14b * 20x Rearranged

Date: 03/11/2002 at 14:13:23
From: Josh Marvel
Subject: Math

What is 14b * 20x ?

Date: 03/11/2002 at 14:27:14
From: Doctor Achilles
Subject: Re: Math

Hi Josh,

Thanks for writing to Dr. Math.

Remember when you learned the rules of multiplication and you learned 
that multiplication is commutative?  That is:

  3 * 4

is equal to:

  4 * 3

and in general:

  x * y = y * x

And you also learned that:

  x * (y * z) = (x * y) * z

If you put those two rules together, what you get is that you can 
rearrange the numbers in any multiplication problem however you like, 
AS LONG AS THERE IS NOTHING BUT MULTIPLICATION going on in the 
problem, and you'll always get the right answer.

So let's take a look at your problem:

  14b * 20x

We can think of this as:

  (14 * b) * (20 * x)

Or just:

  14 * b * 20 * x

Now, we can rearrange that and put the constants (14 and 20) next to 
each other, like this:

  14 * 20 * b * x

And we can add parentheses:

  (14 * 20) * b * x

14 * 20 = 280, so we have:

  280 * b * x

We can add parentheses again and get:

  (280 * b) * x

Or:

  280b * x

Or just:

  280bx

Hope this helps.  If you have other questions about this or you're 
still stuck, please write back.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/