Question

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!)

Answer 1

(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

Answer 2

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

Answer 3

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

Answer 4

499/500