Mixed Numbers

Date: 03/20/2001 at 15:09:35
From: erica
Subject: Mixed numbers

I am having trouble with mixed numbers. Is there an easy way to 
remember how to do them?

Date: 03/21/2001 at 13:52:31
From: Doctor Patti
Subject: Re: Mixed numbers

Hello Erica,

Thank you for writing to Dr. Math.

Let's look at a mixed number.

        2
     5 ---
        3

We know that 
 
           3
      1 = ---
           3
So,

      5 =   1  +  1  +  1  +  1  +  1
  
            3     3     3     3     3 
        =  --- + --- + --- + --- + ---
            3     3     3     3     3

             15
        =   ----
              3

Therefore 
   
             2         15     2
         5  ---  =    ---- + --- 
             3          3     3 

                       17     
                 =    ---- 
                        3

Is there a general rule that you can follow to come up with this 
number? Yes.

              2           3 * 5 + 2
          5  ---  =     ------------
              3               3 
        
                            15 + 2
                  =       ---------
                              3   

                             17
                  =         ----
                              3

In general, the mixed number

           B
        A ---
           C

can be expressed as the improper fraction


           B        C * A + B
        A --- =    -----------
           C            C   
        
I hope this helps.  Please write back if you have any other questions.

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