If 9! x n = 11, what is the value of n?

Remember that 9! (read "9 factorial") is the product of the first 9 integers, or

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

This is a massive number, so sometimes it’s more convenient to simply keep it in factorial form while manipulating it. Dividing both sides of the equation by 9!, we find that n = 11/9!

I’m also going to consider the case where 11 could’ve been a typo, and was originally meant to be a 11!

Then, we’d have n = 11!/9!

11! actually contains 9!, since we can rewrite 11! as 11 x 10 x 9! and it will still have the same meaning. Putting that expression over 9! then cancels both of the 9! terms, and we’re left with

n = (11 x 10 x 9!) / 9! = 11 x 10 = 110

If nine times n equals eleven than the value of n would be 11/9 and to get this all we have to do is divide both sides by 9.