Math
posted by Katie on .
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!)

(1000!999!998!)/(1000!+999!+998!)=
998!(1000*9999991)/998!(1000*999+999+1)=
(1000*9991000)/(1000*999+1000)=
(1000*998)/(1000*1000)=998/1000 and u can simplify this number 
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*9999991)/[998!(1000*999+999+1)]
= 998000/1000000
=499/500 
Both numerator and denominator have a common factor of 998!. Cancel that out and you have
[1000*999 9991]/[1000*999 + 999+1]
=[1000(9991)]/[1000(999+1)]
=449/500 
499/500