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Math Help - Multiplying Fractions

  1. #1
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    Multiplying Fractions

    Hi All,
    I'm trying to multiply the below..

     (100*50*10)/(15*10*4) = (50*25*5)/(25*10*n)

    so this would symplify to

     50/3 = 50/50n (n) leaving  50/3 = n

    But the answer is n = 3/10. So where did I go wrong?


    .. How....?


    Thanks,
    Last edited by dumluck; January 12th 2011 at 05:53 AM.
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  2. #2
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    Hi dumluck,

    Simplifythe equality. Both sides.Then cross multiply.You will then get the right answer

    bjh
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  3. #3
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    Quote Originally Posted by bjhopper View Post
    Hi dumluck,

    Simplifythe equality. Both sides.Then cross multiply.You will then get the right answer

    bjh
    Hi Bjhopper,
    OK let me try...

     (100*50*10)/(15*10*4)  = (10*5)/(15*4) = (50)/(60)
     (50 *25*5)/(25*10*n)  = (10*5)/(5*2n) = (50)/(10n)
    Cross Multiply  (50)/(60) = (50/10n) : (50)(10n) = (50)(60) :  5n = 30 , n = 6

    Where did I go wrong// I'm trying here ?
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  4. #4
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    Hello, dumluck!

    \displaystyle \text{Simplify: }\;\frac{100\cdot50\cdot10}{15\cdot10\cdot4} \;=\; \frac{50\cdot25\cdot5}{25\cdot10\cdot n}

    As bjhopper suggested, reduce the fractions first.


    \displaystyle \text{The fraction on the left: }\;\frac{\rlap{///}100^{20}\cdot\rlap{//}50^5\cdot\rlap{//}10^5}{\rlap{//}15_3\cdot\rlap{//}10\cdot\rlap{/}4_2} \;=\;\frac{500}{6} \:=\:\frac{250}{3}


    \displaystyle\text{The fraction on the right: }\:\frac{50\cdot\rlap{//}25\cdot5}{\rlap{//}25\cdot10\cdot n} \;=\;\frac{\rlap{//}50^5\cdot5}{\rlap{//}10\cdot n} \;=\;\frac{25}{n}


    So we have: . \displaystyle \frac{250}{3} \:=\:\frac{25}{n}


    \text{Multiply by }3n\!:\;\;250n \:=\:75 \quad\Rightarrow\quad n \;=\;\dfrac{75}{250} \;=\;\dfrac{3}{10}

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  5. #5
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    Quote Originally Posted by Soroban View Post
    Hello, dumluck!

    [size=3]
    As bjhopper suggested, reduce the fractions first.


    \displaystyle \text{The fraction on the left: }\;\frac{\rlap{///}100^{20}\cdot\rlap{//}50^5\cdot\rlap{//}10^5}{\rlap{//}15_3\cdot\rlap{//}10\cdot\rlap{/}4_2} \;=\;\frac{500}{6} \:=\:\frac{250}{3}
    Thanks Soroban,
    In the above where you have seperated the symplification into three fractions (i.e you could put a line between the fractions and symplify each seperately); Is that the typical first step? As in, take each fraction and try to find a divisor, if there are no divisors look at the whole (as you have done with the '25' for the fraction on the right?). The concept I grasp, it seems to be the analysis of the problem I'm not grasping.
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  6. #6
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    Quote Originally Posted by dumluck View Post
    Hi All,
    I'm trying to multiply the below..

     (100*50*10)/(15*10*4) = (50*25*5)/(25*10*n)

    so this would symplify to

     50/3 = 50/50n= (n) leaving  50/3 = n
    Your error is thinking that the right side is 50/50n. Canceling the "25"s in numerator and denominator leaves (50*5)(10*n). 10 divides into 50 5 times leaving (5*5)/n= 25/n, not n.


    But the answer is n = 3/10. So where did I go wrong?


    .. How....?


    Thanks,
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  7. #7
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    I get it, thanks for that. Phew.... Think I sweated a little there...
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  8. #8
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    Hi again dumluck,
    You are making mistakes in simplifing.Left side simplifies to 250/3.Right side to 25/n.


    bjh
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