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Math Help - simple fractions??

  1. #1
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    simple fractions??

    not sure if im just being dumb here tbh lol but can anyone explain this step to me?

    1/a + 1/b + 1/c

    = (bc + ac + ab) / abc

    i just dont see it . shoulda listened at high school
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  2. #2
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    Hello,
    Quote Originally Posted by djmccabie View Post
    not sure if im just being dumb here tbh lol but can anyone explain this step to me?

    1/a + 1/b + 1/c

    = (bc + ac + ab) / abc

    i just dont see it . shoulda listened at high school
    Hmmm just get the common denominator. a*b*c

    For example :
    \frac 1a=\frac 1a \cdot \frac{bc}{bc}=\frac{bc}{abc}
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    not sure i understand.

    so for each fraction you do the same?

    so like 1/a = 1/a * bc/bc = bc/abc

    then 1/b = 1/b * ac/ac = ac/abc

    and 1/c = 1/c * ab/ab = ab/abc

    ok it does make more sense but im still confused as to where bc/bc appeared from :/

    worse part is i know this is like primary school stuff and i im goin uni doing maths next year :|
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    Quote Originally Posted by djmccabie View Post
    not sure i understand.

    so for each fraction you do the same?

    so like 1/a = 1/a * bc/bc = bc/abc

    then 1/b = 1/b * ac/ac = ac/abc

    and 1/c = 1/c * ab/ab = ab/abc

    ok it does make more sense but im still confused as to where bc/bc appeared from :/

    worse part is i know this is like primary school stuff and i im goin uni doing maths next year :|
    Yes, that's the thing.

    Now, \frac{bc}{bc}=1 and you can multiply any number by 1 without changing its value.

    What I've done is to make appear the common factor between a,b and c, that is to say abc, because \frac mp+\frac np=\frac{m+n}{p} and it's only when you have a common denominator that you can add up the fractions.
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    i got half way through writing another message to explain something else and it clicked i can sleep tonight now and thankyou!
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    and then straight away im stumped on something similar

    (1/ab) + (1/bc) + (1/ac)

    = (a + b + c)/abc

    cannot get my head around that. beggining to get a headache
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  7. #7
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    Quote Originally Posted by djmccabie View Post
    and then straight away im stumped on something similar

    (1/ab) + (1/bc) + (1/ac)

    = (a + b + c)/abc

    cannot get my head around that. beggining to get a headache
    Okay, the thing is :
    see what the denominator in the end is. It's abc.
    So if you multiply ab by c, you'll have abc.
    If you multiply bc by a, you'll have abc...

    Use the same process as before, that's all !
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  8. #8
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    i have come to the conclusion that i will never understand the proof, so im just gonna learn the method. thanks anyway
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  9. #9
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    Quote Originally Posted by djmccabie View Post
    and then straight away im stumped on something similar

    (1/ab) + (1/bc) + (1/ac)

    = (a + b + c)/abc

    cannot get my head around that. beggining to get a headache
    Try this approach:

    \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac}

    Find LCD = abc. Multiply that LCD times each term and that becomes your new numerator. The denominator will be your LCD of abc. Let me demonstrate:

    \frac{abc\left(\frac{1}{ab}\right)+abc\left(\frac{  1}{bc}\right)+abc\left(\frac{1}{ac}\right)}{abc}

    \frac{c+a+b}{abc}

    \frac{a+b+c}{abc}
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  10. #10
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    so you multiply everything by abc, and divide everything by abc to derive the final fraction? please say yes that sorta makes sense to me lol. sorry for makin a meal out of something 'apparently' so simple lol. nobody's perfect haha
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  11. #11
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    Quote Originally Posted by djmccabie View Post
    so you multiply everything by abc, and divide everything by abc to derive the final fraction? please say yes that sorta makes sense to me lol. sorry for makin a meal out of something 'apparently' so simple lol. nobody's perfect haha
    This technique will always work. Just find the LCD. Multiply each term of the numerator by that LCD. Then place the simplified numerator over the LCD.
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