Adding Fractions

Date: 05/21/2002 at 21:34:39
From: Brandon 
Subject: Adding Fractions

How do you add fractions?

Date: 05/21/2002 at 21:52:03
From: Doctor Ian
Subject: Re: Adding Fractions

Hi Brandon,

It depends on the fractions.  If they have the same denominator, 
you can just add the numerators:

  2   3   2 + 3
  - + - = -----
  7   7     7

The _reason_ you want a common denominator is so you can use the 
distributive property:

  2   3   
  - + - = 2*(1/7) + 3*(1/7) = (2 + 3)*(1/7)
  7   7   

If they don't have the same denominator, you have to change them 
so that they do:

  2   3   14   15   14 + 15
  - + - = -- + -- = -------
  5   7   35   35      35
  
The easiest way to do that is to multiply each fraction by n/n, 
where n is the denominator of the other fraction:

  2   3   2   7     3   5  
  - + - = - * -  +  - * - 
  5   7   5   7     7   5 

          2 * 7     3 * 5
        = -----  +  -----
          5 * 7     7 * 5

          2 * 7  +   3 * 5
        = ----------------
               5 * 7     

          14 + 15
        = -------
            35

Since n/n is always equal to 1, you're just multiplying each 
fraction by 1, which doesn't change the values of the fractions.  
It just changes the way they look. 

Is this what you wanted to know? 

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