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March 27, 2017

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I have no idea how you would do this problem: Express this expression as a rational number in lowest terms.

(1000!-999!-998!)/(1000!+999!+998!)

  • Math - ,

    (1000!-999!-998!)/(1000!+999!+998!)=
    998!(1000*999-999-1)/998!(1000*999+999+1)=
    (1000*999-1000)/(1000*999+1000)=
    (1000*998)/(1000*1000)=998/1000 and u can simplify this number

  • Math - ,

    You have to realize that factorials can be written in several ways
    e.g.

    12! = 12*11*10*9! or
    12! = 12*10*10! I am saying you can stop anywhere

    (1000!-999!-998!)/(1000!+999!+998!)
    = (1000*999*998!-999*998!-998!)/(1000*999*998!+999*998!+998!)
    =998!(1000*999-999-1)/[998!(1000*999+999+1)]
    = 998000/1000000
    =499/500

  • Math - ,

    Both numerator and denominator have a common factor of 998!. Cancel that out and you have
    [1000*999 -999-1]/[1000*999 + 999+1]
    =[1000(999-1)]/[1000(999+1)]
    =449/500

  • Math(correction) - ,

    499/500

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