Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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, 
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


  280b * x

Or just:


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

- Doctor Achilles, The Math Forum
Associated Topics:
High School Basic Algebra
Middle School Algebra

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum