Posted by **Katie** on Saturday, March 1, 2008 at 9:46pm.

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 -
**mk-tintin**, Saturday, March 1, 2008 at 9:53pm
(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 -
**Reiny**, Saturday, March 1, 2008 at 9:58pm
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 -
**drwls**, Saturday, March 1, 2008 at 9:59pm
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) -
**drwls**, Saturday, March 1, 2008 at 10:00pm
499/500

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