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Math Help - dividing fractions, please can anybody help me to understand the concept?

  1. #1
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    Question dividing fractions, please can anybody help me to understand the concept?

    Hi guys,

    im currently trying to refresh my algebra knowledge as i've been out of school for a while...

    I've come across a couple of problems where something is just not clicking, im sure it's very simple but im struggling to understand how the answer has been reached.

    the problem im having is with dividing fractions.

    I know (4/5) / (6/8) we have to flip the second fraction and then multiply the numerators and multiply the denominators so we get 32/30 or 16/15

    I also know that this works when the first term is not a fraction so (s+2) / (6/8) = (s+2) x (8/6) = 8(s+2)/6.

    but i get a bit confused when the 2nd term is not a fraction. eg (6/8) / (s+2) i know the answer is 6/8(s+2) by multiplying the denominator and the second term but im not really sure why or how it works?

    Do i just need to learn and accept that this is the rule and move on or is there an easy way to understand why this is done that I am not seeing?


    The second problem i have is simplifying:

    (3/X+2) / (X/2X+4)

    Could some one please give me a step by step guide to how this is simplified?


    The way I thought this was done is by "flipping" the second fraction and then multiplying both numerators and denominators to get 3(2X+4) / X(X+2) . I know this is wrong the answer is infact 6/X i'm just not really sure how you get there?

    Im sure these problems are blatantly obvious to most but its been a while since I last used any algebra and this issue of simplifying equations where fractions are being divided is all that's holding me back at the moment.

    I would really appreciate an explanation, thanks guys!
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  2. #2
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Quote Originally Posted by jip1 View Post
    I know (4/5) / (6/8) we have to flip the second fraction and then multiply the numerators and multiply the denominators so we get 32/30 or 16/15
    \dfrac{\frac{4}{5}}{\frac{6}{8}}=\frac{(40)\frac{4  }{5}}{(40)\frac{6}{8}}=\frac{32}{30}=\frac{16}{15}
    Thanks from jip1
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  3. #3
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Hi plato thanks for replying, i'd been taught the way of flipping the second fraction and then multiplying.

    Would you be able to help explain how to simplify the two probelms?

    (6/8) / (s+2)

    and

    (3/X+2) / (X/2X+4)

    Thanks
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  4. #4
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Quote Originally Posted by jip1 View Post
    Hi plato thanks for replying, i'd been taught the way of flipping the second fraction and then multiplying. Would you be able to help explain how to simplify the two probelms?
    (6/8) / (s+2)
    and
    (3/X+2) / (X/2X+4)
    \frac{\frac{6}{8}}{s+2}=\frac{(8)\frac{6}{8}}{8(s+  2)}=\frac{6}{8s+16}

    \frac{\frac{3}{x+2}}{\frac{x}{2x+4}}=\frac{(x+2)(2  x+4)\frac{3}{x+2}}{(x+2)(2x+4)\frac{x}{2x+4}}= \frac{3(2x+4)}{x(x+2)}
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  5. #5
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Quote Originally Posted by jip1 View Post
    (6/8) / (s+2)
    and
    (3/X+2) / (X/2X+4)
    (6/8) / (s+2) is same as (3/4) / [(s+2) / 1]
    Just do the usual "flipping":
    (3/4) * [1 / (s+2)] = 3 / [4(s+2)]

    This one: (3/X+2) / (X/2X+4) requires extra brackets:
    (3/(X+2)) / (X/(2X+4)) : if you use 3/X+2, then that means (3/X) + 2: got that?
    Usual flipping:
    (3/(X+2)) * ((2X+4)/X)
    = (3(2X + 4)) / (X(X + 2))
    That can be further simplifed but I'll stop here so you can "digest" it
    Thanks from jip1
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  6. #6
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Thanks wilmer that's really helpful.

    I got the same answer as you the first time i did this question, (3(2X+4)) / (X(X+2)).

    would you be able to explain how you would simply this further?

    The answer that they have in the book is 6/X which is why i presumed my technique was wrong as I dont see how this can be simplified to 6/X?

    I would have thought at most it can be simplified to 3(2X+2)/X so i must still be missing something?

    Thanks for the help!
    Last edited by jip1; September 30th 2012 at 09:20 AM.
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  7. #7
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    Re: dividing fractions, please can anybody help me to understand the concept?

    Quote Originally Posted by jip1 View Post
    (3(2X+4)) / (X(X+2))

    would you be able to explain how you would simply this further?

    The answer that they have in the book is 6/X
    2x + 4 = 2(x + 2)
    so:
    [3(2)(x + 2)] / [x(x + 2)] : OK?
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  8. #8
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    Re: dividing fractions, please can anybody help me to understand the concept?

    oooooooh I see!

    I didnt realise that I could seperate the 2X like that!

    Thanks so much for clearing this up for me I really appreciate it!
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