Homework Help: Math

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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