Distributing Division

Date: 11/23/2003 at 12:50:01
From: Kathryn
Subject: Mathematics Explained For Primary Teachers

Hi,

Hope I'm not wasting your time but I hope that you can help. 

On page 91 of the book _Mathematics Explained For Primary Teachers_
(by Derek Haycock), I find this statement:

  The method is based on the distributive law for division 
  over addition.

Shouldn't this read '....distributive law for multiplication 
over addition'?

Many thanks for your help.
Kathryn 

Date: 11/23/2003 at 22:49:57
From: Doctor Ian
Subject: Re: Mathematics Explained For Primary Teachers

Hi Kathryn,

Well, division _does_ distribute over addition, e.g., 

  (1 + 2)/5 = 1/5 + 2/5

which is why we can add fractions with common denominators by simply
adding their numerators.  However, it's only left-distributive, 

  (1 + 2)/5 = 1/5 + 2/5            Yes

  5/(1 + 2) = 5/1 + 5/2            No

whereas multiplication is both left- and right-distributive:

  5(1 + 2) = 5(1) + 5(2)           Yes

  (1 + 2)5 = 1(5) + 2(5)           Yes

Does this help? 

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