division: to find the answer of "3/4" is the same to say how many "4" in "3" ?

Ryan$

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Hi guys, about division on math, I know what it's mean and read about it but still confused about one of its cases.
lets assume I do 4/2 then it's equal 2 ..it's fine for me! but lets assume I do 3/4 so the answer is 3/4 but it's not making sense, because to find the answer of "3/4" is the same to say how many "4" in "3" ?.... so is the answer for that question 3/4? if so .. it's like something not making sense
 
1) Not everything is a Whole Number. Thus, how many "4 in 3" - if it MUST be a Whole Number, there must be no solution. If you allow rational numbers for answer, that's a different question.

2) If you really want to ponder the mysteries, try 0/0. How many "zero in zero"? 1? Sure. 2? Sure? 17? Sure. [math]\sqrt{2}[/math]? Sure. Rather difficult to pin down.

3) And, just for fun, how about 3/0? How many "zero in 3"? Does [math]\infty[/math] do it?

Have fun thinking. :)
 
I totally with you, so how should I imagine the rational?! I mean once I'm solving and I get the answer as a rational .. it makes for me no sense because I can't imagine it .. so how should I imagine the rational number to be relative to them and be kindle to them?!
 
I totally with you, so how should I imagine the rational?! I mean once I'm solving and I get the answer as a rational .. it makes for me no sense because I can't imagine it .. so how should I imagine the rational number to be relative to them and be kindle to them?!
Cut up a pie.
 
Hi guys, the teacher on the video said that "we will now calculate the value of A,value of B, and then do A on B" , and he did division, why did he do division? is "A on B" a division meaning? musn't we say A divide by B?! thank alot, really confusing how "on" is a division meaning ?!!
 
Please give a link to the video, so we can be sure you are quoting correctly, and to get a sense of the context (region, level of formality, ...). English usage varies around the world, and any usage can be confusing if it is unfamiliar.

I have seen some students, if not teachers, use the phrase "A on B" to mean "A divided by B". I would not use the former, but I can't declare it to be incorrect everywhere in the world on that basis. In America, we often say "A over B", with essentially the same meaning, describing what it looks like on paper.

By the way, I also wouldn't say "A divide by B", as you did! But I'm not about to criticize your English usage based on a triviality. I can understand what you mean (this time, at least).

Also, this has nothing to do with "logic of math", only with "meaning of words".
 
Please give a link to the video, so we can be sure you are quoting correctly, and to get a sense of the context (region, level of formality, ...). English usage varies around the world, and any usage can be confusing if it is unfamiliar.

I have seen some students, if not teachers, use the phrase "A on B" to mean "A divided by B". I would not use the former, but I can't declare it to be incorrect everywhere in the world on that basis. In America, we often say "A over B", with essentially the same meaning, describing what it looks like on paper.

By the way, I also wouldn't say "A divide by B", as you did! But I'm not about to criticize your English usage based on a triviality. I can understand what you mean (this time, at least).

Also, this has nothing to do with "logic of math", only with "meaning of words".

My problem is saying "over" ... who said that A over B says A/B in math?! musn't we say A divided by B then I can say it's A/B? ! I'm finding it hard and really hard how "over" translated in math to "division" ..who said that?! if it's about meaning of words, who said that over means divide?!
I can say "NMAKJSDKAJSDKLASDKLAKSD" and it means for me division , I mean who invested that word "over" means division and all use it like division .. !
 
I told you why "over" is used: When we write, we put the numerator "over" (above) the denominator, so it is common to talk in a way that describes what we are writing. That's just a result of the tendency to shorten anything we say frequently. Since it is perfectly understandable and creates no confusion (in sensible people), we don't complain.

"Who said?" Well, whatever people generally agree on as the meaning of a word, is valid. There is no authority that decrees "correct" words in English. In math, someone suggests a word for a new concept, and if others use it, it becomes the accepted word. (Both the word and its precise definition may change with usage.) For an old concept like division, in an informal context, we commonly use idiomatic language, and that is acceptable too (though probably not in a formal proof in a math journal, which is not your context).

If you were to invent a word for yourself, then no one else would understand you. But if somehow others adopted the word, it could eventually become standard. (That's not very likely, though!)

This is the way language works. Live with it.
 
Hi guys, if someone asks me : how many 2 dollars in 500 dollars ?! why do we do division? * once again I said division because the answer on the book is solving it by division without known why! *


please any help?! how I connect that this question is talking about division? then I must be deeply understandable what's division about .... I mean what's the concept of division in mathematics?
what's the meaning conceptually of using the operator "division" ?
 
Hi guys, if someone asks me : how many 2 dollars in 500 dollars ?! why do we do division? * once again I said division because the answer on the book is solving it by division without known why! *

please any help?! how I connect that this question is talking about division? then I must be deeply understandable what's division about .... I mean what's the concept of division in mathematics?
what's the meaning conceptually of using the operator "division" ?
Division is the inverse of multiplication. That is, it is the operation that "undoes" multiplication.

The answer to a multiplication question of the form "__ times 2 = 500" or "2 times __ = 500" (that is, What is the other factor?) is division: __ = 500 ÷ 2. In fact, in English, the word "quotient" (the result of division) comes from the Latin word for "how many?"

That's all there is to it: a ÷ b = c is equivalent to a = b × c.
 
The operation of division arose out of the concept of splitting a total into equal shares. Put into the language of set theory: if the number of a set is a, then [MATH]a \div b[/MATH] is the number of each of b sets, all of which have an equal number. Notice in this concept b must be a positive integer, or it makes no sense. Let's consider an example: suppose the five children of a shepherd inherit a total of 540 sheep and are to share equally, how many sheep should each child get?

The answer is [MATH]540 \div 5 = 108 \text { sheep each.}[/MATH]
Now we may notice that [MATH]5 \times 108 = 540.[/MATH]
And this fact can be generalized to:

[MATH]b \ne 0 \\text { and } a \div b = c \iff b \ne 0 a = b \times c.[/MATH]
So this idea that division and multiplication are inverse operations is an alternative way of conceiving the meaning of division. Moreover, it is a more general concept because the concept of division into equal sets makes sense only with respect to division by a positive intege whereas the concept of an inverse to multiplication extends to any number except zero.



If we limit ourselves
 
… the book is solving it by division without [explaining] why …
?\(\;\) If the book does not explain division or how we use it, then maybe your book was written for students who have already learned the meaning of division. In your case, you probably need an introductory book (written for people learning arithmetic).

… what's the concept of division in mathematics? …
At your level, division is about separating a quantity into equal-sized pieces.

In word problems, there are two ways 500÷2=250 is used.

(1) We separate the quantity 500 into two equal groups. The answer 250 is the size of each group (i.e., two groups, with 250 in each group).

(2) We separate 500 into groups of size 2. The answer is the number of groups (i.e., 250 groups, with 2 in each group).

For the question "How many 2 dollars in 500 dollars?", we use interpretation (2) above. That is, we want to know how many groups will we have, if we separate $500 into groups of size $2. (500÷2=250 means the number of $2 in $500 is 250.)

Here is a different question, where we would use interpretation (1) above: "How many dollars is one half of $500?" That is, we want to know how big is each group, if we separate $500 into two groups. (500÷2=250 means half of $500 is $250.)

As a child, did you ever share your candy with friends? I had 21 chocolates in a package, and I wanted to share them equally with Matt, Sean and myself. As I took candies out of the package, I put them in three separate groups (one at a time) and said, "One for Matt, one for Sean and one for me … one for Matt, one for Sean and one for me…" After I had separated all the candies, there were three groups. Each group was the same size (seven chocolates). That's division.

21/3 = 7

?
 
My problem is saying "over" …
Here we go, again. You're not willing to accept given information.

Why is that a problem?

Also, Dr. Peterson asked you to post the video link. Did you forget?

:confused:
 
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