Math Is Fun Forum

anyarules

Member

Registered: 2005-07-24

Posts: 29

A really obvious but interesting question

Hi can u plz answer this question. I find it ...well it makes me go
********************************************************************************Why do you need to turn the second fraction upside down when you are dividing a fraction by another fraction?

e.g  4                        1
      _   divided by       _
      9                         2

Why do u make 1/2 into 2/1?
********************************************************************************Thats it...

(don't you just hate simple questions that u cant get the answer out of?)
{}

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: A really obvious but interesting question

Consider a / b.  This could be written as a * 1/b.  Now let a = 3/2 and b = 1/2.  (3/2) / (1/2)

Take the 1/2.  What we want is 1 / (1/2), which would be 1 / b.  Multiply this by 2/2 (which is multiplying it by 1, thus not changing the value).  You get (1 * 2) / ( (1/2)*2 ) = 2 / 1

So 1 / b = 2 / 1.  a * 1 / b = 3/2 * 2 / 1.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Re: A really obvious but interesting question

I think you are right about flipping one of the fractions, only you need to then multiply each side (not divide)

(4/9) / (1/2)  =  (4/9) * (2/1)

4 * 2 = 8
-----------
9 * 1 = 9

But then again, I'm pretty terrible with algebra

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Aloha Nui means Goodbye.

VR Hawks

Member

Registered: 2005-11-26

Posts: 401

Re: A really obvious but interesting question

I don't really know, but let's explain it like this:
------------------------------------------------
4 divided by 2 also equals 4 times 1/2 (2 turned upside down).

4/2 = 4 x 1/2
------------------------------------------------
So, 4/9 divided by 1/2 could also equal 4/9 times 2[/1] (1/2 turned upside down).

4/9 // 1/2 = 4/9 x 2[/1]
------------------------------------------------

Get it?

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Name :: Vincent Raider Hawks
Gender :: Male
Birth Date :: July 4 , 1970

yonski

Member

Registered: 2005-12-14

Posts: 67

Re: A really obvious but interesting question

Rather than struggle to do it in here, i've knocked up a basic proof thingy. I couldn't figure out how to post it as an image, so here's a link to the image instead:

http://img64.imageshack.us/img64/8128/f … of16xb.png

Hope that helps.

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

anyarules

Member

Registered: 2005-07-24

Posts: 29

Re: A really obvious but interesting question

Can you guys make it a bit more simpler?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: A really obvious but interesting question

Dividing by a number is the same as multiplying by 1/number

Example: 5 divided by 7  = 5/7, is the same as 5 multiplied by 1/7 = 5×1/7 = 5/7

So when dividing a fraction it is easier to multiply by 1/fraction.

Read Dividing Fractions

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Re: A really obvious but interesting question

Easy Method!!!

Take the 2 fractions you wish to divide.  Flip one of them over.  Then multiply the 2 new fractions together (multiply the top numbers, then multiply the bottom numbers).  That will give you the correct answer.

4                        1
_   Divided by      _
9                         2

becomes

4                        2
_   Multiplied by    _     <----- This part has been flipped over
9                         1

and thus

4 * 2 = 8
9 * 1 = 9

So your answer  would be 8/9

8
_
9

Last edited by rickyoswaldiow (2006-01-15 21:39:31)

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Aloha Nui means Goodbye.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: A really obvious but interesting question

rickyoswaldiow, (s)he's asking:

Why do u make 1/2 into 2/1?

Not just how.  I guess one reason why is because it's hard to divide fractions, but it's easy to multiply them.  I don't think that one was ever said.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

RickyOswaldIOW

Member

Registered: 2005-11-18

Posts: 212

Re: A really obvious but interesting question

I think the problem was, anya was flipping one fraction but still dividing them.  I was emphasising that you need to multiply it once flipped.  Like you say, it's easier to multiply it that way

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Aloha Nui means Goodbye.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: A really obvious but interesting question

4/9 divided by 1/2

4 divided by 1 is 4 on top.
9 divided by 2 is 4 and a half on bottom.

Hence 40/45

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igloo myrtilles fourmis

anyarules

Member

Registered: 2005-07-24

Posts: 29

Re: A really obvious but interesting question

I still don't get it...........
     

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,423

Re: A really obvious but interesting question

When one rational number is divided by the other, the reciprocal of the second is multiplied by the first.

Examples:-

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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krassi_holmz

Real Member

Registered: 2005-12-02

Posts: 1,905

Re: A really obvious but interesting question

we can represent fractions ae 2d points:
Let a/b-->{a,b}.
Then we define the following functions:
sum({a,b},{c,d})={ad+cb,bd};
product({a,b},{c,d})={ac,bd};
{a,{b,c}}={ac,b};
{{a,b},c}={a,bc};

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