/5 of my quantity" means all of my quantity, because (symbolically) 5 * 1/5 = 1, and because (visually) 1/5 means 1 of 5 equal parts that together equal 1, so that 5 of them equal 1. So 5 times 1/5 of anything means all of it.

And I introduced that as a way of saying verbally that x = 5*1/5*x = 5*1/8 = 5/8; that is, yes, it amounts to multiplying both sides of an equation by 5. And the point is that, since you do understand algebra, you don't need to be able to express these things without symbols, and can drop the whole question.

I have no idea why you are having trouble with this.

 

[Saumyojit]

I was giving in to a request for a visual explanation of a division

yes that is what i also required

like "u"

i was writng fast and in the flow i have written . As long readers can understand u mean you there is no problmn for me.
I can't remember all of the guidiline but will try. there is lot of finanical pressure going in my family and simultanously doing my studies.

as a way of saying verbally

yes thats why i wrote my observation in post 60 . i broke down the steps and then matched with your verbal statemnt . Yes it was quite a stress for me to find out .

"each of those eighths must be 1/5 of the piece I am making"

Ok i think i now understood what this line meant .
Now its a earnest request to see my "ASSOCIATIVE" post ...the last comment i made .
I did not get a reply but i am waiting for anyone to give a reply
Thanking u .
U guys cannot imagine what tremendous amount of help you all are doing to explain my Long confusing doubts .

 

[Saumyojit]

@Dr.Peterson
Q1: Can we add fractions taken from two different sizes of 2 objects? If a regular sized pizza is divided into 3 slices and i took one out of it and there is a big sized pizza and divided into 3 slices and i took one out of it . Then can i add and say the two fractions " 1/3 of a pizza + 1/3 of a pizza =2/3 of a pizza"
But what i feel it cant happen as jomo earlier said "there really is no comparsion between two different sizes of things"

A fraction is a way of writing a single number, which amounts to a division that is not carried out (so that 2/3 means "the number you would get if you divided 2 by 3").

Are u saying fraction looks the same as division "2/3" something like that ;
WHy did u said not carried out?
2 apples / 3 pieces = 2/3 of a apple
i got the fraction only after i divided not before divison .
But if i wrote it as simply like this 2/3 then it would be upto the observer whether he will take it as a fraction or a division acc to context
right?

Q3:
2 apple /3 pieces this means 1 apple /3 pieces + 1 apple/3 pieces =2 apple/3pieces .

Can I say this " addition of fraction with like Denominator "??

I think No as 1 apple/3 pieces + 1 apple /3 pieces these two are not fractions( but they are in the form of Divisions)
but they somehow makes up the equation and give us the feel .
(1apple/3 pieces) + (1 apple/3 pieces)=2 apple/3 pieces

Seeing the equation it feels like two fractions are being added with like Denominator
1/3+1/3=2/3 ( if I remove the captions)

Q4:
Doubt regarding units
In 7 + 21/4 the units are different ones and one fourth so i converted ones to fourth . ok

In rs 7 + rs 21 Unit is "Rs" and we can simply add giving Rs 28


But in Rs 7 +Rs 21/4

In this case what is the unit : one unit is "rs" which is same in both the terms

So if I see that way then I can simply add Rs 7+ Rs 21/4
But wait I need to convert 7 to 28/4 before adding to 21/4 which means another unit is there that is different
"Ones Vs one fourth " unit . So how many unit are there ? one is "rs" and another is " ones and 1/4th"

But if I keep like this Rs 7 and Rs 21/4 converted to Rs 5 1/4 which means Rs 5 and 25 paisa then I can simply add the two terms

Rs 7 + Rs 5 25 paisa=Rs12 25 paisa (here one term is in fully Rs and the other is a mixture of Rs and paisa)
Is the unit same or different .
If it is different as it seems they are getting added without any probs to give Rs 12 25 paisa


If I write the same thing as this then what about this case
Rs 7 + Rs 5.25(this is actually the representation of rs and paisa combined ) =Rs 12.25
Here there is one unit that's is Rs present in both the terms which is fine but the first term is in ones and the second is in decimal format. So units are different isn't it?

Also in this eg : 1/3 of a pizza + 1/3 of a pizza there are also two units i.e 1/3rds and "of a pizza" which you have told mentioning as "consistent unit"

 

[Dr.Peterson]

Q1: Can we add fractions taken from two different sizes of 2 objects? If a regular sized pizza is divided into 3 slices and i took one out of it and there is a big sized pizza and divided into 3 slices and i took one out of it . Then can i add and say the two fractions " 1/3 of a pizza + 1/3 of a pizza =2/3 of a pizza"
But what i feel it cant happen as jomo earlier said "there really is no comparsion between two different sizes of things"

Of course you're right. This is not really "1/3 of a pizza + 1/3 of a pizza", but "1/3 of this pizza + 1/3 of that pizza", and you can't add things with different units, any more than 1 meter + 1 kilometer = 1 of something.

Are u saying fraction looks the same as division "2/3" something like that ;
WHy did u said not carried out?
2 apples / 3 pieces = 2/3 of a apple
i got the fraction only after i divided not before divison .
But if i wrote it as simply like this 2/3 then it would be upto the observer whether he will take it as a fraction or a division acc to context
right?

What I mean is that if you carry out the division, you get 0.6666... . The notation a/b just means division (as it does regularly in algebra); we just use the same notation to represent the number itself. Look at your own notation: "2 apples / 3 pieces = 2/3 of a apple"! On the left "/" means division; on the right, all you've done is to move the labels around. You've done no actual work. That's what I was referring to.

So you're right that when you see "2/3", you can think of it either as division or as a representation of a single number.

Q3:
2 apple /3 pieces this means 1 apple /3 pieces + 1 apple/3 pieces =2 apple/3pieces .

Can I say this " addition of fraction with like Denominator "??

I think No as 1 apple/3 pieces + 1 apple /3 pieces these two are not fractions( but they are in the form of Divisions)
but they somehow makes up the equation and give us the feel .
(1apple/3 pieces) + (1 apple/3 pieces)=2 apple/3 pieces

Seeing the equation it feels like two fractions are being added with like Denominator
1/3+1/3=2/3 ( if I remove the captions)

You are being too rigid again. Since "1 apple /3 pieces" is 1/3, you can certainly think of it as adding two fractions.

If I asked you, "When I add 2 cows + 3 cows, am I adding integers?", wouldn't you complain about a trick question if I said, "no, you are adding two sets of cows"? You are adding integers in order to count cows.

Q4:
Doubt regarding units
In 7 + 21/4 the units are different ones and one fourth so i converted ones to fourth . ok

In rs 7 + rs 21 Unit is "Rs" and we can simply add giving Rs 28

But in Rs 7 +Rs 21/4

In this case what is the unit : one unit is "rs" which is same in both the terms

Yes, the unit is rupees. In carrying out the addition, you have to either convert to the same denominator, or convert 21/4 to a mixed number [as you will do later]; but the denominator is not the unit in the problem. (It can be thought of as the unit in modeling the addition using physical objects, but that is not inherent in the problem itself.)

So if I see that way then I can simply add Rs 7+ Rs 21/4
But wait I need to convert 7 to 28/4 before adding to 21/4 which means another unit is there that is different
"Ones Vs one fourth " unit . So how many unit are there ? one is "rs" and another is " ones and 1/4th"

But if I keep like this Rs 7 and Rs 21/4 converted to Rs 5 1/4 which means Rs 5 and 25 paisa then I can simply add the two terms

Rs 7 + Rs 5 25 paisa=Rs12 25 paisa (here one term is in fully Rs and the other is a mixture of Rs and paisa)
Is the unit same or different .
If it is different as it seems they are getting added without any probs to give Rs 12 25 paisa

Once again, it will help you a lot if you learn to separate the problem itself from the mathematics, and that from the methods used.

The problem has units of rupees. The mathematics is just an addition of numbers, in this case a whole number and a fraction. The work can be done by different methods, which may involve changing denominators or changing form. These are three different things, and must not be confused in you want to keep (or regain) your sanity.

If I write the same thing as this then what about this case
Rs 7 + Rs 5.25(this is actually the representation of rs and paisa combined ) =Rs 12.25
Here there is one unit that's is Rs present in both the terms which is fine but the first term is in ones and the second is in decimal format. So units are different isn't it?

Also in this eg : 1/3 of a pizza + 1/3 of a pizza there are also two units i.e 1/3rds and "of a pizza" which you have told mentioning as "consistent unit"

Why should you consider the unit to have changed when you just wrote the number differently?

In the pizza problem (assuming you are back to assuming "a pizza" is a standard size unit), the unit is "a pizza". "Thirds" arise only in doing the math.

 

[Saumyojit]

"1/3 of this pizza + 1/3 of that pizza"

It will kind of translate to 2/3 of something right after addition? Or it will remain as 1/3 of something as there is no "consistent unit right"

I feel Its kind of same like the eg that u had given long ago in another post

you can't add 1 apple and 2 oranges; you have to use the same unit, such as 1 cup of apple and 2 cups of orange to make 3 cups of fruit.

Making a analogy
1 cup of this (this refers to apple) and 2 cups of that (that refers to oranges)= 3 cups of something ( something referred to as fruit) . Here 2+1 is happening as cup is the unit . So "this" and "that" in the fruit problemn does not matter as the main unit is cup

 

[Dr.Peterson]

It will kind of translate to 2/3 of something right after addition? Or it will remain as 1/3 of something as there is no "consistent unit right"

OF COURSE NOT! In that example, they are two different "somethings", so there is no single "something" for it to be 2/3 of - or 1/3 of, either. You can't add without additional information (e.g. square inches of pizza).

I feel Its kind of same like the eg that u had given long ago in another post Making a analogy
1 cup of this (this refers to apple) and 2 cups of that (that refers to oranges)= 3 cups of something ( something referred to as fruit) . Here 2+1 is happening as cup is the unit . So "this" and "that" in the fruit problem does not matter as the main unit is cup

Right. You can't add without a common unit. 1 apple + 2 oranges can't be added, but 1 cup of fruit + 2 cups of fruit can.