# Math, how do you commute?

I have a math problem that says to commute 100!/99!

Can anyone help :)

oh.. ok well then how do i solve this math problem? can you help?

### 5 Answers

- BretLv 49 years agoBest Answer
100! = 100 *99*98*97...*1

99! = 99*98*97*96...*1 so you have

100 *99*98*97*96...

-----------------------------

99*98*97*96*95.............

everything below the hundred is going to cancel to 1. i.e 99/99 = 1 98/98 =1 so you have ::

100 * 1*1*1*1*1*1... = 100

- pzifissshLv 79 years ago
"Commute?" I don't know. Is it possible that you were supposed to _compute_ the value of that expression? Only thing is, according to the literal definition of "compute," that would be quite a task. Most calculators and spreadsheet programs would be incapable of doing it. You could do it via pencil and paper, but you would need a lot of time and some really big sheets of paper.

Specialized computer software that does "bignum" arithmatic could do it. Or, you probably could use Wolfram Alpha. http://wolframalpha.com/

The easy way to evaluate that expression though is to simplify it, by using the laws of algebra. 100! is the product of all of the integers from one through one hundred. 99! is the product of all of the integers from one through 99. Imagine that fraction written out

1 × 2 × 3 × ⋯ × 99 × 100

----------------------------------

1 × 2 × 3 × ⋯ × 99

Is anything there that could be cancelled out?

- roderick_youngLv 79 years ago
I think there's a typo, and it means to say "compute". To do that, think about the definition of factorial, and cancel common factors before multiplying anything out.

To commute in math means to exchange the order of two things. For example, the addends 5 and 7 in 5 + 7 can be commuted to 7 + 5, and you still get the same sum.

- ℂharlesLv 49 years ago
And the way you COMPUTE these factorials is to write

100! = 100*[[99*98*97*....................*3*2*1]]

and

99! = 99*98*97*..........................3*2*1.

But wait! We could write 100! as

100! = 100* 99!

So divide both sides to get

100!/99! = 100* 99!/99! = 100

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