Adding Fractions

Date: 11/10/97 at 20:49:37
From: Catherine Morrissey
Subject: Addition of Fractions

Hi. I have been having some problems with addition of fractions. I am 
kind of worried because everyone in my math class gets it but me!  The 
first problem I have is 4 2/3 + 3 1/6. I tried solving it by setting 
it up like this
            4 2/3    
           +
            3 1/6
           _______ 
  
but it didn't help. I just don't know how. Please help me!

Date: 11/11/97 at 12:25:20
From: Doctor Mike
Subject: Re: Addition of Fractions

Dear Catherine,
   
Probably there are others in your math class who don't get it, but 
they just keep quiet about it. It can be sort of hard to get the hang 
of fraction addition.
   
Here is the way I think your teacher has in mind for you to do this.  
If you make both fractions have the same denominator, then the problem 
looks like this : 

             4 4/6    
           + 3 1/6
            _______   
             7 5/6  

The easy part is adding the whole numbers together to get 7, and then 
it's easy to add up the fractional parts because they are both the 
same kind.  
   
While we are talking, why don't I answer another question that is 
certain to come up as you continue your homework on this. Look at this 
example, which is similar to your other problem. 

             4 2/3    
          +  3 5/6
            _______ 
  
The first thing to do, as before, is to change whatever is necessary 
to get the fractions to have the same denominator. [By the way, that 
is often called the COMMON denominator, not because it is "common" 
like "ordinary," but because it is "common" as in "the same."]

             4 4/6       
          +  3 5/6
            _______ 
             7 9/6 

Your teacher will NOT want you to leave the answer in this form. There 
are two reasons why. One reason is that 9/6 can be reduced to the 
simpler fraction 3/2, and we like to make fractions as simple as 
possible in writing answers.

Now, what's wrong with 7 3/2 as an answer? Only that we like to have 
the fraction part be a fraction between zero and one. Since 3/2 is 
just "one and one half," we can include the "one" in the whole number 
part, getting 8 1/2. See? 
   
I hope these examples help. Write back if you have more questions.

-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/