Adding Odd Numbers

Date: 02/22/2002 at 22:01:04
From: Norm
Subject: Addition of odd numbers

Why is it you get an even number when adding odd numbers?

Date: 02/22/2002 at 22:57:08
From: Doctor Twe
Subject: Re: Addition of odd numbers

Hi Norm - thanks for writing to Dr. Math.

This is one way you can think of it: an even number of objects can 
be "paired." For example 10 apples can be matched up into 5 pairs of 
apples. An odd number of objects will have one left over when pairing. 
For example, 5 oranges can make 2 pair with 1 left over. (This is 
the definition of odd numbers, having a remainder of 1 when dividing 
by 2).

With two odd numbers, each odd number by itself has one left over, but 
when we add them together, we can combine these two "leftovers" to 
form another pair.

Any time we add an even number of odd numbers, we'll be able to pair 
up the "leftovers" and get an even number for our sum. But if we add 
an odd number of odd numbers, we'll get an odd number for a sum. This 
is because we can only pair up 2 of the 3 leftovers (or 4 of 5, 6 of 
7, etc.)

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.com/dr.math/